smooth pins link the mechanism. when in the shown position, the angular velocity
ID: 1862401 • Letter: S
Question
smooth pins link the mechanism. when in the shown position, the angular velocity and angular acceleration of AB is 10 rad/s and 20 rad/s^2 clockwise. Find the angular velocities of BC and CD. Also find the angular acceleration of CD. I do not think what i did was right because i think i messed up the horizontal and vertical componants equation and math. Please give me a silution and I will rate.
Explanation / Answer
assume a x-axis along BA and y-axis along AC,
I will use vectors to solve this....
first, I will conduct the velocity anaysis,
vB= 2*10j=20j (i,j,k are the unit components of axes)
vC= vi (v is the unknown velocity and it is directed along i)
rCB= 2i + 3j
wCB= wk (w is the unknown angular velocity of CB)
Now,
vC=vB+ wCB*rCB (* is the cross-product)
Substitute,
vi= 20j+ wk*(2i+3j)
vi= 20j+ w(2j-3i)
vi= -3wi+(2w+20)j
Equating parts of i and j on both sides,
2w+20=0
w=-10 rad/s
v=-3w= 30 ft/s
Hence, you get the angular velocity....
Similarly,
aB= 10^2 * 2i+ 20*2j= 200i+ 40j
aC= ai
fCB= fk (f is the angular accelaration)
Substitute all these in the acceleration equation and separate the i and j parts to obtain the solution exactly as done above....In case of any doubts do comment, I will reply asap..
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