Pitch Invariance Reveals Skill-Specific Coordination in Human Movement: A Screw-Theoretic Reanalysis of Golf Swing Dynamics

Background: Skilled human movement, such as the golf swing, emerges from coordinated rotational and translational dynamics. This study investigates pitch—a screw-theoretic invariant defined as the ratio of linear to angular velocity along the instantaneous screw axis (ISA)—as a compact metric for quantifying motor coordination. Methods: We reanalyzed a validated motion capture dataset involving a proficient and a novice female golfer. ISA trajectories and pitch values were computed from 3D marker data, and synchronized with vertical ground reaction force (GRF) signals collected via force plate. Results: The proficient golfer exhibited tightly bounded pitch oscillations (approximately ±0.0025 cm/rad) that were temporally aligned with a single, well-defined GRF peak. In contrast, the novice showed irregular pitch fluctuations (−0.025 to +0.01 cm/rad) and asynchronous GRF patterns with multiple peaks. Conclusions: These findings demonstrate that pitch can serve as a biomechanical indicator of skilled performance, reflecting the degree of intersegmental coordination and force timing. Screw theory thus offers a rigorous framework for evaluating movement efficiency in sport and rehabilitation contexts.