Project ForgeTheory of Machines
Kinematics of Mechanisms
GATE 2020
Expert
The sun (S) and the planet (P) of an epicyclic gear train have identical numbers of teeth. If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed ωS and ωR respectively, then the angular speed of the arm AB is
- (3/4)ωR + (1/4)ωS
- B(1/4)ωR + (3/4)ωS
- C(1/2)ωR − (1/2)ωS
- D(3/4)ωR − (1/4)ωS
Explanation
With identical sun/planet teeth (Ts=Tp=T), the ring has Tr=Ts+2Tp=3T. The standard epicyclic relation is (ωS−ωarm)/(ωR−ωarm) = −Tr/Ts = −3. Solving: ωS−ωarm=−3ωR+3ωarm → ωS+3ωR=4ωarm → ωarm=(1/4)ωS+(3/4)ωR — option (A).
Source: GATE ME 2020 Session 2 (ME-2) (2020)
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