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
Your Session has timed out. Please sign back in to continue.


Grant, G. B., 1899, A Treatise on Gear Wheels, Grant Gear Works, Boston.
Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice Hall, Englewood Cliffs, NJ.
Colbourne, J. R., 1987, The Geometry of Involute Gears, Springer-Verlag, New York.
Hunt, K. H., 1978, The Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, North-Holland Publishing Co., Amsterdam.
Sommer,  H. J., 1992, “Determination of First and Second Order Instant Screw Parameters from Landmark Trajectories,” ASME J. Mech. Des., 114(2), pp. 274–282.
Chen,  N., 1998, “Curvatures and Sliding Ratios of Conjugate Surfaces,” ASME J. Mech. Des., 120, pp. 126–132.
Köse,  Ö., 1999, “A Method of the Determination of a Developable Ruled Surface,” Mech. Mach. Theory, 34, pp. 1187–1193.
Roth, B., 1999, “Second Order Approximations for Ruled-Surface Trajectories,” Tenth World Congress on the Theory of Machines and Mechanisms, Oulu, Finland, June 20–24.
Stachel, H., 2000, “Instantaneous Spatial Kinematics and the Invariants of Axodes,” Ball 2000 Symposium, Cambridge England, July 9–11.
Shtipelman, B. A., 1978, Design and Manufacture of Hypoid Gears, Wiley, New York.
Stadtfeld, H., 1991, Handbook of Bevel and Hypoid Gears, Rochester Institute of Technology, Rochester.
Stadtfeld, H., 1995, Gleason Bevel Gear Technology, The Gleason Works, Rochester.
Wang, X. C., and Ghosh, S. K., 1994, Advanced Theories of Hypoid Gears, Elsevier, Amsterdam.
Lunin, S., 2001, “New Method of Gear Geometry Calculation,” The JSME International Conference on Motion and Power Transmission, Fukuoka Japan, Vol. II, pp. 472–477.
Dudas, I., 2000, The Theory and Practice of Worm Gear Drives, Penton Press, London.
Xiao,  D. Z., and Yang,  A. T., 1989, “Kinematics of Three Dimensional Gearing,” Mech. Mach. Theory, 24, pp. 245–255.
Figliolini, G., and Angeles, J., 1999, “On the Geometry of Kinematic Synthesis of Gears with Skew Axes,” Proceedings of XIV National Congress of the Italian Association of Theoretical and Applied Mechanics, Meccanica delle Machine-Paper N. 31., Como.
Phillips,  J., 1999, “Some Geometrical Aspects of Skew Polyangular Involute Gearing,” Mech. Mach. Theory, 34, pp. 781–790.
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.
Phillips,  J. R., and Hunt,  K. H., 1964, “On the Theorem of Three Axes in the Spatial Motion of Three Bodies,” Australian Journal of Applied Science, 15, pp. 267–287.
Wildhaber,  E., 1946, “Basic Relationship of Hypoid Gears..II,” American Machinist, 28, pp. 131–134.
Disteli,  M., 1914, “Über des Analogen der Savary schen Formel und Konstruktion in der kinematischen Geometrie des Raumes,” Zeitschrift für Mathematic und Physik, 62, pp. 261–309.
Veldkamp,  G. R., 1967, “Conical Systems and Instantaneous Invariants in Spatial Kinematics,” J. Mec., 3, pp. 329–388.
Struik, D. J., 1961, Lectures on Classical Differential Geometry, 2nd edition, Dover Publications, Inc., New York.
Dooner, D. B., 2001, “Design Formulas for Evaluating Contact Stress in Gear Pairs,” Gear Technology: The Journal of Gear Manufacturing, Randall Publishing Inc., May/June, pp. 31–37.
Grill, J., 1999, “Calculating and Optimizing of Grinding Wheels for Manufacturing Grounded Gear Hobs,” 4th World Congress on Gearing and Power Transmission, Paris France, Mar. 16–18, pp. 1661–1671.
Dyson, A., 1969, A General Theory of the Kinematics and Geometry of Gears in Three Dimensions, Clarendon Press, Oxford.
Wu Da-ren, and Luo Jia-shun, 1992, A Geometric Theory of Conjugate Tooth Surfaces, World Scientific, Singapore.


Grahic Jump Location
Nomenclature to define right-angle gear drive
Grahic Jump Location
Relation between input axis of rotation $i, output axis of rotation $o, instantaneous screw axis $isa, and contact normal $l
Grahic Jump Location
Two systems of cylindroidal coordinates that share a common cylindroid (note tangency between pitch surfaces)
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
Curvature in directions perpendicular to tooth surface and pitch surface
Grahic Jump Location
Relative parabolic curvature between mating gear teeth
Grahic Jump Location
Relation between envelope of moving body and envelope of envelopes




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In