ON THE DETERMINATION OF BOUNDARIES TO MANIPULATOR WORKSPACES

The accumulation of two independent, broadly applicable formulations f or determining the boundary to manipulator workspaces, presented elsew here, are compared in this paper. Insights gained from one method are used to explain behavior exhibited in the other. Results are also comp ared and validated. A numerical formulation based on continuation meth ods is used to map curves that are on the boundary of a manipulator wo rkspace. Analytical criteria based on row rank deficiency criteria of the manipulator's analytical Jacobian are used to map a family of one- dimensional solution curves on the boundary. The other formulation, ba sed on a similar rank-deficiency criteria, yields analytic boundaries parametrized in terms of surface patches on the boundary. Results conc erning the applicability of the numerical method to open- and closed-l oop systems are compared with those limited to the open-loop for the a nalytical method. Conclusions regarding the behavior of the manipulato r on geometric entities characterized by singular curves, higher-order bifurcation points, and surfaces inside the workspace are drawn. Appl icability of both methods and their Limitations are also addressed. (C ) 1997 Elsevier Science Ltd.