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Machine Theory
Mechanism and Machine Theory 43 (2008) 1317–1331
ate/mechmt
Contact characteristics of spherical gears
Li-Chi Chao a, Chung-Biau Tsay b,*
a Department of Mechanical Engineering, National Chaio Tung University, Hsinchu 30010, Taiwan
b Department of Mechanical Engineering, Minghsin University of Science and Technology, Hsinchu 30401, Taiwan
Received 13 October 2006; received in revised form 27 July 2007; accepted 18 October 2007
Available online 11 December 2007
Abstract
In this paper, the theory of gearing and the proposed mechanism of spherical gear cutting are applied to develop the
mathematical model of spherical gears. Based on the developed mathematical model of spherical gears, computer graph of
the gear set is plotted, and tooth contact analysis (TCA) of spherical gear sets is also performed. The TCA results provide
useful information about the kinematic errors (KEs), contact ellipses and contact patterns of spherical gear sets.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Spherical gear; Continuous shifting; Tooth contact analysis; Contact ellipse; Kinematic error
1. Introduction
Spherical gear is a new type of gear proposed by Mitome et al. [1]. Geometrically, the spherical gears have
two types of gear tooth profiles convex tooth and concave tooth. The convex tooth of spherical gear is similar
to a part of ball, and the concave tooth of spherical gear looks like a worm gear. The spherical gear sets have
three types of mating assemblies: convex tooth with concave tooth, convex tooth with convex tooth and con-
vex tooth with spur gear. Fig. 1 shows these three types of mating assemblies for the spherical gear set with
axial misalignments. Different from the conventional spur or helical gear sets, the spherical gear set allows var-
iable shaft angles and larger axial misalignments without gear interference in meshing. These are two major
advantages of spherical gears. There