An Elastodynamic Modeling Method for a 3-RPS Parallel Kinematic Machine

An elastodynamic model for a fully flexible 3-RPS parallel kinematic machine (PKM) is proposed based on the component mode synthesis (CMS) and modal reduction technology. In the modeling process, the whole system is divided into moving platform subsystem and three retractable RPS limb subsystems, in which all joint and limb compliances are included. In the elastodynamic model, the sphere joint and the revolute joint are treated as lumped virtual springs with equal stiffness, and the elastodynamic equations of RPS limbs are developed by the modal reduction techniques with the aid of the finite element software. By introducing the compatibility conditions, a global dynamic equation of the system is then proposed. The conclusion reveals that the natural frequencies of different orders vary with the changes of the configuration, and are three-symmetrically distributed. The natural frequencies and vibration modes obtained by the proposed method are further validated by the modal experimental results.