Does external focus motors exist?

I have a Nikon D3100 DSLR, and it doesn't have the screw-drive motor found in the more expensive ones which focuses with D lenses like 50mm f/1.8D. So I was wondering, is there a kind of an external motor attached on the mount which would focus with the D lenses?

There are some sophisticated motor drives that can smoothly zoom a lens that I suppose could be used to focus, but they would not be cost-effective as you could buy a new D7000 much cheaper; which is what you need to do if you want to autofocus AF-D lenses.

My suggestion is to sell your D3100 and buy a D7000. When you start buying lenses, if you buy pro caliber AF-D lenses vs.pro caliber AF-S lenses, you will be ahead by a lot of money.

Unfortunately, no.

Canon have always put the motor in the lens, Pentax and Minolta/Sony in the body (although some lenses for both have since been motorised) - there are arguments for both sides.

Nikon removed the body motor from the D3000/D5000 as a cost-cutting measure, and produced the AF-S lenses to compensate (the 50mm f1.8G works perfectly here).

If you want auto focus with your Nikon D3100 you'll have to buy Nikon AF-S lenses. Your other option is to sell the D3100 and buy a D90 or D7000 since those models have a focusing motor in the camera body and Nikon AF lenses like the AF 50mm f1.8D will auto focus on them.

The answers above are correct, with one minor correction.

Canon introduced a manual focus, but otherwise automatic camera system called the T series (T-50, t-70, and T-90) in the late 70's or early 80's. Along with these cameras, they introduced several autofocus lenses. These lenses were incredibly expensive, but contained the full AF system in the lens. Shortly thereafter they introduced the EOS system, which is still what they use today.

So there were lenses with an external AF motor, but they won't work on your Nikon. That's even assuming you could find one, as Canon didn't sell a lot of them.

It is on the end of your arm.
Wrap fingers round focus ring, twist…

Nikon don't think that their entry level owners deserve focus motors…

No.

It's either the lens has one built-in or none.

That's the first 35mm SLR with an autofocus system to go into production in 1981. Note the huge bulge at the bottom housing the autofocus motor. Even then, it was already internal.