# Computational Dynamics of Multi-Rigid-Body System in Screw Coordinate
## 1 Introduction  
It is well known that a multi-rigid-body system is normally a complex system with many links and joints and is fundamental for mechanism research in robotics, spacecraft, and bionic areas. Studies of multi-rigid-body systems can neglect the flexibility of the bodies and focus on the kinematic and dynamic performance of the mechanisms. Extensive research has proposed a series of theoretical models of multi-rigid-body systems. Parallel mechanisms are common multi-rigid-body systems with high loading ability, good dynamic response, and precise motion. The Gough-Stewart platform as a common parallel mechanism is proposed as a flight simulator by [PERSON] and [PERSON] [1; 2; 3], which has high flexibility. Therefore, the study of the kinematics and dynamics of the Gough-Stewart platform is vital research topics for its application.  
Dynamics analysis has theoretical and practical significance for realizing robot control, stability in motion, and optimization in structure. Scholars presented some dynamics methods for parallel mechanisms. The widely-used methods for multi-rigid-body system dynamics mainly include Lagrange equation [4; 5], Newton-Euler equation [6], virtual work principle equation [7; 8], Kane equation [9], and Gibbs-Appell equation [10]. The Newton-Euler dynamics equation for the Gough-Stewart platform, which is based on the vector method and proposed by [PERSON], is a classic algorithm in dynamics modeling [11; 12]. Newton-Euler equations can express the rotational and translational motion of a rigid body in the absolute coordinate system. Through a single equation with six components in the form of column vectors and matrix, the forces and moments acting on the rigid body and the motion of the center of mass of a rigid body can be combined [13; 14; 15]. [PERSON] [16; 17] proposed dynamics analysis of parallel mechanisms by screw coordinates and the principle of virtual work. The analysis of a multi-rigid-body system is usually solved through analytical methods in classical mechanics and vector equations [18; 19; 20; 21].  
The displacement, velocity, and acceleration obtained in kinematics are essential information for dynamics modeling. To describe the kinematics of a mechanism, the translational and rotational motions should be expressed with a suitable mathematical framework in a relatively general way [22; 23]. Meanwhile, there are also several finite solutions corresponding to different configurations of a multi-rigid-body system [24; 25; 26]. The kinematics modeling of a multi-rigid-body system can be simplified by resorting to screw coordinates. Many researchers have utilized screw coordinates in kinematics analysis [27; 28] of parallel mechanisms.  
This paper focuses on the kinematics and dynamics of a multi-rigid-body system by the Newton-Euler method in screw coordinate. From kinematics analysis, the absolute displacement, velocity, and acceleration of each joint and link can be derived in the absolute coordinate frame, which can be applied directly in dynamics. This method would be much clearer and more straightforward not only for the inverse dynamics problem but also for the derivation of closed-form dynamics formulae.