The planar double-enveloping hourglass have formed a perfect system.The major conical surface enveloping hourglass worm have the same performances as planar double-enveloping hourglass worm gears and can raise efficiency and precision.The mathematical model of this hourglass worm including contact line equation.In this paper,the thickness of sides tooth and the criterion function of undercutting are established.Based on them,the parameters affecting mesh performance and geometry characteristic of this worm gearing were discussed.This kind of worm drive will have good prospects,and the result is got that,the parameters must be optimized to guarantee the good state of worm gearing's mesh performance and geometry characteristics.