There are many ways to make hinges with a CNC machine, but the easiest and most basic way is to use a pair of extrusions attached to a work piece. Hinges designed on this method are centric rotational joints which means they can't be pivoted by hand, but over their long engagement range they provide smooth lap joints
This approach requires a lot less machining than other methods, although it does mean you need more material and time for machine setup. The best part is that the hinge design is straightforward because all parts are made in one operation.
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