In a simple gear pair, the speed ratio of the driven gear to the driver is equal to which of the following?

• A. The ratio of the number of teeth on the driver gear to the number of teeth on the driven gear.
• B. The ratio of the number of teeth on the driven gear to the driver gear.
• C. The sum of the teeth on both gears.
• D. The product of the teeth on both gears.

Answer: (A)

In a simple gear pair, the contact along the pitch circles must move at the same linear speed. That means the pitch-line velocity v is the same for both gears: v = ω_driver × r_driver = ω_driven × r_driven. Since the pitch radius r is proportional to the number of teeth, the angular speeds relate as ω_driven / ω_driver = N_driver / N_driven. So the speed ratio of the driven gear to the driver gear is the ratio of the driver's teeth to the driven gear's teeth.

For example, if the driver has 20 teeth and the driven has 40, the driven gear runs at 20/40 = 0.5 times the driver’s speed (half as fast). The other options don’t fit this inverse relationship: using driven over driver would give the reciprocal, and summing or multiplying the teeth counts has no bearing on the speed ratio.