Patent GB-865453-A (GB)
Title: Improvements relating to electrical interpolating devices
Inventor: ABBOTT DAVID JOHN
IPC: G05B19/4105
Filed: 1957-01-03
Abstract: 865,453. Electric analogue computers. ELECTRIC & MUSICAL INDUSTRIES Ltd. Jan. 3, 1958 [Jan. 3, 1957], No. 294/57. Class 37. An interpolating device particularly for automatic machine-tool control, comprising at least two variable transformers intercoupling three input points and one output point and in which ordinates of a point on a conic arc may be represented by the output, the conic arc being determined by the amplitudes of alternating cophasal analogue signals at the three inputs and one variable the variation of which is represented by the variation of the transformation ratio of one transformer, and the movement of said point along said arc being achieved by variation of the transformation ratio of a second transformer. Interpolation is achieved along curves defined in a complex projecting plane by the use of homogeneous co-ordinate. The particular case of areal co-ordinates is actually used. The triangle of reference X.Y,Z[X(1,0,0)Y(0,1,0)Z(0,0,1)] is so chosen that the vertices X, Z lie on the conic and the vertex Y is the point of intersection of the tangents at X, Z so that the equations ax<SP>2</SP>+by<SP>2</SP>+cz<SP>2</SP>+ 2fyz+2gzy+2hxy=0 reduces to y<SP>2</SP>=k<SP>2</SP>xz, and any point on this conic may be represented as (1/#, k, #), where 6 is a parameter and the value of k determines the type of conic. Points X, Y, Z are referred to a cartesian co-ordinate system and have co-ordinates (x 1 y 1 ) (x 2 y 2 ) and (x 3 y 3 ) respectively and it is shown that the x, y ordinates of a point P also referred to the cartesian co-ordinate system are Thus, if (x 1 y 1 ), (X 2 Y 2 ) '  (x 3 y 3 ) and k are chosen to give a particular conic, the conic may be driven by the variation of the parameter #. The principle of the invention is illustrated by Fig. 2, comprising a transformer having a closed core C and three primary windings L1, L2, L3, the number of turns of which are inversely proportional to 1/#, K and #, respectively. Co-phasal alternating voltages Vx 1 , V x2 , V x3  (the amplitudes of which represent x 1 , x 2 , x 3 , respectively) are supplied to the transformer windings and it is proved that alternating voltage Vxp generated at the junction of the windings is analogous to the x-ordinate of P, said voltage Vxp (amplitude xp) being generated by a suitable choice of Vx 1 , Vx 2  and Vx 3  and k and variation of parameter #, the said variation providing the variation in output to represent a series of points on the desired conic. The particular embodiments are concerned with different methods of varying the value of parameter # employing the variable transformers. In the embodiment of Fig. 5, the primary windings L1, L2, L3 have tapping-points a 1  to a 4 , b 1  to b 4  and C 4  to c 7 , respectively, the secondary windings L4, L5, L6 being connected in series in a loop, which replaces closed core C of Fig. 2, tappings a 4 <SP>1</SP>, a 5  to a 7  and c 4 <SP>1</SP>, c 1  to c 3  being provided on windings L4, L6, respectively. Analogue voltages Vx 1 , Vx 2 , Vx 3  are fed to sliders d 1  to d 3 , and the value of k is defined by the stud b employed. Each tapping on L1, L4 corresponds to a different value of # and each tapping on L3, L6 to a different value of 1/#, # being varied in the range 0-#00 by the synchronous rotation of the sliders d 1 , d 1 <SP>1</SP>, d 3 , d 3 <SP>1</SP>, the transformation ratios of both transformers being thus varied simultaneously. A subinterpolation device for use with the device of Fig. 5 is also described (Fig. 6, not shown). In a further embodiment, Fig. 7, a parameter Z is used which is varied in the range - 1 to + 1, where z is cos 2y, tan γ=#, the equation for the x-ordinate thus becoming a similar equation holding for the y co-ordinate. The device comprises two series of studs m1-m7 and n1-n7 traversed by mechanically and electrically connected contacts M, N, which are movable to represent z in a range - 1 to + 1. Studs m are uniformly spaced and connected to uniformly spaced tappings on the auto-transformer L9 to the input terminals of which are applied Vx 1  and Vx 3 . Studs n are also uniformly spaced and connected to tappings on a winding L10 spaced to represent the values of +#1-z<SP>2</SP> for the value of z represented by the respective contact. L10, L11 form a transformer having a transformation ratio + #1-z<SP>2</SP>: 1, tappings of a further winding L12 being connected to studs q1 to q4 which are engaged by a movable contact Q connected to L11 to represent variation of k. L12 and a further winding L13 form a further transformer having a transformation ratio k: 2 input Vx 2  being applied to L13. It is proved in the Specification that the amplitude xp of the output Vxp is equal to the equation for x stated above. In a modification, L11 and L12 may be omitted and L13 coupled directly to L10 in which case Vx 2  is applied to contact Q and q 1  to q 4  are connected to tappings on L13 spaced to represent 2/k. A development of this is described (Fig. 8) in which tapped windings L10, L13 (forming a transformer of transformation ratio #1- z<SP>2</SP>¸1) are replaced by a series of separate windings connected to the tappings on L9 and Q replaced by a series of contacts connected to the input terminal for Vx, output signal Vxp being derived from a contact R movable to select one of a series of studs rl to r7 which represent parameter z. An alternative embodiment is also described in which there are only two L13 windings (Fig. 9, not shown). Specifications 796,994 and 807,643 are referred to.