Meshing principle of conical surface enveloping spiroid drive

A new type of the spiroid drive is put forward, which may be called the enveloping spiroid drive. The meshing theory is fully established for this drive. The reference-point-based meshing theory is developed. The reference point is recommended to locate on the tooth top of the conical worm at its toe. The computing method is suggested to determine the conjugate zone and the contact line. An approach based upon the elimination method and the geometric construction is put forth to detect the solution existence and to provide the reasonable initial value for iteratively solving the systems of nonlinear equations met during computing the conjugate zone and the contact line. The outcome of the numerical example investigation makes clear that, the working length of an enveloping conical worm can almost cover its whole thread length and the conjugate zone can nearly run through the whole tooth surface of the mating conical worm gear. The local meshing performance of an enveloping conical worm gearing is also excellent.