Academic Journal of Mathematical Sciences, 2025, 6(1); doi: 10.25236/AJMS.2025.060108.
Yuqing Xia1, Zhihan Gong1, Fangyu Wei1
1School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, China
This paper investigates the motion of curved architectures based on the separation axis theorem and iterative algorithm, aiming to model the collision and motion of curved architectures during the execution of complex motions. First, the study utilizes the nature of isometric curves to obtain the position coordinates of the head of the curved architecture at each moment, and fits the motion trajectories of the knuckle body and the tail through an iterative algorithm. In addition, in order to understand the velocity of the knuckle body and the tail, this paper applies the kinematics principle to decompose the combined velocity into radial and tangential velocities, which is then solved. Then, in terms of collision detection, based on the established position and velocity models, the right-angle coordinate system method and the separated axis theorem (SAT) are used to calculate the specific coordinates where the collision occurs. It is further analyzed that the geometric relationship of the turnaround path and the establishment of the velocity model are the key to ensure the validity of the model. Finally, the study also explores the maximum critical velocity of the head of the curved architecture, which is solved to derive the maximum traveling velocity by a step-by-step traversal.
Iterative Algorithms, Collision Detection, Separated Axis Theorem (SAT), Geometric Optimization
Yuqing Xia, Zhihan Gong, Fangyu Wei. Curved Structure Motion Portray Based on Separation Axis Theorem and Iterative Algorithm. Academic Journal of Mathematical Sciences (2025) Vol. 6, Issue 1: 63-72. https://doi.org/10.25236/AJMS.2025.060108.
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