Optimal design of 6-DOF vibration isolation platform based on transfer matrix method for multibody systems

Abstract

The structure parameters of 6-degree of freedom (DOF) vibration isolation platform have a significant effect on its performance. To make the designed vibration isolation platform perform well, non-dominanted sorting genetic algorithm version II (NSGA-II) was applied to optimize its structure based on the transfer matrix method for multibody systems. Firstly, the Jacobian matrix of 6-DOF vibration isolation platform was solved based on kinematics. Secondly, the transfer equation of 6-DOF vibration isolation system was established by the linear transfer matrix method for multibody systems. And the formula of its natural frequency was derived according to the boundary conditions of the system. Thirdly, the manipulability index was constructed based on a dimensionless Jacobian matrix. And a new performance index function was established considering the influence of dynamic isotropic and legs mass. Fourthly, genetic algorithm (GA) and NSGA-II were used to optimize the structure of the 6-DOF vibration isolation platform under the same conditions, respectively. It showed that NSGA-II had higher optimization efficiency, better calculation accuracy and shorter optimization time than that of GA. Finally, NSGA-II was adopted for multi-objective optimization design of 6-DOF vibration isolation platform based on the constraint conditions. Optimal Pareto solutions were obtained, which provides structural parameters for subsequent design work. Therefore, the proposed optimization method and the performance index in this paper provide a theoretical basis for the optimal design of relevant vibration isolation mechanism.