Abstract: In order to infer the machining kinematic relation expressions for double lead spiroid worm gearing with a beeline contact.Studied the The characteristics and the principle to generate tooth surfaces of a double lead spiroid worm gear pair with involute tooth form and characteristics of all the kinds of manufacturing.Result shows that It was indicated that all the tooth surfaces are involute helicoids and how to generate the involute helicoid was analysized.Several ways of cutting tooth surfaces were devised and expounded.The involute helicoid would be the resultant moving path of the parallel movement of a straight line in a plane and the rotational motion of the base cylinder.In view of the above,a methods to cut the tooth surfaces with a milling machine were presented and discussed.The involute helicoid would be spiral motion path of a involute on the base cylinder,and the involute is generated by the moving path of a point in a plane.Accordingly,the tooth surfaces could be cut with a NC lathe.The involute helicoid would be the rolling path of a straight line on the base cylinder.Based on this,the tooth surfaces could be machined by a hobbing machine with fly cutting.