Which arrangement yields a direct drive, i.e., a 1:1 speed ratio, in a planetary gear set?

Which arrangement yields a direct drive, i.e., a 1:1 speed ratio, in a planetary gear set?

• A. Ring gear input, carrier output, sun held
• B. Sun input, carrier held, ring output
• C. Carrier input, sun input, ring output
• D. Carrier input, ring input, sun output

Answer: (C)

In a planetary gear set, the speeds of sun, ring, and carrier are tied together by a compatibility constraint: the relative motion between sun and carrier is related to the relative motion between ring and carrier by the gear teeth count. A convenient expression is that the difference between sun and carrier speeds equals a constant times the difference between ring and carrier speeds.

If you drive both the sun gear and the carrier at the same speed (ω_s = ω_c) and use the ring as the output, the left side becomes zero. That forces the ring’s speed relative to the carrier to be zero as well, so the ring rotates at the same absolute speed as the inputs. In other words, the output ring speed equals the common input speed, giving a direct 1:1 drive.

So, driving both sun and carrier together while the ring is the output yields a direct drive. The other arrangements don’t lock the system into ω_out = ω_in in general, because they leave a single input and/or a fixed element, and the resulting ratio depends on the gear teeth counts rather than producing a equal-speed transfer.