A Calibration Method for a Six-Degree-of-Freedom Parallel Manipulator with a Redundant Passive Chain

Abstract

This paper examines parameter identification for six-degree-of-freedom (6-DOF) parallel manipulators, from the point of view of measurement redundancy. A redundant passive chain with a displacement sensor is installed between the moving stage and the machine frame, and is passively expanded and contracted by actuation of the 6-DOF manipulator. Linear encoders built in seven prismatic joints in the passive chain and six actuated chains measure change in length of the chains during traveling of the end-effector. Moreover, length error in one of the seven chains can be calculated from the forward kinematics of a 6-DOF parallel manipulator consisting of the remaining 6 chains. Consequently, comparison between the measured seven lengths and calculated seven lengths reveals seven length errors at each pose of the end-effector because seven combinations are possible. The least-squares method using a Jacobian matrix corrects 37 kinematic parameters so that the length errors of the seven chains are minimized. The above calculations were repeated until convergence in both numerical simulations and experiments employing a coordinate measuring machine based on the parallel manipulator. Moreover, coordinate measurement using a 3-D ball plate was performed to verify the identified parameters. The measurement result demonstrated that the average coordinate error of 0.161 mm was reduced to 0.066 mm.