In a scenario with ring input, sun held, carrier output, and given tooth counts, Technician A claims the ratio is 1.43:1. Who is correct?

In a scenario with ring input, sun held, carrier output, and given tooth counts, Technician A claims the ratio is 1.43:1. Who is correct?

• A. Technician A
• B. Technician B
• C. Both Technician A and Technician B
• D. Neither Technician A nor Technician B

Answer: (A)

When you have a planetary gear set with the sun gear held stationary, the ring gear as input, and the output on the carrier, the carrier’s speed relative to the ring is determined by the gear teeth counts of the ring and sun. Specifically, the speed ratio of ring to carrier is Nr / (Nr − Ns), where Nr is the number of teeth on the ring gear and Ns is the number of teeth on the sun gear. The sign is typically positive in this configuration, meaning the carrier turns in the same sense as the ring gear. This comes from the constraints of the meshing gears: the tangential velocities at the contact points must match, and with the sun fixed, the rotation of the planets about the carrier produces a carrier speed that depends on how much the ring tooth count exceeds the sun’s count. If the given counts are ring teeth Nr = 66 and sun teeth Ns = 20, the calculation is 66 / (66 − 20) = 66 / 46 ≈ 1.4348, which rounds to 1.43:1. So Technician A’s result aligns with the actual ratio for this arrangement and those counts. In this setup, the other scenarios or counts would lead to different numbers, so the computed 1.43:1 is the correct outcome given the specified configuration.

When you have a planetary gear set with the sun gear held stationary, the ring gear as input, and the output on the carrier, the carrier’s speed relative to the ring is determined by the gear teeth counts of the ring and sun. Specifically, the speed ratio of ring to carrier is Nr / (Nr − Ns), where Nr is the number of teeth on the ring gear and Ns is the number of teeth on the sun gear. The sign is typically positive in this configuration, meaning the carrier turns in the same sense as the ring gear.

This comes from the constraints of the meshing gears: the tangential velocities at the contact points must match, and with the sun fixed, the rotation of the planets about the carrier produces a carrier speed that depends on how much the ring tooth count exceeds the sun’s count.

If the given counts are ring teeth Nr = 66 and sun teeth Ns = 20, the calculation is 66 / (66 − 20) = 66 / 46 ≈ 1.4348, which rounds to 1.43:1. So Technician A’s result aligns with the actual ratio for this arrangement and those counts.

In this setup, the other scenarios or counts would lead to different numbers, so the computed 1.43:1 is the correct outcome given the specified configuration.