A look at some air engine working cycles

1 The Stirling cycle

1 The Rider or Compression engine

1 The Ericsson cycle

1 The Ringbom cycle, named after the inventor Ossian Ringbom of Helsinki, Finland.

1 Free Piston engines

1 The Manson cycle.
A valved single piston/displacer engine so called after a design by A.D Manson published in Newnes Pratical Mechanics in 1952.

The design also appears in a patent granted in Germany to Michael Ruppel in 2000.
This patent describes two version of the engine