Spatial gearing: Kinematic characteristics of the instantaneous contact

  • 1 Graduate School of Engineering Science, Akita University, Japan
  • 2 Institute of Mechanics, Bulgarian Academy of Sciences, Bulgaria

Abstract

In this work, case of rotations transformation between arbitrary crossed shafts (axes of rotations) by means of high kinematic joints, which elements configure active tooth surfaces of hyperboloid gear mechanisms is treated. |Analytical dependencies, defining the law of rotations transformation are illustrated. This law of transformation in this concrete case is a constant function of the relations of the angular velocities of the movable links of the spatial three-link gear mechanism. The shown functions are applicable both to the synthesis of the studied transmissions, and for the determining and control of the kinematic errors of these transmissions, caused by manufacturing and assembly errors.

Keywords

References

  1. Abadjiev, V. Spatial Transformation of Rotation When the Conjugate Tooth Surfaces Contact in the Pitch Contact Point. Engineering Mechanics, Vol. 10, No 4, Brno, 2003, pp. 277-284.
  2. Abadjiev, V. Gearing Theory and Technical Applications of Hyperboloid Mechanisms, Sc. D. Thesis, Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, 2007, 309 p. (In Bulgarian).
  3. Korostelev, L. The Instantaneous Velocity Ratio in Spatial Gearings. Theory of Gears in Machines, Collected papers, edited by Sc. Dr. Prof. F. L. Litvin, Publisher “Mashinostroyeniye”, Moscow, 1970, pp. 39-40.
  4. Yasko, V. Definition of the Instantaneous Velocity Ratio in Relation with Spatial Gear Mechanisms. “Mashinovedenie”, № 5, Moscow, 1973, pp. 48-50.
  5. Litvin, F. Theory of Gearing. Publishing house "Nauka," Moscow, 1968, 584 p. (in Russian).
  6. Litvin, F. Theory of Gearing. NASA Reference Publication 1212, AVSCOM Technical Report 88-C-035, US Government Printing Office, Washington, 1989, 470 p.
  7. Litvin, F. Gearing Geometry and Applied Theory. PTR Prentice Hall, A Paramount Communication Company, Englewood Eliffs, New Jersey 07632, 1994, 724 p.
  8. Litvin, F., Fuentes, A. Gearing Geometry and Applied Theory. Second Edition. Cambridge University Press, Cambridge, New York, Melbourne, Cape Town, Singapure, Sao Paulo, Delhi, Tokyo, Mexico City, 2004, 800 p

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