The principle of this engine is quite simple even though some of the plumbing might look a bit daunting! It consists of an expansion piston  b, and a compressor g. Cold gas is compressed in g, them let out of valve k into the heater m, which just consists of a coiled stainless steel tube with a burner below.  The burner heats the air up to say 600 degrees centigrade and it is then admitted into the expansion cylinder a, through the intake valve h.  The gas expands forcing the piston down and turning the crankshaft by means of Scotch yoke d and p.  The flywheel O returns the piston upwards and the exhaust valve I is opened allowing the expanded gas to enter the water cooled cooler coil n. it is then returned to the compressor inlet j to be recycled.
This engine works on the principle that it takes less work to compress a cold gas, than is returned when the gas is heated and expanded against a piston. The heater m and cooler n are isolated from the working cylinders by valves and so can be made any size you want – lots of surface area for efficient heating and cooling of the working gas. 
The working gas circulated is never released to the atmosphere – therefore a closed cycle heat engine, and conversely, the working gas never comes into contact with the products of combustion – so you can burn any old fuel you wish and not worry about ash and grit fouling up the inside of your engine.
A colleague of mine made one of these using the compressor from a refrigerator and a modified 4-stroke strimmer engine – connected together with a belt drive. The heater was a long length of stainless steel tubing (¼ “ OD)  wound into a coil with a blowlamp playing on it.  The cooler was a length of copper brake tube in a water bath. The strimmer engine needs an extension to the cylinder head so that the piston may be fitted with a stainless steel heat reflecting dome to protect the aluminum piston below. The inlet valve may need some water or oil cooling. It might be possible to adapt a 2-stroke to work on this principle – if you can get adequate lubrication to the piston.  The expansion cylinder will run hot and may be insulated. 
The swept volume of the compressor is 60% that of the expansion cylinder. The heater coil and cooler coils may have quite a large internal volume compared to the working expansion cylinder.  Stoddard suggests air at 500psi and 600 F entering the expansion cylinder. It is there expanded and the pressure drops to 250 psi and then exhausted into the cooler. The temperature is lowered to 62F in the cooler before admitted to the compressor. 
Smart people will use the waste heat of the hot exhaust at i2  to post-heat the compressed air at k2 thereby saving fuel and making the engine more efficient. Stoddard used the expansion of a hot fluid around the cylinder a, to control the burner temperature – so that the engine would self govern – or not-overheat or cook its lubrication.
I hope to OCR the original patent text – so that you can read the finer points of Stoddard’s design. As an aside – tiny CO2 powered engines for model aircraft operate on this principle – I have also seen an engine made of plastic parts running on compressed air, power a toy aeroplane.