I know someone can figure this out: Crane Angle Solving!!!

[walshy723]

Hello All,
I've been perplexed with this one for a few days now: I've attached a sketch of the problem I'm trying to solve. I'm trying to write a formula to that determines angle A as jib and counterweights rotate. Length B is the connecting strut and the dimension is fixed. I'm sure this is probably super simple but I'm having a bear of a time trying to figure out this relationship. It kind of reminds me of a locomotive wheel coupling rod...Any help would be greatly appreciated! Thanks so much.

Regards,
Ryan

 

[tmoria]

If I'm understanding correctly then the law of cosines is probably what you are after

\(\displaystyle CosA=\dfrac{b^2+c^2-a^2}{2bc}\)

In your diagram you have \(\displaystyle b=\dfrac{11869}{32}\) " \(\displaystyle \ \ \ \ and\ \ \ \ c=\dfrac{741}{8}\) "

This gives you \(\displaystyle \ \ \ \ CosA=\dfrac{149658457-1024a^2}{70359432}\)

i.e. the angle \(\displaystyle A\) is determined by length \(\displaystyle a\) and vice versa

 

[walshy723]

RE

Thanks, that helps find A, but is there a formula that can be derived for A as the counterweight angle and job angle move together? For example as the jib angle increases and counterweight angle decreases, what is the formula to determine A or what is the relationship between the two angles. I'm looking to write a formula for the counterweight angle. I know by the data sheet that @ a jib angle of 47 degrees the counterweight angle is 39 degrees and the strut dimension is fixed. I can't figure out how to maintain that ratio over the arc?

The formula that I would like to write would be:
Also attached is a load chart to illustrate this.

Jib angle= 47 degrees
Counterweight angle= () so whatever is input for the jib angle, the formula returns the proper counter weight angle.

Sorry for any headaches.

Thanks for the help.
Regards,

 

[girodd]

one problem here is that the counterweight angle corresponding to a given "jib angle" is not independent of the positions of the centers of the two circles in your attached pdf. I can't tell from the crane drawing whether the two circle centers lie on the same horizontal axis for instance.