This problem is slightly more involved than the other one due for Monday. Although you are asked to find the acceleration of C, you need to first solve the velocity equations. [In what follows, x is horizontal and y is vertical.]
- Consider first the mechanism made up of link OD and slider C.
- Attach an observer to link OD and write down the velocity equation relating O and C.
- At this point the omega of observer on OC is unknown (more on this later).
- The observer "sees" C moving along the slot (that is, (v_C)_rel has both x and y components aligned with the slot). The true motion of C is vertical (that is, v_C has only a j component).
- The omega of the bar AOD can be found by writing the rigid body velocity equation between O and A. In this equation you need to enforce that fact that the x-component of the velocity of A is v_B (edited). This will give you a numerical value for omega of the bar.
- Substitute the now-known omega for the bar into the moving reference velocity equation above. From that you can find (v_C)_rel as well as v_C.
Let us know if you have questions on this.
5 comments:
In the statement:
"In this equation you need to enforce that fact that the x-component of the velocity of A is v_A."
I believe you mean the x-component of the velocity of A is v_B.
Ooops...you are correct. I will edit the original post with that correction. Thanks.
I don't understand how to solve for alpha of bar AOD. Because v_B is constant, I know that there is no acceleration in that direction. To use the rigid-body acceleration equation, you need to know alpha or a_A. I think I need another equation, but I don't know what it is.
Write the acceleration of point A in terms of the acceleration of point O using the rigid body vector acceleration equation. (I added an image to the original post on this problem showing the details of this.) Once you enforce the fact that the horizontal component of acceleration of A is zero and separate out the vector equation into x- and y-components, you will have two scalar equations in terms of a_Ay and alpha_AOD. Therefore, you have two equations in terms of two unknowns. (Note that you can solve for alpha_AOD directly from the x-component equation.)
Let us know if this does not help.
Thank you for the help. I had set up my coordinate system differently, so that solution for alpha was not apparent.
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