From Gear Geometry and Applied Theory, Second Edtion


Hypoid gear drives have found a broad application in the automotive industry for transformation of rotation between crossed axes. Enhanced design and generation of hypoid gear drives requires an approach based on the ideas discussed for spiral bevel gears (see Chapter 21).

The contents of this chapter are limited to (i) design of pitch cones, (ii) pinion and gear machine-tool settings, and (iii) equations of pinion gear tooth surfaces. Design of pitch cones for hypoid gears was the subject of research performed by Baxter [1961], Litvin et al. [1974, 1990] and Litvin [1994]. Details of determination of machine-tool settings for manufacture of hypoid gears are given in Litvin & Gutman [1981].


Spiral bevel gears perform rotation about intersected axes, and their axodes are two cones (Section 3.4). The line of tangency of these cones is the instantaneous axis of rotation in relative motion. In the case of standard spiral bevel gears, the gear axodes coincide with the pitch cones.

Hypoid gears perform rotation about crossed axes, the relative motion is a screw motion, and instead of the instantaneous axis of rotation we have to consider the instantaneous screw axis s s (Section 3.5). The gear axodes are two hyperboloids of revolution that are in tangency along the axis of screw motion s s (Fig. 3.5.1). The hypoid pinion gear axodes (the hyperboloids of revolution) perform in relative motion rotation about and translation along s s.

The concept...

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Hypoid Gears

A hypoid gear is a style of spiral bevel gear whose main variance is that the mating gears' axes do not intersect. The hypoid gear is offset from the gear center, allowing unique configurations and a large diameter shaft. The teeth on a hypoid gear are helical, and the pitch surface is best described as a hyperboloid. A hypoid gear can be considered a cross between a bevel gear and a worm drive.

Bevel and Miter Gears

Bevel gears are gears designed to transmit motion between intersecting axes. Perpendicular arrangements are most common, but bevel gears can be manufactured for nearly any angle. The teeth bearing surface of the gear, or surface pitch, is conically shaped or tapered. Miter gears are bevel gears manufactured in a 1:1 ratio, with the same number of teeth on mating gears and with perpendicular axes.


Gears are rotating mechanical devices employing 'teeth' in order to transmit torque between separate axes. Two or more cooperating gears are called a transmission and can produce a mechanical advantage by changing speed, torque or rotation direction.

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Topics of Interest

23.1 INTRODUCTION Planetary gear trains were the subject of intensive research directed at determination of dynamic response of the trains, vibration, load distribution, efficiency, enhanced design,...

19.2 PITCH SURFACES AND GEAR RATIO We recall that in the case of transformation of motions between crossed axes the relative motion is the screw one and the axodes are hyperboloids of revolution.

14.1 INTRODUCTION Cycloidal gears (Chapter 13) and involute gears (Chapters 10, 11, 14, 15, and 16) have different areas of application. This chapter covers involute gears with parallel axes, whose...

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17.1 INTRODUCTION Wildhaber [1926] and Novikov [1956] have proposed helical gears based on generation by circular arc rack-cutters. The difference between the two inventions is that the gear tooth...

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