Dynamics of momentum screw for a multi-rigid-body system

Dynamics of complicated spatial multi-rigid-body systems provides the theoretical equation of external load and actuation, and position algorithm in control. This paper proposes a dynamics method in momentum screw and force screw for a multi-rigid-body system. The theorem of momentum screw of a rigid body is derived to establish the one-order differential equations between momentum screw of the body and all force screws exerted on it. This forms a foundation for developing efficient dynamics of complex multi-rigid-body systems. Taking two classical manipulators as application cases, the effectiveness and generality of the screw dynamics are validated. Meanwhile, the practical efficiency of the method is verified in detail. This is the main reason for the increase in computational efficiency. In addition, accurate analytical solutions can be obtained when dealing with simple planar robot dynamics. Unlike the Newton-Euler method, the dynamics in momentum screw and force screw is free from any algebraic operation from displacement to acceleration. As a result, the average execution time of the screw dynamics method is greatly reduced compared with the Newton-Euler method. Another benefit of the proposed method is that it simplifies the process of coding on a computer. The code is very brief and straightforward to write. This dynamics methodology is straightforward and will be widely utilized in the future software of multi-rigid-body system dynamics.