Multibody dynamics analysis of the effects of golf club changes on swing motion

Recently, several golf club fitting systems have been developed to analyze golfers’ swings and recommend clubs optimized for individual motion characteristics. These systems have significantly improved the performance of both professional and amateur players. However, most existing analytical approaches do not sufficiently account for how variations in club properties, such as length and mass, affect swing dynamics. Developing a predictive understanding of this relationship is essential for identifying golf clubs that maximize ball flight distance. In this study, golf swings were measured using a motion capture system. Based on the three-dimensional coordinates of multiple markers, a representative swing plane was determined using the least-squares method. A novel analytical model is then proposed to capture the essential features of a three-dimensional golf swing as a two-dimensional motion confined to this plane. The proposed model is formulated as a special type of link system without a fixed point in the inertial frame, allowing for a concise yet physically meaningful description of swing motion. Within this framework, a dynamic model of the swing is derived based on multibody dynamics theory, and the optimization of the golf swing is subsequently investigated. Because the swing optimization problem involves constraints and a free terminal time, it is challenging to solve using conventional numerical techniques. To address this issue, the extended path parameter method, previously proposed by the authors, is employed. This method decouples spatial paths and time trajectories, enabling efficient two-stage optimization. Finally, the validity of the proposed approach is demonstrated by evaluating its ability to predict the effects of club property modifications on swing performance.