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I couldn't find a CNC lathe large enough to make these parts

My interpretation was more like "when looking around my basement full of awesome tools, I didn't have anything readily on hand, so I built one from what I had," not that no such machines existed.

> There is that little black stick on the top right of the canvas, wonder what that is?

It's a mahl stick. http://painting.about.com/od/artglossarym/g/defmahlstick.htm

Learn a new thing every day! Thank you.

  Here is the artist painting himself in his studio:

  I don't see anything like lenses, mirrors or other tricks, mostly just brushes, paint, canvas, the artist and the subject.

To be fair, I doubt that Vermeer himself would have wanted to publicize that he was using "crutches" like the techniques described. As others have mentioned, if these techniques were used, they probably would have been treated as trade secrets.

I'm not sure using mechanical techniques would have the same meaning back then. It might have actually been a high-technology selling point.

>There is that little black stick on the top right of the canvas, wonder what that is? Maybe there is a mirror at the end of it ;)

You mean like that round, brass colored thing that would otherwise look like his hand?

No, I think he means the stick he used to partially rest his hand on. Remember, mirror and lens or not, it takes a LONG time to do that kind of detail work. If they really worked at that angle, I imagine your arm would get VERY tired, and the stick there might offer a bit of relief while working.

No, the black stick that appears to protrude from his hand. Note that it is not the brush and that at the top right part of the black stick there is something round (near the canvas).

I was referring to the "mirror on the end of it" part and just quoted the preceding line.

Compared to the hands of the girl in the picture, the color and the shape of his own hand looked odd. It's too round and looked kind of brassy.