Planar Kinematics: Determine Angular Velocity of Plate BCD

[aolse9]

Homework Statement

The link AB has an angular velocity of 7.6 rad/s in the direction shown.

http://hdimage.org/images/mg122xouxwua5jzgn110.jpg
Determine the angular velocity of plate BCD if the angles are as shown and AB = 58mm and BD = 111mm.

Homework Equations

V_B = V_A + V_B/A

V_D = V_E + V_D/E

V_B/D = V_B - V_D

The Attempt at a Solution

I have made one long thought out attempt at this problem. Basically, I used the above equations, canceling out the velocity of the fixed points. Then by converting the velocities, to i and j components, I got two equations with 3 unknowns, 1. the angular velocity of BCD, 2. the angular velocity of BD and 3. the length BD. By simply counting the angular velocity of BD and the length BD as one unknown, I have 2 unknowns and two equations. My answer was 1.641 rad/s [clockwise]. But this answer is incorrect, any help would be greatly appreciated.

 

[aolse9]

Solved! The answer is +1.641.

 

[Mene]

Thank you for sharing your attempt at solving this problem. It seems like you have approached it correctly by using the equations VB = VA + VB/A and VD = VE + VD/E. However, it is important to note that the velocities of B and D are not independent of each other. They are connected through the link BD and will have a common angular velocity.

To solve for the angular velocity of BCD, you can use the equation VB/D = VB - VD and substitute in the values you have for VB, VD, and BD. This will give you one equation with one unknown, the angular velocity of BCD. You can then solve for it using basic algebraic manipulation.

Alternatively, you can also use the concept of relative velocity to solve this problem. The velocity of BCD is the sum of the velocities of B and CD, where CD is the velocity of point D relative to point B. You can use the equation VB/D = VB + VD/B to solve for the velocity of CD, and then use the equation VD = CD + VD/B to solve for the angular velocity of BCD.

I hope this helps and clarifies any confusion you may have had in solving this problem. Keep up the good work in your studies of planar kinematics!