US3046510A - Non-linear potentiometer - Google Patents

Description

July 24, 1962 D. G. WILLIAMS ET AL NON-LINEAR POTENTIOMETER Filed Aug. 18, 1961 3,046,510 Patented July 24, 1962 3,046,510 NON-LINEAR POTENTIOMETER David G. Williams and Joyce W. Williams, Littleton, Mass., assignors to Ace Electronics Associates, Inc., a corporation of Massachusetts Filed Aug. 18, 1961, Ser. No. 132,322 9 Claims. (Cl. 338-89) The present invention relates to variable resistors, such as potentiometers and rheostats, and is concerned primarily with resistance cards for use in such variable resistors.

` United States Patent Oce In particular, this invention relates to resistance cards f adapted to provide non-linear voltage functions, rsuch-as sine and cosine functions, when traversed over the surface 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 resistance card, whether wire wound, or formed of a molded resistance material, or formed by a deposited layer of resistance material, may be utilizedftoprovide sine-cosine output voltage functions; and one may vobtain such outputs lby imposing a uniform voltage across the card from contacts mounted for unison rotation on `a single shaft.

Itis apparent that Vthe most eliicient manner of ganging a plurality of these potentiometers is to mount a shaft through the centers of the several resistance cards, and to mount on the shaft a variable potentiometer wiper con- .tact arm for each card adjacent 'to the resistance surfaces of the respective cards. The resultant holes in the cards to accommodate the shaft afect'the voltage and current distributions over their surfaces, and thereby destroy or distort the sine-cosine functions originally obtainable yby circular traces or wipes about `the centers of the cards. The art has recognized the existence of this problem, and has sought through various means VAto correct `for these deviations, `as by altering the configuration of the card input terrninalsrapplied along twoi opposite edges of the card (Rosenthal Patent 2,764,657), or by altering the configuration of the two opposite card edges transverse to the input terminal edges of the card (Montgomery Patent 2,653,206);

These proposed `solutions to the problem, however, have been only approximations, and have failed to grasp the basic nature of the problem. `Arhole inthe center of a square resistance card alters the voltage and current distribution over the area of `the card so that the equipotential lines, which originally were straight lines across the card parallel to the voltage input edges of they card, are no longer straight, and differ in configuration at different ,points Vbetween thevoltage input edges. This compound ..mensions, i.e. along the dimensions parallel to and perpen- .v

hole through its center. It has'been found that allfour edges ofthe resistance card should follow complex curves.

For a card having a round hole through itscenter, it has been found that the two opposite edges of the-card generally paralleling the equipot'ential lines across the U 2 card, i.e. thetwo card edges along which the voltage input terminals are applied, should be generally concave; whilethe opposite twoedgesof Ithe card, the orthogonal trajectories, should be generally convex. More specifically, the equipotentialk edges should lfollow `a curve defined by the formula K K2 sin2 1 wherein r is the'dis'tance from the center of the card for various angles qi about the center, a is the radius of the round hole formed in the center of the card, and K is a constant; and the orthogonal trajectory edges should follow a curve defined by the formula 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 sinecosine potentiometer. 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 provide a sine-cosine potentiometer formed from such a card and having a variable tap mounted on -a rotary shaft passing through said hole.

And a further object of the present invention is to provide a plurality of such sine-cosine potentiometers ganged on a common rotary lshaft for the variable tap of each potentiometer. ,f f

Other lobjects and advantages `of the present invention.

|will become apparent tothose skilled in the art from a consideration of the following detailed description of one exemplary specific embodiment of the present invention, had in conjunctionwit'ht-he `accompanying drawings,

wherein like numerals refer to ylike or lcorresponding parts,

and wherein: y n

FIG. l is a plan view ofa flat resistance card formed in accordance with the present invention;

FIG. 2 is a longitudinal sectional view of la plurality of ganged potentiometers, each incorporating aL resistance card as shown in FIG. l; and

FIG. 3 is a cross-sectional View of the ganged potentiometers of FIG. 2, ktaken along the line 3--3` thereof.

The flat resistance card of the present invention-is indicated generally by the numeral 10. Preferably this card is formed as va molded conductive plastic resistance, and is of uniform cross-sectional thickness so as to provide substantially uniform specific resistivity over its extent. For structural support and mounting purposes, the card 10 is 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 resistance card, and may be applied as conductive coatings on the resistance card, or laminated thereto as preformed conductive metal foils, or comolded with the card 410 as conductive metal terminal plates. A hole 16 is formed in the center of the card 10 and overlies a hole 17 of smaller diameter in the insulating disc 11. t n i Leads from a voltage source (not shown) are to bel applied to terminal strips 12 and 13, thereby establishing a voltage gradient across the resistance` card 10 .between these terminals.. A variable potentiometer Wiper contact, to be subsequently described, mounted on a shaft passing through holes 16 `and 17is intended to traverse the surface of resistance card 10 along ya circleindicated for example Eby the phantom line 18. In traversing the circle 18,

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 output function, edges 14 and 15 of the card, referred to herein as the equipotential edges, followaa generally concave curvature, while the other two edges 19 and 20` follow a generally convex curvature. More specifically, a substantially pure sine-cosine output function is obtained 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 dened lby the equation wherein r is the distance from the center of the card (point Z1) for various angles gb about said center, C and K are constants, and a is the radius of hole 16.

In order that the nature of the present invention will be more fully appreciated, the mathematical derivation of the foregoingequations is presented. The Ifollowing derivation and the foregoing equations apply to a flat resistance card of uniform specic resistivity, having a hole 16 of radius a in the center .of the card :about point 21. The 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 `about the center of the card and r is a distance from the center of the card along a radius vector. Then Assuming VU, =R(r) I 15) In polar coordinates WeaaearsaetarLira RU) E dr @((b) =a constant--m2 Let B21 which is the Asolution for the curvature of edges 14 land 15.

From Equation 19,

is the differential equation for the orthogonal trajectories, when equated to Equation 30 is the solution for the curvature of edges 19 and 20.

Referring to FIGS. 2 and 3, the resistance card of FIG.

1 is shown assembled in a potentiometer, and two such J pg 1,).

hub portion S0 which substantially surrounds the shaft 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 isolate the shaft electricallyfrom the Wiper assembly.

The end of the wiper arm support 33 is split at 38 and an end of 4contact element 39 Vis soldered therein. The 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 is rotated, the'assembly 32 is rotated therewith,A causing portion 4G` of wiper contact 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 purposes. A peripheral groove 37 is formed about the annular slip ring 36 to accommodate a brush, usually in the form of a resilient wire lead. 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 ring 36.

For the purpose of simplifying the illustration, the input and output leads have not been shown. However, it is understood that leads may be connected to terminal strips 12 and 13 to develop a voltage drop across the card 10. An output is derived from a lead slidably engaging the groove 37 in slip ring 36, and this output voltage will vary in accordance with a sine-cosine function as the wiper tap 40 is caused to traverse a circular path about the axial center of shaft 30 over the surface 10a. of card 10.

As previously stated, the wiper assembly 32 is clamped to the shaft 30 by means of screw 35 and clamping legs 34. The assembly 32 is located axially along shaft 30 to bring the wiper tap 40` into resilient engagement with the surface 10a of card 10. The wiper assembly and 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 and ring 43 and plate 11, if desired. A plurality of such 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.

The potentiometers thus assembled on shaft 30 are mounted in a housing 46, which may comprise a cupped tubular body 46a having an aperture 4-9` in its bottom wall, and an axial slot or key way 48 along its tubular wall. Each plate 11 is provided with a key 41 which locates in key lway 48 to register the resistance cards and retain them against rotation. An end of shaft 30 is seated in the hole 49 in the bottom wall of the housing. A

cover cap 47 having an aperture 50 is applied over the open end of tubular body 46a to close the housing 46, and support the protruding end 45 of lshaft 30. The shaft is locked in axial position by means of two split rings 44 seated in circumferential grooves in shaft 30 and bearing against the exterior of the two ends of housing 46.

Thus, shaft 30 may be rotated by means of its protruding end 4S, causing the gangedwiper assemblies mounted thereon to rotate therewith, while the resistance cards are restrained against rotation by the keys 41 located in key Way 48. With resistance cards 10` fashioned in the manner aforedescribed, andwith desired voltages applied across the cards, rotation of shaft 30 obtains sine-cosine function voltage outputs from the wiper taps an- d assemblies 39 and 32.

There is thus provided by the present invention a fiat 6 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, traversedinva circularl path by a wiper tap. Because of the circular hole, a plurality of such cards may be mounted over av braced by the spirit and scope of the appended claims, are

contemplated as within the purview of the present invention.

What is claimed is:

1. A potentiometer comprising a resistance card, said card having a hole in the center thereof and four peripheral edges, a terminal strip applied along the length of each of two opposite ones of said four edges for establishing a voltage gradient across the face of the card between said two opposite edges when a voltage is applied to said terminal strips, said two opposite edges being shaped with a generally concave perimeter curvature, and the other two of said four peripheral edges being shaped with a generally convex perimeter curvature, a rotational shaft passing through said hole, a wiper tap supported by said shaft for traversing the surface of said card in a circular parth about said hole, and means for supporting said shaft and card for relative rotation about the axis of said hole.

2. A potentiometer as set forth in claim l, wherein said hole is circular and its center is the center of said card, said card has substantially uniform specific resistivity over its extent, the perimeter of said card is completely defined by said four edges, said curvature of said two opposite edges is defined substantially =by the equation:

and said curvature of said other two edges is defined substantially by the equation:

wherein r is the distance along the radius vector from said center for any angle of rotation qb about said center, a is the radius of said hole, and K and C are constants,

l whereby a sine-cosine function voltage output is tapped by said wiper when caused to traverse the surface of said card in a circular path about said center.

3. A potentiometer as set forth in claim 2, wherein said card is a thin substantially flat card.

4. A potentiometer as set forth in claim 2, comprising a plurality of said cards, said shaft passing through the hole in each said card, and a variable wiper tap for each said card supported by said shaft.

5. A potentiometer as set forth in claim 3, wherein said card is a conductive plastic material.

6. A resistance card adapted for use in a potentiometer, having four peripheral edges and a hole in the center thereof, a terminal strip applied along the length of each of two opposite ones of said four edges for establishing a voltage gradient across the face of the card between said two opposite edges when a voltage is applied to said strips, said two opposite edges being shaped with a generally concave'perirneter curvature, and the other two of said four peripheral edges being shaped with a'generally convex perimeter curvature.

7. A resistance card as set forth in claim 6, wherein said'hole is circular and its center is the center of said 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,

whereby a voltage output tapped from said card by a circular trace about said `center varies as a sine-cosine function when a uniform voltage is vapplied to said terminal strips.

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.

References Cited in the tile of this patent UNITED STATES PATENTS 2,457,178 Richardson et al. Dec. 28, 1948 2,542,478 Clark Feb. 20, 1951 2,648,752 Saunders Aug. 1l, 1953 2,653,206 Montgomery Sept. 22, 1953

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