Mechanics Question: Solve for Theta & L

[oli543]

Hi, I was wondering if I could have a bit of guidance with this question (if you can understand my drawing of it!)

http://img222.imageshack.us/img222/376/scan1md.jpg"

It is basically a representation of the main hydraulic ram and boom assembly for a telescopic handler, similar to this:

http://www.jcb-store.com/BidZone/newImages/HPIM0365(1).JPG"

Theta = angle of boom from the vertical
Phi = angle of cylinder from the horizontal
F = Force from the cylinder piston
m1g = Mass of the boom x gravitational constant
m2g = Mass of load x gravitational constant
b = Total length of boom
c = Length of cylinder
L = Extension of piston from cylinder
d = distance from boom pivot to boom/cylinder connection pivot

The magnitudes of F, m1g, m2g, b, c, d are all constant

Theta, Phi, and L can all vary

When time, t = 0, L=0, theta dot=0, phi dot=0

Basically I need to calculate the values of theta and L at time t.

My working so far (probably gone completely down the wrong path!):

Taking moments about A (the boom pivot point)

(d x F x sin phi) - (1/2b x m1g x sin theta) + (b x m2g x sin theta) = (d x (m1+m2) x "theta double dot")

That's about as far as I can get, and I'm not even sure if that's correct. If anyone can even give me a hint as to how to start this question, that'd be a great help. If any more information/a better diagram is needed, just ask.

Thanks a lot for your help, your all absolute stars

 

[Cyrus]

This is really nasty because I can find no way to relate phi and thata easily to get rid of one of the variables. It would have helped greatly if one pin was directly below the other, but they are not. :-(

 

[oli543]

Thanks a lot mate, if we presume that the pivot point of the boom is at point (0,y1) and the pivot point of the cylinder is at point (x1,0), then the relationship between theta and phi is:

phi = inv.tan (-(dcostheta + y1)/(x1 - dsintheta))

Which can be easily substituted into the left hand side of the equation that I posted at the bottom of my post above.

I'm unsure however about the right hand side of the equation, because it's not taking into account the positions on the boom of the mass of the boom, and the load.

Any help/thoughts would be greatly appreciated.