Bspline approximation of circle arc and straight line for pocket machining

Abstract

This article proposes a new method of 2D curve interpolation using non-uniform cubic B-splines particularly adapted to the interpolation of sequences of straight lines and circle arcs. The purpose of this method is to calculate C2 continuous curves adapted to high feedrate pocket machining. Industrially machined pockets usually present simple forms. Generally, the tool path is defined by circle arcs and line segments that introduce slowdowns during machining. Thus, a method for approximating a sequence of line segments and circle arcs using Bspline curves is proposed. The proposed method ensures exact line interpolation, to approach the tool path precisely, to reduce the number of control points and to avoid thickening and oscillation at the connections between line segments and circle arcs. Various applications are presented and numerous tests on machine tools allow the advantages of this method to be illustrated.