Robotics gear ratios connect motor speed and motor torque to how a robot actually moves, lifts, or pushes. This cheat sheet helps students choose gears for drivetrains, arms, elevators, and intakes. It is useful when a motor spins too fast, stalls too easily, or cannot create enough force at the wheel or mechanism.
Students in grades 8-12 can use it as a quick reference during robot design, building, and troubleshooting.
The core idea is that gears trade speed for torque. A reduction ratio makes the output turn slower but with more torque, while an overdrive ratio makes the output turn faster but with less torque. Important formulas include gear ratio = driven gear teeth / driving gear teeth, output speed = motor speed / gear ratio, and output torque = motor torque x gear ratio x efficiency.
These relationships help predict whether a robot will accelerate, climb, lift, or push effectively.
Key Facts
- Gear ratio = driven gear teeth / driving gear teeth when one gear drives another directly.
- Output speed = input speed / gear ratio, so a 5:1 reduction makes the output spin one fifth as fast.
- Output torque = input torque x gear ratio x efficiency, so reductions increase usable torque after losses are included.
- Wheel force = wheel torque / wheel radius, so smaller wheels create more pushing force for the same axle torque.
- Robot speed = wheel circumference x wheel rpm, where wheel circumference = pi x wheel diameter.
- Power is approximately conserved, so increasing torque with gears decreases speed by a similar factor before efficiency losses.
- A compound gear ratio is found by multiplying each stage, such as total ratio = stage 1 ratio x stage 2 ratio.
- A motor stalls when the load torque is greater than the motor can supply, causing speed to drop near zero and current to rise.
Vocabulary
- Gear Ratio
- The comparison between input rotation and output rotation, usually showing how much gears change speed and torque.
- Torque
- A turning force measured in newton-meters or inch-pounds that causes a shaft, wheel, or arm to rotate.
- Reduction
- A gear setup with a ratio greater than 1:1 that lowers output speed and raises output torque.
- Overdrive
- A gear setup with a ratio less than 1:1 that raises output speed and lowers output torque.
- Efficiency
- The fraction of input power that becomes useful output power after losses from friction, heat, and gear contact.
- Stall Torque
- The maximum torque a motor can produce when its shaft is not rotating.
Common Mistakes to Avoid
- Reversing the gear ratio formula is wrong because the driven gear teeth must be divided by the driving gear teeth for a simple gear pair.
- Ignoring efficiency is wrong because real gearboxes lose energy to friction, so output torque is less than input torque x gear ratio.
- Assuming more torque always makes a better robot is wrong because extra reduction lowers speed and can make the robot too slow for the task.
- Using wheel diameter instead of wheel radius in wheel force is wrong because force = torque / radius, not torque / diameter.
- Comparing free speed only is wrong because motors slow down under load, so design should consider operating torque, current, and stall risk.
Practice Questions
- 1 A 12-tooth gear drives a 60-tooth gear. What is the gear ratio, and is this a reduction or an overdrive?
- 2 A motor spins at 6000 rpm and drives a 10:1 gearbox. What is the output speed before losses?
- 3 A motor produces 0.8 N m of torque into a 6:1 gearbox with 85% efficiency. What is the approximate output torque?
- 4 A robot drivetrain is fast on flat ground but struggles to push another robot. Explain how changing the gear ratio could improve pushing force and what tradeoff would result.