Determination of minimum three-dimensional cutting-tool paths in the presence of barriers

Abstract

A software package is described that finds a minimum path tour for traveling-salesman problems with barriers or obstructions blocking straight-line travel. Numerically-controlled machines often must avoid obstacles on a work piece or fixture while traveling from point to point to accomplish the various machining operations on a part, returning to home position when finished. The problem was solved by Williams and Gupta for the case where all travel was in the same plane. This paper extends the work by considering that the tour of the machine tool might go over obstacles as well as going around them. The package contains modules (1) to determine whether or not nodes (points requiring machining operations) can be connected by straight lines, (2) to find the shortest path between pairs of nodes if barriers are present, and (3) to compute the minimum tour to visit all nodes and void barriers. The user may choose a tour that minimizes distance or minimizes time of travel. The latter assumes constant accelerations and decelerations, and steady-state tool velocity. Illustrations and sample calculations are presented. The set of algorithms in the software package is a heuristic although some aspects such as the shortest path calculations are optimal.