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Moving our hands smoothly is essential to execute ordinary tasks, such ascarrying a glass of water without spilling. Past studies have revealed anatural tendency to generate smooth trajectories when moving the hand from onepoint to another in free space. Here we provide a new perspective on movementsmoothness by showing that smoothness is also enforced when the hand maintainscontact with a curved surface. Maximally smooth motions over curved surfacesoccur along geodesic lines that depend on fundamental features of the surface,such as its radius and center of curvature. Subjects were requested to executemovements of the hand while in contact with a virtual sphere that they couldnot see. We found that with practice, subjects tended to move their hand alongsmooth trajectories, near geodesic pathways joining start to end positions, toreduce contact forces with constrained boundary, variance of contact force,tangential velocity profile error and sum of square jerk along the time span ofmovement. Furthermore, after practicing movements in a region of the sphere,subjects executed near-geodesic movements, less contact forces, less contactforce variance, less tangential velocity profile error and less sum of squarejerk in a different region. These findings suggest that the execution of smoothmovements while the hand is in contact with a surface is a means for extractinginformation about the surface's geometrical features.

Implicit learning of object geometry by reducing contact forces and increasing smoothness