OPTIMAL WORKPIECE SETUPS FOR 4-AXIS NUMERICAL CONTROL MACHINING BASEDON MACHINABILITY

Orienting of a workpiece so as to maximize the number of surfaces mach ined on a 4-axis Numerical Control (NC) machine is formulated as a sph erical computational geometry problem. The orientations along which a sampling point on the part surface is visible to a 3-axis NC machine a re represented as a spherical polygon. The range of rotation of the fo urth axis of a 4-axis NC machine is assumed to be 180 degrees s and is represented as a semi-great circle. The maximization of the number of surfaces machined is formulated as finding a semi-great circle that i ntersects the maximal number of spherical polygons each of which corre sponds to a sample point on the surface of the workpiece. This paper p rovides an O((E + I-wb)N-2) time algorithm for this optimization probl em, where N is the number of spherical polygons, E is the total number of polygonal edges, and I-wb is the number of pairs of polygonal edge s that are antipodal to each other. The solution to this maximization problem helps establishing a heuristic to a workpiece setup optimizati on problem, in which the number of setups for a workpiece to be machin ed by a 4-axis NC machine is to be minimized. In addition to the devel opment of the algorithm, useful properties of geometric duality are al so established. (C) 1998 Elsevier Science B.V. AU rights reserved.