How to compute force on joints of a 3D structure of balls connected by rods? Source
Given the coordinates of n 3D joints (1kg each) connected by m rods. Assume rods have zero mass and joints with z=0 are fixed to the ground while others are free to move, will the shape be move or not? If not, will it be stable?
The totals force at each joint has to be zero for the shape to be stable. how can I compute the total force at each joint?
 A: The approach to solving the official problem as well as determining the forces is actually reversed: We hypothesize that all forces are balanced and work out whether that leads to a contradiction or not. If all goes well, this means that nothing needs to move as soon as we have placed the structure as specified.
Along the way we will have gained equations that describe the relations between
the forces acting on each joint in terms of the forces in rhe rods.
See my long answer to your related question for details.
If you have read that, you will have noticed that solving the official problem does not require you to ultimately work out a solution for the forces in the rods. It is just concerned with solvability, not with actual solutions.
But suppose for now that the system admits a solution, and that you have one solution (out of possibly infinitely many) for the forces in the rods. Then you can use an analogue to equation $(1)$ from the above-linked answer, based on the structure's incidence matrix, to compute the corresponding effective forces $\mathbf{F}_j$ from the rods on the joints.
For the non-grounded joints, the $\mathbf{F}_j$ will already be known; these are the forces balancing the weight of the joints. This has actually been part of the linear system from which we got a solution for the rod forces in the first place.
For the grounded joints however, we can now compute
$\mathbf{R}_j = -(\mathbf{F}_j + m\mathbf{g})$ where 
$m\mathbf{g}$ is the joint's weight and $\mathbf{R}_j$ represents the ground support force which may indeed be worth knowing from an engineer's perspective. However, the official problem does not require you to go so far as computing these.
