The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space

Mehmet Aydınalp; Mustafa Kazaz; Hasan Hüseyin Uğurlu

doi:10.17776/csj.389649

TR EN

The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space

Abstract

In this paper, we investigate the forward kinematics of spin-rolling motion without sliding of one spacelike surface on another spacelike surface along the spacelike contact trajectory curves of the surfaces in Lorentzian 3-space. A Darboux frame method is adopted to develop instantaneous kinematics of spin-rolling motion, which occurs in a nonholonomic system. Then new kinematic formulations of spin-rolling motion of spacelike moving surface with respect to contravariant vectors, rolling velocity, and geometric invariants are obtained. The translational velocity formulation of an arbitrary point and the equation of the angular velocity formulation on the spacelike moving surface are derived. The equation, which is represented with geometric invariants, can be easily applied to arbitrary spacelike parametric surface and spacelike contact trajectory curve and can be differentiated to any order. The influence of the relative curvatures and torsion on spin-rolling kinematics is clearly presented.

2010 AMS Subject Classification: 70B10, 53A17, 53A25, 53A35.

Keywords

Darboux Frame,Forward Kinematics,Lorentzian 3-Space,Rolling Contact,Pure-rolling,Spin-rolling

References

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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Mehmet Aydınalp

Mustafa Kazaz ^*
CELÂL BAYAR ÜNİVERSİTESİ
Türkiye

Hasan Hüseyin Uğurlu

Publication Date

December 24, 2018

Submission Date

February 3, 2018

Acceptance Date

October 15, 2018

Published in Issue

Year 2018 Volume: 39 Number: 4

DOI

https://doi.org/10.17776/csj.389649

IZ

https://izlik.org/JA46PF28TX

Cite

RIS / Bibtex

APA

Aydınalp, M., Kazaz, M., & Uğurlu, H. H. (2018). The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space. Cumhuriyet Science Journal, 39(4), 882-899. https://doi.org/10.17776/csj.389649

The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space

Lorentziyen 3-Uzayda Spacelike Yüzeylerin Kontak Yuvarlanmasinin İleri Kinematiği

Öz

Anahtar Kelimeler

The Forward Kinematics of Rolling Contact of Spacelike Surfaces in Lorentzian 3-Space

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite