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On the synthesis of spatial cycloidal gears

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Abstract

The subject of this paper is the synthesis of spatial cycloidal gears, based on Disteli’s work, which was published at the turn of the 20th century. In particular, the properties of the Plücker conoid or the cylindroid for the relative motion between a pair of skew gears are analyzed in order to extend Camus’ Theorem from the planar and spherical cases to the spatial case with the aim of synthesizing a pair of conjugate cycloidal teeth.

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References

  1. Litvin FL, Fuentes A (2004) Gear geometry and applied theory. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  2. Dooner DB, Seireg AA (1995) The kinematic geometry of gearing: a concurrent engineering approach. Wiley, New York

    Google Scholar 

  3. Phillips J (2003) General spatial involute gearing. Springer, Berlin

    Book  Google Scholar 

  4. Stachel H (2004) On Jack Phillips spatial involute gearing. In: 11th international conference on geometry and graphics, Guangzhou (China), pp 43–48

    Google Scholar 

  5. Ball R (1900) A treatise on the theory of screws. Cambridge University Press, Cambridge

    Google Scholar 

  6. Koenigs G (1897) Leçons de cinématique. Librairie Scientifique A. Hermann, Paris

    MATH  Google Scholar 

  7. Disteli M (1904) Über instantane Schraubengeschwindigkeiten und die Verzahnung der Hyperboloidräder. Z Math Phys 51:51–88

    MATH  Google Scholar 

  8. Disteli M (1911) Über die Verzahnung der Hyperboloidräder mit geradlinigem Eingriff. Z Math Phys 59:244–298

    MATH  Google Scholar 

  9. Schur F (1927) Nachruf auf Martin Disteli. Jahresber Dtsch Math-Ver 36:170–173

    MATH  Google Scholar 

  10. Reuleaux F (1963) The kinematics of machinery. Dover, New York (English version by A.B.W. Kennedy)

    Google Scholar 

  11. Ghigliazza R, Lucifredi A, Michelini R (1974). Meccanica applicata alle macchine. Microlito, Genova

    Google Scholar 

  12. Ferrari C, Romiti A (1966) Meccanica applicata alle macchine. UTET, Torino

    Google Scholar 

  13. Figliolini G, Angeles J (2006) The synthesis of the pitch surfaces of internal and external skew-gears and their racks. ASME J Mech Des 128(4):794–802

    Article  Google Scholar 

  14. Figliolini G, Angeles J (2011) Synthesis of the pitch cones of N-lobed elliptical bevel gears. ASME J Mech Des 133(3):031002

    Article  Google Scholar 

  15. Figliolini G, Stachel H, Angeles J (2007) A new look at the Ball-Disteli diagram and its relevance to spatial gearing. Mech Mach Theory 42(10):1362–1375

    Article  MathSciNet  MATH  Google Scholar 

  16. Figliolini G, Stachel H, Angeles J (2009) The computational fundamentals of spatial cycloidal gearing. In: Kecskeméthy A, Müller A (eds) Proc. of the 5th international workshop on computational kinematics. Springer, Berlin, pp 375–384

    Chapter  Google Scholar 

  17. Camus Ch (1759) Mathématique: Elèments de mécanique statique, vol II. Durand, Paris

    Google Scholar 

  18. Figliolini G, Angeles J (2005) Synthesis of the base curves for N-lobed elliptical gears. ASME J Mech Des 127(5):997–1005

    Article  Google Scholar 

  19. Figliolini G, Angeles J (2005) Algorithms for involute and octoidal bevel-gear generation. ASME J Mech Des 127(4):664–672

    Article  Google Scholar 

  20. Ognjanovic M, Benur M (2011) Experimental research for robust design of power transmission components. Meccanica 46:699–710

    Article  Google Scholar 

  21. Pau M, Leban B, Baldi A, Ginesu F (2012) Experimental contact pattern analysis for a gear-rack system. Meccanica 47:51–61

    Article  Google Scholar 

  22. Cervantes-Sánchez JJ, Rico-Martínez JM, Panduro-Calvario C (2012) A general and systematic framework for the kinematic analysis of complex gear systems. Meccanica 47:3–21

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, Cassino, Italy

    Giorgio Figliolini

  2. Institute of Discrete Mathematics and Geometry, University of Technology, Vienna, Austria

    Hellmuth Stachel

  3. Department of Mechanical Engineering & CIM, McGill University, Montreal, Canada

    Jorge Angeles

Authors
  1. Giorgio Figliolini
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  2. Hellmuth Stachel
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  3. Jorge Angeles
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Corresponding author

Correspondence to Giorgio Figliolini.

Additional information

A preliminary version of this paper was presented at the XIX AIMETA Conference, that took place in Ancona on 14–17 September 2009 under the title “On the kinematic synthesis of spatial cycloidal gears” by the same authors. This paper won the “Ettore Funaioli” Prize for the best scientific paper that was presented at the 2009 AIMETA Conference in the field of the Mechanics of Machinery.

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Figliolini, G., Stachel, H. & Angeles, J. On the synthesis of spatial cycloidal gears. Meccanica 48, 1239–1249 (2013). https://doi.org/10.1007/s11012-012-9664-9

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  • DOI: https://doi.org/10.1007/s11012-012-9664-9

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