Abstract
This paper derives the equations of line-trajectory in spatial motion by means of the E. Study dual-line coordinates. A special emphasis goes to the second-order motion properties for deriving a new proof of the Disteli formulae. As an application concise explicit expressions of the inflection line congruence are directly obtained. Also, a new metric is developed and used to investigate the geometrical properties and kinematics of line trajectory as well as Disteli axis. Finally, a theoretical expressions of point trajectories with special values of velocity and acceleration, which can be considered as a form Euler-Savary equation, for spherical and planar motions are discussed.
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Recommended by Editor Yeon June Kang
R. A. Abdel-Baky is currently a Sciences Faculty for Girls member in the Department of Mathematics at King Abdulaziz University, Jeddah 21352, Saudi Arabia. He received his BSc and MSc in Mathematics from University of Assiut 71516, Egypt. His research interests include geometry of motion and the theory of curves and surfaces, Prof. Rashad received his Ph.D. in mathematics from Ankara University in 1994, Ankara Turcky.
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Al-Ghefari, R.A., Abdel-Baky, R.A. Kinematic geometry of a line trajectory in spatial motion. J Mech Sci Technol 29, 3597–3608 (2015). https://doi.org/10.1007/s12206-015-0803-9
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DOI: https://doi.org/10.1007/s12206-015-0803-9