Computational Dynamics of Multi-Rigid-Body System in Screw Coordinate

Abstract

This paper investigates the kinematics and dynamics of multi-rigid-body systems in screw form. The Newton–Euler dynamics equations are established in screw coordinates. All forces and torques of the multi-rigid-body system can be solved straightforwardly since they are explicit in the form of screw coordinates. The displacement and acceleration are unified in matrix form, which associates the kinematics and dynamics with variable of velocity. A one-step numerical algorithm only is needed to solve the displacements and accelerations. As a result, all absolute displacements, velocities, and accelerations are directly obtained by one kinematic equation. The kinematics and dynamics of Gough–Stewart platform validate this the method. In this paper, the kinematics and dynamics are carried out with the example of a Gough–Stewart platform, which represents the most complex multi-rigid-body system, to verify the computational dynamics method. The proposed algorithm is also fit for the kinematics and dynamics modeling of other multi-rigid-body systems.