Geometric determination of the dexterous workspace of n-RRRR and n-RRPR manipulators

In this work, a geometric method is presented to determine the dexterous workspace of two architectures of kinematically redundant planar parallel manipulators. The architectures studied are the n-RRRR and the n-RRPR. These architectures are characterized by having a revolute actuator as the kinematically redundant actuator added to the base of each kinematic chain. First, the dexterous workspace of the non-redundant sub-chain (RRR or RPR) of each kinematic chain is studied. Then the effect of the redundant actuator is considered to yield a geometric representation of the dexterous workspace of each kinematic chain. The intersection of the dexterous workspaces of all kinematic chains of a manipulator is determined to obtain the geometric representation of the dexterous workspace. The Gauss Divergence Theorem is applied to compute the area of the dexterous workspace. An example is given to demonstrate an application of the method. Finally, some design considerations are given to maximize the size of the workspace.