Research Information System
Hacettepe Journal of Mathematics and Statistics, vol.50, no.6, pp.1583-1594, 2021 (SCI-Expanded, Scopus)
In this paper, we investigate the forward kinematics of dual rolling contact motion without sliding of one dual unit sphere S2 m on the fixed sphere S2 f along their dual spherical curves, which correspond to ruled surfaces generated by the straight lines in the real line space E3. We adopt a dual Darboux frame method to develop instantaneous kinematics of dual rolling motion. We obtain some new kinematic equations of rolling motion of the moving sphere S2 m with regards to dual unit vectors, dual rolling velocity, and dual geometric invariants. Namely, the dual translational velocity equation of an arbitrary dual point and the equation of the dual angular velocity on the moving sphere S2 m are derived. The equation represented by geometric invariants can be handily generalized to suit arbitrary dual spherical curve on S2 m and can be differentiated to any order.