In this paper a study of an innovative volumetric rotary machine is presented . The machine consists in a stator and a number of pistons rotating inside the stator and attached to a crank. The mechanism realizes for every piston a chamber that varies its volume during crank rotation, and consequently it can be used to design a volumetric rotary machine. In order to obtain the analytical equation of the stator profile the geometrical constraints that characterize the mechanism are analyzed. Once the stator profile is determined and suitable design parameters settled, the profile of the rolling pistons is obtained numerically, considering their relative motion in respect to the stator. In order to evaluate the performance of the machine, the specific displacement and the maximum compression ratio are calculated as a function of the design parameters. Finally a basic dynamic analysis of the machine is presented. The results obtained permit to choose the design parameters for a particular application, showing that the mechanism can be particularly suitable for pumps, compressors and pneumatic engines.