All Labs

Gear Trains & Power Transmission Lab

Explore how gears trade speed for torque and vice versa. Build simple pairs, multi-stage compound trains, and belt drives. See how power is conserved while RPM and torque change through each stage.

Guided Experiment: Speed-Torque Trade-off

How does changing the gear ratio affect output speed and torque? Is power conserved across different gear configurations?

Write your hypothesis in the Lab Report panel, then click Next.

Gear Train Diagram

Input 20TOutput 40T

Controls

Input Parameters
N·m
Gear Pair
T
T

Results

Gear Ratio
2:1
GR=2GR = 2
Output RPM
500 RPM
ωout=500\omega_{out} = 500
Output Torque
20 N·m
τout=20\tau_{out} = 20
Power
1047.2 W
P=1047.2 WP = 1047.2\text{ W}
Output Direction: Reversed

Odd number of gear meshings reverses the output direction.

Ratios
Speed Ratio
ωinωout=2\frac{\omega_{in}}{\omega_{out}} = 2
Torque Ratio
τoutτin=2\frac{\tau_{out}}{\tau_{in}} = 2
Key Formulas
GR=NdrivenNdriverGR = \frac{N_{driven}}{N_{driver}}
ωout=ωinGR\omega_{out} = \frac{\omega_{in}}{GR}
τout=τin×GR\tau_{out} = \tau_{in} \times GR
P=τ⋅ωP = \tau \cdot \omega

Data Table

(0 rows)
#ConfigurationInput RPMGear RatioOutput RPMOutput Torque (N·m)Direction
0 / 500
0 / 500
0 / 500

Reference Guide

Gear Ratio Basics

The gear ratio is the ratio of teeth on the driven gear to teeth on the driver gear. A ratio greater than 1 means speed reduction and torque multiplication.

GR=NdrivenNdriverGR = \frac{N_{driven}}{N_{driver}}

A 40-tooth gear driven by a 20-tooth gear produces a 2:1 ratio, halving the speed while doubling the torque.

Compound Gear Trains

In a compound gear train, the overall ratio is the product of each stage's individual ratio. This allows extreme ratios with reasonably sized gears.

GRtotal=GR1×GR2×⋯×GRnGR_{total} = GR_1 \times GR_2 \times \cdots \times GR_n

Each meshing pair reverses the rotation direction. Odd stages produce opposite rotation; even stages restore the original direction.

Torque & Power

Power equals torque times angular velocity. In an ideal (frictionless) gear train, power is conserved. As speed decreases, torque increases proportionally.

P=τ⋅ω=τ⋅2π⋅RPM60P = \tau \cdot \omega = \tau \cdot \frac{2\pi \cdot RPM}{60}

This is why low gears on a bicycle feel easier to pedal uphill but spin the wheel slowly.

Belt Drives

Belt drives transmit power between pulleys using a flexible belt. The ratio depends on pulley diameters instead of teeth, but the math is the same.

GR=DdrivenDdriverGR = \frac{D_{driven}}{D_{driver}}

Unlike meshing gears, belt drives do not reverse rotation direction. Both pulleys spin the same way.