Compliance Analysis of a Novel Tool Head with Parallel Kinematics Considering Joint Clearance

With the proposed novel 3 degrees of freedom (DoFs) tool head of 3-PRRU parallel kinematic mechanism, this paper investigates the compliance of the 3DoFs tool head by taking the joint clearance into account. Since the moving platform needs to bear the external wrench, the internal force of passive joints is deduced with the kinetostatic analysis. Then the compliance model is established considering the joint clearance. Based on this model, the mapping relationship between the clearance and position error of the joint is analyzed. The error transformation matrix is derived by the differentiation of kinematic equations, and translational and rotational errors of the moving platform caused by the joint clearance are determined. Furthermore, the stiffness matrix of the 3DoFs tool head is derived by using the matrix structural analysis. The total deflection of the moving platform is obtained by considering both the joint clearance and the elastic deflection deduced from the stiffness matrix. Simulation results indicate that the deflection caused by joint clearance has a significant impact on the accuracy of the moving platform, and should be considered in the accuracy analysis.