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11Motion

Gears & Gear Trains

Spur, bevel, worm, and rack-and-pinion gears - how teeth, ratios, and gear trains trade speed for torque.

Intermediate ~15 min

Animated spur gears meshing at a 2:1 ratio - the driven gear has twice the teeth of the driver.

1 Experience
2 Reflect
3 Theorize
4 Apply

Gear Ratios

The Core Formula

The gear ratio is the number of teeth on the driven gear divided by the number on the driver.

  • Ratio > 1 (e.g. 3:1): Output turns slower, but with more torque.
  • Ratio < 1 (e.g. 1:2): Output turns faster, but with less torque.
  • Power stays the same: What you gain in force, you lose in speed (and a bit to friction).

Types of Gears

Four Gears That Cover Most Robots

Spur

Straight teeth on parallel shafts. Simple and cheap - your go-to for most drivetrains.

Bevel

Cone-shaped teeth that turn the drive direction through 90°.

Worm

A screw drives a wheel. Huge ratios and self-locking - great for lifts and arms.

Rack & Pinion

Rotation turns into straight-line motion - how car steering works.

Gear Trains - Stacking Ratios

A gear train connects multiple gear pairs in series to reach a bigger ratio than any single pair could provide.

Two Rules to Keep in Mind
  • Multiply the stages: A 3:1 followed by a 4:1 gives 12:1 overall.
  • Same tooth size: Meshing gears must share the same module (tooth size), or they won't fit together.
Robotics rule of thumb: Drivetrains want 3:1 to 10:1. Arms and lifts run 30:1 to 100:1. Keep each stage under 5:1 so no single pair gets huge.
⚙

Challenge

Adjust the gear teeth to achieve exactly a 3:1 gear ratio (output speed 1/3 of input).

⚠ Predict First

If you double the number of teeth on the driven gear, what happens to the output speed?

Gear Ratio = Driven Teeth / Driver Teeth

Ratio > 1: torque multiplication (slower, stronger). Ratio < 1: speed multiplication (faster, weaker).

Power is conserved (minus friction): Torque x Speed = constant

Common ratios in robotics: 3:1 to 100:1 for arms, 1:1 to 5:1 for drivetrains.

Guided Exploration
  1. Set a 1:1 ratio. Note the output speed and torque values.
  2. Find the combination that gives exactly 4:1 torque advantage.
  3. What is the highest ratio you can achieve? Would this be practical for a real robot?
Pause and Reflect
✓ Your reflections are saved automatically
Apply What You Learned

Design a two-stage gear reduction for a robot arm.

  • Calculate the overall ratio you need: motor RPM / output RPM
  • Split the ratio into two stages, each less than 5:1
  • Pick tooth counts that share the same module and give the target ratio
  • Compute the center distance between each pair
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