Graph-based optimization of five-axis machine tool movements by varying tool orientation

There is a relatively vast class of tool path optimization methods that minimize cost functions depending on a whole tool path. In these methods, cost functions are usually limited to convex function because the used optimization approaches cannot either handle nonsmooth functions or perform with an acceptable computational time. This paper describes a developed optimization method that finds a sequence of tool orientations that can minimize various cost functions including displacement of machine rotary axes. Every posture, tool feasible orientation can be represented in discrete fashion as nodes of a directed graph in which the edge weights denote an objective. Shortest paths are sought iteratively by applying Dijkstra's algorithms and narrowing intervals of feasible tool orientations around the previous solution. The developed algorithm is a derivative-free optimization method working in a linear time.