Optimal synthesis of mechanisms is a successful approach for mechanism design to satisfy all the desired characteristics of the designed mechanism. T he 4 - bar crank - rocker mechanism has wide industrial applications and its synthesis is of increasing importance . The optimal design problem in this case is a constrained multi - dimensional problem. Powell optimization technique is used to minimize a special objective function combining the mechanism stroke and time ratio. 3 functional constraint functions are used to perform a successful optimization process leading to satisfying the requirements of a successful operation of the mechanism . The mechanism kine matical functions are derived in a dimensionless form . The results are tabulated for an easy reference to them without any calculations. Power law models are fitted to the optimization results. It was possible to obtain a mechanism stroke between 20 and 55 degrees and a time ratio between 1.05 and 1.204 for a transmis sion angle in the range 45 to 135 degrees. A comparison is conducted between the optimal design results using the tabulated normalized dimensions and the optimal values using the proposed power law models.