Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects

This paper presents a nonlinear dynamic analysis of a 3-PRS series-parallel mechanism with consideration of joint effects which includes flexibility, clearance and friction. The Newtonian approach is applied to derive the equations of motion of the 3-PRS mechanism. The Runge–Kutta method and contact verification criterion are combined to solve the nonlinear piecewise differential equations. The linearization technique is applied to determine the natural frequencies and their associated mode shapes. The simulation results show that the natural frequencies of the 3-PRS mechanism shift with the position of prismatic pairs and the physical interpretations are given by using the associate mode shapes. The effects of joint clearance and friction cause the natural frequencies to decrease and significantly affect the modes of which rotational motions are dominated. It is also shown that the dynamic response becomes larger as the joint clearances increase, and the joint contact forces become larger as joint clearances and friction coefficient increase.