Enumeration of Singular Configurations for Robotic Manipulators

Abstract

Kinematic singularities are important considerations in the design and control of robotic manipulators. For six degree-of-freedom manipulators, the vanishing of the determinant of the Jacobian yields the conditions for the primary singularities. Examining the vanishing of the minors of the Jacobian yields further singularities which are special cases of the primary ones. A systematic procedure is presented to efficiently enumerate all possible singular configurations. Special geometries of representative manipulators are exploited by expressing the Jacobian in terms of vector elements. In contrast to using a joint-angle space approach, the resulting expressions yield direct physical interpretations.