If a simple planetary gear set has 24 teeth on the sun gear and 60 teeth on the ring gear, what will be the ratio if the sun gear is input, the ring gear is held, and the carrier is output?

If a simple planetary gear set has 24 teeth on the sun gear and 60 teeth on the ring gear, what will be the ratio if the sun gear is input, the ring gear is held, and the carrier is output?

• A. 1.4 to 1
• B. 0.4 to 1
• C. 3.5 to 1
• D. 2.5 to 1

Answer: (C)

When a simple planetary gear set has the sun gear as input and the ring gear held, the carrier’s speed is determined by how the sun and ring teeth interact through the planets. The relationship for this arrangement gives the sun-to-carrier speed ratio as 1 plus the ring-to-sun teeth ratio. In numbers, the ring has 60 teeth and the sun has 24, so 60/24 = 2.5. Adding 1 yields 3.5. This means the sun would rotate 3.5 times for every one rotation of the carrier, i.e., a 3.5 to 1 ratio. So the carrier output turns at 1/3.5 of the sun’s speed when the ring is fixed.

When a simple planetary gear set has the sun gear as input and the ring gear held, the carrier’s speed is determined by how the sun and ring teeth interact through the planets. The relationship for this arrangement gives the sun-to-carrier speed ratio as 1 plus the ring-to-sun teeth ratio. In numbers, the ring has 60 teeth and the sun has 24, so 60/24 = 2.5. Adding 1 yields 3.5. This means the sun would rotate 3.5 times for every one rotation of the carrier, i.e., a 3.5 to 1 ratio. So the carrier output turns at 1/3.5 of the sun’s speed when the ring is fixed.