On the condition of avoiding the"undercutting,"and "sharpening" of worm tooth, it is now regarded as an important subject in the field of meshing principle studying of the "multiple-thread small reducation ratio" hourglass worm gearing with developable tooth surfaces to reduce the gorge pitch circle diameter of worm, raise meshing efficiency and strength of the wheel tooth and improve the unresonable structure of the pair. In this paper, a new type of hourglass worm gearing with developable tooth surfaces -"Sphere Re-nveloping Hourglass Worm Gearing" is studied. It shows that 4a satisfied result to above subject can be obtained if this worm gearing is applied.