Releasing winch system without shifters

[Ether]

Originally Posted by magnets

Or, you could derive the equation so you gained mechanical advantage (and torque) as you wound back.

What you want is for the torque required to drive the spiral cam to remain constant (think about it):

One nice feature of a cam is that, with a little math, you can derive the equation for the spiral so that the torque required to drive it remains constant as it is pulling back the arm. Then you can use that equation to cut out the cam.

It takes more force to stretch the surgical tubing at the end than it does at the beginning

True for many (most) designs but not necessarily true for all. It depends on how the mechanical advantage of the linkage changes as the kicker is being pulled back. In any event, what you want is for the torque required to drive the spiral cam to remain constant. To achieve that you would need to take into account the F=k*x spring constant of the tubing as well as any linkage geometry changes