Examining motion of a robot end-effector via the curvature theory of dual Lorentzian curves
Abstract
In this paper, we study the motion of a robot end-effector using the curvature theory of a dual Lorentzian unit spherical spacelike curve which corresponds to a timelike ruled surface with spacelike ruling generated by a line fixed in the end-effector. In this way, we determine linear and angular time dependent differential properties of motion such as velocities and accelerations which are important information in kinematics and robot trajectory planning. Moreover, motion of a robot end-effector in Lorentzian space whose generating surface is a helicoid is examined as a practical example.
Copyright © 2016 Burak Sahiner, Mustafa Kazaz, Hasan Huseyin Ugurlu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
B. Sahiner, M. Kazaz, H. H. Ugurlu, Examining motion of a robot end-effector via the curvature theory of dual Lorentzian curves, J. Math. Comput. Sci. 7 (2017), 12–29.
BibTeX
@article{Sahiner2017,
author = {Sahiner, Burak and Kazaz, Mustafa and Ugurlu, Hasan Huseyin},
title = {Examining motion of a robot end-effector via the curvature theory of dual Lorentzian curves},
journal = {J. Math. Comput. Sci.},
volume = {7},
year = {2017},
pages = {12--29},
doi = {}
}