A unified approach to the accuracy analysis of planar parallel manipulators both with input uncertainties and joint clearance

This paper presents a unified approach to predict the accuracy performance of the general planar parallel manipulators (PPMs) both due to the input uncertainties and the joint clearance. Based on the theory of envelope, a geometric method is employed to uniformly construct the indeterminate influences of these two error sources on the pose (position and orientation) deviation of the manipulators. According to the generalized kinematic mapping of constrained plane motions, the end-effectorʹs exact output error bound for a specified configuration can then be obtained as an accurate and complete description for the manipulatorʹs accuracy performance, from which not only the maximal position and orientation errors but also their coupling relationship can be derived. The planar 3-RPR manipulator is intensively studied as a numerical example and several numerical simulations are provided to demonstrate the correctness and effectiveness the proposed approach.