Patent GB-992791-A (GB)
Title: An improved circuit for generating voltage analogue signals representing trigonometrical functions
Inventor: TYZACK DONALD ERNEST
IPC: G05B19/33
Filed: 1960-06-24
Abstract: 992,791. Programmed control of machine tools. ELECTRIC & MUSICAL INDUSTRIES Ltd. June 26,1961 [June 24, 1960], No. 22115/60. Heading G3N. [Also in Division G4] A circuit for setting up first and second output signals proportional to the sine and cosine of a prescribed angle representing a required displacement comprises an arrangement for deriving first and second signals proportional to the sine and cosine of a major part of the angle, and transformers for forming first and second incremental signals, the primaries of the transformers being energized from the output signals, and their transformation ratios being adjustable in linear steps to represent the minor part of the prescribed angle and thus approximately the tangent of this minor part. The first incremental signal is proportional to the product of the second output signal and the tangent of the minor part and is added to the first derived signal to provide the first output signal; similarly the second incremental signal is proportional to the product of the first output signal and the tangent of the minor part and is added to the second derived signal to provide the second output signal. The prescribed angle # whose sine and cosine functions are to be derived is considered as the sum of a major part # 1  and a minor part # 2 , and the uniselectors U 1  to U 4  (Fig. 1) are set to represent these parts, as described below. A transformer T 1  has its secondary winding tapped so as to provide voltages proportional to the sines and cosines of a series of reference angles, the appropriate tapping, representing # 1 , being selected by the switches SA a , which provides the sines, and SA b , which provides the cosines, on the uniselector U 1  A further uniselector U 2  operates a series of switches arranged to provide phase reversal where necessary when dealing with angles # 1  greater than 90 degrees. The signal between the switches SB a  and SB b , representing sin # 1 , is fed through the windings P2 and P3 on the transformer T2 to the output terminals 24 and 35, while the signal representing cos # 1  between the switches SB c  and SB d , is fed through the windings P4 and P5 on the transformer T3 to the terminals 22 and 23. The turns ratios between the windings S3 and S4 and the windings P2 and P4 respectively are chosen so that P2 and P4 may be tapped linearly to provide voltages which represent small angles in intervals of 1. 8 degrees. Similarly the linear tappings on the windings P3 and P5 are spaced at intervals of 0.18 degrees. The selectors SC a  and SD a  may then be set to represent the minor part # 2  of the desired angle as a combination of two smaller parts, one from the winding P2 and the other from the winding P3. The output voltage across the two windings chosen by these selectors is this V c  # 2  which will be approximately V c  tan # 2 , V c  being the output voltage fed to the primary of the transformer T2 and # 2  lying in the range -9 to +9 degrees. Thus the output voltage V s  = sin # 1  + V c  tan # 2  Similarly the output voltage V c  = cos # 1 - V s  tan # 2 . It is shown in the Specification that V s /V c  = tan (# 1  + # 2 ) = tan 6, so that V s  and V c  are in fact the output voltages required proportional to sin # and cos #. The synthesis of the tangent of an angle # + # is described (Fig. 2, not shown) where # is an angle representing increments from an original displacement #. The described arrangements may form part of a machine tool programming system, the two output voltages being applied to zig-zag inductances on the cursor of a planar positioning device or to the quadrature windings of other types of resolver. The apparatus described may constitute a trigonometric store for the last or most accurate positioning resolver used in a control system. Inherent causes of error in machine tool position programming systems and ways in which they may be compensated are discussed. The described apparatus is a modification of that described in Specification 889,581.