The article discusses the innovative concept of the over-expanded thermodynamic cycle, the author of which is the Polish engineer-designer Mirosław Szymkowiak. This cycle is realized on the basis of a new and innovative, previously unknown design, of a piston-crankshaft linkage mechanism with the aid of an additional element known as a rocker arm. Additionally, the proposed mechanism allows for a smooth change of the compression/expansion ratio of the engine during its operation. In the beginning, the earlier conceptions of the rocker engine developed by Szymkowiak were presented, and then the main construction assumptions and kinematic calculations were described. It was confirmed, that the developed linkage has big potential in improving the engine's thermal efficiency by approximately 12% relative. Additionally, it significantly reduces the exhaust gas pressure, when the exhaust valve is opened, therefore, contributes to the reduction of the noise emitted by the engine.