Workspace, Void, and Volume Determination of the General 5DOF Manipulator

ABSTRACT Algorithms for identifying closed form surface patches on the boundary of five-degree of freedom (DOF) manipulator workspaces are developed and illustrated. Numerical algorithms for the determination of three- and four-DOF manipulator workspaces are available, but formulations for determining equations of surface patches bounding the workspace of five-DOF manipulators have not been presented. In this work, constant singular sets, in terms of generalized variables, are determined. When substituted into the constraint vector function, they yield hyper-entities that exist internal and external to the workspace envelope. The appearance of surfaces parametrized in three variables within the workspace pertaining to coupled singular behavior is also addressed Previous results pertaining to bifurcation points that were unexplained are now addressed and clarified.Examples illustrating results obtained are presented.

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