Optimization of a redundant 4R robot for a shoulder exoskeleton

This paper presents an optimized redundant 4-revolute (4R) spherical wrist mechanism for an active shoulder exoskeleton. Upper limb exoskeletons in the past have used a 3-revolute (3R) spherical wrist mechanism to replicate the spherical movements of the shoulder joint. However, a 3R mechanism has singular configurations in which the exoskeleton´s ability to orient the end-effector degrades significantly. The addition of a redundant 4th revolute joint is proposed to avoid these singular configurations. However, there can be a lot of variability in the design and joint configurations of this redundant mechanism. The design of the 4R mechanism can have a range of possible link angle sizes and base joint positions. In addition, the redundancy of the mechanism indicates that there are infinite solutions to the inverse kinematic problem. Genetic algorithm is used to obtain an optimal set of link angle sizes and identify the optimal joint configurations which ensure the 4R mechanism operates well away from singular configurations. Singularity analysis is done by evaluating the condition number (CN) of 89 discrete configurations throughout the workspace. The global condition number (GCN) and the maximum CN values confirm that the optimized 4R design performs better than the 3R design and an un-optimized 4R design.