Vibration Modeling and Analysis of a Flexible 3-PRR Planar Parallel Manipulator Based on Transfer Matrix Method for Multibody System

This paper presents the vibration model of a 3-prismatic–revolute–revolute (PRR) planar parallel manipulator (PPM) with three flexible intermedia links, utilizing the linear transfer matrix method for multibody systems (MSTMM). The dynamic characteristics of the PRR PPM are also investigated. The dynamic model of the 3-PRR PPM is derived, and the transfer matrix and transfer equation of each component in the system, as well as the overall transfer equation and transfer matrix of the system are obtained. The vibration characteristics of the whole system are determined using the MSTMM and verified through ANSYS simulation. Furthermore, the relationship between the natural frequencies and the flexible PPM configurations is analyzed under a specific circular trajectory. The results demonstrate that the natural frequency of the system changes constantly with the configurations, and the trends of the first six orders are similar. This novel modeling approach does not require global dynamic equations and is both efficient and accurate. Moreover, it can be easily extended to other parallel manipulators with flexible components.