Lesson 6.3: Sizing Chain and Timing Belt Drives
Technical Context
Gears must touch, which means the center distance is fixed by the gears themselves. Chain and belt transmit torque across a distance you choose, which is why they appear wherever a motor cannot sit next to the thing it drives.
Chain and belt come in discrete lengths, so the chosen center distance still needs to match an available loop or include adjustment.
Chain Versus Belt
| Roller chain | Timing belt | |
|---|---|---|
| Tolerance to misalignment | Moderate | Low |
| Noise | Higher | Very low |
| Maintenance | Needs tension checks and lubrication | Essentially none |
| Backlash | Some, increases as it stretches | Very low |
| Failure mode | Stretches gradually, then throws | Skips teeth or shreds |
| Weight | Higher | Lower |
| Debris tolerance | Good | Poor |
For most FTC applications, timing belt is the better default: quieter, lighter, no lubrication, and no stretch. Chain earns its place where the load is high, the environment is dirty, or the exact center distance cannot be controlled well.
The Length Relationship
For a two sprocket or two pulley drive:
L = 2C/p + (N1 + N2)/2 + p*((N2 - N1)/(2*pi))^2 / C
Where L is length in pitches (links for chain, teeth for belt), C is center distance, p is the pitch, and N1 and N2 are the tooth counts.
The first term is the two straight runs. The second accounts for the teeth wrapped around each pulley. The third is a correction for the fact that the wrap is not exactly half on each when the pulleys differ in size.
Roller chain must have an even number of links to close without an offset link, so always round up to an even count.
Belts come in fixed tooth counts, so the practical workflow is reversed: pick a stock belt, then compute the center distance it needs and put the shafts there.
Try It
Chain and Belt Length
Pick a length you can actually buy, then move the center distance to match.
Wrap on the small pulley is healthy. Remember the drive still needs a way to take up slack, because chain stretches and belts relax after their first hours of running.
The stock length moves your center distance by 0.159 in. Slot the mounting holes or add a tensioner so you can absorb that difference during assembly.
Roller chain is sold in whole links and must be an even count to close without a half link. Timing belts are sold in fixed tooth counts, so the practical workflow is to choose a stock belt and then place the shafts at the center distance it needs. Always design in adjustment, either a slot, a tensioner, or a movable motor plate.
Design In Adjustment
Even with the math done correctly, the assembly needs adjustment, for three reasons: the stock length rarely lands exactly on your target center distance, chain stretches over its life, and belts relax after their first hours of running.
Three ways to provide it, in order of preference:
- Slotted motor mount. The motor plate moves along the slot to tension the drive. Simple, robust, adjustable without disassembly.
- Idler pulley or tensioner. A wheel bearing on the slack side, on a slot or a spring. Necessary when the shafts cannot move.
- Adjustable standoffs or shims. Workable but slow to change.
A chain installed at exactly the right tension is loose within a few hours of running, and a loose chain skips teeth and then throws. If your design has no way to take up slack, it has a scheduled failure.
Tension and Wrap
Tension. Too loose and the chain or belt skips. Too tight and it loads the bearings heavily, wastes power to friction, and shortens the life of everything involved. For chain, a common target is a small amount of visible sag on the slack side, roughly a half inch of deflection on a typical FTC span. For timing belt, tension until the slack side stops fluttering and no further.
Wrap angle is how many degrees of the small pulley the belt contacts. More wrap means more teeth in mesh and more torque before it skips. Keep the wrap on the small pulley above roughly 120 degrees where you can. Increasing the center distance, using a larger small pulley, or adding an idler on the slack side all help.
Keep wrap on the small pulley above roughly 120 degrees. Increase the center distance, use a larger small pulley, or add an idler on the slack side.
Timing belts track sideways slightly. A flange on one pulley keeps the belt located. Flanges on both pulleys of a two pulley drive can fight each other and cause the belt to ride up and wear its edges.
Alignment
Both chain and belt need the two sprockets or pulleys in the same plane. This is a stack-up problem, covered in Lesson 4.4, and belts are the least forgiving component on the robot in this respect.
The check: lay a straight edge across the faces of both pulleys. Any visible step is worth correcting with a spacer change before running the drive.
Fill-in-the-Blank Practice
- Roller chain must be an
__________number of links to close without an offset link. - The wrap angle on the small pulley should generally be kept above about
__________degrees. - A drive with no way to take up slack will fail because chain stretches and belts
__________after initial run time.
Show answers
- even
- 120
- relax (loosen)
Exercise
Take one chain or belt drive on your robot. Measure the center distance and count the teeth, then use the calculator to check whether the installed length matches what the geometry requires. Then check whether the drive has any means of adjustment, and add one if it does not.
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