Enlarging the useable workspace of planar parallel robots using mechanisms of variable geometry

This paper demonstrates the efficiency of kinematic redundancy used to increase the useable workspace of planar parallel mechanisms. As examples, we propose kinematically redundant schemes of the well known planar 3RRR and 3RPR mechanisms denoted as 3(P)RRR and 3(P)RPR. In both cases, a prismatic actuator is added allowing a usually fixed base joint to move linearly. Hence, reconfigurations can be performed selectively in order to avoid singularities and to affect the mechanisms' performance directly. Using an interval-based method the useable workspace, i.e. the singularity-free workspace guaranteeing a desired performance, is obtained. Due to the interval analysis any uncertainties can be implemented within the algorithm leading to practical and realistic results. It is shown that due to the additional prismatic actuator the useable workspace increases significantly. Several analysis examples clarify the efficiency of the proposed kinematically redundant mechanisms.