The spherical gear is a gear-driven mechanism with two degrees of freedom (DOF), which can transfer spatial motion. The spherical gear pairs have two types of basic assembly structures including an ideal mechanism and a gimbal mechanism, and whose kinematic characteristics are analyzed. The 2-DOF gearing principle of conjugate tooth surfaces of the spherical gear pair is introduced first. Then, the relative slide between two tooth surfaces in the mesh is analyzed. Finally, the equations of the meshing coned surface and the conjugate surface are established based on the meshing models of the spherical gear pairs. Furthermore, the sliding ratios of the tooth surfaces of the spherical gear pairs are obtained when they mesh in different meshing conditions based on two-parameter movement analysis. The computational results show that the sliding ratios of the spherical gear teeth are related to the angle velocity ratio in the ideal mechanism and they are not only related with angle velocity ratio but also related with the assembly axes in the gimbal mechanism, which are useful in theory for further studying the wear of the spherical gear.

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