A FORMULATION FOR THE WORKSPACE BOUNDARY OF GENERAL N-REVOLUTE MANIPULATORS

An algebraic formulation is proposed to describe the workspace boundar y of general N-R revolute open chain manipulators. The geometry of the generation process by revolving a figure about an axis has been used to deduce a recursive algorithm for the boundary of ring and hyper-rin gs by using the envelope concept. The workspace boundary is obtained f rom the envelope of a torus family which is traced by the parallel cir cles cut in the boundary of a revolving hyper-ring. The formulation is a function of the dimensional parameters in the manipulator chain and specifically of the last revolute joint angle, only. Some illustrativ e examples up to a 6R manipulator have been used to test the numerical procedure and they also provide remarks and show some peculiarities o f the hyper-ring topology. (C) 1996 Elsevier Science Ltd.