Helical Path Simulation and Optimal Turning Design for The Bench Dragon Performance

The "Bench Dragon," a traditional folk cultural activity originating from Zhejiang and Fujian, involves participants linking benches to form a dragon shape, symbolizing unity and cooperation. This paper explores the mathematical essence of the Bench Dragon, focusing on its movement trajectory, velocity variations, and collision detection. By establishing a polar coordinate model, the paper simulates the movement of the Bench Dragon along an Archimedean spiral and calculates the positions and velocities of the benches under constant speed conditions. A convex hull algorithm detects collisions, and a variable step-size method precisely identifies the moments of collision. Additionally, the paper analyzes the optimal turning path for the dragon head bench, aiming to minimize the turning curve while maintaining consistent tangency. The results offer new insights into the mathematical modeling of traditional cultural activities and provide a new methodological approach to the preservation and transmission of traditional culture by combining cultural expression with scientific analysis.