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Патент USA US3046520

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July 24, 1962
D. G. WILLIAMS ET AL
NON-LINEAR POTENTIOMETER
Filed Aug. 18, 1961
â/ /
3,046,510
3,046,510
` United States Patent Oñ?ce
1
Patented July 24, 1962
U
3,046,510
David G. Williams and Joyce W. Williams, Littleton,
NON-LINEAR POTENTIOMETER
while‘the opposite twoedgesof Ithe card, the orthogonal
trajectories, should be generally convex. More specifi
Mass., assignors to Ace Electronics Associates, Inc., a
corporation of Massachusetts
2 .
card, i.e. thetwo card edges along which the voltage
input terminals are applied, should be generally concave;
cally, the equipotentialk edges should lfollow `a curve de
\
fined by the formula `
Filed Aug. 18, 1961, Ser. No. 132,322
9 Claims. (Cl. 338---89)
K
‘
K2
_.
sin2 <1»
The present invention relates to variable resistors, such
as potentiometers and rheostats, and is concerned primar lO
2
ily with resistance cards for use in »such variable resistors.
wherein r is the'dis'tance from the center of the card for
In particular, this invention relates to resistance cards ‘ f various angles qi about the center, a is the radius of the
adapted to provide non-linear voltage functions, rsuch-as
round hole formed in the center of the card, and K is a
sine and cosine functions, when traversed over the surface
constant; and the orthogonal trajectory edges should fol
by a wiper tap along a circular curve having as its center
the center of the card.
It is recognized in the prior yart that a fiat square resist
ance card, whether wire wound, or formed of a molded
resistance material, or formed by a deposited layer of re
sistance material, may be utilizedfto’provide sine-cosine
output voltage functions; and one may vobtain such out
. puts lby imposing a uniform voltage across the card from
low a curve defined by the formula
'
20 wherein r, qs, and a are stated above, and C” is a constant.
Accordingly, it is oneV object of the present invention
to provide a resistance card adapted for use in a sine
one` edgeto the opposite edge thereof, and traversing the
cosine potentiometer.
card in a circular path about its Ycenter with a variable
potentiometer wiper contact. Such potentiometers are
illustrated for example by the U.S. Patents 2,457,178 to
A. G. Richardson, et al., 2,653,206 to I. L. Montgomery,
and 2,764,657 to L. A. Rosenthal.` However, it is recog
nized in the art that in using such potentiometers, it is fre
quently necessary to gang them so that a plurality of cards
‘
_
'
' Another object ‘of the present invention is to pro-`
vide such a card having a -hole in the middle to facilitate
ganging a plurality of sine-cosine potentiometers,
Still another object of the present invention is to pro
vide a sine-cosine potentiometer formed from such a card
and having a variable tap mounted on -a rotary shaft pass
ing through said hole.
can be tapped by respective variable potentiometer wiper
contacts mounted for unison rotation on `a single shaft. ~ -
Itis apparent that Vthe most eliicient manner of ganging
.
,
-
`
And a further object of the present invention is to pro
vide a plurality of such sine-cosine potentiometers ganged
on a common rotary lshaft for the variable tap of each
a plurality of these potentiometers is to mount a shaft
through the centers of the several resistance cards, and 35
potentiometer.
,f
f
Other lobjects and advantages `of the present invention.
to mount on the shaft a variable potentiometer wiper con
|will
become apparent tothose skilled in the art from a
.tact arm for each card adjacent 'to the resistance surfaces - ï»
consideration of the following detailed description of one
of the respective cards. The resultant holes in the cards
exemplary specific embodiment of the present invention,
to accommodate the shaft afîect'the voltage and current
distributions over their surfaces, and thereby destroy or 40 had in conjunctionÍwit'hÍt-he `accompanying drawings,
_wherein like numerals refer to ylike or lcorresponding parts,
distort the sine-cosine functions originally obtainable yby
and wherein:
y
n
,
circular traces or wipes about `the centers of the cards.
FIG. l is a plan view ofa flat resistance card formed
The art has recognized the existence of this problem, and
in accordance with the present invention;
has sought through various means VAto correct `for these
deviations, `as by altering the configuration of the card
FIG. 2 is a longitudinal sectional view of la plurality of
ganged potentiometers, each incorporating aL resistance
input terrninalsrapplied along twoi opposite edges of the
card as shown in FIG. l; and
FIG. 3 is a cross-sectional View of the ganged poten
card (Rosenthal Patent 2,764,657), or by altering the con
figuration of the two opposite card edges transverse to
the input terminal edges of the card (Montgomery Patent
2,653,206);
Í
~
.
-
.
These proposed `solutions to the problem, however, have
tiometers of FIG. 2, ktaken along the line 3--3` thereof.
The flat resistance card of the present invention-is indi
50 cated generally by the numeral 10.
Preferably this card
been only approximations, and have failed to grasp the ¿ _ is formed as va molded conductive plastic resistance, and is
of uniform cross-sectional thickness so as to provide sub
basic nature of the problem. `Arhole inthe center of a
square resistance card alters the voltage and current dis
tribution over the area of `the card so that the equipoten
tial lines, which originally were straight lines across the
card parallel to the voltage input edges of they card, are no
stantially uniform specific resistivity over its extent. For
structural support and mounting purposes, the card 10 is
55
united to an insulating discr 11, which may also -be a plastic,
‘by 'any suitable means such as `a resinglue or`=adhesive,
or by comolding. Conductiveterminal strips 12 and 13
are applied along opposite vedges 14 and 15 of the resist
ance card, and may be applied as> conductive coatings on
deviation results from the fact that any hole in the card 60
the resistance card, or laminated thereto as preformed con
affects the resistance distribution over the card on two di
ductive metal foils, or comolded with the card 410 as con
..mensions, i.e. «along the dimensions parallel to and perpen- .v ductive metal terminal plates. " A hole 16 is formed in the
longer straight, and differ in configuration at different `
,points Vbetween thevoltage input edges. This compound
dicular to either pair of opposite card edges.
'
n,
center of the card 10 and overlies ‘a hole 17 of smaller
Í. vIn accordance with .the present inventionhtaking' into
¿account the two dimensional effect of ahole in 'the resist
diameter in the insulating disc 11.> t n i
ance, onecan obtain asubstantially perfect sine-cosine
plied to terminal strips 12 and 13, thereby establishing a
function from a modified square resistance card having a
hole through its center.
It has'been found that allfour ' `
Leads from a voltage source (not shown) are to bel ap
voltage gradient across the resistance` card , 10 .between
these terminals..Á A variable >potentiometer Wiper contact,
edges ofthe resistance card should follow complex curves.
to >be subsequently described, mounted on a shaft passing
For a card having a round hole through itscenter, it has 70 through holes 16 `and 17„is intended to traverse the sur
been> found that the two opposite edges of the-card
face of resistance card 10 along ya circleindicated for ex
generally paralleling the equipot'ential lines across the
ample Eby the phantom line 18. In traversing the circle 18,
3,046,510
3
the variable contact taps an output voltage from the card
varying in accordance with a sine-cosine function, one
complete sine-cosine cycle for each 360° of traverse over
circle 18.
_
In order to produce a substantially true sine-cosine out~
put function, edges 14 and 15 of the card, referred to
herein as the equipotential edges, followaa generally con
cave curvature, while the »other two edges 19 and 20` fol
low a generally convex curvature. More specifically, a
substantially pure sine-cosine output function is obtained 10
when the curvature of edges 14 and 15 follows the curve
defined by the equation
and the curvature of edges 19 land 20 follows the curve
deûned lby the equation
wherein r is the ‘distance -from the center of the card
which is the Asolution for the curvature of edges 14 land 15.
(point Z1) for various angles gb about said center, C” and
From Equation 19,
K are constants, and a is the radius of hole 16.
In ‘order that the nature of the present invention will be 25
more fully appreciated, the mathematical derivation of the
foregoing‘equations is presented. The Ifollowing deriva
tion and the foregoing equations apply to a flat resistance
card of uniform speciñc resistivity, having a hole 16 of
radius a in the center .of the card :about point 21. The 30
circular wiper track `18 is concentric with lthe hole and has
a radius b.
Let
Vr=b=F sin el»
(1)
where V is la voltage function, «t the displacement angle
is the differential equation for the «orthogonal trajectories,
when equated to
`about the ‘center of the card and r is a distance from the
center of the card along a radius vector. Then
(2)
Assuming
40
.
VU, <í>) =R(r) ‘I’ (<15)
In polar coordinates
(3)
‘
45
WeaaearsaetarLira (5)
RU) E
dr
_
@((b)
50
=a constant--m2
(6)
`I>=A «cos (m¢>) +B sin (mfp)
(7) 55
wherein A and B are constants.
l1>('/)-I-21r)=‘1>(tf1)
(3)
_"i T M)
Ro) dr
dr
_ma
(9)
soml=1, 2, 3 . . . .
60
d2R
1V dR
m2
et+? u; _ze R=0
(10)
65 1 is shown assembled in a potentiometer, and two such‘
which has the 4solution
potentiometersare indicated as ganged for unison opera
R(r) :Crm-l-Dfm
wherein C and »D are constants.
Let B21
Equation 30 is the solution for the curvature of edges
19 and 20‘.
Referring to FIGS. 2 and 3, the resistance card of FIG.
`
(11)
tion on a common shaft.
Shaft 30 passes through hole
17V in the insulating backing plate 11, and throughhole
116' in the resistance card 10. Since hole '16 is larger in
70 'diameter than hole 17, the card 10 is isolated from the
shaft, and is not electrically aifected thereby.
A potentiometer variable wiper assembly, generally in
dicated by the numeral 32v is mounted on shaft 30 in
position to cooperate with the surface 10a of the resist
13) 75 ance card; The wiper assembly comprises a split annular
3,046,510.
5
6
hub portion S0 which -substantially surrounds the shaft
resistance card having a circular hole in rits center, and
formed to generate a sine-cosine voltage output, when
energized in a potentiometer circuit and, traversed‘inv-_a
circularl path by a wiper tap. Because of the circular
30, and yfrom which extend a wiper arm support 33' and
two clamping legs 34. A yscrew 35 threads into the two
legs 34 and operates by compressing the legs 34 to clamp
theannular portion about the shaft. A split sleeve 31
of insulating material is interposed between the annularl
portion 5,0 of the wiper assemblyrand the shaft 30, to
hole, a plurality of such cards may be mounted over av
single shaft to afford a- plurality of such potentiometers
ganged for unison operation by said shaft. To illustrate
isolate the shaft electricallyfrom the Wiper assembly. «
the operational environment of this resistance card, an
The end of the wiper arm support 33 is split at 38 and
illustrative embodiment of a plurality of ganged potenti
an end of 4contact element 39 Vis soldered therein. The 10, ometers employing such cards has been shown and de
contact element 39 extends fromrthe'arrn _33 and is bent
at 40 to resiliently engage the surface 10a of resistance
card 10.` Thus, when shaft 10 is rotated, the'assembly
32 is rotated therewith,A causing portion 4G` of wiper con
tact element 39 to traverse the surface 10a of card 10 in
a circular path.
'
An annular slip ring 36 is spot welded to hub S0 in an
area adjacent the arm 33, leaving split hub 50 resiliently
contractable by compression of legs 34 for clamping pur
scribed, but it is understood that this embodiment is only
illustrative, and is not intended >in any way to restrict the
scope of the invention as Uapplied tothe?esistance card
per se. Accordingly, such variations andmodifications
1,5 of the described embodiment of the invention as are'em
' braced by the spirit and scope of the appended claims, are
-contemplated as within the purview of the present inven
tion.
What is claimed is:
poses. A peripheral groove 37 is formed about the annu 20
card having a hole in the center thereof and four pe
form of a resilient wire lead.
ripheral edges, a terminal strip applied along the length
The entire wiper contact
assembly 32 is made of electrically conductive metal, so
that a voltage tapped at 40, may be obtained at the slip
J „pg
1,).
1. A potentiometer comprising a resistance card, said
lar slip ring 36 to accommodate a brush, usually in the
of each of two opposite ones of said four edges for es
tablishing a voltage gradient across the face of the card
ring 36.
`
25 between said two opposite edges when a voltage is ap
For the purpose of simplifying the illustration, the in
plied to said terminal strips, said two opposite edges be
put and output leads have not been shown. However, it
ing shaped with a generally concave perimeter curvature,
is understood that leads may be connected to terminal
and the other two of said four peripheral edges being
strips 12 and 13 to develop a voltage drop across the card
shaped with a generally convex perimeter curvature, a
10.> An output is derived from a lead slidably engaging
rotational shaft passing through said hole, a wiper tap
supported by said shaft for traversing the surface of said
the groove 37 in slip ring 36, and this output voltage will
vary in accordance with a sine-cosine function as the
card in a circular parth about said hole, and means for
wiper tap 40 is caused to traverse a circular path about
the axial center of shaft 30 over the surface 10a. of
supporting said shaft and card for relative rotation about
the axis of said hole.
35
2. A potentiometer as set forth in claim l, wherein
card 10.
'
'
As previously stated, the wiper assembly 32 is clamped
said hole is circular and its center is the center of said
to the shaft 30 by means of screw 35 and clamping legs
card, said card has substantially uniform specific resistiv
ity over its extent, the perimeter of said card is completely
34. The assembly 32 is located axially along shaft 30
defined by said four edges, said curvature of said two
_to bring the wiper tap 40` into resilient engagement with
the surface 10a of card 10. The wiper assembly and 40 opposite edges is defined substantially =by the equation:
resistance card are preferably separated by an insulating
spacer 42, and the entire assembly'is backed by a split
ring 43, seated in a circumferential groove defined about
shaft 30 to bear against the back of plate 11. Suitable
bushing may, of course, be provided between shaft 30‘ 45 and said curvature of said other two edges is defined
and ring 43 and plate 11, if desired. A plurality of such
substantially by the equation:
potentiometer assemblies may be mounted on shaft 30,
two being shown for illustration purposes in FIG. 2, and
of course their wiper contacts may be phased to any angle
of rotation relative to each other.
50 wherein r is the distance along the radius vector from
The potentiometers thus assembled on shaft 30 are
said center for any angle of rotation qb about said center,
mounted in a housing 46, which may comprise a cupped
a is the radius of said hole, and K and C” are constants,
tubular body 46a having an aperture 4-9` in its bottom
l whereby a sine~cosine function voltage output is tapped
wall, and an axial slot or key way 48 along its tubular
by said wiper when caused to traverse the surface of said
wall. Each plate 11 is provided with a key 41 which 55 card in a circular path about said center.
locates in key lway 48 to register the resistance cards and
3. A potentiometer as set forth in claim 2, wherein
retain them against rotation. An end of shaft 30 is seated
said card is a thin substantially flat card.
' in the hole 49 in the bottom wall of the housing. A
4. A potentiometer as set forth in claim 2, comprising
cover cap 47 having an aperture 50 is applied over the
a plurality of said cards, said shaft passing through the
open end of tubular body 46a to close the housing 46, 60 hole in each said card, and a variable wiper tap for each
and support the protruding end 45 of lshaft 30. The
said card supported by said shaft.
shaft is locked in axial position by means of two split
5. A potentiometer as set forth in claim 3, wherein
rings 44 seated in circumferential grooves in shaft 30 and
said card is a conductive plastic material. _
bearing against the exterior of the two ends of hous
6. A resistance card adapted for use in a potentiom
ing 46.
65 eter, having four peripheral edges and a hole in the cen
Thus, shaft 30 may be rotated by means of its protrud
ter thereof, a terminal strip applied along the length of
ing end 4S, causing the gangedwiper assemblies mounted
each of two opposite ones of said four edges for estab
thereon to rotate therewith, while the resistance cards are
lishing a voltage gradient across the face of the card
restrained against rotation by the keys 41 located in key
between said two opposite edges when a voltage is ap
Way 48. With resistance cards 10` fashioned in the man 70 plied to said strips, said two opposite edges being shaped
ner aforedescribed, and- with desired voltages applied
with a generally concave'perirneter curvature, and the
across the cards, rotation of shaft 30 obtains sine-cosine
other two of said four peripheral edges being shaped with
function voltage outputs from the wiper taps an-d as
a'generally convex perimeter curvature.
semblies 39 and 32. '
7. A resistance card as set forth in claim 6, wherein
There is thus provided by the present invention a fiat 75 said'hole is circular and its center is the center of said
3,046,510»
card, said card has substantially uniform specific resis
whereby a voltage output tapped from said card by a
tivity over its extent, the perimeter of said card is corn
pletely defined by said four edges, said curvature of said
circular trace about said `center varies as a sine-cosine
two opposite edges is defined substantially by the equation:
nal strips.
function when a uniform voltage is vapplied to said termi
8. A resistance card as set forth in claim 7, wherein
said card is a thin substantially flat card.
9. A resistance card as set forth in claim 8, wherein
said card is a conductive plastic material.
2
and said curvature of said other two edges is deiined
substantially by the equation:
wherein r is the distance along a radius vector from said
center for any angle of rotation «p about said center, a
is the radius of said hole, and K and C" are constants,
10
References Cited in the tile of this patent
UNITED STATES PATENTS
2,457,178
2,542,478
2,648,752
2,653,206
Richardson et al. ..... __
Clark _______________ __
Saunders _`_ __________ __
Montgomery _________ __
Dec.
Feb.
Aug.
Sept.
28,
20,
1l,
22,
1948
1951
1953
1953
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