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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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).
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Enlarged view of tooth on ruled hyperboloidal surface
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Enlarged view of hyperboloidal pitch surface
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Inclination angle ξ between tooth spiral tangency and line of contact  
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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
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Relation between envelope of moving body and envelope of envelopes




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