Symmetrically actuated double pointing systems: the basis of singularity-free robot wrists

An analysis is conducted of symmetrically actuated double pointing systems, which are two spherical pointing systems connected serially with a common center. The double pointing systems have four degrees of freedom interrelated by two constraint functions, reducing the systems to two independent degrees of freedom. Together, these constraint functions result in a symmetry in the motion of corresponding links in each pointing system of the double system. A singularity analysis is presented of a generalized symmetrically actuated double pointing system in order to prove that it and the systems derived from it have maximal singularity-free workspaces. Closed-form solutions to the inverse position and velocity problems are presented along with different types of kinematic arrangements. Any of the double pointing systems presented can serve as the basis of a singularity-free wrist.