In a simple gear train, the speed ratio is the inverse of the gear ratio.

In a simple gear train, the speed ratio is the inverse of the gear ratio.

• A. True
• B. False
• C. Sometimes true
• D. Not related

Answer: (A)

Think about how two gears in mesh move together so their contact point has the same tangential speed. The tangential velocity at the pitch line is v = ω1 r1 = ω2 r2. The radii are proportional to the number of teeth, so r ∝ z. This means ω1 ∝ 1/z1 and ω2 ∝ 1/z2, giving ω1/ω2 = z2/z1. If the gear ratio is defined as the driven gear teeth over the driving gear teeth, that ratio is z2/z1. Therefore the speed ratio ω2/ω1 is the reciprocal of the gear ratio. In magnitude, the speed ratio is the inverse of the gear ratio, and the directions reverse in a simple gear mesh.

Think about how two gears in mesh move together so their contact point has the same tangential speed. The tangential velocity at the pitch line is v = ω1 r1 = ω2 r2. The radii are proportional to the number of teeth, so r ∝ z. This means ω1 ∝ 1/z1 and ω2 ∝ 1/z2, giving ω1/ω2 = z2/z1. If the gear ratio is defined as the driven gear teeth over the driving gear teeth, that ratio is z2/z1. Therefore the speed ratio ω2/ω1 is the reciprocal of the gear ratio. In magnitude, the speed ratio is the inverse of the gear ratio, and the directions reverse in a simple gear mesh.