A Calibration Method for a Three-degrees-of-freedom Parallel Manipulator with a Redundant Passive Chain

This paper deals with parameter identification for a three-degrees-of-freedom (3-DOF) parallel manipulator, based on measurement redundancy. A redundant passive chain with a displacement sensor connects the moving stage to the machine frame. The passive chain is sequentially placed in three directions at approximately right angles to one another to reliably detect the motion of the stage. Linear encoders measure changes in lengths of the passive chain and the three actuated chains of the manipulator during traveling of the moving stage. Comparison between the measured length and the length calculated from forward kinematics of the 3-DOF manipulator reveals a length error of the passive chain. The least-squares method using a Jacobian matrix corrects 27 kinematic parameters so that the length errors of the passive chain are minimized. The above calculations were accomplished in both numerical simulations and experiments employing a coordinate measuring machine based on the parallel manipulator. Moreover, a length measurement simulation of gauge block measurement and a measurement experiment using the measuring machine were performed to verify the identified parameters.