A DDA parabolic interpolator for computer numerical control of machine tools

Abstract

This paper is primarily concerned with the development of a parabolic interpolation algorithm for implementation in a computer numerical control (CNC) system to perform tool path control with constant tangential velocity (feedrate). Less segments of parabolic curves are required than of line or circular arcs for piece-wise approximation of higher-order 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-time implementation using assembly language or digital hardware. The developed parabolic interpolator has been implemented on a multiprocessor CNC system. Results of tests of the implemented algorithm are compared with those obtained from a hardware interpolator with parabolic interpolation capability. Results of fitting techniques using linear, circular and parabolic segments are also presented and plotted. Considerations in the parabolic interpolation include the accuracy in following the theoretical parabolic curve and the ability to maintain a constant tangential velocity. Word address codes for NC programming to generate the parabolic curves are also proposed. © 1994.