Study on the effect of axial forces on dynamic stiffening of a 3-RPR planar parallel manipulator with flexible intermediate links

This paper presents the effect of axial forces on the dynamic stiffening of a flexible 3-RPR parallel manipulator in motion with high-speed. The intermediate links are modeled as Euler-Bernoulli beams with fixed-pinned boundary conditions based on the assumed mode method (AMM) and the effect of axial forces on lateral stiffness is investigated. Frequencies of bending vibration of the intermediate links are derived as the functions of axial force and rigid-body motion of the manipulator. Numerical simulations are performed to illustrate the effect of axial forces on the dynamic characteristics of the flexible parallel manipulator. Simulation results of mode shape, deformations, axial forces and frequencies are presented. These results provide a new insight to the optimization, design and control of the 3-RPR parallel manipulators with flexible intermediate links moving in a specified path with high speed.