We build the model for the enveloping worm helix parametric equation and then analyze its relations with the enveloping worm helix tooth surface equation,thus establishing the characteristic model of the involute helicoid enveloping worm′s generative gears.

Based on the modeling of enveloping worm helix analytical equation and constructing of TI-worm,the article analyzes geometry characteristics of the involute helicoids double-enveloping worm wheel,demonstrates the whole process by means of finite time Boolean calculation approach method with characteristic model of TI-worm,and establishes the involute helicoids double-enveloping worm gear pairs.