Identification of the workspace boundary of a general 3-R manipulator

In this paper an algebraic formulation is presented for the boundary workspace of 3-R manipulators in Cartesian Space. It is shown that the cross-section boundary curve can be described by a 16th order polynomial as function of radial and axial reaches. The cross-section boundary curve and workspace boundary surface are fully cyclic. Geometric singularities of the curve are identified and characterized. Numerical examples are presented to show the usefulness of the proposed investigation and to classify the design characteristics.