Instructions for that but in Japanese, photos say it all though: http://df1.github.io/blog/2012/05/01/cat-wheel-diy/
Edit: this commercial wheel is actually made from coroplast/corrugated plastic, wow, and they charge a ton for what turns out to be cheap plastic and roller skate wheels. Maybe I'll use that instead. http://www.gocatwheel.net/
This guy used sonotube(concrete forms) to make a cat wheel. I found it because I was thinking of this. Pre-made in wheel shape and you can buy any size you might need: https://www.youtube.com/watch?v=9p95dcBXZOM
How he did it:
A Sonotube 36" (mason's supplies), cut to 1' wide, carpet, 16 rollerblade bearings set in pairs on the inside of the outer ring, 2 long plastic strips bent at the right angle (lowes), two strips of 1" wide brown dense cardboard-like sheets (lowes) for guides, wrapped around the outside of inner ring. I wish I could find 38" sonotube for the outer ring, but as it was I had to cut the outer sonotube and spread it about 8" apart, to be able to fit the inside ring with 1" to spare for the bearings.
Thick plywood (7 layers) for the stand, screws, dowels for the bearings, glue gun. The inside ring is made 2" wider than the outside (using the carpet), to prevent cat paws from grabbing onto the stationary pieces. It's important to place 2 sets of bearings at the very top because cats like to sit on top of the wheel. I have pictures I can share, they used to be on my web site but I got hacked and spammed, so it is currently down.
circle, cut the outer ring to extend its radius by 2", screw it in with any screws long enough, attach the 8 pairs of bearings, glue in the carpet (I used a very sticky double-sided tape that was a millimeter thick with tiny wire mesh embedded in it), glue the carpet around and you are done. Mike P.S. I couldn't find 38" Sonotube, that is why I bought 36" and constructed the whole thing by cutting the outer ring.
The bearings are attached to the outer ring. I used 1' wooden dowels to glue them in place, one bearing on each side, with cut-out. Plastic (and heavy cardboard) prevents the inner ring from wiggling side to side. Basically the pair of them makes the railing within which the inner ring rotates; sort of locked as a large bearing. Please be sure to make the inner ring larger by about 2" then the outer one. Cut out both sides of the foundation with 38" wide
One site I found has the snonotube for less than $30 per foot for the 30" Shipping is pricey though due to size. If you can find a cheap local place this seems a good option, except they may make you buy a whole tube which are several feet, maybe make wheels for your friends too, or use the extra for other pet furniture and enrichment projects.
I'm thinking to TRY a different idea with no wheels used. I'll paint it a smooth durable paint and then mount high quality furniture movers in the base for it to slide on. It'll just need a rim to keep it from sliding off. Then use silicon spray lubricant to make it even slipperier. Should be quieter too, if it works. It will be more like this but maybe just rim on the base part rather than rim the whole wheel, that's harder: https://www.youtube.com/watch?v=TpdeJeCCe54
Once you know the basics you can get fancy with it if you want: https://www.youtube.com/watch?v=jzF2yU5yzDs
Or real cheap make a wheel from a kiddy pool but depending on your pet you may not be able to find the size you want. I love his self adhesive cork mat idea for the footing material: https://www.youtube.com/watch?v=wDR0920HcIY
Then if you don't mind it not being round: https://www.youtube.com/watch?v=uZaVZg3VFIY
This is typical wood one but using a castor. Castor does seem quieter than all the wheel ones: http://stitchesnsews.blogspot.com/2013/ ... wheel.html
Or this wood one but you don't want holes in it like they did: https://www.youtube.com/watch?v=LEdnCGfoHkM#t=1586
And this is pretty: http://lumberjocks.com/projects/59777