Old 02-14-17, 01:16 PM
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Here's a slightly more visual explanation (motivated by my own efforts to convince myself that what I said in my previous post was correct).

The model I was using to calculate cable pull based on the pivot radius is assuming that the amount of cable pulled is approximately the same as the distance traveled by the anchor point. I mentioned in post 18 where I introduced this method that the cable pulled was actually the chord cut across the virtual circle traveled by the pivot point but for most levers that's a pretty good approximation. This assumes that the pivot point is near the top of the virtual circle. (See Figure 1 on the attached image.)

If the cable is anchored significantly left of the top (relative to the cable exit) of the virtual circle, the approximation would break down, as seen in Figure 2. Here the amount of cable pulled is actually the difference in the distance from the original anchor position to the exit point and the distance from the final anchor position to the exit point, assuming nothing restricts the cable's freedom of movement within the virtual circle.

However, the geometry of Shimano levers since the 5700/6700/7900 series is more complicated. These levers have the cable anchored toward the front of the virtual circle, but the cable rests on a "shelf" that is near the top of the virtual circle. The result is that the cable pull is actually determined by the travel of the resting point, not the travel of the anchor point. Figure 3 attempts to illustrate this idea. You can see there how the inner circle interferes with the movement of the cable and makes the original approximation good, if based on the inner circle rather than the outer circle.

The fact that the cable rests on a shelf rather than a single point complicates this a little bit more. If you imagine a flat shelf extending along the blue line in Figure 3 and then rotating with the circle, you'll see that the effective diameter of the inner circle (i.e. where it pushes against the cable) will increase as the lever rotates, meaning that it would pull more cable later in the motion of the lever. And if that's not enough to confuse you, I believe the Shimano levers don't use a flat "shelf" but rather a curved one so that the rate at which the effective inner circle radius changes is reduced.

In any event, this is a fine tuning effect and the simple approximation based on the inner circle tells you enough to understand approximately how the brake will respond.
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