GATE ME 2024 Set 1 — Question 52
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Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Simple, Compound & Epicyclic Trains
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Question
The Levai type-A train illustrated in the figure has gears with module mm/tooth. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at 20 rev/min counter-clockwise. The magnitude of angular velocity of the arm is__________ rev/min. (rounded off to 2 decimal places)
Correct answer
15 to 16
Solution
1.Identify the gear train configuration: The Levai type-A is an epicyclic gear train where gear 2 is the sun gear, gear 3 is the planet gear, gear 4 is the internal ring gear, and 1 is the arm.
2.Determine the number of teeth on gear 4 (): For an internal gear meshing with a planet that meshes with a sun gear, the radii relationship is . Since , we have .
3.Speed Analysis using the Tabular Method:
- Let be the speed of the arm ().
- Let be the speed of gear 2 relative to the arm.
- Speed of Arm =
- Speed of Gear 2 () =
- Speed of Gear 4 () = (Note: Gear 2 and 4 rotate in opposite directions relative to the arm because gear 3 acts as an idler between an external and an internal mesh).
- Gear 2 is fixed: .
- Gear 4 rotates at 20 rpm CCW: .
- rev/min.
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