Analytic Determination of Workspace and Singularities in a Parallel Pointing System

摘要

This paper studies a parallel pointing system, named U-2PUS, used in biomechanic and aerospace applications. In the literature, U-2PUS position analysis has already been solved in closed form, whereas simple and efficient tools to address workspace determination and singularity locations are still lacking. In this paper, the analytic expression of the U-2PUS workspace is derived, and a bidimensional representation of the workspace is proposed. The U-2PUS mobility analysis is addressed, and a singularity locus analytic expression, explicitly containing the manipulator geometric parameters and the end-effector orientation parameters, is derived. Moreover, it is shown that the U-2PUS singularity locus can be represented by curves (singularity curves) on a Cartesian plane having the U-2PUS generalized coordinates on the coordinate axes. Finally, the presented singularity conditions are geometrically interpreted.