| Problem statement Solution video |
DISCUSSION THREAD
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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/D - ωDE2rE/D
What should we leave the answer in terms of? I'm assuming it wants it in terms of omega_OA and L, right?
Yes, in terms of L and omega_OA.
Am I correct in finding that AB and DE are in pure translation?
Yes!
When calcuating the speed of Ve, we do not need to inlcude a direction do we?
It would be a good idea to include the direction along with the speed.
Am I correct in thinking alphaBC is 0?
It would be dangerous to assume that. Let your math tell you if it is true.
When finding omega_BC I solve it in relation to omega_OA but I am having issues determining the sign. Does the sign not matter if I say what direction it is turning? If not do I solve Va as Va = - omega_0A * r_OA or is there no negative because the value of omega_OA is negative because of the right-hand rule?