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Which relationship holds between the wheel speeds and the cage speed?

  • A.The cage speed equals the higher of the two wheel speeds, since the planets are carried by the faster shaft
  • B.The cage speed equals the difference
  • C.The cage speed is the product of the two wheel speeds divided by their sum, which gives the harmonic mean of them
  • D.The cage speed is the mean of the two wheel speeds

Answer: D

The differential constrains the sum of the two output speeds to twice the cage speed, so if one wheel is held stationary the other turns at twice the cage speed. This is the fundamental kinematic relation and the origin of the runaway wheelspin problem. The order in which the effects act is what decides the outcome, so it is worth establishing first. Naming the cost of a choice alongside its benefit is what turns a fact into a design decision.

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