Generation and Undercut of Tooth Surfaces of Helical Noncircular Gears

A general mathematical model for generating tooth surfaces of helical noncircular gears is established. Two basic parameters and a first order differential equation characterize this model. The condition for determining the cusp of tooth surfaces is also presented. Transverse pressure angle and normal length are introduced to deal with the model. The different tooth surfaces could be generated logically and systematically by using this model and defining transverse pressure angle as a function of the two parameters. It is believed that the model may provide a simple logical method for the design of helical noncircular gears.