# Calculate velocity of a mechanism

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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• Is it 0 or 0.66 for bd – Archis Welankar Dec 23 '15 at 14:15
• What do you mean? The shafts length? – privetDruzia Dec 23 '15 at 14:26
• Angular velocity – Archis Welankar Dec 23 '15 at 14:27
• this angular velocity is not given. But according to the answers it is 0 (for some mysterious reason) – privetDruzia Dec 23 '15 at 15:01
• I am talking about answer is it 0.6 for Ab so approx $0$ – Archis Welankar Dec 23 '15 at 15:21

Hint $\omega=\frac{v}{r}$ you can calculate $r$ by pythaogoras theorem for BD same for DE and no need of pythagoras theorem there
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 $$r_{AB}\omega_{AB}=r_{ED}\omega_{ED}\implies \omega_{ED}=\frac{r_{AB}}{r_{ED}}\omega_{AB}=\frac{150\text{mm}}{225\text{mm}}3\text{rad/s}=2\text{rad/s}$$