The design of cams for dynamic performance and manufacturability depends critically on identifying curvilinear profiles that yield desired characteristics of the output motion, and manufacturing the profiles by precise CNC machining systems. The displacement function of cam profile typically is specified as the follower motion h in terms of the cam rotation angle θ. The current cam design practice, based on acceleration curves defined by trigonometric, polynomial, or spline functions of the rotation angle, result in profiles that require approximation before they can be imported to CAD systems or downloaded to CNC machines. A novel approach which employs Pythagorean hodograph (PH) curves to define transitional segments of the pitch curve has the following advantages. First, the polynomial rectification and rational offset properties of these curves eliminate computational limitation to the accuracy of cam manufacture. In addition, the pitch curve and cam shape both admit exact representation in CAD systems, which can be passed directly to a CNC milling machine. In this research, an algorithm for degree-9 PH curves is presented that requires only the solution of a complex quadratic equation

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