Project ForgeAn epicyclic gear train has gears A (sun, 20 teeth), B (planet, 30 teeth), and D (20 teeth) on separate axes, and gear C (80 teeth on its inner surface, 100 teeth on its outer surface) — B meshes internally with C's inner surface, and C's outer surface meshes externally with D. If the carrier arm AB is fixed and the sun gear A rotates at 300 rpm clockwise, then the rpm of D in the clockwise direction is
- A240
- B−240
- 375
- D−375
Explanation
With arm AB fixed, every gear's axis position is fixed, so this reduces to an ordinary fixed-axis gear train. A meshes B (external mesh, reverses sign): ωB = −ωA(TA/TB) = −300×20/30 = −200 rpm. B meshes C's inner teeth (internal mesh, same sign): ωC = ωB(TB/TC,inner) = −200×30/80 = −75 rpm. C's outer teeth mesh D (external mesh, reverses sign): ωD = −ωC(TC,outer/TD) = −(−75)×100/20 = +375 rpm, i.e., clockwise (same sense as A) at 375 rpm.
Source: GATE ME 2018 Session 1 (Set 1) (2018)
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