A practical continuous-curvature Bézier transition algorithm for high-speed machining of linear tool path

Abstract

A continuous-curvature smoothing algorithm is developed to approximate the linear tool path for high speed machining. The new tool path composed of cubic Bézier curves and lines, which is everywhere G 2 continuous, is obtained to replace the conventional linear tool path. Both the tangency and curvature discontinuities at the segment junctions of the linear tool path are avoided. The feed motion will be more stable since the discontinuities are the most important source of feed fluctuation. The algorithm is based upon the transition cubic Bézier curve that has closed-form expression. The approximation error at the segment junction can be accurately guaranteed. The maximal curvature in the transition curve, which is critical for velocity planning, is analytically computed and optimized. The curvature radii of all transition Bézier curves are also globally optimized to pursue the high feed speed by a linear programm model. Therefore, the algorithm is easy to implement and can be integrated into a post-process system. © 2011 Springer-Verlag.