Workspace, void, and volume determination of the general 5DOF manipulator

Algorithms for identifying closed form surface patches on the boundary of f ive-degree of freedom (DOF) manipulator workspaces are developed and illust rated. Numerical algorithms for the determination of three- and four-DOF ma nipulator workspaces are available, but formulations for determining equati ons of surface patches bounding the workspace of five-DOF manipulators have not been presented. In this work, constant singular sets, in terms of gene ralized variables, are determined. When substituted into the constraint vec tor function, they yield hyperentities that exist internal and external to the workspace envelope. The appearance of surfaces parametrized in three va riables within the workspace pertaining to coupled singular behavior is als o addressed. Previous results pertaining to bifurcation points that were un explained are now addressed and clarified. Examples illustrating results ob tained are presented.