Bobillier Teoreminin Kinematik Yaklaşımlarla Kapsamlı Bir Analizi

Yıl 2024, Cilt: 5 Sayı: 2, 149 - 155, 20.12.2024

Engin Can

https://doi.org/10.58769/joinssr.1586211

Öz

Bu makale, Bobillier Teoremi'nin uygulamalarına özel bir vurgu yaparak, kinematik yaklaşımlar perspektifinden eğrilik teorisinin kapsamlı bir incelemesini sunmaktadır. Eğrilik teorisi, diferansiyel geometri içinde önemli bir rol oynar ve hem statik hem de dinamik ortamlarda nesne yörüngeleri, normal eğrilik ve eğrilik merkez yörüngelerinin incelenmesi için temeldir. Bu çalışma, klasik geometrik analizi dinamik uygulamalarla bağlamak için Bobillier Teoremi'ni vurgulayarak, eğrilik teorisine kinematik bir yaklaşım benimsemektedir.

Anahtar Kelimeler

Eğrilik, Bobillier tasarımı, Hartmann kuralı

A Comprehensive Analysis through Kinematic Approaches of Bobillier’s Theorem

Öz

This paper presents a comprehensive examination of curvature theory through the lens of kinematic approaches, with a particular focus on the applications of Bobillier’s Theorem. Curvature theory plays a central role in differential geometry and is fundamental to the study of object trajectories, normal curvature, and center of curvature paths in both static and dynamic settings. This study employs a kinematic approach to curvature theory, emphasizing Bobillier’s Theorem to connect classical geometric analysis with dynamic applications.

Anahtar Kelimeler

Curvature, Bobillier’s design, Hartmann’s rule

Kaynakça

• [1] G. Dittrich, R. Braune, Getriebetechnik in Beispielen, R. Oldenbourg Verlag, München, 1978.
• [2] E.A. Dijksman, Motion Geometry of Mechanisms, Cambridge University Press, 1976.
• [3] L. Hagedorn, Konstruktive Getriebelehre. 3. Aufl., Hermann Schroedel Verlag KG, Hannover, 1976.
• [4] F. Hohenberg, Konstruktive Geometrie in der Technik, 3. Aufl., Springer Verlag, Wien, 1966.
• [5] H. Kerle, B. Corves, R. Pittschellis, Einführung in die Getriebelehre: Analyse und Synthese ungleichmaeßig übersetzender Getriebe, 3. Aufl., B.G. Teubner Verlag, Wiesbaden, 2007.
• [6] F.L. Litvin, A. Fuentes, Gear Geometry and Applied Theory, 2nd ed., Cambridge University Press, 2004.
• [7] K. Luck, K.-H. Modler, Getriebetechnik, Springer Verlag Wien, New York, 1990.
• [8] F. Reuleaux, Lehrbuch der Kinematik, I. Theoretische Kinematik, Friedrich Vieweg und Sohn, Braunschweig, 1875.
• [9] J.E. Shigley, J.J. Uicker, Theory of Machines and Mechanisms, McGraw-Hill, New York, 1980.
• [10] W. Steinhilper, H. Hennerici, S. Britz, Kinematische Grundlagen ebener Mechanismen und Getriebe, Vogel Buchverlag, Würzburg, 1993.
• [11] W. Wunderlich, Ebene Kinematik, BI–Hochschultaschenbücher, Band 447, Bibliographisches Institut, Mannheim, 1970.
• [12] T. Arens, F. Hettlich, Ch. Karpfinger, U. Kockelkorn, K., Lichtenegger, H. Stachel, Mathematik, 2. Aufl., Spektrum Akademischer Verlag, Heidelberg, 2011.
• [13] M. P. do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, 1976.
• [14] D. J. Struik, Lectures on Classical Differential Geometry, Addison-Wesley, 1961.
• [15] M. Spivak, A Comprehensive Introduction to Differential Geometry, Vol. 2, 3rd. Edition, Publish or Perish, 1999.
• [16] A. Gray, Modern Differential Geometry of Curves and Surfaces with Mathematica, CRC Press, 1998