DEXTEROUS WORKSPACE OF A 3-PRRR KINEMATICALLY REDUNDANT PLANAR PARALLEL MANIPULATOR

In this work, the dexterous workspace of a general geometry 3-PRRR kinematically redundant planar parallel manipulator with six actuated joints, three of which are redundant, is determined. The 3-PRRR manipulator is an adaptation of the 3-RRR manipulator with a redundant prismatic actuator added to each leg. Obtaining the dexterous workspace by discretizing a large area around the manipulator and determining if each point is in the workspace is relatively simple though computationally inefficient. This work proposes a geometrical method to determine the dexterous workspace of a 3-PRRR planar parallel manipulator. With this method, an exact solution of the workspace boundaries is obtained. The geometrical method uses the four-bar mechanism analogy to determine the dexterous workspace. Though the method is applied to a 3-PRRR planar manipulator, it can be readily applied to any n-PRRR planar manipulator, where n is the number of chains.