Kinematic calibration of a symmetric parallel kinematic machine using sensitivity-based iterative planning

Abstract

Since kinematic calibration will induce variations in the structural parameter values, the forward kinematics may have multiple or no solutions after calibration. This paper proposes a novel kinematic calibration method to obtain the optimal solution and high accuracy after calibration. We use the closed-loop vector to represent the clearance and the concomitant motion and convert the angular to a dimensionless variable to simplify the kinematic calibration model. Thus, we can calculate the global sensitivity index (GSI) of the symmetric parallel kinematic machine (sPKM). Then, we present a sensitivity-based iterative planning method to ensure iterative convergence and obtain the optimal solution. Due to the large difference in magnitude between the position and orientation errors, we adopt a segmental calibration approach to calibrate the two types of errors to improve the calibration accuracy. Finally, the Levenberg-Marquard(L-M) iterative algorithm is used to obtain the parameter errors. Simulations and experiments are performed on a 3-PPR sPKM. The results show that the proposed method prevents the kinematics with multiple solutions or without solutions after the calibration and reduces the position and orientation errors by 89.74% and 90.71%, respectively.