I worked through this problem and got an incorrect answer. I've gone over my approach and I do not see what I am doing wrong. Here is what I did:
1. I used the ridged body velocity equation from O to A to find the velocity at A.
2. I saw that I would need the position of C to A and C to B, so I found the angle link BC makes with the vertical axis.
I found this by starting with the position of O to A, 100cos30i+100sin30j. Then I added on 300j. Then I took the inverse tangent of the i component over j component to find
the angle.
3. I used the relative velocity equation from C to A to find the angular velocity of link CB.
For the relative velocity component I used the angle I found in step 2. so Vrel(sin(angle)i+cos(angle)j)
4. Last I used the ridge body velocity equation from C to B to find the velocity of B
I would appreciate any suggestions.
6 comments:
Emily,
I may not be accurately following your step 2, but you may want to revisit it to ensure that you are computing the angle correctly. Provided the 'relative velocity' equation you are referring to in step 3 is the one corresponding to a rotating reference frame, the rest of your steps essentially match mine.
I followed the step 2 to get an angle of about 76 degrees. I am confused on how to put step 3 together though. What is the relative velocity equation from c to a. Is it v(a)= v(c) +(v(a/c))rel + omega(ac)k X r(ac). Which turns into v(a)= y(dot)*cos76i+ y(dot)*sin76j-.361omega(ac)i?
me boiler:
I got an angle of 14 degrees but that's just because I used the opposite side of the link.
For my relative velocity equation I'm using:
v(a)= v(c) +(v(a/c))rel + omega(bc)k X r(ac)
So expanding that gives me:
v(a)= (v(a/c))rel*cos76i+ (v(a/c))rel*sin76j-(300+100sin(30))omega(bc)i+100cos(30)omega(bc)j
Your equation didn't contain a the j component that comes from the cross product of the angular velocity and the position.
When I solved that equation for omega(bc) I got 3 rad/s. I've tried to find omega(ab) in a few different ways and I keep getting 3 rad/s. Is that even correct?
I started to problem over and got the correct answer using the same approach. I still don't know where I went wrong the first time through. Thanks for the suggestions though!
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