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The Role of the Orthogonal Helicoid in the Generation of the Tooth Flanks of Involute-Gear Pairs With Skew Axes

[+] Author Affiliations
Giorgio Figliolini

University of Cassino, Cassino, FR, Italy

Hellmuth Stachel

Vienna University of Technology, Wien, Austria

Jorge Angeles

McGill University, Montréal, QC, Canada

Paper No. DETC2014-34932, pp. V05AT08A065; 10 pages
  • ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5A: 38th Mechanisms and Robotics Conference
  • Buffalo, New York, USA, August 17–20, 2014
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-4636-0
  • Copyright © 2014 by ASME


Camus’ concept of Auxiliary Surface (AS) is extended to the case of involute gears with skew axes. In the case at hand, we show that the AS is an orthogonal helicoid whose axis a) lies in the cylindroid and b) is normal to the instant screw axis of one gear with respect to its meshing counterpart; in general, the helicoid axis is skew with respect to the latter. According to the spatial version of Camus’ Theorem, any line attached to the AS, in particular any generator g of AS itself, can be chosen to generate a pair of conjugate flanks with line contact.

While the pair of conjugate flanks is geometrically feasible, as they always share a line of contact and the tangent plane at each point of this line, there are poses where the flanks even have a common Disteli axis. Then there is a G2-contact at the striction point and the two surfaces penetrate each other.

The outcome is that the surfaces are not realizable as tooth flanks. Nevertheless, this is a fundamental step towards the synthesis of the flanks of involute gears with skew axes.

Copyright © 2014 by ASME
Topics: Gears



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