Stiffness Optimization of Redundant Mechanism Based on Elastic Coupling and Inertial Coupling Characteristics

Abstract

Aiming to redundant parallel mechanism, on the basis of the kinetic energy method, virtual work principle, and perturbation method, the generalized mass matrix and generalized stiffness matrix are obtained, respectively. Two indices on inertial coupling and elastic coupling are defined to measure the decoupling level of the redundant parallel mechanism in terms of two generalized matrices. Furthermore, an algebraic solution method for natural frequency equation of the mechanism is utilized to obtain the natural frequency by means of the Cholesky decomposition method. Then, in order to minimize inertial coupling and elastic coupling and maximize the natural frequency of the mechanism, two indices and natural frequency are taken as objective functions to optimize the structural parameters of the redundant mechanism so that optimal dynamic performance of the mechanism is acquired. Two optimal solutions are selected in the optimization of natural frequency. One is to consider inertial coupling and elastic coupling, the other is to ignore inertial coupling and elastic coupling. Finally, the dynamic performance of the solution considering two indexes is better by comparing the dexterity of the two solutions.