Seemingly simple kinematics exercise

1. May 18, 2013

dunn

1. The problem statement, all variables and given/known data
Rigid body
The plane rigid body ABCD shown in the figure has rectangular shape and
slides along the orthogonal runners X, Y. The points A and B are always in
contact with the ranners.
Data: ω=3 rad/s (angular velocity counterclockwise); $\Theta$=30°; AB=CD=1m;
Determine:
The A and C velocities;
The position of instantaneous rotation center;
The value of $\Theta$ for which the horizontal velocity component of D is null.

2. Relevant equations

Fundamental geometric identities

3. The attempt at a solution

Without knowing the center of rotation or the relevant velocities a priori I don't know how one can be solved for the other. So really, I can't make it past the first step.

The instructor gave us this solution which to me makes no sense.

He claims that Va = Va/b + Vb

and that Va/b = ω*AB

But this makes no sense since it assumes the center of rotation is at point B, or else Va/b wouldn't be given as the product of ω times the length of segment AB.

Am I missing something or did the instructor forget to inform us that ω refers to point B?

Last edited: May 18, 2013
2. May 18, 2013

CWatters

I may not get chance to come back to this for a few days and I'm not even 100% sure but...

Lets call the instantaneous center of rotation point O. I believe the walls must be tangential/right angles to OB and OA.

3. May 18, 2013

dunn

Here's the (sloppy) solution as given to us. Does this make any sense?

Attached Files:

• sheet1_1.pdf
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4. May 18, 2013

dunn

Hrm, I was completely overlooking the fact that in rigid bodies and angular velocity and angular acceleration are independent of the reference point of the body.

It makes sense now.