A geometric model of a spherical gear with a double degree of freedom

This paper presents a double degree of freedom spherical gear mechanism with circular arc teeth. The developed spherical gear is very suitable for the flexible wrist of a robot. Based on the envelope theory of a two-parameter family of generating surfaces, mathematical and geometrical models of a spherical gear with circular arc teeth are proposed. In the process of machining a gear blank, the required tool path can be generated by using the obtained geometric models, the forms of which are determined easily by envelope theory. Finally, the geometric model of the spherical gear can be obtained simultaneously by Mastercam and SolidWorks software.