It's the chainwheel that is eccentric, Bradley Wiggins being one who likes them.
The purpose is simple, the small diameter sections are with the cranks at the top and bottom which means the chainwheel and cranks are taken rapidly through those non-productive parts of the rotation at a given road speed. i.e. lower geared so higher cadence at those points.
That also means the larger diameter chainwheel sections are at the top (and bottom) of rotation when the cranks are horizontal. Since that's where the rider exerts the maximum leverage, the advantage is effectively a momentary higher gear at the point of maximum leverage in each crank stroke, imcreasing rider strength utilisation.
The disadvantage is the irregular speed of rotation within each revolution, something only some riders get on with.
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