By using fixed/floating coordinate system and the support function method, the instantaneous 1-D linear area and interval sets were proposed. The rise motion, return motion and whole motion interval sets were put forward. The basic principles of solving the allowable selected area of the flat-faced line and the allowable value range of the cam basic radius were proposed. The analytic formulae were derived. Then the analytical criterion of the solution existence and its existing form were obtained. The class Ⅱ synthesis of disc cam mechanism with flat-faced follower in planar motion was resolved. 