The arc-toothed cylindrical worm has an arc tooth profile in a section, which may be the axial or normal section of the worm helicoid, or an offsetting plane which parallels to some section of the worm helicoid through the origin of coordinate system associated with the helicoid. The meshing principle for a gearing containing such a worm is established and the meshing performance parameters are obtained without the help of the curvature parameters of the worm helicoid. The numerical results show that the worm working length can be beyond half of the thread length and the meshing zone of the worm pair can be full of the most of the worm gear tooth surface. The instantaneous contact lines are uniformly distributed and the worm pair forms double-line contact. The numerical outcomes of the induced principal curvature show that the contact stress level between the teeth is higher in the middle of the worm gear tooth surface and near its dedendum. The forming condition of the lubricating oil film is poorer in the middle of the worm gear tooth surface and from addendum to dedendum as demonstrated by the numerical results of the sliding angle. The normal arc-toothed worm lathed by an offsetting cutter is recommended to apply in industry after various researches and analyses. The cutting geometric condition of the worm is investigated quantitatively. It is discovered that the rule of the cutter working relief angle changes along the cutting edge during lathing the worm.