Actually the 3 point are the minimum required to form a plane and so all three point will carry equal loads. A 4 point stand can allow a single point have less load than the other 3. With that said a 3 point stand can be a bit less stable if your are cantilevering mass outside its foot print.
I bought a large wood lathe for my wife, it weights 400 pound on its own. she put a relatively small piece of wood on it which was slightly out of round and the thing almost walked out of the garage. I added a shelf underneath the lathe and put 450 pound on concrete in it, its between the bottom of the machine and the floor on the legs and now it stays put.... Mass is king.
Am I thinking about this correctly that the less points the better. So the vibration in the base will focus on less points meaning less system vibration. Or do I have it backwards where more points share more force. I keep thinking if you have a cylinder standing on edge and you introduce vibration that the thing will have a tendency to walk more if the floor is in contact with the full end. Instead having 3 points it would want to stay put because those 3 points "focus" vibration.
There are both good and bad points to consider if using 3 feet. 3 points are the least number of point required to create a plane, simple geometry, this is the concept a tripod is based upon. By using 3 points having an equal load on all points cannot be avoided, this is good, and leveling becomes very simple, this is why large granite plates are setup with 3 points of contact. If you use 3 points/legs there will be a greater load per contact point and you'll need to spread the feet out a bit to avoid the possibility of exceeding the foot print with enough mass to topple the mill, you can also add mass to the base to mitigate this issue. If you built the base so that it is big enough to allow the foot print of the mill to be within the triangle and place 2 point under the table it should be stable.
Unless you can balance the machine on 2 point, a line, you'll have equal loading on all three point with the machine setting in the middle of the triangle. If you have 4 or more points it becomes easy to have a poorly distributed load where 1 or more points will have less than the others. I do not have a masters degree in this but I do have over 40 years of experience dealing with large pieces of rotating equipment.
I think you're assuming a symmetric machine with its center of mass in the center. The point you're making about 3-point support, I believe, is that adjusting the feet does not change the load distribution. That does not mean the load is shared equally among the three feet.
