Singularity avoidance for the 3-RRR mechanism using kinematic redundancy.

摘要

Based on its simple structure, base-fixed actuators, high payload capacity, high accuracy, and high mechanical rigidity, the 3- RRR mechanism is a valuable planar parallel manipulator. However, the 3-RRR mechanism is known to have singular loci within its workspace affecting its use. In this research; singularity avoidance of the 3-RRR mechanism using kinematic redundancy is presented. First, feasible kinematic redundancy configurations for the 3-RRR mechanism are considered and singularity analysis of the kinematically redundant mechanisms is described. Then, based on local optimization, a general, simple and effective redundancy resolution algorithm for singularity avoidance is developed. Here, the cost function in the optimization is designed to avoid the most problematic singularity configurations, where the end-effector can be locally moved even though all actuated joints are locked. Results from simulation show that kinematic redundancy can be effectively used for avoiding singularities associated with the 3-RRR mechanism, and enlarges the singularity-free workspace. In addition, determination of the redundant active prismatic joint variable ranges of a mechanism to allow given trajectories to be singularity-free is addressed. Since for a kinematically redundant mechanism the initial configuration is crucial for redundancy resolution, using permutations, the proposed algorithm considers all possible points where kinematic redundancy resolution begins. Simulation results demonstrate that the proposed algorithm can successfully find the kinematically redundant active joint variable ranges required for singularity-free trajectories. Therefore, it is apparent that the suggested algorithm can give guidelines for designing kinematically redundant planar parallel mechanisms.