Quantitative Analysis and Application of The Bench Dragon's Movement on An Archimedean Spiral

To optimize the kinematic parameters of the "Bench Dragon" in Chinese folk culture, it is requisite to establish a mathematical model to conduct real-time simulation of the motion state of the Bench Dragon when it moves along the Archimedean Spiral. At present, there are relatively few related studies on such issues. Thus, in this paper, by utilizing the properties of the Archimedean Spiral and differential equations in the polar coordinate system, a mathematical motion model of the "Bench Dragon" is established. The model is solved by employing the Runge-Kutta Method and the Finite Difference Method, obtaining the velocity and position of the "Bench Dragon" when it moves along the trajectory of the Archimedean Spiral. Simultaneously, this model is also applicable to deducing the real-time motion state of other chain-like objects moving along the Archimedean Spiral, and holds significant guiding significance for the design and operation of objects involving chains or link structures.