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TECHNICAL PAPERS

On the Three Laws of Gearing

[+] Author and Article Information
David B. Dooner

Department of Mechanical Engineering, University of Puerto Rico—Mayagüez, Mayagüez, PR 00681-9045e-mail: d_dooner@me.uprm.edu

J. Mech. Des 124(4), 733-744 (Nov 26, 2002) (12 pages) doi:10.1115/1.1518501 History: Received August 01, 2000; Revised May 01, 2002; Online November 26, 2002
Copyright © 2002 by ASME
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References

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Honda, S., 2001, “A Unified Designing Method Applicable to All Kinds of Gears for Power Transmission,” The JSME International Conference on Motion and Power Transmission, Fukuoka Japan, Vol. II, pp. 506–5512.
Ito,  N., and Takahashi,  K., 2000, “Differential Geometrical Conditions of Hypiod Gears with Conjugate Tooth Surfaces,” ASME J. Mech. Des., 122(3), pp. 323–330.
Dooner, D. B., and Seireg, A. A., 1995, The Kinematic Geometry of Gearing: A Concurrent Engineering Approach, John Wiley and Sons, Inc., New York.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press, London.
Beggs, J. S., 1959, “Ein Beitrag zur Analyze Räumlicher Mechanismem,” Doctoral Thesis, Technische Hochschule Hannover, Hanover.
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Figures

Grahic Jump Location
Nomenclature to define right-angle gear drive
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Relation between input axis of rotation $i, output axis of rotation $o, instantaneous screw axis $isa, and contact normal $l
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Two systems of cylindroidal coordinates that share a common cylindroid (note tangency between pitch surfaces)
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Ruled hyperboloidal pitch surface with instantaneous generator $pi and tangent to tooth surface Sψi (also perpendicular to null plane). The spiral angle ψ is defined such that the tooth surface normal is reciprocal to the ISA (regardless of pressure angle).
Grahic Jump Location
Enlarged view of tooth on ruled hyperboloidal surface
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Enlarged view of hyperboloidal pitch surface
Grahic Jump Location
Inclination angle ξ between tooth spiral tangency and line of contact  
Grahic Jump Location
Relative displacements for pitch point p and of contact c
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Curvature in directions perpendicular to tooth surface and pitch surface
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Relative parabolic curvature between mating gear teeth
Grahic Jump Location
Relation between envelope of moving body and envelope of envelopes

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