GATE ME 2014 Set 3 — Question 21
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Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Simple, Compound & Epicyclic Trains
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Question
Gear 2 rotates at 1200 rpm in counter clockwise direction and engages with Gear 3. Gear 3 and Gear 4 are mounted on the same shaft. Gear 5 engages with Gear 4. The numbers of teeth on Gears 2, 3, 4 and 5 are 20, 40, 15 and 30, respectively. The angular speed of Gear 5 is
Correct answer
(A) 300 rpm counterclockwise
Solution
Given data:
Angular speed of Gear 2, rpm (counterclockwise)
Number of teeth on Gear 2,
Number of teeth on Gear 3,
Number of teeth on Gear 4,
Number of teeth on Gear 5, Step 1: Calculate the speed and direction of Gear 3.
Gear 2 and Gear 3 are meshing. The speed ratio is inversely proportional to the number of teeth:
Since Gear 2 rotates counterclockwise, Gear 3 will rotate in the opposite direction, i.e., clockwise.Step 2: Determine the speed and direction of Gear 4.
Gear 3 and Gear 4 are mounted on the same shaft. Therefore, they have the same angular speed and direction:
Gear 4 rotates clockwise.Step 3: Calculate the speed and direction of Gear 5.
Gear 4 and Gear 5 are meshing. The speed ratio is:
Since Gear 4 rotates clockwise, Gear 5 will rotate in the opposite direction, i.e., counterclockwise.Thus, the angular speed of Gear 5 is 300 rpm counterclockwise.The final answer is
Angular speed of Gear 2, rpm (counterclockwise)
Number of teeth on Gear 2,
Number of teeth on Gear 3,
Number of teeth on Gear 4,
Number of teeth on Gear 5, Step 1: Calculate the speed and direction of Gear 3.
Gear 2 and Gear 3 are meshing. The speed ratio is inversely proportional to the number of teeth:
Since Gear 2 rotates counterclockwise, Gear 3 will rotate in the opposite direction, i.e., clockwise.Step 2: Determine the speed and direction of Gear 4.
Gear 3 and Gear 4 are mounted on the same shaft. Therefore, they have the same angular speed and direction:
Gear 4 rotates clockwise.Step 3: Calculate the speed and direction of Gear 5.
Gear 4 and Gear 5 are meshing. The speed ratio is:
Since Gear 4 rotates clockwise, Gear 5 will rotate in the opposite direction, i.e., counterclockwise.Thus, the angular speed of Gear 5 is 300 rpm counterclockwise.The final answer is
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