Suggestions:
This problem is asking for us to determine acceleration information on points A and B. Before doing so, you should first focus on the mechanism shown above in red corresponding to pins O, C, D and E. Then tackle the acceleration of A with respect to B.
- Write down the rigid body velocity equations for links OC, CD and DE.
- Solve these equations for the unknowns of omega_OC and omega_CD (similar to how you solved Problem 5/76) for the given omega_DE.
- Write down the rigid body acceleration equations for links OC, CD an DE.
- Solve these equations for the unknowns of alpha_OC and alpha_CD for the given alpha_DE.
- Now you can write down: a_A/B = alpha_AB x r_A/B - omega_AB^2*r_A/B . Note that alpha_AB = alpha_OC since OC and AB are parts of the same rigid body.
8 comments:
Would omega_AB = omega_OC as well then? I'm assuming this would be true in order to reach my final answer.
-Jeff Wojcicki
That's a correct assumption. Any points on a rigid body have the same angular velocity or acceleration.
i agree.
can we say V_E = 0?
Yes, link DE is pinned to ground at E. (This is not very clear from the figure.) Therefore, v_E = 0.
For unknown angular velocities,do we always assume K direction as positive (ccw)?
Good question.
You can start out any unknown angular velocity vector as either "+" or "-". For example, you can write EITHER omega = +omega*k (assuming CCW) OR omega = -omega*k (assuming CW). The math will take care of signs so long as you are consistent all the way through your work. A positive answer means that you guessed correctly at the start; a negative answer means that you guess incorrectly, and is was rotating the opposite of what you assumed.
To make it easy, I suggest that you always assume "+" at the start and stick with that all the way through. That way, if you get a positive answer, it means CCW rotation, an if you get a negative answer, it means CW. Just a suggestion.
All of the above also applies to angular accelerations.
Thanks for asking this very important question.
thanks for answering it!
-steve
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