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The paper presents a method of synthesising cam profiles based on the use of piecewise polynomials together with an optimisation technique. Special cases and limitations are discussed and illustrated, making the procedure complete and systematic for any design requirements. Using piecewise polynomials, the complete cam profile can be designed as a combined linear system. The optimisation technique described goes even further, manipulating the variables in the linear system to select the ideal combination. In addition, a means to prove the validity of the results is explained.