Abstract: Based on the measuring information of the redundant kinematic chain, the kinematic self-calibration of a kind of parallel kinematic machines (PKMs) with redundant chain is presented. Based on differential of the closed-loop vector chain, the redundant chain’s kinematic error model is obtained, and the identifying Jacobian matrix of self-calibration is got by combining the error transfer matrixes in a few poses. To solve the difficult identifiability problem of some kinematic parameter errors, an identification analysis method is presented based on the linear correlation analysis of the identifying Jacobian matrix’ column vectors, and by this method, the kinematic parameter errors’ identifiable linear combinations can be got and the identification equation can be simplified to enhance the identifiability. Finally, based on the measuring information from the incremental angle encoder of the redundant chain, the self-calibration of a 4RRR redundant PKM is completed. Simulation result shows that the kinemamtic self-calibration based on redundant chain can effectively improve the motion accuracies of the redundant chain and the end-effector.

Key words: Identifiability analysis, Kinematic self-calibration, Parallel kinematic machine, Redundant kinematic chain, clamping device, constant force output, forging manipulator