Calculate velocity of a mechanism

Question

I have tried many times to solve this problem in different ways but with nos success: The angular velocity of the shaft AB is 3rad/s counterclockwise. Calculate the velocity of the shafts BD and DE.

Could someone please show me how it should be done?

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expected answers: 0 rad/s, 2 rad/s

Answer 1

Hint $\omega=\frac{v}{r}$ you can calculate $r$ by pythaogoras theorem for BD same for DE and no need of pythagoras theorem there

Answer 2

In the given position, the velocity of $B$ and $D$ are vertical, the first one tangent to the circle of center $A$ and passing though $B$, the second tangent to the circle of center $E$ and passing through $D$.

The center of rotation of $BD$ is at the intersection of the lines perpendicular to this two velocities, but being the velocities parallel, also the two perpendicular lines are parallel, so there is no intersection, and this mean that $BD$ does not rotate, but translate, so its angular velocity is $0\text{rad/s}$ and $v_B=v_D$.

Furthermore, given that $v_B=r_{AB}\omega_{AB}$ and $v_D=r_{ED}\omega_{ED}$, then $$ r_{AB}\omega_{AB}=r_{ED}\omega_{ED}\implies \omega_{ED}=\frac{r_{AB}}{r_{ED}}\omega_{AB}=\frac{150\text{mm}}{225\text{mm}}3\text{rad/s}=2\text{rad/s} $$