In a simple gear train, the gear ratio equals the number of teeth on the driven gear divided by the number of teeth on the driver gear.

In a simple gear train, the gear ratio equals the number of teeth on the driven gear divided by the number of teeth on the driver gear.

• A. The gear ratio equals the driver teeth divided by driven teeth
• B. The gear ratio equals the driven teeth divided by the driver teeth
• C. The gear ratio equals the sum of teeth
• D. The gear ratio equals the product of teeth

Answer: (B)

When two gears mesh, the speed relationship comes from the fact that the pitch-line velocity must be the same for both gears: ω_driver · r_driver = ω_driven · r_driven. The radii are proportional to the number of teeth, so r ∝ N. This gives ω_driven/ω_driver = N_driver/N_driven. If the gear ratio is defined as the input speed divided by the output speed, then that ratio equals N_driven/N_driver—the driven teeth divided by the driver teeth. That’s why the gear ratio is expressed as the number of teeth on the driven gear divided by the number of teeth on the driver gear. A larger driven gear increases this ratio, which means the output turns more slowly relative to the input.

When two gears mesh, the speed relationship comes from the fact that the pitch-line velocity must be the same for both gears: ω_driver · r_driver = ω_driven · r_driven. The radii are proportional to the number of teeth, so r ∝ N. This gives ω_driven/ω_driver = N_driver/N_driven. If the gear ratio is defined as the input speed divided by the output speed, then that ratio equals N_driven/N_driver—the driven teeth divided by the driver teeth. That’s why the gear ratio is expressed as the number of teeth on the driven gear divided by the number of teeth on the driver gear. A larger driven gear increases this ratio, which means the output turns more slowly relative to the input.