The contents of the paper cover: a brief history of some concepts of the theory of gearing, and new developments in this area, (i) theory of enveloping curves and surfaces, (ii) simulation of meshing and contact of gear tooth surfaces, (iii) basic kinematic relations as the key to the determination of direct relations between the curvatures of contacting surfaces, and avoidance of singularities, (iv) transfer from line contact of tooth surfaces to point contact, and (v) design and manufacturing of gears with compensated transmission errors caused by misalignment.

Issue Section:
Research Papers
Topics:
Design, Errors, Gear teeth, Gears, Kinematics, Manufacturing, Simulation
1.
Baxter, M. L., 1961, “Basic Geometry and Tooth Contact of Hypoid Gears,” Indust. Math., pp. 1–28.
2.
Baxter
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Second-Order Surface Generation
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3.
Buckingham, E., 1963, Analytical Mechanics of Gears, 2nd ed., Dover, NY.
4.
Dudley, D. W., 1969, The Evolution of the Gear Art, AGMA.
5.
Dudley, D. W., 1954, Practical Gear Design, McGraw-Hill Book Co., NY.
6.
Dudley, D. W., 1984, Handbook of Practical Gear Design, McGraw-Hill Book Co.
7.
Dudley, D. W., ed., 1962, Gear Handbook, 1st edition, McGraw-Hill Book Co., NY.
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Favard, J., Course of Local Differential Geometry, Gauthier-Villars, Paris (in French, Translated into Russian).
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Finikov, S. P., 1961, Differential Geometry, Moscow University (in Russian).
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11.
Korn, G. A., and Korn, T. M., 1968, Mathematics Handbook for Scientists and Engineers, 2nd ed., McGraw-Hill, NY.
12.
Litvin, F. L., 1960, 1968, Theory of Gearing, 1st ed. (1960), 2nd ed. (1968), Nauka (in Russian).
13.
Litvin
F. L.
,
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Die Beziehungen Zwischen den Kru¨mmungen der Zahnoberfia¨chen bei Ra¨umlichen Verzahnungen
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14.
Litvin
F. L.
,
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N. N.
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Erikhov
M. L.
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Generation of Tooth Surfaces by Twoparametric Enveloping
,”
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15.
Litvin
F. L.
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Y. I.
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,”
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16.
Litvin, F. L., 1989, Theory of Gearing, NASA Reference Publication 1212.
17.
Litvin, F. L., 1994, Gear Geometry and Applied Theory, Prentice Hall.
18.
Stadtfeld, H. J., 1993, Handbook of Bevel and Hypoid Gears, Rochester Institute of Technology.
19.
Stoker, J. J., 1969, Differential Geometry, Willey-Interscience.
20.
Townsend, P.S., ed., 1991, Dudley’s Gear Handbook, 2nd ed., McGraw-Hill, NY.
21.
Wildhaber, E., 1926, U.S. Patent No. 1,601,750.
22.
Wildhaber
E.
,
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a, “
Basic Relationships of Hypoid Gears
,”
Amer. Mach.
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23.
Wildhaber
E.
,
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(b), “
Conjugate Pitch Surfaces
,”
Amer. Mach.
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, pp.
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24.
Wildhaber
E.
,
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Tooth Contact
,”
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25.
Wildhaber
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Surface Curvature
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26.
Zalgaller, V. A., 1975, Theory of Envelopes, Nauka, Moscow (in Russian).
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 by The American Society of Mechanical Engineers
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