Determination of the kinematically redundant active prismatic joint variable ranges of a planar parallel mechanism for singularity-free trajectories

Based on its simple structure, base-fixed actuators, high payload capacity, high accuracy, and high mechanical rigidity, the 3-RRR mechanism1 is a practical planar parallel manipulator. However, the 3-RRR mechanism is known to have singular loci within its workspace affecting its use. A recent paper by these authors introduced a singularity avoidance algorithm for the 3-RRR mechanism using kinematic redundancy. This paper extends the earlier work and allows for determination of the required ranges of the kinematically redundant active prismatic joint variables of a mechanism to allow given trajectories to be singularity-free. Since for a kinematically redundant mechanism the initial configuration is crucial for redundancy resolution, the proposed algorithm uses permutations to consider all possible points where kinematic redundancy resolution begins. The efficacy of the algorithm is demonstrated through simulation.