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.
If you like it, please vote for me!
Step 1: Crate a "blank Ring"
The first step is to create a ring blank. Basically a very generic 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
You need to create two guide-geometry elements
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
This step creates a small message on the inside of the ring. I chose to say "you complete me" because you know... it's a puzzle!
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)
At this step, your file splits in to two parts.
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..
Step 5: Make Puzzle Cuts (2/3)
Now you can draw the actual puzzle cuts!
Jigsaw puzzles have a certain pattern to them, like drawing a bead from out of syrup. It's hard to describe, but look up images of jigsaw puzzles, and study the edges of the pieces. You'll notice that they have a "flare in, flare out" quality to them.
I tried showing that in these images. Use the "Spline" tool to create jigsaw puzzle cuts.
The second image has a "single puzzle bump" sketched below it. This entire spline is basically permutations of that bump.
The other thing to keep in mind here is to make sure that the first/last part of the cut are tangent (so that when you wrap this sketch, it doesn't have a weird jump in it)
Make sure your spline runs the entire length of the guideline from step 1/3
this is where your file splits in to two files. The sketch in the first fill will be the "top" part of the ring, and the other sketch will be the "bottom" part. There is no difference in the two parts except this sketch.
Since cuts have to be "closed" in solidworks, you're going to close the spine on the top in one file, and the bottom in the other file. The horizontal black line in image 3 of this step should clarify things (it's the same view of the two different sketches)
Step 6: Make Puzzle Cuts (3/3)
After making this sketch, create a "wrap" cut. Use the "Deboss" option, to have the sketch be cutting into the ring blank. The Emboss option would have the sketch going out of the ring blank, and might be useful for some other project. But that's not what we're up to here!
You'll notice an 'extra tab' in your part. Don't worry about this, since it's so thin that the printer probably won't even recognize it. you can always snap it off, or file it down later. Also, it's useful in the next step!
That's basically it! You'll have two files at this point, and just to be pedantic, you can create an assembly to make sure they fit.
Step 7: Check With an Assembly
Create a new assembly, and anchor the "top" part of the ring.
Insert the second part of the ring, and use the 'extra tab' to ensure proper rotation.
Step 8: Export
Export both the top and bottom parts as appropriate parts for your printer, either STL, or STEP.
Now you're done. Give it to your fellow nerd/sweety, and vote for this instructable!