For this sort of automation and precision, the machine-tool requires qualified engineering and assemblies (common knowledge, although I'm unsure if you are aware). I'm talking about thermally stable composites, alloy parts & mechanisms, tuned force/inertia motion driven axis'es (accel/decel), damping, and reliable harmonics/resonant frequencies. As in; the "bare minimum essential" that you need and certainly aren't going to get for $4k. That amount of money, more or less, will only get you a machine that "appears and move" like a Pick & Place machine (and the shipping crate it comes in), that's all.
Therefore I wouldn't bother at all if I were you. Save that extra capital and outsource to a fab house equipped with half-decent machine-tools.