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For more than eighteen years, the author has been engaged in the development of Stirling engines and coolers. The author has developed a very simple harmonic graphic vector analysis for the first estimation of performance of various Stirling machines including engine, cooler, and VM. (Vuilleumier) machines. This has been shown to be very useful for early estimation and understanding of each machine. So at this time, the author want to report this method. This method uses the Schmidt assumption at its base, and harmonic approximation, that was called the ellipsoidal assumption by the author previously ( 1 ). This method is applied to α, β, γ type Stirling machines and generalized three temperature machine including VM. machines. It provides very easy graphic way to show which cylinder generates power or coldness and how much power, or heat is generated, utilizing volume variation vectors (for each cylinder and the total volume) and a pressure variation vector.

To get a simple and low cost Stirling engine that would be manufactured and used in any district of the world, a unique atmospheric Stirling engine named NAS-1 is under study at NIHON University. NAS-1 was originally planned to be used for the solar field, so the cylinder head was designed to have a glass head at its top with the concentrated solar beam penetrating the glass. NAS-1 uses a rubber diaphragm for the power piston, and it has proved to be very reliable and successful. It has James Watt's approximate linear motion link mechanisms (Watt link) for the main crank shaft, instead of the usual crossed head to eliminate liquid oil lubrication. This kind of engine has been thought to furnish very simple, low cost and efficient power for future clean energy fields. This engine design is simple, low in cost, and doses not involve problems of high pressure, and does not produce any pollutants whatsoever such as carbonic acid gas, NOx and others' pollution.