How does a compound bow work, particularly the function of the cams and the “let off”?
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Compound bows are much stiffer than other bows, so for the same energy stored, the limbs move much less. This is more efficient. It is also much more difficult to draw, because a slight change in draw length makes a big difference in energy. A short draw length also flexes the arrow more, as more energy is imparted in a short amount of time. Bows with traditionally short draw lengths, like crossbows, tend to use bolts rather than arrows to deal with that.
So to lengthen the draw length, a pulley system is used. The trade-off is force against distance. You can pull with less force, but you have to pull back further to deflect the short limbs a certain amount (impart a certain amount of energy).
And if you are putting pulleys in your bow anyway, you can add another trick: eccentric pulleys. So when the pulley is small, you have less leverage against the limbs than if the pulley is big. A limb with a small pulley will impart more force on the string, and thus on the arrow; which is what you want. A big pulley will give you extra leverage against the limb, and allow you to have to impart less force on the bow; which you want too. But the first one is important when the bow is driving the arrow, the second is important when you are holding the bow to aim.
So making a pulley that has a big radius on one side and small on the other; for example if it has the shape of a snail shell, marries the two concepts: a bow imparting a lot of energy when firing, but with a ‘let down’ that needs much less force to keep drawn when drawn far enough so you are in the wide part of the cam.
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