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One design I've found is a beam compass, which requires three components:

* Beam - some kind of straight stick
* Point holder - the part that holds a needle that will stay fixed at the centers of arcs
* Pencil holder - the part where you will put the pencil, must be able to slide up and down the beam so that you can set the radius

[Woodgears has a design](https://www.woodgears.ca/measure/compass.html) where the beam is cut to a trapezoid profile, while both holders are two dovetailed pieces with screws clamping them down.

I think this design can be simplified further.

* The bevel can be eliminated if the beam is cut from 1x2 in board or thin project plywood.
* It is only necessary for one of the blocks to move. Either the point or the pencil can be fixed on the beam, which simplifies the design.
* The point needs changing less often than the pencil, so it should be fixed. With a 1x2 board, you can screw a 3 in wood screw all the way through one end, and it will protrude by 1 in providing a point.
* The pencil holder can be a simple block with through mortise cut into it for the beam to pass through. A second hole, drilled perpendicular to the mortise, can hold a pencil. If possible, you could also make the pencil channel a narrow through-mortise so that it can accept a flat carpentry pencil, which will make subsequent design easier.
* Fixing the mobile block can be done in a few ways:
    * If you can work with tight tolerances, you can cut the mortises tight enough that friction will hold the beam and pencil in place, but you'll have to be careful not to move things around as you draw with it.
    * If the mortises are wider, you can insert a piece of folded paper, cardboard, wooden shim or wedge to increase friction while in use. Over time, this may split the wood, so it will reduce longevity.
    * You can drill a third hole into the pencil holder, perpendicular to both the pencil and beam mortises. Put a dowel into this hole and press it against the beam/pencil with a small clamp or a thumb.
    * Similar to the previous idea of pressing a dowel, you can tap a ["threaded insert"](https://www.mcmaster.com/92105A002/) into the channel so that you can use a wing-headed screw to press the pencil against the beam and thereby fix the whole assembly as needed.

With these adjustments, you should be able to construct a functional  compass with a total of:

* 2 rectangular pieces cut, precision unimportant (the exact length of the beam or outer dimensions of the pencil holders are not important)
* 2 mortises cut (ideally you would need a drill press, but a drill or router might do)
* 1 screw inserted into beam (probably better to drill a pilot hole first to avoid splitting)
* 1 circular hole drilled or threaded insert tapped
* 1 carpentry or regular pencil

I imagine someone looking for designs of their own woodworking compass should be able to interpret the above instructions without much trouble, but I might post detailed drawings/photos later.