Computation of the Available Force Set of a 3-RPRR Kinematically Redundant Planar Parallel Manipulator

An algorithm is developed to determine the available force set (AFS) of the 3-RPRR kinematically redundant planar parallel manipulator. The results of the algorithm are verified against a brute force approach and are found to yield exact results with significantly less computational time. The use of the AFS in a robot design context is illustrated through the analysis of two performance indices: the maximum pure force capable of being applied in any direction and the maximum pure force capable of being applied in a given direction. The algorithm is used to compute the AFS and the performance indices throughout the 3-RPRR robot’s workspace. The proposed methodology is a useful tool for the design and analysis of the 3-RPRR robot and could be adapted to other kinematically redundant planar parallel manipulators.