Kinematically-redundant variations of the 3-(R)under-barR mechanism and local optimization-based singularity avoidance

To avoid the singular loci of the 3-(R) under bar RR mechanism that exist within its workspace, this paper applies kinematic redundancy. First, three feasible kinematic redundancy configurations for the 3-(R) under bar RR mechanism are presented and singularity analysis of the kinematically redundant mechanisms is described. Then, based on local optimization suitable for real-time control, a general, simple, and effective redundancy resolution algorithm for the mechanisms is developed. Here, the cost function in the optimization is designed to avoid the most problematic singularity configurations, where the endeffector can be locally moved even though all actuated joints are locked. The kinematically redundant mechanisms are shown to effectively avoid singularities and correspondingly increase the singularity-free workspace.