Extended research has not shown any application of the geometric law that a straightedge orbiting an ellipse describes a circle (known as Fermat-Apollonius circle). Proposed here is the use of this simple geometry for pumps, compressors and combustion engines.

Pinning down the centre of an ellipse and the corner point of a straightedge at a distance R (with R squared equal to t squared plus s squared, with t and s the lengths of the ellipse’s semi-axes) will make a variable volume in between, as the ellipse rotates and the straightedge pivots (as in above logo). This can be applied to transport liquids in pumps, or to compress or expand gas in compressors or in steam, Stirling, combustion or explosion engines. Based on this principle, other shapes than the ellipse and straightedge can be defined, inclosing a variable volume, enabling a simple, compact, light, cheap and robust engine with otherwise hard to achieve features like variable compression, high gas flow, high swirl, high efficiency, high speed, high specific power and low (e.g. NOx ) emissions, while allowing proper sealing, lubrication and cooling.

As an example of an explosion engine, a HCCI engine is shown with 4x250cc chambers measuring approximately 50x40x30cm and a total weight of under 50 kg.  As example of a compressor a similar design is shown with 4 main chambers and 4 auxiliary  out-of-phase chambers, which could also be applied as steam or Stirling engine.