Machines. Technologies. Materials.
Vol. 20 (2026), Issue 4, pg(s) 137-141

MACHINES

On the Geometric Role of the Distribution Parameter in Conic Spatial Rack Drives

  • 1 Institute of Mechanics - Bulgarian Academy of Science, Sofia, Bulgaria

Abstract

This paper presents a study of some geometric characteristics of conic spatial rack drives with linear helicoids. Three variants of the conic configuration are considered — with convolute, involute, and Archimedean helicoids — and their action surface properties are analyzed in relation to the distribution parameter. The role of the distribution parameter in determining the geometry of the action surface and the position of each variant in the design parameter space is discussed.

Keywords

References

  1. Abadjieva, E., 2010. Mathematical Models of the Kinematic Processes in Spatial Rack Mechanisms and their Application. Ph.D. Thesis, Institute of Mechanics, Bulgarian Academy of Sciences, Sofia (in Bulgarian).
  2. Abadjiev, V., 2007. Gearing Theory and Technical Applications of Hyperboloid Mechanisms. D.Sc. Thesis, Institute of Mechanics, Bulgarian Academy of Sciences, Sofia (in Bulgarian).
  3. Abadjiev, V., Abadjieva, E., 2021. Conic linear helicoids: Part
  4. Applications in the synthesis and design of spatial motions transformers. Mechanisms and Machine Science, Vol. 101, Springer, Cham, pp. 361–387.
  5. Minkov, K., 1986. Mechanical and Mathematical Modeling of Hyperbolic Gears. Sc. D. Thesis, Sofia (in Bulgarian). 5. Olivier, T., 1842. Théorie Géométrique des Engrenages. Bachelier, Paris.
  6. F. Litvin, 1994, Geometry and Applied Theory, PTR Prentice Hall, A Paramount Communication Company, Englewood Cliffs, New Jersey 07632, p. 724.
  7. Abadjieva, E., Abadjiev, V., 2008. On the kinematic theory of spatial rack drives. Comptes Rendus de l'Académie Bulgare des Sciences, 61(12), 1525–1534.
  8. Trahanov, K.T., Ilinski, V.N., 1973. Rack-conic drive with inconstant velocity ratio. In: Theory of Gears in Machines, Nauka, Moscow, pp. 49–56 (in Russian).
  9. Watanabe, M., Maki, M., 2006. A study on new type WN rack and pinion. Proc. 2nd Int. Conf. Power Transmissions, Novi Sad, pp. 27–32.
  10. Rashevsky, P. 1956, Course of Differential Geometry. Ed. State Publishing House of Technical and Theoretical Literature, Moscow 420 p.
  11. BDS 8540-84, 1985. Gear sets. Common terms. Definitions and symbols. Institute of Standardization, Sofia.
  12. Kovatchev, G., Abadjiev, V. 1990, On the Synthesis of Spatial Rack Mechanisms. Proc. 6-th National Congress of Theor. And Appl. Mech., Varna, 1, pp. 35-38, (in Russian).

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