Cutting Geometry and Base-Cone Parameters of Manufacturing Hypoid Gears by Generating-Line Method

Linan Li*, Zhaojun Yang, Yankun Wang, Xuecheng Zhang
School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China.

© 2011 Li et al

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the School of Mechanical Science and Engineering, Jilin University, Changchun 130025, China; Tel: +86-431-85095839(office); +86-13844010585 (Mobile); Fax: +86-431-85095839; E-mails:;


Generating-line method, which is based on the generating process of spherical involute curve, is a new processing theory of cutting ideal spherical involute gears. Based on the principle of the new method, this paper expands the traditional geometrical relationship into the cutting geometry of generating-line method, and proposes the base-cone parameters with their formulas to provide necessary parameters for further study. The application examples, such as establishing the coordinate systems and the equation of gear generating line, show the importance of these researches, and the example of calculating geometric parameters illustrate the way to adjust the base-cone parameters. It can be seen from the researches, the cutting geometry contains the tangent relationships between two base cones and a base plane respectively, and the planar conjugated relationship between two generating lines of pinion and gear. The base-cone parameters determine the relationships among base cones, base plane and generating lines. If some of the base-cone parameters need to be adjusted, it can be realized by modify the value of the parameter r2, ε or Z0.

Keywords: Hypoid gear, generating-line method, cutting geometry, base-cone parameters.