Mathematical Model of a Ring-Involute-Teeth Spherical Gear with a Double Degree of Freedom

Abstract

A simple procedure using gear theory for a family of rack cutters to determine the profile of a spherical gear of the ring-involute-teeth type, with a double degree of freedom, is presented. The analytical profile of the spherical gear can be obtained by the following two steps. First, gear theory is used to find an envelope for a family of rack cutters; and secondly, the envelope obtained is used to rotate an angle about an axis. Based on these two steps, a mathematical model for a spherical gear, with ring-involute teeth and with two degrees of freedom can be generated. The procedure is illustrated by application to a spherical gear with ring-involute teeth analytically formulated. In the machining process, the required cutting path is simulated and provided by a software package. The mechanism of the generated spherical gear is produced with the aid of CAD software.