Patent GB-866319-A (GB)
Title: Improvements relating to quadratic interpolating devices
Inventor: SPENCER ROLF EDMUND
IPC: G06G7/30
Filed: 1956-06-19
Abstract: 866,319. Electric analogue calculating. ELECTRIC & MUSICAL INDUSTRIES Ltd. June 11, 1957 [June 19, 1956], No. 18903/56. Addition to 796,994. Class 37. In an improvement in or modification of the interpolating apparatus claimed in the parent Specification, three input points and one or more output points are inter-coupled by two transformers whose turns ratios are selected and arranged so that on application respectively to predetermined input terminals of co-phased alternating electric signals having amplitudes representing values of a co-ordinate of discrete points on a parabolic curve and of the intersection of the tangents at such discrete points, a signal is developed at the or each output point having amplitude representing the value of said co-ordinate of a further point on the curve. A parabolic interpolation curve ACB (Fig. 1), intersecting points A(x 1 y 1 ) and B(x 3 Y 3 ) joined by a chord ADB has tangents AT, BT, intersecting at point T(x T y T ), lying on the line CD bisecting AB, where x T  = x 2  and TC = CD, and abscissal values x 1  x 2 , x 3  are equally spaced. In an interpolating apparatus as above (Fig. 2), a linearly tapped autotransformer TO 1 -T 5  6  has its outer ends connected to ordinal input voltages 1, 3 representing y 1 , y 3  and respectively to the extremities of an array of 7 output circuits; its centre point connected to the centre output circuit through transformer primary T 3  and its remaining tappings connected to corresponding intermediate output circuits through transformer secondaries T 1 , T 2 , T 4'  T 5 , having windings whose ratios to T 3  are quadratically related to the intervals between the centre and the respective tappings on the linear autotransformer. A switch S enables the ordinal voltage Y T  to be connected to the outer end of T 3  either directly, or through a winding T 3a  equivalent to T 3  and on the same core as windings T 1  to T 5 , so that the voltage at the junction of T 3  and T 3a  represents the y coordinate of C (Fig. 1); the voltage across T 3a  represents TC, and that across T 3  represents CD; while the voltages successively derived from the remaining output circuits represent the interpolated values of y for corresponding subdivisions of x, following the law of curve ACB. Thus instead of inputs representing discrete ordinal values y, y 2 , y 3  for successive values of x, the apparatus may be supplied with inputs from recorded data representing y 1 , y 3  and the calculated ordinal co-ordinate y T  of the tangent intersection point. Alternatively the successive slope values of the required curve at A,B may be obtained from a record and the co-ordinates x T ,  YT  computed from these in conjunction with the co-ordinates (y 1 , x 1 ) and (y 3 , x 3 ) of A,B. The switch S may be relay operated in response to auxiliary recorded signals to changeover to a programme of the above data. The system is stated to give continuity of the first differential of the curve at reference points along a profile to be mechanically cut, whereby a smooth transition is obtained. The system is applicable also to parametric interpolating devices of the kind described in Specification 830,462 for determining the several co-ordinates of points on a locus as functions of a common independent parameter.