Geometric Kinematics of Rigid Bodies with Point Contact

This paper applies Darboux frame method to developing geometric kinematics of sliding-spin-rolling motion of rigid objects with point contact. For the first time, the geodesic curvatures, normal curvatures and geodesic torsions of both the sliding motion and rolling motion are derived in terms of known geometric entities. The geometric kinematics of the moving object is represented with geometric invariants. Effect of the relative curvatures and torsion on sliding-spin-rolling kinematics is explicitly presented.