Abstract：In order to study the relationship between the theoretical contact lines and the actual contact lines of Hindley worm drive,it is proved the tool path and the worm wheel tooth surface of the envelope in the central ridge is tangent,through investigating the relationship between the worm gear hob surface and the theoretical contact line,and solving tool path and worm tooth surface of the envelope at any point in the central ridge at the unit normal vector. Thus,the relationship of theoretical contact lines and the actual contact lines of Hindley worm pair was discussed and the existence of theoretical contact lines was proved at the right of the midline of the worm gear. Furthermore,it explained why only half of the tooth surface involved in conjugate drive of Hindley worm pair and the second contact lines focused on the left part of tooth surface of the worm gear.

Keyword：Hindley worm drive;contact lines;tool surface;envelope surface;