A, B, and C are relative depending on what you are working on.
No need in reinventing the formulas.
Look up law of cosines......and see if you can understand that......because if you can....you are 90% there.
If you cannot, there is no point in me writing out the formula....because law of cosines is basically it.
All law of cosines is doing is allowing you to find the effective angle of the cylinder.
It seems you understand that there are 3 points. Base of the cylinder, rod of the cylinder, and the pivot point of whatever the cylinder is moving. In this thread it happens to be the pivot of the
grapple lid.
Since the
grapple lid is moving, the line drawn between its pivot and the rod end is the line you want to find the angle of the cylinder in relationship to.
Law of cosines formula allows you to find that angle when the only "known" measurements is the lengths of the 3 points.
Once you know the angle.....it gets simple. Formula for a cylinders force on an angle is the force times the sin of that angle. I "think" you understand that.
Now it simply becomes about leverage. Because that force that was just calculated using the sin of the angle....that force is rarely applied where the work is happening. Like on a loader....who cares how much lift force there is where the cylinder is attached. Same with
grapple. Dont care about where the cylinder is connected, rather out at the teeth.
But you can eliminate the law of cosines if you are in physical possession of whatever you are wanting to figure, as well as a $4 angle finder and a straight edge. Something I dont have the luxury of when helping someone online, thus I ask for those three measurements and I can figure the angle pretty simply.
If you want, send me a pic of the tree spade and some measurements, but dont be afraid to try to solve it yourself. If you get stuck, just ask.