Screw Dynamics of a Multibody System by a Schoenflies Manipulator

This paper presents a screw dynamics method for multi-rigid-body systems. It establishes the relationship between velocity screw (twist) and force screw (wrench) in the theorem of momentum screw. Then, the structure of a 2UPS + 2UPU parallel manipulator is introduced as an example of application. By analyzing the constraint wrench of each limb and the twist of the moving platform in the theorem of momentum screw, the dynamics equation for solving the driving force makes the method very convenient for computer programming. The dynamics equation can be reorganized into a non-homogeneous linear equation and establishes the relationship between the constraint wrench of each limb and the twist of the moving platform in screw coordinate. The outstanding advantage of the algorithm proposed in this paper is that the average calculation time is only 83.21% of that of the Newton-Euler method for the 2UPS + 2UPU parallel manipulator on the same computer. This methodology provides a convenient canonical form for the dynamics analysis of multi-rigid-body systems.