Mathematical Modeling and Dynamic Trajectory Analysis in a Virtual Reality Welding Simulator

This study presents a mathematical and kinematic modeling framework for analyzing trajectory behavior in a virtual reality (VR) welding simulator. Twenty novice participants performed repeated welding trials across three sessions, with torch trajectories recorded at 50 Hz in the task space. The proposed framework combines trial-level performance descriptors with derivative-based dynamic features, including spectral arc length (SPARC), log-normalized jerk (LNJ), and the number of velocity peaks (NVP), to characterize movement smoothness, intermittency, and longitudinal trajectory organization in a computer-simulated manual welding task. The results showed that spatial welding error decreased most clearly during the earliest stage of practice, with mean absolute lateral error declining from approximately 2.8 mm in the first trial to approximately 1.7 mm by the third trial. This early improvement was then broadly preserved across subsequent sessions. In contrast, smoothness- and fragmentation-related metrics exhibited more variable temporal patterns, indicating that improvements in task-space accuracy were not necessarily accompanied by uniform reorganization of movement dynamics. Associations between spatial error and kinematic features remained limited, suggesting that geometric task accuracy and dynamic trajectory organization represent complementary aspects of simulated manual performance. Overall, the findings show that high-frequency trajectory analysis in VR provides a useful basis for the mathematical modeling of dynamic behavior in simulated welding systems and supports the use of computer simulation for process-level investigation of manual task execution.