A kinematic calibration method for parallel mechanisms integrating error modeling using Abbe criterion with pose repeatability weighting identification

• The graphical interpretation of error modeling based on Abbe criterion is proposed. • The relationship between pose repeatability and measurement data information is constructed. • The measurement data are weighted based on pose repeatability to complete parameter identification. • An optimal weight determination method based on PSO algorithm is proposed. • A measurement scheme for the pose error of robots is systematically introduced. Parallel mechanisms are widely used due to their high rigidity, high precision and fast response characteristics. Absolute positioning accuracy is the foundation for ensuring the performance of the mechanism, while kinematic calibration is an effective way to improve the performance of the platform. Error modeling and parameter identification represent two critical stages in the kinematic calibration process. This paper presents a graphical interpretation of error modeling based on the Abbe criterion. Combined with the screw theory, the geometric error model of the 6-U P S Stewart platform was established. Subsequently, the probabilistic ellipsoid was used to evaluate the pose repeatability, and a weighted parameter identification algorithm based on direction decoupling was proposed. The core of this algorithm lies in establishing the intrinsic relationship between pose repeatability and pose error. Thirdly, the prediction accuracy of the weighted algorithm and the non-weighted algorithm was compared through computer simulation, and a method for determining the optimal weight using the particle swarm optimization algorithm was proposed. Finally, the accuracy and reliability of the weighting algorithm were experimentally verified on the robot prototype.