Abstract: This paper analyses tile defects of the method proposed by R.C.Johnson. Owing to the successive adjustment of the displacement and acceleration curves, it is both a Tedious and complex method,not to say that it almost can't fulfill the arbitrnrily assigned follower motion by utilizing the formulas derived in this paper and starting from tile prescribed -best acceleration curve,one call .calculate the displacement values directly) and tire defects inherent In Johnson's method may be eliminated.The authors' method can also be applied to calculate the cnm profile of high speed duns with it flexible follower system At the end of this paper, an improved design for the cam profile of an engine is presented as an example.