840,111. Programmed electric control systems. ELECTRIC & MUSICAL INDUSTRIES Ltd. Aug. 2, 1956 [Aug. 10, 1955], No. 23002/55. Class 38 (6). An automatic machine comprises interpolating means 34, 35 for generating control signals to produce relative displacement between two components of the machine in response to input signals which represent discrete reference points defining a desired locus, and rate-varying means responsive to a predetermined control signal for causing said interpolating means to generate control signals capable of varying said rate of relative displacement in a predetermined manner independently of the choice of the reference points. The table 1 of a milling-machine is moved relatively to the tool, which is located at the reference-point 6, by screws 3, 10 controlled by servo-motors 2, 9. The servo-motor 9 (2) is controlled by the output of an amplifier 12 (16), receiving continuously-variable signals from quadratic interpolating means 13 (17), and negative feed-back signals from the tap 14 (18) of a potentiometer 15 (19), which latter signals consist of a voltage analogue of the instantaneous value of x (y). The potentiometers may comprise several cascaded rotary potentiometers. Discrete values of x, y are recorded in adjacent columns on a punched tape 20. The output of the tape-reader 21 for, say, the recorded value of x, is in the form of a group of pulses which is a binary-decimal code representation of the corresponding value of x. This group of pulses is applied by a series of parallel conductors 25 to five auto-transformers 26-30 forming temporary stores, which are sensitized in cyclic order by a programme unit 32. The voltage-analogues set up by the stores 26-30 are applied by a selector switch 31 in successive groups of three to quadratic interpolators 34, 35 forming part of the means 13. Each interpolator has eleven output studs, the end studs of each group being " half "-studs. The stud circle is scanned by a contact 37 on a shaft 38 driven by a motor 39. The operation of the selector switch 31 is controlled by the shaft 38, through a connection 53, so that co-ordinates x 1 , x 2 , x 3 are supplied to the interpolator 34, and co-ordinates x 3 , x 4 , x 5 to the interpolator 35. The brush 37 is of the make-before-break type so that a virtually continuously-variable output alternating voltage is supplied to the amplifier 12. The amplifier 16 is supplied similarly with the voltage for the y co-ordinate. The machine is thus similar to that described in Specification 830,462. However, additional interpolating means 60, 61 are provided. These interpolating means can be switched into circuit instead of the interpolating means 13, 17 by switches 82, 83, operated through a relay 84 by a signal recorded on a separate track on the tape 20 or otherwise. The interpolators 62, 63, 66 and 67 of the additional means are such that the interval between successive output studs represents unequal variations of the independent variable. Thus, for instance, the interpolator 62 may be an auto-transformer having 100 turns tapped at 0, 2, 8, 18, 32, 50, 68, 82, 92, 98 and 100 turns respectively. Automatic acceleration and retardation is thus provided over a short span. If all such spans are to be straight, there is need only for two input connections to the interpolators. In a modification, the additional interpolators are eliminated by providing a switch 85, Fig. 3, operated by a signal to close a circuit controlling the motor 39, which normally runs at a constant speed. Whenever the switch is closed, the servomotor 39 is accelerated from the beginning of the corresponding span to its equilibrium velocity. This velocity is maintained until the interpolation progresses so closely to the end of the span that the signal, which is derived from a potentiometer 88, scanned by contacts 86, 87 on the shaft 38, through a non-linear amplifier 89 and, a rectifier 90, is less than the signal derived from a tachogenerator 92 driven from the shaft 38. Thereupon maximum reverse torque is applied to the motor 39 so that it has only sufficient velocity to coast to the end of the span, to allow the next set of instructions to be acted upon. A similar motor control is described in Specification 678,520. In another modification, the interpolators 34, 35, 48 and 49 are so constructed that the interpolators 62, 63, 66 and 67, and their associated stud - switches, can be eliminated. In a further modification, the interpolating means 60, 61 are eliminated and subinterpolators are used, the interpolating means 13 then being as shown in Fig. 5. The interpolator 34 comprises an auto-transformer 140 and differs from that shown in Specification 830,462 in that the last stud b 10 of the studcircle is connected to a switch 141a. The input leads 142 to 144 are connected to the studs b 0 , b 5 and b 10 . If the switch 141a connects the stud b 10 to the end-point of the auto-transformer 140, the interpolating means is normal. In its other position, however, the switch connects the stud to the mid-point of the last section of the autotransformer. The windings 145-153 of a second transformer are connected in the leads from the auto-transformer taps, the number of turns of the windings being related according to a quadratic law, such that if three co-phasal alternating voltages, with amplitudes representing successive values of one co-ordinate of a locus, are applied by leads 142-144, the voltages set up by the studs b 0 -b 10 represent the values of more closely-spaced co-ordinates on a quadratic curve defined by the input voltages. The second interpolator 35 is identical. Both sets of studs b 0 -b 10 and b<SP>1</SP> 0 -b<SP>1</SP> 10 are arranged in two rows, each circular row being shown as a straight line for convenience. The brush 37 has four contacts 154-157, each pair scanning one row. For linear sub-interpolation, two auto-transformers 158, 159 are provided. For quadratic sub-interpolation, a single auto-transformer 160 is provided, since such interpolation is only employed in the last sub-span, during which the output is always derived from the same pair of contacts 154, 157. A brush 162 scans the stud-circle of the autotransformers 158, 159 and performs one halfrevolution for a displacement of the brush 37 by one stud. A brush 165 similarly scans the stud-circle of the auto-transformer 160. The output is normally derived from the brush 162, but is derived from the brush 165 when a relay 167 is energized through switches 141b, 168 and 169. The switches 141a, 141b are operated by the signal-controlled relay 84, Fig. 1, the switch 168 is closed by the brush 37 each time it first engages the stud b 10 (b<SP>1</SP> 10 ), and the switch 169 is closed by the brush 165 each time it commences to scan the auto-transformer 160. The yco-ordinate interpolating means 17 is similarly constructed, and is also operated by the relay 84. The brush 162 is positioned relatively to the brush 37 so that it always scans an autotransformer to which a sub-span voltage is applied, and sub-divides the voltage linearly so that the output of the interpolating means is equal to the voltage on one of the studs plus a portion of the sub-span voltage added by the auto-transformer 158 or 159. If, however, it is desired to stop the machine rapidly at the end of a relatively-long linear span, the winding 159 may, if desired, be automatically short-circuited when a linear-span is encountered, to disable the quadratic transformer. When input signals representing the x co-ordinates are applied to the leads 142, 144, the relay 84 is energized, and the signal on the lead 144 is thus applied to the auto-transformer 140 at a point one half-subspan inside the normal end-point. The x-component of the displacement of the work-table is thus rapidly reduced in the sub-span x 9 to x 10 , as also the y-component may be. A similar arrangement may be used for acceleration at the beginning of a span. The brushes of the quadratic interpolating means may be advanced intermittently instead of continuously. The machine may be modified for other than cartesian co-ordinates, or for three-dimensional control, or for controlling the movement of the toolholder. The record may define the profile to be cut instead of points on the locus of the tool axis, and provision made to compensate for tool size as in Specification 830,461. The Provisional Specification describes a machine having a rotatable work-table on a slide traversed by a screw, the data-input being in terms of R, 0. Specification 796,994 also is referred to.