Dynamics and vibration of a 3-PSP parallel robot with flexible moving platform

Abstract

In this research, first an analytical model is presented for dynamic and vibration analysis of a 3-PSP parallel robot with a flexible moving platform. Next, the presented analytical model is solved using an approximate analytical method. The moving platform is assumed to be made of three Euler-Bernoulli beams joined together to form a star. Each of the three beams of the star slides through a passive prismatic joint. Then, three-dimensional vibration analysis of the flexible moving platform, star, with three passive prismatic joints is the main subject of the present research. Only vibration during free motion is considered. Therefore, it is assumed that only inertia forces of the star are the main source of its vibration. First, direct kinematics is used for acceleration analysis of the rigid robot and inertia forces are obtained. For dynamic modeling, the passive prismatic joints and junction point of the three beams are modeled using a new set of geometric constraints. Additionally, a previously developed constrained motion equation for a planar Euler-Bernoulli beam having a prismatic joint is further developed for the three beams of the star. Next, an approximate analytical solution method, called the “constrained assumed modes method”, is used for inverse dynamics and vibration analysis of the robot. Furthermore, the developed model can be used for direct dynamics analysis of the robot. Finally, several input trajectories and two different groups of mode shapes are considered to investigate the model efficiency. The results of the presented model are compared with the results of a commercial finite element method software.