Kinematic Calibration of a 2-DoF Over-Constrained Parallel Mechanism Using Real Inverse Kinematics

The kinematic accuracy improvement is a key challenge in the development of over-constrained parallel mechanisms (PMs). Taking a two degree-of-freedom (DoF) over-constrained PM applied in assembly line as an example, this paper addresses the kinematic calibration problem of over-constrained PM to improve accuracy and promote its practical application. Instead of establishing conventional error mapping model, a nonlinear error model is built by inserting geometric errors of parts to the real inverse position analysis. On this basis, a set of nonlinear identification equations are formulated. Unlike other methods that identify the geometric errors by an identification Jacobian matrix and pay extra attention to the robustness of the matrix, these nonlinear identification equations are directly solved by optimization technique. Herein, the hybrid genetic algorithm is adopted in the optimization due to its high robustness, efficiency, and accuracy. Finally, error compensation is implemented by modifying the motor outputs in the controller. Simulations and experiments are then carried out to verify the calibration method, which show that the orientation accuracy of the 2-DoF over-constrained PM improves by 93.96% and 90.38%, respectively. Comparative studies to the conventional regularization method and four other optimization algorithms are also investigated. The results further confirm the high accuracy of the proposed kinematic calibration method for over-constrained PMs.