Allied & ICAR Exam Bank • ALLIED_1100NAT • 2 Marks
Section 2: Farm Machinery
Machine Design
Subtopic: Epicyclic Gear Trains
Question Statement:
In a planetary gear set with sun gear $S$ having 24 teeth and annular ring gear $A$ having 72 teeth, the arm $C$ carries planet gears $P$. If the ring gear is fixed and the sun gear rotates at 120 rpm, the rotational speed of the arm $C$ in rpm is:
Answer Key:
30
Step-by-Step Solution & Explanation
Speed ratio formula with fixed ring gear: $\frac{N_S - N_C}{N_A - N_C} = -\frac{T_A}{T_S}$. Since $N_A = 0$: $\frac{120 - N_C}{-N_C} = -\frac{72}{24} = -3 \implies 120 - N_C = 3 N_C \implies 4 N_C = 120 \implies N_C = 30\text{ rpm}$.