Meshing Limit Line of Offset Normal Arc-Toothed Cylindrical Worm Drive

In this paper, the theory of solving the meshing limit line is built for the offset normal arc-toothed cylindrical worm drive, and some fundamental and important results are obtained, for example the tooth surface equations of the worm drive, the meshing function, and the meshing limit function. The computation of the meshing limit line of the worm drive is boiled down to solve a nonlinear equation set. After solving the nonlinear equation set iteratively by means of the elimination method and the geometric construction, the numerical study concerning the meshing limit line of the worm drive is conducted. The numerical results demonstrate that there is always a meshing limit line on the worm helicoid and this will cause the length of the worm cannot be fully used. The conjugate line of the meshing limit line is roughly located in the middle area of the worm gear tooth surface.