Improved Particle Swarm Optimization Algorithm Based on a Three-Dimensional Convex Hull for Fitting a Screw Thread Central Axis

To meet the needs of three-dimensional (3D) measurement and to achieve the high-precision fitting of the central axis of a screw thread, this study performed complex processing of the 3D structures on the surface of the thread central axis. Moreover, this study examined the problems of long processing time and low accuracy caused by the use of a point cloud with a large data volume. An improved particle swarm optimization algorithm was used to develop a fitting method for the central axis of the three-dimensional (3D) thread of a 3D convex hull. SolidWorks was used to simulate the 3D parts of a standard thread, and the Point Cloud Library was used to generate a 3D simulated point cloud for the thread surface. The maximum deviation between the fitted line and the line obtained in the two-dimensional (2D) projection method was $0.12~\mu \text{m}$ . An experiment was conducted using data regarding the tip of the plug gauge surface. The variation in the distance between the obtained straight line and the 3D point cloud was smaller than that between the obtained straight line and the 2D point cloud. Moreover, the calculation speed was higher when using the 3D method than when using the 2D method.