Gear Basics
STAGE 1B · POWER — Spur Gears, Diametral Pitch, and the Fusion SpurGear Add-In
Gears Move Power
A motor spins fast but weak — gears fix that.
- Gears trade speed for torque (or the reverse).
- Bigger gear driven by smaller = more torque.
- Two meshing gears must share the same tooth size.
- Everything on the robot rides on gears.
Open with the core idea: a NEO or Kraken spins ~6000 RPM but can't lift anything alone. Gears turn that fast-weak output into slow-strong motion at the wheel or arm. Ask students where they've seen gears (bikes, drills). Stress the big rule we'll prove today: two gears only mesh if their teeth are the same size — that's what diametral pitch guarantees.
Five Numbers To Know
- Tooth count (N): how many teeth.
- Diametral pitch (DP): tooth size standard.
- Pitch diameter (PD): the 'effective' circle.
- Pressure angle: tooth face angle, usually 20 degrees.
- Center distance: gap between two gear centers.
Don't drown them — just name the five terms now, then teach each on its own slide. The pitch diameter is the most abstract; preview it as an invisible 'rolling circle' that does the real work, not the outer tip of the teeth. Tell them 20-degree pressure angle is the FRC default and they'll almost never change it.
Diametral Pitch (Dp)
DP = teeth per inch of pitch diameter.
- Higher DP = smaller teeth. Lower DP = bigger teeth.
- 20 DP is the FRC standard for gearboxes.
- Gears only mesh if DP matches exactly.
- Think of DP like a thread pitch for gears.
This is THE key concept. DP = N / PD. A 20DP gear and a 32DP gear will NOT mesh even if they're the same diameter — the teeth are different sizes and will grind. The classic rookie mistake is buying an AndyMark gear and a REV gear with mismatched DP. Tell them: when in doubt on 7558, use 20DP — that's what our WCP and AndyMark gearbox gears use.
Pitch Diameter Formula
PD = Tooth Count / Diametral Pitch.
- Example: 40 teeth at 20DP = 2.000 inch PD.
- Example: 12 teeth at 20DP = 0.600 inch PD.
- PD is where the teeth effectively 'roll'.
- The gear's OD is slightly larger than PD.
Walk the formula live. PD = N/DP. Have them compute a 30T 20DP gear (1.5in) out loud. Emphasize PD is NOT the outer diameter you'd measure with calipers — the tips stick out past it. This matters because center distance is built from PD, not OD. Common mistake: students try to measure gear size with calipers on the teeth and get confused.
Center Distance
Center distance = (PD1 + PD2) / 2.
- It's the gap between the two shaft centers.
- Equals the sum of the two pitch radii.
- Wrong center distance = gears bind or skip.
- This sets where you drill your holes.
This is where the math becomes a real CAD decision. If you have a 12T and a 40T at 20DP: PDs are 0.6 and 2.0, so center distance = (0.6+2.0)/2 = 1.3in. That's exactly how far apart you place the two shaft holes. Too close and gears jam; too far and they skip teeth under load. This is the number students will actually use to position holes in 2x1 tube or a gearbox plate.
Same DP. Same pressure angle. Or they don't mesh.
Two gears only run together if their tooth size (DP) and pressure angle (20 degrees) match — diameter and tooth count can differ freely.
Get The Spurgear Add-In
Fusion has a built-in SpurGear script.
- Utilities tab > Add-Ins > Scripts and Add-Ins.
- Find 'SpurGear' under the Samples list.
- Select it and click Run.
- A dialog pops up to enter gear specs.
Demo this live and have them follow. The SpurGear generator ships with Fusion — no download needed. Path: Utilities > Add-Ins > Scripts and Add-Ins, scroll the Samples to SpurGear, Run. If a student can't find it, make sure they're on the Samples tab, not My Scripts. This is the Fusion equivalent of Onshape's gear FeatureScript.
Fill In The Specs
- Pressure Angle: 20 degrees
- Module OR Diametral Pitch
- Number of Teeth
- Gear Thickness (face width)
- Pressure angle = 20 deg
- Set units to imperial, DP = 20
- Teeth = your design (e.g. 40)
- Thickness = 0.375in or 0.5in
The dialog can default to metric 'module' — switch the unit dropdown so you enter Diametral Pitch = 20 instead. Module and DP are two ways of saying tooth size (Module = 25.4/DP, so 20DP ≈ 1.27 module). Thickness is the gear's face width; 3/8in is common for FRC gearbox gears. Walk them through generating a 40T 20DP gear so everyone has one on screen.
Add The Bore And Hub
The add-in makes teeth only — you add the rest.
- Cut the center bore: 1/2in hex is FRC standard.
- Use a hex sketch, not a circle, for hex shaft.
- Add lightening holes to save weight.
- Save it as its own component.
The generator only gives you the toothed disc. Real FRC gears ride on 1/2in hex shaft (or sometimes 3/8in hex / round with a key). Show how to sketch a 1/2in hex and extrude-cut the bore. Mention lightening holes are about weight, not strength here. Tell them to make each gear its own Component (not just a body) so they can joint it to a shaft later. This connects to our Joints lesson.
Your Task
- Generate two meshing 20DP gears.
- Pinion: 14 teeth. Gear: 50 teeth.
- Cut a 1/2in hex bore in each.
- Place them at correct center distance.
- PD: 14/20 = 0.7in, 50/20 = 2.5in
- Center dist = (0.7+2.5)/2 = 1.6in
- Dimension the gap to confirm 1.6in
- Submit: Fusion Share > Public Link
Give them ~20 minutes. Watch for: forgetting to switch units to DP (they get a tiny metric gear), using a circle instead of hex for the bore, and placing gears by eye instead of the calculated 1.6in. The reduction here is 50/14 = 3.57:1. Have them paste their Fusion Share public link on AltHub when done. Spot-check that the dimensioned center distance reads 1.6in.
🧰 Add-ins for this step
Use the installed AltSkripts / FRC-COTS tools here — don't do it the slow way.
- C-C Distance — Sketch ▸ Create ▸ AltSkripts gives 20DP gear spacing plus pitch/OD circles.
Gears Trade Speed For Torque
- PD = Tooth Count / Diametral Pitch.
- Center distance = (PD1 + PD2) / 2.
- Match DP and 20-degree pressure angle or no mesh.
- Use Utilities > Add-Ins > SpurGear, then add a hex bore.
Your Task
- Model what this lesson covers in Fusion 360.
- Use the AltSkripts tools where they apply.
- Save it with a clear name.
- In Fusion: Share → Public Link → Copy.
- Paste the link below.
- A coach reviews it in AltHub.