A novel method for the dynamic modeling of Stewart parallel mechanism

Abstract

This paper presents a new scenario for the dynamic modeling of Stewart parallel mechanism based on transfer matrix method for linear multibody systems (linear MSTMM). The mechanism is modeled as a flexible multibody system, where the platform is rigid while the legs are flexible. All the element transfer equations are re-written in the same inertial coordinate system, which significantly simplifies the deduction of the system overall transfer equation. The vibration characteristics are computed by solving homogeneous linear algebraic equations, and then the augmented eigenvector and body dynamics equation are adopted to derive the state space representation by combining modal superposition method. Without deducing system global dynamics equation, the proposed scenario is easy to formulate, systematic to apply, and can model the legs as flexible bodies without spatial discretization. Then, Hankel model reduction and LQR control are employed to demonstrate how to make use of the derived state space representation. A numerical study is performed to validate the presented method. Although the system considered in this work is Stewart parallel mechanism, the scenario is general and can be used for other linear time invariant multibody systems.