Sorry, but I must disagree with some of this. When 10 lbs are applied to the primary side, that force will move two things at once, the brake cam lever on that side and the balance beam in the opposite direction which in turn applies a force to the other brake, thus distributing the 10 lbs into two halves. The brake cam lever will never see all of the 10 lbs. They are halved because the balance beam has its pivot in the center. Had it been off-centered, the splitting would have been proportional to the ratio between the lengths of the two sections, right and left.
Another way to look at is to imagine fastening a clamp to the cable on the primary side just below the balance beam and trying to squeeze the clamp and balance beam together. That's what the setup is really doing. That pulling together is obviously dividing the force evenly between the cable below and the beam above.
Still another way to think of it is this. Imagine two springs attached parallel to each other to a fixed object and a bar joining their other ends. Suppose we pull on the bar in the center with 10 lbs of force. Will each spring see 10 lbs? Whatever force they experience, they will apply in return. If so, wouldn't their forces add together and pull back with 20 lbs? If we can do that, we are well on our way to building a perpetual motion machine. If we pull with 10 but feel 20 then we are pulling with 20 so should feel 40..... It's obvious that the two springs will work together and return the same 10 lbs of pull: opposite and equal. Therefore, each spring will see and oppose 5 lbs assuming they are of the same strength.
In any case an important point is that if we are to use the balance beam to actuate brakes designed for direct pulls, we will introduce a doubling of the handlebar lever movement the system was designed for. That's why Nigel had to modify the lever. The standard lever has less leverage than what the Speet brake requires because in the standard setup, there's a mechanical advantage provided by the balance beam. And that's why if we use the balance beam with the Speet brakes, we need to shorten the levers at the brakes
to reduce the leverage there to compensate for the extra leverage provided by the beam.
Another way to automatically evenly distribute the force is to use a whiffletree or whippletree
https://en.wikipedia.org/wiki/Whippletree_(mechanism). I think I've seen such a setup on a bike somewhere, as well as disparaging comments regarding them. I don't remember where I saw that. Any thoughts about that?
Gary