Abstract: The concept of conjugate curves is put forward based on the definition of continuous and tangent contact, and the basic conditions of conjugation contact between a pair of conjugate curves are given. The fundamental principle of conjugate curves for gear transmission is provided: The normal vector to arbitrary direction of contact angle is calculated; the meshing equation is derived and the necessary and sufficient conditions of conjugation meshing for these curves are demonstrated simultaneously; the corresponding conjugated curve can be identified and line of action is also deduced with this method. A general conjugation model is therefore established according to the aforementioned theory and the result is demonstrated with parallel axis gearing as well as cylindrical helix. The geometric properties of conjugation in arbitrary contact angle direction are revealed and the characteristics of meshing motion of conjugate curves are discussed. The versatility of the principle and the outstanding contact features become obvious with treating any gear transmission. The freedom of selecting contact curve suggests the possibility of optimal conjugation design. The results provide a new method for the generation of gear tooth profile and lay a solid foundation for the further study of the gear meshing theory of conjugate curves.

Key words: conjugate curves;contact angle;equation of meshing;cylindrical helix;optimal conjugation design