How to make a pivot point?

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Hi, I made a new account to look for advice on how to make a kind of specific thing for a school project. I don't know if there's a technical name for what I'm trying to do but basically I want to make something that allows two planks of wood to pivot on each other.

So what I 'm imagining is if you take a square board and you cut a circular piece out in the middle, the circular piece is free to spin around inside that board. However I want to limit how much that circle can rotate within the board, say it can only spin 180 degrees for example. Any ideas on how I can go about doing this? Or, even better, if there is something I can buy at Home Depot or something that would do the same thing, that would be great too.

If anything I said is unclear or confusing, I apologize. Feel free to ask any clarifying questions and thank you for your help!
 
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Something like this? It's come out with a black background for some reason, but the inner darker grey part is attached to the fixed part, while the outer, lighter grey part is attached to the rotating part. The position of the cuts for the "stops" are adjusted to give the desired amount of rotation.
 

Something like this? It's come out with a black background for some reason, but the inner darker grey part is attached to the fixed part, while the outer, lighter grey part is attached to the rotating part. The position of the cuts for the "stops" are adjusted to give the desired amount of rotation.

Yes! That's what I'm trying to make. Is there an easier way to make that, or will I have to make those intricate cuts out of a wooden board?
 
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I suppose you could cut the circles and screw and glue stop blocks on to suit.
To be honest though, if you mark two circles on the wood, and radii for the stops, then shade in of cross hatch the part that is scrap in pencil to avoid mistakes, it should be a reasonably easy job with a jigsaw i'd have thought. i'd make the stops part nearly equal in size on the parts rather than have the one part much smaller as I've shown. Stronger that way.
Someone may come up with something else too.
Thinking about it, you could put a round spacer like a thick washer between the two boards and screw and glue stops just a bit thinner than the spacer to appropriate places to the faces of the boards. That's simpler
 

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