Wrench Capabilities of Planar Parallel Manipulators and their Effects Under Redundancy

This work presents a method to understand and quantify wrench capabilities of PPMs. Wrench capabilities are determined by projecting the actuator torque capabilities into the wrench space. This projection is a linear transformation that leads to a convex set, i.e., a wrench polytope. To numerically evaluate wrench polytopes, six wrench performance indices are derived. Each index is associated to a particular operational condition of the manipulator. These indices are plotted throughout the workspace of the manipulator. As a design tool, the wrench workspaces allow for easy visualization of the differences in wrench capabilities between different PPM architectures. For an existing manipulator, this visual representation can be employed to improve path planning. The wrench capability analysis is implemented to three non-redundant layouts: 3-RRR, 3RPR, and 3-PRR. In addition, the effects of including in-branch redundancy (3-RRR, 3-RPR, and 3-PRR) and branch redundancy (4-RRR, 4-RPR, and 4-PRR) are presented. It is concluded that in-branch redundancy yields greater forces; whereas, branch redundancy offers greater moments.