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don't comprehend how it works
I assume you mean the biomechanical bit, rather than the levers. Put simply, within the narrow range defined by common crank lengths, the product of force exerted by muscle and the speed of contraction is very nearly constant. I imagine this is because power is limited by the fuel delivery rate across a range even larger than the above.
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I'm putting this down in the category of science not understanding why cycles stay up.
But we know how they stay up. I guess maybe you're aware the gyroscopic effect of the wheels has been debunked by that guy who put counter-rotating wheels next to the working wheels? Which leaves a single possibility: the steering geometry makes it so the bike automatically steers into whichever direction it's falling.
Essentially, all bikes get down the road by subtly zigzagging as they continually begin to fall left and right.
But you have to move your feet faster because they're going in bigger circles. Power is force times speed. There's no free lunch.