When discussing gear ratios, which quantity is used in the numerator to determine the ratio for speed?

• A. Driven Gear Pitch Diameter
• B. Driver Gear Pitch Diameter
• C. Sum of Pitch Diameters
• D. Difference of Pitch Diameters

Answer: (A)

When gears mesh, the tangential velocity at the pitch line must be the same for both gears. This means the driver’s angular speed times its pitch diameter equals the driven gear’s angular speed times its pitch diameter: ω_driver × D_driver = ω_driven × D_driven. If you define the speed ratio as driver speed divided by driven speed, then ω_driver/ω_driven = D_driven / D_driver. So the quantity that appears in the numerator of this speed ratio is the driven gear pitch diameter. The other options—sum or difference of pitch diameters—don’t govern the speed relationship, and the pitch diameters are the relevant quantities for this ratio.