saujs Sakarya University Journal of Science 2147-835X Sakarya University 10.16984/saufenbilder.400272 Mathematical Sciences Matematik Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame https://orcid.org/0000-0002-0786-8860 Bulut Vahide 12 01 2018 22 6 1787 1792 03 02 2018 06 14 2018 Copyright © 1997, Sakarya University Journal of Science 1997 Sakarya University Journal of Science

Controlling the relative motion between two contactingrigid bodies is necessary when manipulation and locomotion tasks areencountered in robotics. In this paper, we express the kinematics ofspin-rolling motion of rigid objects with point contact based on thelocal-surface frame method. We give the relationship between the Darboux frameand local-surface frame, and also between the Frenet-Serret frame and local-surfaceframe. Additionally, we obtain velocity of the moving object according to thelocal-surface frame curvatures of the respective contact curve and geometricinvariants. We can have proper information about trajectory planning if we takethe formulations of moving object into consideration according to thelocal-surface frame.

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