Are there any commercial production recumbent trikes using a non-circular pedal action? I am sure that experimental builders have tried all sorts of variations involving elliptical cranks and other such devices.
One obvious possibility would be the arrangement traditionally used on a child's pedal car where the pedals swing back and forth on arc with connecting rods going to a driven crankshaft.
It seems to me this would avoid wasting the rider's energy in raising and lowering the centre of his legs so much. It would also provide better forward visibility and the possibility of a smaller front fairing. It might also be possible to avoid using such a long chain.
I am certainly not claiming any of this to be novel ideas, but I am simply curious as to whether anybody has ever managed to apply anything along these lines to a production machine.