You can’t quite drip metal the same way you drip plastic, because metal doesn’t hold its shape as well. But there are other ways people have gotten around this.
The most popular method nowadays is Selective Laser Sintering (SLS). The machine lays down a thin layer of metal powder, then uses a laser to sinter parts of the powder in the shape the layer is supposed to be. Then the machine puts down another layer of powder, and the process repeats.
Another way is very similar to how FDM printers print plastic (and can even be used with the same printers): they mix some plastic with the metal powder, turn this into filament, and then print the way you would print with just plastic. By itself, this just creates a plastic object with a lot of metal powder in it, but there’s a way to use a kiln to burn away the plastic and sinter the metal together.
More recently, a method has been patented that acts very similar to resin printing. There’s a big tank of electrolyte, and a grid of electrodes on the bottom. This grid is used to electroplate a thin layer of metal onto a build plate, in the shape you want the layer to be. Then the build plate is raised up a small amount, so the next layer can be plated on.
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