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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 13 Issue: 1

On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces

Mustafa Bilici(ONDOKUZ MAYIS ÜNİVERSİTESİ)0000-0002-3502-5027
Pages
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Publication Date
2021-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally we illustrate these surfaces by presenting some examples.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, ruled surfaces formed by Frenet's trihedral of involute curve $\beta $ of a given curve $\alpha $ are discussed.
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Key Findings & Data:These surfaces are named as involute trajectory ruled surfaces.
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Conclusion & Impact:Finally we illustrate these surfaces by presenting some examples.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Trajectory ruled surface · developable ruled surface · involute-evolute

Abstract

In this study, ruled surfaces formed by Frenet's trihedral of involute curve $\beta $ of a given curve $\alpha $ are discussed. These surfaces are named as involute trajectory ruled surfaces. These type of ruled surfaces are expressed depending on the angle $\theta $ between the binormal vector $b$ and Darboux vector $D$ of the main curve (evolute) $\alpha $. Also, some new results and theorems related to the developability of the involute trajectory ruled surfaces are obtained. Finally we illustrate these surfaces by presenting some examples.

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Cite This Article

Bilici, M. (2021). On the Developability and Distribution Parameters of the Involute Trajectory Ruled Surfaces. Turkish Journal of Mathematics and Computer Science, Volume: 13 Issue: 1. https://doi.org/10.47000/tjmcs.803690

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References (16)

  1. Bayram, E., Bilici, M., Surface family with a common involute asymptotic curve, Int. J. Geom. Methods Mod. Phys, 13(5)(2016), 1650062 (9 pages).
  2. Çalışkan, M., Bilici, M., Some characterizations for the pair of Involute-Evolute curves in Euclidean space, Bull. Pure Appl. Sci., 21(2)(2002), 289–294.
  3. Do Carmo, M.P., Differantial Geometry of Curves and Surfaces, Prentice Hall, Englewood Cliffs, New Jersey, 1976.
  4. Farouki, R.T., The approximation of non-degenerate offset surfaces, Computer Aided Geometric Design, 3(1986), 15–43.
  5. Gürsoy, O., Küçük, A., On the invariants of trajectory surfaces, Mech and Mach Theory, 34(4)(1999), 587–597.
  6. Küçük, A., On the developable of Bertrand trajectory ruled surface o sets, Intern. Math. Journal, 4(1)(2003), 57–64.
  7. Küçük, A., On the developable timelike trajectory ruled surfaces in Lorentz 3-space R31, App. Math. and Comp., 157(2004), 483–489.
  8. Laugwitz, D., Differential and Riemannian Geometry, Academic Press, New York, 1965.
  9. O’Neill, B., Semi-Riemannian Geometry with Application to relativity, Academic Press, New York, 1983.
  10. Orbay, K., Aydemir, I., The ruled surfaces generated by Frenet vectors of a curve in R31, C.B.U. Journal of Science, 6(2)(2010), 155–160.
  11. Perriollat, M., Bartoli, A., A computational model of bounded developable surfaces with application to image-based three-dimensional reconstruction, Computer Animation & Virtual Worlds, 24(5) (2013) 459–476. doi:10.1002/cav.1478.
  12. Pottmann, H., Asperl, A., Hofer, M., Kilian, A., Architectural Geometry, Bentley Institute Press, Exton, 2007.
  13. Ravani, B., Ku, T.S., Bertrand offsets of ruled and developable surfaces, Comp. Aided Geom. Design, 23(2)(1991), 145–152.
  14. Yang, A.T., Kirson, Y., Both, B., On a kinematics theory for ruled surface, Proceedings of Fourth World Congress on the Theory of Machines and Mechanisms, Newcastle Upon Tyne, England, 1975, 737-742.
  15. Yaylı Y., Saracoglu, S., On developable ruled surfaces in Minkowski space, Advances in Applied Clifford Algebras, 22(2)(2012), 499-510.
  16. Orbay, K., Aydemir, I., The ruled surfaces generated by Frenet vectors of a curve in R31, C.B.U. Journal of Science, 6(2)(2010), 155–160.