GATE ME 2017 Set 1 — Question 45
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Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Simple, Compound & Epicyclic Trains
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Question
In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at . Let the number of teeth on the sun, planet and outer gears be , , and , respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ______.
Correct answer
3 to 3
Solution
Let be the angular velocities of the sun, planet, outer ring, and carrier arm respectively.
Given: (fixed), (CCW), .Using the relative velocity method:
Relative to carrier, (since sun and ring rotate in opposite directions relative to carrier)Now for the planet gear relative to the sun gear:The ratio of magnitudes is:
Given: (fixed), (CCW), .Using the relative velocity method:
Relative to carrier, (since sun and ring rotate in opposite directions relative to carrier)Now for the planet gear relative to the sun gear:The ratio of magnitudes is:
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