GATE ME 2022 Set 1 — Question 53

NAT+2 / -0MediumSimple, Compound & Epicyclic TrainsCams, Gears & Gear TrainsTheory of Machines & Vibrations

Theory of Machines & Vibrations → Cams, Gears & Gear Trains → Simple, Compound & Epicyclic Trains

Last updated 5 September 2026

Question

A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3 has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter clockwise (ccw), the magnitude of angular velocity of arm OP is__________rpm (in integer).

T_1

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T_1

Component	Arm OP	Gear 1	Gear 2	Gear 3
Arm fixed, Gear 1 rotates $+x$	0	$+x$	$-x(T_1/T_2)$	$-x(T_1/T_3)$
Add arm rotation $y$	$y$	$y+x$	$y-x(T_1/T_2)$	$y-x(T_1/T_3)$

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