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"I want to be able to hold the arm in place against the force of gravity... Both arms can rotate in any direction around their respective attachment points." Your system is unstable, which is caused by the fact that there is no fixity against rotation. Note that the "probable force" in the lower sketch can be induced by the deflection ...


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there is a big difference if you are considering the static or the dynamic case. static case In the static case the simplest way is to add the torque from all the forces. (Although this might sound weird) because you are working in a 3D problem the simplest way would be to use the cross product form of the moment (for all load in the system including self ...


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Your moment equation is missing the positive moment, $PL$ at the left support. $$M= PL-P(L-x)$$


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As addressed before, you should formulate the problem with the x-axis pointing from the free end to the fixed end, which is the conventional method, and was used by the wiki example as well. On wiki example: I've carefully reviewed the wiki example, the solution seems incorrect. However, I've failed to pinpoint the root problems, as the steps jump around ...


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