DE1138965B - Device for performing an interpolation or extrapolation - Google Patents

Description

INTERNAT. KL. G 06 g

GERMAN

PATENT OFFICE

E 9628 IXc / 42m

REGISTRATION DATE: OCTOBER 1, 1954

NOTICE
THE REGISTRATION
AND ISSUE OF
EDITORIAL: OCTOBER 31, 1962

The invention relates to an analog computer system for the interpolation or extrapolation of in the form electrical voltage or currents predetermined curves, in particular for the control of automatic machine tools can be used.

An automatic machine tool can be used for milling or for other shaping of a Workpiece according to a pattern of any shape are required. If one considers z. B. a vertical milling machine, in which the milling cutter can be rotated about a fixed vertical axis, one task is to achieve the Calculate displacements from a certain point (roughly the axis of the milling cutter) that of the tool holder must make to the desired dimensions of the workpiece at successive To produce points. This can be done by converting the calculated shifts into suitable Fixed point recordings are recorded, e.g. B. on punched strips, the recorded information ao are read out one after the other according to the progress of the milling operation and a servo system control, which in turn controls the individual displacements of the machine tool. If at such a Arrangement the pattern should be followed exactly, so an interpolation between the stored Shifts may be necessary, otherwise the amount of information to be stored may be too large will. Linear interpolation can be done by using an autotransformer. In the meantime in some cases it is not sufficient to just linear interpolation between the reference points because the number of reference points must still be excessively high in order to have a steady curve a sufficient accuracy. On the other hand, the cost and size of a this required interpolation device become an obstacle.

The need for continuous curve interpolation can also be found in many other automatic control systems and occur in the calculation of devices. One purpose of the present invention consists in specifying a simple robust interpolation device for continuous curves, which in some Cases can also carry out an extrapolation.

According to the present invention, interpolation or extrapolation is effected by at least three input terminals through at least two series of transformer windings together are coupled. The input terminals are supplied with alternating current signals, their amplitudes by the values of three ordinates of the device to be approximated for implementation an interpolation or extrapolation

Applicant:

Electric & Musical Industries Limited, Hayes, Middlesex (Great Britain)

Representative: Dr. K. R. Eikenberg, patent attorney, Hanover, Am Klagesmarkt 10/11

Claimed priority:

Great Britain October 3, 1953 and September 22, 1954 (No. 27 179)

Rolf Edmund Spencer,

Geoffrey Huson Stephenson, London,

Christopher Archibald Gordon LeMay,

Greenford, Middlesex,

and Sidney Charles Dudman,

West Drayton, Middlesex (Great Britain) have been named as inventors

mating curves are determined, with one input terminal with the other two input terminals via the windings of a transformer and the primary windings of another transformer is connected, its secondary windings each with graded numbers of turns in the connection line to the relevant output terminal for the according to the interpolation law sought interpolation or extrapolation value.

The invention is explained in more detail with the aid of some exemplary embodiments shown in the drawings. It shows

1 shows an example of an interpolation device according to the invention,

FIG. 2 is a graphic representation of the mode of operation of the arrangement according to FIG. 1,

3, 4 and 5 modifications of part of the arrangement according to FIG. 1,

FIG. 6 is an addition to FIG. 1 in order to cover successive ranges of the variables, 7 shows a modification of part of FIG. 1, FIG. 8 shows a graphic explanation of FIGS FIG. 9 shows another modification of FIG. 1.

20? 679/171

3 4

In the drawings, the arrangement according to the lung factor equals one. Under this assumption, Fig. 1 shows an interpolation device which is suitable for generating the three alternating voltages yl, yl, y3, the control of a milling machine or other machine at the terminals 1, 2, 3 are introduced to the. For the sake of simplicity, the description should focus on points aO, al, al ... electromotive forces, which only affect the displacement of an element, for example the 5 ordinate with a small distance on a parallel table of a milling machine in the y-coordinate bolic curve through the points xlyl, xlyl, refer to direction, while the workbench after up- x3j> 3 (whereby initially any subsequent points in the direction of an additional electromotive forces induced by Wick's other coordinates, for example in the direction of the x-co-hings to the right of D. neglected ordinate, which in this case are the io). This state is represented by Fig. 2, (b) again independent variables. The graph given, which is drawn with a different scale than that of FIG. 1 in FIG. 2, («) represents the y- shift, and in which the amplitudes of the electrode are required for various values of χ. There are motor forces which act on ad, al, al. .. generated it is assumed that successive discrete points are calculated by the corresponding ordinates of the ge values of the displacement yl, yl, j3 ... for the designated parabolic curve, at which χ the values xl , The location of aO, al, al ... represents consecutive xl, x3 ... hat. The difference of χ between discrete values of χ in the interval xl to x3, successive reference points is constantly the same and consequently alternating voltages of k can be taken. The calculated values of y are taken from the contacts aO, al, al ... , for example recorded on a punched tape. 20 whose amplitudes represent values of the function y , the recorded information is read out, which is obtained by quadratic interpolation in the interval when it is needed, and selectively the interval x1 to χ3. Quadratic interpolation device of FIG. 1 supplied. The polishing means that every value of y which is obtained from the output of the device to a servo system of one of the contacts a 0, a1, a1 ... , which effects the y-coordinate shift. 25 is represented by the following equation: If the interpolator operates, so
it interpolates values of y between the calculated / dy Λ Ax ² [ d ² y \

Expand yl, yl, y3 ..., while χ values between y = yn + Ax 1 "^ rH γ ~ \ ~ dx ^ j '

the values xl, xl, x3 ... of the reference points - \ UU

takes, so that the y- shift for values of χ 30

is precisely controlled, the distance between which is small compared to k . where yn is one of the stored values of y (ie

For the description of FIG. 1 it is assumed that yl, yl or j3) represents and Ax represents the distance of that alternating voltages with the same phase and with the corresponding contact from the contact, at the amplitudes which are proportional to yl, yl, y 3 yn is created. In the following discussion, three input terminals 1, 2 and 3 are applied to ground 35 this equation will be in the form. As the milling operation progresses, the voltages applied to terminals 1, 2, 3 change / dy \ Ax ^z ( d ² y \ one after the other. The interpolation ^{device contains y = y} ^ ^ \ ~ άχ) "*" ~ 2 ~ \ άΐ? ), a series of fixed, equally spaced χ = χΐ - x = 2 * contacts located aO, al, al ..., and although 40

only seven such contacts shown can be used, with Ax running from + k to - k. Due to the fact the actual number will be higher. The input of the assumption explained is the distance between terminals 1, 2, 3 are with the contacts aO, a3, a6 aO and a6 a change of 2k in χ, z. B. connected so that the distance between aO and a3 xl to x3, so that the EMF between the lower one means a change k in χ and also the distance 45 end of TOl and the upper end of TS6 one between a3 and a6 one Change k in χ means. Yl has the same Distance between aO and al is a change - - amplitude according y3 in χ represents the distance between aO and 2 k I 3.

al represents a change - = - in χ, etc. This is because

Contacts are connected to one another by a series of (- ^ - 1 = - ^ - ~ transformer windings TOl, TU, T23 ... ver \ dxJ _{x = xZ} x3 - xl, which are wound on a common core represented by C, and by a second 55, provided that y in the interval xl series of transformer windings Tl, Tl, T3 ..., to x3 is a quadratic function of χ, which is assumed on a common, by the dashed in quadratic interpolation Rectangle D. Therefore, the amplitude of the winding between earth and that of core D is not equal to any voltage generated at contact aO on the left side of T3 or the winding connected to contact α 6

Windings TOl, TU, T23 ... have the same win- yl + Jk I ^dy )

application number. Meanwhile, the windings Tl, Tl, \ dx ') _{x = x2} ' T3 ... are arranged in such a way that the windings in them are

Flux fluctuation in the core D induced electro- The amplitude e of the voltage over the Wickmotorischen forces have a quadratic ratio 65 ment T3 is then the difference between. All windings on core C are

closely coupled. Likewise, the windings on the y% and yl + k ( \

Core!" closely coupled. Theoretically, the Kopp- \ ^ ^x L = x2

Since y is quadratic by the assumption, yl can be exactly as

yl-k l- ~ ^ l

are represented so that the amplitude e is the value

/ c ²

Ux ²

represents if along Γ3 is counted positively from left to right. Since Tl has nl turns, T2 has nl turns, etc., all of which are wound in the same sense, the emf is between al and earth

' ² - τ

- - ^ r e + e.

For an accurate interpolation, this voltage should be the same

yl-

be there

--xl

is. Are similar

~ n3 ~ ⁼

and the translations
«4
~ n3
always the same

and

2 3

j 3

«5

and - = -

nl ni are accordingly arranged at an angle to one another around the shaft axis. The shaft is represented in the drawing by the reference symbol S and shall be called the low-speed shaft. The potential difference that occurs between the two brushes is applied to an autotransformer AT , which has taps located close to one another and connected to a number of contacts ei, el, e3 ... These contacts are arranged at an angle and are swept over by the diametrically opposed brushes Fl, Fl , which are attached to a shaft HS which rotates at high speed. The shaft HS is coupled to the shaft S via a gear so that it executes one revolution for each displacement of the brushes Bl, Bl over twice the distance between the contacts α O, al, al ... The series of contacts el, el ... extend over an angle that is slightly greater than 180 °. The brushes Bl and Bl are with

zo those taps of the autotransformer AT connected, which lead to two contacts that are 180 ° apart. The overlap when the brushes Fl and Fl are working, which is caused by the contacts el, el, e3 ...

Extending over an arc greater than 180 ° allows an uncertainty in the transition of B1 and B1 from one contact to the other. The brushes Fl and Fl are arranged in such a way that Fl or Fl touches the center contact of the autotransformer AT when the brushes Bl and Bl are each one of the contacts in the row aO, al, al ... at the center point. The potential difference that occurs between the brush F1 and the center point of AT is applied to the primary winding G of a transformer, the core of which is represented by the dashed rectangle H. Similarly, the potential difference occurring between the brush F1 and the center point of AT is applied to the primary winding / a transformer, the core of which is represented by the dashed rectangle K. The transformer core H carries a system of secondary windings SHO, SH1, SH4, ..., each of which has the same number of turns and is connected to the supply lines to the contacts with even numbers aO, al .... Likewise has the

Therefore, the first order differential coefficient required for interpolation becomes implicit by the
Windings TOl, TIl ... generated on the core C, 45 transformer winding K a system of secondary, while the differential coefficient of the second order windings SKI, SK3, SK5 in the leads to through the winding T3 on the core D is generated. the contacts with odd numbers al, a3 ... There is a linear relationship between the The arrangement is made so that a voltage

Number of turns of Γ01, TU ... and the change reduction ratio of 2: 1 between G and stanchions of x, represented by the distance between the 50 each of its secondary windings and contacts a 0, al ..., whereas a square between / and each of its secondary windings. The relationship between the number of turns Tl, Tl ...
and the changes in χ , where the changes in χ are expressed as fractions of k .

The interpolation device is, however, also suitable for performing a linear interpolation between the values of y represented by ordinates at points a0, a1, al ... m in Fig. 2, (b) . This interpolation is used herein and in the claims

referred to as linear subinterpolation. The contacts 60 ± [ ^xa n + i ~ ^xa i)

aO, al, al ... are swept over by two brushes Bl and Bl , which are located at a distance from each other that is twice as large as the contact distance. The brushes are needed to get the value of χ reduction ratio of 2: 1 of the transformers H and K , since the components of the subinterpolation are spread over the range:

₁ -xa _n

extend, although the autotransformer to the

remote contacts is connected.

Assuming that the brushes Bl and Bl are on al and aA and the brush Fl is the contact row el,

to represent, shifted. Although it is shown as scanning 65 el, e3 ..., the displacement of Fl

are as if they were on a straight line at a distance from the center contact of the contact series the deviation

lie on top of each other, they are attached to the shaft whose values of χ differ from the discrete values represented by α 3

Represents angular displacement χ , where the contacts represent. Let this be drawn with δ χ. The attached to AT

■. 7 8

Voltage is the difference between y when a4 and y interpolation circuit work together. In this at al [Fig. 2, (b)], and the voltage applied to the figure, the rectangles 10 and 11 of two identical transformer primary windings G , represent the devices for quadratic interpolation of the product of this last difference with δ χ . The half in Fig. 5 represents the construction shown by adding this product to the voltages, which is added by 5 transformers such as H, K of FIG. al and «4 are removed, added. The two devices belong to a single actual voltage at the midpoint of AT is low-speed rotating shaft S, consequently the one indicated by the ordinate of on the two brushes Bl and Bl, as in Fig. 1, be-2 - [ _ _va d are consolidated. These brushes feel a circular shape

- 7 ~ - ίο way from in which the contacts aO, al ... α6 the

² device 10 occupy a semicircle and the

is shown, which is approximately equal to ya3 in Fig. 2, (b) corresponding contacts of the device 11, plus an increase defined by linear inter- other semicircles, the latter contacts with

polation in the interval a'O, a'l ... a'6 are designated. The entrance

xal + XA3 XA3 + XA4 ^l5 of the device terminals 10 are connected to the reference

to - r denotes characters 1, 2, 3 and that of the device 11

^{2 2} with 1 ', 2' and 3 '. The input terminals 1, 2 and 3

is obtained. are connected to the selector brushes 15, 16 and 17

3, 4 and 5 show modified arrangements and the input terminals 1 ', T and 3' with one which can be adapted to the two systems of transformer 20 second group of selector brushes 21, 22 and 23 windings, which one qua- The selector brushes 15, 16, 17 and 21, 22, 23 are designed to perform dratic interpolation. The transformers, the axes of which are shown in the vertical contact direction indicated by the arrow 24, are wound on a core and seUQml, ml, m3 ... m6 , which, as shown, are staggered those with horizontal axes on a different core. 25 is arranged so that the contacts with odd The sense of winding and the number of turns of the winding numbers through the brushes 15, 17 and 22, the contacts lungs with horizontal axes is chosen so that with even numbers through the brushes 21, 16 and 23 the desired quadratic interpolation obtained can be swept over. The Kontaktemi to m6 are will. In the drawing, those windings are arranged at an angle to one another around the axis of the shaft carrying the brushes in the square series, which in one sense supports the shaft. To make it easier to wind, on one side of the linear winding of the illustration, the contacts are laid in series and the windings are shown in the square, and the axis for the brushes, which are wound in the opposite direction, is left. If successive discrete values to the other side of the linear series of windings. Are taken in by y from the record, as the case of the arrangement shown in Fig. 5 is a 35 analog voltages to the relevant interpolation ml only about half of the total margin contacts of the series, ml, m3 ... placed. This is how the linear transformer works. In the jl placed at ml, y 1 at m 1 etc. The wave 5 is with Fig. 3, 4 and 5 is not a linear subinterpolation by the wave, the six selector brushes 15,16,17 and introduction of voltages in the supply line to the 21, 22, 23 carries, so coupled by a gear, contacts α 0, al, al ... provided. This can be done so that the shaft S makes one revolution, while that of course can be done if desired. six selector brushes move a distance,

From Fig. 3 it can be seen that some primary windings of the second transformer TO, Tl, Tl ... of adjacent contacts in the same row, for example in the connection from input 1 to input 2, ml to m3, is. The analog voltages are present while other primary windings in the connection are used by three at the same time, and there are three connections from input 2 to input 3. If these analogs are in use, the next value also applies to the arrangement according to FIG. 4 with that of y taken from the recording, for the span modification that the transformer is made a savings analog and is connected to the next contransformer, this being and the linear economy clock m4 laid, etc. in progressive order. Open transformer J ¹ Ol, TIl, T13 ... Temporary storage devices for which the voltage analogs are required alternately in succession are divided into sections 50. Usually it is arranged. however, it is preferable to put the value of y in the

For the arrangements according to FIGS. 3, 4 and 5 drawing in the form of a binary code, the transmission ratios of the windings can increase. The output y is determined from the uterpolation of the square transformer from an expander 10 over the interval of χ from the center of the formulas for the arrangement of Fig. 1 between xl and xl to the center between xl and x3 by noting that the taps of the linear transformer taken and taken from the interpolation device 11 correspond to points from the center between xl and x3 to the center between equal distances on a rope. The x3 and x4 are taken, etc. The linear subintering needed for the square windings 60 polation is carried out by a circuit which is similar to that corresponding therefore to the elevations that are necessary to in Fig. 1, with corresponding parts of the straight rope bear the same reference numbers on the curve in a parallel. During the Bürzur curve axis to arrive in the lying direction. most Bl and Bl in Fig. 6 from the contact holding Fig. 6 illustrates an arrangement in which A'6 for ex- pands a0 ... a6 to the latch circuit A'O ... on lighterage the switching of the switch 65, the calculated values are represented by the devices 10 and 11 of y representing voltage alternately two equal EMFs applied to the contacts α6 and a'O used parabolic interpolation devices. This means that the two contacts will correspond to the one with a common linear sub- same small area of χ . This

9 10

can be achieved by the arrangement of the contacts, which in this example are the same: the, z. B. by each of the contacts a6 and a'O over

half the range is effective. A similar approach J (_k \ ² 1 ^ y \

Order applies to contacts a'6 and aO. 2 \ 3 / \ dx ² ) _{x = x2}

Instead of a series of contacts ml, ml, m3 ..., 5

as indicated, can use four contacts and is constant. The number of turns of the windings T1, offset from one another by 90 ° in a circle, T2. .. is still in a quadratic relationship which are scanned cyclically by the six brushes. to the associated changes in x, it is only in this case, while the device 11 would present a different constant. Of course, when the voltages y 1 are in use, other types of quadratic interpolation clocks ml can also be released from the cones and replaced by voltage analogs, devices with respect to those shown in FIGS. 3 to 5 which represent j> 5, etc. The arrangement be used. Furthermore, the size voltages according to FIGS. 1, 3 and 4 can also be arranged according to the correction in the linear subinterpolation that they are only changed over half the interval Generate output signals. 15 other points gives exact values.

Instead of the output from a device with Fig. 9 shows another way to be linear

quadratic interpolation from the middle between interpolation between the discrete values of y,

xl and x2 to the middle between x2 and x3 and then which are obtained by quadratic interpolation,

from the other from the middle between x2 and x3 . With this modification, the

to the middle between x3 and x4 etc., as in Fig. 6, 20 contacts aO, al, al ... staggered so that the con-

To take, a device can be arranged so that even numbered bars are in a bank and

that it sweeps the interval χ 1 to xl, the next the contacts with odd numbers in another

from x2 to x3 etc. The devices for quadra-Bank. The shaft S carries four brushes Bl, B2, B3, 54,

Table interpolation of FIGS. 3 and 4 are for this where the brushes Bl and B3 with the contacts

Case used when the contacts α4, α 5 and α 6 sweep over 25 odd numbers and the brushes B2

according to Fig. 1 and the turns in the leads and B4 the contacts with even numbers. the

these contacts can be omitted. HS shaft with high rotational speed only carries

It should be pointed out that in Fig. 1 and also - a brush F, and this makes half a turn, if in Fig. 6 the linear subinterpolation is carried out in this way - while the four brushes B1, B1 , B3, B4 are kidnapped, that the output of the area of x, 30 traverse distance, which is equal to the center-to-center distance of the contacts aO, al, al ... covered by a contact, for example a3. The brush F is scanned, representing the central ordinate of a chord which connects the alternating two autotransformers AT1 and AT2 values of y, which are sampled at the adjacent contacts, while the potential difference between them. Thereof an illustration is FIG. 8, brushes Bl and B3 to the autotransformer ATl showing that when applied BL and at the midpoints 35 and the potential difference between the contacts al and a4 are, the output of the brushes Bl and B4 to the autotransformer ATl. Ordinate represents y'a3 . Since the exact output ya3 is the autotransformers ATl and ATl , the assumed method of linear as a result of linear subinterpolation during subinterpolation brings a small error at the reference point of the crossing of alternating contacts of y 3. This can, however, be corrected by 40 series α 0, al, al ... used. During one of the that, as indicated in Fig. 7, the electromotive autotransformers is in use by bridging two forces, which in the line through the square adjacent contacts, takes place in the interpolation windings Tl, Tl ... and by additions a skipping of the contact pair, which tion of further windings TO and T6 are introduced, has just been swept over to the one that is now being changed, so that a parabolic curve 45 is swept over. In this case the Trans is generated as it is not used by the dashed line in formators H and K , and the output of FIG. 8 is drawn. This will get the values from the brush F directly. For linear of y, which occur at the contacts al and a4, Subinterpolation the arrangement of FIG. 7 modified so that the mean value of the affected values are used, in order to output at other points of Yal and Ya4 equal ya3. Make 5 ° correct as yal, yal , etc.

Linear sub-interpolation creates new voltages. Although the invention is described with reference to milling machines which are defined by the ordinates of the points on the line 26 at which the displacements are given within the area a3 in FIG which represents the tangent to the parabola through the points, the invention can of course also be used there yal, ya3 and ya4 . To achieve this 55, where the shifts in values of other results is the input terminal 2 at a coordinate, e.g. B. cylindrical coordinates, indicated intermediate tap of the winding 73 connected, wäh- are. The invention can also be applied to other negative windings TO and T6 between the machines in order to automatically mill an input 1 and 3 and the contacts aO and a6 workpiece or with the aid of a control. In FIG. 7, the dashed parabola 24 is to be otherwise shaped through 60 by instructions which determine the points yl, yl and j3, while these relate only to discrete reference points. The invention, dashed curve 25, which by the EMFs of which also relates in its application not only to points aO, al, al ... represents certain parabolas. on the control of automatic machines, so the change of the EMFs fed to the contacts can also be applied to computing devices or other is required in order to make a correction proportional to interpolation tasks in general.

In addition, other systems from Trans-

± ( ^xa4 IZ.X- ^a } \ (A ^) formator windings analogous to Tl, Tl, T3 ... in the

² \ 2 / \ dx ² ) _{x = xa3} supply lines to the contacts al, al, a3 ...

be switched to achieve a cubic or other type of interpolation. In this case, it is necessary to bring a correspondingly larger number of signals representing values of y to suitable introduction points. If desired, the device can also be used for extrapolations. Assuming that 3, the input signals al, "4 and a.6 supplied to the contacts in Fig., An extrapolation occurs at the contacts aO, al, al and A8 a. In addition, by taking into account the arrangement according to FIG. 7, it can be seen that it is not necessary to arrange the input signals on the same curves as the output signals, the position of the curve being naturally determined by the input signals.

Instead of voltages, currents can also be used, whereby it is not necessary to adhere to a specific one Freqenz and curve shape matter, it is only essential that in the signals alternating components are included.

Claims (12)

PATENT CLAIMS: 1. A device for performing an interpolation or extrapolation, in which two input terminals and at least one output terminal are connected to one another via windings of a transformer and the input terminals are supplied with alternating current signals, the amplitudes of which are determined by the values of two ordinates of the curve to be approximated, characterized in that at least one third input terminal (2) is provided to which a signal with an amplitude is fed which is determined by a third ordinate on the curve, the third input terminal with the other two input terminals (1,3) not only via the windings of the The aforementioned transformer (TOl, TU, T23 ...), but also via the primary windings of another transformer (Tl, Tl, TZ ...) , whose secondary windings each have a number of turns in the connection line to the relevant output terminal that is graded according to the law of interpolation (al or al ... ) for the interpolation or extrapolation value sought. 2. Apparatus according to claim 1, wherein the transformation ratio of the first transformer is linearly related to the differences in the abscissa values which are represented by the input terminals and the output terminal, characterized in that the transformation ratio of the other transformer (Tl to TS) has a quadratic relationship stands for these differences. 3. Apparatus according to claim 1 and 2, characterized in that the first transformer (Γ01 to Γ56) is designed as an autotransformer, one half of the winding between the one input terminal (1) and the third input terminal (2) and the other half of the winding between the third Input terminal (2) and the other input terminal (3) so that the abscissa value of the curve corresponding to the third input terminal is the mean value between the abscissa values represented by the two input terminals (1, 3). 4. Apparatus according to claim 3, characterized in that the primary winding of the other transformer (7Ί to TS) to the connection between the one input terminal (1) to the third input terminal (2) and to the connection from the third input terminal (2) to the other Input terminal (3) is connected. 5. Apparatus according to claim 3, characterized in that some primary turns of the other transformer (Tl to TS) in the connection from the first input terminal (1) to the third input terminal (3) and other primary turns of this transformer in the connection from the third input terminal ( 2) to the other input terminal (3). 6. Apparatus according to claim 3, characterized in that primary windings of the other transformer (Tl to TS) lie in groups between different sections of the autotransformer. 7. Apparatus according to claim 1 to 6, characterized in that a contact arm (Bl, Bl) successively connects to successive output terminals and that a potentiometer (AT) is used to sub-interpolate the output signal by the output signal depending on the displacement of the Contact arm between the individual output terminals changed. 8. Apparatus according to claim 7, characterized in that additional signals are fed in by transformers (H, K) in front of the output terminals so that a subinterpolation is effected. 9. Apparatus according to claim 7, characterized in that the output terminals downstream switching connections additional signals for subinterpolation are fed. 10. Apparatus according to claim 8 or 9, characterized in that the contact arm (B1, 52) consists of at least two parts which can simultaneously pick up signals from different output terminals, and that the means for sub-interpolation comprise a transformer (AT) variable transmission ratio , which is connected so that it is fed by the voltage difference between the two parts of the contact arm. 11. Interpolation device with two interpolators according to claim 1 to 7, characterized in that a selector is assigned jointly to the output terminals of the two devices, which alternately sweeps over the output terminals so that successive abscissa values are displayed, and that switches synchronized with the selector are provided ( ml to mS), which alternately feed the input signals to the input terminals of the devices in a predetermined order. 12. Interpolation device according to one or more of claims 1 to 11, characterized by using this device in conjunction with a function value memory as automatic control system, in particular for machine tools. For this purpose 2 sheets of drawings © 209 679/171 10.62