Project ForgeA 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).
Explanation
Center-distance constraint (O to P equals both R1+R2 and R3−R2): T1=T3−2T2=80−40=40. Tabular method (arm fixed, sun +1 rev): planet turns −(T1/T2)=−2 rev; ring (internal mesh, same sign as planet) turns −2×(T2/T3)=−0.5 rev. So (ωR−ωA)/(ωS−ωA)=−T1/T3=−0.5. With ωS=0, ωR=900: (900−ωA)/(0−ωA)=−0.5 → 900−ωA=0.5ωA → ωA=600 rpm.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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