Dynamics Problem, Relative velocity of rigid body in planar motion

CaityAnn

http://wps.prenhall.com/wps/media/ob.../9e_16_43.html
That is the image of the problem, which includes a solution. PROBLEM- Besides being really confused on their work, the solution they give and the solution in the back of my book are both different! They said Wcd is 15.1 rad/s and my book says 4.03 rad/s, they have the same dimensions and everything.


heres what im doing, despire the crazy solution given.. Im just trying to get some sort of method and understanding of this stuff, Im taking this course in 5 weeks so its sort of a rush to get it all in..

I want to find Angular velocity of link CD at the instant shown

Vc=Vd+Vc/d ; Vc=Vd+(Wcd x Rcd) Vd wont be moving so it goes to zero
So Vc=(WcdxRcd) ((((So I must need to solve for Vc to get Wcd))))

Va= Vb+ Va/b; Va= Vb + (Wab x Rab), Va wont be moving so it goes to zero
Vb= (Wabx Rab), I can solve for this because I am given Wab and Rab, Vb=18 in/s

Vc=Vb+Vc/d; Vc=Vb+(WcdxRcd) Vc= 8 + (WcdxRcd)
So I just need to find Vc somehow.. On the solution given they do some insane trig that I just dont get, your input is much appreciated so thanks ahead..

AlephZero

I agree with your book's solution.

First suppose D is free to move, and write down the motion of points B C and D in terms of the angular velocities (positive anticlockwise)

Vb = (0, -18) in/sec
Vc = Vb + (8Wbc cos 30, -8 Wbc sin 30)
Vd = Vc + (4Wcd sin 45, 4 Wcd cos 45)

But Vd = 0 since it is pinned. So

8 Wbc cos 30 + 4 Wcd sin 45 = 0
-18 - 8 Wbc sin 30 + 4 Wcd cos 45 = 0

Eliminating Wcd (remembering sin 45 = cos 45) gives

-18 - 8 Wbc (sin 30 + cos 30) = 0
Wbc = -1.647 rad/s

And
Wcd = -2 Wbc cos 30/sin 45 = 4.034 rad/s

I didn't try to find what why this is different from the web page solution.