The other end of the chain/rope (i'm just going to call it a chain from now on, but wire-rope is as common) is pulled off a capstan which is grooved to place the chain in repeatable turns. The capstan is a parabolic cone so, as the spring barrel winds down imparting less force (pull) on the chain, the grooved path guides the chain up to the progressively larger diameter portion of the capstan thus setting the reduced tension against a longer lever-arm to equalise the force imparted on the mechanism.
An elegantly simple method of making the mechanism "regular" and repeatable throughout the winding cycle.
Clocks and watches are such beautiful mechanisms. I just love 'em.
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