Some Results on Point-Line Trajectories in Lorentz 3-space

Yıl 2016, Cilt: 9 Sayı: 2, 44 - 49, 30.10.2016

Tunahan Turhan Vildan Özdemir Nihat Ayyıldız

https://doi.org/10.36890/iejg.584581

Cited By: 3

Öz

In this paper, we study curvature theory of point-line trajectories in Lorentz 3-space. We give

the characterization by indicatrix, directrix and their relationship in Lorentz 3-space. We use this

characterization and relationship to depict a point-line trajectory.

Anahtar Kelimeler

Curvature, Directrix; Indicatrix, Point-line trajectories, Lorentzian 3-space

Kaynakça

• [1] Aydoğmus¸, Ö., Kula, L. and Yaylı, Y., On point-line displacement in Minkowski 3-space. Differential Geometry-Dynamical Systems, 10(2008), 32-43.
• [2] Bottema, O., and Roth, B., Theoretical Kinematics, Dover Publications, New York, 1990.
• [3] Hunt, K. H., Kinematic Geometry of Mechanisms, Clarendon Press, Oxford, England, 465 p., 1978.
• [4] Kirson, Y., Higher order curvature theory in space kinematics. Ph.D dissertation, University of California at Berkeley, 140 p., 1975.
• [5] Kim, J. H., Ruyh, B. S., and Pennock, G. R., Development of a Trajectory Generation Method for a Five-Axis NC Machine. Mech. Mach.Theory, 36 (2001), 983-996.
• [6] McCarthy, J. M., and Roth, B., The Curvature Theory of Line Trajectories in Spatial Kinematics. ASME J. Mech. Des., 103 (1981), 718-724.
• [7] McCarthy, J. M., The Instantaneous Kinematics of Line Trajectories in Terms of a Kinematic Mapping of Spatial Rigid Motion. ASME J. Mech., Transm., Autom. Des., 109 (1987), 98-100.
• [8] O’Neill, B., Semi-Riemannian Geometry with Applications to Relativity, Academic Press, London, 1983.
• [9] Ryuh, B. S., Robot trajectory planning using the curvature theory of ruled surfaces. Doctoral dissertation, Purdue University, West Lafayette, Ind, USA, 1989.
• [10] Ryuh, B. S., and Pennock, G. R., Accurate Motion of a Robot End-Effector Using the Curvature Theory of Ruled Surface. ASME J. Mech.Transm. Autom. Des., 110 (1988), 383-388.
• [11] Roth, B., Finding Geometric Invariants From Time-Based Invariants for Spherical and Spatial Motions. ASME Journal of Mechanical Design, 127 (2005), 227-231.
• [12] Stachel, H., Instantaneous Spatial Kinematics and the Invariants of the Axodes, Proceedings Ball 2000 Symposium, Cambridge University Press, London, 23 (2000).
• [13] Ting, K. L., Zhang, Y., and Bunduwongse, R., Characterization and Coordination of Point-line Trajectories. ASME Journal of Mechanical Design, 127 (2005), 502-505.
• [14] Yücesan, A., Özkan, G., Generalized relaxed elastic line on a non-degenerate surface. International Conference: Mathematical Science andApplications, 26-30 December 2012, Abu Dhabi, UAE.