Haptic Flow as a Symmetry-Bearing Invariant in Skilled Human Movement: A Screw-Theoretic Extension of Gibson’s Optic Flow

Gibson’s concept of optic flow established that perception is grounded in lawful structure generated by action. However, no formal mechanical framework has described the invariant structure of action-generated kinesthetic information during skilled manipulation. This study introduces haptic flow as a screw-theoretic invariant defined by the coupled rotational–translational organization of a body–object system. Motion capture data from a two-case comparison (one proficient and one novice golfer) were analyzed using instantaneous screw axes (ISA), pitch evolution, and cylindroid geometry derived from a linear line-complex formulation. The proficient golfer exhibited (1) progressive convergence of ISAs toward a coherent bundle, (2) stabilization of screw pitch through impact, and (3) co-cylindrical alignment of harmonic screws consistent with inertial–restoring conjugacy. In contrast, the novice golfer showed fragmented ISA organization and elevated pitch variability. These differences were descriptive rather than inferential and do not imply population-level generalization. The findings suggest that skilled manipulation is characterized by stabilization of symmetry-bearing screw invariants rather than by independent joint control. Interpreted ecologically, haptic flow is proposed as a mechanically specified candidate invariant generated by lawful body–object coupling. The present study establishes a geometric framework for quantifying such invariants while identifying the need for cross-task and perceptual validation.