GATE 2022 ME (ME1) – Question 53

Theory of Machines · Gears and gear trains · 2 marks · Numerical answer

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).

the sun gear 1 at the centre O (0 rpm), the planet gear 2 (20 teeth) on the arm OP, and the ring gear 3 (80 teeth, 900 rpm ccw) around them.

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Correct answer: 600

Explanation

The three gears are concentric in mesh: $T_3 = T_1 + 2T_2$, so $T_1 = 80 - 40 = 40$. The train value between gear 3 and gear 1 (external-external then external-internal, so overall opposite in sign) is $\frac{\omega_3 - \omega_a}{\omega_1 - \omega_a} = -\frac{T_1}{T_3} = -0.5$. With $\omega_1 = 0$ and $\omega_3 = 900$: $\frac{900 - \omega_a}{-\omega_a} = -0.5$, so $900 - \omega_a = 0.5\omega_a$ and $\omega_a = 600$ rpm.