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GATE 2020 ME (ME2) – Question 39

Theory of Machines · Gears and gear trains · 2 marks · Multiple choice

The sun S and planet P in the epicyclic gear train have identical tooth counts. If sun and outer ring R rotate in the same direction at angular speeds $\omega_S$ and $\omega_R$, find angular speed of arm AB.

Diagram for GATE 2020 ME (ME2) question 39
  1. $\frac34\omega_R+\frac14\omega_S$
  2. $\frac14\omega_R+\frac34\omega_S$
  3. $\frac12\omega_R-\frac12\omega_S$
  4. $\frac34\omega_R-\frac14\omega_S$

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Correct answer: (A) $\frac34\omega_R+\frac14\omega_S$

Explanation

Ring tooth count is Nr=Ns+2Np=3Ns. Willis relation is $(\omega_s-\omega_c)/(\omega_r-\omega_c)=-N_r/N_s=-3$. Solving gives **ωc=(ωs+3ωr)/4,A**. The signs account for the internal ring mesh.