GATE 2017 ME (ME1) – Question 55
An epicyclic gear train has a fixed outer ring, a sun rotating counterclockwise at 100 rpm, and 50, 25 and 100 teeth on sun, planet and ring respectively. Find the magnitude ratio of planet angular velocity to carrier-arm angular velocity.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 3 to 3
Explanation
Willis’s relation gives $(\omega_s-\omega_c)/(\omega_r-\omega_c)=-N_r/N_s=-2$. With $\omega_r=0$ and $\omega_s=100$, this yields $\omega_c=100/3$ rpm. Sun–planet external meshing gives $\omega_p-\omega_c=-(N_s/N_p)(\omega_s-\omega_c)=-2(200/3)$, hence $\omega_p=-100$ rpm. The requested magnitude ratio is $100/(100/3)=3$.