The requirements on the movement law of the follower imposed by disc cam mechanism of roller follower are considered, and the influencing factors of the relative motion between the roller and the cam contour are investigated. The requirements on the roller radius for the rolling motion of the roller that is relative to the cam contour are analyzed. It can be found that the constant speed movement, one of the common follower motion laws, cannot be applied alone to roller follower disc cam mechanism; otherwise movement distortion for the follower will happen. The movement distortion caused by inappropriate choice of the movement law can not be avoided by increasing cam base circle radius or by decreasing roller radius. There is a required minimum roller radius for the relative movement between the roller and the cam contour to be rolling movement. The minimum radius is inversely proportional to the rolling friction coefficient between the roller and the cam contour, proportional to the radius of the friction circle of the revolute pair between the roller and the follower lever, and independent of the load of the cam mechanism, pressure angle and other dimension parameters.