Analysis and Optimization of Bench Dragon Model: A Joint Application of Traversal optimization method and Differential Method

Pingcheng Ming

doi:10.54097/bffzwq06

Authors

Pingcheng Ming

DOI:

https://doi.org/10.54097/bffzwq06

Keywords:

Bench Dragon, Runge-Kutta 4th Order Method, Traversal Algorithms, Backward Differential Method, Limits and Microelements.

Abstract

Bench dragon is a series of benches that go end to end and move along an equidistant spiral. Through mathematical modeling, the movement process of the bench dragon and the shortest turning distance under specific circumstances are discussed. Firstly, with the help of Runge-Kutta 4th Order Method and the Microelement Method, the model of the relationship between the position of the dragon head and the time, and the model of the relationship between the position of each bench and the time were constructed. Then, to determine the minimum pitch so that the benches would not collide with each other, A spiral model with variable pitch is established, as well as the relationship between the pitch and the position of the front handle of the dragon head at the end time. Then, a small enough step size is taken to traverse within a certain range to obtain the minimum pitch that satisfies the condition. Lastly, to determine the shortest turning path and the movement of the bench dragon when coiling out, a possible turning path was put forward. The shortest possible turning path and the movement of each bench was thus calculated and solved by using Microelement Method and Backward Differential Method.

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