Solving AC Movement with Shafts A & B: Find P & Vc

[Femme_physics]

Homework Statement

http://img34.imageshack.us/img34/9415/rock1x.jpg

Shaft's AC movement is regulated by runways A and B. The angular velocity of the shaft is 3 rad/sec, counterclockwise. When angle psi = 40 degrees. Calculate:

A) The velocities of pistons A and B (Va, Vb)
B) The velocity of point C (Vc) - magnitude and direction towards the horizontal axis.

The Attempt at a Solution

My problem is finding P - the instantaneous axis of rotation. I picked this:

http://img600.imageshack.us/img600/5510/getppppppppppppp.jpg Picking it, I got the correct Va, the correct Vb, and the correct Vc. (I'm still working on the angle of Vc to the horizontal axis - so far it's not correct but maybe I'm doing something obviously wrong.)

And the solution manual picked that:

http://img835.imageshack.us/img835/3412/pppppppppppppp.jpg

Are they both correct?

 

[Quinzio]

There is a very straightforward way to relate Vc to Va and Vb.
The book solutions are correct but they're complicated

 

[I like Serena]

The instantaneous axis is the center of movement.
This means that all points of the body make a circular motion around this axis.

In your case you know the direction of the speed at 2 points.
Are they making a circular motion around your P?

 

[Femme_physics]

Well I just want to know how come P is in the opposite direction to my P? It's pretty easy to solve this the way the manual did actually. You just find the distance from point B to P and the distance from point A to P and the distance from point C to P and do angular velocity times this distance and you get the answer. Finding the angle of C is a bit more tricky, but I first of all want to know if I got the correct P because it gives me the same result as they...

Edit: Nevermind, I get it. It depends on the direction of the rotation! :)

 

[I like Serena]

Edit: Nevermind, I get it. It depends on the direction of the rotation! :)

Hmm, I would have worded it differently.

I'd have said that any speed vector must be perpendicular...

 

[Femme_physics]

Fair enough, but if my P is where the solution manual says, then I get opposite results for Va and Vb to what the manual says I should get!

http://img560.imageshack.us/img560/739/usingthisp.jpg

 

[I like Serena]

Fair enough, but if my P is where the solution manual says, then I get opposite results for Va and Vb to what the manual says I should get!

Perhaps if you switched the letters A and B around?

You might say of course that you're not allowed to do that.
But then, if I look at the original problem, it seems to me that they did exactly that!

 

[Femme_physics]

*an embarrassing look*

Oh.

*slaps forehead*

Ouch.
I really got to stop doing that...

Thanks ILS :) Problema el solva (I have no idea if what I wrote is lingually correct)...

 

[I like Serena]

*slaps forehead*

Ouch.
I really got to stop doing that...

What? The switching around of letters and similar stuff?
Or the slapping?

You can slap me if you want!

Thanks ILS :) Problema el solva (I have no idea if what I wrote is lingually correct)...

If it is or not, it sounds nice!

 

[Femme_physics]

Actually, still one problem. Finding the angle of Vc to the horizontal axis. I get 61.4 but the manual gets 59.21... I feel it's too much to chalk it up to "rounding errors".http://img64.imageshack.us/img64/5067/angllllllllllllles.jpg

Uploaded with ImageShack.us

What? The switching around of letters and similar stuff?
Or the slapping?

Both!

You can slap me if you want!

Slap you? But why?!? I can't. I'm too gentle and soft. And you're too harmless. Well, maybe a little. *soft slap*... *little less of a soft slap*...

*slaps!*
*SLAPS!*
*THUMPS!*
*MONSTER THUMP!*

Woah, sorry, lost control :shy::shy:

Told you I'm a fast learner and adapter. ^^

 

[I like Serena]

Actually, still one problem. Finding the angle of Vc to the horizontal axis. I get 61.4 but the manual gets 59.21... I feel it's too much to chalk it up to "rounding errors".

Yes dear madam, it is too much for rounding errors. ;)

How did you get the angle of 28.5 degrees?

Both!

Aha, now I understand the head band.
It is both to protect your forehead from the slap, and to hide the bruises under it!

Slap you? But why?!? I can't. I'm too gentle and soft. And you're too harmless. Well, maybe a little. *soft slap*... *little less of a soft slap*...

*slaps!*
*SLAPS!*
*THUMPS!*
*MONSTER THUMP!*

Woah, sorry, lost control :shy::shy:

Told you I'm a fast learner and adapter. ^^

aw, aw, aw, aw, Aw, Aw, AW, AWW, AWWWW, AIEEEH!

More please :shy::shy::!)

 

[Femme_physics]

Yes dear madam, it is too much for rounding errors. ;)

How did you get the angle of 28.5 degrees?

Law of sines.

BP/sin(beta) = CP/sin(130)

When I know that CP = 641.45
And BP = 306.4

 

[I like Serena]

Law of sines.

BP/sin(beta) = CP/sin(130)

When I know that CP = 641.45
And BP = 306.4

All right, so how did you get BP and CP?

EDIT: Did you perhaps take BP from the drawing where you switched the letters A and B around?

EDIT2: You wrote in your problem that the angle is "psi", but actually that is "phi".

$\phi$ or $\varphi$ is phi​

and $\psi$ is psi​

 

[Femme_physics]

I most certainly did not switch A and B ar...no wait...wait...I most certainly did!
Your corrections are all correct-- as always. All solved ;)

thanks!