Accuracy analysis and synthesis of asymmetric parallel mechanism based on Sobol-QMC

Abstract

Aiming at the aircraft composite skin grinding, a new three degree-of-freedom (DOF) parallel mechanism with asymmetrical structure (TAM) is proposed to replace manual grinding. The TAM is achieved by integrating one of active limbs into the passive limb while keeping the required DOF unchanged, which is divided into two closed-loop chains: telescopic rod and parallelogram. The inverse kinematics models of the two chains are established according to closed-loop vector method. Thus, the actuation and the constraint Jacobian matrix are obtained. Based on the perturbation principle, the error modeling of the TAM is built. Adopting the constraint Jacobian matrix, 15 uncompensated errors are distinguished from the error model. In order to improve the working accuracy of the TAM, accuracy analysis and synthesis are necessary for all the uncompensated errors. The mapping function reflects the influence of uncompensated errors on the pose accuracy. The global sensitivity evaluation indexes are established by mapping function. Since Sobol sequences are superior in uniformity and convergence, the Quasi-Monte Carlo method based on Sobol sequences (Sobol-QMC) is introduced for sensitivity analysis. Taking the minimum manufacturing and installation costs as the optimization target, the objective function of accuracy synthesis is constructed. Ultimately, the reasonable tolerance zone of each uncompensated error is calculated by genetic algorithm. Simulation is performed by Sobol-QMC to verify the rationality of the optimization. The results show the probability is above 97% where most pose errors are in [[Formula: see text], [Formula: see text]] within the workspace. Therefore, accuracy synthesis is correct and practical.