Patent GB-1033101-A (GB)
Title: Improvements in or relating to methods and devices for generating a curve
IPC: G06K15/22
Filed: 1963-02-01
Abstract: 1,033,101. Programmed control of machine tools. REGIE NATIONALE DES USINES RENAULT. Feb. 1,1963 [Dec. 3, 1962], No. 4292/63. Heading G3N. [Also in Division G4] Apparatus for generating a curve from data stored in digital form comprises an analogue computer controlling tracing means and adapted to generate the co-ordinates of successive points of an elementary arc of the curve from a parametric equation of a curve, the co-ordinate of the point at the end of each elementary arc being measured and compared with the desired co-ordinate, and the differences resulting from the comparison being used to correct the calculation of the next elementary arc. Referring to Fig.2 the co-ordinates of points A and B at each end of an elementary arc are known, and so are the co-ordinates of point T, the point at which tangents at A and B intersect. As an approximation to the curve the parametric equations x = e (1 - cos #) + f sin # and y = g (1 - cos #) + h sin 6 are used, where e and/ are the differences in the X co-ordinates of B and T an and T and A,g and h are the corresponding differences in Y co-ordinates, and # is a parameter which varies from 0 to #/2 over the length of the arc. If, owing to an error in drawing the previous arc, the co-ordinates of point A are incorrect by amounts # x and # y, the equations are modified to x = (e - # x)(1 - cos #) + f sin # and y = (g - # y)(1 - cos #) + h sin #. Figure 5 shows an arrangement for controlling two carriages 10,11 in respective co-ordinate directions, the carriages being adapted, for example example, to move a tool for machining a material. A tape 20 stores the successive values of e,f,g and h which are read by a reader 21 and converted to analogue form in unit 22. The values X t Y t  of the co-ordinates of the initial point of an elementary arc are also read from the tape and compared with the actual co-ordinates of the carriages 10 and 11, as measured by transducers 24 and 24<SP>1</SP>, in unit 23 to derive the errors # x and # y which are fed to unit 22. The parameter # is produced by a motor 26 and the functions (1 - cos #) and sin # are produced in units 25 and 25<SP>1</SP>, for example by transformers having a rotary primary winding, and multiplied respectively by (e -# x) and f, and the outputs of the units are added in unit 27 to produce x. The distance x a  travelled by carriage 10 since the beginning of an elementary arc is measured by a transducer 32 or 33; these operate alternately, one being re-set to zero whilst the other follows an elementary arc. The difference between x and x a  controls the speed of the motor 12 driving carriage 10 in the X co-ordinate direction, and similar circuits (not shown) drive the carriage 11 in the Y direction. If the curve is to be traced at a given velocity V this velocity is read from the tape and passed to a comparator unit 51. The actual velocity is derived by differentiating x in unit 52, squaring the output in unit 53 to give V x <SP>2</SP>, adding Vy<SP>2</SP> in unit 54, and taking the square root in unit 55. The actual velocity V e  is then compared with V in unit 51 and the difference used to control the speed of motor 26 which generates the parameter #. If the apparatus is used to operate a rotary tool of radius r, it is shown that the X coordinates should be corrected by a term r V y /V e .   This is produced by units 60-62 and fed to unit 27.