Patent GB-967239-A (GB)
Title: Improvements relating to devices for interpolating or extrapolating amongst electrical signals
Inventor: HARTLEY FREDERICK WALTER
IPC: G05B19/4105
Filed: 1959-12-09
Abstract: 967,239. Electric analogue calculating. ELECTRIC & MUSICAL INDUSTRIES Ltd. Dec. 9, 1960 [Dec. 9, 1959], No. 41803/59. Heading G4G. [Also in Division G3] An electrical interpolating or extrapolating device comprises a source of reference voltage, a plurality of stores having input connections, output connections and means of adjustment responsive to respective values of a variable, so that the signals at the respective output connections are proportioned to the signals applied to the respective input connections according to the respective values of the variable; means being provided for applying relatively variable fractions of the reference signal to the input connections of the stores and for combining signals from the output connections of the stores so as to produce a resultant signal representing an interpolated or extrapolated value of the input variable. Fig. 1 shows an interpolator for e.g. machine tool control wherein a reference alternating voltage energizes an equally tapped autotransformer 4 traversed by a wiper 5; the voltages between the wiper and extremities 2, 3 respectively energizing similar stores A and B which comprise autotransformers A1, B1 tapped every 10 turns from A4, B4 to A13, B13 and every turn from A13, B13 to A22, B22. In store A, wipers A23, A24 traverse taps A4 to A13 and wipers A24, A25 traverse taps A13 to A22 to respectively energize the primary of 100:1 step down transformer A2 and that of 1: 1 transformer A3 in series with the secondary of A2. Wipers B23, B24 and B25, B26 operate similarly in store B to energize the primaries of transformers B2, B3 and the outputs of transformers A3, B3 are additively combined. Input information recorded e.g. on a punched tape operates e.g. a uniselector or relay tree (not shown) in known manner to position wipers, A25, A26, A23, A24 to represent decimal digits in descending order of significance, so that the output of A3 represents the decimal fraction of the voltage applied to A1 to 4 significant figures which is set in by wipers A23 to A26. The transformer B1 and wipers B23 to 26 operate similarly, so that if the initial value of a variable to be interpolated is set into store A and its final variable into store B and wiper 5 set to the lower extremity of transformer 4, A is fully energized and B is de-energized so that the output voltage represents the initial stored variable. As wiper 5 traverses the taps of transformer 4, the output voltage varies linearly towards the final stored variable as a function of the wiper position. The voltage steps derived from transformer 4 may be reduced in magnitude by the use of a linear subinterpolator of the kind described in Specification 802, 472 with a variable transformer of the kind described in Specification 799, 356 or an interpolating voltage divider of the kind described in Specification 910, 281. In a modification (Fig. 2) three similar stores 7, 8, 9 are energized from the wiper and one extremity of the input autotransformer 4 and three other similar stores 10, 11, 12 are energized from the wiper and the other extremity; the outputs of corresponding pairs of stores 7, 10; 8, 11 and 9, 12 being additively connected to the inputs of a quadrature interpolator 13 of the kind described in Specification 796, 994 or Specification 830, 462. Digital information from a recording tape representing respective reference coordinates of a point of surface (e.g. a turbine blade) requiring linear interpolation in one direction and quadratic interpolation in another direction is fed in, so that stores 7, 8, 9 contain information of three points not necessarily in a straight line; in such manner that straight lines in the surface join the points whose information is contained by stores 7, 10; 8, 11; and 9, 12 respectively and linearly interpolated voltages along these lines are fed to the inputs of the interpolator 13 which produces a quadratically interpolated voltage representing a coordinate of a point on a parabola (Fig. 3 not shown) intersecting three points represented by the respective inputs, and thus of a point on a surface defined by the six reference points, which may be scanned by the interpolated point to control a cutter, either along straight lines by arresting the quadrature interpolator or along parabolic lines by arresting the linear interpolator. Both interpolators may be operated simultaneously to describe an e.g. conical surface. In a further modification (Fig. 4) utilized in the control of a cutter machining a surface defined by nine reference points A to J (Fig. 5) having coordinates <SP>x</SP>(A to J) <SP>y</SP>(A to J) and Z(A to J) with quadratic by quadratic interpolation, alternating voltage energizes symmetrical points 21, 22 of a nonlinearly tapped autotransformer 23 having two symmetrical synchronized wipes 24, 25 moving over the taps. Twenty-seven stores Sx(A to J) Sy(A to J) and Sz(A to J) similar to those of Fig. 1 are arranged in cubical groups of nine receiving recorded information of the respective x, y and z coordinates of the nine reference surface points. Wiper 24 and terminal 21 energizes the A, B, C, stores, wipers 24, 25 the D, E, F, stores and wiper 25 and terminal 22 the C. H. J stores, whilst the outputs of stores SxA, D, G; SxB, E, H; SxC, F, J are respectively additively combined at the three inputs of quadratic interpolator 26. Corresponding Sy and Sz stores are additively combined at the three inputs of the quadratic interpolators 27 and 28, of the kind described in Specifications 796, 994 and 830, 462, whose output voltages represent points on parabolae intersecting points represented by the corresponding input voltages. A linear subinterpolator with a variable linkage transformer or slidewire potentiometer may be used as before, and the analog output voltages of the quadrature interpolators are applied to control retroactive servo systems 29, 30, 32; 33, 34, 35; and 36, 37, 38 controlling the movement of a work table 31 along its x, y and z axes, relatively to a cutter (not shown). At a particular setting of wipers 24, 25 representing a parameter t, the quadratic interpolators produce voltages continuously defining the x, y and z coordinates of a parabolically curved line PQR lying in the three dimensional surface, and for successive values of t set in by adjustment of taps 24, 25 a succession of such lines may be defined by the cutter along the surface to be machined, so describing a raster over the surface. The autotransformers 4 and 23 may be modified to operate as extrapolators. The operation of the stores is set forth in Specification 846, 381, and other interpolation or extrapolation formulae may be employed e.g. that set forth in Specification 865, 453.