An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

Abstract

Dynamic modeling serves as the fundamental basis for dynamic performance analysis and is an essential aspect of the control scheme design of parallel manipulators. This report presents a concise and efficient solution to the dynamics of Stewart parallel manipulators based on the screw theory. The initial pose of these manipulators is described. Then the pose matrix of each link of the Stewart parallel mechanism is obtained using an inverse kinematics solution and an exponential product formula. Considering the constraint relationship between joints, the constraint matrix of the Stewart parallel manipulator is deduced. In addition, the Jacobian matrix and the twist of each link are obtained. Moreover, by deriving the differential form of the constraint matrix, the spatial acceleration of each link is obtained. Based on the force balance relationship of each link, the inverse dynamics and the general form of the dynamic model of the Stewart parallel manipulator is established and the process of inverse dynamics is summarized. The dynamic model is then verified via dynamic simulation using the ADAMS software. A numerical example is considered to demonstrate the feasibility and effectiveness of this model. The proposed dynamic modeling approach serves as a fundamental basis for structural optimization and control scheme design of the Stewart parallel manipulators.