Homework H2.I - Fa22

Problem statement
Solution video

NOTE: At time marker 13:58 on the solution video for this problem, a sign error was made in writing down the y-component of the position vector rE/D. Below shows the needed subsequent corrections in the solution due to this sign error.


DISCUSSION THREAD

We encourage you to interact with your colleagues here in conversations about this homework problem.


Before starting this problem, make note of the type of motion for each component in the mechanism:

  • Links OA and BC are in pure rotation about their centers of rotation O and C, respectively. From this, we know that the paths of points A, B and C are circular, as seen in the animation below.
  • Block E is in pure translation.
  • Links AB and DE have both translational and rotation components of motion.

Question: What are the locations of the instant centers (ICs) of AB and DE at this instant? Reflect back on the observations above in answering this. What do these locations say about the angular velocities of AB and DE at this position?

HINTS:
Once you have found the angular velocities for all of the links, you can then tackle the acceleration analysis.

  • For finding the angular acceleration of links AB and BC, use the following rigid body acceleration equations:
    aA = aO + αOA x rA/O - ωOA2rA/O
    aB = aC + αBC x rB/C - ωBC2rB/C
    aB = aA + αAB x rB/A - ωAB2rB/A
    This will give you the equations that you need to solve for the desired angular accelerations.
  • Repeat the above for link DE to determine its angular acceleration:
    aD = aC + αBC x rD/C - ωBC2rD/C
    aE = aD + αDE x rE/O - ωDE2rE/O

2 thoughts on “Homework H2.I - Fa22”

  1. In the solution video for part b final part, r(E/D) is written as (sqrt(8)Li + Lj) but I think it should be (sqrt(8)Li - Lj) because point E is below point D, and so block E is speeding up (also consistent with the simulation). Am I missing something or is there an error in the solution?

    1. KENNETH: Yes, there was a sign error in writing down that position vector, with this error leading to an incorrect conclusion regarding the rate of change of speed for slider E. It was good of you to check the solution vs. the animation provided regarding the slowing down/speeding up of slider E.

      Thanks for pointing out this error. I hope to re-record the solution video over the next few days.

Leave a Reply