In a simple gear train, if the drive gear has 14 teeth and a driven gear has 42 teeth, what is the gear ratio?

The gear ratio in a gear train can be calculated by taking the number of teeth on the driven gear and dividing it by the number of teeth on the drive gear. In this case, the drive gear has 14 teeth, and the driven gear has 42 teeth. The gear ratio calculation would be:

Gear Ratio = Number of Teeth on Driven Gear / Number of Teeth on Drive Gear

Gear Ratio = 42 / 14

Gear Ratio = 3

When expressed as a ratio, this can be indicated as 1:3. This means that for every 1 rotation of the drive gear, the driven gear will rotate 1/3 of a turn, effectively resulting in the driven gear turning more slowly due to having more teeth. This configuration is commonly used to increase torque while reducing the speed of the driven gear compared to the drive gear, which is a key function of gear systems in machinery and vehicles.