Singularity-Free Trajectory Planning of a 3-RPRR Planar Kinematically Redundant Parallel Mechanism for Minimum Actuating Effort

Kinematic redundancy is a way to enlarge the workspace and to eliminate the singularities of parallel mechanisms. The objective of the present research is to introduce a new motion planning strategy for singularity avoidance and reducing the actuator forces, especially in the vicinity of singular configurations. The method is implemented to a planar kinematically redundant mechanism categorized as 3- RP RR type. Dynamic equations of motion are derived using the principle of virtual work, and the optimum inverse dynamics is obtained. Some numerical examples are solved, and the results are compared with those obtained in the counterpart non-redundant mechanisms. It is illustrated that the redundant mechanism can avoid singular configurations and track the given trajectory with feasible generalized forces.