Yıl 2018, Cilt 22, Sayı 6, Sayfalar 1787 - 1792 2018-12-01

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

Vahide Bulut [1]

57 131

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.

Frenet-Serret frame, Darboux frame, Local-Surface frame, kinematics, point contact
  • [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.
Birincil Dil en
Konular Matematik
Yayımlanma Tarihi December 2018
Dergi Bölümü Araştırma Makalesi
Yazarlar

Orcid: 0000-0002-0786-8860
Yazar: Vahide Bulut (Sorumlu Yazar)
Ülke: Turkey


Bibtex @araştırma makalesi { saufenbilder400272, journal = {Sakarya University Journal of Science}, issn = {1301-4048}, eissn = {2147-835X}, address = {Sakarya Üniversitesi}, year = {2018}, volume = {22}, pages = {1787 - 1792}, doi = {10.16984/saufenbilder.400272}, title = {Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame}, key = {cite}, author = {Bulut, Vahide} }
APA Bulut, V . (2018). Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame. Sakarya University Journal of Science, 22 (6), 1787-1792. DOI: 10.16984/saufenbilder.400272
MLA Bulut, V . "Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame". Sakarya University Journal of Science 22 (2018): 1787-1792 <http://www.saujs.sakarya.edu.tr/issue/31266/400272>
Chicago Bulut, V . "Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame". Sakarya University Journal of Science 22 (2018): 1787-1792
RIS TY - JOUR T1 - Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame AU - Vahide Bulut Y1 - 2018 PY - 2018 N1 - doi: 10.16984/saufenbilder.400272 DO - 10.16984/saufenbilder.400272 T2 - Sakarya University Journal of Science JF - Journal JO - JOR SP - 1787 EP - 1792 VL - 22 IS - 6 SN - 1301-4048-2147-835X M3 - doi: 10.16984/saufenbilder.400272 UR - http://dx.doi.org/10.16984/saufenbilder.400272 Y2 - 2018 ER -
EndNote %0 Sakarya University Journal of Science Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame %A Vahide Bulut %T Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame %D 2018 %J Sakarya University Journal of Science %P 1301-4048-2147-835X %V 22 %N 6 %R doi: 10.16984/saufenbilder.400272 %U 10.16984/saufenbilder.400272
ISNAD Bulut, Vahide . "Geometric Kinematic Approach to Rigid Objects with Point Contact Based on A Local-Surface Frame". Sakarya University Journal of Science 22 / 6 (Aralık 2018): 1787-1792. http://dx.doi.org/10.16984/saufenbilder.400272