Three-dimensional reference pulse linear and circular interpolators for CNC systems

Abstract

Three-dimensional (3D) linear and circular interpolations are a basic element in the machining of complex shapes. Because of the lack of accurate and efficient algorithms for the generation of 3D lines and circles, a full realization for the available machine tool resolution is difficult. This paper presents new algorithms for 3D linear and circular interpolation in the reference pulse technique. In 3D space, the line or circle cannot be represented as a general implicit equation. The natural way to represent a line or circle is as the intersection of two surfaces. Based on these facts, interpolation algorithms were designed to follow intersection curves in searching for a minimum path error strategy, and a real-time 3D linear and circular interpolator was developed in software using a PC. The software implementations in a PC and the hardware implementation on a retrofitted milling machine have shown promising results in interpolation error and speed performance. It is expected that this can be applied to the computerized numerical control systems for the machining of 3D lines, circles and some other complex shapes.