Singularity Curves of a Parallel Pointing System

This paper studies a parallel pointing system used in aerospace applications for orientating parabolic antennas. In the literature 6, 7], the position analysis of this device has been already solved in closed form, whereas simple and efficient tools to address singularities distribution are still lacking. In this paper, its velocity analysis is addressed, and a singularity locus analytic expression, containing the manipulator geometric parameters and the end-effector orientation parameters, is derived. Moreover, it is shown that the determined singularity locus can be represented by curves (singularity curves) on a Cartesian plane having the generalized coordinates of the mechanism on the coordinate axes. Finally, an example showing the use of the proposed relationships is given and discussed.