Dexterous Workspace of N-PRRR Planar Parallel Manipulators

In this work, a method is presented to geometrically determine the dexterous workspace boundary of kinematically redundant n-PRRR planar parallel manipulators. The dexterous workspace of each non-redundant RRR kinematic chain is first determined using a four-bar mechanism analogy. The effect of the prismatic actuator is then considered to yield the workspace of each PRRR kinematic chain. The intersection of the dexterous workspaces of all the kinematic chains is then obtained to determine the dexterous workspace of the planar n-PRRR manipulator. The Gauss Divergence Theorem applied to planar surfaces is implemented to compute the total dexterous workspace area. Finally, two examples are shown to demonstrate applications of the method.