Analysis on Rigid-Elastic Coupling Characteristics of Planar 3-RRR Flexible Parallel Mechanisms

Based on the finite element method and Lagrange equation, high dimensions, time-invariant, nonlinear rigid-elastic coupling dynamic equations are established, in which the coupling influence of elastic deformation motion and the rigid body motion are considered. A comparative analysis of one-step method and two-step method for solving nonlinear rigid-elastic coupling dynamic equations is given. The simulation results show that the elastic vibrations of the flexible links have important effect on rigid body motion, particularly for angular velocity and angular acceleration. There are some errors in the amplitudes and phases of the elastic displacements and the elastic rotation angle for the two methods, rigid-elastic coupling of flexible links will critical influence elastic deformation displacements and elastic rotate angle of the moving platform, but change rule of the kinematic variables are basically consistent. So, one-pass method is used to solve dynamic equation of rigid-elastic coupling system that can reflect the dynamic characteristics well, it can provide guidance for controller design in future.