GATE ME 2016 Set 1 — Question 46
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Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Simple, Compound & Epicyclic Trains
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Question
In the gear train shown, gear 3 is carried on arm 5. Gear 3 meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and 4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4 rotates with an angular velocity of in the counterclockwise direction, the angular speed of arm 5 (in rpm) is
Correct answer
(C) 62.5 counterclockwise
Solution
Using the relative velocity method for epicyclic gear trains:
1.Let be the speed of arm 5 and be the speed of gear 2 relative to the arm.
2.Absolute speed of gear 2: (since gear 2 is fixed) .
3.Gear 2 and 3 mesh externally, while gear 3 and 4 mesh internally. The speed of gear 4 relative to the arm is: .
4.Absolute speed of gear 4: .
5.Substitute : .
6.Given counterclockwise (positive): .
7.Since is positive, the arm rotates in the same direction as gear 4, which is counterclockwise.
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