Chains, Belts, and Gears: Adders/Spacing

During my short time in FRC, I have noticed that the reasoning behind doing adders/subtractors (is that a word) is unknown by many students and they blindly follow it. I wanted to make this thread mainly as a resource for my own team, and some others may also benefit.

What is an adder/subtractor/offset?
Usually, when teams use chains, gears, and/or belts, they will add or subtract a specific number from the calculated center to center distance (C-C) in order to maintain proper tensioning within their system. These numbers that are added/subtracted from the C-C come from many different places, which is what this post will explore.

Chain
Whenever running chain, be it on your drivetrain, arm, etc. it is extremely important to run proper tensioning, in order to prevent the chain from falling off the sprockets, slipping, or just to stop it from slapping against your bellypan while driving.

Center to Center Calculator
Currently, the most optimal chain c-c calculator is http://www.islandpondrailroad.com/chain.htm. This has an advantage to the more common one, http://www.botlanta.org/converters/dale-calc/sprocket.html, due to the pin position model that it uses. The specifications are far above my head but the differences are explained both on their respective websites and in this thread Chain length calculator.
Edit: With @a_cool_username’s comment, we can see that there is little difference between the two, take this as you will.

Why do we need an adder in chain?
From @AriMB:

What is the adder for chain?
Usually, teams will add .018in for #25 chain and .012in for #35 chain to their calculated C-C distance in CAD. As AriMB said, this is an approximation gained from testing, and can vary from supplier. Teams like 254 have found that it can vary by distance and test each brand/batch of chain that they buy. For teams that don’t have the resources to do this extensive testing, the constant will still work (credit AriMB).

Where does this come from?
This all comes from a 2013 talk from Paul Copioli at MSC, or at least it was popularized at that point within FRC, the concept wasn’t completely new. The numbers come from the testing that they did, but others have found slightly different results. The talk can be found here, the calculator he uses here, and the accompanying thread that contains testing and team experiences here.

Belts
Whenever running belts, in certain use cases, ex. in a high speed, low torque application, the amount of load on the pullies/belts will not be significant enough to make the belt skip, so you would use a negative adder. In places where there is high torque, a negative adder should not be used because the friction is not significant but the load will cause skipping. (credit AriMB).

Center to Center Calculator
Currently, there are two main belt center-center calculators. First, WCP - How To: Belts is quite common, but I have heard that it does “weird stuff”. Secondly, - SDP/SI eStore calculator is a popular alternative. The accompanying thread is here.

Why do we need an adder/subtractor for belts?
When using an adder for belt, teams aim to decrease friction and increase efficiency in the system. In certain applications this is optimal (low load), but in others (high load) it can cause skipping.

What is the adder for belt?
The amount of negative adder will vary by qualified application, depending on the load and other factors. This will need prototyping.

Where does this come from?
This comes from understanding the loads in a belted system.

Gears
Whenever running gears in a gearbox, ensuring that you have proper spacing is important to reduce backlash, increase efficiency, and more.

Center to Center Calculator
For this, the simple formula is (PitchDiameterGear1+PitchDiameterGear2)/2. For a more convenient option, use WCP - How To: Gears.

Why do we need an adder in gears?
This is due to the tolerances specifications of a majority of gears, meaning that we would need a certain amount of spacing to allow for this variation. There is also a variable amount of tolerance in the shaft that would hold the gear. Also, this decreases friction, and theoretically increases efficiency. When gears are spaced farther apart, there is lower efficiency and increased backlash, but it is more optimal than if they were too close together and would have increased friction and the possibility of binding.

What is the adder for gears?
Usually, teams will add .002in-.003in to their calculated gear c-c. No matter what, it is important to have a positive adder rather than negative.

Please correct any and all of my errors below, I would greatly appreciate it.
Edit: Thank you to AriMB, a_cool_unsername, and others for correcting my many errors.

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Good post. Someone will inevitably point out that chain adders vary based on the length of the chain, to which I say: It’s probably still fine. Most of the adder comes from wearing in the chain, slop in hex, and slop in the sprockets themselves. You can run with 0 center add for short runs of #25 and #35 (up to 4-5") but beyond that it’s fine to just run with the 0.018" and 0.012" adders respectively. Your chain might be a little loose or tight based on the length, but really any chain run more than 18" or so should use a tensioner anyway, and if it’s a little tight it will probably wear in with time.

You can get away with big subtractions on belts (as much as 1/16" easily), especially for shorter runs. This helps reduce the force required to drive the belt, which is handy for things that are low-power like intakes or game piece conveyors.

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I second this, more or less. On my high school team, 418, we didn’t even do c-c calculations, usually. We just let the shafts be wherever they needed to be, and made the chain to length, with a half-link if need be. I’m sure the efficiency wasn’t optimal, but we never broke nor threw a chain.

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We used half links this year. We didn’t throw a ton of chains but they were thrown enough for it to be a concern. Had to add several tensioners, especially on runs that were right at the cusp of adding a whole extra link.

To be fair, I should add that half links should be avoided, if only because it’s one more small finicky item that you have to keep in stock and know how to install. Plus, chains that are too tight or too loose decrease your efficiency. Properly calculating your c-c distances is definitely the right way to do it. But when it comes down to it, chain lengths are fairly forgiving.

Use one-and-a-half links (McMaster calls them add-and-connect links) rather than half links, they’re stronger.

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If anyone wants to mess around making their own calculator (or just really like plugging and chugging equations), these are the formulas for belt and chain. (Conveniently formatted to be paste-able into a one-line equation box, like Inventor or Excel)

Belt Center Distance
b = 4 * ( belt_teeth * pitch ) - 2 * PI * ( pulley_1_pd + pulley_2_pd)

center_distance = ( b + ( b ^ 2 - 32  * ( ( pulley_1_pd - pulley_2_pd ) ^ 2 ) ) ^ 0.5 ) / 16
Chain Center Distance
center_distance = pitch * 1 / 8 * ( 2 * chain_links - sprocket_1_teeth - sprocket_2_teeth + sqrt( ( 2 * chain_links - sprocket_1_teeth - sprocket_2_teeth ) ^ 2 - ( 8 / ( ( PI ) ^ 2 ) ) * ( ( sprocket_1_teeth - sprocket_2_teeth ) ^ 2 ) ) )
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For the argument that the pin position model is better, here’s the actual difference:

I modeled a system with a 20 tooth sprocket, and 30 tooth sprocket, and 100 chain links (center distance of approximately 9.4 inches, for scale).

I set the center distance to the distance given by the formula that the Botlanta calculator uses. I then applied a pin position model, with one pin allowed to be slightly off, to measure the difference between the models.

What I found was that the pitch length differed by .0000807 inches between the two models, with the pin position giving the very slightly shorter distance.

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Andymark sells these now too, I totally forgot about them!

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I have some points to clarify here:

There’s no real argument here as to why to use adders. Roller chain has a lot of small bushings and pins that wear and shift following a typical wear curve. This is commonly referred to as “chain stretch”, though this is really a misnomer since the steel chain doesn’t actually stretch by any significant amount. To correct for this so that the chain will be properly tensioned for the majority of its life, you can either use an adjustable chain tensioner or a C-C adder.

 

The 0.018" / 0.012" chain adder can be thought of as a very basic approximation. Different lengths of chain runs would benefit from different adders, and the amount of adder varies with different chain brands and even different batches. Some teams like the Poofs have a testing setup to find the optimal adder for each batch of chain they use. But if you don’t have the time/resources to investigate so thoroughly, using the constant is better than nothing.

 

Belt adders don’t really vary by belt type or length, but by use case. Using a negative adder decreases the friction in the system, but also invites belt skipping. A belt in a low-speed/high-torque application (e.g. an arm) shouldn’t get any adder because the small amount of friction will be negligible, while the high loads will make the belt skip. A high-speed/low-torque belt (e.g. in a intake or shooter) doesn’t have enough load to cause skipping while the small amount of friction will negate a large percent of the torque going through the belt, so you should use a negative adder.

 

The number doesn’t vary by team so much as it varies by application. As I said above, it’s a tradeoff between friction and skipping.

 

I haven’t seen any real debate on this issue either. The reason we use an adder for gears is due to manufacturing tolerances in both the gears and the part that holds them. Gears that are spaced too close together are very inefficient and can bind together; a very bad situation. Gears that are spaced too far apart have a slightly lower efficiency and a bit more backlash; not ideal but not a huge problem. So it’s important that any position tolerance should be in the positive range instead of the negative range. A typical tolerance half-range for a well-manufactured gear reduction is about 0.003", so that is the amount to add to make sure that the minimum tolerance is positive. There’s no “big FRC” pushing unnecessary adders.

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Hello! Thank you for correcting my many errors and filling in the gaps in my knowledge, I greatly appreciate it. I have made the proper edits to my original post to reflect this information and have credited you (if I have missed any place, please let me know). In reference to your first and last quotation of me (specifically the argument parts), I have seen some older technical mentors who believe that we do not need to do use adders for chain and gears. This may not be a universal experience, but I just wanted to include those parts for the students on my team.