Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame

Year 2018, Volume: 22 Issue: 6, 1787 - 1792, 01.12.2018

Vahide Bulut

https://doi.org/10.16984/saufenbilder.400272

Abstract

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

Keywords

Frenet-Serret frame, Darboux frame, Local-Surface frame, kinematics, point contact

References

• [1] J. S. Beggs, “Advanced Mechanism”, The Macmillan Company, New York, 1966.
• [2] D. L. Brock, “Enhancing the dexterity of a robot hand using controlled slip”, In In 1988 IEEE Conference on Robotics and Automation, 1988.
• [3] C. Cai and B. Roth, “On the planar motion of rigid bodies with point contact”, Mechanism and Machine Theory, 21(6):453-466, 1986.
• [4] C. Cai and B. Roth, “On the spatial motion of rigid bodies with point contact”, In In Proceedings of 1987 International Conference on Robotics and Automation, 1987.
• [5] C. Cai and B. Roth, “On the spatial motion of rigid bodies with line contact”, In In Proceedings of 1988 International Conference on Robotics and Automation, 1988.
• [6] L. Cui and J.S. Dai, “A darboux frame based formulation of spin-rolling motion of rigid objects with point contact”, In IEEE Transactions on Robotics 26, 2010.
• [7] A. S. Hall, “Kinematics and Linkage Design”, Balt Publishers, West Lafayette, Indiana, 1966.
• [8] D. J. Montana, “The kinematics of contact and grasp”, The International Journal of Robotics Research, 7(3):17-32, 1988.
• [9] A. W. Nutbourne and R. R. Martin, “Differential Geometry Applied to Curve and Surface Design”, 1:Foundations,West Sussex, Chichester, UK; E.Horwood, NY,USA, 1988.
• [10] B. O'Neill, “Elemantery Differential Geometry”, Academic press Inc. New York, 1966.
• [11] L. A. Pars, “A Treatise on Analytical Dynamics”. Wiley, New York, 1968.
• [12] B. Paul, “Kinematics and Dynamics of Planar Machinery”, Prentice-Hall, Inc., Englewoods Cli s, N.J., 1979.
• [13] N. Rosenauer and A.H. Willis, “Kinematics of Mechanisms”, Associated General Publications Pty Ltd, Sydney, Australia, 1953.
• [14] E. T. Whittaker, “A Treatise on the Analytical Dynamics of Particles & Rigid Bodies”, Cambridge University Press, 1988.