Abstract: The outspread principle of involute and enveloping principle of curve is applied to build the model of double involutes gear contrate profile, the veracity is verified by the data. On the base of the mathematical model of double involutes gear contrate profile, the mathematical model of double involutes gear teeth surfaces is built, which is on any rotary angle. The 3D simulation pictures of double involutes gear of three typical cut tooth top’s circular arc radius and simulation of mesh are obtained by mathematical model of double involutes gear teeth surfaces, the correctness and feasibility of model is validated. The expression is very simple and coordinate is not translated by using, the any point of double involutes gear teeth surfaces is fast and truly described on any rotary angle, the simple and speedily new theory gist is offered for 3D numerical design, manufacture and the analysis of mesh, kinematics and dynamics of double invo-lutes gears.

Key words: Contrate profile of gear Mathematical model of gear teeth surfaces, Double involutes gear, Involute outspread Curve envelop