The Forward Kinematics of Rolling Contact of Timelike Surfaces With Spacelike Trajectory Curves

Authors

• Mehmet Aydinalp Manisa Celal Bayar University, Faculty of Arts and Sciences, Department of Mathematics, 45140, Manisa
• Mustafa Kazaz Manisa Celal Bayar University, Faculty of Arts and Sciences, Department of Mathematics, 45140, Manisa
• Hüseyin Uğurlu Gazi University, Faculty of Education, Department of Secondary Education Science and Mathematics Teaching, Mathematics Teaching Program, 06560, Ankara

Keywords:

Lorentzian 3-Space, Darboux frame, Forward kinematics, Pure-rolling, Rolling contact, Spin-rolling

Abstract

In this paper, we investigate the forward kinematics of spin-rolling motion without sliding of one timelike surface on another timelike 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 timelike moving surface with regards to contravariant vectors, rolling velocity, and geometric invariants are obtained. Namely, the translational velocity formulation of an arbitrary point and the equation of the angular velocity formulation on the timelike 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.

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2019-07-30
CITATION

How to Cite

Aydinalp, M., Kazaz, M., & Uğurlu, H. (2019). The Forward Kinematics of Rolling Contact of Timelike Surfaces With Spacelike Trajectory Curves. Journal of Informatics and Mathematical Sciences, 11(2), 133–146. https://doi.org/10.26713/jims.v11i2.881

Section

Research Articles