Determination of spherical cam profiles by envelope theory

Based on envelope theory and differential geometry, this paper presents a general expression for the surface geometry of spherical cams with a meshing follower. One of the significant advantages of using the concept of a cam formed as the envelope of the parameter family of the follower surfaces is that an expression can be derived which describes the cam surface. According to the transformation of the coordinates of the contact point, the meshing condition can be obtained without knowing the relative velocity between the cam and the follower. The surface analysis including the instantaneous contact lines, induced normal curvatures, comprehensive curvatures, and a limit curve of the second kind are shown for the manufacture and design of spherical cams. Moreover, the weight of the follower can be decreased by a limit curve of the second kind. A numerical example is given to illustrate the application of this method.