I've gotten a few comments on this, so I guess I should clarify that the ring assembles to a tight fit through elastic deformation of the printed substrate.
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Step 1: Crate a "blank ring"
Create two concentric circles of different size (an annulus), then extrude them.
The inner circle should have the same circumference as the target finger. This website should help convert from ring size to circumference: http://lovejoyjewelry.com/ringsize.htm
The length for the extrusion is up to you. I chose .375 inches, just because that's how big another ring I have is.
Step 2: Create guide geometry
The first is an axis that intersects two planes (for me, it was front and right). Use the image to figure out which two planes you should use.
The next guide-geometry element is a plane that is tangent to your ring blank, and perpendicular to the axis you just made (OR parallel to the plane not used to create that axis- for me, it was the top plane)
Step 3: (Optional) Create secret text
Draw a guideline parallel and slightly above (since some letters dip below the line) the ring face. Insert the text of your choice, and anchor it to that line (the "curves" option)
Use the "Wrap" option to emboss the text on the inside face of the ring.
Step 4: Make puzzle cuts (1/3)
Create a new sketch on the plane made in step 2.
Make a guideline with length equal to the outer circumference (top part of first picture)
Crate another guideline as long as that line, only parallel to the ring face, and originating at the vertical line that is parallel to the central axis of the ring..