Especially where these disks are used, its origin as a Japanese art can be obscured, and the disk may simply be referred to as a "braiding wheel". It's important to me to keep sight of the origins of any art I practice, though, and kumihimo is no exception. For this reason, after making my first short braid with a disk cut out of corrugated cardboard, I made my own traditional kumihimo frame, a marudai. It's a simple project (I completed it and made a 22" cord in an evening), and the only special tools you'll need are a set of Forstner bits. You can pick up all the materials at your local hobby shop (I purchased everything at Michael's).
* A round wooden clock base the diameter you wish for the kagami (top surface)
* A square wooden clock base a couple inches larger than the kagami
* 5/8" dowling long enough for four legs (I used two 36" dowels for four 18" legs)
* Wood glue
* Forstner bit the diameter of the central hole in the kagami (I used 1")
* Forstner bit the diameter of the legs (in my case, 5/8")
* 8 or 16 (depending on the patterns you want to create) wooden spools with center holes
* Steel baling wire or safety wire
Step 1: Mark Leg Socket Positions on Kagami
Leg spacing is not fussy, but you'll probably want about an inch or so clearance from the edges for stability. Look at proportions in commercial marudais and do what feels right. I spaced my leg sockets 90 degrees apart, 2-1/2" from the center.
(As an aside, this is probably the point you want to sand all the edges smooth to avoid thread damage when you're actually braiding.)
Step 2: Mark Leg Socket Positions on Base
Step 3: Drill Leg Sockets and Kagami Central Well
Then drill the center of the kagami (I used the reverse surface of the base as a backstop). Best of luck to you.
Incidentally, the existence of a central hole is the only reason I used a clock face. If you can get a wood round the size you want, and are comfortable with center-finding jigs, you can use one of those instead. Since I was not using a drill press, the lack of wood for the center point of the 1" Forstner bit to bit into made the drilling of the central hole difficult, and in the end, off-center. An undrilled round, a cardboard center finder, and five minutes would've made this quite a bit more precise. So there, learn from my mistake.
Step 4: Assemble and Glue the Marudai
Step 5: Make Tamas (optional)
1. Curl over the end of a piece of steel wire.
2. Put it through the center hole of the spool in question to measure its length, and bend it 90 degrees.
3. Complete the bend with your fingers (or pliers, depending on the wire gauge).
4. Crimp the bend to a tight hairpin with pliers.
5. Start the next bend with pliers next to the "curl", and complete it by hand or with pliers.
6. Crimp that bend to a hairpin as well.
7. Continue to fold as many plies as will tightly fit into the spool's center.
8. Break off the last ply from the rest of the wire's length by working it back and forth with pliers.
9. Curl end over as in step one.
10. Using pliers, force the bundle into the spool as far as possible, and finish by hammering it into place.
Of course, using lead will be better, and if you have a drill press, you can enlarge the holes to hold more wire, but these still make nice tamas for small projects.
Step 6: Exclaim "Woot!"
And lastly, some links.
Ee0r's Kumihimo Marudais and Braids
CraftDesignOnline Kumihimo Braid Designers (lots of braids to choose from)
Kumiplanner (8-strand kongoh-gumi only)