Dynamics Analysis of Parallel Mechanism With Flexible Moving Platform Based on Floating Frame of Reference Formulation

Abstract

The dynamics model of 4-SPS/PS parallel mechanism with a flexible moving platform is formulated based on the equation of motion. Firstly, the dynamics model of flexible moving platform is formulated based on the floating frame of reference formulation. In order to avoid the wrong solutions caused by an inappropriate set of reference conditions, the fixed-fixed reference conditions are carefully selected according to the structure of parallel mechanism. Secondly, considering that the original Craig–Bampton (CB) method only represents the free-free modes. In order to use CB method to obtain fixed-fixed modes, the original CB method is improved by imposing the reference conditions prior to obtaining the static correction modes and fixed interface modes. In addition, the dynamics analysis of 4-SPS/PS parallel mechanism with flexible moving platform based on both free-free modes and fixed-fixed modes are implemented, respectively. Finally, the simulations show that the dynamic responses obtained using fixed-fixed modes are close to the ideal dynamic response, which proves the correctness of improved CB method. Moreover, the maximum percentage error of simulation results between using free-free modes and using fixed-fixed modes exceeds 100%, it is clear that the solutions based on free-free modes are not reasonable. Eventually, the conclusions prove that the deformation caused by high-speed and heavy-load should not be neglected in the parallel mechanism.