GATE 2019 ME (ME2) – Question 49
The shown four-bar has $O_2O_4=O_2A=L$ and $AB=O_4B=\sqrt2L$. Input link 2 rotates anticlockwise at constant $\omega_2$. At the instant it makes 90° with $O_2O_4$, find output/input angular-speed magnitude ratio $\omega_4/\omega_2$, to two decimal places.
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Correct answer: .78 to .80
Explanation
Set L = 1, $O_2=(0,0)$, $O_4=(1,0)$ and A = (0,1). The shown intersection of the radius-√2 circles gives B = (b,b), $b=(1+\sqrt3)/2$. Velocities are $v_A=(-\omega_2,0)$ and $v_B=\omega_4(-b,b-1)$. Rigid AB requires $(v_B-v_A)\cdot(B-A)=0$, giving $\omega_4/\omega_2=b/[b^2-(b-1)^2]=0.788675$. **0.79**.