Elastodynamic modelling and inherent characteristics prediction for a 3-PRS manipulator

This paper proposes an elastodynamic modelling method for a 3-degree-of-freedom (3-DOF) parallel kinematic machine (PKM) manipulator. Firstly, the architecture of the manipulator is described and its inverse kinematics is analyzed. Then, the manipulator is divided into limb subsystems and moving platform subsystem, whose dynamic equations are derived, respectively. The method of kineto-elastic-dynamics (KED) is applied in the deduce of limb subsystems and the Newton´s 2^nd Law is used in that of moving platform subsystem. The effects of spherical and revolute joints flexibility on system dynamics are taken into consideration by simplifying them into linear springs with equivalent stiffness. With the deformation compatibility conditions, the dynamic equations of subsystems are condensed into system´s governing equations. The solution of eigenvalue problem of governing equations leads to the prediction for the manipulator´s inherent characteristics. Finally, the sensitivities of design variables to inherent characteristics are revealed.