Research on Dynamic Modeling of Multibody Systems Based on Equiangular Helix Motion

Abstract

Focusing on the motion characteristics of multi-body equidistant spiral motion, this paper takes the "bench dragon", a traditional folk activity in the Zhejiang-Fujian region, as an example to establish a dynamic mathematical model based on the equidistant spiral trajectory. It realizes numerical solution and analysis through MATLAB, and explores the motion trajectory of complex multi-body joint motion systems in equidistant spiral motion.In this paper, the differential equation of the spiral is derived through geometric relations, and the evolution laws of position and velocity during the initial coiling process of the spiral are studied. Combined with the rigid body fixed-axis rotation model and the constant velocity condition at the starting point of equidistant spiral motion, the fourth-order Runge-Kutta method and nonlinear equations are used to solve, so as to accurately calculate the position and velocity data of each physical motion in multi-body equidistant spiral motion. At the same time, focusing on the collision of each equidistant spiral motion, the overlap is determined by coordinate discretization and rotation matrix method, which further reveals the collision constraint mechanism of the multi-body joint motion system in the close cooperative motion.This paper not only provides a scientific basis for optimizing the motion trajectory of traditional folk activities, but also offers important theoretical references and methodological inspirations for fields such as motion planning, collision avoidance and cooperative control of complex joint multi-body systems, and has broad application prospects.