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Very good question! Tip machining is by physically breaking a wire, followed by etching, followed by conditioning of the tip by putting a voltage through it until excess atoms are removed from the tip. It is not exactly a reproducible process, which is why it is not routinely used in the industry

As for the small distances, I am not too sure of the mechanics of it, but I believe that a piezoelectric tube is used, and the tip is bent over a small distance back and forth by fine controlling the voltage.