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That's why I said "absent of outside forces..." If you isolate the robot itself from outside forces, then I think it will hold itself very still. Maybe not the scientific answer you were looking for, but that my "from the floor" experience.
Just siting there holding a weight I'd expect zero movement. No motion, not a sub-micron once the sag is out of the joints and beams. It should be dead silent.
Such a system should not be dithering, hunting, or vibrating at all. If it does the control loop is just plain puked up but yes, seen this done even on expensive machine tools.
Now make it do something or have a big forklft drive by, different.
33 inches out of a base rotary joint calls for very insane high res if you need a tenth once things start moving so you tend to go with Cartesian robots there and it begins to look like a machine tool not a robot.
A 40 inch HMC or VMC, how much should it oscillate sitting and waiting? It is a robot. They come in many flavors.
Arms most think of are just A and B rotaries. Same deal, same guts and servos. How tight can you hold the tolerance on a A axis part?
It's a joint length to base resolution problem along with beam deflection under load when actually working. Even just mean ole mister gravity screws things up accuracy wise.
Free of outside influence it should hold within a level you most likely can not measure, it will not be accurate or where you want it to be.
Of very little help to OP and maybe makes no sense so feel free with the dope slap here John.
Bob