28 INSTRUMENTATION IN SCIENTIFIC RESEARCH [Chap. 1 



is wound, and two brushes B x and B 2 moving in a circle relative to the 

 card. The accuracy is about J°. 



For details concerning sine, cosine, and other nonlinear potentiometers, see 

 F. E. Dole, in John F. Blackburn (ed.), "Components Handbook," M.I.T. 

 Radiation Laboratory Series, vol. 17, sees. 8.5 and 8.9; F. B. Berger and E. F. 

 MacNichol, Jr., in Britton Chance, F. C. Williams, V. W. Hughes, D. Sayre, 

 and E. F. MacNichol, Jr. (eds.), "Waveforms," M.I.T. Radiation Laboratory 

 Series, vol. 19, sec. 12.4; D. MacRae, Jr., and W. Roth, in Ivan A. Greenwood, 

 Jr., J. Vance Holdam, Jr., and Duncan MacRae, Jr., "Electronic Instruments," 

 M.I.T. Radiation Laboratory Series, vol. 21, sec. 5.7, all McGraw-Hill Book 

 Company, Inc., New York, 1948. 



The torque requirement to start the movement of the brush in 

 precision potentiometers is generally between 10 and 1 oz-in., and it 

 takes about half this amount to keep the brush in motion. Special 

 potentiometers are commercially available which require not more 

 than 0.003 oz-in. (200 dyne-cm) to move the brush. Intermittently 

 acting torque-free slide-wire resistances can be made by means of a 

 contact arm which moves over the resistance track, separated from 

 the track by a short distance, i.e., without touching the resistance 

 wire, and which is pressed against the resistance wire at periodic 

 intervals. 



A torque-free potentiometer for use in a-c circuits in whioh the 

 contact arm moves at a short distance from the slide wire to which it is 

 capacitively coupled is described by Dimeff and Fryer. 1 Over an 

 angular range of ±30° the error is within ^0.02°. 



Nonlinearity of potentiometers is largely a matter of definition. 2 

 The deviation from the best-fitting straight line which can be drawn 

 through the actual points of resistance is called "normal," or 

 "independent," nonlinearity. It is distinguished from zero-base non- 

 linearity (deviation from the best-fitting straight line passing through 

 the zero point) and from terminal nonlinearity (deviation from a 

 straight line passing through both end points of the electric travel). 

 The deviation from linearity in high-precision potentiometer trans- 

 ducers can reach values as low as 0.05 per cent, but it is generally of 

 the order of 0.5 per cent of the total resistance value. The higher the 

 total resistance, i.e., the thinner the resistance wire is, the higher the 

 linearity that can be obtained. In some potentiometers nonlinearity 

 occurs primarily in the region near the ends. 



If the actuating force is given, the dynamic response of a linear 



1 J. Dimeff and T. B. Fryer, Electronics, 30, 143 (February, 1957). 



2 See D. C. Duncan, Characteristics of Precision Servo Computer Potentiom- 

 eters, AIEE Conference on Feedback Control Systems, Atlantic City, N.J., 

 Dec. 6, 1951. 



