The quasi-plane double enveloping hourglass worm is generated by a large diameter two-sided symmetry conical grinding wheel. The mathematical model of this hourglass worm including contact line equation

the thickness of sides tooth and the criterion function of undercutting are established. With which the parameters primarily effecting mesh performance and geometry characteristic of this worm gearing were discussed. The optimizing object function and the bound for objective function were set up. Based on the contact lines’ own characteristics

the complex method is improved to be well suitable for this kind of optimizing. The examples show this optimizing method can successfully solve the problem that how to choose the design parameters in common speed ratio and "multi-thread and low-speed" conditions.