Project ForgeTheory of Machines
Kinematics of Mechanisms
GATE 2016
Hard
In an epicyclic gear train, gear 3 (20 teeth) is carried on arm 5 and meshes with gear 2 (60 teeth, sun) and gear 4 (100 teeth, internal/annulus). Gear 2 is fixed. If gear 4 rotates at 100 rpm counterclockwise, the angular speed of arm 5 (in rpm) is
- A166.7 counterclockwise
- B166.7 clockwise
- 62.5 counterclockwise
- D62.5 clockwise
Explanation
Using relative-to-arm speeds, the idler gear 3's tooth count cancels: (ω4-ωarm)/(ω2-ωarm) = -N2/N4 = -0.6. With ω2=0: (ω4-ωarm)/(-ωarm)=-0.6 → ω4=1.6·ωarm → ωarm=100/1.6=62.5 rpm, same sense as ω4 (counterclockwise).
Source: GATE ME 2016 Set-1 (2016)
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