⚙ Hardware · Engineer · Beginner → Intermediate
Gear Ratios & Motor Speed
How gears change speed and torque, how to calculate your drivetrain or arm output, and why choosing the wrong cartridge ruins a good robot.
The core tradeoff: Gear up = faster, less torque. Gear down = slower, more torque. Every mechanism on your robot is a tradeoff. This guide gives you the math to make that tradeoff on purpose, not by accident.
A gear ratio describes how many times the driver gear turns for every one turn of the driven gear. If the driver has 36 teeth and the driven has 48 teeth, the ratio is 36÷48 = 0.75. The driven gear turns at 0.75× the motor speed but with 1÷0.75 = 1.33× the torque.
For compound gear trains (multiple stages), multiply the ratios together: 0.75 × 0.6 = 0.45 overall ratio.
| Mechanism | Cartridge | Common Ratio | Result |
|---|
| Drivetrain (fast) | Blue 600 | 36:48 (0.75) | 450 RPM — ~4.5 ft/s on 3.25" wheels |
| Drivetrain (balanced) | Green 200 | Direct drive | 200 RPM — ~3.4 ft/s on 4" wheels |
| Drivetrain (torque) | Red 100 | Direct drive | 100 RPM — max pushing force |
| Intake rollers | Blue 600 | Direct drive | 600 RPM — pulls game elements fast |
| Chain bar / arm | Red 100 | 1:5 or 1:7 | 15–20 RPM — high torque for lifting |
| Catapult / puncher | Red 100 | 1:25 to 1:35 | 3–4 RPM — slow wind-up, massive force |
⚠ The 3 Biggest Gear Ratio Mistakes
- Gearing for top speed, ignoring pushing: A 600 RPM drivetrain that gets pushed backward by a 200 RPM robot loses auton bonus and position every match. Test pushing force, not just speed.
- Wrong cartridge for the mechanism: Blue 600 RPM on an arm = motor stall and overheating within 30 seconds. Arms need Red 100 RPM cartridges and a compound gear-down ratio.
- Measuring diameter wrong: The "4 inch wheel" in the VEX catalog is often 3.95–4.05 inches when measured. Use calipers and the actual measured value in any speed calculation — it matters more than you think.
Gear ratios apply the law of conservation of energy: power in equals power out minus friction losses. Since P = τω, a gear ratio that multiplies torque must divide speed by the same factor. A 5:1 reduction delivers 5x torque at 1/5 the speed. This is not a design choice — it is a physical law. Understanding it means a team can predict mechanism performance from gear ratio before building.
🎤 Interview line: “We calculate gear ratios from requirements before building. For our intake, we needed 90 RPM and 0.8 N·m of torque. Using P = τω and our motor specs, we back-calculated the required gear reduction. We built the correct ratio the first time because the physics told us exactly what we needed.”
Your motor outputs 100 RPM. You apply a 3:1 external reduction. What is the final output RPM?
⬛ 300 RPM — the reduction multiplies speed
⬛ 33 RPM — divide by the ratio: 100 ÷ 3
⬛ 97 RPM — subtract the ratio from the RPM
📝Notebook entry tip: Select Best Solution — Purple slide — Write a gear ratio decision entry for each major mechanism: required output speed or torque, your calculation from motor specs, and the ratio chosen. If you tested multiple ratios, include the performance data from each. A gear ratio that is calculated from requirements — not estimated from experience — is one of the clearest demonstrations of mechanical engineering thinking in a VRC notebook.