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, action-generated structure rather than in discrete sensory signals. While optic flow specifies self-motion visually, no corresponding framework has been formally established for the mechanical and kinesthetic information generated during skilled action. This study introduces haptic flow as a screw-structured, symmetry-bearing invariant that specifies kinesthetic information in human movement. Using screw theory, we model haptic flow as the continuous evolution of instantaneous screw axes and pitch, capturing the coupled rotational–translational dynamics of the body–object system. This framework is applied to the golf swing as a paradigmatic case of skilled manipulation. Motion data from proficient and novice performers reveal clear geometric differences: proficient performance is characterized by coherent alignment between instantaneous screw axes and the club’s principal inertia axis, stabilization of pitch through impact, and the emergence of harmonic screws lying on a common cylindroid. In contrast, novice performance exhibits fragmented screw organization, elevated pitch variability, and pronounced geometric asymmetry. These results demonstrate that skilled manipulation is structured by a continuous, internally generated flow of mechanical information that is invariant across critical phases of action. Interpreted in Gibsonian terms, harmonic screws function as perceivable affordances—symmetry-stabilized modes that couple inertia and potential and guide action without reliance on explicit feedback or internal models. The proposed concept of haptic flow thus extends ecological perception–action theory into the mechanical domain and provides a quantitative symmetry-based framework for analyzing skilled human movement.