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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 484802, 12 pages
Research Article

Geometric and Meshing Properties of Conjugate Curves for Gear Transmission

State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400044, China

Received 23 June 2014; Revised 13 November 2014; Accepted 16 November 2014; Published 7 December 2014

Academic Editor: Evangelos J. Sapountzakis

Copyright © 2014 Dong Liang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Conjugate curves have been put forward previously by authors for gear transmission. Compared with traditional conjugate surfaces, the conjugate curves have more flexibility and diversity in aspects of gear design and generation. To further extend its application in power transmission, the geometric and meshing properties of conjugate curves are discussed in this paper. Firstly, general principle descriptions of conjugate curves for arbitrary axial position are introduced. Secondly, geometric analysis of conjugate curves is carried out based on differential geometry including tangent and normal in arbitrary contact direction, characteristic point, and curvature relationships. Then, meshing properties of conjugate curves are further revealed. According to a given plane or spatial curve, the uniqueness of conjugated curve under different contact angle conditions is discussed. Meshing commonality of conjugate curves is also demonstrated in terms of a class of spiral curves contacting in the given direction for various gear axes. Finally, a conclusive summary of this study is given.