Error Modeling for the 3-UPU Parallel Manipulator in Terms of Joint Clearance and Link Deformation

Abstract

Joint clearance and link compliance play an essential role in affecting the accuracy of the 3-UPU parallel manipulator. However, previous methods regarding accuracy mostly neglected these two factors, or just took into account one of them only. Therefore, to predict the pose error accurately, this study pro-poses a new method of error modeling considering joint clearance and link de-formation simultaneously. First, the pose change of the manipulator is divided into two stages—before and after the joint journal comes into contact with the bearing. Then, for the first stage where the link is a rigid body, the output deviation, caused by clearances only, is calculated via combining the principle of virtual work and local contact model of the revolute joint. Sequentially, through utilizing two virtual simple passive joints to simulate the motion of the joint journal inside the bearing and characterizing the compliant property of the flexible component by means of the 6-dof virtual spring joint, the formulations of static equilibrium and forward kinematics are developed. Thereon, recurring to the differential forward kinematics and the numerical iteration technology, the final position and orientation error of the end-effector is derived. Consequently, the actual pose deviation is the addition of the errors of the two stages. Finally, an example is showcased to demonstrate the validity of the proposed method.