Analysis of Helical Structures Based on Simulated Annealing Algorithms and Geometric Constraints

The study of spiral structures helps optimize space utilization, enhance structural stability and efficiency, and promote engineering design innovation. In this paper, the motion mechanism and path planning of the spiral structure are discussed in depth, and a solution model of the spiral disk-in path based on the numerical integration method is proposed. First, the position and velocity of the head end and each segment of the structure are iteratively calculated by establishing polar coordinate equations, and geometric constraints are utilized to ensure the consistency of motion under rigid connection. For collision detection, the left front part of the first end is selected as the key detection point, and the distance between this point and the main body of the structure is calculated to determine the time when the collision occurs. In addition, for the spatial limitation of the steering region, the minimum pitch is derived and the steering path length is optimized by the gradient descent method to ensure smooth transition and path optimization in the motion of the structure. Finally, this paper establishes a velocity decreasing model by simulated annealing algorithm to ensure that the velocity of the first end does not exceed the safety limit, thus guaranteeing the safe motion of the spiral structure. The research results provide a theoretical basis for the precise control of the path planning of the spiral structure.