# Meshing principle of conjugate curve bevel gear

The traditional conjugate curve bevel gear design theory is conjugate surface meshing theory, and its mathematical basis is envelope theory. The conjugate curve bevel gear designed according to the conjugate surface meshing theory can envelope each other through a given motion. Typical conjugate curve bevel gears include involute gears, cycloidal gears and so on. The contact characteristic of this conjugate curve bevel gear in meshing is line contact, that is, the tooth surface contact trace always shows one or more curves at any time. The application of conjugate surface meshing theory to parallel shaft gear has been very mature, but in intersecting or staggered shaft gear transmission, due to the complex motion and three-dimensional motion, the tooth surface equations derived from conjugate surface meshing theory are relatively complex and difficult to analyze.

In nature, curve and surface can be used as the basic elements of component contact, and conjugate surface is only one of the optional surfaces of conjugate curve bevel gear profile. Compared with surfaces, the contact between curves is often more diverse. For example, the contact of two arcs can be in plane or in space; It can be either circumscribed contact or inscribed contact. Making full use of the diversity of curve contact can provide a new idea for us to study the new principle of conjugate curve bevel gear transmission. Therefore, starting from the basic principle of conjugate curve meshing, this chapter tries to study the general properties and design methods of spatial conjugate curve meshing gears.

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