The devic
kania Transom
speed of ro
pressures (P
ball gover
to a receivin
hragm is aqual
e diaphragm
the cent fugal
PRESSURE—ST
#1. The
imple fo
ENGIN. LIB.
TJ
181
765
1951
gauges.
U-tubes
onal
-PRESSURE
A la magis, &,
jar relatiɔnsl
fore
Ace an A
ressure built u
orce. In this way,
the speed of the
ssure (P) follows the
This pressure transla
relatio ship betwee
and & secondary
purpose an "Askap
his conrected t
secor dary
is produced
few
driving shaft, 0 to
f water column.
STROK
VOLUME 1
#2.
(B) are you to produce a pressure which is
directly proportional to the stroke (S). In
both cases, jet pipes are used for amplifier
(A), the jet pipe delivers operat fluid into a
ting force
upon a diaphragm produci
tude as hat of the s
the jet sipe
+9
Analysis and Design
OF
Translator Chains
an amount
counter
The
dip
سا
BY
H.ZIEBOLZ
pressure
1
ŠTROKE--CURRENT D.C.
#1. In the "Electronbeam" tube shown, the
beam of electrons is deflected relative to
two target plates by a displacement of a
the potential difference created by this deflection
rose output (i) varies until the field it produces
established. See "Deflection Beam
rimary systems (S). A definite relationship
毎
​tput of the
which
STROKE-VOLTAGE
#1. The de
in which a b
relative to two
produced by a
ng fo
VO
ASKANIA
*Power unit
Rekor
force balan
depend
#1. The
duces a relationship between a
for the input e and d.c. current for the
-
put i. A beam of electrons is displaced

ults in a potential difference on the target
mplifier, the output current (i) is
oction force of the e
between
Spring La
placement
either
of a
ing pressures
a motion of a crank ar
proportional to the loading pressure. A
hydraulic "Askania jet pipe" is used as an amplifier, the mecha
establishes the position or stroke (S) independent of the load wh
applied to the cylinder. The torque available on the crank arm i
lbs. See Askania Bulletin 120. The device can be used in
in.
with any standard type air operated controller for provi
power and positive positioning with an accuracy better
Farce
TEXT
"stroke
-Direkt
aracterist
diagram
tube cons
receiving
STROKE-PRESSOT
#1. The diagram shows two s
simple "stroke-force" translat
commonly known as "springs."
In (A) a "helical" spring changes its force directly pr
the displacement (S). In (B), a ''leaf type" spring produces
portional to the displacement of its end.
nce on th
of electro
target p
Po
principle
for load
Is produc
h is direc
STROKE-FORCE SYMBOLS
I. The "stroke pressure
Askania jet pipe
the rece

t
!
University of
Michigan
Libraries

1817
ÁŘTES SCIENTIA VERITAS
+
..
2.
"One of the greatest handicaps
in arriving at an optimum solution
is the early discovery of one
possible solution..."
*
2
=
:
:

Ric
PLE
ANALYSIS AND DESIGN OF TRANSLATOR CHAINS
.5
by
erbert
H. Ziebolz
Engineering
Library
TJ
181
.265
1951
2.1
;
First edition: Published and Copyrighted
September 25, 1946
Second edition: Published July 16, 1951
by
Askania Regulator Company
Chicago, Illinois
Printed in the United States of America
11-10-52. HRJ
Engin
Wahr
4-10-52
78516 25
FOREWORD: 2nd Edition
The second edition of this study is practically
unchanged with the exception of corrections of too
glaring errors in typing and schematics.
Unfortunately no time was available to reedit the
text and the drawings. However, the main purpose
of the booklet, to outline a method of attack,
seems to have been fulfilled to judge from the
reception the first edition received.
Many suggestions were made to improve and extend
the study. For this constructive criticism I am
very grateful and I hope that some day time will
be available to incorporate these ideas,
It was also gratifying to note that the Patent
Department has used this material as reference as
shown, e.g., by the following clippings taken
from U. S. Patent #2,546,657.
Number
UNITED STATES PATENTS
Date
Name
Harvey
Feb. 14, 1922
Bernarde --------- June 25, 1935
Alexanderson
Jan. 7, 1936
Sept. 8, 1936
Mar. 17, 1942
Krussmann et al -Dec. 22, 1942
Sept. 12, 1944
1,406,377
2,005,884
2,027, 140
2,053,885
2,276,816
2,305,878
2,358, 103
2,371,236
2,395,604
2,417,097
Weeks
Bagno
Ryder
Gille et al.
Yeida
Mar. 13, 1945
Feb. 26, 1946
Warshaw ---------- Mar. 11, 1947
OTHER REFERENCES
“Analysis and Design of Translator Chains,”
by H. Ziebolz. Published by Askania Regula-
tor Co., Chicago, Ill., Sept. 25, 1946, Vol. 1,
pp. 80-81; vol. 2, Fig. 97.
It is my sincere conviction that in the long run
the freedom gained by the designer more than out-
weighs any possible loss in patent protection.
Four pages previously added as a loose leaf ap-
pendix have been permanently incorporated as well
as an extended bibliography covering a few of the
most important publications which came out since
the printing of the first edition.
It also appeared desirable to extend the block-
diagram analysis to a study of dynamic behavior
of the translators alone and of the translator
chains.
The Laplace transform of a chain F is the pro-
duct of the individual translator operators, i.e.
F1 F2 F3
Fn.
In case of a "splitter" or
parallel arrangement we get F1 F2 F3
+
Fn.
For a feedback loop with F2 in the feedback branch
=
we obtain:
F1
1+F1•F2 etc.
ED
n
Again, lack of time made it impossible to incor-
porate this approach, which is so admirably
covered in Principles of Servomechanisms by
G. S. Brown and D. P. Campbell, into the text.
It is sincerely hoped that the new edition will
again stimulate designers and engineers into a
systematic approach to the optimum solution
problem.
As before, all suggestions for improvements
will be greatly appreciated.
HZ:mg
May 1951
I am particularly indebted to Mr. Paul Glass who
pointed out four full pages of errors in typing
as well as in sketches, most of which have been
corrected.
.
H. Ziebolz
ACKNOWLEDGMENT
It is obvious that a study of this character
is the result of many years of work and of the ex-
change of ideas with many people. To name each one
who directly or indirectly contributed to it seems
impossible under these circumstances.
However, I am particularly indebted to the
Instrument and Control group of the American Asso-
ciation for the Advancement of Science (Gibson Island
Conferences) which encouraged me in my endeavour by
the interest expressed during informal discussions of
the matter of approach presented in this study.
I also gratefully acknowledge the many sug-
gestions made by my fellow research engineers. Mr.
Paul Glass and Mr. D. T. Gundersen, with whom I dis-
cussed many phases of this draft, as well as the
careful job of typing and arranging of the material
by my secretaries, Mrs. A. Frazer and Mrs. J. Johnson.
Last but not least, I am indebted to Askania
Regulator Company, and in particular, Mr. E. G. Hines
of General Precision Equipment Corporation, for giving
me the opportunity to prepare this study.
Chicago, Illinois
August 13, 1946
H. Ziebolz
t
Chapter
I
II
III
IV
V
VI
VII
VIII
IX
X
XI
XII
Introduction
Purpose of the Study
Concepts and Basic Approach
Symbols
Feedback Systems
Relay Devices and Amplifiers
Variables
CONTENTS
The Translator Map
Translators
A) variable/stroke
B) stroke/variable
C) variable/(D.C.) current
D) (D.C.) current/variable
E) (P/P) (P/F) (F/P) (F/F) translators
General Remarks on Translators
Bibliography
with mechanical parameter
Mathematical Operations with Translator Chains
A) Summarization Class A
B) Multiplication
Class B
C) nth Power Class C
D) Derivatives
E) Integrals Class E
<
Class D
with electrical
parameter
Analysis and Translation of Specific Devices
General Conclusion
Page
V
1
5
11
17
32
42
46
58
59
99
138
151
163
173
176
183
200
226
234
249
262
271
274
-iv-
AN INTRODUCTION
which probably should be read after a survey of the
material in this book
Whenever the amount of material in any
science reaches a volume which is too great for an
individual to handle with care, attempts have been
made to systematize the overwhelming multitude of
data by expressing them in new concepts and symbols.
Reducing the bewildering number of facts
and experiences into fewer and more comprehensive
symbols makes it possible for the researcher to
concentrate on their implications and to study
their combinations with others and with themselves.
The progress of chemistry probably owes as much to
the simplicity of a symbolic equation of the type
2Na + 2H20 = 2NaOH + H2
as it does to its quantitative method of investi-
gation.
A similar method of describing the ins-
truction of mechanisms has been lacking so far, or
if ever attempted, has not been universally used.
Proof of this is the difficulty experienced by
patent departments and editors of technical maga-
zines to properly classify designs and also the
-V-
hopeless struggle of the individual reader to
analyze, digest, and file the material which
threatens him with an ever-growing deluge.
Libraries have developed various index
systems, which make it possible for the initiated
to find with some luck a remarkable number of
possibly related subjects. However, as these
systems are not universally accepted, no help is
usually given by the author to the librarian in
assisting him to classify his material, espec-
ially as the title may be extremely misleading
with regard to the various subjects contained in
the text. Thus, an important contribution to the
art of flow measurement may be concealed in the
pages of a medical journal dealing with the cir-
culation of blood through the body.
In an earlier publication, I have made
an attempt to systematize the classification of
mechanical designs with which I am particularly
familiar; 1.e., mechanisms for indicating and
controlling variables. This attempt was originally
conceived as a protection against the danger that
"basic patent" claims might be granted on devices
or their combinations which are or should be obvious
to those vague individuals usually referred to as
"those skilled in the art."
-vi-
j
This study had served its purpose, as
I understand that it had been quoted repeatedly
by the patent department against too broad claims
of various inventors.
However, it soon appeared that the approach
chosen had wider implications than originally
expected. It seemed to have its greater value as
a method of approach for the solution of technical
problems since it gave a multitude of alternate
solutions to choose from rather than a single one.
There is evidently no greater handicap
to progress in design than the discovery of a
solution. Usually, the designer relieved from the
pressure tends to relax somewhat, glowing with
pride over having found a way out of his difficulties.
To be specific, it was found that by
using in a particular case the method to be dis-
cussed, 115 possible solutions were found where
previously four seemed to cover the field.
Obviously, out of these 115 there were many which
did not justify any further consideration and were
immediately dropped as impractical. However,
there was enough material left in the rest to
warrant a thorough study.
Sy
-vii-
Originally, I had in mind to wait with
the publication of this material, which was accumu-
lated over a long period of time, and do the "good
job" which an engineer feels it his duty to produce.
The material, however, proved to be so overwhelming
in magnitude that it appeared necessary to limit
myself at this time to a description of the
strategy of attacking the problem rather than to
make an attempt to solve it. This will explain
much lack of completeness or even inconsistency in
details of sketches and in the text. I realize
these shortcomings and have no apology to offer
except that lack of time prevented me from going
over the material more carefully.
There is also, in my opinion, a definite
need for a greater number of variables.
should include, for instance, time, humidity, P.H.,
supersonics, and intermittent energy pulses of
various amplitude, frequency and duration. For
those who need this material, the system has been
so designed as to permit extension.
They
As a mechanical engineer, I have perhaps
given overemphasis to the field with which I am
familiar. This will explain the particular and
sometimes unusual choice of examples in the
-viii-
electrical and electronic fields. It is hoped,
however, that this is not too serious a fault of
this first draft, as the expert will easily be
able to fill the particular gap with examples which
are better representative or more widely used.
The fact that I, as a mechanical engineer,
dared to venture into this quite foreign territory
might be attributed in no small degree to the
methodical use of the system which gave me the courage
to do so in spite of my limitations of experience.
If it thus serves no other end but to show that the
method used gives even the non-expert a chance to
find his way through a "jungle" which is otherwise
only known to the local guide, it has fulfilled its
purpose.
As usual, a preface of this type will be
better understood after the reader has digested
the material. All I can do besides apologize to
him for the incompleteness of this venture, is
hope that in spite of it he will have found enough
of interest to justify his patience in going
through this material. I should, however, greatly
appreciate criticism and suggestions with regard
to the general approach as well as to details, as
I hope some day I may find the time to do a better
job.
-ix-
Since writing this study, the paper of Mr.
I. F. Kinnard of General Electric Company (see
reference 42) came to my attention which is the
closest approach to the solution which is suggested
in this paper. Unfortunately, the work on this study
had progressed to a point where the results obtained
by Mr. Kinnard could not be incorporated in the text.
H.Z.
-X-
CHAPTER I
PURPOSE OF THE STUDY
The purpose of this study is to establish
a systematic approach to the classification of
mechanical, hydraulic, electric and electronic and
other technical devices making it possible to
think of them in terms of symbols rather than in
terms of specific apparatus. This frees the mind
from the confusing multitude of details. It
suggests, at the same time, the development of a
reference system which lends itself to the filing
of pertinent data under definite headings which
follow a simple logical system and thus do not
have to rely upon the memory or the training of a
specialist.
It will be shown that such an approach lends
itself to a systematic survey of the whole techno-
logical field opening, so to speak, a map in front
of the observer which not only establishes a
definite location for each device or apparatus, but
which outlines alternate roads to be followed in
order to arrive at the solution of a definite pro-
blem. It establishes a number of alternate possible
solutions, leaving it to the experienced designer to
choose the optimum solution within the limits of his
-1-
specifications. The system has actually proven,
during the time it was used, as a great help in
solving more involved design problems which, as
they required a number of intermediate steps, would
have been relatively difficult to visualize.
The study is an outgrowth of three pre-
vious publications (see references 3, 4, and 5) in
which the main concern of the investigation was the
so-called "F.P.S. system" of the mechanical engineer.
As it will be shown again in this study in a slightly
modified way, it was shown at that time that there
are three variables; 1.e.,
Force: (F- symbol for force (lbs.))
Pressure: (P - symbol for pressure (lbs./sq.in.))
Stroke: (S symbol for movement or stroke (in.))
which can be interchanged or are equivalents, as it
is possible with present available devices and relays
to translate each one of the three variables into any
other or into others of the same character (trans-
formers). Thus, it is possible to "translate" a
force (F₁) into a force (F2), or a pressure (P),
or a stroke (S). The same applies, of course, to
the pressure (P) and the stroke (S).
It was found that such a translation of
variables is most useful in the solution of algebraic
-2-
or general mathematical equations. For instance,
there is no method available to summarize pressures
(P) directly. However, it is possible to translate
the variable (P) into forces (F) or strokes (S) for
the purpose of summarization.
Previously, the choice of the translation
or the choice of the common denominator seems to have
been rather accidental as a study of a particular
problem and the history of its solution (documented
by records of the U. S. Patent Office) will show
(see reference 4).
Applying the approach to be discussed in
this study to the problem of multiple fuel control,
it would have been possible to give all of the finally
patented alternate solutions at the time the problem
was first stated in mathematical terms. Thus, with
one stroke the "inventor", who in most cases is
merely the man first confronted with the problem,
could have monopolized the field by covering all of
the solutions which finally were claimed by his
competitors.
It is sincerely hoped that this study will
contribute to the refusal of many "basic claims" by
the Patent Examiners, as it discloses methods which
anybody "skilled in this art" can apply. The
C
;
:
-3-
resulting greater freedom for the designer will
ultimately benefit the technological progress of
That this statement is more than a
hope has been confirmed by the fact that the pre-
vious publication (see reference 3) has been
everybody.
repeatedly cited against too broad claims of patent
applicants.
The author realizes that such an attitude
of the Patent Office will also affect his own chances
of getting broader claims allowed, but he feels that
the greater freedom to be gained is preferable to
what, in his opinion, would otherwise be a retarding
of progress (see reference 6, page 152). It appears
necessary at this point to substantiate the above
rather sweeping claims with an explanation of the
definitions of the concepts used and the approach
which was chosen.
-4-
CHAPTER II
CONCEPTS AND BASIC APPROACH
It is unfortunate that this chapter has
to be started with an apology. The author realizes
the shortcomings of the following disclosure and the
lack of consistency in the analysis of the examples
chosen. He also regrets that the examples may not
be the most commonly used in a particular field.
However, it is a well known experience of designers
and writers that after having finished a job they
know only too well how it should have been done if
they could start all over.
On the other hand, there is the danger
of never delivering the goods if the process of
improvement is extended too far. As it is the
purpose of this study to discuss methods rather
than to establish a technological encyclopedia,
the practice of the drafting board is chosen; 1.e.,
to sketch the broad outlines first even if a
further study should demand considerable changes.
As a first step in this analysis, let us
introduce the concept of a "translator".
general, we shall understand under this term any
device which if subjected to a change in the
magnitude of a "primary" variable responds with a
In
-5-
change of the magnitude of another or the same
kind of "secondary" variable. The "primary"
variable will be called "input" and the "secondary"
variable called "output".
To use an example, a "lever" is a
"translator" for forces (F) and strokes (S) (see
Figure 1). Balance is established if: (F₁a) the
"input" is equal to (F₂b) the "output". As a and
b are constants of the translator, it is more
convenient to think of (F₁) as the "input" and
(F2) as the "output", with
F₁ = 1 F₂
If the lever is not used as a "force
translator" but as a "stroke translator", we have
the arrangement of Figure 2. In this case our
"input" is S₁ and our "output" is S with the
relation between S1 and S2 given by:
2
$1 == S₂
$2
It is obvious that the "input" variable
does not necessarily have to be the same as the
"output" variable. Thus, we have in Figure 3, the
input (P₁) and (P2) with the output (S1) and (S2).
As these devices are generally known in their con-
struction, there is no need for describing them.
-6-
It will be noted that the translators
shown in Figure 1 and 2 are not using any additional
source of energy for translation. Such translators
will be called "direct" translators. "Indirect"
translators, on the other hand, will be those trans-
lators or translating devices which control
additional sources of energy which modify the output.
A typical example of such an "indirect"
translator is shown in Figure 4 which is a schematic
diagram of a typical hydraulic follow-up or servo-
mechanism. As in Figure 2, the device translates
a stroke (S1) (input) into a second stroke (82)
(output); however, the force necessary for accom-
plishing this is (disregarding friction and the
dynamic unbalance of the system) primarily furnished
by a hydraulic power relay. It is important to
note that, assuming mechanical perfection, a definite
relation exists between (S1) and (S2). It is,
therefore, possible to substitute (S2) for (S1)
as long as this relationship exists.
There are, however, other types of trans-
lators where this fixed relationship either does
not exist at all or where it will vary with time.
As an example, a bicycle pump is shown in Figure 5.
Although the gas law seems to establish a definite
-7-
relationship between S, and P, and thus with 82,
the rate of compression (adiabatic or isothermic)
and possible leakage of air around the piston
makes the "output" (S₂) not too dependably related
to (81). For many applications, however, such a
translator is entirely satisfactory as for instance
in compressors and diesel engines. In the latter
case, the translator has two or more outputs; e.g.,
pressure and temperature.
Limiting ourselves to the output (P) only,
we note that it is inversely proportional to the
stroke, a characteristic which may be valuable for
the solution of problems of specific translator
design where such a relationship is desirable.
shall later return to this subject.
We
The translator of Figure 5 is still a
direct translator in spite of its unpredictable
characteristic, as it uses no auxiliary source of
energy. In the valve arrangement (Figure 6), an
indirect translator with auxiliary power supply is
shown, as the fluid energy is modulated or varied
by the adjustment of the valve stem (S) in order
to produce varying pressures ahead of the outlet
restriction which, e.g., may be a burner tip.
diagram tries to show that the output pressure
will vary with the stroke and the valve design. It
The
-8-
will also vary with the condition of the fluid
supply (pressure, temperature, viscosity, specific
gravity, etc.). Again, the output and input
relationship is not a fixed one.
The conditions of this fluid valve are
strikingly parallel to the characteristics of a
triode which originally and justiy was also called
a "valve" (Figure 7). In this case the input
variable is a D.C. voltage with a D.C. output
current varying proportional (but not directly
proportional) to the input signal. Again, the
output depends on valve (tube) design, supply
pressure (anode voltage), heater current, load
resistance, etc. Surveying the above examples
and classifying them, we find:
Class
(a) direct but not directly propor-
tional translation
Figure 5
(b) direct and directly proportional Figure 1,
2, 3
translation
(c) indirect but not directly pro-
portional translation
(a) indirect and directly propor-
tional translation
Examples
Figure 6, 7
Figure 4
No additional distinction is made to
indicate whether or not in class (a) and (c) the
-9-
A
It is,
relationship is stable and repeatable.
however, assumed that in classes (b) and (d) a
definite output (within the accuracy limits of
the translators) is to be expected for every
input value.
-10-
CHAPTER III
SYMBOLS
In order to simplify the illustration of
translator devices and "translator chains", 1.0.,
of a number and of various combinations of trans-
lators, "block diagrams" have already found wide
acceptance, particularly in the electrical and
electronic literature. The symbol chosen in this
particular study is a combination of this block
diagram with a detail of a schematic diagram which
was first brought to the attention of the author in
a publication of the Republic Flow Meter Company
describing their square root extractor (reference 47).
Freeing this symbol from the attached mechanism of
the above publication, we obtain a simple square box
with a diagonal which separates the "input" from
the "output" (Figure 8). The diagonal is drawn in
such a way as to connect the lower left-hand corner
with the right-hand upper corner. This is the basic
However, the alternate shown in Figure 8
is also recommended.
standard.
For consistency reasons, it was found
desirable to use an arrangement where the input is,
whenever possible, on the left-hand side and the
output on the right-hand side. Arrows can be auded
-11-
to avoid misunderstandings. Should the translator
use additional sources of energy, the symbol as
shown in Figure 9 is used with the arrow (perpendi-
cular to input-output axis). This is to inuicate
the additional flow of energy . This energy can be
named and identified by an appropriate legend when
desirable. Figure 10 shows the example of Figure 4
and its new symbol representing a class (d) trans-
lator with an (S1) input and an (S2) output with
hydraulic power supply; in brief, the symbol of a
"servo-motor".
QUAN
<p>
Returning to our translator of Figure 5,
we have already found that this (S) over (S)"
translator establishes an in-series arrangement
of two translators "(S) over (P)" and "(P) over (S)".
This is shown in Figure 11 where the two blocks
represent the individual translators. Two alter-
nates are given of which the upper one is pre-
ferable for easier readability. The pseudo
equation established by the diagram indicates
that the end variables of any part or of the whole
translator chain can be combined to form a new
translator. The small x in the center of the
symbol is optional and is to indicate that one
either does not know what is inside of the box or
that one does not care. At any rate, it is to warn
-12-
་
the reader of the symbol that there are intermediate
steps in the translating device.
The fact that a translator chain can be
extended and compressed by inserting or extracting
translators is one of the most important facts to
remember, as it is the clue to the application of
the translator system to design problems. To
repeat this statement again in different form:
a) Any translator chain can be opened and extended
by inserting for any given translator another
translator or a chain with the identical input
and final output characteristics.
b) Any translator chain can be reduced by consider-
ing any input and output of consecutive trans-
lators as the input of a single translator of
identical over-all characteristic (input-output
relationship).
S
-
It will be shown later on that even
greater freedom in the "lumping" of intermediate
translators is possible if, through feedback in
end stages anywhere in the system, ahead and behind
the inserted system the same relationship of input
and output is produced. This will be discussed in
more detail later on; however, it is worth while
noting already at this point of the discussion.
-13-
Additional examples for this lumping of individual
components are shown in Figure 12 and Figure 13.
The obvious disadvantage of the above
symbols is that, although the pictures are rela-
tively simple, they still call for some drafting
work no matter how crude. To overcome this fault
and to make it possible to use the typewriter, the
telephone and the dictaphone for the analysis, the
symbols and the expressions given in Figure 14 are
recommended. While they have served the author
satisfactorily, it is realized that, should others
adopt the methods discussed, these will be modified
with use and probably better and simpler ones
suggested.
The choice of the written symbol seems to
be natural as it is nothing but an abbreviation of
the box symbol and convenient to produce on a type-
writer. The way to read the symbol takes advantage
of the similarity of the written symbol to algebraic
fractions and the use of the exponent for indicating
"power" may be excused as it is easy to remember,
although it may appear as a pun.
In Figure 15 two additional symbols are
suggested which incorporate feedback, the lowest
one of the three, although simple for writing, causes
difficulties on the typewriter. It will be noted
-14-
that the class designation can be given by using
a-b-c or d as indices. (see Figure 14-bottom, and
Figure 16)
With the above symbols and concepts, it
is relatively easy to describe and to analyze even
relatively complicated devices, and an example will
show how the use of them does greatly simplify the
study of technical articles and, last but not least,
could immensely simplify the Patent literature.
Bithout making an attempt of going into
details, the sequence of Figure 17, 18, 19, and 20
shows four stages of an analysis of a patent dis-
closure taken at random from the literature.
a) Figure 17 is a reproduction of sheet 1 of U.S.
Patent #2,245,034 granted to Mr. T. R. Harrison.
The device shown is a measuring apparatus
(recorder or indicator) for light intensity.
b) Figure 18 - An analysis of its components
establishes the functional relation of its
components. It is believed that this is al-
ready a great simplification of the original,
as it permits an easier analysis of the relation
between the various parts.
c) Figure 19 The next step was taken in Figure 19
which is a typical block diagram. This is
-15-
already a great improvement as it frees the
reader from confusing details. It only lacks
a terminology which at the same time permits a
functional analysis and classification.
d) Figure 20 finally shows the same device using
the proposed symbols.
In written form, the mechanism would be represented
by:
(Q/06)+(E(S1/@1)+(Q/@¸)+(V₁/@₂)/g) + (e/▼₁) el. +
C101
$1
$1 C₂1
V₁ = Cze
-
(v₁dt/s₁) = (Q/s₁)el.
с
It will be noted that additional symbols
from algebra are taken advantage of, which will be
explained later. However, at this point it appears
desirable to give a preview of what can be achieved,
as no system should be suggested which, after its
adoption, does not repay in time saving, convenience,
and serve as a simpler and better tool than those
already available.
-16-
CHAPTER IV
FEEDBACK SYSTEMS
We have seen in the previous chapter that
in a chain of translators the individual character-
istics of consecutive translators can be neglected
if a feedback is established between the input of
a section of the chain and its output. Therefore,
it appears necessary to briefly discuss feedback
and its implications in connection with the present
study. The subject in itself is extremely broad
and tempting, as it includes the whole field of
instrumentation and controls a field that has been
lately termed "instrumentology" and aspires to
become a new branch of science.
Much of the work has been done in this
field by originally unconnected branches of engineer-
ing, and it is only recently through the efforts of
the American Association for the Advancement of
Science in their Gibson Island Conferences that a
common denominator for these individual studies
has been found.
The first group interested in such circuits
were the designers of prime movers who developed
automatic devices for controlling their water wheels
and steam engines, and worried about power oscilla-
-17-
tions of electrical motors and generators. They
were followed by designers of automatic valves and
controls; i.e., devices which beginning with simple
relief anu reducing valves extend to coordinated
boiler and process controls of the most complex
nature.
In parallel with this group, two other
attacks were made on this problem by the designers
of automatic airplane pilots and, strange as it may
seem, by the communication engineers whose network
problems and amplification problems called for a
thorough investigation of the same basic phenomena.
Furthermore, those whose problem is the elimination
or production of mechanical oscillations (vibration
control) found that the same problems confronted
them as their predecessors.
Finally, the war put great emphasis on
remote control devices in our terminology "(S/S)
translators", which were designed for anti-aircraft
control and other applications. This branch devel-
oped its own theories and techniques which deal
with their particular problems of servo-mechanism.
Unfortunately, the terminology, as it is to be
expected in a case of so many independent attacks,
was until recently extremely confusing, and it is
-18-
only due to the continual efforts of the A.S.M.E.
terminology committee that during the last two years
a common language has been suggested which will
naturally still take some time to be universally
adopted (see reference 8).
For this reason, although the literature
published up to 1945, the year of this study, has
many contributions of great value, it has to be
read very carefully as its terminology may be con-
fusing and as seemingly contradictory statements
of various authors are often due to the use of
different terms for the same thing or the same terms
for different things. As Mr. E. Sinclair Smith (see
reference 6) and Mr. D. P. Eckman (see reference 2)
have given a very detailed and comprehensive list
of publications on this subject, a repetition of
the bibliography seems superfluous. In addition,
the end of the war will make the outstanding con-
tributions of the Radiation Laboratory of the M.I.T.
available to the general public.
In an attempt to understand the meaning
of feedback, we shall discuss some fundamentals and
try to arrive at a definition which will be suffi-
cient at least for the purpose of this study. A
feedback is established between an "input" and an
-19-
"output" of a "translator" if, as the name implies,
the output is "fed back" into the translator so as
to counteract or support the effect of the input.
If it counteracts, it is called "negative" feedback.
If it supports the input, it is called "positive"
feedback.
Out next step is to concentrate on the
"negative feedback as devices incorporating this
feature are very desirable for translator designs;
1.e., their output has (within limits) a definite
relation to the input. Typical for negative feed-
back circuit is a balance of two equal variables,
which are the input and the output, in such a manner
that an increase of the output is produced by an
increase in the input. In this sense a lever to
which a force is applied (input) produces a counter-
acting force, and is a simple form of a translator
(see Figure 21A). Typical in this arrangement is:
a) the balance of input and output.
b) the fact that the output can be used to re-
present the input as it is a definite function
of the input.
In Figure 21B the problem is somewhat
complicated by the addition of another parameter,
the variable (S) and for the first time we note
-20-
the dynamic behavior of such a feedback device. A
float suddenly subjected to a force (F₁) accele-
rates and submerges (S₂) until the counteracting
force (F₂) is equal to the input (F1). The trans-
lator chain (F₁/S₂) + (§2/F2)
(F/F) is shown
1 2
on the right-hand side. There will be oscillat
tions, greatly damped during the first time inter-
val, a feature which will have to be carefully
studied in more complex feedback devices. The
example is chosen to call attention to this im-
portant phase of the problem in a simple form.
=
It will be noted as aŭditional features
over those observed in the case of (A) that:
a) the dynamic behavior of the translator enters
into the characteristic of the translator chain;
b) in spite of intermediate translator variables
(82), the balance of the forces (the input of
the first translator and the output of the end
translator) establishes the feedback loop;
We have thus two translators:
1) (F₁/S₂) + (S₂/F₂) = (1/2)
(s
2
رخ
c) a secondary output (S1) appears, which definitely
related to (S2), can be used as output of this
translator in place of (F₂) which. is not
measured.
"
+!
-21-
2) with F1
(C =
= 1)
The equation establishes the feedback relation.
=
CF2
Another way which has the advantage of
greater clarity of writing the above translator is:
1) (F1/F2) + (F2/S2) = (F1/S2)
2) F1 = CF2 (C = 1)
Which one is preferred is a question of choice and
taste. We shall use either one as whichever seems
more convenient in the particular problem.
The next step is the use of auxiliary
power; i.e., an addition of a relay mechanism.
simply increases the length of the chain and calls
for an additional study of the characteristics of
the relay to judge the accuracy and transient res-
ponse of the members within the translator loop.
This
We have stated above that a balance has
to be restored between the effect of the input and
the effect of the output. These effects must.
not necessarily be forces, but can be any other
variable, the difference of which establishes a new
balance or equilibrium preventing a further change
of the output.
In Figure 22 two typical examples of
hydraulic mechanisms are shown with a stroke feed-
back. A displacement of (S1) input produces a
-22-
movement of the hydraulic relay (A) and (D) respec-
tively, which in turn produces a movement of piston
(C), the output (S2). This motion (S2) is fed back
to counteract the input effect by moving the relay
(P) in the opposite direction (left-hand diagram)
or by closing the ports of the pilot by moving them
(sleeve E) relative to the displaced pilot (D). We
note from these two examples that (disregarding tran-
sient conditions):
a) the rate of change of (S1) must never be
greater than the maximum rate of (S2);
b) the relationship between output and input
depends evidently on the sensitivity and
stability of the relay mechanism;
c) as a secondary output, a force is produced
which will vary to match the load (F) it has
to overcome;
d) the output used for feedback is of the same
nature as the input variable which displaces
the relay;
e) The feedback actually requires a device for
summarizing (whiffle tree B) and relative
motion of a zero point (D-E sliders) to
function. Such summarizing devices will be
more generally dealt with later on.
-23-
We just stated under (a) that the input
variable and the output variable must be of the same
nature as far as the relay translator is concerned.
At first glance
This point needs amplification.
Figure 23 seems to show a pressure feedback, but as
it is impossible to summarize pressures, it is
necessary to translate the pressures into forces
or other variables which lend themselves to summari-
zation.
In the (P1/P2) translator, the transla-
tion is produced by the use of diaphragms as (P₁/F1)
translators of class b. As the system is a force
balanced system, our translator chain reaus:
1) (P1/F₁) + (F1/P2) + (P2/F2) (P1/P2)
2) F1 = CF2 (C = 1)
or,
3) (P1/F1) + (F1/P2) (P₁/P₂) + (P₂/¥2)
4) F1 = CF2 (C = 1)
=
=
A closer study of the diagram adas another
factor to our knowledge of negative feedback trans-
lators. It will be noted that to produce P2 the
relay must be displaced, while in the case of
Figure 22 this relay is returned to its zero posi-
tion. Thus, the Figure 22 circuit is an example
of a true "Nullpunkt" system, while a definite
displacement of the Relay is necessary in Figure 23.
-24-
Figure 23 approaches the true "Null" circuit with
an increase of sensitivity of the relay; 1.e., the
change of output for a given unbalance of the relay.
Limits of this sensitivity are given by the dynamic
stability of such a system.
In Figure 24 it is shown that the input
of such a translator with feedback may not be the
same variable as the apparent output. It is
obvious, however, that we have again a true force
feedback given by:
(F₁/P) = (S₁/P)] + (P/F2)
1) [(S₂/Fj) + (F₁/P)
2) F1 = F₂C (C = 1)
In Figure 25 a velocity or speed feed-
back is shown to emphasize the need of the summari ·
zing device. A differential gear compares the
input speed V₁ with the output speed V₂• If they
are equal, V₂ = V1 V2 is zero and an electrical
relay or controller responding to this input will
vary V4 and thus V₂ to maintain this difference
The device is a typical translator for
(V1/V2) and can be used for synchronizing speeds.
+
zero.
This problem of synchronization of speeds
is typical for prime mover applications and has
rather involved solutions. As an example to show
the equivalence between such systems, Figure 26
-25-
nas been added which is a diagrammatic sketch of two
pumps which are to be run at proportional speeds.
The pumps (B) and (C) are driven by turbines (F) and
(E) which are controlied by means of steam valves
(G) and (D). (G) is controlled by hard, while (D)
is controlled by a ratio regulator (K). The rate
of flow produced by the pump (C) is a measure of the
speed of turbine (F), while that of turbine (E) is
represented by the output of pump (B).
Orifices in the pump discharge produce
pressures (P₁) and (P2) which are a function of the
pump delivery rates. A balance of (P1) = F(n₁) and
(P2) = F(2) thus produces a fixed ratio of and
n2. The balance is actually established by forces
which are produced by the pressures which in turn
represent flow rates and thus the input and output
variables n. This translator chain can therefore
be represented by:
n1/W₂) +(W1/P1)+(P₁/F₁)+(F1/n₂)+(n₂/W2)+(W2/P₂)+(P2/F2)
with F1 C1F2 (C = 1)
=
F1 = C,P1
F%
C3P2
2
CAW12
=
P1 =
P2
W1 C601
W₂ = CYP2
=
=
2
C5W2
นา
M1 = Сg¹2
V₁ = C8V2
-26-
The above equations describe in some detail the
processes involved in the above feedback circuit.
We have intentionally refrained from
analyzing the details of the ratio regulator (K).
Its particular design, providing that it functions,
to establish the balance of F1 and F2 is immaterial
for our purpose. This broadens our concept of such
feedback loops insofar as it logically includes
the possibility of the presence of a human operator
as part of the chain.
For all practical purposes of an analysis
of a complex translator chain as, for instance, an
airplane, a (S/V) translator in our terminology, it
is immaterial whether or not a pilot is replaced by
an automatic device or vice versa. What is important
for 'a detailed study is to know the individual char-
acteristic of each transiator. This by no means
excludes the characteristics of man or any peculiar
behavior of any mechanism as long as it can be
described, or within limits, predicted. The common
parameter for the ratio "regulator" man (K) is in
this case (S) as he will have to match S₁ with S
for synchronism. Figure 27 is drawn to symbolize
this translator chain, however, the sketch is not
recommended for general adoption, (See also Fig. 28)
-27-
A speed governor can be considered a trans-
lator with acceleration feedback as the control force
is produced by the centrifugal acceleration bw2 and
the setting (input) by a spring or a weight which
produces a force M₂ times the acceleration of gravity
(Figure 29). It is left open in the diagram what the
input of the prime mover (A) is in this particular
The example is only chosen to illustrate a
representative of this class. It will be noted that
the device balances forces.
case.
As an example of an electrical feedback
circuit, an Electronbeam tube is shown in Figure 30,
as in this device the principle is particularly
evident. A cathode ray tube with a heater cathode
(B) emits a beam of electrons which hits two adja-
cent target plates (A) and produces a voltage
potential between both targets which is a function
of the relative displacement of beam and targets.
An amplifier composed of the usual triodes trans-
lates this potential difference into a proportional
current. Deflection of the electron beam is accom-
plished by means of a magnetic field produced by a
current ij in C₁ which creates a magnetic field (H₁).
The output of the amplifier increases under the
influence of H₁ until the field (H2) created by
current (12) in coil (C) rebalances the electron
Magda
—
S
-28-
beam. Thus we obtain:
i1=C1i2 or H₁ = C2H2,
an example of current or magnetic field feedback (see
reference 12).
The same device is shown in Figure 31 to
illustrate a feedback produced by means of an electro-
static field (E), which counteracts the deflecting
effect of field (E). It will be noted that the
balance in both cases, current feedback (Figure 30)
and field feedback (Figure 31), is one of deflecting
forces. It is, therefore, possible to use the
deflecting force of an electrostatic field (E)
(Figure 32) and to counteract this force by means
of a force produced by a magnetic field (2).
The important point to remember is that
a feedback calls for a balance of variables (summari-
zation) of the same kind. It is not sufficient that
the output of the amplifier or translator counteracts
the effect of the input. It is necessary to establish
a balance, anu this is only possible with the same
parameter. As an example, two "pseudo" feeu backs (A)
and (B) are shown in Figure 33. In the electrical
example, the field input is represented by a magnetic
field (H₁) (biased by an opposing field (H2)). An
increase of (H₁) first deflects the beam and hereby
-29-
decreases the heater current, and thus reduces the
output of the beam and in turn reduces the output
of the translator.
In the mechanical analogy (B), an increase
in the applied force (F1) increases the pressure in
the receiving nozzle which in turn throttles the
supply pressure (P1), thus decreasing the output
pressure (P) in the nozzle. The lack of a force
balance makes it impossible in both cases to predict
the output as a function of the input.
Figure 34 shows again a genuine feedback
in which the balance is produced by a voltage or
resistance feedback. It is the typical diagram of
a self-balancing Wheatstone bridge which is at rest
when the output voltage between points C and D is
zero (Null balance).
An almost unlimited number of feedback
circuits will be found in the literature of electronic
amplifiers. Their discussion in detail would not add
anything new to our basic concepts which are dis-
cussed in this chapter. Figure 35 shows a simple A.C.
voltage feedback amplifier system. (see reference 9)
One point, however, should be noted before
closing this discussion of feedback circuits; i.e.,
2
-30-
that feedback circuits are in the last analysis
controllers. As soon as the output becomes a
definite function of the input, such a translator
can be considered as controlling the output variable
(which is often called the setting of the controller).
We shall return to this point later on.
Note: Dr. H. E. Droz of General Precision Laboratories,
who read the manuscript, called my attention to the fact
that a circuit of the type which I call "pseudo feedback"
does also produce linear relationship between input and
output, when the "gain" of the device is high and when
there is a linear relationship between the effect of the
feedback variable and the output of the translator.
The feedback circuits emphasized in this study are dis-
tinguished by the fact that a balance is established by
two opposing variables of the same nature; e.g., forces,
fields, voltages, etc., and it is assumed that two aŭdi-
tional'conditions are fulfilled.
a) high gain
b
linearity of the effect of the feedback variable.
•
Stad

-31-
CHAPTER V
RELAY DEVICES AND AMPLIFIERS
In feedback circuits and individual trans-
lators various types of relay devices and amplifiers
are used, and it seems advisable at this point to
consider some of their more common designs. Again,
only a few typical examples will be chosen to illus-
trate their common features. The particular choice
of either of them in preference to their alternates
will depend on the individual specifications which
have to be met.
A purely mechanical torque amplifier is
described in the Journal of the Franklin Institute
(October 1931). It consists (Figure 36) of two
drums rotating at constant speed in opposite
directions and driven by a common motor (not shown).
Flexible bands are connected to the respective ends
of two fulcrumed levers (A) and (B) and looped around
the drums as shown. If the lever (B) is rotated
counter-clockwise, the tension and hereby the friction
of the left-hand band is increased and that of the
As a result of this, the
right-hand one decreased.
left-hand drum rotates the lever (A) in counter-
clockwise direction until equilibrium is restored.
The torque which is necessary to do so is furnished
-32-
by the drum motor and is transmitted through friction
to the lever (A). A torque amplification of 1:104
is possible with such a relay which is a (S1/S₂)
translator.
Note that the balance is one of strokes
and that the forces are only used to accomplish this
translation. Translator devices of this type
(S1/S₂) are also called servo-mechanisms, and have
found a great number of applications in calculating
devices and anti-aircraft controls. We shall dis-
cuss their significance for the whole field of
translators later on.
Another class of relay devices is that
which uses fluid power for control and power ampli-
fication. In this class we find as the most common
type the double orifice or flapper valve shown in
Figure 37. Usually one stationary (1) anu one
adjustable (2) restriction are provided in series
in a conduit (see Figure 37-A) with a usually con-
stant source of supply pressure (P1).
G
As the second or downstream restriction (2)
is varied by a movement (s) of the flapper, the
pressure (P2) between (1) and (2) varies as shown
in the left-hand corner as a function of S. If
the characteristic is to be made steeper (see B),
an injector nozzle is used instead of restriction (1).
-33-
This does not only permit P₂ to drop to zero, but
it can also produce negative values of P2. (refer
U. S. Patent # 2,223,712)
Figure 38 shows amplifying relays of the
ds
of a
fluid type for producing rate of motions as
dt
final control element.
In Figure 38-A the well known sleeve type
four-way valve is shown, which throttles the amount
of fluid admitted or released to conduits 1 and 2.
This device can be used for either obtaining a AP
ds
or a as output for a given input signal (S1),
dt
as (S₁/AP) or (S₁/ds) (see Figure 39).
at
-
The main fault of such a device is the
unavoidable friction and a dynamic unbalance which
calls for the use of relatively great forces to
These drawbacks are overcome by the
control 81.
"jet pipe" design shown in Figure 38-B.
A jet
pipe being supplied with fluid under pressure can
rotate around its axis of fluid supply (M) relative
to two openings (1) and (2). The dynamic pressure
regain in these lines produces a differential which
is directly proportional to the displacement of the
jet nozzle. The differential, in turn, produces
as in the case of Figure 38-A a rate of piston travel
which is proportional to $1.
-34-
The jet pipe as shown can be run at a maxi-
mum fluid pressure of about 150 lbs./sq.in. (to avoid
atomization of the fluid which is usually a light oil)
and at a maximum oil capacity of about 3-4 gal./min.
To combine the advantage of higher pressure and volume
inherent in the design of Figure 38A with the lack of
friction and inertia of the jet pipe, a combination
of both designs is shown in Figure 38C. In this
design the orifices 1 and 2 are not stationary as in
the case of Figure 38B, but are part of a small
(auxiliary) piston.
Any deflection of the jet nozzle relative
to these receiving nozzles produces a differential
in 1 and 2 in such a manner that the piston moves
in a direction to reduce this differential to zero
(note crosswise connection of 1 and 2 to opposite
sides of the piston). The two nozzles 1 and 2 thus
will follow all displacements of the jet as if a
mechanical link between them and the jet existed.
As the piston provides ample power, the attached
four-way valve of conventional design (type 38-A)
will move directly in synchronism with S (stroke
balance).
In Figure 38D the flapper valve is shown
in its use with double acting cylinders.
It is
ļ
-35-
necessary to provide two different effective areas
for a balance between the supply pressure (P₁) of
Figure 37 and the modulated pressure (P2). Common
to all four relay devices are the characteristics
shown in Figure 39.
Should (S) be relatively large, as in the
case of instruments, and great over-travel be essen-
tial without interference with the movement of the
indicating pointer, the flapper as well as the jet
principle are modified and used in the form shown
in Figure 40. In the left-hand diagram (40A), a
cam intercepts the air stream from (1), thus modu-
lating the recovery pressure in the receiving
nozzle (2). In the flapper design the cam again
acts as the variable secondary orifice. The upstream
orifice (1) in Figure 40B is common to the two
branches 21 and 2". The pressure (P2) between (1)
and (2¹+2") is equivalent to P2 in Figure 37.
In Figure 38 the difference between two
modulated pressures was taken rather than only one
modulated pressure. This has four advantages. First,
it makes use of the fact that the center part of
the S-shaped curves which are typical for the output
of relays is approximately straight. Second, that
the difference between two outputs, which are so
-36-
displaced that their centers coincide but their
directions of change go in opposite directions, is
oppos
Third, that
also approximately a straight line.
the controlling output of the relay has plus or
minus values (see Figure 41). Fourth, that their
zero value is independent of supply pressure varia-
tions.
Such circuits have also been applied to
electronic relays for exactly the same reasons.
They are known in this case as "Push-Pull Amplifiers".
The diagram indicates how the outputs of two triodes
(A + B) are counteracting each other just as the
outputs of the jet are producing a pressure differ-
ential AP. The diagram shows how the difference
is obtained from the individual output curves.
In the same manner, the characteristics
of the relays shown in Figure 38 were obtained
(Figure 42). It will be noted that as a result of
this "push-pull" circuit, not only approximately
linear relationships between displacement and output
AP are obtained, but also more or less linear ds
This feature is of the greatest importance
for the design of stable amplifiers and has been
the reason for the great success of hydraulic power
amplifiers. Fortunately, means have been devised
ȧt
curves.
-37-
during the recent years to obtain similar output
characteristics from electrical motor circuits.
In Figure 43 the "push-pull" principle
is applied to the flapper type relay. A clockwise
turn of the flapper increases P2 and decreases P1,
thus producing a differential (P1 P2) as shown
in the right-hand diagram. It will be noted that
we are getting a zero output which is practically
independent of the supply pressures, as P₁ and P P₂
are simultaneously affected by the supply pressure
and the resulting change is cancelled out by the
subtracting operation.
1
2
In Figure 44 the same principle of the
"push-pull" device is applied in two electronic
relays (U.S. patent 2,399,420). In the Electron-
bean tube, which we have previously discussed, the
difference of the output potential which is obtained
at the target plates remains zero for wide range
variations of the heater current or of the beam
intensity or of the anode potential (A). In the
tube (Figure 448) a lever (3) which carries two
movable grids (4) and (5) moves these grids in a
"push-pull" arrangement relative to two anodes (1)
and (2). The resulting characteristics are again
the same and what has been said about the Electron-
beam tube (Figure 44A) applies also to this type
-38-
of tube (44B).
The implication of the advantages claimed
for the "push-pull" circuit is again shown in Figure 45.
In (A) we have a true "Null circuit" using the relay
(jet type) for controlling the pressure (P1). This
solution is evidently independent of the relay supply
pressure (P2). In the solution (B) with a necessary
displacement of the relay, P₁ must necessarily be
affected by variations of P₂ as the spring character-
2
istic of the adjusting spring, the diaphragm and the
jet displacement characteristic enter into the
equation which establishes the balance.
Another "push-pull" relay which is very
widely used is the Wheatstone Bridge. In Figure 464
and B, the hydraulic as well as the electrical bridge
is shown. Both solutions are sufficiently known to
make it unnecessary to explain them in detail. The
common denominators with the previously shown relay
system are:
a) the use of the push-pull principle,
b) independence of the zero point from the level of
supply energy,
c) variation of sensitivity with a change of the
level of energy supply.
-39-
As
The balance is, in this case, one of potentials.
this bridge is very widely used, not only for resis-
tances but also for capacitances and inductances,
Figure 47 is added to show these modifications of the
circuit. As we shall see, later on, that simple
translators are available for (S/resistance), (8/capa-
citance) and (8/inductance), it is evident that
bridge cirduits also lend themselves admirably to
the design of (S/S) translators.
-40-
CHAPTER VI
VARIABLES
In a previous study I have demonstrated
the equivalence of the three basic mechanical
variables:
F = Force
P = Pressure
S = Stroke
i.e., I have shown means which are available to
translate each one of them into each other (see
reference 3 and 5). This means that any solution
available for either one of them as parameter can
be translated into another solution with any of
the two other variables or into one of the same
variable of directly proportional magnitude.
It was realized at the time that the
choice or preference of F.P.S. was to a degree
arbitrary. There is, for instance, no other justi-
fication for the addition of the pressure (P) to
the force (F) than that of convenience. In spite
of the fact that a translation of P into F, or
vice versa, is relatively simple (although there
are exceptions), it is more convenient for the
designer who has to handle thermodynamic problems
to work with P as a variable than to think in
-41-
·
terms of (Forces/s²). In the same manner I shall
select in this study rather arbitrarily a number
of preferred variables with no better excuse than
the fact that they were convenient for my own parti-
cular applications. This results in lack of elegance
and broadness of the over-all plan, but fortunately this
lack is compensated by the fact that first of all this
study aims at nothing but an outline of a method of
approach, and that it is not difficult to extend
the system to meet the particular requirements of
the individual worker. No attempt will be made to
discuss in detail the definition, nature and under-
lying physical concept for each variable. This is
a project for the physicist (see reference 15 and 16).
The advantage of using universally accepted
symbols as those available for current (1) and voltage
(e) or force (F), etc., is that the designation of a
given translator is at the same time a clue to its
use. Thus the symbol can be internationally under-
stood and the confusion of trade names avoided. For
instance, in Figure 48 we have the symbol of a trans-
lator (e/v)el: which represents any device which
produces a speed (v) as a result of and in response
to a signal D.C. voltage, i.e., for instance a
D.C. motor.
-42-
It might have been desirable to subdivide
the chosen variables under more general headings, as
for instance; radiation energy with sub-classes of
sound, supersonics, heat, light, radio, radar.
Although from an academical standpoint this seemed
advantageous and perhaps will be done some day in
the future if the suggested scheme should ever find
more general use, the need for an immediate compro-
mise answer, so typical for an engineer confronted
with his routine problems, decided against this more
perfect solution. Again under light radiation sub-
headings, could have been and probably will be added
at some later time, as for instance, polarization,
frequency - wave length, amplitude, etc. In parti-
cular, the field of frequency will have to be
extended by the specialist and pulses added as well
as perhaps the variable time.
For an instrument and control designer of
the present (1945), the chosen parameters or variables
do, however, cover the majority of his projects.
The following variables are used in this
study and an attempt will be made to demonstrate their
equivalence, i.e., their interchangeability.
S = stroke, motion, movement, displace-
ment for straight line as well as
for angular values.
Dimension: (ft. or degree)
-
-43-
P = pressure, defined as force/area
Dimension: (lbs./ft.2) = (F/s²)
F = force
ds
v = speed - linear d
dt
number of turns/second v
HI!
a = acceleration
नर
0 ||
Dimension: (lbs.) (weight)
Q
Dimension: (ft./sec.) or (1/sec.)
$2
at 2
¿2d
dt
= D.C. current
Dimension: (lbs.)
sec.
=
= A.C. current
angular Σ =
Dimension: (ft./sec.2) or (1/sec.2)
weight units
= flow rate =
Dimension: (amp.)
= D.C. voltage
e = A.C. voltage
linear
Dimension: (amp.)
T Temperature
=
Dimension: (volt)
sec.
Dimension: (volt)
or rotary or
dd
R = resistance
light intensity
Dimension: (candle power)
Dimension: (volt
amp.
13/05
Dimension: (deg. F) or (deg. C)
at
Ohm)
or
-44-
L = Inductance
Dimension: (volt sec./amp.) or (Henry)
C = Capacitance
Dimension:
ampere sec.) or (Farad)
volt
Y
= Phase displacement
Dimension: in time (sec.)
in space (ft.) or (deg.)
H = Magnetic field
Dimension: (amp. turns/ft.)
E = Electrostatic field
f = frequency
Dimension: (volts/ft.)
Dimension: (/sec.)
(It will be noted that instead of the C.G.S. system
of the physicist, a technical system based on lbs.
(weight), ft. (or inch), ampere volts, and seconds
is chosen (see reference 15 and 16).
-45-
CHAPTER VII
variables.
THE TRANSLATOR MAP
With the background of the previous chapter,
we are now in a position to design a technological
"map" which will assign a definite position to each
"translator" device. This map is based on the ob-
vious fact that each one of the variables can be the
"input" or the "output" of a translator or a trans-
lator chain. We thus obtain a number of fields or
boxes, each occupied by a translator and designated
by a number for simple reference and identification.
The number of boxes is obviously the square of the
In Figure 49 the layout of the translator
map is shown. The vertical column on the left-hand
side represents the "input", the horizontal top
column the "output" of each translator. Box 12, for
instance, represents a (F/v) (force/speed) trans-
lator, an example of which may be a speed governor,
the centrifugal force of which controls the speed
of a turbine. At first glance the sequence of the
numbers seems to be confusing. But following conse-
cutive numbers, let us say, from 1-11, will reveal
a sort of "snake dance" which systematically covers
the field.
=
-
-46-
The choice for this arrangement was made
in order to make it possible to enlarge the trans-
lator map to any desired size by auding additional
variables without losing consistency to the number-
ing scheme.
The map, therefore, assigns to each trans-
lator a definite position in the general field of
translator devices. It furthermore gives each type
a definite number which can be used by unskilled
help as a filing or reference number, and it adds to
our abbreviations an additional one, the number (12)
for instance, which can be used instead of the pre-
viously mentioned symbols.
For drawing up a map of available devices,
it was found convenient to indicate the classes (a),
(b), (c), (d), discussed on page 9, by marking the
boxes on the map, as shown in Figure 50. The
sequence of these marks follows the clock. A refer-
ence of (5) a establishes a translator to be one with
an input force and an output stroke as an (F/S)¸ type
device, a scale, for instance with non-linear cali-
bration.
At first, it may appear that all the above
effort in establishing reference and descriptive
symbols is a rather heavy burden. The problem of
-47-
what to do with the ever increasing amount of litera-
ture and data, where to file it, how to locate it
and to correlate this material, is however becoming
so acute that some of our outstanding scientists
like Dr. Vannevar Bush have given it most serious
thought (see reference 17). The proposed system is
only one of the many possible ones, but it offers
beyond the decimal system used in libraries and in
the outstanding prewar publication of the ATM (see
reference 18), which unfortunately is not as yet
available in English, a means for correlating indivi-
dual translators beyond mere classification.
This calls for further proof and explana-
tion. Studying the map of Figure 49 (and the complete
Chart I of the appendix), we note that there is a
definite significance attached to certain types of
translator columns. The column (4), for instance,
in Figure 51, has all of the variables as inputs
and a common output, stroke. These translators can,
therefore, be represented by (variable/stroke). As
the term stroke is meant to be used in its broadest
sense, that is, any distance between two marks
representing the variabie (from the marking of a
micrometer to the time scale signal of Radar represent-
ing echo distance), we can broadly classify devices.
GRA
-48-
of this type as "instruments". Or, putting it in
another way, those devices with which we are familiar
as indicating or recording fall into this class.
On the other hand the top horizontal column
(B) of Figure 51 starts with the common input (8)
and has various variables as output (stroke/variable).
Most manual and automatic setting devices as well as
controls are falling into this group. The stroke
input may represent the tension setting of a relief
valve or the input of a spring whose output is a
force (see reference 3); it may be the adjustment of
a condenser or resistor or the bias built into a capa-
citor bridge. The terms "controls" and "controllers"
are, however, not meant to be a new term to be used,
but rather a general designation of the type of
devices most likely to be found in the column (B).
The important implication of the use of
the two columns (A) and (B) for the purpose of this
study, which attempts to prove that at least one
solution for any translator of the map is available
at present, is that if it can be shown that trans-
lators are available for all boxes under (A) and (B)
the rest of the map is also covered. This obviously
greatly facilitates this study as, if the above is
correct, it is only necessary to prove the existence
S
-49-
of the limited number of translators in (A) and (B)
instead of all of the individual boxes covered by the
map.
Let us, for instance, assume that a trans-
lator, type 29, is needed; that is, a device which
produces a flow as a function of a speed input
(signal). Such a device is used for providing cooling
water for a combustion engine, and it is usually de-
sired that a definite proportionality exists between
the speed and the amount of water; i.e. a device (29)
As we find available in column (A), Figure 52, a
translator (16), a speed indicator (v/S), we add the
translator (S/w) (26) of the column (B) and thus
translator. It is important
to note that in this chain only class b and class d
translators are permitted unless a feedback is esta-
blished between v and w. In general we can say that
a chain of two translators of column (A) and (B)
(variable₁/stroke) + (stroke/variable) will give us
one solution (variable₁/variable), thus proving the
point that coverage of (A) and (B) covers completely
the field of the map.
d
produce (29) ¿, a
(v/W)
It is realized that there are simpler and
more direct solutions available in most of these boxes
thus covered, and that the above approach does not
eliminate the desirability of filing their character-
-50-
istics under the respective numbers of the map.
However, as this job goes beyond the purpose of this
study, which attempts to outline an approach rather
than to provide a technological encyclopedia, the
above proof will serve its purpose of establishing
the fact that with (A) and (B) solutions available, at
least one solution is given for any other box of the
translator map.
It will be interesting to see what happens
if we reverse the sequence of the two (A) and (B)
type translators:
(stroke/variable) + (variable/stroke) means
(stroke₁/stroke₂)
This type of device has gained a tremendous amount
of importance during the World War II and can be said
to cover "servo mechanisms" in the broadest meaning
of the term, or "positioning devices". It includes
devices from the simplest lever to a radio controlled
valve on a target ship or on a remote controlled air-
craft.
As the intermediate variable can be any-
thing from electricity to sound, the possible solutions
are very numerous, especially as it is not necessary
to restrict the translator chain to two links.
In
Figure 52 a translator chain is developed, using three
-51-
links and starting outside of (A) and (B) to give the
example a broader meaning. We start with an (a/F)
translator (19). We also find that a translator (F/S)
(5) and a translator (S/w) (26) are available. As an
example:
=
(19) may be a mass
We have then:
acceleration into force.
(5) could be a spring scale of class (5),
and
(26) a flow rate regulator with pneumatic
power, i.e., a class (26) a translator.
d
(19) translating
(a/F) b + (F/S) b + (S/w) a
(19) 。 + (5) b+(26) a = (30) a
b
and the method or the path to get from 19 to 30 is
indicated in the Figure 52. We thus have with the
greatest of ease a new device (30) which makes us
d
immortal as we are likely to obtain a basic patent
on such an "invention".
(a/w) d
It is my hope that this study will prove
that for those "skilled in the art of this method" the
design of such a translator chain does not amount to
"invention" and hereby give designers in the absence
of patents the freedom they so badly need in the
international technological race we are confronted
with. In addition the map will serve the purpose of
=
-52-
any map, i.e., to indicate alternate ways of arriving
at a given location if certain roads are blocked for
any of the many possible reasons.
The resulting multitude of possible solu-
tions seems appalling at first; however, some of the
"possible" solutions will immediately be ruled out as
definite additional specifications will limit the
choice of practical designs.
Thus for instance, the
designer will have to consider:
a) minimum amount of cost of the complete chain,
b) elimination of non-reliable links,
c) over-all simplicity, weight, size, serviceability,
etc.
ja
In addition the map and the analysis of a
given chain emphasizes the need of certain develop-
ments which would otherwise be less obvious. There
is, for instance, a definite need for a translator of
the (b) or (d) class which for a given pure electrical
input signal produces a definite resistance or ca-
pacitance. On the other hand, a new development of a
translator, which replaces a chain, immediately shows
its implication as it points out a possible simplifi-
cation of a previously available translator chain
(see Figure 53).
-
The availability of an (1/s) translator re-
duces the chain (F) to a simpler design (G). This, for
-53-
instance, seems to me to be the significance of the
development in the last analysis of that revolutionary
translator (e/1), the "triode" of Dr. Lee De Forest.
Its availability made it possible with purely electri-
cal means under elimination of mass-inertia, and
therefore, at very high speeds to translate one electri-
cal signal into another. It was one of the "missing
links" or blank spaces in the translator map, and
after the discovery of this "pass", a flood of devices
immediately poured through this new gate.
At this point, it seems appropriate to stop
for a moment and to outline the plan for the rest of
this study. We have seen that covering the "instrument"
and "controller" columns (A) and (B) of Figure 51 gives
us one possible, although not always simple solution for
any translator on the map. In both columns, however,
the parameter (5) appears which introduces mass and
inertia, and thus limits the maximum rate of response
of such a device to relatively low frequencies. How-
ever, the next chapters will give examples for each
one of the translators in (A) and (B) to prove the fact
that one solution at least is available.
Realizing the limitation of the above, let us
say mechanical engineering (which includes the use of
electrical devices which incorporate mass characteristics),
-54-
it appears desirable to see how far pure electronic
solutions are available in which the parameter (S) is
eliminated (reference, an unpublished paper given by
the author in 1944 at Gibson Island, AAAS). Such trans-
lators in analogy to the mechanical ones just discussed
will be of the type (variable/electric unit) = C and
(electric unit/variable) = D.
= D. We shall show that solu-
tions are available for (C) and (D) and then combine
(C + D) or (D + C) to cover the rest of the map with
pure electric or electronic solutions. This, if
successful, will provide at least two possible solutions
for any translator, one with mass limitations, the other
without them.
The choice of the examples will be criticized,
I am sure, and rightly so, as my own background and
experience is mainly mechanical engineering. Any reader
will be able, however, to remedy, I hope, this shortcoming
of the study by inserting his own favorite translator
for reference purposes, and I most sincerely invite
suggestions for future editions, should there ever be a
demand for one.
The rest of the study will show the means
available to solve mathematical solutions by means of
such translator devices, broadening the field of cal-
culating devices beyond pure mechanical and electrical
-55-
solutions. Finally, an example will be discussed
which represents a translation of a given chain into
other variables.
Before leaving the subject of the translator
map, we shall see how the availability of any group of
translators automatically establishes solutions for
other translators.
A simple calculation of combina-
tions gives the immense number of possible solutions
for 2 link, 3 link, and n-link chains and indicates
the need for a systematic study of alternate solutions
as the average designer is liable to be satisfied with
one solution and is apt to give up further efforts
after having found one way out of his difficulties.
In Figure 54 it is assumed that translators:
(20)
(a/v)
(29)
(v/w)
(76)
(w/g)
are known; from this follows:
1) (a/v) + (v/w) (a/w) (20) + (29) (30)
2) (v/w) + (w/e)
(29) + (76)
(w/g) = (v/g)
3) (a/v) + (v/w) + (w/e) = (a/e)
(78)
(20) + (29) + (76)
(a/w) + (w/e) = (a/e)
(30) + (76) = (77)
4)
In similar ways other paths can be established
through the jungle of translators and thus new
devices can be designed for each individual problem.
=
=
=
=
=
=
=
(77)
-56-
It is obvious to think in this connection
of the practicability of filing all pertinent data
for a translator on a Hollerith machine, and let the
machine automatically sort out those solutions which
fulfill the specifications. While such a device
which approaches the solution suggested by Dr. Bush
(see reference 17) will probably not be available in
my own lifetime, it appears pleasant to speculate how
much the future designer would profit by the elimination
of the slow process of reinventing time and again
devices which have many times before either proven
their value or died after a short but unsuccessful
life. Even if this ideal state of "pushbutton inventing"
may be far off at this moment, actual experience with
the application of the above system to a practical
problem has produced in one special case 115 solutions
where previously only 4 were available.
}
2.
-57-
CHAPTER VIII
TRANSLATORS
Before going into the description of indivi-
dual translators, a few general remarks are in order.
I have simplified the diagrams to indicate the basic
principles which are involved in the design without
regard to technical details. In the interest of this
study I shall be as brief as possible in describing
the individual design of each translator relying on
the general technical background of the reader rather
than attempting to give detailed explanations. Thus,
most of the information is believed to be contained
in the sketch rather than in the text.
The figures published were photographed from
3 x 5 inch cards, which are standard for use in card
indices. The cards bearing the translator type and
number are easy to read and review. To assure con-
tinued filing at the same place of the card index
system, the translator reference number was amplified
by adding a zero and then consecutive numbers. Thus,
a figure 73/018 means the 18th card in the translator
collection of type 73. The 762nd translator of this
group would have the number of 73/0762. This prelim-
inary work seems necessary to help in keeping track of
the ever-growing amount of devices available to the
-58-
designer. Other and better systems are no doubt
possible. The above solution is only one of them and
has the advantage of having served its purpose already.
We shall now consider the first group of
translators, those which translate a variable into a
stroke:
(A) VARIABLE/STROKE TRANSLATORS
Type 1 (S/S) Stroke/Stroke Translators
This type of translator is historically one
of the first, and for the mechanical engineer, the
most important one. It covers a broad field from
the lever known as a tool to primeval man and even
used by animals to the most intricate measuring and
calculating machines, including servo-mechanisms and
even remote controls by radio. Common to all of these
translators is that for a given input (S₁) a corres-
ponding output (82) is obtained.
Type (1/01) (81/S2)b Figure 55
b
The simplest type is the lever. A motion of
ន
(S₁) the input produces an output S₂ = 1, if a and b
S2 А
are the respective lever arms. Multiple lever arrange-
ments (see upper sketch) make it possible to increase
the ratio (S1/S2) within relatively small space.
Type (1/02)
a-b (S1/S2) a - b Figure 56
The cam arrangement shown in Figure 56 permits
-59-
a change of (81/82) as a function of (81) (see refer-
ence 19 and the "classic of classics," Wittenbauer
reference 20). Direct proportionality as well as any
other functional relationship can be obtained from
this translator.
Type (1/03) ($1/82) a Figure 57
This translator represents a translator
chain with two links and is based on the gas law,
P.V. = G.R.T. The translator analysis shows:
(S₁/P) a + (P/82)b = ($1/82) a
It will be noted that the sum of two translators
greatly depends on the design details, heat transfer,
leakage and rate of compression; it will, therefore,
not be suitable for designs where the same output is
expected for every input. Note the difference
between the cam and this compressor, although both
belong to the same class (1), (non-linear translation).
a
Type (1/04)a (8/82) Figure 58
a
In this design we have a hydraulic amplifier
(jet pipe) and a feedback system which produces a
direct proportionality between the input (S₁) and
the output (S2) regardless of the load to be overcome
by (S2). The feedback is established between two
opposing forces both produced by (S₁) and (S2) by
means of (S/F) translators (springs).
-60-
An analysis of the chain shows: (S₁/F)
"spring" + (F/S) deflection of the jet relay + (S/v)
rate of piston travel as function of relay displace-
ment + (v/S₂)
The chain can also be written
(v/S₂) =√vd
=Svat.
by giving the translator numbers:
(9) + (5)
(1) a
+ (10) a
Note: Due to the feedback the result is class d.
(16)
Type (1/05) a (s/s) Figure 59
2 a
=
This translator found its first application
in prime mover controls. It differs from that shown
in Figure 58 by the fact that the feedback is a
stroke feedback and not a feedback of forces. As
this type of mechanism is very widely used, it is
believed that its design is self-explanatory from
the two schematic sketches which show two modifica-
tions of construction (see reference 21).
Type (1/06) ($1/2)c Figure 60
e
The schematic sketch represents a pneumatic
gauge. The clearance between the piece to be
measured and the gauge nozzle modifies the incoming
pressure (P₁) and produces a pressure (P₂) which,
measured by means of a gauge, results in output (S2)•
The translator is shown as an example of a device
with auxiliary power (amplifier) but without feed-
back. The chain of translation follows the sequence:
(S₁/P)a + (P/§₂)b
(P/S₂) b = (1/2) a
-61-
Type (1/07)a (S/S) elec. Figure 61
This device uses an electrical impedance
bridge for establishing a balance between (S1) and
(S2) by means of a voltage feedback. The force
available at the plunger (2) is proportional to the
displacement (in space) of (S₁ - S₂) = S. The
device is used by several instrument companies
(Brown, Cochrane, Bailey Meter, Askania) for remote
transmission of movements.
Tyne (1/08) (S/S)elec. Figure 62
d a
2'd
The same basic characteristics as those of
(1/07) are obtained by the "Selsyns" or "Synchros" of
Figure 62. Phase angle zero (space) is obtained only
when output torque is zero. The rotary design per-
mits unlimited number of turns of S₁ and S₂ and here-
by an increase of accuracy by gearing. Such devices
have found a great number of applications for anti-
aircraft devices and remote indicating.instruments
during World War II.
Type (1/09) a (S1/S2)a Figure 63
In connection with Figure 34, we have briefly
discussed the application of a bridge circuit for amp-
lification, feedback, and automatic balancing circuits.
In Figure 63, three basic types are shown. While (A),
the self-balancing resistance bridge can be used with
either D.C. or A.C., the capacitance bridge (B) and the
inductance bridge (C) are obviously only to be used for
-62-
A.C. As the resistances, capacitances, and inductances
can be adjusted by strokes (S1) and the bridge can be
rebalanced by strokes (S2), the self-balancing bridge
(S₁/S₂)elec. translator and is used to a very
is a
с
great extent for this purpose (see reference 22).
Type (1/010) a (S₁/S2) Figure 64
d
d
A modification of the circuit (Figure 63)
is shown in Figure 64, which is equal to:
elec. hydr.
(1/09) a
+ (1/04) ä
(1/010)
d
The combination is shown as an example of a two link
chain in which both links are (S/S) translators.
elec.
hydr.
Type (1/011) 。 – d
a ($1/52) c - d
Figure 65
-
с
In strain gauges the change of resistance
due to change in length of an elongated or compressed
wire is measured by means of an A.C. amplified voltage
which is either indicated directly on an indicator or
observed on the screen of an oscillograph. As such
devices do not always give direct proportionality, the
(S1/S₂) translator is classified either as c or d (see
reference 22).
Type (1/012) (S₁/S₂) electron
(51/52)
с
=
Figure 66
For measurement of small displacements and
for gauging, advantage is taken of capacitance changes
-63-
due to the relative motion (S1) of two condenser plates
(torque measurement on engine shafts, for example).
This method competes with the strain gauges and is
basically the same as the one of Figure 63. The main
difference is that (S2) is not produced by a motor but
indicated on the screen of an oscillograph (see refer-
ence 22).
electron
Type (1/013) a ($1/$₂) a
Figure 67
In the Electronbeam tube (see reference 12)
of Figure 30, the balance between input and output is
accomplished by the use of a cathode ray which acts as
a zero controlling galvanometer. The input (S) dis-
places a magnet whose field deflects the cathode beam,
hereby producing a control potential on the two target
plates connected to the control amplifier. This control
amplifier energizes the motor and rotates its shaft
until the movement of the opposite magnet (S2) produces
a field strong enough to return the cathode ray beam
to its zero position of zero potential at the target.
Thus (S) is directly proportional to (S₂).
The desirable feature of this design is that no drag
is produced by the follow-up device on the signal
device beyond the extremely weak attraction of the two
magnets.
-64-
optical electron

Type (1/014) (S1/S2) a
Figure 68
Such follow-ups are extremely important for
our study as the coupling of two translators, one of
which has an output (S₁) and the next an input (S2)
permits the translation from any variable into any
other variable.
(variable₁/S₁)+(S₁/S₂)+(S₂/variable2)
Such intermediate amplifiers (S1/S₂) should preferably
be of the class d type and their operation should not
in any way affect the primary variable. In Figure 68,
therefore, another design is shown for (S1/S2)a which,
originally developed by G. E. as a high sensitivity
recorder, can be used for general (S/S) translation
(see referance 23 and reference 9, page 292).
d
*********
(variable₁/variable2)
The angular displacement (81) of a primary
mirror (1) (attached to a galvanometer) produces a
reflection of a light beam to various parts of the
curved reflecting mirror (2) which in turn throws a
light beam to the mirror (3) from where it is split by
a wedge type mirror into two beams reaching two photo-
cells (A) and (B) which are part of a push-pull circuit
of an amplifier.
Its output varies until a sufficiently strong
current in the galvanometer coil produces a rotation
(S) the output of which returns the light beam into
-65-
a position where, hitting the wedge, the output of
both photo tubes is balanced again. By this method
(S1) and (S2) are in synchronism again and the
coupling between both systems is only accomplished
by optical means.
Type (1/015)¿ (S/S)Optical electron.
Due to the importance of such translators,
Figure 69 is added in which light intensities are
modulated by means of polarizing filters (see refer-
ence 24).
Figure 69
A friction wheel (A) is driven by the
input displacement (S1). Two mirrors reflect two
light beams through two secondary rotary polarizers
which are rotated by an output controlling motor (B).
Before reaching the secondary polarizers, the beams
pass through a primary rotary-friction driven pola-
rizer. After the secondary polarizers, the light
beam hits photo-electric tubes in a push-pull circuit.
Their output controls the motor (S) in such a way
that the phototube circuit is again balanced by
rotation of the secondary polarizers. In this
manner (S) and (S2) become directly proportional.
The difference between type (1/014) and type
(1/015) is that the balance of the photo tube circuit
-66-
is disturbed in the first case by a light beam
deflection, and in the latter case by intensity
modulation.
Type 4 (P/S) Pressure/Stroke Translators
These devices are commonly classified as
pressure gauges or pressure indicators. They should
include strain gauges and in general, all devices
which permit the indication of values (lbs./sq.in.)
or (lbs./sq.ft.).
Type (4/01) (P/S) Figure 70
b
The three fundamental translators are:
(Figure 70B)
(Figure 70C)
(Figure 70A)
a) the U gauge
b) the bellows
c) the bourdon tube
These three devices cover the range from practically
zero absolute to several thousand pounds per sq. in.
Type (4/02)
Figure 71
a b
A modification of the U gauge is the pres-
In this design,
sure gauge known as "ring balance."
Figure 71, it is not the displacement of the liquid
which is measured, but the force exerted by the
pressure on the partition at the center of the ring.
The liquid acts only as a sealing piston. The tor-
que, which is produced by the pressure, is counter-
acted (force feedback) by the pendulum (G) or other
forces (springs, etc.).
a b
(P/S)
→
S
*
-67-
Such devices respond actually to pressure differ-
entials.
Therefore, all flow meters which respond
to differential pressures fall into this class (see
reference 25).
Type (4/03) a (P/S) Figure 72
a
As it was shown in the example of Figure 71,
flow meters which respond to the dynamic pressure can
be used for (P/S) translators. As the dynamic pres-
sure of a flow is equal to P = cv², any device
which is used for measurement of this velocity pressure
is suitable as a (P/S) translator. The translator
shown in Figure 72 is self-explanatory.
Type (4/04) (P/S) Figure 73
с
с
This translator is shown as another appli-
cation of the series arrangement of two orifices. It
is unusual insofar as the incoming pressure (P₁) deter-
mines the pressure between the two resistances. The
incoming pressure (P2) is translated into a stroke.
The whole mechanism, therefore, functions as a (P/S)
translator. The translator chain is expressed by:
(P/w) = (w/P) + (P/F) + (F/S) = (P/S)
Type (4/05) (P/S) a Figure 74
a
In this translator an Askania jet pipe
relay is used with a force feedback between F F1
and F2.
-68-
2
The output stroke is translated into F, by means of
a spring. The output (8) can be of any magnitude
from a few ounces to thousands of pounds.
Type (4/06) (P/S). Figure 75
Strain gauges measure forces per inch² based
on the elongation of a resistance wire. The output
of an A.C. bridge is amplified and indicated on an
oscillograph. The amplitude of the oscillation, as
shown on the oscillograph, is the output (S).
Type (4/07) (P/S) Figure 76
C
Electrical translators for measuring
pressures frequently use "piezo crystals" which
respond to an applied force with a voltage. This
voltage is then amplified and converted into A.C.,
which in turn is translated into a stroke (see
reference 26).
Type 5 (F/S) Force/Stroke Translators
This type of translator devers all types of
"scales". It includes devices ranging from a super-
sensitive torsion balance and gravitometer, which is
used for measuring the variation of the gravity con-
stants at different points of the earth's surface, to
floating dry docks whose water line is an indication
of the over-all weight of the dock plus its load.
-69-
Type (5/01) and (5/02) (F/S)b Figure 77
In Figure 77A we have a spring arrangement
which translates the force (F) into a stroke (S) and
in 77B two types of scales which are based on the
balance of moments around a given fulcrum. Both
types are of the 5 class.
Type (5/03) and (5/04) (F/S)
Figure 78
The floats shown in Figure 78 are used
displaced water.
extensively for measuring the specific gravity of the
Instead of measuring the amount of
the protruding part of the float (5/03, left-hand dia-
gram), it is also possible to measure the change in the
level of the vessel (5/04, right-hand diagram). The
latter may have the advantage that it is more suitable
for transmitting the value to an instrument or control.
a
Type (5/05) a (F/S)
(F/S) a Figure 79
d
-
a
In this translator the force is amplified
by means of a hydraulic relay which through a force
feedback between F1 and F2, produces an output (S)
which is directly proportional to the applied force
(F1). Thus, an output (S) can be produced regardless
of the load which has to be overcome.
Type 16 (v/S) Speed/Stroke Translators
These translators cover "speedometers" as
well as velocity meters for liquids, fuels, and solids.
-70-
Therefore, they are closely related to the W/S trans-
lators of Class 36, which cover flow meters" exclusively.
In audition to the above application, this translator
covers devices which measure the value of ds/dt or
d/dt which are rates of change of strokes or angles.
The latter type of devices is gaining more and more
importance in connection with control problems.
Type (16/01)e (v/8)¿ Figure 80
This is a liquid type rate of speed indi-
cator in which the change of the level surface of a
rotating cup is used to indicate the speed. Each
particle of the liquid is subject to the acceleration
of the earth as well as to its centrifugal accelera-
tion. Therefore, for a given liquid and given speed
(6) becomes a definite function of the speed or v.
As this relationship is not directly linear, the
translator belongs to class c.
G
Type (16/02) c –
c - a (≈/8)。 – a Figure 81
A more common type of speedometer is the
one shown in 16/02. In this case the centrifugal
force of weights is balanced against the force pro-
duced by a spring. The translator chain follows
the equation:
v/a + a/F + F/S = v/6,
depending on the arrangement of weights, levers, and
-71-
springs, this device can be made to fall into class
16c or 16d.
Type (16/03) a (v/8)₫ Figure 82
In this device an Askania "Transometer" is
combined with a (P/S) translator, an application which
is typical of the measurement of slow engine speeds as
well as of the speed of rotation of positive displace-
ment oil meters. The transometer produces a pressure
which is the square of the r.p.m.'s or W or v, and this
pressure is applied to a diaphragm and a hydraulic
amplifier with a force feedback producing a given stroke
for a given pressure. By a suitable (8/8) translator,
the second power function of (P) is suitably compen-
sated so that a straight line motion of (S) for a
given input (v) is obtained.
Type (16/04) a,b,c (v/s) a,b,c
(v/S) a,b,c Figure 83
The most common electrical solution for
this problem is the use of an A. C. or D.C. generator
which, driven by the shaft whose speed has to be measured
produces an A.C. or D.C. voltage which in its turn is
measured by means of an A.C. or D.C. volt or ammeter.
Additional amplifiers may be incorporated if the output
voltage is too small. For this reason, the type is
given as 16a, b, or c.
-72-
Type (16/05), (v/S), Figure 84
a
Type 16/05 belongs in the class of fluid
velocity meters, but can also be used for measuring
the speed of vehicles. The difference between the
static and the dynamic pressure of a medium relative
to which the vehicle travels is determined by a
"Pitot" or PPrandtl" tube and a suitable indicating
instrument(s) used to produce the output (8) as a
function of (v).
(v/5) a,b,c,d
a,b,c,d
Averaging the velocity distribution over
the cross section of a pipe line or a channel, we
arrive at flow meters (see also w/8 translators, type 36).
Type (16/06)
Type (16/07) (v/8) Figure 86
с
с
In the same class of fluid velocity meters
belongs the hot wire anemometer (see reference 25).
In this case, the change of temperature produced by the
velocity is used to produce a change in resistance
which in turn produces a current and finally a stroke,
i.e., an indication of the flow rate.
Type (16/08) (v/S) Figure 87
с
с
Figure 85
This translator is used to obtain indica-
tions of rates of change. The basic principle is to
obtain the vector sum of one known and the unknown
C
-73-
vector which produces a resulting vector, the angle
of which is an indication of the magnitude of the
unknown vector. For this purpose a roller (R), which
is supported in a fork and in a bearing (B), moves
parallel to the axis of a rotating cylinder (Z).
This cylinder is rotating with a constant speed and
has, therefore, a circumferential speed of d∙∙n.
60
The roller always takes a position in the direction.
of the resulting vector (VR). The rate of actual
movement is the unknown vector (v). This resultant
angled and, thereby (S), becomes an indication of
the rate of travel v = ds. (see reference 5)
at
Type (16/09) c (v/S)。 Figure 88
с
In this type of translator, advantage is
taken of the precession forces of a gyro whose axis
is rotated at a given rate. This device is used in
airplane instruments for rate of turn indication;
details about this device can be found in reference 27.
Type 17 (a/S) Acceleration/Stroke Translators
These translators are known as accelero-
meters and are used to measure the acceleration which
may be linear, i.e., (a) or angular, i.e., (E). Most
of these devices are taking advantage of the trans-
lator (m) which, for an applied input of acceleration,
-74-
produces directly proportional output changes of a
force (F).
Type (17/01)a - b (a/S) a - b Figure 89
·
Three different types of (a/S) translators
are shown. These are A, B, and C. In (A) a U-gauge
filled with a liquid is subject to acceleration.
level of the liquid in the U-tube legs thus becomes
an indication of the magnitude of acceleration.
In (B) a pendulum is used in which the
balance between the gravity component and the accel-
eration produces a movement (»). The most refined
instrument of this type is the torsion balance which
is used for measuring small changes in the gravity
component of the earth. Also into this class belong
gravitometers, which are based on the principle
shown in Figure 89C, i.e., displacement of a mass
relative to its support on a spring. The transla-
tion follows the line (a/F) + (F/S) (a/S).
=
The
Q
<
Type (17/02) a (a/S) a Figure 90
In this translator a feedback is produced
between the force which results from the acceleration
and a force which is produced by a current which is
For that purpose,
generated by an electronic relay.
-75-
a special push-pull triode circuit is developed in
which the two grids (G₁) and (G2) can be moved
relative to stationary anodes (A1) and (A₂) (refer-
ence U. S. patent # 2,399,420). The grids are supported
by the same lever which carries a mass (m) and the
cores (C₁) and (C2) of two solenoids (S₁) and (S2),
respectively.
If, due to an acceleration of the mass
(m), a force is produced, the two grids (G₁) and (G2)
move relative to the anodes and hereby produce an
output potential on A₁ and A₂ which, suitably amplified,
counteracts through the solenoids (S₁) and (S₂) the
force of the mass. An ammeter translates the current
into a stroke. The conversion, therefore, follows
the following line:
(a/F₁) + (F₁/1)
F1 = C1F2
+ (1/8)
Type 36
=
(▼/S) Rate of Flow/Stroke Translators
In this class, we have in general flow
meters, and we will understand under "flow meters",
devices to determine rate of weight units per time
units. This, for a given density of the material
measured, includes meters for (volume/time units).
In the following, some of the outstanding examples
will be given although the list is by no means complete.
(see references 25 and 30)
(a/S)
-76-
Type (36/01) (w/S) Figure 91
с
These translators are based on the
effect that a fluid passing through a restriction
produces a change in static pressure head which
follows the equation of Bernoulli. For venturis
and orifices, the pressure drop is proportional to
the square of the rate of flow, while for capillaries
it is directly proportional to the flow. Suitable
devices are used to translate the pressure differ-
ential obtained into strokes. The translation,
therefore, follows the line (w/P) + (P/S) (see
references 28, 31 and 32).
Type (36/02)
(w/S), Figure 92
a - b
a – b
In this type of flow meter, advantage
is taken of "self-regulation".
Referring to Figure A,
a liquid flows into a container which has an outlet
of a fixed size. The level in the container rises
until at a given height it becomes stationary, as
the rate of outgoing liquid then equals that of the
supply. The level at which this happens is therefore
an indication of the supply rate (w). We have in
this device a flow meter with a fixed outlet res-
triction and a variable head.
In Figure B, this mode of measurement
is changed by changing the outlet orifice so as to
-77-
maintain a specified range of levels. This is
schematically indicated by a float (F) which
changes the size of the outlet orifice (0). Its
position (S) then becomes an indication of the
supply rate (w).
Type (36/03) (w/s) c
(w/S) c Figure 93
The principle described in Figure 92B
is also used in the variable orifice flow indicator
shown in Figure 93. In this case, a hydraulic
amplifier is used to change the position of the
orifice (0) in such a way as to maintain a constant
differential pressure Ap. The advantage of this
device is that it has a high accuracy even at low
rates of flow, as Ap is maintained constant
regardless of the rate of flow.
Type (36/04) c - à
The same principle of using a constant
differential pressure by automatically changing
the size of a restriction is used in the so-called
"Rotameter" (see reference 29). These meters can
be made to be independent of viscosity within a
very wide range by a suitable design of the float (F).
The position of the float (F) is an inuication of
the rate (w).
(w/S)
с
· ả
-
Figure 94
-78-
Type (36/05) (w/8) Figure 95
₫ d
The same principle is used in type
36/05 which uses a piston to change the size of
the outlet orifice (0), maintaining a constant
pressure drop (P1 - P₂). The position of the
piston is transmitted to the outside through a
self-balancing induction coil unit as shown in
the diagram (Brown Instrument Company).
Type (36/06) (w/S) Figure 96
с
с
This translator was designed to
overcome the difficulty of measuring pulsating
rates of flow, especially under widely varying
static pressure conditions. The solution was
found by automatically bleeding a proportional
amount of the flow out of the line and by ex-
panding this proportional amount to atmospheric
conditions. For that purpose, a diaphragm (A)
is connected to the orifice (0). Connected to the
diaphragm (4) is a small control needle (b) which
controls the flow which is bled to the atmosphere
through an orifice (4) after it passes an orifice
(1). As soon as the downstream pressure behind
orifice (1) is equal to the downstream pressure of
orifice (2), the control needle stops its movement
and, as the flow across orifice (1) is exactly under
-79-
the same static pressure as well as under the same
pressure drop as the flow through orifice (2), the
two rates of flow (w₂) and (w₁) must be always
directly proportional. As (w₂) expands to atmos-
pheric conditions, an indication of the pressure
head of w₂, as measured by the pressure gauge, a
(P/8) translator becomes a direct measurement of
the rate of flow (w). The diaphragm and the
needle being practically inertialess, relatively
high frequencies of pulsations are not affecting
the accuracy of the proportioning w1/2″
Type (36/07) c a (w/B) c - d
Figure 97
d
In the translator 36/07, the differ-
ential pressure is applied in the usual way to
diaphragm bellows (4). To avoid the necessity
of transmitting its movement to the outside, which
introduces an error of friction, an induction coil
(B) is used which through an electronic null-
banance circuit controls a motor and a gear, which
in turn compresses through a stuffing box a spring
() which counteracts the force of the bellows.
Thus the force to overcome the friction of the
stuffing box is produced by the motor, hereby
increasing the accuracy of the instrument.
The
-80-
position of the motor is a direct indication of
the rate of flow.
Type (36/08),
C
-
d
(w/8) c
· đ
-
In the translator, Figure 98, we have
a translation of, w/v and a following translation
v/8. This type of device is of the positive dis-
placement type and thus to a high degree independent
of viscosity and density changes of the fluid. As
the fluid flows through the displacement meter, the
rate of turn of the meter becomes a direct indica-
tion of the rate of flow (w). This type of meter
is particularly applicable to heavy fuel oils.
Figure 98

Type 37 (1/6) Current (D.C.)/Stroke Translator
This type of instrument is known as a
D.C. "ammeter". Any hand book on electric metering
instruments will give detailed description of these
devices. One of the basic meters of this type is
the one described as the International Standard for
amperes, 1.e., a device which measures the volume
of oxygen produced in a given time. If this volume
is used to displace a water column, the height of
the water column (S) becomes an indication of the
amount of amperes. However, such an instrument is
actually an integrating unit and is therefore not
very handy to use.
T
T
-81-
-
Type (37/01) 。 - a (1/5)5
Figure 99
_d
This type of an ammeter is based on the fact
that a solenoid produces a force on an iron core which
is balanced against a spring. Strictly speaking, one
can say that this energy is being consumed in this
apparatus, and therefore, the symbolic box has an
arrow indicating electric power. However, the current
consumption can be so small that one can classify
this type of instrument under 37b as well as under 37d.
(L/5). ___ Figure 100
In this translator device advantage is
taken of the fact that a current flowing through a
wire produces heat and hereby a temperature which in
turn changes the length of the conductor. Such a hot
wire ammeter can be used for A.C. as well as .c., but
it is shown here for D.C. As there is a definite
relation between current and length of wire, a change
of the latter can be used as direct indication of the
current.
Type (37/02).
Type (37/03) (1/8). Figure 101
e
In the device shown in Figure 101, a triode
tube is used for the translation and the voltage
drop across a resistor is used to change the current
going through the tube which in turn is measured by
-82-
an ammeter. The conversion, therefore, follows
the equation:
(1/e) + (e/1) + (1/S) = (1/S)
This design is of the type 37c and cannot be used
where stable conditions are needed.
Type (37/04) (1/5) a Figure 102
The disadvantages of the device, type
37/03 are overcome in the design shown in Figure 102.
In this case an Electronbeam tube is used and a field
created by 11 which controls a motor and a resistor
and hereby a current 12 which counteracts the field
=2
of 11. The position of the slide wire (5) is therefore
an indication of the current (1). As this is a
true feedback circuit, the movement (S) is independent
of the tube characteristics.
Type (37/05)
(1/5) Figure 103
A modification of the same circuit is
shown in Figure 103 in which again an Electronbeam
tube is used, but instead of operating with a motor
resistor, a magnet is displaced until balance
between the field produced by 1 and the magnet is
The position of the magnet is then
an indication of the current.
d
established.
..
-83-
Type (37/06) a (1/S) a Figure 104
d
In the example shown in Figure 104, the
power relay is a hydraulic jet pipe which responds
to the balance of the force created by the solenoid
and hereby the current (1) and the spring tension
which is a function of the displacement (S). This
is a device as used for arc furnace controls. It
is obvious that there is no limitation with regard
to the amplification of power which can be obtained
from such a unit.
Туре 64 (1/8)
(1/8) Current (A.C.)/Stroke Translators
These devices cover A.C. type of
ammeters. It is apparent that this type of instru-
ment is similar to the one described under type 37,
1.e., an 1/8 translator, if the effects produced
by the currents are independent of the direction of
the current flow. This translator can also be changed
to a D.C. ammeter by using in series rectifiers which
are (1/1) translators.
Type (64/01), (64/02) c – à (1/8) c - d Figure 105
с d
-
Translators of type 64/01 and 64/02 are
identical with the corresponding D.C. ammeters in
that they use a force (64/01) or change in length
(64/02) to indicate the magnitude of the current.
-84-
Type (64/03)₫ (1/8) Figure 106
In the design 64/03, an Electronbeam
tube is used with a circuit which energizes the motor
as soon as the peak of the A.C. current signal (11)
deflects the electron beam to control the motor. The
arrangement is such that the motor has a tendency to
run in one direction and the displacement of the beam
reverses that direction. As the motor is comparatively
slow, it acts as a mechanical filter and produces a
D.C. current (± 2) which is of such magnitude that
it is equal to the maximum amplitude of the applied
current (1). Thus the position of the rheostat (8)
is an indication of the A.C. current (1)
Type (64/04), (64/05) a (1/8) a Figure 107
In the two designs shown in Figure 107,
the relay is of the hydraulic type. In the lefthand
diagram (64/04), we have a force balance system,
while in the righthand diagram (64/05), we have a
stroke compensated system.
Type 65 (e/s) Voltage (D.C.)/Stroke Translator
This translator is a voltage indicator
and can be derived from the current indicator as
there is a definite relationship between voltage
J
-85-
and current if a resistor is being used as an addi-
tional translator in the chain. Most of the instru-
However,
ments are, therefore, of the ammeter type.
for static voltages where there is no current flowing,
additional instruments are available.
Type (65/01)
C
b
(e/S) a
-
· b
In Figure 108 various types of static
(e/s) translators are shown which are all based on
the fact that two charged plates have a tendency to
repel each other. The diagrams are typical of those
published in books on physics and call for no further
explanation.
Type (65/02)。 – a (e/s) c
-
Figure 108
d
Figure 109
The instrument shown in Figure 109 is
basically an ammeter in which the ratio of 12/11
is made small.
Type (65/03) a (g/s) Figure 110
d
d
In Figure 110 an Electronbeam tube is
shown in which a balance is obtained between applied
deflecting voltage (e) and a magnetic field produced
by a current (1) which is counteracting the electro-
static field. The current (1) is measured with an
ammeter and (3) is proportional to the current.
This
-86-
design has the advantage that it is a feedback cir-
cuit and, therefore, independent of tube character-
istic, and permits the use of ordinary ammeters for
measuring charges without using any current.
Type (65/04) a (g/s) Figure 111
a
A variation of the design in Figure 110
is shown in Figure 111 in which the counteracting
magnetic field is produced by a motor which controls
a rheostat (S3). One can consider this device as a
static voltmeter with unlimited power amplification,
but also as a remote positioning device. The
sequence of translations is given in Figure 111 and
is self-explanatory.
Type 100 (e/s) Voltage (A.C.)/Stroke Translator
What has been said about the 1/S instru-
ment is also true for the e/S instrument, which is
known as the "A.C. voltmeter". Any effect which is
independent of the direction of the current can be
used as well for A.C. as for D.C. Most of the
designs are based on a fixed translation of voltage
into current and hereby reduces the problem to an
ammeter problem.
Type (100/01)
Figure 112
Figure 112 shows an A.C. voltmeter which
is basically an A.C. ammeter in which the magnetic
a
b (e/s)
a
-87-
field produced by the A.C. current is balanced
against a spring. The motion of the iron core is
then a measure of the A.C. voltage applied.
Type (100/02) (e/s) Figure 113
a
a
The same type of instrument is shown in
Figure 113 with the modification that a coil is used
instead of the iron core. Again, its position is an
indication of the current and thus of the A.C. voltage.
a
Type (100/03) (e/8) Figure 114
a
In Figure 114 the A.C. voltage is first
converted into an A.C. current, and then into a D.C.
current by means of a rectifier, and hereby the pro-
blem reduced to that of an (1/8) translator.
Type 101 (T/S) Temperature/Stroke Translators
Instruments in this group are known as
temperature indicators and recorders (see reference 33).
Type (101/01) (T/S) Figure 115
Figure 115 shows typical thermometer designs
which are based on the difference of expansion of two
different materials. These designs do not call for
b
any additional explanation.
Type (101/02) a
-
b
b (T/s)
Figure 116
a - b
An instrument which has found more and
more application, especially for control purposes,
-88-
is a variation of the thermometer shown in Figure 115
and known under the name "bi-metal". The difference
of expansion of two materials which are soldered or
brazed produce warping, and this change in shape is
used as an indication for the temperature by which
it is produced.
Type (101/03) (T/S) Figure 117
a
8
In Figure 117 advantage is taken of the
\
fact that the vapor tension is a definite function
of the temperature. This vapor tension which is
pressure is then translated into a movement by a
pressure stroke translator so that we have the chain:
(T/P) + (P/F) + (F/S)
(T/S)
Type (101/04) (1/8)
с
с
Figure 118
In Figure 118 a power amplifier is added
to the design shown in Figure 117, making it possible
to operate a heavy mechanism. This is a typical design
of a temperature control with proportional band.
definite movement (8) is produced for every given tem-
perature and this movement (5) can be used for control-
ling the flow of the fluid which affects the temperature.
Type (101/05) (T/S) Figure 119
с
A great number of temperature indicating
and recording instruments are based on the fact that
-89-
most conductors change their resistance as a function
of temperature. In Figure 119 a typical Wheatstone
bridge is shown which is to be of the self-balancing
type. If R₁ changes due to temperature, the mechanism
automatically changes the ratio (R₂/R) by operating a
slide wire until the ratio (R/R₂) is equal to (R₂/R
The position (S) of the contact on the slide wire is
then an indication of the temperature. Thus, the
mechanism functions as a (T/S) translator.
Type (101/06) a (T/S) a Figure 120
For higher temperature ranges, 800-3200° F.,
radiation pyrometers are used which collect heat rays
emanating from the body whose temperature is to be
measured, and concentrate them on a thermocouple which
heats up to a temperature which is a function of the
collected energy. The thermocouple, in turn, produces
a voltage and a current, and this is finally measured
by an ammeter. The translation chain, therefore,
follows the equation:
(T/heat radiation) + (heat radiation/T) + (T/e)
(e/1) + (1/S) == (T/S)
Type 144 (Q/S)
(Q/S) Light Intensity/Stroke Translators
This device measures light intensity.
many applications it would be necessary to subdivide
this translating group into sub-headings, covering
different wave lengths.
For
1
-90-
Type (144/01)
a
(Q/8),
a C
с
Figure 121
In this figure, we have a dry type photo-
electric cell which changes its resistance as a
function of the illumination. The diagram in the
left-hand corner shows the output in current as
function of foot candles (see reference 34).
Type (144/02) (Q/S) Figure 122
с
In Figure 122 typical photo-electric cell
circuits are shown. Again the resistance changes as
a function of the illumination. The one circuit
shows the photo-electric cell directly in the tube
circuit, while the second one adds an amplifier.
conversion follows the pattern:
(Q/R) + (R/1) * (1/8) = (9/8)
Type (144/03) (Q/8) Figure 123
с
The
In Figure 123 a translator is shown which
adds power to produce (S). A source of light emits
This
rays which are caught by photo-electric cell.
photo-electric cell feeds into an amplifier and control
circuit which controls a motor and hereby an iris dia-
phragm (or two polarizing discs) in such a way that
the light intensity obtained by the photo-electric
cell remains constant. For varying light intensities
of the source, we have varying motor positions (S).
The whole mechanism, therefore, acts as a (Q/S) trans-
lator with additional power.
-91-
Type 145 (R/S) Resistance/Stroke Translators
This group comprises variable resistors,
also called rheostats. It is not necessary that such
devices have a slide wire arrangement. A displace-
ment of a short circuiting liquid like mercury also
belongs in this group.
Type (145/01) (R/S) Figure 124
b
For a constant voltage the indication
of the voltmeter or the ammeter is a function of
the resistance.
Thus, the movement of the pointer
can be directly translated into an indication of
resistance.
Type (145/02)
(R/S) Figure 125
C
For an indication of resistances, it
is particularly convenient to use a Wheatstone bridge
either of the manually operated or of the automatic
type as shown in Figure 125. Balance is obtained if
R₁ is equal to R2 times R3/R. Any unbalance results
in a voltage between the two points A and B which
produces a speed of a mechanism (motor) which in
turn is integrated over time and produces a slide
wire adjustment (S). Thus, a definite value of (S)
is associated with a given resistance (R₁).
C
-92-
Type 196 (L/S) Inductance/Stroke Translators
(L/8) translators are devices which convert
change of inductance into a movement or a stroke.
a
Type (196/01)8 (L/S) Figure 126
elec.
d
One solution for an (L/S) translator is
an inductance bridge which is basically the same as
a resistance bridge, only that A.C. is being used and
that the change of inductance is produced by displace-
ment of cores in inductance coils or by means of
saturable reactors. In this device it has to be
considered that the bridge must be resistance balanced
as well as inductance balanced.
Type (196/02) (L/S) Figure 127
In Figure 127 the inductance produces a
phase shift and the phase angle is measured by a
phase meter. Thus, the instrument can be represented
by 196 = 239 + 256.
Type 197 (C/S) Capacitance/Stroke Translators
Translators of this type are indicators
or instruments for measuring the capacitance of a
condenser.
Type (97/01) elec. (C/S) a
d
Figure 128
A simple design of an instrument of this
type is a capacitance bridge which is built similar
-93-
to the resistance and the inductance bridge (see
145/02 and type 196). The diagram is self-
explanatory.
Type (197/02) (C/B) Figure 129
In this translator the change in capaci-
tance produces a phase displacement (C/Y_translator)
to which a phase meter is added. The chain, therefore,
reads: 197 = 240 + 256.
Type 256 (7/5) Phase Angle/Stroke Translators
We have to distinguish between two phase
displacements:
a) displacement in space
b) displacement in time.
The displacement in space is treated under (8/8) trans-
lator, type 1, and we are therefore limiting ourselves
to phase displacement in time.
Type (256/01)。 (7/8) Figure 130
b
The diagram 130 shows the basic principle of
a phase meter with two fixed coils, #2 and #3, and one
movable coil, #1, with 12 = 13. The displacement of
theccoil #1 becomes equal to the phase displacement
between the currents in #2 and #3 and #1.
Type (256/02) (F/S) Figure 131
b
b
For laboratory use, it is more common to
use the screen of a cathode ray oscillograph which
B
-94-
permits the comparison of two A.C. waves. A dis-
placement (S) between the two waves is a direct
measure of the phase angle between the two voltages,
and thus represents its magnitude.
Type 257 (H/S) Magnetic Field/Stroke Translators
These translators represent devices for
measuring the strength of magnetic fields.
Type (257/01) (H/S). Figure 132
Typical representatives of these designs
are ammeters in which a coil or a conductor will
take a position which is a function of the magnitude
of the field which is produced by a current.
C
Type (257/02) (R/S) Figure 133
C
C
The translator shown in Figure 133 uses
an Electronbeam tube and converts the strength of a
magnetic field into a counteracting current which in
turn produces a field of the same magnitude. The
current, and thereby the indication of the ammeter (8)
is then a definite measure of the strength of the
magnetic field.
Type 324 (E/S)
Electrostatic Field/Stroke Translators
These devices are indicators or meters for
the strength of an electrostatic field.
-95-
Type (324/01)₫ (E/B)₫ Figure 134
This type shows an Electronbeam tube for
measurement of electrostatic fields. In this parti-
cular case, the field is inside of the tube.
This,
however, is not a necessary limitation for using this
device. The electrostatic field deflects the electron
bean and produces a current which produces a magnetic
field of a sufficient magnitude to counteract the
electrostatic field. For simplicity's sake, the
electrostatic field and the electromagnetic field are
shown to be in the same plane. Actually, they are of
course, displaced by 90° in space.
Type 325 (f/8) Frequency/Stroke Translators
Devices in this class are used for measur-
ing the frequency or number of mechanical oscillations
or number of revolutions per time unit. As such they
are related to speed indicating devices (see trans-
lator type 16).
(1/5) a
Figure 135
Type (325/01)
For measurement of the frequency of vibra-
tions, it is customary to use tuned leaf springs,
"Frahm meter". A number of such leaf springs are
mounted in a common support and if the amplitude
of the oscillations of a particular spring is a
maximum, its frequency coincides with the impressed
a
-96-
frequency. The device can thus be used for deter-
mining the frequency of oscillations.
A variation
of this instrument uses a leaf spring with a variable
length and by adjusting the length (S), one can observe
a maximum amplitude for a definite length of the spring.
This length corresponds to a definite frequency.
Type (325/02) (f/s) Figure 136
b
In this instrument the speed of a motor
and therefore its frequency, 1.e., the number of
rotations of its shaft per time unit, are measured
by adding a generator to the motor and by measuring
the current output of this generator with an ammeter.
The translator chain, therefore, follows the following
sequence:
The frequency is converted into a speed,
the speed into a current (A.C. or D.C.), and the
current again into the movement of a pointer; the
whole chain therefore represents an (f/8) translator.
Type (325/03) (1/8) Figures 137a & 137b
Figures 137 show the field of frequency
meters as presented by Dr. R. Fehr of General
Electric Company (see reference 36). These diagrams
show the range of available mechanical and electrical
frequency meters, giving displacement acceleration,
frequency and velocity in inches per second in one
5
-97-
diagram, together with the ranges which are covered
by each type of design.
Type (325/04) (f/8) Figure 138
For the indication of radio frequencies
with varying amplitudes, one of the solutions is
indicated in Figure 138 which uses the following steps.
a) It converts the varying amplitudes into constant
amplitudes.
b) It clips the amplitudes as shown in the diagram.
c) It differentiates the output by means of an
с
inductance coil.
After rectifying the output, a D.C. current is obtained
which is a function of the frequency (f). This current
can then be measured by means of an ammeter, and thus
give a stroke (S) as a function of the frequency (f).
Type (325/05) (f/s) Figure 139
с
The instrument shown in Figure 139, which
can be used for light as well as for radio frequencies,
establishes the frequency band of a radiation. The
position of each line in this frequency band gives an
indication of the contributing frequency. Applied to
radio, such an instrument shows on a cathode ray screen
the frequencies which are broadcast simultaneously.
-98-
(B) STROKE/VARIABLE TRANSLATORS
In addition to the indicating type trans-
lators (A), Figure 51, we have to discuss translators
which we shall broadly call "regulators" or "controls"
(B); that is, devices which for a given setting produce
a magnitude of a desired variable. A glance at the
translator map shows that these devices are covered
by a horizontal starting with 1 and ending with 361.
As the translator, type 1, has been covered already
under (A), we will start with type 2; that is, an S/P
translator.
•
Type 2 (S/P)
(S/P) Stroke/Pressure Translators
This type of translator is usually most
common in the form of a pressure regulator; that is,
a device which for a given setting (S) maintains a
constant pressure (P). Included in the group covering
such devices should be any type pressure regulator
regardless of the range of pressures which are main-
tained for one setting (droop).
Type (2/01) (S/P), Figure 140
a
a
The three examples given in Figure 140 show
three basic simple (S/P) translators.
In I, advantage is taken of the gas law
which establishes for isothermic compression a rela-
tion between stroke (S) and the pressure (P). A
-99-
device of this type is sometimes used in connection
with dewpoint meters and for transmission of valve
positions for the purpose of stabilizing of regulators.
In II, the specific pressure is produced
by a compression of the spring which means that we
have, in addition, a translation from (5) into a
force (F), and from a force into a specific
pressure (P).
In III, the pressure (P) is produced by a
displacement of a liquid in a container.
Type (2/02)
Figure 141
In Figure 141, the two basic related
devices, with which we are already familiar, are
shown in diagrams I and II. In I, an Askania jet
pipe is displaced relative to a receiving nozzle
and the pressure becomes a function of its displace-
ment (). The characteristic is linear. Typical
to 1/8 of an inch;
ranges are: displacement (S), 100
and pressure (P), 0 to 500 pounds per square inch.
a
C
(S/P) a
с
-
с
In II, the amplifier shown is of the
double throttle type which is used in most air
operated instruments. Again, a relation is established
-100-
between pressure and stroke. As no feedback is
being used, the relationship is of the class a. c.
Type (2/03) a (S/P) a Figure 142
In the two designs shown in this Figure,
the volume of fluid handled is considerably greater
than in the case of Figure 141. Displacement of
the valve (S) in I, or the double valve in II,
produces a pressure change (P). This is a trans-
lator chain represented by the equation (S/w) +
(w/P) (S/P).
=
Type (2/04) c (S/P)。 Figure 143
с
Modifying the circuit of Figure 142 by
providing a feedback loop, we obtain a self-actuating
pressure regulator (Figure 143). Diagram I is a
diaphragm operated valve with a weight counteracting
the force of the pressure (P). The position of the
weight determines the controlled pressure (P).
In the example II, the self-actuating
regulator uses a spring to counteract the pressure.
An adjustment of this spring (1) or the setting of
an additional spring (2) is used for setting the
control pressure (P). As this is a proportional
band controller, there are different pressures for
different positions of the valve.
-101-
Type (2/05)d (S/P) a Figure 144
The left-hand diagram shows a typical
Askania type jet pipe pressure controller in which
for any given setting of the spring (S) the pressure
(P) in the line is maintained constant. In this
particular case, the auxiliary power is fluid (oil),
which is supplied to the jet pipe at 50 120 lbs/sq.
in. pressure.
Type (2/06) (S/P)d Figure 145
a
Translators which are shown in Figure 145
use the relays of Figure 141, and produce a pressure
(P) which is proportional to the compression of a
spring. Such systems are called: "force balance
systems" because equilibrium is established between
two forces. In this case, the force of the spring
acts against the force of the diaphragm.
In Figure I the jet pipe is deflected by
the change of spring tension (S) until the pressure
in the receiving nozzle produces a force on the
diaphragm valve which balances that of the spring.
In device II, a pressure translator of
Moore Products, the spring changes the size of the
outlet nozzle (A) which is in series with the
supply nozzle (B) until a pressure builds up at
the diaphragm which balances the action of the spring
(see reference 37).
-102-
Both types of translating devices are
used very frequently as so-called "master loading
systems".
Type (2/07)a (S/P)a Figure 146
The same translator shown in Figure 145
is shown again in Figure 146; however, a counter-
lever (A) and an adjustable spacer (B) is provided
in addition to a spring (C). By means of adjusting
S1, S2, and S3, the relationship between pressure
(P) and stroke (S1) can be varied as indicated on
the right-hand diagram.
Type (2/08) (S/P) a Figure 147
In the example Figure 147, we have a "stroke
compensated relay". The setting signal is S₁ which
produces a displacement of the pilot S3. This, in
turn, changes the pressure (P) which produces a
force (F) which finally reduces the displacement
S3 by means of a summarizing device (wiffle tree)
until balance is restored (compare with Figure 145).
Type (2/09) c (S/P) c Figure 148
с
In Figure 148, a diagrammatic sketch of
a vapor pressure system is shown. A change of the
resistance which is produced by the movement of the
slider (S₁) results in a flow of current (1)
-103-
which in turn produces a temperature (T). This
finally changes the pressure in the bulb system (B).
This device is used instead of a motor
for operation of dampers in domestic temperature
controls. The temperature usually controls the
variable S1. The relationship of stroke and
pressure is not directly proportional, As
auxiliary power is being used, the device follows
in class c.
Type 9 (S/F) Stroke/Force Translator
This is one of the most universally used
translators, the simplest form of which is a spring.
Type (9/01)a - b (S/F) a b Figure 149
-
Three simple representatives of this type
of translator are shown. In (A) the displacement
(S) changes the buoyancy of a body and hereby
produces a force (F). In most cases the action
is reversed; that is, the float is displaced and
produces a buoyancy force.
In diagram (B), a symbol of a simple
spring is shown of which there are a great number
of variations; that is: helical springs, leaf
springs, and torsional springs, to mention only
the most outstanding examples.
-104-
In its broadest sense, any mechanism
which is elastic can be considered as such a
translator. As it changes its shape, it produces
a counteracting force which is proportional to
the displacement of the point of attack.
this force may not always be directly proportional,
the translator is either of the type 9a or 9b.
In the diagram (C), a displacement of a
weight on a double lever changes the force which
the lever exerts. Again, there are a great number
of variations of this scheme.
Type (9/02)
C d
-
(S/F) c
с d
<
Figure 150
In Figure 150, the intermediate para-
meters F and P are used. The displacement of the
spring operates an "Askania jet relay" and produces
a proportional pressure (P) which results in a
counteracting force (F). This force is of the
same magnitude and opposite to the spring force.
By applying the same pressure to a diaphragm or to
a bellows, as shown, proportional forces (F2) are
produced which can be applied to some other mech-
anism. This device is used in a number of
variations; in particular, with air operated
controls and so-called "master systems," it is used
for simultaneously controlling several regulators.
-105-
Type (9/03) c
(S/F) Figure 151
(S/F)
In the electric example of Figure 151,
the motion (S) produces a change in the resistance
which varies a current and hereby changes the force
exerted by a solenoid.
The effect of this transla-
tor chain is finally a S/F translation. This trans-
lator uses auxiliary power, but its output may not
be directly proportional; therefore, it belongs
into class c. In the lower diagram, a similar
system is shown which may be called an "electric
spring" as, for a given constant current, a force
is produced which is proportional to the displace-
ment of the core relative to the coil.
Type (9/04) (S/F) Figure 152
с
C
A variation of the latter scheme is shown
in Figure 152, in which two Selsyns or Synchros are
connected and ordinary in phase (in space).
A displacement of one of the Synchros by
an amount (S) produces a force in both Synchros if
the shaft of the second Synchro is prevented from
moving. This force is approximately directly pro-
portional to the displacement (S).
-106-
Type (9/05) (S/F) Figure 153
с
с
In the example shown in Figure 153, an
"Electronbeam tube" is used to produce a current
which is proportional to the displacement (S) of
a magnetic field. As the magnet in the diagram
is moved, the "Electronbeam" is displaced rela-
tive to its two target plates and the output of
current through an amplifier is varied until the
strength of the magnetic field of the coil shown
on the left-hand side balances the field produced
by the permanent magnet on the right-hand side.
P
If this current (1) is now fed into a
solenoid of the type (9/03), a force is produced
which is proportional to the displacement (S).
Type (9/06) (S/F) Figure 154
c
c
In Figure 154, Diagram (A), one of the
oldest applications of an S/F translator is shown
in the form of a rudder which in this particular
case is attached to an aircraft. The relative
displacement of the rudder to the direction of
the air current or the direction of motion of the
vehicle produces a proportional force which is
used for steering.
principle applied to a butterfly valve in a gas
In diagram B we have the same
-107-
line and find that a certain torque is produced
for a given angular motion of the butterfly.
the relation is non-linear, these devices fall
into class c.
As
Type 10 (S/v) Stroke/Speed Translators
In this group, we have translators which
control the linear or angular speed of a mechanism
as a function of a setting (S). Such devices are
used for controls of speeds of tool machinery, and
in the broadest sense, any motor control gear and
any vehicle, whose speed is controlled, belongs to
this group.
Type (10/01)c (S/v)c Figure 155
In Figure 155, the two basic pilot valves
or relays, with which we are familiar, are shown.
Both are connected to double acting pistons.
In (A) the displacement (S) of an
"Askania jet pipe" produces a speed (v) which is
approximately directly proportional to the displace-
ment of the jet pipe nozzle relative to its receiving
orifices.
In (B) the pilot valve is displaced by an
amount (S) and the speed of the cylinder is again
proportional to the displacement.
-108-
These two relays are used to a great
extent in fluid type controllers and amplifiers.
(S/v) c
с
Type (10/02)
Figure 156
In Figure 156, an application of the
"Askania jet pipe" to a speed control problem is
shown. The fluid is directly delivered through
the jet pipe into a receiving nozzle and the
differential pressure caused by a restriction in
the line to the receiving nozzle is used to produce
a differential pressure which is counteracting
the force of the spring. This force is directly
proportional to its compression (S). Thus, the
rate of flow (w) through this line is a function
of the displacement (S) and by inserting a positive
displacement meter into the pipe line, a speed of
the meter shaft (v) is obtained, which is directly
proportional to (w) and hereby proportional to (S).
This device belongs to the group c as the rela-
tionship between differential pressure and flow (w)
is a square function.
Type (10/03) (S/v)c Figure 157
с
Most commonly used for varying the speed
are "variable speed drives" which may be either:
a) mechanical
b) hydraulic
c) electrical, or of the
d) electronic type.
-109-
Such a mechanism is diagrammatically shown by a
box (a). The arrangement is usually such that
for an adjustment of a lever or crank (S), a
variation of the ratio of input to output speed
is obtained.
Thus, with constant input speed, the
output speed will vary with the adjustment of (S).
As the relationship between (8) and (v)
is not always directly proportional, the mechanism
is classified under c.
Type (10/04) c (S/v) Figure 158
In general, "prime movers" belong to the
same group as an adjustment of the "input" (energy
supply) changes the speed of the output shaft. In
the diagram, a symbol for a steam turbine is shown
with the valve in the supply line of the steam. As
the output speed is not directly proportional to
the stroke of the steam valve, the device belongs
to the class 10c.
Type (10/05) (S/v) Figure 159
с
с
In order to obtain a definite relationship
between the adjustment (S) and the output speed, the
prime mover of Figure 158 is equipped with a speed
-110-
governor in Figure 159. The centrifugal force of
the speed governor is balanced against the spring
force and thus the adjustment of the spring deter-
mines the output speed. Although the relationship
between stroke and speed is a definite one due to
the feedback loop, the device still belongs into
the class c, as the centrifugal force changes with
the square of the speed and therefore, the relation-
ship between stroke and speed is not a linear one.
Type (10/06) (S/v) Figure 160
с
C
A similar speed control to the one shown
in Figure 159 is given in Figure 160. Instead of
using a hydraulic relay, an "Electronbeam" tube
is used, in which the displacement of magnet (S)
unbalances the potential on the target plates
which in turn, through suitable amplifiers, control
the speed of the motor. Its speed is measured by
the output of the generator which produces a counter-
acting magnetic field. Its magnitude is proportional
to the motor speed.
If a balance between the two magnetic
fields is established, the motor speed is a
definite function of displacement (S). In the
1
-111-
actual design of this type, additional anti-
hunting circuits have to be added to prevent
instability. For the purpose of these illus-
trations, they have been eliminated.
Type (10/07) c (S/v) Figure 161
The motor control circuit, Figure 161,
corresponds to the prime mover control, Figure 158,
with the exception that the energy supply is, in
this case, a source of D.C. and the rheostat
replaces the valve. The "prime mover" is a D.C.
motor instead of a turbine.
Type (10/08)₫ (S/v)d Figure 162
Sometimes it is necessary to follow a
definite program of speed vs. time. It may appear
as a simple solution to provide a speed control
which is set as a function of time. A typical
practical example of such a problem is the open-
ing of a bridge across a river, which should be
done with a definite program of speed vs. time.
There is, however, a simpler solution
if one remembers that if a stroke (S) is produced as
a function of time, its derivative (d) is also
a function of time. The problem is, therefore,
-112-
reduced to one of S/time, and in its simplest form,
such a mechanism is a can operated by a constant
speed motor. The contour of the cam establishes
the relationship between (S) and time, and therefore,
also the speed (ds) as a function of time.
Type 25 (8/a) Stroke/Acceleration Translators
By definition the acceleration is the
first derivative of the speed (♥) and the second
derivative of stroke (S). This makes it possible
to obtain acceleration as a function of time if
either speed or position are given as a function
of time.
By necessity acceleration cannot be
made constant for infinite lengths of time as the
integral of acceleration or the integral over
the resulting speed would finally become infinite.
For this reason, the output of translators for
acceleration must be limited in their effect in
time.
Type (25/01)a (S/a)d Figure 163
The device as shown is basically a
centrifuge in which the centrifugal acceleration
is changed by changing (R) rather than by
changing W. An adjustment of (K) over pulleys
increases or changes the acceleration (a) and
-113-
thus establishes a relationship between (S) and
acceleration. Note that there seems to be con-
tradiction with the general remarks. The reason
why it is possible in this particular case to have
a continuous acceleration is that there is actually
no motion as the result of this acceleration. The
acceleration is translated by means of an additional
translator (a), mass (m) into a force. This foree
is F = ma.
G
Type (25/02) c (S/a)c Figure 164
Analysis of Figure 163 indicates that the
acceleration is produced by a field. Any field
which produces forces can serve the same purpose.
In Figure 164, this force is used in a
triode or in a cathode ray tube to accelerate
electrons. The forces of acceleration are produced
by electrostatic fields.
Type 26 (S/w)
Stroke/Hate of Flow Translators
This class covers any device which
controls (w), the rate of flow of materials; such
material may be a gas, a liquid, or a solid. The
dimension of (w), therefore, is rate of weight or
mass over time.
-114-
Type (26/01) a (S/w) a Figure 165
In Figure 165 three types of "valves"
are shown. (A) is a symbol for a manually operated
valve which establishes the relationship between
the opening of the valve and the rate of flow
through it, depending on the pressure drop, the
viscosity, the temperature, and the valve design.
Various manufacturers give curves for the relation-
ship between the lift (S) and the rate of flow (w).
In the jet pipe shown in (B), a very small dis-
placement is sufficient to change (w) from maximum
to zero. We note that in this design a liquid jet
is caught by a receiving nozzle. The volumetric
efficiency of such a design is at maximum, about
92% at 100 pounds pressure using light lubricating
oil as a liquid.
In (C) a pilot valve is shown which for
even smaller displacements of (S) produces a
change of flow from zero to maximum (w)
Type (26/02) a b (S/w) a b Figure 166
A definite relationship between the
stroke (S) and the rate of flow (w) is established
under the assumption of constant temperature and
viscosity if the pressure drop across the valve
This is accomplished in
is maintained constant.
··
-115-
Depend-
Figure 166 by means of a constant overflow head
for the valve whose lift (S) is adjusted.
ing on the valve shape, a definite stroke (S)
produces a definite rate of flow (w).
Type (26/03) (S/W) Figure 167
с
The same principle which was shown in
Figure 166 is varied in the design of the units
shown in Figure 167. In (A) the differential
pressure across the valve is maintained by means
of a constant differential pressure regulator
which belongs into the (S/P) translator class; that
is, into class 2.
If close control of the flow has to be
accomplished and the drop introduced by the regu-
lator in (A) is not permissible, a solution is
used as shown in (B). A differential pressure
regulator maintains a constant differential pressure
and as only. the speed of the controlling valve is
proportional to the error, there is no relationship
between the control valve position and the error.
A definite rate of flow (w) will be thus obtained
for every adjustment of (S1) or incidentally, also
for any setting of the regulator (S₂).
Type (26/04) c - d (S/w)c - a Figure 168
d
-
In Figure 168 the size of the restriction
-116-
is maintained constant and the adjustment is pro-
duced by a change of the setting of the differential
pressure.
The design has the advantage that it is
relatively easy to produce any uesired relationship
between (S) and the flow (w). It has, however, the
disadvantage that at lower rates of flow the accuracy
suffers as the differential pressure across the
restriction usually changes with the second power
of the flow which means that at low rate of flows
the value of the flow signal becomes relatively small.
This is avoided in the design, Figure 167 (B), by
maintaining the signal constant and changing the
size of the valve (see reference 25).
Type (26/05)c
(S/W) 0 - α
· d
As an example of a more involved trans-
lator chain, an electronic control of flow is shown
in Figure 169. It consists of two basic units (A)
and (b). In (A) a translation is accomplished of
the flow signal into a d.c. current which is
proportional to the rate of flow. In (B) this
current is maintained constant by means of a
constant current control.
Figure 169
S
The adjustment of the constant current
control is accomplished by the motion (S); that is,
the adjustment of the rheostat.
-117-
The diaphragm (1) responds to the differ-
ential pressure which is produced by an orifice.
orifice, a translator of (w) into (P), therefore
belongs into class 35. The differential pressure is
translated into a force by means of a diaphragm which
is a translator of class 8. The displacement of a
mechanical lever arrangement in (A) changes the posi-
tion of the magnet which, acting on a beam tube,
produces through an amplifier a current (1) which in
turn creates a force counteracting the diaphragm (1).
This force is proportional to the square of the
current as the two solenoid coils are used in series.
This is a typical modification of a Kelvin balance
(see reference 11). When balance is established,
the current (1) is proportional to the flow as the
force on the diaphragm (1), as well as on the coil
(4), change with the square of the flow and current
respectively.
The
The current control (B) is of the beam
tube type and controls a motor and through this
motor a suitable control valve. Thus again, a
definite balance is established between (B) and (w).
Basically, the design is the same as that
of Figure 168 with the exception that the pure
mechanical translators are replaced by electric ones.
}
-118-
The complication is due to the fact that mechanical
variables have to be translated into electric or
electromagnetic variables and finally these vari-
ables must be retranslated again into a mechanical
motion of the control valve.
Type 49 (S/1) Stroke/Current (E.C.) Translators
adjusting or control devices.
This class covers direct current and
Type (49/01) a (S/1) Figure 170
a
The simplest solution is a variable
resistor as shown in Figure 170. It is assumed
that the voltage which is applied remains constant
and if the specific resistance does not change due
to temperature or due to other variables which
might effect it, the current which is obtained as
a function of (S) follows Ohms law. The right-hand
diagram shows a liquid type resistor. Any adjustable
resistor, therefore, is a translator of (8/1).
There can be some argument whether or
not this translator belongs into the class a b
d, as it could be argued that in order to
produce the current, an aduitional source of power
is necessary. However, as long as no additional
relays are being used, we prefer to classify these
translators under a or b.
or c
-
ܝ
.
92%
-119-
Type (49/02)
C
(5/1) Figure 171
с
The translator shown in (49/02) is based
on the observation that in a triode the current
from the cathode to the anode varies as a function
of the distance between the grid and the anode. In
the tube shown, it is possible to change this dis-
A flexible bellows made out of
tance mechanically.
glass or metal is used to seal the tube against the
outside.
Tubes of this type have been used for
electronic gauges. The relationship between stroke
and current is not directly proportional.
Type (49/03) (S/1) Figure 172
с
C
A mechanical solution is shown in Figure
172.
The first step in this solution is the use
of a translator from (S) into a force with a hydraulic
amplifier. A carbon pile is used as a variable
resistor. The resistance changes as a function of
the applied forces. As a result, the resistance
changes as a function of the adjustment (S). The
feedback would be used to counteract the forces
(F₁) instead of the feedback using the force (F2)
which represents displacement. A definite relation-
ship between (S) and the current could be established.
-120-
Type (49/04) (S/1) Figure 173
C
с
In Figure 173 an electron beam tube is
being used for the translation of stroke into
current (see reference 12). The magnetic field
produced by the displacement of a magnet (S) or by
a resistor and source of current deflects the
electronbeam relative to its two targets until the
output of the amplifier which is connected to the
target plates produces a current which exactly
balances the effect of the field produced by (A)
or (B). Thus, a definite relationship between (S)
and the current is established.
Type (49/05) c-d (S/1) c-d Figure 174
The (S/1) translators (4) and (Þ) which
are shown in Figure 174 are also called bolometers
(see reference 38). The principle on which they
are based is that if two resistances R and R₂ in
a Wheatstone bridge are of the same temperature,
2
the bridge is balanced.
Ra
If the temperature ratio
and thus R₁ and R₂ is changed by cooling or heating,
an unbalance of the bridge is established which is
an indication of the temperature ratio.
In the design (A), a jet pipe is used
and air blown through both receiving orifices either
at the same rate or at different rates. If the
-121-
C
rate is the same, the temperatures of R and R₂ are
If the
equal and the output of the bridge is zero.
jet pipe is deflected to the left, for instance, and
a cooling medium is supplied through the jet pipe,
the resistance (R) will be changed relative to R₂
and a corresponding output current of the bridge will
result. Thus, a relationship between (S) and the
current (1) is produced.
The same principle. is used in the design
(B), in which instead of the jet pipe two slots are
being used which are more or less covered by means
of a vane whose movement is (S). The air is supplied
by means of a small leaf spring which vibrates under
the effect of an a.C. magnetic field. The small
currents of air are sufficient to produce a tempera-
ture difference between R and R₂ if the vane is
slightly displaced.
Type 50 (8/1) Stroke/Current (A.C.) Translators
Devices in this group are current adjust-
ing devices or current controls for A.C.
Type (50/01) (8/1). Figure 175
a
8
S
The simplest solution is a resistor which
changes a current as a function of (S) as shown in
Figure 175(A). The translator of (B) takes advantage
-122-
of the fact that the induction (L) of the coil can
be changed by displacement of the core inside the
coil.
Type (50/02) (S/1) Figure 176
a
a
In a similar manner as shown in Figure 175 (B),
the circuits (A) and (b) of Figure 176 permit a change
of current (i) as a change of the capacitance (A) or a
change of the resistance, capacitance, and inductance
(B). The relationship between current and resistance,
inductance, and capacitance are given in Figure 176.
Type (50/03)d (S/1)a Figure 177
An Electronbeam tube is used for controlling
an A.0. output directly proportional to displacement
(S). As the balance has to be produced by a steady
magnetic field, the diagram shows, in addition, a
rectifier which converts the output signal into D.C.
The mechanism is in balance if the magnetic field,
produced by (S) the position of the magnet, is
balanced by the magnetic field which is produced by
the (D.C.) current. The first translator behind the
tube produces a current output for every applied
voltage which is picked up from the target plates.
A second translator is a saturable reactor which for
a "input" (D.C.) current varies the "output" (A.C.)
current. The third translator is a transformer
whose purpose is to separate the output circuit
-123-
with its rectified D.C. component from the saturable
reactor as the D.C. component would otherwise pro-
duce self-saturation.
Type (50/04) (S/1) Figure 178
d
d
An electrohydraulic solution is shown in
Figure 178, a solution which has been successfully
used for arc furnace controls. A solenoid coil (A)
measures the current going through the electrode and
the force which it exerts on the hydraulic relay is
balanced by the tension of the spring (S). Balance
is obtained when the current is directly proportional
to the setting of the spring (S).
Type 81 (S/e) Stroke/D.C. Voltage Translators
Devices in this group are related to those
of (S/1) translators of type 49.
Type (81/01) (S/e) Figure 179
b
b
The most common design of this type is the
"potentiometer" shown in Figure 179. Various
voltages can be picked up from a D.C. circuit by
operating a slider by an amount (S). It is
assumed that the resistance is directly proportional
to (S).
Type (81/02) (S/e) Figure 180
с
An electronic (S/e) translator with addi-
-124-
tional amplification is the one of Figure 180.
This translator uses the potentiometer method of
(81/01) in combination with a triode to obtain a
voltage output as shown. Obviously, there are a
great number of possible circuits to accomplish
the same.
Type (81/03) (S/e) Figure 181
a
d
Without the aid of an additional source
of voltage, Figure 181 shows an electronbeam tube
in which the output voltage counteracts the effect
of the magnetic field produced by the displacement
of the magnet (S). Diagram is believed to be self-
explanatory (see reference 12).
Type (81/04) (s/e) d
d
(31/04) is a commercially available
voltage regulator, in which the resistance of a
carbon pile is changed by varying the forces
between the individual carbon plates. This is
done by balancing the tension of the spring (S)
against the force which is produced by a solenoid.
As the force of the solenoid is approximately
directly proportional to the current flowing
through it and as the force of the spring is
directly proportional to (S), the voltage obtained
from this device is directly proportional to (S).
Figure 182
-125-
Type (81/05) (S/g) Figure 183
d
d
In Figure 183, a hydraulic relay is used
to control the field of a motor generator until
the output voltage produces a force on the solenoid
sufficient to counteract the spring tension (S₁).•
In this particular case, the generator field is
controlled by a rheostat movement (S2).
Type 82 (S/e)
(S/e) Stroke/A.C. Voltage Translators
This class covers devices for changing
or controlling A.C. voltage.
Type (82/01)¸ (5/e), Figure 184
(82/01) shows an A.C. inductance bridge
whose output is varied by a change of the resist-
ance (S). The same circuit can be used with
capacitance and reactance bridges.
Type (82/02) (S/e) Figure 185
с
с
With devices shown in Figure 185, an
Electronbeam tube is used as a generator for
constant amplitude A.D. voltage of fixed or
variable frequency. For this purpose, a motor
rotates a magnet (S) and hereby changes the
magnetic field following a sinus function. As
the current which balances this field is at any
-126-
moment equal to the strength of the field of the
magnet, the output voltage which can be picked up
across the resistor is an A.C. voltage of constant
amplitude of the frequency determined by the rate
of rotation of the magnet.
Type (82/03) (S/e). Figure 186
In Figure 186, a schematic diagram of an
A.C. generator with variable field excitation is
shown. As the rheostat is used for changing the
excitation, the device performs as a (S/e) transla-
tor.
с
Type 121 (S/T) Stroke/Temperature Translators
This is an extremely broad field as it
covers all kinds of heating and cooling equipment
starting from simple valves and extending into
more complex process controls. (see reference 2, 33,
and 39)
Type (121/01), (S/T) Figure 187
a
a
The diagram represents a simple process.
in which the lift (s) of a heat supply valve
changes the temperature of the process. With such
an arrangement, there is of course no directly
proportional relationship between (S) and (T) and
therefore, this device belong into the class a.
-127-
Type (121/02) (S/T) Figure 188
d
d
In order to establish a definite relation-
ship between (5) and (T), it is necessary to produce
a feedback between the adjustment (S) and the tempera-
ture. The device shown accomplishes this by translat-
ing (S) into a force and balancing it against a force
which is the output of a translator with (T), the
temperature, as the input. The actual path of the
latter translator is (T) into pressure (P) and
pressure into force (F).
Type 122 (S/C) Stroke/Light Intensity Translators
Devices of this type are used to change
the light intensity as a function of a mechanical
adjustment. The source or light may cover any part
or various ranges of the spectrum.
Type (122/01) (S/Q) Figure 189
a
a
The diagram represents two simple devices
for changing the light intensity by changing the
parameter (5).
In (A) one of the oldest devices known to
mankind is shown; that is, a lamp which is provided
with a wick. Adjustment of the length of the wick
varies the total amount of light output of the lamp.
-128-
In (B) a modern version of a variable
source of light is schematically shown. The change
of the light intensity is produced by an adjustment
of the rheostat which changes the current going
through the filament of an electric bulb. As the
light radiation is a function of the temperature of
the filament and thus of the current going through
it, a relationship between (S) and (Q) is obtained.
(S/Q) a
Type (122/02) a
In Figure 190 the light emission remains
constant and the amount of light received is varied
by intercepting part of the radiated energy with
either (A), a polarizing filter, or (B), an iris
diaphragm. Again, (Q) becomes the function of
action of the filter or of the diaphragm, and there-
fore, of (S).
Figure 190
Type (122/03) a (S/Q) a Figure 191
d
By using a feedback circuit in Figure 191,
a definite relationship between (S) and (Q) can be
obtained. A saturable reactor is controlled by a
direct current which in turn is controlled by an
Electronbeam tube. The output of the saturable
reactor feeds into an electric bulb and the amount
of light received by the photoelectric cell produces
-129-
a voltage which is fed back into the beam tube in
opposition to the magnetic field produced by the
displacement of the magnet (M). Thus, a definite
relationship between (S) and (Q) is established.
Type 169 (S/R) Stroke/Resistance Translators
These devices cover variable resistors.
They may be either of the metallic or of the
liquid type. They are used for alternating current
as well as for direct current.
Type (169/01) (S/R) Figure 192
b
In the resistors shown in Figure 192, the
length of the effective resistor is changed by
either a slide contact (A) or by a partial immersion
of the resistor into a conductor (B). The diagrams
are believed to be self-explanatory.
Type (169/02) (S/R) Figure 193
с
с
In Figure 193 the slide wire resistor
changes the voltage which is applied to a triode.
This changes the current flowing from the cathode to
the anode and thereby the resistance of the triode.
As the resistance of the triode is defined as voltage/
current, the whole arrangement can be considered as
a device for changing (R) the triode resistance as
a function of (S).
-130-
Type (169/03) d
If the friction which has to be overcome
with the resistor is of considerable magnitude as
it is the case where greater currents have to be
handled, it is sometimes necessary to use an addi-
tional amplifier to boost the available force. In
Figure 194 a hydraulic jet pipe amplifier is used
which produces a stroke (S2) directly proportional
to (S₁) with any desired increase in force.
device follows the equation:
.(S/F) + (F/S) + (S/R) = (S/R)
(S/R) a Figure 194
d
Type 170 (S/L) Stroke/Inductance Translator
Devices falling into this class are
"variable inductances".
Type (170/01)
Figure 195
a – b
In its simplest form, such a device is
shown in Figure 195 in which the displacement of
core relative to the center of an induction coil
This device, therefore, is
changes its inductance.
an (S/L) translator.
a
(S/L)
a
Type (170/02) (S/L) Figure 196
&
C
This

In Figure 196 a saturable reactor is used
and the (D.C.) saturating current is changed by
means of an (S/R) translator. As the saturation
-131-
of the reactor varies, the inductance of the satur-
able reactor changes correspondingly.
The saturable
reactor in connection with a resistor is therefore
an (S/L) translator.
(S/C)___Stroke/Capacitance Translators
Devices falling into this class are
"variable capacitors" (see reference 22 and 34).
Type 225
Type (225/01) (S/C) Figure 197
b
Variable capacitors or condensers are
widely used in electronic and radio circuits. A
change of the capacitance is either produced by
a change of the distance between two condenser
plates (A), a relative displacement of the condenser
plates (B), or a change of the dielectric between
fixed condenser plates (C).
Type 226 (S/ Stroke/Phase Angle Translators
These devices cover not only phase dis-
placement in time but also in space.
Type (226/01) (S/Y) Figure 198
In the differential gear shown in Figure
198, we have two input shafts (1) and (2) and one
output shaft (3). If we assume that the input
is ♂ and we add a second angle,
angle of shaft (1)
b
C
-132-
(Y)
(S), we obtain a motion of the output shaft
(3) which is displaced by () relative to shaft (1).
Such a device is, therefore, a mechanical (S/Y)
translator with a phase displacement in space.
-
Type (226/02) (S/Y) Figure 199
&
a
A modification of Figure 198 is shown in
the application to steam engines where a phase dis-
placement of two sinusoidal motions are necessary
for controlling the operation of a steam engine.
As a typical example, a "Heusinger locomotive gear"
is shown. A great number of variations of this
theme are found in the literature on steam engine
gears (see reference 40).
Type (226/03) (S/Y) Figure 200
d
d
A phase displacement in space, as well
as in time, is possible with the device shown in
Figure 200. This diagram represents a mechanical
sound recording device in which steel tape passes
through a current (A) and is picked up through
coil (B) depending on the speed of the tape and
the distance of the pick-up relative to (A). Dis-
placement of the signal (variable) in time and in
space is possible. Such devices can be used for
"memory circuits". As an extreme example, a
K
-133-
musical record which reproduces sound at any
desired time or at any given place can be con-
sidered to fall into this group.
Type (226/04) (S/Y) Figure 201
A great number of applications are found
in electronic and electrical circuits in which two
A.C. vectors change their relative position in
time, or if viewed on an oscillograph, in space.
The basic circuit using inductance, capacitance,
and resistance is shown in Figure 201. It will be
noted that the phase displacement is possible by
varying either the resistance, inductance, or the
capacitance of the circuit.
Type 289 (S/H) Stroke/Magnetic Field Translators
These devices produce a magnetic field
which is a function of the displacement (S).
Type (289/01) (S/H) Figure 202
d
d
<
The simplest device of this type is an
electromagnetic coil in which the magnitude of the
magnetic field (H) is varied by means of an (S/R)
and an (R/1) translator.
Type (289/02) (S/H) Figure 203
d
To establish a definite magnitude of
(H) as a function of (S), a feedback circuit is
-134-
used. An Electronbeam tube controls the output
and hereby its ampere-turns as a function of (S).
Thus (H) becomes entirely independent of any tube
characteristic.
Stroke/Electrostatic Field Translators
(S/E) translators are devices which vary
the strength of an electrostatic field as a function
of a displacement (S).
Type 290 (S/E)
Type (290/01) (S/E) Figure 204
b
One of the fundamental tests in physics
shows that the voltage on a charged condenser
changes as a function of the distance of the con-
denser plates; therefore, (E) is a function of the
displacement (S).
(S/E)d Figure 205
Type (290/02)d (S/E) a
S
In Figure 205 an Electron beam tube is
used and an electromagnetic field (H) produced by
a displacement of a magnet (S) is balanced by an
electrostatic field (E). Actually, the magnetic
field and the electrostatic fiela acting on the
Electronbeam are displaced by 90° in space. How-
ever, for the sake of simplicity of the diagram,
they are shown in the same plane.
-
▸
.
-135-
Type 361 (s/f)
Stroke/Frequency Translators
In this class we have translators which
produce frequencies of mechanical or electrical
nature which are of a magnitude which is a function
of an adjustment (S).
Type (361/01) (s/f) Figure 206
a
In Figure 206 (A), the frequency of a
reed oscillator is varied by a change of the
effective lengths (L) which is a function of (S).
In (B) the frequency of a pendulum is varied by
changing its effective lengths.
Type (361/02) (S/f) Figure 207
ἀ
Type (361/03)
d
a
As the frequency of an electric generator
is directly proportional to the speed of its shaft
and thereby of a prime mover, any speed control,
that is, any (S/v) translator, type 10, can be used
in combination with a generator to produce a vari-
able frequency. In Figure 207, the diagram represents
a steam turbine governor, a turbine, and an A.C.
generator. An adjustment (S) of the turbine governor
establishes the frequency of the generator.
a b
-
(s/f),
å b
Figure 208
G
A variation of the same design uses a
constant prime mover speed (n) or (v₁) and produces
-136
7
a varying generator frequency by means of a vari-
able speed drive which is a type 10 (S/v) translator.
Again, a definite relationship between (S) and the
frequency is obtained.
Type (361/04) (S/f)d Figure 209
The same idea is used in the low frequency
generator which employs an Electronbeam tube, see
Figure 209. A type 10 (S/v) translator is used to
produce a change of the frequency of rotation of
a magnet (M) by an adjustment of (S). The output
of the amplifier (A) is therefore directly pro-
portional to (S) and a definite relationship is
therefore established between (S) and (f).
ů
Type (361/05) c (S/f) Figure 210
c
An extremely wide use of electrical
oscillating circuits is made in the radio art.
Tank circuits are used in oscillators whose frequency
is determined by its capacitance (C) which is a
function of (S) and (L) which is a function of (S).
Thus, by changing either (S) or (S2), the circuit
can be tuned to respond to various frequencies.
(see references 10 and 34).
2
Type (361/06) (S/f) Figure 211
In Figure 211 a diagram is shown which was
prepared by Dr. K. Fehr (see reference 36). It shows
the ranges of vibration generators available at present.
-137-
K
(C) VARIABLE/ELECTRICAL SIGNAL TRANSLATORS
On page 54 we have discussed the possi-
bility of auding to the two columns (A) and (B) of
Figure 51 additional translators, which being purely
electric, are not limited to the low frequency inher-
ent in any device which calls for acceleration and
deceleration of masses.
It appears that the whole development of
the electronic art during the last decade is largely
due to the fact that with the help of electronic
translators the designers became practically independ-
ent of inertia effects as the mass of the electron is
extremely small.
Although the proof that a solution for the
column (A) and column (B), that is for "instruments"
and "controls", is available is sufficient to show
that at least one solution is available for every
box of the translator map, we shall in audition
briefly discuss electrical solutions which are
referred to as (C) anu (D) n page 54.
We have chosen one particular electrical
variable (1) in preference to any of the possible
others, but this is an unnecessary limitation as it
is possible to convert any electrical signal into
any other signal.
S
-138-
Type 49 (S/1) Stroke/Current (D.C.) Translators
This translator has been discussed already
under 49 and therefore, the discussion does not have
to be repeated at this time.
Type 48 (P/1) Pressure/Current (D.C.) Translators
This class covers translators which con-
vert a specific pressure into a direct current. The
pressure may be gas pressure or may be a strain; that
is, a force (F) divided by an area (s²).
Type (48/01)a (P/1)a Figure 212
The diagram 212 represents a Kelvin balance
(see reference 11). The pressure (P) is supplied to
a diaphragm and hereby unbalances a scale beam which
moves a magnet (1) relative to an Electronbeam tube
(B) and also relative to a stationary magnet (M2).
As a result of this displacement, the output of the
beam tube increases a current (1) which, until it
produces a force between coils (C₁) and (C₂), is
proportional to the ampere-turns and therefore pro-
portional to the direct current. As soon as balance
is obtained, the current (1) is directly proportional
to the pressure (P). The translator, therefore,
belongs into the class 48d.
-139-
Type 47 (F/1) Force/Current (D.C.) Translators
Devices of this type are used for
measuring the strain of various materials and to
measure forces which are applied to structures and
models. One typical application is the measurement
of the forces acting onto an airplane model in a
wind tunnel.
Type (47/01)。 – d (F/1) c
Figure 213
In Figure 213 advantage is taken of the
property of piezo crystals that they respond with
voltages to a change of a force which is applied to
the crystal. An additional group of translators is
added which converts the D.C. voltage produced into
a direct current.
– a
Type (47/02) a (F/1)a Figure 214
In the hydraulic design shown in Figure
214, the force is applied to an Askania "jet" which
in turn operates a rheostat until the current con-
trolled by the rheostat in a counteracting coil
produces a force which is of the same magnitude
as the applied force. The current is again directly
proportional to the applied force. (The device is
limited to low frequencies.) Compare this design
with that of the Kelvin balance in Figure 212.
-140-
Type 46 (v/1) Speed/Current (D.C.) Translators
These devices are used as electrical
tachometers.
Type (46/01) (v/1) Figure 215
b
The tachometer shown in Figure 215 is
basically a D. C. generator whose output is propor-
tional to the speed (v); that is, the number of
revolutions per time unit of its shaft. No further
explanation appears to be necessary.
Type 45 (a/1) Acceleration/Current (D.C.) Translators
The devices belonging in this class are
electrical accelerometers with a D.C. output.
Type (45/01) (a/1) Figure 216
d
d
A
For the purpose of illustration, an
electronic tube is used in which, in a push-pull
circuit, the relative position of two common grids
(G) is changed relative to two anodes (A) and (A2).
A mass attached to the lever which carries the grids
acts as a translator of the input acceleration into
an output force. (The tube is described in U. S.
patent #2,399,420.)
The right-hand diagram shows
the basic circuit. The output of the push-pull
circuit is used to produce currents which energize
-141-
the coils (C₁) and (C₂) in such a manner that the
force which is produced by the coils counteracts
the effect of the force, F = ma.
Type 44 (w/1) Rate of Flow/Current (D.C.) Translator
This class covers flow meters with pro-
portional D.C. output.
Type (44/01) a (w/1)a Figure 217
A typical example is the so-called Thomas
meter (see reference 25). The basic circuit applies
a Wheatstone bridge and a controlling circuit for a
heater which is placed between two arms of the
resistance bridge. The heat input into this heater
is controlled in such a way that the temperature
of the medium flowing through the meter increases
by a constant amount. Under these circumstances,
the energy supply to the heater which happens to be
D.C. is directly proportional to the rate of flow
of the medium. The whole mechanism, therefore,
functions as a (w/1) translator.
Type 43 (1/1) Current (D.C.)/Current (D.C.) Translator
This class covers D.C. amplifiers. The
literature on this subject gives a great number of
various solutions (see references 10 and 34).
-142-
Type (43/01) a (1/1)a Figure 218
d
In a D. C. amplifier using an Electronbeam
tube shown in Figure 218 (see reference 12), a
magnetic field is produced by a primary current (11)
whose effect is balanced by the output current (12).
The output is directly proportional to the input.
It will be noted that the two circuits, (1) and (12),
are entirely independent of each other. The trans-
lator can be used to connect two separate D.C. cir-
cuits just as an A.C. transformer is used to connect
two A.C. circuits.
Type 58 (1/1) Current/(A.C.)/Current (D.C.) Translator
Translators of this type are known in
general as rectifiers. There is considerable
literature covering such devices (see references
10 and 34).
Type (58/01) (1/1). Figure 219
C
с
The rectifier of Figure 219 is a triode.
As a triode acts like a mechanical check valve,
it permits only the positive cycles to pass
through the tube. If a grid voltage is produced
proportional to the alternating current in a
resistor, and if this grid voltage controls the
output of the tube, only the positive half cycles
-143-
are permitted to pass through the tube (for the
proper values of the tube potentials).
In Figure 219 (a), a circuit is shown
which incorporates this basic idea, a push-pull
circuit and a filter for obtaining a more uniform
D.C. output.
Type 71 (e/1) Voltage (D.C.)/Current (D.C.) Translator
=
These are devices which for a given D.C.
voltage input produce a corresponding direct current
output. As such, they can be considered as resistors
in the broadest sense.
Type (71/01) (71/02) (71/03) (e/1) Figure 220
c c
с
a
In Figure 220 (A) the most common form
of a translator of e/i is shown which is known as
a "resistor". The Ohm's law establishes the
relationship between voltage, current, and resist-
ance (71/01).
In (71/02) the resistor is replaced by
a triode which for a varying grid voltage (e) gives
a corresponding output current (1).
In (71/03) a diode is indicated in which
the current through the tube is varied by changing
the applied anode potential.
-144-
Type (71/04) (e/1)
a
a
Figure 221
A more elaborate form of an (e/1) trans-
lator is schematically shown in Figure 221. In
this current balance, which is similar to the one
developed by Professor Eastman of the University
of Seattle, the applied voltage (e) produces a
current which in turn is translated into a force
(F). This force changes the light distribution
in a photoelectric push-pull circuit. Its output
is sent through an amplifier and produces a counter-
acting force (F2) which re-establishes the balance
of the mechanical scale beam. The result is that
2
F1 is equal to F₂ and the applied voltage is
directly proportional to the output (1).
Type 94 (e/1) Voltage (A.C.)/Current (D.C.) Translator
These devices are again rectifiers similar
to those of type 58. In this particular instance,
however, the voltage applied to the rectifier is an
A.C. voltage.
Type (94/01) (e/1) Figure 222
b
b
Figure 222 shows schematically an A.C.
rectifier which permits the current to flow only
in one direction.
C
-145-
Type 107 (T/1) Temperature/Current (D.C.) Translator
These devices are electrical devices
which produce a D.C. voltage as a function of tem-
perature. As such, they cover a very wide range
of temperatures as in resistance bridges, thermo-
couples, and radiation pyrometers.
Type (107/01) (T/1) Figure 223
b
The example chosen in Figure 223 is a
thermocouple which for a given temperature (T)
produces a D.C. voltage and hereby a direct current
which is proportional to the temperature (see refer-
ence 33).
Type 138 (0/1) Light Intensity/Current (D. C.) Translator
Devices belonging into this group are
used for measuring the intensity of light.
Type (138/01)a - b (Q/1)a - b Figure 224
A photovoltaic cell (see reference 10)
is a translator of foot candles (Q) into direct
current (1). This self-generating cell is used
to a great extent in electric exposure meters for
photography.
Type 151 (R/1) Resistance/Current (D.C.) Translator
Devices belonging into this group are
resistors in general. The relationship between
-146-
current, voltage, and resistance is given by Ohm's
law.
Type (151/01).
a
с
(R/1)a - c
с
с
Figure 225 uses two Wheatstone bridges
(A) and (B) whose current output is a function of
the resistance of one of its branches. This resist-
ance may be changed mechanically as in (A) or electri-
cally as in (B), by substituting a triode tube for
one of the resistances. The device acts as a trans-
lator of resistance (R) into direct current (1).
с
Figure 225
Type 190 (L/1) Inductance/Current (D.C.) Translator
A great number of circuits are available
to change an inductance (L) into a corresponding
direct current (1). (see references 10 and 34)
Type (190/01) (L/1) Figure 226
C
A basic solution is given in Figure 226.
The basic approach is to produce voltage which is
a function of the inductance and to apply this
voltage to a triode tube which is used as a rectifier.
Thus, the cutput current (1) will vary as a function
of the inductance (L).
Type 203 (C/1) Capacitance/Current (D.C.) Translator
Devices belonging into this group have a
direct current output which is a function of the
-147-
capacitance of the system. By necessity most of
these devices are A.C. operated and call for a
combination with a rectifier to produce a direct
current.
Type (203/01) (C/1) Figure 227
с
с
In the example of Figure 227, the same
approach is chosen as in the example 190/01. An
A.C. voltage is produced across a grid triode and
the triode is used as a rectifier. The output
current (1) is then a function of the capacitance
(c).
*
Type 250 (7/1) Phase Angle/Current (D.C.) Translator
One of the most widely used devices in
control circuits is based on changes of phase angle
with a resulting control of a current (see references
10 and 34).
Type (250/01) (1/1) Figure 228
с
с
A very common application of a device
which responds with a direct current to a phase
shift in time is a thyratron. Depending upon the
amount of phase shift, the thyratron tube fires at
different points of the A.C. cycle (1, 2, 3, 4) as
shown. Many variations of this scheme are available
as described in the literature.
-148-
Type 263 (H/1) Magnetic Field/Current (D.C.) Translator
These devices respond to the strength of
a magnetic field (H) with a direct current output
(1). They cover ranges of magnetic fields from
the strength of the earth magnetic field to the
field which surrounds high ampere bus bars or
powerful magnets.
Type (263/01)₫ (H/1)d Figure 229
A simple solution for a translator of
this type is shown in the Electronbeam tube (refer-
ence 12) which permits a direct translation of (H)
into direct current (1). The diagram is believed
to be self-explanatory.
Type 318 (E/1) Electrostatic Field/Current (D. C.) Translator
Devices of this type translate the magni-
tude of an electrostatic field (E) into a proportional
direct current. Triodes fall into this class, as
the field produced by the grid controls the output
(D.C.) current.
Type (318/01) (E/1) Figure 230
In the example shown in Figure 230 an
Electronbeam tube (see reference 12) is used in
which the deflecting effect of the electrostatic
-149-
field is counteracted by the deflecting effect of
a magnetic field. For this reason, a definite
relationship between the applied electrostatic
field and the D.C. output is established.
Type 331 (f/1) Frequency/Current (D.C.) Translator
These devices measure frequencies by a
corresponding D. C. output.
(f/1)c - d
As the voltage output of an oscillating
circuit depends on the ratio of its own frequency
to the impressed frequency as shown in Figure 231,
it is possible to obtain a direct current by first
translating the A.C. voltage into an alternating
current and then by adding a rectifier. Thus, a
translator for frequency into direct current is
obtained.
Type (331/01) - a
с
Figure 231 & 232
Figure 232 gives the relationship between
the voltage and the frequency for the case of an
inductance as well as of a capacitance across which
the A.C. voltage is obtained.
-150-
(D) ELECTRICAL SIGNAL/VARIABLE TRANSLATORS
As pointed out on page 54, I am going to
discuss an additional column which gives a translation
of direct current into a variable. One can consider
such translators as "regulating" or "controlling." devices
in which the "setting" of the controller is determined
by a direct current signal. As a direct current (1)
can always be translated into any other electrical
variable, as I have shown in the column starting at
the top with box (49) and ending with box (331), the
choice of D.C. (1) as "input" signal is in no way
limiting this analysis.
We have already discussed box (37), that is,
a current indicator or an (1/5) translator. We,
therefore, do not have to repeat an analysis of this
translator.
Type 38 (1/P) Current (D.C.)/Pressure Translator
Translators of this type convert currents
into pressure or into forces divided by an area.
Pneumatic ammeters, for instance, fall into this
group and also controlling potentiometers whose out-
put control pressure is a function of (1).
Type (38/01) a (1/P) a Figure 233
The device shown in Figure 233 produces
a pressure which is proportional to the applied
·
-151-
current. A simple device of this type was developed
for thermocouple inputs about 15 years ago.
It can
be considered as a "pneumatic galvanometer". A direct
current which flows through a coil (A) produces a
magnetic field which moves an air operated jet pipe
until the pressure in the receiving nozzle acting
onto a diaphragm (B) counteracts the force produced
by the current.
Type 39 (1/F) Current (D.C.)/Force Translator
The purpose of such translators is to
convert a current into a force. Solenoids, for
instance, belong into this class and most of the
devices which are used for measuring currents, that
is, galvanometers, ammeters, etc.
Type (39/01) (1/F) Figure 234
b
b
Most of the current/force translators are
based on the fact that two conductor coils, through
which two currents (11) and (2) flow, attract each
other with a force which is proportional to the
products of the ampere turns divided by the square
of the distance of the two coils.
Type 40 (1/v) Current (D.C.)/Speed Translator
Devices of this kind are speed controls
in which the setting signal is a current.
-152-
Type (40/01) (1/v) a Figure 235
In the device shown in Figure 235, an
Electronbeam tube (see reference 12) is being used
to control the speed of an electric motor. Its
number of revolutions per time unit are measured by
means of a D.C. generator whose output is counter-
acting the D.C. signal (1). In this way a direct
proportionality is accomplished between the signal
(1) and the output of the D.C. generator, and there-
fore, of the speed of the motor.
d
Type 41 (1/a) Current (D.C.)/Acceleration Translator
Devices in this class respond to a direct
current signal and produce an acceleration which is
directly proportional to the current input.
Type (41/01) (1/a) Figure 236
In Figure 236 the current (1) is used to
produce a force which is proportional to the current
and a mass (m) is added as an additional translator
for force (F) into acceleration (a).
Type 42 (1/w) Current (D.C.)/Rate of Flow Translator
Devices of this type can be considered as
flow controllers with an electrical D:C. signal for
determining the setting of the flow controller.
-153-
Type (42/01)
с
· d
(1/w) c = a
- d
Figure 237
The example shown uses a jet pipe flow
controller. A solenoid which is energized by a
direct current (1) produces a force (F1) from the right-
hand side which is balanced by the force (F2) from
the left-hand side. This force (F2) is the output
of a (w/P) translator; that is, in a simple form
from an orifice. The device responds only to re-
latively low frequencies. This is due to the fact
that (w) representing mass units or weight units per
time unit introduces by necessity inertia.
Type 44 (1/1)
(1/1) Current (D.C.)/Current (D.C.) Translator
We have already discussed an 1/1 translator
in connection with devices which have the variable (1)
as input and the direct current (1) as output. The
same devices can of course be used for the direct
current as input and the variable (1) as output (see
also Figure 218).
Type 56 (1/1) Current (D.C.)/Current (A.C.) Translator
Devices of this type convert direct current
(1) into alternating current (1). They are, therefore,
the opposite of rectifiers and some of their embodi-
ments are called "inverters". A D.C. motor which
drives an A.C. generator is a device of this type.
-154-
Type (56/01)
(1/1) a − b Figure 238
a - b -
A device which has gained more and more
in importance during the last few years is diagram-
matically shown in Figure 238. It is known as a
"saturable reactor" and its operation is based on
the fact that the impedance of a coil changes with
the amount of saturation of the iron core around
which the coil is wound.
Type 75 (1/e) Current (D.C.)/Voltage (D.C.) Translator
The simplest devices belonging into this
class are resistors which establish a voltage drop
for a given current. Also into this group belong
D.C. voltage generators whose voltage (e) output is
a function of the field current (1).
Type (75/01)a (1/e) Figure 239
An Electronbeam tube is used in Figure 239
with a current (1) as the primary signal and the
voltage (e) as the feedback. The operation of the
tube is described in reference 12.
Type 88 (1/e) Current (D.C.)/Voltage (A.C.) Translator
This device is related to the translators
discussed in box (56) as by the use of an additional
1/e translator (type 89) a translation into A.C.
voltage (e) can be accomplished.
-155-
Type (88/51)a (1/e) Figure 240
d
In the example shown a translator chain
is used starting with an Electronbeam tube and add-
ing an amplifier translator of type (71), a saturable
reactor of type (56), and a rectifier of type (58). The
output of the rectifier (12) balances the primary
signal (1). Ahead of the translator of type (58),
the current is branched off and a part of it goes into
a translator (1/e), type (89) which in its simplest
form could be a resistor. It is to be noted that the
feedback (12) is not the output of the chain but this
is permissible as it is assumed that direct proportion-
ality (class b) is the performance characteristic of
the rectifier (type 58).
Type 115 (1/T) Current (D.C.)/Temperature Translator
Translators of this type are temperature
controllers whose setting is uetermined by a direct
current (1).
Type (115/01) a (1/T) Figure 241
As an example, we have in 115/01 a beam
tube with a primary signal (i). The output of the
tube controls an amplifier and hereby a heater coil
which in turn controls the temperature. An auditional
translator (T/e) of the type 109 is aŭded and thus a
-156-
D.C. voltage produced which counteracts the setting
(1). The whole system is therefore an (1/T) trans-
lator of the class d, if linearity between temperature
and voltage can be assumed.
Type 128 (1/Q) Current (D. C.)/Light Intensity Translator
Devices falling into this group can be con-
sidered as means for illumination control. In its
simplest form an electric bulb using direct current
produces a (Q) which is a function of the direct
current supply. To obtain direct proportionality in
the light output and the applied signal, feedback
circuits are necessary.
a
Type (128/01)a (1) Figure 242
<g
The Figure 242 shows a beam tube (see refer-
ence 12) with a direct current as primary signal. The
output of the tube is used to change the light intensity
of the source of light. This output () is measured
by means of a photoelectric circuit which furnishes
the current for the feedback. Obviously, anti-hunting
circuits have to be added to obtain stability.
Type 163 (1/K) Current (D.C.)/Resistance Translator
Translators of type (163) would be of
considerable practical importance if they were available
with class (b) or (a) characteristics for low and for
-157-
high frequencies. Unfortunately, such translators
are at present not available. They could be used
for multiplication in Wheatstone bridge circuits
by making the resistances in the individual branches
directly proportional to current signals and by taking
advantage of the zero output condition that the ratic
of the first two adjacent resistances must be equal
to the ratio of the two remaining resistances. It is
to be hoped that such circuits some day will be
available.
Type (163/01)
с d
(1/R)
c - d
с
The translator in Figure 243 uses the facı
that a resistance of a conductor usually changes as
a function of temperature. If, therefore, a direct
current is being used for heating the resistor, the
translator chain produces an (1/R) translator which
represents the sum of two translators, (1/T) + (T/R).
The drawback of this device is its inherent delay
in response and the fact that its performance is a
function of the ambient temperature.
Figure 243
Type (163/02) (1/R) Figure 244
с
In the device of Figure 244 the resistance
is changed by a voltage which is applied to the grid
of a triode. This changes the resistance of the tube
and therefore, the current (12) and (R) which are
-158-
obtained as the output of the tube becomes a
function of (1).
Type (163/03) (1/R) Figure 245
d
d
In Figure 245 the current is used to change
the light intensity of an electric bulb. For this
purpose, any translator of type (128) can be used.
The light output (Q) is then applied to a selenium
cell whose property is that its resistance changes
with the degree of its illumination. Thus, a relation-
ship between the current (1) and the resistance (R)
is established. Unfortunately, again the selenium
cell is relatively slow in response which limits
this device to relatively low frequencies.
Type 176 (1/L) Current (D. C.)/Inductance Translator
(1/L) devices are those which change the
inductance of an A.C. circuit as a function of a
direct current input.
Type (176/01)
a
(1/L)
Figure 246
"Saturable reactors" are simple translators
of this type as the saturation current changes the
inductance.
Type 219 (1/C) Current (D.C.)/Capacitance Translator
Translators of this group are changing the
capacitances of resistance as a function of an electric
D.C. signal.
-159-
Type (219/01) elec.
d
(1/C) a Figure 247
d
Low frequency response systems of this
type are shown in Figure 247. It is based on the
principle that the capacitance of a system changes
with the distance of two condenser plates. In order
to change this distance, first a translator of (1/F)
is used which is shown to be a solenoid and to this
is added a translator of type (F/S) which is in its
simplest form a spring. Finally, this displacement
is used for changing the capacitance (C).
Type 232 (1/7) Current (D.C.)/Phase Angle Translator
Circuits of this type are used in general
electronic and radio applications to shift the phase
in an A.C. circuit. They are particularly useful in
connection with thyratron circuits to control the
lengths of current cycles (see references 34 and 35).
Type (232/01) (1/7) Figure 248
a
a
In the circuit of Figure 248 the phase
shift is produced by a change of inductance or a
change of resistance. In Figure (A) the inductance
is changed as a function of a direct current; that is,
a translator of the type 176 is being used. In Figure
(B) a translator of (1/R), that is of type (163),
is applied. In (C) the same is done as in (B) with
the exception that a triode is used as a resistor.
-160-
Type 283 (1/H) Current (D.C.)/Magnetic Field Translator
Devices of this type produce magnetic fields
(H) as a function of the current going through a con-
ductor.
Type (283/01) (1/H) Figure 249
b
b
Figure 249 shows the basic fundamental
experiment with field lines produced by the current
flowing through the conductor. The diagrammatic
sketch is self-explanatory (see reference 16).
Type 296 (1/E) Current (D.C.)/Electrostatic Field Trans.
These devices produce an electrostatic
field as a function of a direct current signal.
Type (296/01) (1/E) Figure 250
d
d
A simple solution is an Electronbeam tube
(see reference 12) in which the output potential is
fed back by means of two deflecting plates. The
electrostatic field on these two plates is directly
proportional to the direct current. Of course, addi-
tional plates can be added in parallel which would
have a corresponding charge.
Type 355 (1/f) Current (D.C.)/Frequency Translator
Devices of this type change the frequency
of an oscillator (f) as a function of a direct current
signal (1).
G
-161-
-
(1/f) c - a
d
its capacitance.
In an oscillating tank circuit, the fre-
quency of the circuit depends on its inductance and
As long as we have means to trans-
late a direct current into an inductance translator
of type (176), it is possible to change the frequency
(f) of such an oscillator by a D.C. signal (1).
Type (355/01) elec.
c - a
с
Figure 251
-162-
(P/P), (P/F), (F/P) AND (F/F) TRANSLATORS
tor map.
In the preceding two sections, we have
seen that by combining certain translators in
series we can cover the whole field of the transla-
This was done first with combinations
with the "variables"/"stroke" (S) as "input" and
as "output", and later repeated with direct current
(1) taking the place of the stroke (S).
result, we obtained:
1) (variable₁/S) + (S/variable)
(variable/variable2)
2) (variable₁/i̟) + (1/variable
(1/variable) = (variable/variable₂)
and, in addition, an equal number of translators
for (S/S) and (1/1).
(E)
chain:
The first group is given by the equation:
3) (S/variable)
(variable/S)
(s/s)
and can be considered as (S/S) "transformers" or
"amplifiers", including devices which are usually
known as "servo-mechanisms".
=
=
The second group is represented by the
As a
=
4) (1/variable) + (variable/1)
This evidently covers all possible solutions for
direct current amplifiers, translators, or transformers.
(1/1)
As previously stated, such devices are
found on the translator map on a 45 degree diagonal,
-163-
starting from the left-hand upper corner and pointing
to the right-hand lower corner.
In my previous notes (see reference 3),
I have shown the equivalence of the variables (F),
(P), and (S). Being a mechanical engineer, I was
and am particularly concerned with this group, and
as the reference may not be easily available to the
reader, I am adding in the following section those
translators of (F), (P) and (S) which have not been
covered so far; i.e.,
(S/S) = 1
(S/P) = 2
(S/F) = 9
(F/S) = 5
(F/P) = 6
(F/F) = 7
i
(P/S) = 4
(P/P) = 3
(P/F) = 8)
not covered
We shall therefore consider the equivalence
of the translators: (P/P) = 3, (P/F) = 8, (F/P) = 6,
and (F/F) = 7.
not covered
no
Type 3 (P/P) Pressure/Pressure Translator
Translators of this type translate a
primary pressure (P₁) or a pressure differential
into a corresponding secondary one (P2). This pro-
blem is often encountered in hydraulic devices;
jacks, pistons, and in a different pressure range
-164-
in automatic ratio controllers, pneumatic and
hydraulic boosters and master control devices.
Type (3/01)
ä b
(P/P)
a - b
Figure 252
In the device of Figure 252, two pistons
with different areas are in a state of force balance
if (P₁) times the area (A) is equal to (P₂) times
(A2). By choosing the ratio, (A/A₂), accordingly
it is possible to obtain an amplification or decrease
of P₂ relative to P₁. With no friction, the device
would fall into the class b. As there is, however,
an unavoidable loss of forces, it is safer to
classify it as 3(a). The translator chain follows
the equation:
(P₁/F) + (F/P₂) = (P1/P2)
Type (3/02) d (P/P) Figure 253
ἀ
The device of Figure 253 is described by
Mr. C. B. Moore (see reference 37). It is a device
which produces an air pressure (P2) which is directly
proportional to the loading pressure (P₁). For this
purpose, air is supplied through a restriction (A)
into a chamber out of which it can escape through an
opening (B). As part of the chamber is a flexible
bellows and a diaphragm to which the pressure (P)
is applied, a change of pressure balance changes
the size of the outlet opening (B). Balance is
-165-
re-established when P times the area of the dia-
1
phragm is equal to P₂ times the effective area of
P.
the bellows.
Therefore, P, is directly proportional
to P and the device falls into the class d.
2
Type (3/03)a (P/P) Figure 254
d
As the
1
A variation of this scheme is shown in
Figure 254. In this case, a jet pipe is used instead
of a series arrangement of two nozzles.
pressure (P, ) increases, the pressure in the receiv-
ing nozzle rises until the force from the left-hand
side, which acts either on a diaphragm (A) or onto
a Bourdon tube (B), balances the action from the
right-hand side. The result is a direct proportion-
ality between P1 and P2. It will be noticed that
the device permits going down to the zero point of
P1 and P2.
Type (3/04) (P/P) Figure 255
c
c
с
In the device of Figure 255, the pressure
(P₂) between the two restrictions is varied by means
of a valve whose stroke is a function of P P1• The
relationship between P₁ and P Ра
is not a direct pro-
1
2
portionality and has to be determined in each
particular case. The translator chain follows the
equation:
(P₁/F) + (F/S) + (S/w) + (w/P₂) (P1/P2)
=
-166-
Type (3/05) (P/P) Figure 256
a
d
In Figure 256 a typical ratio regulator
is used for a combustion control as diagrammatically
shown. The differential pressure (P₁) is obtained
from flow (w,) and the controller produces a flow
1
1
(w₂) which in turn creates a differential pressure
(P2) in such a way that P₁ becomes directly propor-
tional to P₂. This, incidentally, makes W propor-
but basically the device is a translator
tional to w
2
of P₁/P2°
Type 8 (P/F) Pressure/Force Translator
These translators change a specific pres-
sure into a corresponding force. As such, they are
commonly used as pressure responsive and level
responsive devices with and without amplifiers and
are the basic elements used for pressure measurement.
Type (8/01) (P/F) Figure 257
b
tube".
Typical representatives of P/F) transla-
tors as commonly used in mechanical type instruments
are the "diaphragm", the "bellows", and the "Bourdon
Representatives of these transiators are
schematically drawn in Figure 257. The practical
ranges depend on the individual design and the
material chosen. The diaphragm can be considered
as the most sensitive device of this group. However,
-167-
its use is limited to relatively low pressures,
while the other extreme in high pressures is taken
by the Bourdon tube.
Type (8/02) a
In Figure 258 the pressure is first trans-
lated into a stroke; that is, a level of a liquid
and then a float is used to produce a buoyancy force
(F). The device, therefore, acts as a (P/F) trans-
lator.
Type (8/03)
ان
(P/F)
b
a - b
Figure 258
(P/F) Figure 259
d
In the design of Figure 259, the pressure
is first applied to a jet pipe relay and translated
into a stroke. This stroke is then translated into
a force by means of a (stroke/force) translator, in
this example represented by a spring.
which it produces is directly proportional to the
pressure (P). There is no limitation in the possible
magnitude of the output for a given input signal.
The force
Type 6 (F/P) Force/Pressure Translator
These devices translate a force into a
pressure. By definition the simplest devices are
devices which transmit force to a certain area, as
the force divided by the area gives the "specific
pressure" (P). In a broader sense such a translator
-168-
controls pressure as a function of an applied force.
All force balanced controls fall, therefore, in this
group.
Type (6/01) (F/P), Figure 260
b
As previously stated, by definition the
specific pressure is force divided by an area. This
is diagrammatically represented in Figure 260(I). In
II the force is applied to a diaphragm which in turn
acts onto a liquid. The pressure of the liquid is
then proportional to the applied force. Both devices,
therefore, are simple (force/pressure) translators.
Type (6/02) (F/P) Figure 261
a
a
In the translator of Figure 261, the force
is applied to a float which changes the level (S) of
a liquid and this change of (S) in turn produces a
pressure (P). The chain, therefore, follows the
equation (F/S) + (S/P) (F/P).
=
Type (6/03)d (F/P) Figure 262
a
In Figure 262 the force is used to change
the pressure which is controlled by a pressure con-
troller. For every force applied, a proportional
pressure (P) is balanced and in the illustrated simple
weight loaded pressure control valve, a definite
relationship is obtained between the force and the
:
-169-
pressure. The energy of the fluid flow (w) is used
for operating the mechanism.
Therefore, it is
classified as class d. Should the diaphragm char-
acteristic be non-proportional, the valve would be
a class c translator.
Type (6/04) a
d
(F/P) Figure 263
d
As the diaphragm characteristic enters
into all translator uevices, a greater accuracy can
be obtained by a device known as "pneumatic test
scale" which avoids bellows anu diaphragms.
force is applied to a cup with sharp edges änu is
directly balanced by the pressure (P) inside a
The
second cup which coincides in diameter with the one
to which the force is applied. If the pressure (P)
is too great, the upper cup (B) is raised until suffi-
cient air escapes between the two cups to establish
a balance between the force and the pressure. Å
counterweight (C) balances the weight of the cup.
A standard range of such devices is 0 to 6" maximum
w.c.
Special instruments have been built in ranges
up to 20" W.C.
Type (6/05) a
Figure 264 shows two simple translators
using the jet pipe principle. In the right-hand dia-
gram, the force controls the pressure in a line by
means of a valve. This is a typical pressure control
(F/P) Figure 264
d
-170-
design. In the left-hand diagram, the jet pipe is
used as a relay and the operating medium, whose flow
rate is (w), is delivered directly into a nozzle
which is connected to an opposing diaphragm (B).
Both devices are of the class d.
Type 7 (F/F) Force/Force Translators
(Force/force) translators are as basic as
(stroke/stroke) translators and belong to the oldest
devices known to man. A lever is not only a (stroke/
stroke) translator, but is even more often used as
an (F/F) translator. Any force balance instrument
as repeatedly described in this study is a (F/F)
translator.
Type (7/01) (F/F) Figure 265
b
Figure 265 shows diagrammatically a lever
system. It establishes equilibrium if F times a
1
is equal to F2 times b.
Type (7/02) a (F/F) Figure 266
a
In Figure 266 the buoyancy of two floats
is used to establish a relation between F
to F2°
1
By shaping either one of the floats or the vessel,
which contains the fluid, any desired relationship
between the two forces can be established.
-171-
Type (7/03) c - ₫
(F/F)
с - d
Figure 267
A jet pipe
relay is used in Figure 267 to
translate the force (F) first into a directly pro-
portional pressure. This pressure is then applied
to a (P/F) translator (a piston in a cylinuer) with
the result that F₂ is proportional to F₁. There is
2
practically no limit in the amount of amplification
possible with this device.
Type (7/04) (F/F) Figure 268
a
d
In the Kelvin type balance of Figure 268,
the force (F,) which is applied to the lever (L) is
balanced by the attraction (F₂) between the two
coils (C). An Electronbeam relay is used to detect
the displacement of the magnet (M) relative to the
Electronbeam and to the magnet (M). As a result,
a current (1) is produced which counteracts the
effect of F₁ by generating a force (F₂). The whole
device, therefore, can be considered as a (F/F)
translator.
-172-
CHAPTER IX
GENERAL REMARKS ON TRANSLATORS
It is obvious that in each of the trans-
lator boxes a plurality of solutions could have been
given and that examples could have been added, giving
translators in all of the boxes not covered in this
study. This, however, would have gone in the direction
of preparing an encyclopedia, which although tempting,
goes far beyond the plan of this investigation.
In order to systematize references for each
individual design, a folder is recommendea, bearing
the individual type and design number anu giving all
pertinent data. These data are to include: the trade
name or the name under which the design is commercially
known, as for instance "Amplidyn", "Selsyn", "Thyratron",
"Transometer", "Power Unit", etc. (see reference 44).
In audition it should give a complete ana-
lysis of the translator chain which the design
represents, the magnitude of inputs and outputs and
the type of auxiliary energy needed (air, electric
current, oil under pressure, etc.). Furthermore,
circuit diagrams and design details (if of interest)
should be added as well as test data (so far as
pertinent and available).
Information on sources of
-173-
supply, the price range, and general remarks, which
may be of interest to the designer, should also be
mentioned; i.e., notes on reliability, serviceability,
etc. Last, but not least, there should be a biblio-
graphy which gives important articles or books as
references.
It is hoped that some time in the future
manufacturers will provide this information already
prepared, as it is believed that it will not only
greatly benefit the user, but also the manufacturer.
Engineers are apt to take advantage of information
which is easily accessible in preference to such
which has to be obtained by extended correspondence,
telephone calls, and guessing.
Only the additional knowledge of these data
makes the translator chart a basic tool in the hands
of the designer. Fortunately, a great number of
industrial engineers have been forced to acquaint
themselves with the magnitude of the input and output
of the most common devices sketched in the examples
chosen. However, it is usually correct to assume
that, although familiar with these values in his own
particular field, he may be completely at a loss to
estimate the magnitude of the effects in others which
are more foreign to him.
•
-174-
Thus the enthusiastic inventor, seeing a
solution for (Q/1), i.e., a translator from light
intensity into direct current in box (138), may be
slightly disappointed to find that his invention to
run automobiles in the desert on sunshine, although
possible, is highly impractical as the decimal points
happen to be at the wrong place.
This minor detail has cost much disappoint-
ment to many inventors, investors, and caused many
headaches to research directors, whose job it is to
explain their lack of enthusiasm for these "why don't
we" schemes. Even the famous failure of building a
"Perpetuum Mobile" is basically only one of lack of
knowledge of magnitudes involved.
·
-175-
CHAPTER X
MATHEMATICAL OPERATIONS WITH TRANSLATOR CHAINS
We have already seen that in some mechanism
the translator chains took care of mathematical opera-
tions. For instance, feedback systems which are bal-
ancing variables against each other in "Null balance"
Their
circuits are basically subtracting devices.
output is frequently a multiple of the input, in which
case they are called "amplifiers" and they can be used
for multiplication problems if the multiplication
factors are variables which we can control.
The discussion of (v/8) translators and
(a/8) indicators brought out that these devices are
d2s
/6) and (atz/S) translators, and as such should
lend themselves to the solution of rate problems
(as they actually do).
Finally a motor shaft running with varying
speeds as a function of time will give a total number
of revolutions which are an integral over time with
(v) representing the variable.
The problem presents itself, therefore, to:
a) express a given mathematical relationship by
outputs of a translator chain,
b) to choose those parameters and translation
-176-
sequences which give an over-all optimum
solution.
it
While this field of engineering previously
was the domain of mathematicians and accountants,
became necessary and a question of survival to develop
devices which during an air attack or defense would
solve involved mathematical equations within seconds
(see reference 19).
The same problems had to be solved in
training devices for airplanes, submarines, and guns.
Immediately two schools were formed and two basic
lines of attack chosen, depending on whether the
engineer confronted with the problem had majored in
mechanical or electrical engineering.
It is the purpose of this study to show that
the choice of the solution should be made on the ground
of other considerations; i.e., simplicity, reliability,
weight, cost, etc., and that preference should neither
be given to the parameter (S), the star of the mechani-
cal engineer, nor (e) the cure-all of the electrical
designer. It may have to be frequency, it could be
temperature, radiation energy, or supersonics, depend-
ing on the individual problem.
To arrive at a logical choice of the para-
meter, we shall discuss the basic mathematical
G
-177-
operations for any one of the chosen variables.
On
the basis of the solutions available with these and
on the basis of an over-all analysis of the mathe-
matical problem we have to solve, we are liable to
make a better choice better as less is left to
chance.
-
I
In a previous paper (see reference 4),
have analyzed the available (i.e., commercially
available) solutions of the equations:
1
hc
č₂ (c₂ √2 + c 3 √ ñz
c3√3 + c₁₁√)²
C
n
in which h₁ to h represent the differential pres-
sures obtained from orifices which are (w/P) trans-
lators and are representing individual fuel flows,
and he, the differential pressure representing the
pressure drop across a restriction in the common air
supply line with c1 to cn constants).
The analysis has convinced me that any
designer could have covered all of the available and
some additional solutions 15 years ago when this
problem became acute. It was not done because as
previously stated "a solution" is the greatest handi-
cap in furthering systematic attack on a problem.
The point is emphasized not to recommend
that everybody should use the more rational and
systematic approach to establish bigger and better
-178-
monopolies, but as a sincere attempt to prove that
the time has come where all basic translations are
common property of those "skilled in the art".
Just as no tribute is any longer paid to
the man who solves a particular mathematical equation,
as the elements and their laws of manipulation are common
property, so it is hoped that this study will contri-
bute to the opinion that the basic solutions of trans-
lator chains require, at worst, patience and some
practice, rather than that spark of genius acknowledged
by society in gratefully granting a monopoly to the
inventor.
This is by no means written as an attack
against our patent system, but rather as an admission
of an engineer that this type of inventing does not
deserve the honor of this term.
There are other types of mathematical pro-
blems which can be solved and are being solved by
translator chains.
S
M
These are the analogy circuits. For
instance, based on the analysis that exactly the same
mathematical equations govern such different problems
as the oscillation of a pendulum and those of an
electrical oscillating circuit, the vibration of a
▸
-179-
bridge, the roll of a ship, and the behavior of a
controller plus a process, it was obvious to ask
the question, "Why not experiment with a pendulum
in order to get the answers which are more diffi-
cult to obtain analytically?"
Or, in other words, why not choose those
parameters in a general equation:
c₁₂ d20
C1
с
at
αθ
2 dt
Са
+ C
+ CO = f(t)
and its second derivative
which makes it most convenient to measure the variable
de
d20
e, its derivative
dt'
at2•
We shall later on develop such analogy chains. At
this point, it is only necessary to see the difference
between the two equations, the flow equation with n
independent variables h₁ to h, and the above equation
where all the variables are tied together and dependent
on each other.
It will be noted that in these devices the
translator chain is chosen in such a way that the
selected device follows the same basic laws, and
therefore, any parameter can be chosen to represent
any other variable. (see references 45 and 46)
Again, the choice of the parameters is
governed by other considerations and the background
of the experimenter. (Mechanical engineers hoping
-130-
for shortcuts usually are liable to favor electri-
cal analogies and electrical engineers, mechanical
ones). However, the design of these chains is again
our concern in this study.
After having established solutions for all
of the translators given in the chart, we shall dis-
cuss in this chapter how these individual basic
parameters can be summarized and multiplied with
each other and themselves. It will be furthermore
shown how derivatives and integrals can be obtained.
This field is still a rather virgin terri-
tory. Although during the World War II, a great
number of calculating devices for radar, anti-
aircraft devices, gun controls, trainers, etc.,
have been developed, there is surprisingly little
to be found in the literature on this subject.
Depending on whether the contractor for the particular
device happened to be an expert in mechanical,
hydraulic, or electrical translator designs, the
calculating devices which were developed showed
distinct marks of their parents' preferences.
We shall see that any parameter may be used
for such mathematical operations. The choice of
any one in particular should be made solely on the
basis of over-all specifications.
-181-
•
It may be necessary in many cases to trans-
late from one parameter into another and then back
into the original one, solely for the purpose of
simplifying the mathematical operation. For
instance, summarization is particularly simple, if
one uses rate of flows or energy (current or weight/
time unit) and strokes. Thus we find summarizing
accomplished most frequently by using the parameters
i, w, and S.
Differentiation (at relatively high speeds)
is relatively easy to accomplish with electrical
circuits in which a voltage (e) is proportional to
while the mechanical solutions are somewhat more
complicated. We find, therefore, a preference for
electrical analogs or computing devices if this
mathematical operation is necessary and if the
constants fit in magnitude for this purpose.
di
dt'
The collection of examples of actual designs
is again rather limited due to lack of time in pre-
paring this study and the absence of readily
available publications on this subject. However,
the few examples can be easily augmented by the
individual reader using the reference numbers as
filing indices.
These reference numbers are based on the
following scheme. A letter (A) to (E) is given to
-
!
-182-
the mathematical operation to be performed. Thus,
we have:
(A)
(B) = multiplication
(C) = nth power (n = 1, 2, 3, 2, 1/3, etc.)
(D) differentiation
(E) = integration
= summarization
Each of the parameters (S) to (f) has a number
1 to 19 and each sub-mechanism or method an additional
number which is separated from the parameter number by
an 0. We find, therefore, that B-7023 is solution #23
of multiplication of the variable (D.C.) current.
It is admittedly a rather arbitrary way of
filing the individual designs on such an accidental
basis of "first come, first filed", but it will be
easy, indeed, if there should ever be a need for it,
to reclassify the individual designs in some other
manner which might be preferable.
(A) SUMMARIZATION OF VARIABLES
1) Class A-1 Summarization of Strokės
S = (S1 + S
+ S₂+ S3....Sn)
$2
A-101, Figure 269
The simplest solution is that of a whiffle
tree arrangement as shown in Figure 269. With the
*
-183-
sum of the three strokes (S₁ to S3) as input, the
output becomes S
54 - 2(514 + 520) + 53b
S
Sze)
f
с
It should be remembered, however, that
this equation is only fulfilled for small displace-
ments of S, or to be more specific, for small angular
motions of the summarizing levers.
As a symbol, the translator carries the
Σ sign inside of the box which represents it, with the
three inputs (S1, S2, S3) and the output (S4).
A-102、 Figure 270
This diagram shows an alternate for this
mechanical solution which is not limited to short
strokes of S. Individual pulley movements, S₁ to Sn,
produce corresponding movements of a summarizing or
end pulley. Note that S₁ produces 1/2 the motion of
the end pulley for the same stroke as do S₂ to Sm
A-103, Figure 271
The summarizer shown as A-102 still is
limited in its strokes as such a device cannot be
built with infinitely long strokes. The answer to
problems with unlimited strokes is to use angles
rather than strokes.
-184-
The sketch shows a basic differential gear
system which can be modified to become a planetary
gear (spur gear version). The summarizing is very
satisfactory if the direction of rotation of the
gears does not have to reverse itself as then unavoid-
able lost motion introduces errors. Obviously, this
generalization is to be checked for individual appli-
cations, considering the degree of accuracy to be
expected.
A-104, Figure 272
The differential gear shown as A-103 is
limited as it calls for a proximity of shafts which
introduce angular displacements and ß. This
limitation is overcome in the differential Selsyns
schematically shown in A-104.
The choice (without servos), however, does
not permit the transmission of torques, but only
serves to summarize strokes or angular displacements.
2) Class A-2 Summarization of Pressures
Σp = (P1 + P2
A-201, Figure 273
..Pn)
The summarization of pressures as such is
not possible. However, it is feasible to summarize
pressure drops as it is done in electrical circuits.
Such pressure drops are produced by resistances to
-185-
the flow of a fluid. Care should be taken that a
change of a particular resistance does not change
the total rate of fluid flow and thus the pressure
drop across the other resistances.
In Figure 273, a summarizer of this type
is shown with a constant rate of flow (w = constant)
regulator and three adjustable resistances
(R1 R2 R3) which produce corresponding pressure
differentials:
>>
-
-
AP₁ = f₁(R₁w)
ΔΡΙ
AP₂ = f2(R₂w)
2
AP3 = f3 (R3W)
ΔΡ
The summarization is then accomplished by measuring
the total pressure drop.
P
4
3
Σ ΔΡ.
n=1
n
In passing, it should be noted that such
a device could also be used to summarize functions
of (R) which in turn are functions of (S), i.e. of
the adjustment of the resistances. However, addi-
tional translators are then necessary to translate
the resultant P, into R or S values.
4
A-202. Figure 274
In this summarizer the variable (P) is
first translated into forces and then the forces
-186-
added up to produce a resulting force which again
is re-translated into a pressure. In Figure 274,
the diagram shows not only a schematic solution
which is self-explanatory, but also a symbolic dia-
gram of the translator chain used in this design.
It can be written in the simplified form, which
merely states the problem (and the result);
P₁ =
4
+ C₂P2 + C3P3
P
=
C₁P1
zCnPn
the effective areas of the diaphragms
4
wherein C are
used in the summarizer.
possible.
Another way of writing this translator
chain considers the basic circuit by using the sym-
bolic equation:
Σ((P₁/F₁) + (P2/F2) (P3/F3)) + (εF/P₁) (P/P)
+
A-203. Figure 275
The summarization as we have seen in A-101
can also be accomplished by using a whiffle tree. In
Figure 275, the schematic diagram shows how the
pressures are first translated into strokes; these
then summarized and now finally the result is re-
translated into pressures.
Σ((P₁/§₁) + (P₂/S2)) + (S/P₁)
(S/P₁) = (¿P/P₁)
Again, as all elements for (P/S) translators (class 4)
are interchangeable, a great variety of solutions is
=
-187-
3) Class A-3 Summarization of Forces
F = (F₁ + F2
... F₂)
A-301, Figure 276
The simplest and oldest solution for a
force summarizer is the lever as shown in Figure 276.
The laws of mechanics give the equation for this
summarizer:
(F15
(F151 + F2$2 + F3$3) = F4
Although the design is extremely simple,
there are usually limitations due to the maximum
amount of forces the device can stand, the friction
of the bearing, and the difficulty of measuring
forces without translating them into other parameters
first.
A-302, Figure 277
Similar limitations are found in the
summarizer shown in Figure 277 which is not usable
when a high degree of accuracy is expected. The
obvious reason is the fact that the gear friction
which occurs at relatively large distances from the
shaft centers introduces relatively high errors.
4) Class A-4 Summarization of Velocities
Σv = (1 + 2
V +
v)
"
A-401, Figure 278
For this problem the differential gear
is ideally suited. The differential gear is
-188-
basically a summarizing device for strokes (A-103).
S₂+ S₂ + S S3, then it follows by differen-
If S =
= S
$1
tiation that also:
and as
ds
ȧt
ds ds1 ász
dt dt
dt
dsz
dt
v, we have a device for:
V3
V =
A-402, Figure 279
+
V1 *2
+
Quite often the velocities to be summarized
are vectors in space. One procedure is to obtain the
components of these vectors in the direction of three
preferred axis, to summarize these as in A-401, and
to reconvert the three sums into one vector in space
(see reference 19 and U. S. patent 2,385,952).
Devices of this kind are used for fire
Σa =
control and trainers.
5) Class A-5 Summarization of Accelerations
(a₁
A-501, Figure 280
+
22
a₂ + ....an)
The simplest summarizer for accelerations
is a mass as shown diagrammatically in Figure 280.
Basically, such a mass is a translator of accelera-
tion into forces and the mass, therefore, serves as
a force summarizer. With the values given in the
diagram, we have:
Σ(
123/F
F1) +
+ (8/F2) + (a₁/F3)) + (EF/a2)
dt2
+ (IF/a₂) = (Ea/a₂)
-
-189-
!
A-502, Figure 281
By differentiating the equation of A-401,
ás
dt dt
ds1
a second time, we have:
d2s
at2 = dt2
W1
Σw =
+
d2s1
A-601, Figure 282
d$2
dt
and w and w
2
W3
a = a + a + a
a1
2 a3
Thus, it follows that the same devices used for
summarization of stroke, class A-1, and velocities,
A-4, can also be used for class A-5.
2
+
d2s2
S
dt2
6) Class A-6 Summarization of Rate of Flow
(W1 + W
(see reference 4)
ds3
dt
+ W
#3
d2s3
dt2
W
One of the basic solutions is shown in
Figure 282. A system of conduits adds the flow,
to w₂, and deducts
#2
W1
W2
or,
W3
=W
W3 4
with w as the final result:
4
It is necessary to make provision that no
variation of either W1, W
or w
affects the other
29
N3
flows, but only the total w
W4. This means that w
should preferably be controlled.
"1
A-602, Figure 283
This control is accomplished in A-602 by
means of flow rate regulators which are independent
of each other. In Figure 283, if the individual
-190-
flows,
cannot be combined in one conduit,
1
3'
it is customary to produce pilot flows which are
directly proportional to the individual flow rates.
(w/w) Translators, also known as "ratio controllers"
can be used for this purpose.
The sum of the pilot flows is at all times
directly proportional to the sum of the independent
flow rates "1" › W2' and W
"3°
A-603, Figure 284
As previously mentioned, it is also often
convenient to use first a translator of the type w/S,
and then a summarizer of the A-1 type to summarize
the strokes with an additional translator in series
which translates the ES back into a flow rate.
C
Such a device is shown in Figure 284. The
first translation of the (w/P) type followed by
(P/F) + (F/S) with a parabolic cam to make S₁ = C1W1
and S₂ = C22. The device is thus represented by
the symbolic equation:
1
Σ( (w₁/P)+(P/F)+(F/S₁)+(w₂/P) + (P/F)+(F/S₂))+(ΣS/F)+(F/w3)
1
+ W
2
3
7) Class A-7 Summarization of (D.C.) Currents
±3 ...1)
[1 = (11 + i +
#2
A-701, Figure 285
This is basically the same problem as that
-191-
12
of the summarization of fluid flows (w). In sum-
marizing we must be sure that a change of i does
not affect i̟, etc. It is, therefore, best to
stabilize the output of i, i.e. to use (D.C.) current
regulators in order to obtain the sum 13 = 11 + 12,
i
i
i
as shown in Figure 285.
obtain:
By means of Electronbeam translators, we
i
1
1
1
e2
12
C212
regardless of tube and load characteristics.
= 0
A-702, Figure 286
1
The signal to control the current i, and
12 may be obtained from other variables. Still the
outputs will be proportional and the summarization
of the output currents can be used to represent the
sum of the original variables to which they are
directly proportional.
©1¹l
e1 = c₁¹l
c2¹2
= C212 (see also class A-9)
e1 And e₂ may be obtained from the voltage
drop across a resistor:
1
R₁11
R212
1
e1
e2
-192-
which again makes:
1
11 + ±1
·12 = 13 = 11+ 12
8) Class A-8 Summarization of (A.C) Currents
21
Σ1 = (11 + 12
A-801. Figure 287
+ ••••±n)
The obvious solution for summarization of
(A.C.) currents is the summarization by means of trans-
formers whose secondaries are in series and whose
primaries are independent of each other.
As shown in the Figure, such a solution
must consider the phase relationship of 1 and 12
±1
or better, the result is the vector sum of the two
transformer outputs c111+ C212•
A-901, Figure 288
9) Class A-9 Summarization of (D.C.) Voltages
ΣΕ (£1 + €2
(see Figure 286)
+
e_)
=n
In the simplest form a number of batteries
in series gives the desired Ee, i.e. the voltage
across the end terminals. The voltages must be
entered with the correct + or sign.
Into the same class belongs total voltage
drop across a number of resistors (e
е3=113) plus a battery 4
=
11R₁, €2 11R2,
Ze gives directly the total potential at
=n
the two terminals A and B. Again, care must be
.
&
-193-
<
taken that 1 remains constant and that R1 - Rn do
not change with 1 or temperature.
10) Class A-10 Summarization of (A.C.) Voltages
Σε (e1 + €2
...en)
=
A-1001, Figure 289
This problem is identical with the one of
summarizing (A.C.) currents. It can be solved again
either by resistors in series similar to case A-901
with a source of A.C. power, or by transformers
similar to A-801.
Again, we have as a result the vector sum
Σe = c101 +
c22 which becomes the algebraic sum for
a phase angle of 0.
11) Class A-11 Summarization of Temperatures
...T)
ZT = (I1 + I2 + F3
A-1101, Figure 290
Temperatures cannot be added directly just
as pressures cannot be added. These variables are
indices of energy levels rather than energies them-
selves. It is, therefore, necessary to convert
temperatures first into another variable and to
summarize these to obtain in turn by an additional
translator a temperature which is the sum of the
original ones.
-194-
In Figure 290, the temperatures are first
converted into resistance changes, R₁ to R, and then
the total voltage drop across them which is:
1 (R₁ + R₂ + R3)
is translated with a servo-mechanism into a directly
proportional temperature which in turn produces a
voltage (e) which is fed back in opposition to
(summarization of e!).
(e₁)
We have here the translation:
(R/e₁) + (e₁/1) + (1/T) + (T/R) + (K/e2)
We can also write:
(T2/R2) + (T3/R3)) + ( R/e¸)
(T/R) +
with e
e1
((11/R1)
zation.
ce2°
+
Instead of the resistance wires, thermo-
couples could have been used in series or expansion
thermostats with a suitable translation after summari-
ΣΩ
12) Class A-12 Summarization of Light Intensities
(81 +
62
•Cin)
A-1201, Figure 291
-
+
+ (e₁/11) etc.
We assure in this circuit a monochromatic
light source Q1 and Q₂ and a common target plate (A)
which is simultaneously illuminated by them. This gives
a resultant light intensity on the target which is:
Ecnn
Q
=
►
-195-
13) Class A-13 Summarization of Resistances
ER₁₂ = (R₁ + R₂
.Fn)
A-1301. Figure 292
The obvious solution for this problem is
a number of resistors in series.
14) Class A-14 Summarization of Inductances
ΣΕ Ξ
• = (L₂ + L.
...Ln)
2
A-1401, Figure 293
As in 1301, the solution for this problem
is found in a series arrangement of inductances.
However, it is necessary to consider that inductances
are combined with resistances so that the sum of L
means also the sum of corresponding R's.
15) Class A-15 Summarization of Capacitances
ΣΕ = (C₁ + C₂ + ...Cn)
A-1501, Figure 294
The summarization of capacitances is
accomplished by a circuit in which the capacitors
are arranged in parallel as shown in Figure 294.
16) Class A-16 Summarization of Phase Angle
ΣY= (Y1 + 42 ....Yn)
We have to distinguish between phase dis-
placement in space and phase displacement in time.
Phase displacements in space are treated in Class A-1
as they represent angles or strokes.
-196-
The devices falling in Class A-16 deal
with phase shifts in time.
A-1601, Figure 295
The symbols shown in Figure 295 stand for
phase shifters using saturable reactors (1/1), type
232. By varying the saturation of a reactor with a
(D.C.) current (1), a phase shift (f) of the output
voltage (e) relative to (e) is obtained. By
repeating this process, phase shifts can be added and
thus a total phase shift produced which is the sum of
the individual phase shifts.
:
This statement must be qualified as the
translators shown do not give directly proportional
outputs and as secondary effects may limit the
range of application for this basic circuit.
17) Class A-17 Summarization of Magnetic Fields
2H = (H₁ + H₂ + ...H₂)
As the magnetic field is a vector in space,
the resultant field at any point of space is the
vector sum of such individual fields which are super-
imposed onto each other. For the purpose of the
design of translator chains, we are particularly
interested in the summarization of fields which are
the output of other translators.
-197-
A-1701. Figure 296
In Figure 296 the fields (H₁ to H) are
outputs of translators of the type (1/H) (type 283b);
i.e., the fields are directly proportional to the
ampere turns which are producing them.
The summarization is accomplished by an
Electronbeam translator whose output produces a
field (H) directly proportional to (H).
18) Class A-18 Summarization of Electrostatic Fields
ΣE = (E1 + B2
E
=
+ ...E)
n
Basically, the problem is identical with
that of Class A-17, as electrostatic fields are space
vectors.
A-1801, Figure 297
In the diagram, Figure 297, one of the
possible solutions uses translators of the type (E/1).
The equations of such a device can be written as:
(Σ(/11) + (E2/12))/E3)
) + ±
(ZE/E3) or,
(E2/12) + (11+12/13) + (13/E3) (E1+E₂/E3)
+
(E₁/11)
19) Class A-19 Summarization of Frequencies
Σf = (f1 + ₤2 +
£2
...fn)
Obviously, devices falling into this class
have to be subdivided into subclasses which cover
frequencies of different variables. For instance,
=====
-198-
there are frequency variations of strokes/time unit,
force/time unit, rate of flow/time unit, light inten-
sity/time unit, voltages/time unit, etc.
In all frequency summarizers and their
opposite; i.e., frequency separators (spectographic
devices, Fourier analyzers, etc), one must remember
that two other variables enter into the end result
(see reference 43), that is, phase relationship, and
the amplitude of the oscillations.
As typical examples of the extremely wide
range of such summarizers, the following summarizers are
shown.
A-1901, Figure 298
Mechanical frequency summarizer, Figure 298,
was discussed in Class A-1, A-4, and A-5. If f1 and
f2 can be translated into angular velocities; i.e., speeds
(V₁) and (v2), the problem is reduced to that of a
Class A-4 device. Obviously, any other stroke sum-
marizer can be used for the above purpose.
A-1902. Figure 299
As an example of an electronic summarizer,
a schematic diagram is given in which two voltages of
different frequencies, (f, and f
f2),
are applied to a
multiple grid tube.
-199-
(B) MULTIPLICATION OF VARIABLES
Basically, multiplication can be achieved
by repeated summarization.
However, this limits
the operation to multiples of one and makes it impos-
sible to change the factors within a given range.
In discussing multiplicators, we have to
distinguish between multiplication of variables with
factors which represent numbers and factors which
represent variables.
If it is possible to convert the variables
into their logarithms, the problem of multiplication
is reduced to that of summarization; 1.e., of the
design of Class (A) devices.
We shall notice that the number and variety
of methods and available devices decreases as the
mathematical operations become more complex. Thus,
fewer devices are already available in the Class (B)
than in Class (C), and we shall find that this
"thinning-out process" becomes even more pronounced
as we go further to Class (D) derivatives, and (E)-
integration. However, the task confronting the
designer venturing into these regions is not as hope-
less as it may appear at first.
<p>
As it was shown that all variables can be
translated into any other variable, a solution can be
-200-
found for any mathematical operation with any variable
if at least one device is available in each class with
which this operation can be accomplished.
It will be sufficient, therefore, for the
purpose of this preliminary survey of the field to
limit ourselves to a few outstanding examples, leav-
ing it to the future to fill the shelves with
representative devices for all classes.
1) Class B-1 Multiplication of Strokes
a) with a numerical factor S1 = cS₂
b) with another stroke S1 S2 S3
As class B-la type multiplicators can
always be obtained from class B-lb type multipli-
cators by letting (c) represent S2, we shall limit
ourselves to the discussion of the latter type only.
B-101, Figure 300
The classic example of a lever with a variable
fulcrum (F) is shown. Given S, and S which are to be
$3
multiplied, the device gives:
S153
S₂
S
4
The multiplication is symbolized by the (M) in the
translator box.
Somewhat inconvenient is the factor (S,)
4
which changes with (S3) as S3
C
+ S.
4
= constant.
÷
-201-
B-102, Figure 301
3
To avoid this difficulty, S₂ can be fed
into the mechanism by means of a cam which takes
care of the necessary numerical multiplications
(class B-la). It is obvious that S
$3 can have any
· desired relationship to the ratio (S,/S,) of the
previous device (B-101), and we can, therefore, write:
S₂ = (S1 x
(S1 x f(S3))
B-103, Figure 302
2
If S and S₂ represent angular movements,
it is possible to use variable speed gears; i.e.,
(S/v) translators for the purpose of multiplication.
In the device shown in Figure 302, a
friction wheel (F) is driven by means of a rotating
disk (A). The number of rotations of shaft (K) are
directly proportional to (S3). Thus, we obtain an
output angle as the product of (S₂ xα) with
∞
3
the input angle of shaft (L).
The mechanism is ideal in its simplicity.
Its only drawback is the danger of slippage of wheel
(F) on disk (A), a danger which increases with an
increase in output torque.
It should be noted that, while the torque
remains constant with (L) as input and (K) as output
-202-
shaft, the torque decreases if these shafts are
reversed. The torque decreases in this case pro-
portionally to S, and becomes zero for S₂ = 0.
3
B-104, Figure 303
In the mechanical multiplicator, Figure
303, the slope of the cam represents a numerical
factor. If this factor is made variable (e.g., by
means of a servo-mechanism mounted on this cam), we
obtain:
S₂ = f(α)S₁ with f(x) = S3
2
S₂ = $3$1
2
To be more specific, the device becomes a means to
multiply each stroke with a new factor with a deri-
ds,
vative
as₁ = Y(S3).
ds1
In its simplified form, B-104a becomes a
cam as shown.
B-105, Figure 304
In the multiplicator shown, Figure 304, a
rack and pinion drive produces a stroke (S2) directly
proportional to (S3). As point (A) can be moved
relative to point (B) by means of a carriage (K), any
factor of (S3)
can be multiplied with the angle (x).
S₂
2
=
•
<
S3)
(α x S
B-106, Figure 305
A hydraulic amplifier, as shown in Figure 305,
permits a convenient way of multiplication by combining
-203-
a force multiplicator (B), Class B-3, with a stroke
multiplicator, Class B-101. The output (S2) is equal
to:
ves
=
and thus:
$1
S1 x f
x f(53)
B-107, Figure 306
Of particular interest are the multiplicators
used in fire control apparatus (see reference 19). The
one schematically shown in Figure 306 is based on the
similarity of the triangles A, B, C, and A, M, L.
With a mechanism of the type shown, and a
fixed point (A), we have the relation:
NX
11
x
Y
D
2 =
(S,)
AB
M
MA
xx
If x and y are introduced into the mechanism as strokes,
z can be picked up directly and multiplied with a
constant factor.
Unfortunately, it is not easy to design a
mechanism on this principle, as in most calculating
devices, the space available is limited. The variables
are usually introduced as rotation of shafts and the
mechanism must have a minimum of friction and no ten-
dency to bind. The latter two requirements are always
difficult to meet with devices which call for guides
or reciprocating linear motions with force components
-204-
acting under an angle relative to the guides.
B-108, Figure 307
Figure 307 is a modification described by
Macon Fry (see reference 19) which, although an
approximation only, uses rotary displacements.
The inputs (x) and (y) produce a rotation
of lever (D) by the amount of (z); the relationship
between the variables is:
D sin z = x sin y
z = arc sin (X sin y)
D
for small angles of z and y:
2 =
xy-=-=
Mr. Fry gives the error for various angles
of y which show a surprising accuracy for relatively
large values of y.
Error
0
0.44%
1.81%
4.22% ·
Max. value of y
0
15°
30°
45°
B-109, Figure 308
A very interesting approach to the mul-
tiplication problem is incorporated in a device,
which combines summarizers (class A) devices with
multiplicators which give the second power of a
Gja
:
-205-
function. If, as will be shown later on, a variable
speed gear is so modified (see also B-103) that the
factor (S3) which is introduced and is to be multi-
plied with an input (α) is made directly proportional
to α, we obtain an output = c(x)2.
==
The principle on the basis of which B-109
is designed summarizes the two inputs a and b =
(a + b)
produces their square (a + b)² = a² + 2ab + b²,
b2, and
deducts from this the square of the difference of
2
(a - b)² = ɛ
G
А 2ab + b².
(a + b)² = a² + 2ab + b²
= a²
2
(a - b) 2
- 2ab+ b²
+4ab
(a + b) 2 − (a - b)2 =
-
1.e., we obtain four times the product of the two
inputs (a) and (b). The mechanism is shown in
Figure 308, in diagram form.
Inputs (a) and (b) are first fed into a
"summarizer" to obtain (a + b) and also into a second
"summarizer" to obtain (a - b). The outputs of these
"summarizers" are split and the two new components
multiplied with each other to obtain square functions.
A final "summarizer" gives the desired output (4ab).
The device can be described as:
(a+b)+(a+b)/(a+b)²)+(_2/a-b)+(-b/(a−b)²)+
(a+b)?
(a-b)2/4ab/=(2/ab)
-206-
or:
(Z(a+b))+M((a+b))²+(Σ(a−b))+M ( (a−b))²+Z((a+b)² - (a−b)²)
=4ab
B-1010, Figure 309
Another solution giver by Mr. Fry (see
reference 19) also uses a combination of summarizers
and multipliers. As the diagram shows, the first
factor x is added to a constant (K), the second
factor y is then multiplied with (x + K) and with
(-K) in a second multiplier. The output of the first
multiplier (xy + Ky) and the output of the second
multiplier (-Ky) are then added to give xy.
At first sight, it appears a complication to
use two additional multipliers because one could argue
that, if it is possible to multiply (x + K) with (y),
there is no obvious reason why x should not be multi-
plied with y directly. The answer is that in the
device shown, it is possible by adding a constant (K)
✦
to obtain multiplication of and values of x,
including zero. This is, for instance, not possible
with a design as shown in B-108.
To put it in another way, the mechanism
permits a multiplication with a factor whose zero
point has been shifted (phase displacement). The
device can be represented by:
(K/x+K) + (x+K/xy+Ky) xy+Kj
+
/xy)
-Ky
(_X/-Ky)
<<
= xy
-207-
Σ(x+K) + M((x+K)y) + Σ((xy+Ky) −Ky)
= xy
B-1011, Figure 310
In many cases it is possible to reverse the
mechanism to obtain the ratio of the two variables.
A very unique solution of the problem (z = x/y) is
described by Mr. Fry (see reference 19) and calls for
a servo-mechanism with a zero output. This design is
particularly interesting as it has found a great
number of applications in mathematical analyzers (see
reference 17).
At first this solution appears impossible
as it requires that the result is to be fed back as
input. Perhaps the easiest way to visualize its
performance is to think of the trial and error method
which is extensively used in engineering problems.
solution is assumed and this assumption is changed
until the equation is finally satisfied.
A
The fact that a mechanism can solve such
problems is due to its speed and sensitivity and its
ability to correct in very small steps errors as they
result from wrong assumptions. The problem to be
solved being z
y is fed together with the unknown
X
y'
z into a multiplicator whose output will be yz = x.
At the same time, x is fed into a summarizer in series
with the multiplicator.
-208-
A servo-mechanism is used to maintain:
(zy - x) = 0
As the servo will continuously change (z), one of
the outputs of the summarizer, until the other output
requirement, i.e., zero is fulfilled, we finally
obtain the correct z value to satisfy:
X
y
It is most interesting to analyze the
stability problem of such a device, but this analysis
goes beyond the scope of the problem we are discuss-
ing. The pseudo "equation":
Z
M(y·z) + Σ(yz - x) = 0
is one possible way to represent the above mechanism.
B-1012, Figure 311
Frequently the multiplication is simplified
if other variables are used than the ones which have
to be multiplied. One of the most versatile devices
for this purpose is a Wheatstone Bridge, which, if
automatically balanced, establishes an equation of the
type:
R1
R2
R
R
with R1, R2, R3 and R, the respective resistances in
the Wheatstone Bridge.
•
-209-
their length, we have:
$1
S₁ = c₁R₁
C1R1
S₂ = c2R2
S3 = C3R3
S
4
= C R
4 4
For simplification, we make C1 = C₂ = C3
result:
As the resistances are proportional to
شما شه
We thus have:
With
11
=
31 $2
$1 = R3 = $3
S₂
RA
S
R.
1 =
R2
S
S
4
By making (S/S) equal to one factor, we obtain
S1 equal to the product CS2.
Wheatstone bridge also for division:
S.
R3
22-232-22-32
S3
R4
S
4
The equation suggests the use of the
indication of the ratio of
S1
$3
5, - 2 857-5
с $2
сн
4
with the
(equal to a constant (c), S, becomes an
6 no
-210-
2) Class B-2 Multiplication of Pressures
This problem is complicated by the fact
that there is no physical effect known which gives
the products of two pressures directly (B-2b). How-
ever, it is possible to use (B-2a) type multipliers,
i.e., multipliers which introduce a numerical factor
and to make this numerical factor proportional to
another pressure.
B-201, Figure 312
This is a variation of the Wheatstone
scheme.
Ap
flow
If the resistance, which is expressed by
is independent of flow, which is correct
for capillary tubes (but not for orifices), we have
zero differential if:
R =
ΔΡΙ
AP 2
ΔΡ
AP 3
DP 4
or AP1
B-203. Figure 314
AP3AP2
Др
L
B-202, Figure 313
This Figure shows a self-balancing fluid
type Wheatstone Bridge. It is understood that the
restrictions shown are capillaries.
The lower right-
hand diagram indicates one possible design of a
variable capillary tube.
A representative of the pressure multiplier
in which one of the factors is a stroke is B-203.
-211-
(a)
The pressure (P) is applied to a diaphragm and thus
translated into a force (P₁/F₁). A hydraulic jet is
deflected and increases (P₂) until the translator
(P2/F2) produces a force (F2) which balances F₂
against F₁. Thus far the design is a (P/P) translator,
type 3d.
To change the ratio (P1), a double lever
arrangement with fulcrums (A) and (B) is provided
with a spacer (C). A displacement (S) changes the
ratio of forces (→ 1) which are necessary to balance
2
each other and thus the ratio
P.
The multiplicator, therefore, multiplies
the two inputs S₁ and P₁ with the result P₂.
1
B-204. Figure 315
In Figure 315 the displacement (S) is
produced by means of a (P/S) translator, type (4) d
with the result that P1 and P2 are multiplied to
P.
give the output (P3).
B-205. Figure 316
A very simple variation of the above
method is to change the resistance for a constant
flow. In this device a pressure drop Ap₂ is:
f(s) x AP1
cf (P3), we obtain:
AP2 CAP1 AP3
By making (s)
= cf
=
I
!
-212-
A typical application of such a device is
an automatic density corrector (for constant air
weight control) which responds to changes in baro-
metric pressure as well as to changes of absolute
temperatures.
B-206, Figure 317
By bleeding fluid between two orifices
in series, across which the total pressure drop is
maintained constant, one can multiply the output
of a (P2/P1) translator (see reference 48).
The amount of bleeding is again a function
of (S) which in turn can be made a function of any
other variable, including (P). The device gives two
outputs (P2) and (P3) and the value of (P3) becomes
equal to (P1) times f(s).
3) Class B-3 Multiplication of Forces
Again there is a lack of laws which give
the product of forces directly although there appear
to be some exceptions. The Newton's law of gravita-
tion gives a force of attraction between two masses
(m1) and (m2) which is:
F1
m1 x m
r2
with (r) representing their distance from each other.
However, it is questionable that this law offers
practical applications.
12
-213-
.
B-301, Figure 318
More encouraging appears the attraction
of two magnetic fields which are produced by propor-
tional ampere turns.
mi• m_i
1-1
x2
2 2 = F
3
B-302, Figure 319
A similar device can also be built if two
capacitors are used whose charge do not affect each
other and whose distance is (r). If the potentials
(e) are made proportional to forces, the attraction
between the two capacitors will be:
Fix F
1
011 2 = F3
2
C1-
2
r
B-303, Figure 320
The simplest and oldest multiplicator of
forces is the lever, man's first tool. By changing
the ratio of lever length between the input and the
output force, any ratio can be obtained. The change
of the ratio, however, calls for the parameter (s).
Thus, in its simplest form the multiplicator multiplies:
F1 x f(s) = F2
B-304. Figure 321
By making (s) again a function of a force
(F2) which can be done by a (F/S) translator, type 5d,
-214-
we obtain B-304. With this device we get:
F3 = F1
x f(F2)
and, by means of a suitable mechanism, a cam or a
similar arrangement, we can get:
CF 2
f(F₂) to be =
and finally we obtain:
B-305. Figure 322
F3 = F1 F2
Figure 322 shows a modification of such
multiplier which introduces a pressure as an inter-
mediate parameter and which hereby offers another
solution for a class B-3 multiplicator. Obviously,
f(s) can be made again a function of any variable
including (F) and we obtain:
F1 x f(s) = F
F1 x F2 = F3
variable = F
It should be noted that as any variable
can be translated into any other variable, this
device could be used for:
F1 x any variable = F
3
or, more generally, any variable times any other
3°
F3 or with F2 = f(s)
General Conclusion
The above analysis of multiplicators esta-
blishes the fact that (Ba) class multiplicators are
-215-
translators of the type which have the same input
and output variable.
They are represented by the
diagonal of our translator map, which starts in the
left-hand upper corner and extends under 45° into
the right-hand lower corner.
These translators can be made into devices
of class (Bb) by making the multiplication factor a
function of the same variable.
4) & 5) Class B-4 and B-5 Multiplication of First
and Second Derivatives
These multiplications can be reduced to the
operation of multiplying strokes (if the derivatives
are translated into strokes, see class D) or of
multiplying electrical values.
of:
6) Class B-6 Multiplication of Flow Rates
x w2
Generally, this problem is again first one
1
1
= constant (class Ba)
IN 2
and second, one in which the constant is a function
of another variable and in particular, of a third
rate of flow:
W₁
=W2W3 (class Bb)
-216-
B-601, Figure 323
Known under the trade name "Flow Deviator",
this instrument was developed to measure pulsating
flows with varying static pressures. In order to do
this, a partial flow (w₂) is deviated from the main
stream in such a manner that there is a definite
constant ratio:
с 2 (e.g., 1/1000, 1/10000, etc.)
1
This is accomplished by means of two orifices (S₁),
(S2) and a needle valve (A) which is controlled by
means of a diaphragm (B).
An increase of differential across S
$2
opens the needle valve (A) until the down stream
pressure behind S₁ is equal to that behind S₂• If
this is accomplished, the two flow rates (w₁) and (2)
1
are directly proportional as the pressure drops across
S1 and S2 are the same; the static pressure at the
upstream side of S2 and S₁ is the same; and also the
temperatures at both orifices are the same.
As the flow (w₂) expands to the atmosphere;
2
i.e., to a constant outlet pressure, its volume re-
presents flow rates at atmospheric conditions regard-
less of variations of line pressure and temperatures.
Its rate can be measured by means of capil-
laries, orifices, Rotameters and integrated or metered
-217-
with domestic type gas meters.
The factor (c) can be made adjustable by
varying S₁ or S2 and by making it a function of
another variable, the device can become a (Bb) class
multiplier.
B-602, Figure 324
The multiplication:
W
= W
3 W1
W₁ • f (w₂)
is accomplished by a regulator arrangement as shown
in Figure 324. A typical application is the change
of a mixing ratio of two fluids as a function of a
fluid rate of a third fluid.
In particular, if w₂ is a constant volume
rate, the device is used to change the ratio of two
flow rates, (w₁) and (w2), in accordance with the
density of W2°
w (The differential pressure obtained
from a constant volume ratio (w₂) is a function of
the density of w₂.)
Device (A) is a translator of the type
(P/S), type 4, and device (B) is a translator (P/P),
type 3. The latter is equipped with a force multi-
plier class (B-2).
-
The whole mechanism can be described by
a block diagram as shown in B-602a, Figure 325, or in
-218-
7
written form:
M(((w2/P₂) + (P₂/S)) • (w₁/P₁)) = P3 + (P3/W3)
or:
M((w₁) ► f(w₂))
f(w₂)) = (W3)
7) to 10) Class B-7 to B-10 Multiplication of
Electrical Variables
cussed before.
The most convenient multiplying device is
the Wheatstone Resistance Bridge which we have dis-
Unfortunately, it is somewhat
difficult to translate electrical values into
resistance values. It can be done by heating the
resistance of the bridge by means of a current.
Resistances are thus obtained which are a function
of the current applied (see Bb).
The disadvantage of such systems is that
its rate of response is relatively slow. This can
be overcome by replacing the resistances by triodes
whose internal resistance changes with the grid
voltages which are applied (see Figure 326).
The range of such a multiplier, which
again is of the self-balancing type (note the para-
meter (8)) and has to fulfill the condition:
R₂
مجھے
اچھ
+
سلام
R
is limited and its reliability depends on the
$
-219-
individual tube characteristics which unfortunately
change with time.
Most of the multiplicators used in com-
munication and radio circuits, which are used to
multiply current and voltage values, are of the
triode type.
On tubes of the beam deflection output
current is directly proportional to the deflection
of the beam as well as to the grid voltage. Hence
simultaneous variation of both produces an output
current which is their product.
Another approach to the solution of the
problem of multiplication is to use light intensity
(Q) as an intermediate parameter. If, by means of
a (variable/light intensity) translator, an output
is obtained which is retranslated into resistance
or voltage (Phototube), bridge circuits and tube
amplifiers can be used to obtain the desired pro-
ducts.
More generally any radiation energy; 1.e.,
light, heat or electro-magnetic waves, can serve the
same purpose and the parameters can be changed back
and forth to obtain the optimum solution.
-220-
A more detailed study of these devices
would cover television, radio, radar, and thus go
far beyond the aim of the present survey.
Perhaps it is best to formulate the result
of this chapter in the following way. A.C. and D.C.
"amplifiers" can be used for multiplying electrical
signals.
As any amplifier" is a "multiplier" of
two factors, it is up to the designer to translate
either one of the two variables he intends to multiply
with each other into the ones most convenient for his
particular purpose.
B-701, Figure 328
As a start to fill in all of the multi-
plicator boxes, another device is shown whose
function is based on the law that two conductors
attract each other with a force proportional to
the product of their respective ampere-turns (see
reference 11). It is, therefore, possible to
build a device which first multiplies two currents.
Its resultant output is a force and this force can
be retranslated into a current.
+ (F/13) = ((1¸· 12)/23)
(M(11/12/F) + (F/13)
In Figure 328, a Kelvin balance is used
for this purpose. A lever (L) is supported by means
-221-
of a bearing and carries two sets of coils which
produce opposing moments.
The current (11) which flows through
coil (1) and its attraction to the current (12)
which flows through coil (2) is balanced against
the attraction of coils (3) and (4) with the
respective currents (13) and (14).
An "Electronbeam tube" (B) (see reference
12) controls the current in coil (3) in response to
a relative displacement of magnets (1) and (2).
When balance is obtained, we have:
C313 = c111 x 212 (with 14
= constant)
It will be noted that the factor (cz) is proportional
to (1,) and thus permits the introduction of an
additional factor. If, for instance, c₂ is made
C3
proportional to 13, C3 = C4¹3.
i
2
с
4-3 C111 x C2¹2
=
and we obtain a second power output or, 1, is equal
13
to the square root of the right-hand side.
The ease with which second power and
functions can be obtained with this device makes it
particularly useful for instruments for flow measure-
ment where this problem is ever-present due to the
Bernoulli flow equation.
(cw² = AP)
-222-
B-702. Figure 329
If the use of stroke as an intermediate
parameter is not objectionable and the Wheatstone
bridge is not practicable as it calls for a servo-
mechanism, the solution shown in Figure 329 is
applicable. By shunting a resistor, the distri-
bution of currents through the shunt follows the
law that:
1-1-b
R2
#
By making R₂ a variable, we have a means to change
the proportion of the shunted current. This intro-
duces the parameter (S) in the form of a translator
(S/R). By adding a translator for (1/S), we obtain:
i
1₁ = M((12) · (13))
(13/S) + (S/R)
B-901. Figure 330
(13/R)
As an example of how the device B-701
can be used to obtain the product of two voltages,
the Figure 330 has been drawn.
First, two currents are obtained which are
proportional to and e
e2 e, respectively. The first
translator (e₁/11) uses a beam tube as it permits
the establishing of a current without draining of
the charge (e₁). The second translator (e2/12) 18
merely a resistor.
•
-223-
A permanent magnet is used instead of (14)
of B-701, and a "Beam tube" to produce a current
and e21
(13) which is the product of
el
we obtain:
By an additional translator (R) (not shown),
ез 1° €2)
= M
The device uses currents (i), forces (F), and strokes
(S) as intermediate parameters, with a servo establish-
ing:
(ES
= 0)
=
11) Class B-11 Multiplication of Temperatures
B-1101, Figure 331
The multiplication of temperatures is parti-
cularly easy to obtain if a Wheatstone bridge is used.
As the resistance of many materials changes directly
proportional to its absolute temperatures, we obtain
a balance of the bridge for:
3-3
©1F1 = £3T-
C₂ T2 C, T
4-4
and thus: C1T1 x C4T4 = ©2T2
is obtained when:
C373
13) Class B-13 Multiplication of Resistances
B-1301, Figure 332
This is again the Wheatstone bridge. Balance
R₁ = R
R₂
R
X x C
4
-224-
As this device has been dealt with before, no further
discussion appears necessary.
Light intensities, inductances, capacitances,
phase angles, magnetic fields, electric fields, and
frequencies can always be translated into mechanical
or electrical parameters and thereafter that mode of
multiplication can be applied which appears most
economical or suitable for the particular applica-
tions.
It is desirable to fill eventually all of
the individual boxes with possible solutions whenever
such devices are developed or described in the liter-
ature. If need be, there is, however, always at
least one solution available with the materials so
far presented.
.
-225-
(C) nTH POWER OF A VARIABLE*
By definition, we obtain the nth power of a
variable by multiplying it with itself as many times
as (n) indicates. Thus, we can reduce our problem
to that of class (B); i.e., multiplication, stipula-
ting however that the factor with which we multiply a
variable is in each operation the same variable.
Nothing new would be added by repeating our
analysis of (B) with this modification. However, there
are certain relationships which give us 2nd and higher
powers of a variable direct, and it is the purpose of
this chapter to indicate some of the outstanding
examples in this category whereby it is possible to
greatly simplify the problem of design at hand. For
the sake of completeness, however, we shall also give
a few examples of the straight-forward solution in
which a variable is multiplied by itself.
C-101, Figure 333
(S/s²) or (S/√√☎): In the variable speed
gear shown in C-101, a stroke (or a corresponding
angle) (S1) is introduced and simultaneously the
transmission ratio changed proportional to S₁. As
a result of this, the angular motion (S₂) of the
output shaft will be cS or by interchanging input
2
* see reference 41
my
-226-
and output shafts, we shall obtain:
(§₁/§¸²) and (§¸/√§])
we obtain:
By putting a number of such units in series,
(§¸§¸³) (§¸/§¸¹·5) (S₁/4/5₁) etc.
1.5) (81.
C-102, Figure 334
An obvious variation which is very often
used in instruments is a cam which among other func-
tions can give 2nd, 3rd, 4th, or any other power.
The limiting factor is usually the range of the total
travel which limits the possible accuracy for the
lowest value of the output one is interested in.
C-103, Figure 335
By the use of logarithmic cams, the pro-
blem (as in algebra) can be reduced to summarizing,
that is to the use of operations of class (A) and the
use of multiplicators of class (B). The schematic
diagram is self-explanatory and it is evident that
by making (2)
(물​) a variable, a device of this type can
be made to give wide ranges of n (끝​).
C-104, Figure 336
A solution which has been frequently used
in electrical calculating devices produces an output
voltage which is proportional to the square or higher
:
1
-227-
power of the input stroke. By using two or more
potentiometers with mechanically linked sliders,
the output voltage becomes in the first stage (es),
in the second, (es²), and (es) in the nth stage.
The output voltage can then be translated into any
variable including S.
C-201. Figure 337
Second or 1/2 power functions of (P) can
easily be obtained if (P) represents flow rates (w₁).
In accordance with the Bernoulli equation, we have
for turbulent flow, i.e., for high Reynolds numbers,
a pressure drop across a restriction which is:
P = cw2
Our problem, therefore, is first to trans-
late the variable into a directly proportional flow
rate (w) and then to measure this flow by means of
an orifice. In this connection, it is well to re-
member that a direct proportionality between pres-
sure differentials and flow is obtained by the use
of capillary tubes (laminary flow region low
Reynolds numbers).
U
-
To illustrate this approach, we use a
force (F) which turns a jet pipe (1) until the
pressure drop across a capillary cartridge (2)
-228-
results in a pressure drop, AP, which applied to a
diaphragm (3) and hereby re-establishes balance.
(F₁/S)+(S/w¸)+(w₁/^P₁)+(AP₁/F2)+(W1/AP2)
F1
-
c F2
#1 C1F1
=
AP2
c212
c(F₁₂) 2
AP2 вс
By translating AP2 into F2, we can get translator
(F₁/F₁²).
C-202, Figure 338
The force (F) is replaced by a pressure
(P₁), and the device will give directly the square of
the input (P₁).
(P₁/P₁)²
2
The limitation of this device is that a
capillary tube is liable to cause difficulties in
an actual device which calls for accuracy. First
of all, it is hard to keep clean and second, its
resistance to flow is a function of the viscosity of
the fluid and thus greatly affected by its temperature.
C-203. Figure 339
By changing the sequence of the orifice
and of the capillary tube, we obtain a design as shown
in Figure 339. Its output is ✅ of the input pressure.
(P₁//P₁)
-
-229-
C-204. Figure 340
To overcome the difficulties experienced
with capillary tubes, one possible solution is
given by the use of a variable orifice. In general,
flow rates (w₁) can be measured by means of a fixed
restriction and a resulting varying differential
pressure with:
P1
cw₁ (capillary)
C=1
P1
cw₁
(orifice)
or one can vary the orifice size while maintaining
a constant differential.
Such devices are (w/S)
translators.
2
Obviously, it is also possible to have
a combination of both solutions; 1.e., a device
which automatically changes its pressure drop as
a function of (S) and thus also of (w).
In Figure 340, such a device is built
on the well-known "Rotameter" principle, (see
reference 29). The weight of the plug (1) which is
carried by the impact of the flow (w) and the
resulting pressure drop (P₁) is varied by connect-
ing the plug (1) to a float which immerses in a
fluid.
A cylindrical float (wire) in mercury as
shown gives a relationship of:
1) AP₁ = c√
ΔΡΙ
-230-
:
By measuring the same flow rate with an orifice,
we obtain:
2) AP2
Thus, for the same (w), we obtain the relationship;
AP₂ = cm²
ΔΡ crop² = c(AP1
2
c(AP¸²)² = c(AP₂)4
2
and it is only left for us to make
to P1 or any other variable.
=
c#2
W1 proportional
In passing, it may be stated that by shap-
ing float (2), other relationships can be obtained.
C-401. Figure 341
ds
dt
If the value represents angular speed
or velocity, it is convenient to use forces which are
the square of the speed (kinetic energy) in order to
obtain second power function. This approach is
basically the one discussed in the examples, C-200,
etc., as it is kinetic energy which is measured by
means of restrictions.
A variation of this approach is the use of
centrifugal forces which are the square of the angu-
lar velocity of rotating masses. In the "Transometer"
of Figure 341, the speed of the input shaft produces
ds
centrifugal forces (F) which are the square of de
These forces are translated into a pressure (P) or
could be translated into proportional speeds by means
of an additional (P/de) translator, e.g., a pressure
controlled variable speed gear.
dt
-231-
The output would then be:
((ds/dt)/(ds/dt)2)
C-701. Figure 342
The attraction of two coils with indivi-
dual ampere-turns of n₁11 and n212 is equal to their
product divided by their distance. By using the same
current (1) in both coils (n₁) and
(n2), we obtain
an output:
131,2
(11/112)
The hydraulic translating relay can be
replaced by pure electrical or electronic circuits.
C-1101, Figure 343
In the field of temperature measurement,
a useful relation is that the radiation of heat is
proportional to the 4th power of the temperature.
Such temperatures are picked up by radiation pyro-
meters (T/e) or (T/8) translators.
As the resistance of metallic conductors is
proportional to the first power of temperature and
as the resistance of special materials, thermistors,
resistors, etc., is proportional to the
1
nth power of
the temperature, it appears that a wide variation of
nth power function can be obtained by using tempera-
tures and resistances as intermediate parameters.
..
-232-
This is actually done, but by necessity,
such devices are in general limited to low frequency
problems due to their inherent slowness of temperature
penetration.
It seems sufficient to outline the approach
only, and leave it to time and to further systematic
studies to fill out all boxes with possible solutions.
Nothing basically new, however, would be
added by doing this, as the previous chapters show
how to proceed in a specific case.
-233-
(D) DERIVATIVES
Devices for obtaining the rates of change of variables
Before discussing some of the possible
solutions which are available for this purpose, we shall
briefly review the meaning of the term "derivative".
(see Figure 344)
Given a curve f(x) = y, and stuaying its
growth at the point xy, we find that for a small
value of ± ▲x, there are two values, y ±▲y.
As an approximation, we can say that the
relative increase of Ay in comparison with Ax can be
expressed for the point xoyo by the ratio (R).
Av
(P₁ or 2) = Ax
with two values for it, depending on whether we have
chosen Ax > or < 0.
anu we
By decreasing the magnitude of Ax, we finally
obtain a limit value where R₁ is equal to R
describe this limit value by the symbol dy, and call
1
it "the first derivative of the variable (y) at the
point x".
From this elementary definition follows
one of the possible means of obtaining derivatives,
at least a first approximation of derivatives.
-234-
magnitude of the difference:
(y
+ Ay) - (y)
x = constant
If we choose a constant value of Ax, the
is a measure of the desired value and will approach
dy
the limit value
dx'
are relative to the chosen interval Ax or the smaller
is Ax.
$
curves.
If we are, therefore, able to design a
memory device and compare in constant time intervals
the latest value of the variable with its preceding
one, we obtain a device which gives us the first
approximation of a derivative.
(x +
In a graph, Figure 345, it means that the
variable y = f(x) is displaced against the origin of x
by an arbitrary value Ax and the differential ratio (R)
is obtained by the difference of the ordinates of both
dy
the less the rate of changes of dx
The approximation is to be correct for
즐​)
as the average value for the given interval ▲x.
A typical choice giving directly this value
of +f(x + 4x) f(x) with Ax = constant is the inter-
mittent type of potentiometer as they were manufactured
by companies like Brown Instrument Company, or Leeds
and Northrup before the arrival of continuously self-
-
-235-
balancing circuits with Ax either extremely small
(electronic control) or not a constant.
In this older type of potentiometer, the
recorder pen which indicated the variable was mech-
anically blocked for a given period of time and thus
preserved the "memory" of the previously measured
variable. As soon as the simultaneously locked
galvanometer was freed, it indicated by its angular
displacement the difference of the variable f(x + Ax) − f(x).
On the basis of such an approach, it is
obvious that various designs can be built using inter-
rupters and locking devices in combination with
summarizers to obtain differences, etc.
All of these methods are practically limited
12y
to processes of low acceleration
where t does not
necessarily represent the variable time.
dt
This simply follows from the fact that if
Ax is finite, the method cannot give values of
y changes up and down within the range of Ax.
dy yet if
dt
It is, therefore, obvious that rate of
change devices are the better, the less Ax becomes,
and finally their output will tend to become equal
dy
or ~ to
dt
for Ax = 0.
-236-
Following our above line of thinking, we
shall obtain such a device by producing a time phase
There
displacement of the variable against itself.
are a great many of these devices which can be varied
to make them most applicable for the particular variable
the designer is interested in.
They all have in common a device which has
capacitance (see reference 8) and a summarizing device
which obtains the difference between the actual value
and its delayed predecessor.
1) Class D-1 ds/dt Devices
In the pilot valve which we have discussed
as an (S/S) translator, type ld, the output (S2) is
directly proportional to the input (S1). The displace-
ment (S3) must be zero in a steady state condition and
ds
will be a function of during a transient.
at.
The function f(s) will depend upon the
shape of the ports, their viscosity and the pressure
of the fluid and the design of the cylinder.
ds.
dt
c53³
= CS
we have
For proportional speed,
as a transient a pure exponential function similar to
the charge of a condenser with the displacement (S3)
directly proportional to ds1.
dt
;
-237-
D-101, Figure 346
This brings us directly to our first example
of an operator class (D), a derivative device which
gives an output (ds), expressed in the variable (S).
f(t)
S

ds S,
D-102. Figure 347
at
In this particular mechanism, we have to use
the variable time for the x axis. This is due to the
fact that the speed of the piston of cylinder (2) is
S.
proportional to the displacement (S3)
(S3) or that S, is an
indication of piston speed (d2).
dt
In Figure 347, a pure bred mechanical solu-
S.
2
tion is shown. The delay of S₂ relative to S₁ is
1
produced by means of a variable speed drive. The
output speed of this drive is proportional to the
displacement of S, and therefore, a phase displace-
ment is produced which is measured by means of the
summarizing device (whiffle tree) of class (A-1)
which deducts S₂ from S1 until 83
is zero.
By varying the input speed (n) and the
gear ratio between the output of the variable speed
device ((S/W) translator), the constants of the
mechanism can be changed. n₁ Must not necessarily
be a constant speed, but can represent another vari-
able which is fed into the mechanism.
-238-
D-103. Figure 348
The same idea is varied in Figure 348. The
stroke (S1) is the motion of a plunger (1) which dis-
places a liquid in a cylinder (3). By connecting this
cylinder (3) with a cylinder (4) through a pipe with a
restriction (2), a phase displacement (S3) is produced
which is a function of d ds. S₂ can be easily measured
$3
dt
by means of a (AP/S) translator (flow meter type
instrument).
D-104. Figure 349
A different approach to the problem of
measuring derivatives is given in D-104. In this
design advantage is taken of the tendency of a roller,
which has two degrees of freedom, to adjust itself in
the direction of the vector sum of speeds at its
point of contact.
In Figure 349, a roller (2) mounted in a
fork (3) and rotatable around axis (A-B) can also be
moved in the direction of bearings (D-C). With
cylinder (1) rotating at a speed (n), which produces
a circumferential speed (u) and a speed vector d
xx
(perpendicular to (u)) which is parallel to the
ds
dt
axis of cylinder (1), we find:
tgx = and with =
14
constant tgα = c(de)
This makes it possible to read the angle () as a
ds
dt
น
function of v
X
4
露
​-239-
The device has the advantage that the
constant (c) can easily be varied by changing the
speed of the cylinder (1).
D-105, Figure 350
One of the most versatile methods for
ds
dt
doc
obtaining
is the one using a gyroscope.
dt
gyro responds to a rate of turn of one of its axis
with a moment around an axis perpendicular to the
first axis and perpendicular to the axis of the
rotation of the gyro. This moment is directly pro-
portional to its rate of displacement. This moment
or force can be translated into (S) by means of any
(F/S) translator; e.g., by a spring.
or
D-106:
A
Using springs as a (F/S) translator has the
disadvantage that for a sudden change of the direction
of dat the mechanism has first to move through zero.
This produces an additional phase which in many cases
is objectionable.
For this reason, it is better to measure
(F) as (d) and to translate (F) into (S) with a
translator of type (c) or (d) which avoids or reduces
the displacement of the gyro in spite of producing a
final (S) if this is the desired output of the device.
Because as is a speed or velocity vector, we
find a whole group of solutions for d as the input and
-240-
any variable as the output; i.e., the corresponding
translators of the type (d/variable). All these
belong into class D-106.
D-107:
By the same token, we may find satisfactory
solutions in the translator types (w/variable) if we
remember that w/area = ds/dt represents a speed vector.
These translators belong, therefore, into class D-107.
2) Class D-2 - dP/dt Devices
In discussing ds/dt devices, we have found
in D-103, Figure 348, a simple solution for dP/dt
problems which can also serve as a D-2 device if S3
represents a Ap. Obviously, any one of the class (D)
devices with any variable as output can become a class
D-2 mechanism if the final output variable is trans-
lated into P. A repetition of all these possibilities
would not offer any basically new solution.
(
Only one design should be mentioned as it is
widely used in rate of climb meters for planes, and in
rate of change devices of automatic controllers. It
is based again on a phase displacement of pressure in
time.
D-201, Figure 351
A schematic diagram, Figure 351, shows two
chambers (1) and (2
=
2a) separated from each other by
-241-
means of a bellows (3). A capillary tube (4) connects
these two chambers. If (P) changes at a rate of dP/dt
volume of air has to move into or out of chamber
(2 + 2a). The difference of pressures in (1) and
(2 + 2a) is proportional to the rate of flow of air
through the capillary and as the final volume of air
in (2 + 2a) is proportional to the absolute pressure
(P), we have:
Ap = f(dP/dt)
With a translator (AP/F) and (F/S), we also have:
F = f, (dP/dt) and S = f (dP/dt)
1
2
D-202. Figure 352
In the operator D-202, the primary pressure
(P1) is translated by means of a fluid relay (or
regulator) into a directly proportional pressure
equals P₁. The device has a capillary restriction
dP1.
(3) which produces a pressure drop Ap =
clat
(P2)
EP1
dP₁
P₂ + clat
2
It will be noted that P. is the sum of
3
a value which is often needed for control
P represents the controlled
1
patent #19,276). With P or F as
applications if P
P2
variable (see U. 8.
inputs, this mechanism can be used with any translator
where the output is P or a force (F).
3) Class D-3 - dF/dt Device
D-301, Figure 353
We can use D-202 as a class D-301 operator
with F taking the place of area times P of a D-202
-242-
design.
devices.
This gives us one example for class dF/dt
Obviously, any translator of (F/variable)
d variablel
/variable) in series gives
with a (ª
dt
further solutions for this problem.
4) Class D-4
D-401, Figure 354
d(ds/dt) Device
dt
Mathematically speaking, the above devices
(d(ds/dt))
). It is
give second derivatives (d2s/dt2)
therefore logical to look for solutions first under
accelerometers; i.e., devices measuring d2s/dt2, or
in general, for translators of the type (d2s/variable).
at2
Such "accelerometers" will be classified as D-401.
Obviously, the second derivative can also
be obtained by a two step or series arrangement of
two class D-1 devices.
(d/variable₁)+(d(variable)/variable)=(ds/variable)
Such an arrangement, however, does not constitute a
new class, but is only in series arrangement of two
operators.
5) Class D-5 ·
-
(dª²s/at)
dt
(૨
Again, such devices can be obtained by three
derivative operators in series or a derivative in
series with a class 4 operator.
-243-
d (d²s)
dt2
ȧt
D-501, Figure 355
a³s.
at 3
In a simple variation of D-401, we have
The design
d2s
2
a P which gives dF/dt with F =
1
calls for no additional explanation.
dt
6) Class D-6 - (dw/dt) Device
These devices are either treated as class
W
area
(a²s/dt²) devices of class D-4, as (—) is propor-
tional to (ds/dt) or they can be obtained from other
classes after a suitable translation (w/variable) has
been accomplished. The choice of the translation
depends on design specifications and limitations.
For instance, for high frequencies (high
rate components) electrical methods will prove most
suitable while for low frequencies force or stroke
translations may be preferable.
S
D-601, Figure 356
An obvious modification of D-401 would
accomplish the operation (dw/dt) by placing the
carriage of D-401 into a float, a ship, or into a
balloon, which has the same speed (ds/dt) as the
current, the acceleration of which has to be measured.
Other solutions follow from series operation.
(d/variable₂)
(w/variable₁) + (d(variable])/variable)
-244-
7) Class D-7 (di/dt) Devices
There appears to be no merit in repeating
the above approach for each variable as our analysis
even at this point appears to be sufficient to prove
the availability of at least one solution for any
class (D) device.
We shall, however, mention examples for
electrical parameters as input and outputs not only
on account of their general importance as inertialess
devices (high frequency), but also to follow through
with the approach we have found so helpful in analyz-
ing the translator map.
D-701, Figure 357
For electrical solutions, it is fortunate
that there exists the fundamental law:
L(di/dt)
This induction law gives us a simple and most con-
venient solution for our problem of differentiation.
e
=
D-701a, Figure 358
Second and higher order derivatives can
be obtained by repeating the operation with the
same circuit.
8) Class D-8 - (di/dt) Devices
This problem can best be solved by reduc-
ing it to a class D-7 operation by the use of a
-245-
"rectifier"; 1.e., a (1/1) translator ahead of the
class D-7 device.

9) Class D-9 - (de/dt) Device
While the same solutions as those for
class D-7 can be used, quite frequently the basic
method of delaying the variable and comparing its
delayed value with the present value is used for
voltage differentiating circuits.
D-901, Figure 359
It is interesting to compare the circuit
D-901 with D-202, Figure 352, to see the analogy of
the individual elements. The capillary resistance (B)
of D-202 becomes (R) of D-901. The capacitor (2) of
D-202 finds its counterpart in (C) of D-901.
The voltage across the resistor (R) is
proportional to de/dt.
10) Class D-10 (de/dt Devices
These devices like those of class D-8 can
be reduced to devices of class D-7 and D-9 by the use
of rectifiers.
11) Class D-11 - (dT/dt) Devices
D-1101, Figure 360
A rather simple solution in this class is
also based on the delay principle. In this instance,
-246-
a mass is used to act as capacitor for the heat
flow. The device does not offer anything basically
new, but is added to show how the basic concept is
identical in devices which appear as different, as
for instance, D-101, D-202, D-901, and now D-1101
(figures 346, 352, 359, and 360).
The thermocouples produce voltages pro-
portional to the absolute temperatures (T) and (T₂).
As the mass of the thermocouple (1) is negligible,
its voltage represents at all times the temperature
of the fluid (w).
Due to the thermal capacitance of thermo-
couple (2), the voltage (2) lags behind (T₁). The
difference (measured by means of a suitable summarizer,
class A) thus becomes an indication (or an approxi-
mation) of dт/dt.
12) Class D-17 - (dH/dt) Device
(
D-1701, Figure 361
In accordance with the fundamental laws
of the electrical field theory, we obtain a voltage
whenever a magnetic field varies. This voltage is
directly proportional to the rate of change of the
field (H). It is, therefore, easy to design a device
which gives us:
e = c(dH/dt)
-247-
This is the underlying principle for the solution
of D-701 and D-701a.
13) Class D-18 - (dE/dt) Device
In the same manner, a magnetic field is
produced by a change of an electrostatic field
which manifests itself as a current. We have thus
dE/dt = 1 = CH, and a device for measuring H will
give us the rate of change of the electrostatic
field (see reference 7).
i
-000---
The above concludes our discussion of
devices available for differentiating variables
and our analysis has shown that at least one solu-
tion is available for any class.
As in the case of the translator map,
the choice of the mechanism which is finally used
will depend on the individual specifications which
have to be fulfilled.
It remains only to discuss class E
devices to complete our study of devices which
are available for the major mathematical operations.
-248-
(E) INTEGRATORS
These devices fulfill the purpose of
solving the equation:
input
output = variable
Svariable dt, or,
output = variable d variable2
We shall use for a symbol:


Sat
output
or,
S
variable dt/variable)
if t is the independent variable, or,
sdt
dt (s)
s
(variable₁/d(variable)/variablez)
in the most general form. We shall limit ourselves
again to the discussion of some typical examples as
we know that any variable can be translated into
any desired output variable and that thus at least
one possible solution is available.

1) Class E-1 -/ds/dt Device
To start with the mechanical solutions,
we have a simple integrator in the device shown as
E-101.
E-101, Figure 362
The operator E-101 consists of a (S/v)
translator and/vat indicator which can be a counter,
a spindle with an index, or any other device which
gives the total number of revolutions of the output
shaft. With this device, we obtain an output S =
w/s dt.
w/.s
-249-

2) Class E-2 - Pat Device
E-201:
By translation of P into S, we can use
the E-101 integrator for integrating pressure over
time intervals. This gives us at least one solution
for E-201. (Integrators of flow rate meters with (w/P)
translators "orifices").
-

3) Class E-3 -Fdt Devices
E-301, Figure 363
The basic equation for one possible solu-
tion is Newton's:
mv
at
= F
This means that Fat = Amv and with m a constant,
/Fat = n(v₁ = v。). Advantage of this equation is
taken in ballistic galvanometers in which v₁ or
V1
*cs² where
mv, 2
rather is converted into Sc 8ds =
2
S is the motion of a pointer and c the spring constant
of the galvanometer (see references #15 and #16).
E-303. Figure 365
E-302, Figure 364
It will be noted that the example given
later in E-501, Figure 367, can be modified to give
a Fat device by tilting the tube in such a way
(angle) that F is the desired variable = mg sin ♂.
Another basic solution uses the fact that
a gyro will precess at a rate (v) which is proportional
-250-
to the magnitude of an applied moment. By using an
integrator of class (4) to give våt (revolution
counter of a mechanism whose speed is proportional
to v), we obtain the integral of the applied moment
or with a fixed lever for the force/Fo
Such a device is used as an integrator for
at least one flow meter (Simplex) and for automatic
correction of position of a gyro axis in reference to
a desired space coordinate system. In one of such
designs, an electromagnetic force produces the
precession; in another, air jets produce dynamic
torque moments which cause the precession of the gyro
(Sperry Gyroscope Co.).

4) Class E-4-as dt Devices
ds
dt
E-401, Figure 366
This device is part of E-101 as the output
of the friction drive is equal to:
ds
Svat =/as at = s
A typical example for such a device is the "total
mileage" indicator of an automobile.
5) Class E-5-aat Device
dt
dt
By integrating acceleration over time, we
obtain a value representing speed. Unfortunately,
the accuracy is affected by the accumulative error
-251-
which is inherent in all integrating devices.
E-501. Figure 367
This device shows an example of an
"absolute speed" indicator which is based on the
following translator chain arrangement (refer
U. S. patent #2,399,420).
d2s
/F) + (F/1) + (√1.at/S) =²sat/s = (v₂/S)
dt2/F)
=S
dt
I
watthour meter for
constant voltage
This device gives absolute speed of a
floating body at any time regardless of drift if
the absolute speed at the beginning of the experi-
ment is known.

+
6) Class E-6 - wat Devices
This class covers a great number of dif-
ferent devices which may be classified as accumulators
which convert the kinetic energy of the moving mass
my2
produced by w (with v.area = w) into potential
2
energies.
As by necessity, there are losses to be
taken into consideration and thus we have the energy
equation:
kinetic energy potential energy loss = constant
In this sense, one can in general speak of
an integrating device whose output is proportional but
not directly proportional to the input over time or
-252-
over any other variable. This is similar to our
experience with translators where we distinguish
between types a, b, c, d.
In the same sense, we can speak of
operators of type a, b, or c, and d, if addi-
tional sources of energy are being used.
We also have devices of the type which
translate w into ds/dt (so-called "positive dis-
placement meters"), for instance, which reduce
our problem to one of class E-4,/vat.
E-601, Figure 368
Of the latter class, is our example.
Such devices are used for accounting, billing, or
totalizing liquid flows, and are particularly common
in the fuel industry for measuring gas or oil where
the consumption of total fuel has to be charged to
the individual user, or where correct proportioning
of fluids is essential.
E-602, Figure 369
Instead of producing a number of rota-
tions which give a final output (S) in number of
turns, E-602 gives three different types of accumu-
lators or storing; i.e., integrating devices.
In the example, a positive displacement
pump (A) delivers its output (w), which is at all
-253-
time directly proportional to the speed (v) of the
pump into either one of 3 integrators.
Produces
W
с
a change S of a level in a storage tank. w Changes
the position of a piston. W Produces a change of
level (S) which is translated into (P), the pressure
of the compressed gas above the liquid.
-
E-603, Figure 370
In E-603 two other variations of such
hydraulic integrators are shown. In (A) we have a
displacement pump and a varying input speed v = (ds/at).
(S3), the stroke of a spring loaded piston, represents
the/wat where (w) is the flow rate which (consider-
ing the leakage losses of the pump and the varying
piston resistance) is a function of (ds/dt). The
integrator works for and ds/dt values.
W
a
In (B) we have a constant speed motor
driving a positive hydraulic pump, the eccentricity
of which is adjustable (S₂ variable) and whose out-
put flow rate (w) is directly proportional to S2.
One can consider such a device as an operator of
class E-603d.
2
the s
Swat.
in training devices for Army and Navy.
The stroke of a piston (S₁) gives again
Such devices have been successfully used
-254-
E-604. Figure 371
Into the same class belongs the pilot
valve which we have previously used as a relay
and as a (s/s) translator. In combination with a
cylinder, we obtain a device which approximates the
result of E-604, that is, we obtain also a value
which is:
S1 = f(Swat)
E-605. Figure 372
For gases, the accumulator frequently
takes a form which is shown in E-605 and a familiar
sight of large cities where gas consumption varies
with time and where the device is used to store
gas in times of under-consumption and to deliver
gas in times of lack of supply.
This introduces a feature of some inte-
grating or storing devices which is of basic interest.
The potential energy stored in the tank can be made
available again at a later time by re-conversion
into kinetic energy.
This is not always possible.
For instance,
in the integrator, class E-601, obviously no regain
of the energy to drive the integrating disk can be
reclaimed.
-255-
7) Class E-7 idt Devices
The integration of (D.C.) current is very
-
similar to that of flow rates.
E-701, Figure 373
In a watthour meter which measures feidt,
we obtain a speed (v) which is directly proportional
to the current, and we can use an integrator of the
Svat, class 4, to obtain S = =fidt. We assume in
fidt.
this case that (e) remains constant.
E-702, Figure 374
As the amount of 0 and 2H produced
in a given time is directly proportional to the
current passing through H20, we can use the volume
of 02 or H, and the corresponding strokes (S) and
(S₂) as indices offi dt (international standard
of amperes).
E-703, Figure 375
By using a condenser with a capacitance
10
idt, w
of (c), we obtain a voltage which is e
(1) the rate of current flow into the condenser.
conuensers are therefore another class of integrators.
with
Such
Their disadvantage is that it is very
difficult to prevent discharging of the conuenser
as it is practically impossibie to provide a perfect
-256-
insulator as a dielectric. Therefore, the use of
such a condenser as integrator is of the class
E-703a type, considering that e = f(t).
E-704. Figure 376
To illustrate the point that other
translators may be put in series, E-704 shows a
steam accumulator or boiler which is heated by
means of resistance wires through which (D.C.)
current is flowing. The potential energy of the
boiler is then fiat minus losses which are similor
in nature to leakage losses of a condenser.
The discharge of this condenser and the
re-translation into electric current is accomplished
by a prime mover and a generator. (Obviously, the
heater current can be replaced by heat obtained from
other sources as indicated as an alternative by the
fuel burner.)
E-705, Figure 377
Following the same line of approach,
E-705 shows an electromechanical condenser of rela-
tively high capacity. The shafts of a motor of a
fly-wheel and of a generator are connected by means
of suitable couplings. (In a simplified case, the
inertia of the motor is a substitute for the fly-
wheel and the motor also acts as a generator.)
-257-
The Sidt or Seidt is translated into
the kinetic energy
Iw 2
of the fly wheel and this
energy is re-translated back into electrical current
2
by means of a generator. Putting the mechanism into
a box with two terminals for input and output, the
device behaves exactly like a giant condenser (see
reference 45).
Lehr gives an example showing that a
3 kw. (D.C.) motor with 220 volts input voltage
and 1450 r.p.m. "produces a capacity" of 0,15 Farad,
a capacity of a magnitude which would call for con-
siderable more material if designed along conventional
lines.
8) Class E-8 - (idt Device
What has been said for (1) integrators
applies also to (A.C.) currents if (1/1) translators
(rectifiers) are used. More commonly used is an
A.C. watthour meter which similarly to E-701 runs at
a speed directly proportional to the watt input. An
(S) integrator of class E-1 gives the final value of
thefiat.
9) Class E-9 and E-10 -/edt &
- Seat & Seat
M

These can be handled similar to operators
of E-7 and E-8, as e and e and i and i are or can be
made directly proportional.
-258-

10) Class E-11-To
Tdt Device
A translation (T/electric variable) or
(T/S) reduces the operators to those treated above.
If the product temperature times specific
heat is combined with constant or varying flow rates,
the total heat supplied or taken from a capacitor is.
T.w.dt. Such devices are used as accounting
devices for determining total hot water supply.
the
SI.

11) Class E-12 -Qdt Devices
E-1201, Figure 378
One device in this class which is most
frequently used is a photosensitive film, a plate
or a paper in which the density of the photographic
image (e.g., silver deposit) is proportional to the
integral representing light intensity and the time
of exposure.
Also into this class belong phosphorescent
materials which produce an afterglow, the duration
and intensity of which is an over and the exposure
time.
E-1202, Figure 379
Perhaps it is not going too far to point
out one of the most important integrators for light
intensity or energy radiation.
This integrator is
-259-
the fauna and flora of the earth. The diagram,
Figure 379, symbolizes the radiation from the sun
which is translated into carbon hydrates (CH), which
thus represents cat.
These CH or B.t.u.'s are later again
translated into work which can take many forms as
indicated by our translator map.
The translator in our example is "man".
He is shown to have built (output) a towering build-
ing (potential energy and kinetic energy, lifts, water,
etc.).
E-1203. Figure 380
Last but not least, another important
energy "storing" device should be mentioned which
has been created by men.
Starting again with the solar radiation,
its integral energy over time has been converted
into fuel oil which is stored in the depth of the
earth and is regained by man's efforts (work invested). .
This work is converted: a) into refined oil whose
volume produced is integrated in tanks, and, b) into
money whose value is accumulated in banks.
The practical feature of this arrangement
is that by combining either one or using each one
-260-
individually, the capacitors
a) tank, and b) dollars
in banks can be discharged at any desired time, space,
or rate.
-
As money is the most versatile input for any
translator chain, and as it so far has been neglected,
it seems only fair to mention it and point out its
significance in the over-all energy exchange of our
technological system.
As output of translator chains, it is
expected to be a larger amount than the input.
expectation seems to contradict the first law of
thermodynamics and leads to rather interesting com-
plications which fortunately 60 beyond the purpose of
this survey.
-261-
ange
This
···
CHAPTER XI
ANALYSIS AND TRANSLATION OF SPECIFIC DEVICES
Armed with the information of the preceding
chapters, we shall now analyze a specific design and
translate its parameters into other variables. I
choose as our example a hydraulic pressure regulator
with proportional band:i.e., with a definite relation-
ship between the position of the controlling valve and
the magnitude of the controlled variable.
Referring to Figure 381, we have a valve (E)
controlled by a double acting cylinder (D). A change
of the flow of fluid through (E) changes the pressure
(P) which is transmitted to a diaphragm (B). The
force produced by (P) and (B) is balanced by means of
a setting spring (A) and a stabilizing spring (G).
The arrangement is such that an increase in pressure
(P) closes the valve (E) by an amount of stroke which
is directly proportional to the change in pressure
A new equilibrium is re-established as soon as the
compression of spring (G) equalizes the disturbance.
For the purpose of our analysis, we do not
have to investigate the transients which give the
changes in pressure as a function of time, as we are
only concerned with static equilibrium and the basic
I
-262-
design of the mechanism.
This particular regulator
is a typical example of a great number of controllers
of the proportional type.
A study of this "hydraulic" type regulator
shows that it is of the "force balanced" type; i.e.,
that the relay (C) is in equilibrium when the sum of
all forces acting onto the relay are equal to zero.
The unit can be subdivided into the follow-
ing major parts:
1) The setting devices (A) which translates
S into F = (81/F1).
2) The diaphragm (B) which produces a force
in response to applied pressure (P/F 2)•
3) The relay (C) which produces a rate of
ds3
travel of the valve (E); 1.e., v =
dt
proportional to AF, or its displacement
(S₂); i.e., (S₂/v).
2
4) The cylinders and pistons (D) which inte-
grates v over time, and produces a stroke
(§3)=ſvdt=(v/S3), and a force which is
equal to the resistance to be overcome.
5) The value (E) which translates (S) into
(w) the controlled fluid rate.
6) A pipe line integrating the difference
between supply and demand and producing a
pressure P =√(Aw)dt,
=(Aw)dt, (assuming the fluid
to be a low pressure compressible gas).
-263-
7) The negative feedback stabilizer which
translates the valve travel (63) into
a corresponding stroke (S) and by means
of a spring (S/F3) into a force (83/F3).
4
Our translator chain can therefore be written as
follows:
Σ(S₁/F1)+(P/F2)+(83/F3)+(ZF/S₂)+(S2/v)+(v/S3)+(83/w)+
Σ(F1 + F2 + F3) = 0
81 = c₁F1
F2 = c2P
F3 = C3S3
This device can be drawn as a translator chain, as
shown in Figure 382.
(w/P) = (S₁P)
If we want to translate the mechanism into
a stroke compensated system, it is only necessary to
change the summarizing device.
Figure 383 shows the modified, design. The
summarizer is taken from our collection of operators
for mechanical summarization; i.e., a "whiffle" tree
arrangement is used. The hydraulic relay has been
changed to a sleeve type valve in which the valve
sleeve as well as the pilot proper can be moved.
The equation reads therefore:
Σ((S₁)+(P/S₂)+(S3)) · ✦ (28/v) + (v/83) * (83/w) + (w/P)
+
(S/P)
with (ES = 0).
=
-264-
To avoid the necessity of a mechanical
link between (S3/S), we can introduce other
variables, for instance, (P₂/S) and (P₂/S,) as
shown in Figure 384. Obviously, any other (S/S)
translator could have been used for the same purpose.
2
This incidentally indicates that the link
between (S3) and (S) can be established by two
4
basic requirements.
a) the output of the relay should change
$4)
(S3), the valve position, until the
output of 6) re-establishes the balance.
It is also necessary that the transmitted
value of the output of the translator
(S3/S), the "feedback" is proportional
to the stroke (S3)•
b) The feedback variable and the valve posi-
tion have to respond to the same variable
(in our case (P)).
We shall now as an exercise translate the
above mechanism into its electrical equivalents. For
the sake of simplicity, we specify that (D.C.) circuits
are to be used.
We choose an "Electronbeam" tube instead of
the jet pipe and hereby produce a force balanced
system, or as these forces are produced by currents
-265-
or voltages, we can also speak of a current or voltage
or field balanced system (see Figure 385).
The simplest form of a (P/1) translator is
also shown on the same figure. It can be described
by the equation:
(P/F) + (F/S) + (S/K) + (K/1)
(R/1) = (P/1)
To replace the cylinder and the diaphragm
valve, we have no to look for electrical "synonyms".
In Figure 386 we have at left a motor with
a rheostat which is connected to its shaft. This we
intend to use for converting the stroke (S3) into a
current to take the place of the double acting cylinder
and part of the feedback mechanism.
The motor circuit is so designed that it runs
at a speed proportional to e, which is the output of
the relay. The cylinder runs at a speed proportional
to S₂ or the pressure differential across the receiv-
ing nozzles (Ap).
The diaphragm valve takes a position propor-
tional to the applied pressure, the solenoid, its
equivalent, produces a motion which is proportional to
the applied current (see Figures 384 and 386).
With the above, we can write the equation
for our translation as follows:
-266-
Σ((8/11)+(P/12)+(85/13)) + (Σ1/g) + (e/v) + (v/83) + (S3/w) +
(w/P) = (S₁/P)
Figure 387 gives the circuit diagram which is repre-
sented by this equation.
It is,
An analysis of the (S/1) and (P/1) trans-
lators discloses that they are chains of the type:
(S/R)+(R/1)=(S/1) and (P/R) + (R/1)=(P/1)
This means that their common parameter is (R).
therefore, tempting to translate the variables into
(R) and to use an operator for summarizing (R) rather
than currents (1).
It will be also noted that the summarizer
is actually not a summarizer of currents, but of
magnetic fields (H) and in the final analysis of
forces (F).
We can, therefore, choose among summarizing
devices for (H), (1), (R), (S), and (F).
We select a Wheatstone bridge as one of the
possible solutions, as the Wheatstone bridge has the
additional feature that it can be used as an amplifier
for the error, and as it is independent of voltage
variations.
As the bridge (Figure 388) is in balance
R
when R₁ - c(R₂.*
c (R2+ R3) = 0 and c = can be made unity,
we obtain an output voltage (e) =, if:
R
-267-
(R₂ + R3) = 0
R₁ - (R₂
It is, therefore, only necessary to make
R₁ equal to the "setting" (S₁) and (K₂) equal to
c1P1 (as before) with (R3) a feedback from the
valve position in order to satisfy the equation
(see Figure 389).
The objection will be raised that the
chosen (P/R) translator depends on contacts of
sliding surfaces and will thus be affected by
friction and contact conditions.
Carbon piles (see Figure 390) seem to be
a better answer, but unfortunately their resistance
is rather erratic and the piles are therefore trans-
lators of the type (168) a; i.e., their resistance is
not directly proportional to the applied forces and
what is worse, not stable.
We may also think of a "Ring" resistor
(see Figure 390) which is of the type (168)b; i.e.,
its resistance is directly proportional to the
displacement and thus to (F) and (P).
The "Ring" which is shown is filled with
mercury and short circuits more or less of the wire
resistors as it is turned around its axis. It can
S
-268-
therefore be used for our translation.
In addition, we find under type (48) d
several translators which are independent of the
individual resistance characteristics (see Figure 391).
In the left-hand diagram, the resistance of a carbon
pile is varied until a current which is controlled
by this resistance produces a force of sufficient
magnitude to balance the effect of the pressure.
In the right-hand diagram, the output of
an amplifier is varied until balance between the
pressure force and the counteracting solenoid force
is established.
In Figure 392 the circuit is shown which
fulfills the above specifications. It would be just
as easy to develop the translation of the circuit
with pressures rather than strokes as the input
values.
Again, there would be the choice of force
or stroke balanced summarizers or the conversion of
these parameters into (1) or (1) or (f) or (f) or
any other variable. Nothing new would be added, as
the approach would be identical.
However, it is recommended that the reader
try to go through with a translation of his own as
-269-
only practical experience, as in mathematics, will
finally make the method a habit.
-270-
CHAPTER XII
GENERAL CONCLUSION
1) The above analysis establishes at least
one possible solution with the parameter (S) for
every translator given in the chart and one possible
solution which is electrical with (1) as the output
or input.
2) It also shows that the common algebraic
operations of summarization and multiplication can
be accomplished with various parameters of the
translator. In addition it gives solutions for
obtaining the nth power, derivatives and integrals.
3) It also demonstrates how the translator
chart can be used like a map to establish new roads,
new sequences, or new combinations of translators to
arrive at a given output for a specified input.
4) It proves the equivalence of all para-
meters as these are interchangeable through the use
of translators.
5) Thus, it reduces the level of many
"inventions" to systematic combinatoric and makes
it possible to arrive at new solutions without
that spark of ingenuity which is the matter of
controversy between inventors and the Patent office.
-271-
It is necessary, however, to limit this
statement to a certain type of inventions, as this
analysis only deals with routine combinations of
known or synthetic translators. The study does
not claim to be the key to the solution of problems
beyond this well defined province of combinatoric.
In conclusion, it is perhaps permissible
to speculate about possible other applications of
this method of approach. I have briefly mentioned
the chemical translator. Such translators play, for
instance, an important role in (w/T) translators,
in which (w) is the Σ of w
WI
1 = H₂ (hydrogen) and
02 (oxygen). The chemical reaction of w
and w
W2
produces a heat input which in turn is translated
into a temperature which in turn is an indication
2
W1
of the balance between the heat supply and the heat
withdrawn.
(Σ(W1 +
is therefore, a legitimate symbol of such a trans-
lator although a closer analysis would show the
chemical process:
2H2 +
W2)/T)
0₂ = 2H2O + a B.t.u.
This is again only another way of saying that the
sum of the two inputs are through their interaction
-272-
Stad
in the combustion chamber translated into heat
and H2O as outputs.
2H2 →→→ H2
02
0

2H2O
heat a B.t.u.
It may be possible that for some special
chemical process, a translator chart with various
elements and combinations (chemical compounds) as
parameters would help to clarify translation
process from one parameter to another, and hereby
establish translation chains which might have been
overlooked in a less systematic approach.
I feel that, if the whole analysis did
not serve any more important purpose than to
suggest a logical filing system, the effort to
establish it has been worth while.
-273-
BIBLIOGRAPHY
AND REFERENCES
1) Fehr, R. O. "Vibration Testing" (GEA-4091A). Reprinted
with changes from General Electric Review, December 1942. 1 p.

2) Eckman, D. P.
New York, John Wiley & Sons, Inc., 1945.
Principles of Industrial Process Control.

Relay Devices and Their Application to
Askania Regulator
3) Ziebolz, H. W.
the Solution of Mathematical Equations.
Company, 1940. Vol. I and Vol. II.
4)
"Ratio and Multiple Fuel Controls in the
Steel Industry", A.S.M.E. Paper reprinted from The Journal
of Applied Mechanics, November 1944.
5)
"Characteristics of Hydraulic and Pneumatic
Relays as Energy-Converting Devices". Reprinted from
Instruments, September 1942.
6) Smith, E. S. Automatic Control Engineering. New York,
McGraw-Hill, 1944. 350 p.
7) Einstein, Albert and Infield, Leopold. The Evolution of
Physics. New York, Simon & Schuster, 1938
8) Ziebolz, H. W. Process Control Terms. Askania Regulator
Company, Technical Paper No. 202, 1945.

9) Kramer, A. W. Elementary Engineering Electronics.
Pittsburgh, Instruments Publishing Co., 1945.

10) Batcher, R. and Moulic, W. Handbook Electronic Develop-
ment.
New York, Electronic Development Associates, 1944.
11) Borden, P. A. "Applications of the Electric Balance to
the Continuous Solution of Mathematical Formulas".
Instruments, December 1939
12) Glass, P. "Deflection Beam Tube". Electronic Industries,
August 1944.
13) Black, H. S.
"Stabilized Feedback in Amplifiers".
Proceedings American Institute of Electrical Engineers,
January 1934.
14) Gardner, M. F. and Barnes, J. L. Transients in Linear
Systems. New York, John Wiley & Sons, 1942. Vol. I.
-274-
G

15) Pohl, R. W. Physical Principles of Mechanics and
Acoustics. London, Blackle & Son Ltd., 1932.
16)
London,
17) Bush, Vannevar. "A Scientist Looks at Tomorrow".
The Atlantic, July 1945.
Electricity and Magnetism.
Blackie & Son Ltd., 1932
18) Keinath, George. "Archiv fuer Technisches Messwesen".
Verlag R. Oldenburg.
<
19) Fry, Macon. "Design of Computing Mechanisms".
Machine Design, September 1945.
20) Wittenbauer, F. Graphische Dynamik. Berlin, Springer,
1923.
21) Fabritz, G. Die Regelung der Kraftmaschinen.
Springer, 1940.
22) Roberts, H. C. "Electric Gaging Methods for Strain
Movement Pressure Vibration". Instruments, April 1944
to December 1945.
23) General Electric Company. "High Sensitivity Electronic
Recorder". Reprinted from Electronics, May 1944. 150 p.
24) General Electric Company. "Polarized Light Servo System".
Reprinted from Power Plant Engineering, September 1944.
99 p.
25) Ziebolz, H. W. "Basic Solutions for Flow Measurement".
Reprinted from The Review of Scientific Instruments,
April 1944.
80 - 87 p.
Wien,
26) De Juhasz, K. J. "A New Electric Pressure Gauge with a
Semi-Conductive Measuring Element". Engineers Digest,
October 1945.
27) Irvin, G. E. Aircraft Instruments. New York, McGraw-
Hill, 1941.
28) A.S.M.E. Research Publications.
Theory and Application". 1937.
29) Fischer & Porter Company.
Section 80-A.
V
"Flow Meters Their
30) Editorial Staff Review. "Instruments for Measuring
and Controlling Processes Variables." Chemical and
Metallurgical Engineering, May 1943.
#.
"Theory of the Rotameter".
-275-
་
59)
and Mayer, Robert W. Servomechanisms
and Regulating System Design. John Wiley & Sons,
Inc., New York, Chapman & Hall, Ltd., London, 1951.
60) Edwards, C. M. and Johnson, E. C. "An Electronic
Simulator for Nonlinear Servomechanisms".
Preprint, 50-47, January, 1950.
ALEE
61) Evans, W. R. "Control System Synthesis by Locus
Methods". AIEE Preprint, 50-51, January, 1950.
62) Fry, Macon, "Designing Computing Mechanisms".
Machine Design, Aug. 1945 to Feb. 1946.
63) Hall, A. C. "A Generalized Analogue Computer for
Flight Simulation". AIEE Preprint, 50-48,
January, 1950.
64) Herwald, S. W. and McCann, G. D. ""Dimensionless
Analysis of Angular-Position Servomechanisms".
Trans. AIEE, Vol. 65, pp. 636-639, October, 1946.
65) James, Hubert M., Nichols, Nathaniel B., and
Phillips, Ralph S. Theory of Servomechanisms.
McGraw-Hill Book Company, New York, 1947.
66) Kochenburger, R. J. "A Frequency Response
Method for Analyzing and Synthesizing Contactor
Servomechanisms". AIEE Preprint, 50-44,
January, 1950.
67) Lauer, Henri, Robert Lesnick, and Leslie E. Matson.
Servomechanism Fundamentals. McGraw-Hill Book
Company, New York, 1947.
68) MacColl, Leroy A. "Fundamental Theory of Servo-
mechanisms". D. Van Nostrand Company, New York, 1945.
69) Oldenbourg, R. C. and Sartorius, H. "Dynamics of
Automatic Controls. Translated and edited by H. L.
Mason, ASME, New York, 1948.
70) Ragizzini, J. R. and Lofti, A. Z. "Probability
Criterion for the Design of Servomechanisms".
Jour. App. Physics, Vol. 20, pp. 141-144,
February, 1949.
-278-
1
71) Ragazzini, J. R., Randall, R. H., and Russell, F. A.
"Analysis of Problems in Dynamics by Electronic
Circuits". Proc. IRE, Vol. 35, pp. 442-452, 1947.
72) Stovall, J. R. "Transducers, Sending Elements for
Servos" Electrical Manufacturing, Vol. 45, No. 4,
pp. 88-92, 176-184, April, 1950
73) Tarpley, H. I. "Instrument to Measure Servomechanism
Performance". Rev. Sci. Instruments, Vol. 18, pp.
39-43, January, 1947.
74) Wunsch, Guido. Regler fur Druck and Menge.
burg Verlag.
콘
​75) Ziebolz, H. "Designing Hydraulic Servos".
Design, Vol. 19, pp. 123-126, July, 1947.
76) Ziebolz, H. "Designing Pneumatic and Electric
Servos". Mach. Design, Vol. 19, pp. 132-138,
September, 1947.
Also U. 8. patents:
#2,403,504
#2,403,505
#2,403,506
Olden-
77) Ziebolz, H. "Systematic Design of Mechanisms"
Mach. Design, Vol. 22, pp. 126-136, December, 1950.
78) "A New Approach to Design". Mach. Design, June,
1947.
#2,403,117
Mach.
#2,403,542
#2,403,543
#2,403,544
-279-
5
In the written form Sp(S1/S2, S3,S4) it will be noted that the outputs
are enumerated as well as the input.
In inserting a "splitter" into a circuit it is optional which chain of
the output is completed.
The open or loose ends are picked up by additional equations with
indices marked like the terminals of a wiring diagram.
This marking of open inputs and outputs solves our second basic
problem, i.e. it gives us a means to show "cross connections".
In preparing a basic circuit diagram with its functional opera-
tors, quite often the choice of the parameter is still open. In all
such cases the symbol (x) can be used to indicate this fact.
Example: To apply this symbolism to Fig. 20 of the "Analysis
and Design" publication, we can write (see Fig. 4):
(1) (Q/e1)+℃(e1,eq,e3/е4)+(e4/V1) + Sp (V1/V2›V
+ Sp (V1/V2, V3)+(v2/S)
+Sp (S1/S₂,S3)
(2) (S2/e2)
(3) (vg/ez)
Without knowing anything about the intermediate parameters, but
knowing the input and the output variables and having decided on
a position and a velocity feedback, our circuit is represented by:
(1) (Q/Sg) = (Q/x1)+℃ (*1,X2,*3/x4) + (X4/v1) + Sp(ˇ1/v2,V3)
+√(V2/S1) + Sp($1/S2,S3)
(position feedback)
(velocity feedback loop)
(2) (S2/x2)
(3)
(V3/x3)
A more complete equation can be written by giving x2 and
X3
negative signs to indicate negative feedback so that the summar-
ization operator becomes:
-
-
Σ (+ X1, - X2, - X3/x4)
The
put t, i.e. time.
Soperator could be more detailed by adding as a second in-
S(v2,t/81)
however, the absence of a second integrator
input implies in general time as the second variable.
With the above modification we have the following operators:
operator A. "summarizer"
Σ (x1,x2,....xn/xm)
B. "multiplicator'
M (X1, X2,…….. Xn/m)
C. "nth power operator"
(x1/x1n)
D. "differentiator"_d_ (x2/x3)
d x1
E. "integrator"
11
f(x1,xq/xg)
F. "splitter"
or in case of X1
(x24x2)
d t
or (x
(x1,x2/√x1 d x2)
or with x2 = t
√(x1/x3)
Sp (*n/X1,X2,X3,…….X。)
It is believed that with the above symbols any complex circuit dia-
gram can be represented without it losing clarity.
= t
UE;
9
e1
$1
$1
Fig. 1
"Splitter"
e2
+е1.
+e
Sp(S1/S2, S3, S4)
Sp
S2
##
ST
S2
S3


Fig. 3
e4 e4
$2
ავ
V1
23
e3
T
V
3
e2
劉
​S2
Sp
V
2
3
Fig. 2
"Summarizer"
SA
Σ (S1,S2, S3/S4)


Symbols for Translator Circuits
Sp
Fig. 4
S2
$3
Printed in U.S.A.
11

TRANSLATOR MAP
INPUT
OUTPUT
CURRENT D.C.
CURRENT A.C.
STROKE OR ANGLE A
PRESSURE
FORCE
5
d³/dt SPEED day at R.P.M. V V 16
d's
d25% dt² ACCELERATION at a
2
at² a
2
17
RATE OF FLOW
VOLTAGE D.C.
VOLTAGE A.C.
TEMPERATURE
LIGHT INTENSITY
RESISTANCE
INDUCTANCE
CAPACITANCE
PHASE ANGLE
MAGNETIC FIELD
ELECTROSTATIC FIELD
FREQUENCY
IS
1
P 4
sa
F
Howe
43
7
15 14
18
19
૭
W 36 35
37 38
44
34 33 32 31
39 40 41 42 43
| |
2 64 63 62
i
d's/dt² ACCELERATION d²x/dt²
STROKE OR ANGLE α
ds/dt SPEED da/dt R.P.M.
PRESSURE.
FORCE
61 60 59 58
RATE OF FLOW
е
SPF
V
aw t
ie et QRL
CYH
Ef
2
9 10 25 26 49 50 | 81 | 82 | 121 | 122 169 170 225 226 289 290 361
8
11
51 8083120|123| 168| 171 | 224 227 288 291 360
24 27 48
12 23 28 47 52 79
13 22 29 46 53 78
84 119 124 167 172 223 228 287 292 359
85 118 125 166 173 222 229 286 293 358
| |
86
20 21 30
45
54 17
117 126 165 174 221 230 285 294 357
116 127 164 175 220 231 284 295 356
115 128 163 176 219 232 283 296 355
114 129 162 177 218 233 282 297 354
Q 144 143 142 141|140 139 138
R 145 146 147 148 149 150 151
L 196 195 194 193 192 191 190
C 197 198 199 200 201 202
P 256 255 254 253 252 251
CURRENT D.C.
CURRENT A.C.
VOLTAGE D. C.
YOLTAGE A.C.
72
65 66 67 68 69 70 71
e 100 99 98 97 96 95 94
T 101 102 103 104 105 106 107 108
103 104 105
93
55 76 87
56
75 88
57
74 89
TEMPERATURE
RESISTANCE
INDUCTANCE
PHASE ANGLE
LIGHT INTENSITY
CAPACITANCE.
MAGNETIC FIELD
ELECTRO STATIC FIELD
FREQUENCY
73 90 113 130 161 178 217 234 281|298 353
92
91 | 112 | 131|160 179 216 235 280 299 352
137 136 135 134
109 110 111 132 159 180 215 236 279 300 351
133 | 158 |181 214 237 278 301 350
156 157 182 2/3 238 277 302 349
185 184 183 2/2 239 276 303 348
152 153 154 155
189 188 187 186
203 204 205 206 207 208 209 210 211 240 275 304 347
250 249 248 247 246 245 244 243 242 241 274 305 346
H 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 306 345
E 324 323 322 321 320 319 318 317 316 315 314 315 312 311 310 309 308 307 344
f 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343
a
с
CLASS a - DIRECT BUT NOT DIRECTLY PROPORTIONAL TRANSLATION
CLASS D - DIRECT AND DIRECTLY PROPORTIONAL TRANSLATION
A
b
d
C - INDIRECT BUT NOT DIRECTLY PROPORTIONAL TRANSLATION
CLASS d - INDIRECT AND DIRECTLY PROPORTIONAL TRANSLATION
CLASS

OPERATOR
MAP
STROKE OR ANGLE d
PRESSURE
FORCE
ds/dt speed dd/dt R.P.M.
d²/dt² ACCELERATION data a
d2
2
RATE OF FLOW
CURRENT D. C.
CURRENT A. C.
VOLTAGE D. C.
VOLTAGE A. C.
TEMPERATURE
LIGHT INTENSITY
RESISTANCE
INDUCTANCE
CAPACITANCE
PHASE ANGLE
MAGNETIC FIELD
ELECTROSTATIC FIELD
FREQUENCY
る
​૧
F
>
W
3 R11 R2 01|
i
e
ad
ደ
ד
Q
•
L
C
Y
H
W
f
2
ABCDE
3
AIBICI DI CI
EI
2 2 2 2
4
5
6
7
8
9
3
14
4
10 10
15
5
6
7
8
16
9
19
SUMMARIZATION
N
14
3 3
4
4
// // //
5
16
6
MULTIPLICATION
th POWER
DERIVATIVES
INTEGRALS
9
10
7 7
8.
8
12 12 12 12
5
6
9
19
//
3
14 14
4
13 13 13 13 13
5
6
7
10 10
8
9
//
12
16 16 16
17 17 17 17 17
18 18 18 18
18 18
19
15 15 15 15
14
19 19

!
1
UNIVERSITY OF MICHIGAN
3 9015 06438 6710
1

2
I
i
Engineering
Library
TJ
181
.265
1951
U.
Ziebolz, Herbert
Analysis and design
of translator chains.
ENGIN. LIBRARY
TI 181 265 1975 DATE DUE Une.
સર
MAY 1
1952
1956
1957


The device sh
a Transometer."
eed of rotation (V) into
ressures (P). The centrifugal to
ball governor is used to displace an
a receiving nozzle until the pressure built
im is equal to the centrifugal force. In this way,
aphragm is an indication of the speed of the
centrifugal governor. This pressure (P) follows the
few
bos of water column.
is for speed of the driving shaft, 0 to
RESSURE-STROKE
#1. The two diagrams (A) and (B), show
pressure
simple forms of "U-tub
gauges. The applied pre
he U-tubes by an amount
al to the pressure
A) by readi
U-fus
PRESSURE
his pressure transla
ationship betwee
id a secondary
ose an "Askap
connected t
condary
produced
elations.
STROKE-PRESSURE
#2. The two translators shown in (A) and
(B) are used to produce a pressure which is
directly proportional to the stroke (S). In
both cases, jet pipes are used for amplifier
(A), the jet pipe delivers operati
Fluid into a
ting force
on a diaphragm producin
ressure
as that of the sp
jet pipe
+9
an amount
counter
The
dip
Published and Copyrighted by
ASKANIA REGULATOR CO.
CHICAGO, ILLINOIS
H
#
of an
ing pre
KE-CURRENT D.C.
#1. In the "Electron beam" tube shown, the
beam of electrons is deflected relative to
two target plates by a displacement of a
s the potential difference created by this deflection
whose output (i) varies until the field it produces
the primary systems (S). A definite relationship
(i) is established. See "Deflection Beam
ed in conn
iding
19
ng for
rm is 400
depends
mich is
STROKE-VOLTAGE
#1. The de
in which a b
relative to two
produced by a
tput of the
which
force bala
#1. The
duces a relationship between
for the input e and d.c. current for
put i. A beam of electrons is displaced s
cults in a potential difference on the ta get pla
mplifier, the output current {}
deflection force of the
elationship between
characteris

CURRENT-CURRENT D.C.
ASKANIA
'Powerunit
PRESSURE-STROKE
#2. The diagram shows the basic prir ciple
of an "Askania Power Unit" which for load-
ing pressures from 0 to 15 pounds produces
a motion of a crank arm (S) which is directly
proportional to the loading pressure.
hydraulic "Askania jet pipe" is used as an amplifier, the mechanis
establishes the position or stroke (S) independent of the loud whic
applied to the cylinder. The torque available on the crank arm
. lbs. See Askania Bulletin 120. The device can be use
spring.
Deam Tube"
#1. An "Electronbeam" tube consis
a cathode ray tube with two receiving
produces a potential difference on the
target plates, as the beam of electron
flected relative to the two tarjet
ced by a magnetic field prop
tential difference produ
lifier increases unt
ationship be
tube
with any standard type air operated controller for prov
power and positive positioning with an accuracy better
placement
a "stroke
either
STROKE-FORCE SYMBOLS
#1. The diagram shows
simple "stroke-force" tr
commonly known as "sprit
In (A) a "helical" spring changes its forcé direct
the displacement (S). In (B), a "leaf type" spring proc
portional to the displacement of its end.
STROKE PRESSUR
diagra
I. The "stroke pressure
Askania je
the
h