Research on the Movement of Bench Dragon

Traditional Chinese bench-dragon performances necessitate precise multi-body dynamic modeling for choreographic optimization. Confronting the systematic deficiency in real-time position/velocity computation of interconnected segments along equidistant spiral trajectories in existing research, this study proposes a dynamic recursive model based on Archimedean spiral characteristics and a low-complexity geometric projection collision detection algorithm. By integrating polar-Cartesian coordinate transformation with numerical integration techniques, a recursive framework for segment motion parameter resolution is established. The implementation of 3D-to-2D geometric projection achieves collision detection complexity reduction to logarithmic scale while maintaining 98.7% accuracy. MATLAB simulations demonstrate that: (1) A minimum spiral pitch of 0.455 meters enables bidirectional motion transition within a 9-meter performance zone; (2) Regulating the dragon-head velocity below 1.905 m/s effectively prevents tail-end speed overshooting. Experimental validation reveals 72% positional error reduction compared to empirical approaches, successfully ensuring kinematic continuity across 233 interconnected segments. This research establishes an interdisciplinary nexus between computational mechanics and cultural heritage preservation, providing scalable solutions for intangible cultural digitization and multi-body dynamic systems.