Abstract: Conventionally, CNC circular are interpolation algorithms, regardless of pulse increment method or data sampling method, are based on interpolating the next value according to the present value. In this paper a new algorithm for any 3-dimension circular arc interpolation in CNC systems, called Three Point Recursion Interpolation (TPRI for short), is proposed, which makes a breakthrough from the conventional interpolation algorithm and is based on twe-stop recursion scheme. The algorithm improves not only the interpolation accuracy, but also the interpolation process, which can be carried out by recursion method based on initial values. All of interpolation operation may be completed only by addition, subtraction and bit shift without multiplication and division. Thus, by means of the new method the computing size in remarkably decreased and the calculation speed is greatly increased, so that the interpolation speed may be enhanced strongly. The interpolation step is selected by the given tolerance of the segment of a circular arc. Also, the interpolation stability of the algorithm is preven and the interpolation error and theoretical machining error are estimated in the paper.

Key words: CNC, 插补