Geometrical/analytical approach for reciprocal screw-based singularity analysis of a novel dexterous minimally invasive manipulator

This paper is concerned with the singularity analysis of a novel 4-DOF endoscopic surgical parallel manipulator (2-PUU_2-PUS). This parallel manipulator has larger bending angles compared to previously existing surgical parallel manipulators. It is easy to imagine the singular configurations inside the workspace of a manipulator with a zero pitch and infinity pitch reciprocal screws. On the other hand, the (2-PUU_2-PUS) surgical manipulator has two reciprocal screws of h-pitch. Hence, the singular configurations of this manipulator could not be provided by the known reciprocal screw-based geometrical approach. Therefore, the geometrical/analytical approach for reciprocal screw-based singularity analysis of 2-PUU_2-PUS is proposed in this work. The results illustrate the feasibility of the proposed algorithm to find all singular configurations of the 2-PUU_2-PUS manipulator. The discovered singularity configurations greatly shrink the singularity-free workspace to be one-fourth of the original workspace. In order to be able to work through the entire workspace, we suggest changing the topology structure of the manipulator.