An algorithm for reducing tool retractions in zigzag pocket machining

Abstract

An important issue in zigzag pocket machining is to design a machining strategy such that the resulting tool path requires a minimum number of tool retraction motions. The minimization is further classified as either local or global. In a local minimization, the inclination of a zigzag path is given a priori, and the goal is to partition the planar region to be machined into a minimum number of retraction-free subregions. The global minimization finds an inclination angle such that the local minimization with respect to this inclination is the minimum among all the possible inclination angles. This paper presents simple O( n log n) algorithms for solving both the local and the global minimization problems of a region with holes, where n is the number of line segments or arcs on the boundary of the region. The optimality of the presented algorithms is proved by using geometric analysis.