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Machine Theory
Mechanism and Machine Theory 43 (2008) 1543–1556
ate/mechmt
The generation principle and mathematical models
of a novel cosine gear drive
Shanming Luo a,*, Yue Wu b, Jian Wang a
a School of Mechanical Engineering, Hunan University of Science and Technology, Taoyuan Road, Xiangtan 411201, China
b School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter EX4 4QF, UK
Received 19 November 2006; received in revised form 11 December 2007; accepted 26 December 2007
Available online 14 February 2008
Abstract
A novel cosine gear drive is presented in this paper. The pinion of the drive utilizes a cosine curve as the tooth profile. It
takes the zero line of the cosine curve as the pitch circle, a period of the curve as a tooth space, and the amplitude of the
curve as the tooth addendum. The generation principle of the cosine gear is described. The mathematical models, including
the equation of the cosine tooth profile, the equation of the conjugate tooth profile and the equation of the line of action,
are established based on the meshing theory. An example drive in solid model is presented and puterized simulation
is carried out. A few characteristics, such as the contact and bending stresses, the sliding coefficient and the contact ratio, of
this new drive are analyzed. parison study of these characteristics with the involute gear drive was also carried out in
this work. The results confirm that the cosine gear drive has lower sliding coefficients and the contact and bending stresses
of the cosine gear are reduced parison with the involute gear.
Ó 2008 Elsevier Ltd. All rights reserved.
Keywords: Gear drive; Cosine gear; Tooth profile; Meshing theory; Mathematical model
1. Introduction
Tooth profile of gear is a fundamental element to determine transmission performance of a gear drive. At
present, there are three types of tooth profiles: involute, cycloid and circular-arc, w