Patent GB-796994-A (GB)
Title: Improvements relating to interpolating or extrapolating devices especially for the control of automatic machine tools
Inventor: SPENCER ROLF EDMUND
IPC: G05B19/4105
Filed: 1953-10-03
Abstract: 796,994. Electric analogue calculating systems. ELECTRIC & MUSICAL INDUSTRIES, Ltd. Sept. 22, 1954 [Oct. 3, 1953], No. 27179/53. Class 37. An interpolating or extrapolating device comprises a first transformer of which certain primary turns are included in the connection between a first input terminal and a second input terminal and of which other primary turns are included in a connection between the second input terminal and a third input terminal, such terminals representing successive discrete abscissal points of the curve of a predetermined function; and a second transformer having primary turns connected in at least one of the connections of the input terminals, whereby on application of co-phased alternating voltages representing successive ordinal points of the function curve to the input points corresponding to the appropriate abscissal points, a potential gradient is set up across the primary turns of the second transformer which is variable in dependence on the second derivative of a curvi-linear function determined by the design of the transformers and by the amplitudes of the input signals; there being provided a series of output terminals representing equally spaced abscissal points of the curvi-linear function, with conductive connections from the second input terminal to each of the output terminals which selectively include secondary turns of the first and second transformers; the numbers of the secondary turns of the first transformer inserted in the connections being linearly related to the abscissal spacings between the several output and the second input terminal, and the numbers of the secondary turns of the second transformer being quadratically related to such abscissal spacings, so that alternating voltages are developed at the several output terminals representing ordinal values of interpolated or extra-polated points on the curve determined by the transformers and input amplitudes; such voltages representing ordinal values being discretely selectible from the plural output terminals. In apparatus automatically controlling a milling or other machine tool wherein a worktable is displaceable uniformly along an x axis through successive abscissal positions x 1 , x 2 , x 3 , &c. separated by intervals k, corresponding alternating signals representing predetermined ordinal displacements y 1 , y 2 , y 3 , &c. (Fig. 2a), are produced in succession from a control record (e.g. a punched tape) to operate a servo system displacing the work-table through successive ordinal positions corresponding to the abscissal positions relatively to a cutter operative in a fixed position. Cophazed signals representing displacements y 1 , y 2 , y 3  from the record are supplied respectively to input terminals 1, 2, 3 of an interpolating device (Fig. 1). A range of seven circularly arranged contacts a 0  to a 6  are provided over which a pair of contacts B 1 , B 2  separated by twice the contact spacing is movable by shaft S rotationally representing the successive values of x so that one rotation corresponds to an k interval k and one contact spacing to -. 3 An auto-transformer C having equal windings T 01 , T 12 , T 23'  T 34'  T 45  and T 56  connected in series across terminals 1, 3 is interconnected with the contacts a 0 , a 6  through secondaries SH 0 , SH 6  of transformer H, while the junction of windings T 23'  T 34  is connected to terminal 2 through primary T 3  of transformer D (the ratios of whose secondary windings T 1 , T 5  and T 2'  T 4  to the primary are shown to be respectively, so that the voltages developed across such respective secondaries are respectively quadratically related to the voltage across T 3 ). Terminal 2 is connected in turn to contact a 3  over secondary SK 3  of transformer K, while junctions T 01 , T 12'  T 12'  T 23 , T 34 , T 45  and T 45'  T 56  of transformer C are respectively connected to contacts a 1 , a 2 , a 4  and a 5  through windings T 1 , T 2 , T 4'  T 5  of transformer D 1  contacts SKi, SK 5  of transformer K and contacts SH 2 , SH 4  of transformer H. The ratios of transformers H, K are each 2 : 1, and contacts B 1 , B 2  engaging contacts a 0  to a 6  in accordance with the value of x derive a voltage which energizes an auto-transformer AT having multiple taps e 1 , e 2 , &c. circularly arranged and engaged by 180 degrees spaced sliders F 1 , F 2 , rotatable by shaft HS geared to shaft S through one turn for each displacement of contacts B 1 , B 2  over the spacing of a pair of the contacts a 0  to a 6 . The latter contacts energize transformer AT between 180 degrees spaced tapping points separated by a centre tap, and the primaries G, J of transformers H, K are respectively energized between the centre tap and sliders F 1 , F 2 ; one or other slider engaging the centre tap when brushes B 1 , B 2  are situated on contact midpoints. It is shown that, for the transformer ratios stated, the value of voltage representing y derived from one of the contacts a 0  to a 6  in dependence on interpolated values of x is given by where yn is a discrete value of y derived from the control record, #x is the separation of the output contact from the contact to which yn is applied, so that the values of y on contacts a 1 , a 2  and a 4 , a 5  lying between contacts a 0 , a 3  and a 6  corresponding to discrete recorded values y 1 , y 2 , y 3  are given by a parabola intersecting points (x 1 , y 1 ), (x 2 , y 2 ), and (x 3 , y 3 ) (Fig. 2b). Additional voltages corresponding to linear interpolation between the y voltages appearing on contacts a 0  to a 6  are derived from rotary sliders F 1 , F 2  driven by shaft HS and injected through the appropriate secondaries SH 0'  SH 2 , SH 4 , SH 6  and SK 1 , SK 3 , SK 5  of transformers H, K so that the voltage derived from the device to control the servo-operated deflection of the work-table in the y direction for continuous variations of x is continuously variable : (1) by quadratic interpolation of y over steps of <SP>1</SP>/ 3  the separations between successive values of x 1 , x 2 , x 3 ; (2) linear interpolation for values of x falling within such steps. Thus for continuous variations of displacement x through discrete values x 1 , x 2 , x 3  ... xn the corresponding displacement y is varied continuously through discrete values y 1 , y 2 , y 3  ... yn, which values are derived in succession from a record movable in accordance with x and applied in successive groups of three to terminals 1, 2, 3 of the interpolation unit. Modified transformer arrangements for improved quadratic interpolation may be employed while greater numbers of switching contacts a 0 , a 1 , a 2 , &c. may be used with or without linear subinterpolation (Figs. 3, 4, not shown). Fig. 6 shows a modification wherein rectangles 10, 11 represent two identical quadratic interpolating devices of the kind shown in Fig. 5 wherein an auto-transformer energized from inputs 1, 3 is tapped at points separating windings T 01 , T 12 , T 23 , T 34 , T 45 , T 56  which are connected respectively over intercoupled windings T 1 , T 2 , T 3 , T 4 , T 5  of a second interpolating transformer to contacts a 0 , a 1 , a 2 , a 3 , a 4 , a 5 , a 6 ; the input 2 being connected to the junction of T 3  and a 3 , the respective inputs 1, 2, 3 and 1<SP>1</SP>, 2<SP>1</SP>, 3<SP>1</SP>, are respectively connected to selector brushes 15, 16, 17 and 21, 22, 23 respectively rotated by a single shaft in accordance with the x movements to scan a range of contacts m 1 , m 2 , m 3 , m 4 , m 5 , m 6 , &c., which are staggered so that inputs 1, 2, 3 and 1<SP>1</SP>, 2<SP>1</SP>, 3<SP>1</SP> are respectively and alternately connected to contacts m 1 , m 2 , m 3  ; m 2 , m 3 , m 4  ; m 3 , m 4'  m 5  ; m 4 , m 5 , m 6 , &c., which contacts are correspondingly energized with successive discrete voltage analogue values of y, i.e. y 1 , y 2 , y 3 , y 4 , y 6 , &c., taken three at a time and applied to the corresponding contacts from the coded control record; the values from which may be converted from binary digital to analogue form and temp orarily stored until the appropriate contacts are engaged, in apparatus of the kind described in Specifications 731,650 and 796,993, [both in Group XXXVIII]. The outputs of the devices 10, 11 are respectively connected through the secondaries of transformers H, K, as shown in Fig. 1, to semi-circular ranges of contacts a 0  to a 6 ; a<SP>1</SP> 0  to a<SP>1</SP> 6 ; which are scanned circularly by brushes B 1 , B 2  driven by shaft S to excite a sub-interpolating auto transformer AT and its tapping switch having arms F 1 , F 2  driven by shaft HS to energize primaries G, J of transformers H, K. Shaft S is driven through 1 revolution while the brushes 15, 16, 17 and 21, 22, 23 move over the displacement between the centres of contacts in the same odd or even row, so that interpolating device 10 responds to the voltage analogues of displacements y 1 , y 2 , y 3 ; y 3 , y 4 , y 5 , &c., alternately with interpolating device 11 responding to the voltage analogues of displacements y 2 , y 3 , y 4 ; y 4 , y 5'  y 6 , &c., to produce quadratic interpolation and linear sub-interpolation as set forth in connection with Fig. 1 above. The output ya 3  (Fig. 8) over the x range covered by any single contact (e.g. a 3 ) represents the midordinate of a chord joining values ya 2 , ya 4 , defined by the adjacent contacts a 2 , a 4 , introducing an error from the required value ya 3 , which is connectible (Fig. 7), by further windings T 0 -T 6 in series with the inputs 1, 2, 3; to correct the voltages injected by windings T 1  to T 5  and modify the y-voltages at contacts a 2 , a 4  so that their mean value is ya 3 , and linear sub-interpolation now produces ordinal voltages lying on the tangent 26 to the parabola containing ya 2 , ya 3'  ya 4 . Windings To, T 6  are negatively connected between input terminals