An interpolation scheme for tool-radius compensated parabolic paths for CNC

In general, NC systems provide only linear and circular interpolations. Complex shapes to be machined are first approximated with linear and circular segments to some predetermined tolerance. Parabolic curves are more suitable for piecewise approximation of higher-order curves because less segments than lines or circular arcs are required. In machining operations, the tool motion controlled by the interpolator does not move along the profile of the job. The tool path is offset from the profile by the tool radius. Tool-radius compensations for linear and circular tool paths involve simple offsets of the initial and final points. The tool paths remain linear or circular. For parabolic profiles, the offset tool paths are not parabolic; hence, parabolic interpolations cannot be used to generate the offset paths. This paper presents an algorithm to perform interpolations for the tool to follow parabolic curves as well as the offset paths passing through two user-defined end points. The parabolic interpolation is based on the principle of operation of the Digital Differential Analyzer (DDA) integrator and is capable of constant tangential velocity.