Roy gave a good basic view of it. This 'enhanced version' might help those who wish to dig deeper...
First let’s understand that “Timing the limbs” means “balancing the limbs’ strength at full draw relative to the archer’s holds on the bow and string”… or perhaps better defined as ‘full draw dynamic balance’.
It can be achieved in a couple of ways.
The method I use most often is accomplished by mimicking the archer’s holds on bow and string as closely as possible(very important) on the rope and pulley type tillering tree, and then adjusting the strength of the limbs so the string fulcrum comes straight back(or down as drawn on the tree). This means NOT pulling the string from directly behind the center of the handle in any instance… as nobody shoots a bow this way, but rather, we hold and draw the bow on the tree the way we do so in ‘real life’.
Dynamic balance means, if the limbs are of equal strength relative to the archer’s holds, at full draw the string hand fulcrum(hook on the string) will follow a line projected perpendicular from the bow… a line drawn on the wall to indicate perfect string fulcrum travel. The pulley down by the floor is placed precisely on, or plumb to, this line as well so that it attempts to pull straight back/down, not toward one limb or the other. Additionally, the bow’s handle area should be level in the tree to start, regardless of whether one limb tip is farther ahead of the handle than the other, etc.
To note: Bows that aren’t dynamically balanced reveal themselves as they tip forward or back in the archer’s hands at full draw… more obvious of course if they’re ‘off’ enough.
Each person must figure out the exact location of the indicator line(and where to hook onto the bowstring to draw the bow) for themselves, as it will vary depending on how they hold the string and where they prefer to nock the arrow. I have taken provisions to make my cradle and lower pulleys adjustable to account for the various idioms of the archer’s I intend to make bows for, but building it to suit YOU specifically, is a good start.
The ‘indicator line’ drawn on the wall, our main reference, is our beacon, and could also be drawn to indicate perfect perpendicular travel of the arrow nock, instead of the string hand fulcrum. I have done it both ways and either will give satisfactory and practically the same results.
Once it’s set up and the bow is drawn, if one limb is stronger than the other in the ‘dynamic sense’, it will flex less and its tip will travel less distance as its drawn than its weaker counterpart. If the bow handle doesn’t tip in the tree’s cradle, the effects of this imbalance will cause the string fulcrum and/or nock point to drift toward the stronger limb as the bow is drawn. Adjustments can then be made with confidence as we deem fit.
This is true whether we’re using a “long tillering string”, a string that allows for a very low brace height, or a proper length string for the bow… so this method can be applied very early in the process. There are a few caveats we can discuss later.
Sometimes folks prefer to leave the bottom limb a bit stronger than the top, as in the case of asymmetrical bows, and that can be done by allowing the fulcrum and/or nock to drift to that side of the line a little bit. If I do that, I allow 1/8” or so of drift toward the bottom limb at full draw. “Relativity” is the name of the game here. 1/8” drift at full draw is relative to the archer’s holds and has virtually nothing in common with a 1/8” positive tiller at brace. Think about it. How could it? What if one heel’s the grip? What if one limb has deflex and the other has reflex? Don’t let it be confusing. What it tells us is what it is. Set up to mimic your particulars, and trust what your tree tells you.
The popular brace height measurement differences… i.e. 1/4” positive tiller and such, what many folks use arbitrarily for limb strength reference, can be completely misleading in regards to relative limb strength and are not used at all to help judge a bow’s ‘dynamic balance’ at full draw with the above method. Read that again… it’s fundamental.
The only thing I do with those measurements is mentally record them after the bow is complete and use them to judge whether the tiller has shifted as the bow is shot in. By the way, balancing bows with the above method, tiller is MUCH less likely to shift as it’s shot-in. There will be no reason to ‘flip the bow’ end for end to mask shifting tiller. I have NEVER had to do that.
This method can reveal truths to the discerning bowyer about design relative to shooting idioms, bow performance, feel, arrow performance, tuning, and such that he may have never entertained without it. It will also allow for a more straightforward tillering practice with no backtracking, missing weight due to said backtracking, losing weight or acquiring set due to shooting it differently than it was tillered/timed for, and will result in a bow that is inherently tuned(one of my favorite by-products) and soooo sweet to shoot. Since the arrow nocking point was ‘ground zero’ from the get-go and the bow was timed around it,(inherent tuning) there will be no need to move the nocking point up and down trying to make the bow behave or mask inadequacies, while seeking good arrow flight. You set it where it was designed for and tiller to/timed for. Good arrow flight and limb harmony was built into the bow from the beginning. Tuning is an afterthought. Any discernable handshock is due entirely some other place… and in fact, even if it was created some other place… as-in due to an overbuilt limb design… it won’t be magnified by poor limb timing.
With proper dynamic balance, efficiency can be epitomized, handshock minimized, the arrow is sent straight away and recovers faster… the bow is doing what it is meant to do as well as it can do it.
Oh, there’s more…. Like I said, I could write a book :^)
I respect your wherewithall if you've stuck with me so far.