Simple Machines and Gear Ratio Basics

Simple machines, mapped to your robot#

Every mechanism, however complex, is a combination of a few simple machines. You don't need the textbook recital — you need to recognize them on a robot:

• Lever — a bar on a fulcrum (last lesson). Arms and claws.
• Wheel and axle — a wheel keyed to a shaft. Every drivetrain.
• Pulley — a grooved wheel with a rope or belt; redirects force and, in combination, multiplies it. Elevators and climbers (cascade and continuous rigging).
• Inclined plane / wedge — a ramp or a point that funnels or grips. Intake ramps and game-piece guides.
• Screw — an inclined plane wrapped around a cylinder; turns rotation into precise linear motion. Lead screws and every bolt on the robot.

A compound machine is two or more of these working together — which is basically every FRC mechanism.

Gears are rotating levers#

A gear is a toothed wheel that meshes with another so they can't slip. When one turns, it forces the other to turn a precise, predictable amount. That lets you transmit rotation and, crucially, trade torque for speed. In FRC, standard gears share 20 diametral pitch (20DP) teeth so any two of them mesh, and they're bored for hex shaft (commonly 1/2 inch hex) so they key on without slipping.

The gear ratio#

The gear ratio is the most important number in a gearbox:

Gear ratio = teeth on driven gear ÷ teeth on driving gear

The driving gear connects to the motor; the driven gear connects to the load. A 12-tooth driving a 60-tooth gives:

• Ratio = 60 ÷ 12 = 5:1 (a "5-to-1 reduction")
• The motor spins 5 times for one output turn
• Output speed ÷ 5, output torque × 5

The torque–speed tradeoff#

This is the iron law: you can't get more torque and more speed at once. Gears conserve energy, just like levers.

• A reduction (greater than 1:1, like 5:1) gives more torque, less speed — heavy arms and climbers.
• An overdrive (less than 1:1, like 1:1.5) gives more speed, less torque — flywheels and shooters.

Ratios cascade: a 4:1 stage feeding a 3:1 stage is 4 × 3 = 12:1 overall. That's how a compact two- or three-stage gearbox reaches the big reductions arms need.

Putting it together#

FRC motors spin fast and make little torque on their own — geared 1:1, a NEO or Kraken would spin your wheels uselessly fast with no push. So almost every mechanism uses a reduction to convert speed into usable torque:

• Drivetrains typically land around 6:1 to 8:1, balancing top speed against pushing force.
• Arms and elevators use large reductions to move heavy loads slowly and under control.
• Shooters run close to 1:1 or overdriven to keep wheel surface speed high.

Software feels the ratio too: in WPILib, position and velocity control has to convert motor rotations into real distance or angle, so you tell it the gear ratio (and wheel size). Pick the wrong ratio and the motor either stalls — too little reduction — or crawls — too much. Choosing the gear ratio is the core design decision of nearly every FRC mechanism.