A DDA PARABOLIC INTERPOLATOR FOR COMPUTER NUMERICAL CONTROL OF MACHINE-TOOLS

This paper is primarily concerned with the development of a parabolic interpolation algorithm for implementation in a computer numerical con trol (CNC) system to perform tool path control with constant tangentia l velocity (feedrate). Less segments of parabolic curves are required than of line or circular arcs for piece-wise approximation of higher-o rder curves. Hence, there is a need to develop an efficient algorithm for real-time control of a tool to follow a specified parabolic curve. A software approach based on the digital differential analyzer (DDA) method is presented. This integer computation method simplifies real-t ime implementation using assembly language or digital hardware. The de veloped parabolic interpolator has been implemented on a multiprocesso r CNC system. Results of tests of the implemented algorithm are compar ed with those obtained from a hardware interpolator with parabolic int erpolation capability. Results of fitting techniques using linear, cir cular and parabolic segments are also presented and plotted. Considera tions in the parabolic interpolation include the accuracy in following the theoretical parabolic curve and the ability to maintain a constan t tangential velocity. Word address codes for NC programming to genera te the parabolic curves are also proposed.