US2238863A - Translation device for phonographs - Google Patents

Description

April 15, 1941. L. D. NORTON TRANSLATION DEVICE FOR PHONOGRAPHS 2 Sheets-Sheet 1 Filed March 21, 1939 n W O M m TN YN M Q V T m V U u mym W .15 6 u L M w m Wk 4 w I I 0 5 y 3 W w a f 5 3 1% April 1941- L. D. NORTON 2,238,863

I TRANSLATION DEVICE FOR PHONOGRAPHS Filed March 21, 1939 2 Sheets-Sheet 2 INVENTOR LeZg nd v D. jVoiton ATTO Patented Apr. 15, 1941 TRANSLATION DEVICE FOR rnonocaarns Leland D. Norton, Bridgeport, Conn., assignor to Dictaphone Corporation, New York, N. Y., a corporation of New York Application March 21, 1939, Serial No. 263,229

16 Claims.

This invention relates to electromechanical translating devices and more particularly to commercial phonograph recorders or reproducers.

An object of this invention is to provide an improved device of this type, which is of simple construction, inexpensive to make, and yet capable of very high quality performance over a wide range of audible frequencies.

It is a further object of this invention to provide such a device which may be designed to have any desired predetermined non-linear or non-proportional relationship between the mechanical and electrical forces therein, whereby known eccentric characteristics of materials or of the apparatus with which the device is used may be compensated for so as to produce a faithful reproduction of the original audible frequencies.

Other objects will be in part obvious and in part pointed out hereinafter.

These and other beneficial objects of this invention are attained by the novel structure described in the following specification which may be more readily understood by reference to the accompanying drawings, wherein:

Figure 1 is a perspective view of a commercial phonograph reproducer unit embodying the invention;

Figure 2 is a top view of the reproducer unit shown in Figure 1, with a portion thereof shown unit shown in Figure 1; and

Figure 7 is an exploded view of the armature support and damping mechanism of this reproducer unit.

For the purpose of this description, an electromechanical translating device embodying the invention is shown incorporated in a suitable phonographic transcribing machine. For the purpose of illustrating the invention a portion of such a machine is shown in Figure 5, having I a carriage 2 mounted on guide rods, one of which is shown at 4, and a bracket 6 adapted to support a reproducer or pick-up unit, generally indicated at 8, for reproducing sound recorded upon a record cylinder H) which is mounted in a well-known manner upon a rotatable mandrel or record support l2. Carriage, guide rods, mandrel, and driving mechanism (not shown) are all suitably mounted upon a frame (not shown) also of well-known construction.

The reproducer unit 8 comprises an electromagnetic translation device, best shown in Figure 1 and indicated generally in Figure 5 by the reference character 14, supported within a housing it, and an adjustable counterweight (not shown) supported within a forward extension l8 of housing I 6, all of which is pivotally supported on the bracket 6 by a pivot arrangement, generally indicated at 20.

The translation unit 14 is adapted to be completely assembled independently of its housing, and, after assembly, to be received within the rear portion of the housing It where it is held in place by a cover plate ii. The cover plate I5 is secured to housing l6 by a screw l1 threaded into the rear surface of housing l6 and by a screw l9 threaded into a post 2| fastened to the upper inner surface of housing 16 as shown in dotted lines in Figure 5. Post 2| passes through a hole in a lug 22 extending from the translation unit l4, as shown in Figures 1, 3, and 6, to aid in positioning the unit in the housing.

Referring to Figures 1, 2, 3, 6, and 'I, the trans-= lation unit l4 comprisesvery'few parts, all attached more or less directly to a U-shaped bracket member 24 formed of non-magnetic sheet metal. The center portion 26 of'this bracket member 24 at the base of the U is bent forward slightly, as is shown in Figure 1, to provide a means for mounting the armature supporting structure 50 in proper relation to an air gap, as will be more fully described hereinafter. -The base portion of this U-shaped bracket member 24 also extends downwardly to form the abovementioned lug 22. Two soft-iron pole pieces having rectangular base portions 30 and S-shaped pole tips 34, shaped substantially as shown in Figures 1 and 2, are attached to the arms of the bracket 24 by means of screws 32 which thread into suitably tapped holes in base portions'3ll of the pole pieces. The S-shaped pole tips 34 are substantially square in cross-sections and extend toward each other. The ends 36 of these pole tips 34 are tapered tea square cross-section of about one-fourth of the cross-section at their bases to concentrate the magnetic flux therethrough, and terminate in joblique planes 38 which term a V-shaped trough-like air gap 62 therebetween, as shown in Figure 2. Each oi the pole tips 34 supports a coil 46 wound on square coil forms 46. These coils M are connected so that their eiiect is additive. The coil forms 56 fit snugly around the pole pieces at the points where the S-shaped portions 36 meet the base portions 30. The S-shaped pole tips 8% are provided with rounded corners at the bends 83 and 35 so that the coils may be readily slipped into place to facilitate assembly of the translation unit.

The vibratory armature support of the translation device M, which may be seen more clearly in Figure 7, consists of a small approximately triangular shaped piece 50 of very light resilient non-magnetic sheet metal, flat at its base ti? and or other similar damping material is secured to the back surface of the projecting portion 62 of plate be so as to act as a resilient separator between this projection and the base 53 of the armature. The proper adjustment of plate 58 is such that the legs SI of the triangular armature 52 are normally separated from the faces 38 of the pole tips 34 by small air gaps, and it is bent to a V-shape at its apex 48. A triangular opening 49 is provided in this sheet to reduce its weight and increase its resilience. The base t'd of the member 50 is attached by two screws 28 to the raised center portion 26 of the bracket 26. The armature, comprising a strip of soft magnetic iron 52, is bent in triangular shape so that its forward faces 5| correspond with the contour of the air gap 42, and its base 53 provides an additional path for the magnetic flux through the armature. It is attached to the upper end tit? of the armature support 50 by means of rivets 5d, and a reproducing stylus 5G is suitably attached to the apex of this triangular shaped armature 52 where it is joined to the upper end as of the armature support 50. The armature support 5b is so formed that it holds the armature 52 in the trough-shaped air gap 42 and gently urges the two converging forward faces SI of the armature toward the oblique faces 38 of the ends 36 of the pole tips 34.

It is preferable that this entire armature structure be as light as possible and that the resilient non-magnetic support 50 be extremely light and flexible so that the entire moving unit has little inertia.- This low inertia of the moving parts is desirable so that when the translation device it is used upon wax records of the type usually used with commercial phonographs, the movement of the vibratory parts may accurately follow the undulation of the sound grooves in the record over a very wide range of frequencies, and be capable of transmitting accurately the higher frequencies of speech, even up to and above frequencies of 6000 cycles. If the mass of this moving portion of the translation device were high, the stylus would not follow the variations of the sound,

track rapidly enough, particularly in respectto the higher frequencies, and would tend to scrape off the higher portions of the wax in the sound track, thus ruining the recording for further reproduction and at the same time producing distortions.

In order properly to position the armature and provide means for damping its oscillation at its natural frequency, an adjustable damping support is provided. This support comprises a plate 58 having a lug 50 projecting from one side. A

portion 62 of this lug 60 is bent at right angles to the plane of the plate, as shown in Figure 7.

The plate 58 is secured to the pole tips 34 by securely fastened in this position by means of the screws 64%.

A permanent magnet E0 in the shape of a rectangular bar, preferably made of some highly retentive magnetic material such as that commercially known as Nipermag is provided to supply the magnetic flux to the translation unit M. This magnet it, as is more clearly shown in Figure 6, fits snugly between the inner faces 60 of pole pieces 3d where it is held in place solely by its own magnetic attraction to these pole pieces. Its great magnetic force, however, renders this attraction sufiicient to adequately secure this magnet in this position.

From the foregoing description it is apparent that this translation unit I4 is composed of a few simple parts which may be quickly and easily assembled. This assembly operation is preferably performed by first sliding the coils 44, wound on their rectangular spools 35, onto their respective pole tips 36. The pole pieces 30 are then attached to bracket 24 by screws 32 and the armature assembly support 50 is fastened to the raised portion 26 of bracket 24 by screws 28. The armature position and the amount of damping is then determined by the adjustment of plate 58. Finally, the permanent magnet 10 is slid into place. This completes the assembly of the translation unit [4 so that when it is fastened in position in housing it by means of cover plate I5, and the coils Ml are suitably connected, it is ready for operation.

This ease of assembly is very desirable in quantity production of such units, for it facilitates the proper assembly of delicate reproducersby relatively unskilled workmen. Locating the armature in the air gap by means of adjustment plate 58 is the only delicate adjustment in this device, and this one precise adjustment can be made by skilled operators after the device has been assem-bled by relatively unskilled workmen. In addition, because of the V-shaped contours of the air gap and the armature, this adjustment can be made accurately by means of the plate 58 without the need for close tolerances in manufacturing the parts. This permits the various parts to be manufactured in quantity with fairly large tolerances, and thus they may be interchangeable from one unit to the other without in any way impairing the operation or efliciency of the device. I

Numerous advantages are obtained by using a simple rectangularly-shaped bar magnet of high retentivity to provide the magnetic flux. The use of such highly retentive magnetic material, such as the above-mentioned Nipermag, enables a very strong magnetic field to be produced by a smalllpermanent magnet. Further, by usi g a simple rectangularly-shaped bar magnet whic merely slips into position and is held in place between the pole pieces by its own magnetic attraction instead of by screws, many machining operations are eliminated.

known manner. The undulations in the record but previously by recording apparatus, move the stylus n and um the armature n in and out of the trough-shaped air gap 42, thus varying the reluctance of the magnetic circuit comprising the air gap 42, pole pieces 30, and the permanent magnet Ill. Coils 44 are inductively coupled to this magnetic circuit so that variations in its reluctance cause variations in the magnetic lines of force cutting the coils N. Such changes in the magnetic field through the coils ll develop voltages in the coils which are proportional to the changes in magnetic lines in the magnetic circuit. These voltages in turn may be amplified and reproduced as sound, as by means of a suitable amplifier and loudspeaker unit.

In accordance with the present invention certain eccentric characteristics of the recording apparatus or of the amplifier or reproducer may be compensated for by proper design of the translation unit so as to produce a faithful reproduction ofthe original audible frequencies. This is accomplished by predetermining the shape of the air gap 42 and the armature 52 so that the relationship between the mechanical motion of the armature and the voltage generated in coils N follows any predetermined desired function.

For example, in the embodiment of the invention herein described. the flux in the magnetic circuit is inversely proportional to the length of the air gap. Thus, neglecting flux leakages, and second order effects such as variation in the permeability of the iron, this may be expressed in the following equation:

where: =total flux in the magnetic path I =length of the air gap, and k'=a constant.

Further, as the voltage developed in the coils is proportional to the time rate of change of flux, then:

where: e =voltage in the coils k"=a second constant, As:

d k' dl E? F assuming that the velocity of the armature is constant, then:

where k"'=a third constant.

Thus, with this arrangement the veloped in the coils 44 varies inversely with the square of the length of the air gap, thereby producing a response which provides a predetermined non-linear relationship between the movement of the reproducing stylus and the voltage developed in the reproducer coils.

One kind of eccentric characteristic of recording apparatus which might be compensated for in this manner, for example, is the inherent characteristic of hill and dale" wax records of offering increased resistance to the cutting stylus of the recording apparatus as the depth of the cut increases. In the type of commercial phonographs most frequently used for recording on voltage decylindrical wax records, if a pure sine wave tone is impressed on the instrument, approximately equal power will be exerted on the cutting stylus during both halves of each cycle. Figure 4 shows schematically a greatly magnified cross-section of a portion of a record taken along the line of cut of a recording stylus. In this figure, line I! represents the surface of the record, and the dash line ll represents the depth of the mean cut of the recording stylus when no sound is impressed upon the recording apparatus. Under these conditions, the dotted line curve 16 represents the undulation in the record groove which theoretically should be cut by the recording stylus for a pure sine wave tone. In actual operation, however, when recording such a pure sine wave tone, the curve of the cut in the record groove will more nearly simulate that shown in an exaggerated manner by the solid line curve I8. This discrepancy between the actual curve 18 and the theoretical curve 18 is caused by the fact that the recording stylus meets considerably increased resistance as it cuts deeper into the record, so that, with equal force exerted on the recording stylus for each half of a cycle, the extent of motion of the recording stylus is much greater for the half cycle in which it is moving away from the mean line 14 toward the surface of the record than it is for the half of the cycle when it is moving from the mean line "It down into the record, thus producing an actual out similar to curve 18. According to the present invention, in order to produce a tone in the output of the reproducer, which is a faithful reproduction of the tone impressed upon the recording apparatus, the air gap 42 in the translation device ll forms a V-shaped trough, and the forward faces ii of the armature 52 similarly form a. V to correspond to the contour of this air gap. With such a design, when the armature moves from its normal position toward the pole faces 0 as it slides down into the valleys of the record groove the reluctance of the magnetic circuit of the translation device It decreases at a greater rate than the reluctance increases as the armature 52 moves from its normal position away from the pole faces 40. Therefore, the rate of change in the magnetic flux cutting coils 44 is much greater when the stylus 56 moves into the record than it is when the stylus moves toward the surface of the record. Thus, by proper design of the air gap 42 and the armature 52, this non-proportional characteristic of the translation device It can be made to compensate for the eccentric characteristic of the recording apparatus so as to produce an output voltage curve which closely approximates curve I6.

It is of course to be understood that this example is given for illustrative purposes only and that the pole faces 40 and the armature 52 may be given any suitable curvature both with respect to each other and with respect to the path of motion of the armature so as to make the relationship between the motion of stylus 56 and the voltage developed in coils 44 correspond to any desired function. Further, it is of course not necessary that this predetermined characteristic of the translation element It be such as to compensate for eccentricities in the characteristics of the rest of the apparatus used. It is entirely possible that the translation unit It may be used to introduce eccentricities into the response of the recording apparatus if such should prove desirable.

is meant any trough or wedge of suitable crosssection and having parallel elements of generation, and in which two faces of the trough. or wedge converge. For example, the cross-section might be semicircular or elliptical. In addition, it is also to be understood that the armature may have a cross-section of a given form and the air gap a cross-section of different form if such an arrangement provides the desired predetermined non-linear relationship between movement of the stylus and the voltage developed in the reproducer coils.

As many possible embodiments of the present invention may be made without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative only and not in a limiting sense.

I claim:

1. An electro-mechanical translating device, comprising, in combination, means forming a magnetic circuit including a trough-shaped air gap of predetermined form'having pole faces symmetrically disposed with respect to a plane lolsecting said air gap, a wedge-shaped armature of predetermined form positioned in said air gap, means for mounting said armature for movement in said air gap along a path parallel to'said bisecting plane in correspondence to changes in the flux in said magnetic circuit, and electrical means associated with said magnetic circuit having an electrical characteristic variable in correspondence with said flux changes therein, the forms of said air gap and armature being chosen so that the relationship between the movement of said armature and the change of flux of said magnetic circuit follows a predetermined nonlinear function.

2. An electro-mechanical translating device comprising, in combination, means forming a magnetic circuit including a trough-shaped air gapof V-shaped cross-section having pole faces symmetrically disposed with respect to a plane bisecting said air gap, a wedge-shaped armature of V-shaped cross-section positioned in said air gap, means for mounting said armature for movement in said air gap along a path parallel to said bisecting plane in correspondence to changes in the flux in said magnetic circuit, and electrical means associated with said magnetic circuit having an electrical characteristic variable in correspondence with said flux changes therein, the forms of said air gaps and armature being chosen so that the rate of change of the flux in said magnetic circuit is approximately inversely proportional to the square of the effective,instan-- taneous length of said air gap.

3. In a reproducing device for phonographs, in combination, means forming a magnetic circuit including a trough-shaped air gap of predetermined form having pole faces symmetrically disposed with respect to a plane bisecting said air gap, awedge-shaped armature of predetermined form positioned in said air gap, a stylus associated with said armature, means cooperating with lationship between the movement of said stylus and the change of the flux in said magnetic circuit follows a predetermined non-linear function.

4. In an electro-magnetic translating device, in combination, a frame, magnetic means secured to said frame and having a trough-shaped air gap between its pole tips, the pole faces of said magnetic means lying in intersecting planes symmetrically disposed with respect to a plane bisecting said air gap, a wedge-shaped armature member having two flat faces disposed in intersecting planes, means for mounting said armature member for movement in said air gap along a path parallel to said bisecting plane so that the line of intersection of the planes of the faces of said armature is parallel to and may move toward and away from the line of intersection of the planes of the faces of said pole tips, mechanical means movable with said armature in correspondence with the change of flux in the magnetic cincuit formed by said magnetic means, air gap, and armature, and electrical means associated with said magnetic circuit having an electrical characteristic variable in correspondence with the changes in the magnetic flux therein.

5. In an electro-magnetic translating device, in combination, a frame, magnetic means secured to said frame and having a trough-shaped air gap between its pole tips, the pole faces of said magnetic means lying in intersecting planes symmetrically disposed with respect to a plane bisecting said air gap, a wedge-shaped armature member having two flat faces disposed in intersecting planes, means for mounting said armature member for movement in said air gap along a path parallel to said bisecting plane so that the line of intersection of the planes of the faces of said armature is parallel to and may move toward and away from the line of intersection of the planes of the faces of said pole tips, mechanical means movable with said armature in correspondence with the change of flux in the magnetic circuit formed by said magnetic means, V3.1! gap, and armature, electrical means associated with said magnetic circuit having an electrical characteristic variable in correspondence with the changes in the magnetic flux therein,

and means for determining the limits of approach of said armature to said pole tips.

6. In an electromagnetic translating device, in combination, a frame, a magnet secured to said frame and having a trough-shaped air gap between its pole tips, the faces of said pole tips being flat and in intersectingplanes, a wedgeshaped armature member having two flat faces disposed in intersecting planes movably mounted on said frame and adapted to move in said air gap so that the line of intersection of the planes of the faces of said armature-is parallel to and may move toward and away from the line of intersection of the planes of the faces of said pole tips, mechanical means associated with said armature for moving it in said air gap to vary the flux in the magnetic circuit formed'by said magnet, air gap, and armature, electrical means associated with said magnetic circuit and responsive to changes in the magnetic flux therein, the plane of'motion of said armature being perpendicular to the line of intersection of the planes of its faces, said armature having a hole in it perpendicular to its plane of motion, a projecting portion rigidly secured to the frame approximately perpendicular to the plane of motion of said armature and projecting into the hole in the armature but not physically contacting the same,

and damping means interposed between said pro- Jecting portion and at least a portion of the walls of the hole in the armature to damp the oscillations of the latter.

7. In an electromagnetic translating device, in combination, a frame, a magnet secured to said frame and having a trough-shaped air gap between its pole tips, the faces of said pole tips being flat and in intersecting planes, a wedgeshaped armature member having two flat faces disposed in intersecting planes movably mounted on said frame and adapted to move in said air gap so that the line of intersection of the planes of the faces of said armature is parallel to and may move toward and away from the line of intersection of the planes of the faces of said pole tips, mechanical means associated with said armature for moving it in said air gap to vary the flux in the magnetic circuit formed by said magnet, air gap, and armature, electrical means associated with said magnetic circuit and responsive to changes in the magnetic flux therein, the plane of motion of said armature being perpendicular to the line of intersection of the planes oi its faces, said armature having a hole in it perpendicular to its plane of motion, a projecting portion rigidly secured to the frame approximately perpendicular to the plane of motion of said armature and projecting into the hole in the armature but not physically contacting the same, damping means interposed between said projecting portion and at least a portion of the walls of the hole in the armature to damp the oscillations of the latter, and means to position said projecting portion with respect to said frame,

thereby to position said armature in said air gap.

8. A translation device assembly for phonographs, comprising, in combination, a non-magnetic support member, two pole pieces comprising a portion of a magnetic circuit supported by said member in spaced relationship to form two air gaps between ends thereof, an armature mounted on said support member andpositioned to move in the one of said air gaps, a stylus attached to said armature member for moving it in said one air gap in response to undulations of a record groove, a permanent magnet operatively interposed in the other of said air gaps to complete said magnetic circuit through said pole pieces, said first air gap, and said armature, said permanent magnet being held in place solely by its own magnetic attraction to said pole pieces, and electrical means associated with said magnetic circuit responsive to the change in magnetic flux therethrough.

9. A reproducer assembly for phonographs, comprising, in combination, a non-magnetic plate-like support member, two pole pieces comprising a portion of a magnetic circuit attached at one end to the ends of said support member and held thereby in spaced relationship to form an air gap, of predetermined size between the free ends thereof, pick up coils surrounding each of said pole pieces, an armature member resiliently supported on said support member and positioned to move in said air gap. a stylus attached to said armature member for moving it in said air gap in response to undulations of a record groove, and a permanent bar magnet operatively interposed between the fixed ends of said pole pieces to complete said magnetic circuit through the pole pieces, air gap, and said armature, said bar magnet being held in position solely by its own magnetic attraction to said pole pieces.

10. A reproducer assembly for phonographs,

- in response to undulations of a record groove, a

but

permanent bar magnet operatively interposed between the ilxed ends of said pole pieces to complete said magnetic circuit through the pole pieces, air gap, and said armature, said bar magnet being held in position solely by its own magnetic attraction to said pole pieces, and an adjustment member rigidly secured to said support member and flexibly associated with said armature member to aid in positioning said armature member and to damp its oscillations.

11. An electro-mechanical translating device, comprising, in combination, means forming a magnetic circuit including a trough-shaped air gap of predetermined form, a wedge-shaped armature of predetermined form occupying a given normal position in said air gap, means for mounting saidarmature for movement in said air gap in correspondence to changes in the flux in said I magnetic'circuit, a stylus adapted. to cooperate with a record surface, means mechanically connecting said stylus to the apex of said wedgeshaped armature, and electrical means having an electrical characteristic corresponding to said change of flux in said magnetic circuit, whereby the rate of change of said electrical characteristic corresponding to a movement of said armature in one direction from said normal position is greater than the rate of change of said electrical characteristic corresponding to a similar movement of said armature in the opposite direction.

12. An electro-mechanical translating device for use in vertical-cut recording systems, comprising, in combination, means forming a magnetic circuit including a trough-shaped air gap, a wedge-shaped armature positioned in said air gap, means for mounting said armature for movement in and out of said air gap, the movement of said armature corresponding to changes in the flux in said magnetic circuit, a stylus adapted to cooperate with a record surface, means connecting said stylus to said armature for moving said armature into said air gap when saidstylus approaches said record surface and out of said air gap when said stylus moves away from said record surface, and electrical means associated with said magnetic circuit means having an electrical characteristic corresponding to said changes of flux in said magnetic circuit.

13. An electro-mechanical translating device, comprising, in combination, means forming a magnetic circuit including a trough-shaped air gap of predetermined form, a wedge-shaped armature "of predetermined form movably mounted in a normal position in said air gap for movement in and out of said air gap toward and away from said normal position in correspondence to changes in the flux in said magnetic circuit, and electrical means associated with said magnetic circuit having an electrical characteristic variable in correspondence with said flux changes therein, whereby said electrical characteristic changes more rapidly with a given movement of said armature in one direction from said normal position than with a corresponding movement of said armature from said normal position in the opposite direction.

14. In an electromagnetic translating device, in combination, a frame, a magnet secured to said frame and having an air gap between its pole tips, an armature member movably mounted on said frame for movement in said air gap in correspondence to changes in the flux in the magnetic circuit formed by said magnet, said air gap, and said armature, mechanical means associated with said armature for movement in correspondence to changes in the flux in said magnetic cir cuit, inductive means associated with said magnetic circuit having an electrical characteristic variable in correspondence with the flux changes therein, said armature having a hole in it perpendicular to its plane of motion, a rigid projecting portion secured to the frame approximately perpendicular to the plane of motion of said armature and projecting into the hole in the armature but not in physical contact therewith, and damping means interposed between said projecting portion and at least a portion of the wall of the hole in the armature to damp the oscillations of the latter.

15. In an electromagnetic translating device, in combination, a frame, a magnet secured to said frame and having an air gap between its pole tips, an armature member movably mounted on said frame for movement in said air gap in correspondence to changes in the flux in the magnetic circuit formed by said magnet, said air gap, and said armature, mechanical means associated with said armature for movement in correspondence to changes inthe flux in said magnetic circuit, inductive means associated with said magnetic circuit having an electrical characteristic variable in correspondence with the flux changes therein, said armature having a hole in it perpendicular to its plane of motion, a rigid projecting portion secured to the frame approximately perpendicular to the plane of motion of said armature and projecting into the hole in the armature but not in physical contact therewith, damping means interposed between said projecting portion and at least a portion of the wall of the hole in the armature to damp the oscillations of the latter, and means to position said projecting portion relatively to said frame to position said armature in the air gap.-

16. An electro-mechanical translating device comprising, in combination, means forming a trough-shaped air gap of predetermined form having faces symmetrically disposed with respect to a plane bisecting said air gap, a movable wedgeshaped member of predetermined form positioned in said air gap, means for mounting said movable member for movement in said air gap along a path parallel to said bisecting plane, and electrical means associatedwith said air gap and having an electrical characteristic variable in correspondence with changes in the lengths of said air gap, the forms of said air gap and said movable member being chosen so that the relaticnship between the movement of said movable member and the change of said electrical characteristic follows a predetermined non-linear function.

LELAND D. NORTON.

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