This article is a two-part one: (1) the generating surface; (2) the mathematic model of the worm gear tooth surface. In this paper, a general method is presented for the description of generating surface enveloping any kind of worm tooth surface. This method is laid on the parametric description of the dresser curve as an initial curve. The initial curves of four common dressers are presented. By using these descriptions, the mathematical description and properties of any kind of worm gear tooth surface can also be obtained.

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