Boundary Surfaces, Limit Surfaces, Crossable and Noncrossable Surfaces in Workspace of Mechanical Manipulators

Abstract

The workspace of a regional structure of a manipulator is bounded by a Jacobian surface (where the Jacobian is singular) or a D -surface (where one or more of the joints achieve a limit position). The Jacobian surfaces and D -surfaces may also appear inside the workspace. In such a case, these surfaces are noncrossable for certain configurations and crossable for certain other configurations. In addition, there may be singular points which are crossable by all configurations of the manipulator. In this paper, a workspace analysis method has been developed for identification of these surfaces. Examples of RPP and 3R regional structures are presented for illustration.