Frequency Analysis of a Spatial Rigid-flexible Coupling Parallel Manipulator

Abstract

The primary goal of this research is frequency analysis of the spatial flexible-rigid coupled parallel manipulator.A new model of spatial flexible beam element is proposed.The dynamic equation of the spatial flexible beam element is derived based on the finite element theory and Lagrange equations.The kinematic constraint conditions of the movable platform and the sub-chains of the flexible-rigid coupled parallel manipulator are derived,based on the elastic displacements of the movable platform and the sub-chains.The dynamic model of the movable platform is developed based on the Newton-Euler principle.By using the kinematic constraint equations and dynamic model of the moving platform,the overall system dynamic equations of the flexible-rigid coupled parallel manipulator are obtained through assembling the dynamic equations of elements.Then,the natural frequencies of a 3-RRS flexible-rigid coupled parallel manipulator are studied through numerical simulation.From the simulation results,the natural frequencies are relatively sensitive to the structure size,section parameter,and characteristic parameter of material on mechanisms.The results provide important knowledge to researchers to the dynamic analysis and optimal design of flexible-rigid coupled parallel manipulators.