Subtopic: Design and selection of machine elements – gears, pulleys, chains and sprockets and belts
Question Statement:
In an epicyclic gear train, an arm carries two wheels A and B having 24 teeth and 30 teeth respectively. If the arm rotates at 100 rpm in the clockwise direction about the centre of the wheel A which is fixed, then the speed of wheel B on its own axis is
Options:
(A) 20 rpm, anti-clockwise
(B) 25 rpm, anti-clockwise
(C) 180 rpm, clockwise
(D) 225 rpm, clockwise
Official Answer Key:
C
Step-by-Step Solution & Explanation
Tabular method: let arm speed = +100 (CW, taken positive). With arm held stationary, let gear A turn +x; gear B then turns −x(T_A/T_B) = −x(24/30). Adding the arm's own +100 to every element: A's absolute speed = x+100 = 0 (A is fixed) → x = −100. B's absolute speed = −x(24/30)+100 = 80+100 = 180 rpm, in the same (clockwise) sense as the arm.
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