In this article the mathematical formulas for generating second order aspherio surfaces are derived. The aspheric surface to be worked is treated as an envelope of spheres with different radius of curvature at different zones. δp and αp are taken as parameters to describe the motion of grinding tool, where δp is the distance between vertex of surface and lowest point of the tool; and αp is the angle between tool axis and aspheric surface axis. In order to realize the design of practical machine, it is convenient to change the angle aP around a point M oil tool axis rather than any other point. So that the equations for determining the coordinates of point M are also derived. In the case of mass production, pure mechanism is better than computer control of tho grinding machine and the best mechanism seems to be cam pair, because such mechanism makes the grinding process repeatable and it is possible to produce a smooth aspherical surface. So that th? mathematical equations for cam design are also given.