A Comprehensive Analysis through Kinematic Approaches of Bobillier’s Theorem

This paper presents a comprehensive examination of curvature theory through the lens of kinematic approaches, with a particular focus on the applications of Bobillier’s Theorem. Curvature theory plays a central role in differential geometry and is fundamental to the study of object trajectories, normal curvature, and center of curvature paths in both static and dynamic settings. This study employs a kinematic approach to curvature theory, emphasizing Bobillier’s Theorem to connect classical geometric analysis with dynamic applications.