Parallel manipulator domains of singularity free functionality

Abstract

A mechanics-based parallel manipulator formulation with mechanism generalized coordinates, kinematic constraints, input coordinates, and output coordinates is employed to account for singularities that conventional input-output models cannot represent. Criteria are presented at the configuration level that assure local existence of differentiable forward and inverse kinematic mappings. Basic results of differential topology are used to extend local kinematic relationships to singularity free, path connected, maximal domains of functionality, on which reliable manipulator planning and control may be implemented. It is shown that any trajectory in manipulator configuration space between points in distinct domains of functionality must encounter a singularity. Methods are presented that define domains of functionality, using only linear algebra and multivariable calculus for implementation, and illustrated with three parallel manipulators of varying levels of complexity. The first example is a simple manipulator that demonstrates concepts. The second defines 16 domains of functionality in a seven-dimensional configuration space. The third is a construction earth moving manipulator, for which maximal domains of functionality and more conservative domains with input bounds that uniformly avoid singularities are presented.

Communicated by Bogdan Gavrea.

Keywords:

• Singularity free domains of functionality
• parallel manipulator
• kinematics of machines

Acknowledgment

The author gratefully acknowledges contributions by Dr. Adrian Peidro of Miguel Hernandez University, Elche, Spain in relating the domains of functionality approach presented herein to issues involving parallel manipulator singularities and assembly modes.