This is an Atkinson-cycle engine, though in this modern world, it has become a bit confusing about what that actually means. This is a working example of one that uses actual Atkinson-style linkages. The path of motion energy transfer is a bit convoluted, resulting in a wheel that turns once for every two cycles of the piston (it's a four-stroke engine, so you end up with one revolution per combustion/exhaust cycle).

My understanding is that the strange linkages came about because Mr. Atkinson wanted to find a way around the patents on engines of the day so that he could make his own engines without paying royalties.