A Novel Iterative Method of Determining the Pose Error of Planar Clearance-Affected Flexible Parallel Mechanisms Under Loaded Mode

Abstract

Clearance and flexibility play an essential role in determining the accuracy of a planar parallel mechanism. However, previous accuracy prediction methods either considered only one of them or combined them in linear superposition. Therefore, this study proposes a novel iterative method for determining the pose error by considering clearance and flexibility simultaneously. First, the rigid-flexible model of the mechanism with clearances is developed based on the virtual joint method, in which the equilibrium conditions under the external load are established via the virtual work principle and differential forward kinematics. Then, using a Taylor series approximation, the “instant” stiffness matrix corresponding to a specific load is deduced. On this basis, an iterative scheme is explored to search for the final equilibrium pose, in which a child iterative scheme is constructed to determine the joint variables and suffered wrench of the single chain given a pose. Finally, the developed method is demonstrated by calculating the comparative pose errors of the planar five-bar mechanism and 3-RPR robot.