Abstract
A kinematically-(joint)-redundant spatial manipulator will not be velocity degenerate (singular) if any combination of six of its joints span the 6-system of general velocity. Therefore, all 6x6 sub-matrices of the matrix of joint screw coordinates J (commonly referred to as the Jacobian) must be rank deficient for a spatial joint-redundant manipulator to be velocity degenerate. Concurrency of zero 6x6 sub-matrix determinants of J allows sets of joint-displacement conditions leading to velocity-degenerate configurations to be identified. For actual manipulators, each set of degeneracy conditions must be checked to see if the conditions are feasible for existing device dimensions and occur within existing joint displacement limits. Within this work, the concept of concurrency of zero 6x6-sub-matrix determinants of J is considered and applied to the identification of velocity degeneracies for the Canadian Space Agency (CSA)/International Submarine Engineering (ISE) STEAR Testbed Manipulator (STM). The STM consists of two 7-jointed arms that are kinematically similar to the arms of the Special Purpose Dextrous Manipulator (SPDM) proposed for use on the International Space Station (ISS). Five unique 2-condition families of velocity degenerate configurations are found to cause velocity degeneracies for each of the 7-jointed arms. It is shown that only four of these five potential degeneracies correspond to reachable families of joint-displacement configurations for the CSA/ISE STM arms.
