Project ForgeAn epicyclic gear train has a sun gear 2 (input shaft, 20 teeth, external) meshing with a planet gear 3 (40 teeth, external), which meshes with a fixed ring gear 5 (100 teeth, internal). The arm 4 is attached to the output shaft. Gear 2 is rotating at 60 rpm ccw (ring 5 fixed). The arm 4 will rotate at
- 10 rpm ccw
- B10 rpm cw
- C12 rpm cw
- D12 rpm ccw
Explanation
Tabular method: with the arm fixed and the sun given +1 rev, the external sun-planet mesh reverses direction (planet=-20/40=-0.5) while the external planet-internal ring mesh does NOT reverse (ring=-0.5×40/100=-0.2). So (arm fixed, sun=+y): ring=-0.2y. Adding arm motion +x to all members: arm=x, sun=x+y=60, ring=x-0.2y=0 (fixed). From the ring equation x=0.2y; substituting: 0.2y+y=60 ⟹ y=50, x=10. Arm speed=10 rpm, same sense (ccw) as the sun.
Source: GATE ME 2009 (2009)
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