Hi!

I'm trying to complete a static force analysis on the bar linkage shown below. The goal is to find the payload mass in terms of the cylinder forces and everything else in a static environment.

To simplify things I've made the assumption that the mass of the payload in the bucket acts at the centre of mass of the bucket. Also, the bucket cylinder is attached to the boom, and the boom is attached to an anchor point.

From what I understand, to do the static force analysis, you freeze everything in place, and then calculate the force and torque that each link must exert on each other for it to hold that position.

My attempt at the problem has been to break the linkage apart and try to work my way through each component and write down the forces and moments acting on them. For example, the bucket has a force from the boom, a force from the bucket link, and a force downwards from payload mass.

Then, I've tried to do the next component like the bucket link, and repeat the process. My attempt for the bucket and bucket link are below in the photo.

However, I'm terrible at this, so would anyone be able to help me? To reiterate, my end goal is to get an expression for the payload mass in the bucket, in terms of cylinder forces and everything else. I'm thinking the best way would be to take a sum of the torques around the boom pivot point, but I'm not really sure how to get there.

Many thanks in advance.