A novel reciprocity-based method for identifying 1-DOF (degree-of-freedom) loss velocity-degenerate (singular) configurations of kinematically-redundant manipulators is presented. The developed methodology uses the properties of reciprocal screws to determine the 1-DOF-loss velocity-degenerate configurations. A by-product of the methodology is that a reciprocal screw related to the lost motion DOF for each degenerate configuration is determined. The methodology is successfully applied to determine the 1-DOF-loss velocity-degenerate configurations of four redundant serial manipulators:​ the 7-joint spherical-revolute-spherical manipulator;​ the 7-joint double-elbow manipulator;​ the twin 7-joint CSA/ISE STEAR Testbed Manipulator (STM) arms;​ and the 8-joint NASA Advanced Research Manipulator II (ARMII).

The reciprocity-based method for identifying 1-DOF-loss velocity-degenerate configurations is then extended to the case of identifying multi-DOF-loss velocity-degenerate configurations of kinematically-redundant manipulators. As with the 1-DOF-loss methodology, a by-product of the multi-DOF-loss methodology is that reciprocal screws related to the lost motion DOFs for each degenerate configuration are determined. The methodology is successfully applied to determine the 2-DOF-loss velocity-degenerate configurations of two redundant serial manipulators:​ the 7-joint spherical-revolute-spherical manipulator and the 7-joint double-elbow manipulator.

The utilization of velocity-degenerate configurations to optimize the pose of either non-redundant or redundant serial manipulators to sustain desired wrenches is considered. An algorithm is developed that determines a desirable start point for the optimization of a serial manipulator's pose. The start-point algorithm (SPA) uses the knowledge of the velocity-degenerate configurations of a serial manipulator to determine a pose that would be best suitable to sustain a desired wrench. The SPA is tested on three manipulators:​ the 7-joint spherical-revolute-spherical manipulator, the 6-joint zero-offset PUMA-type manipulator, and the 7-joint STM-1 manipulator. The results for all three examples show that by using the SPA with the optimization routine, the resulting poses obtained usually required less effort from the actuators when compared to the poses obtained without using the SPA.