Abstarct: Nowadays, attractions are focused on Stirling engines because of their low noise, external combustion, and the possibility of employing solar energy. These engines can be designed and applied in cases of low or high-temperature differences, as needed. Evidently, the cylinder’s layouts and how they are arranged and the used movement mechanism can affect the engine performance. Experts and Engineers are always looking to increase efficiency and also increase the output work and Improve other features of the Stirling engines. In this study, the dimensional synthesis of the kinematic chain using in the Stirling engine and also reducing fluctuation in the stable speed of the Alpha type sterling engine with a crankshaft mechanism and using a combined thermodynamic and dynamic modeling. will be discussed. For this purpose, kinematic relationships of different layouts of Stirling are extracted, and by optimizing the mechanism baxsed on the maximum output work, the optimal values of the geometrical parameters of the mechanism and the lengths of its lixnks are obtained. To reduce engine speed fluctuation, first thermodynamic and dynamic relations will be extracted and combined, and then by optimizing the mechanism baxsed on the minimum of engine speed fluctuations, the optimal values of geometric parameters and the length of the lixnks will be obtained. Evolutionary optimization Algorithms, including genetic algorithm, particle swarm optimization, and imperialist competition algorithm methods are employed to optimize the problem, and their obtained results are compared.