Mathematical and geometry model of a spherical gear with three degree of freedom

Abstract

This paper proposes a spherical gear pair with three degrees of freedom based on meshing transmission principle. The kinematic meshing relationship between the spherical gear pair is illustrated with its pitch spheres and pitch cones. This determines that the spherical gear surface is completed with two tooth surfaces of ring-involute spherical gear and a semi-spherical bevel gear. Mathematical models and numerical results of the two tooth surfaces are presented for obtaining geometry model of the spherical gear pair with the CAD three-dimensional molding technique. This study provides the basis for future studies to design and analyze a novel spherical gear.