Let’s start from top dead center of the hot piston. The hot piston moves to the upper part of the cylinder and the cold piston moves to the lower part of the cylinder during the first 90 degrees of revolution. The working air is moved from the cold space to the hot space. And the pressure in the engine is increased.
During the next 90 degrees of revolution, the two pistons both move the lower part accepting the air pressure. The engine gets its power during this portion of its cycle.
The crankshaft revolves by power stored in the flywheel for the next 90 degrees. The hot piston moves to the lower part and the cold piston moves to the upper part. The air is moved from the hot space to the cold space. And the pressure in the engine is decreased.
The two pistons are moved to upper part by the contraction of the air during the next 90 degrees. The engine also gets power during this portion of its cycle. The two piston type Stirling engine then repeats this cycle.
A special thanks to Koichi Hirata for the excellent illustrations!