Fast NURBS interpolation based on the biarc guide curve

Abstract

In parametric spline interpolation, the real-time parameter update is a crucial step which will directly affect the processing performance such as the feed rate fluctuation, the contour error, the online computational effort, etc. The use of Taylor approximation interpolation method to identify the next interpolate point will cause large feed rate fluctuation due to the accumulation error and the truncation error, which will affect the machining quality. As there is no accurate analytic expression between the parameter u and arc length S and the mapping between them is nonlinear, and in order to reduce the feed rate fluctuation and light computation requirement for online interpolation, the paper first samples the tool path with step parameter and Gauss integration, with the sampled points being in the coordinate system defined by parameter u and arc length S. Then, the sampled points are fitted into the guide curve with the use of the biarc fitting method, and the analytic expression between parameter u and arc length S is established. The biarc so derived can be used to realize a fast NURBS interpolation and the simulation results validate the reliability and effectiveness of the proposed method.