For this set of problems should we still use the given find format?
In my opinion, I believe the answer to your question would be yes. Each given diagram is asking for the instant center(IC) of different links. For example, the first diagram asks for the IC of link AB whereas the second diagram asks for the IC of link AD. The format will take a little bit longer to write and in turn you don't lose detail from the instructions.
1
The problem statement doesn't have a given and find like it normally does so I would actually think we don't need to include it. Probably best to just include it or wait for the instructor's comment though.
Please include a Given and Find. You can make those short.
For Mechanism No. 4 are we to take the points the rack meets with the gears to be the place the velocity acts? And therefore, the the lines drawn to find the IC would be directly on top of one another? Then this would mean that the IC would be infinite?
Having an IC that is at infinity says that the perpendiculars to the velocities at the two points cross only at infinity.
What you describe above (having the perpendiculars existing on top of one another) means that they intersect everywhere along that line. Therefore, the IC exists somewhere on that line, not at infinity.
Here, you then need to use an additional idea that we have learned from ICs; the speed of a point on the rigid body is proportional to the distance from that point to the IC. You know the velocity at those two points (where the gear is in contact with the racks). At what point along the line connecting those two points are these two speeds proportional to the distance from the contact points? Find that point, and you have found the IC for the gear.
1
How do we start to find the velocities for the 4th mechanism? Do we draw the lines perpendicular to velocities A and B?
How do you find the Vd for mechanism 2?
I am also struggling with this, it's difficult to visualize the motion of this system.
To find the Vd for mechanism 2, I first looked at link BD. Because point B is fixed, we know that point D is going to move tangentially in a circular motion around center B. From there, we only need to determine the direction of motion. Looking at the motion from the string and pully, we know that point C and A are being pulled downward, which is thus pulling link AD downwards. Additionally, because we know that this device is pinned at point O, it will have to rotate in a circle around point O. And because this motion is originally downward, it's going to have a tendency to go left, which would then push link AD to the left as well. So, we then know that Vd will follow this motion and go towards the left. I hope this helps.
Please keep in mind that finding the location of the IC for link AD is key to answering the questions about the directions of rotation. Once you know that location, the directions of rotation fall into place.
wheres the problem statement
I just updated the HW. I apologize for the delay.
For this set of problems should we still use the given find format?
In my opinion, I believe the answer to your question would be yes. Each given diagram is asking for the instant center(IC) of different links. For example, the first diagram asks for the IC of link AB whereas the second diagram asks for the IC of link AD. The format will take a little bit longer to write and in turn you don't lose detail from the instructions.
The problem statement doesn't have a given and find like it normally does so I would actually think we don't need to include it. Probably best to just include it or wait for the instructor's comment though.
Please include a Given and Find. You can make those short.
For Mechanism No. 4 are we to take the points the rack meets with the gears to be the place the velocity acts? And therefore, the the lines drawn to find the IC would be directly on top of one another? Then this would mean that the IC would be infinite?
Having an IC that is at infinity says that the perpendiculars to the velocities at the two points cross only at infinity.
What you describe above (having the perpendiculars existing on top of one another) means that they intersect everywhere along that line. Therefore, the IC exists somewhere on that line, not at infinity.
Here, you then need to use an additional idea that we have learned from ICs; the speed of a point on the rigid body is proportional to the distance from that point to the IC. You know the velocity at those two points (where the gear is in contact with the racks). At what point along the line connecting those two points are these two speeds proportional to the distance from the contact points? Find that point, and you have found the IC for the gear.
How do we start to find the velocities for the 4th mechanism? Do we draw the lines perpendicular to velocities A and B?
How do you find the Vd for mechanism 2?
I am also struggling with this, it's difficult to visualize the motion of this system.
To find the Vd for mechanism 2, I first looked at link BD. Because point B is fixed, we know that point D is going to move tangentially in a circular motion around center B. From there, we only need to determine the direction of motion. Looking at the motion from the string and pully, we know that point C and A are being pulled downward, which is thus pulling link AD downwards. Additionally, because we know that this device is pinned at point O, it will have to rotate in a circle around point O. And because this motion is originally downward, it's going to have a tendency to go left, which would then push link AD to the left as well. So, we then know that Vd will follow this motion and go towards the left. I hope this helps.
Please keep in mind that finding the location of the IC for link AD is key to answering the questions about the directions of rotation. Once you know that location, the directions of rotation fall into place.