The dynamic modeling and solution of the 3-■RS spatial parallel manipulators with flexible links were investigated.Firstly,a new model of spatial flexible beam element was proposed,and the dynamic equations of elements and branches of the parallel manipulator were derived.Secondly,according to the kinematic coupling relationship between the moving platform and flexible links,the kinematic constraints of the flexible parallel manipulator were proposed.Thirdly,using the kinematic constraint equations and dynamic model of the moving platform,the overall system dynamic equations of the parallel manipulator were obtained by assembling the dynamic equations of branches.Furthermore,a few commonly used effective solutions of second-order differential equation system with variable coefficients were discussed.Newmark numerical method was used to solve the dynamic equations of the flexible parallel manipulator.Finally,the dynamic responses of the moving platform and driving torques of the 3-■RS parallel mechanism with flexible links were analyzed through numerical simulation.The results provide important information for analysis of dynamic performance,dynamics optimization design,dynamic simulation and control of the 3-■RS flexible parallel manipulator.
