The cylindrical worm processed by annular grinding wheel envelope in two degree of freedom motion state is a novel worm. This paper explains the shaping principle of such a worm. To improve meshing quality and the properties of contact and lubrication, the multi objective optimization has been conducted for the first time to the parameters of such a worm pair by the fuzzy optimal method. The results show that, the shape of the contact line is visibly more sloped than before being optimized, lubrication angle is apparently bigger, and the distribution of contact lines is much improved.
