Efficient computation of motion error of parallel robots with joint clearances based on joint force model

Abstract

This paper proposes a method to compute positioning error of a parallel mechanism having passive spherical joints with clearances in motion without numerical integration nor iterative calculation. A model of passive spherical joints, in which the relationship between the relative displacement between the joint elements and the joint force obtained without taking the clearance into consideration is defined, is presented. Based on this model and the principle of virtual work, a procedure to calculate the output position error caused by joint clearance is proposed. Experiments for a DELTA parallel robot with joint clearances were conducted to evaluate the effectiveness of the proposed method comparing the measured output position error with the computational results. The applicability of the proposed method was discussed with a time variable for the relative displacement of the joint elements to converge, when the joint reaction force changes, defined as stabilization time. An index, representing an approximation of the stabilization time, was defined under consideration of rebounding and sliding motions between joint elements. The validity of the index was confirmed by investigating the correspondence between calculated index and the stabilization time obtained with experiments when changing the acceleration of the robot.

Keywords

• kinematics
• sensitvity
• parallel mechanism
• joint clearance
• high-speed computation
• principle of virtual work