From Bicycles to Robots: Understanding Gear Ratios

You ride a bike up a steep hill. You shift to “Low Gear” (Big sprocket on wheel). You pedal fast, but move slow. You ride down the hill. You shift to “High Gear” (Small sprocket on wheel). You pedal slow, but move fast. You instinctively understand Torque vs. Speed.

Power is Constant

The Law of Conservation of Energy: Power In = Power Out (minus friction). $$Power = Torque \times Speed$$. You can’t increase both. You have to trade one for the other.

The Robot Gearbox

We buy motors (like the GoBilda Yellow Jacket) that come with “Pre-installed Transmissions.”

• 3.7:1 Ratio: High Speed. Used for Flywheel Shooters (6000 RPM). No torque.
• 117:1 Ratio: High Torque. Used for climbing arms. Very slow (50 RPM). Can lift a brick.

Idler Gears (The Distraction)

A common mistake new engineers make: “I have a 10-tooth gear, connected to a 100-tooth gear, connected to a 20-tooth gear.” The middle gear (Idler) does nothing for the ratio. Ratio = Output / Input. The idler just changes direction or spacing. It doesn’t add strength.

Conclusion

A gearbox is just a lever that spins. Understanding how to swap gears is the difference between a robot that burns out its motors trying to lift an arm, and a robot that lifts the arm effortlessly (but slowly). Always shift for the hill you are climbing.