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).
Answer :
Correct answer is : 600
T1 = ?, T2 = 20, T3 = 80
N3 = 900 rpm (ccw), N1 = 0 rpm (fixed)
Since the module of all mating gears is always the same, hence radius can be expressed as:
r3 = r1 + 2r2
⇒ T3 = T1 + 2T2
T1 = 80 - 40 = 40 teeth
According to the tabular method:
| Motions | Arm | Gear 1 (40) |
Gear 2 (20) |
Gear 3 (80) |
| Arm fixed, gear1 rotate +x revolutions |
0 | + x | ||
| Arm effect is considered |
y | y + x | y - 2x | y - (x/2) |
It is given that:
N1 = 0 ⇒ y + x = 0
N3 = 900 rpm ⇒ y - (x/2) = 900
on solving we get,
3y/2 = 900 ⇒ y = 600 rpm
x = - 600 rpm
Speed of arm OP = y (from table)
Speed of arm is 600 rpm counter - clockwise.
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