This is a simple design I came up with back in 2011 well before the whole fidget 
spinners fad. Now that the fad for fidget spinners is finally fading - in part because of all the teachers banning them from their classrooms - I decided to bring the gear rings back out of retirement as a more subtle and less distracting way to "fidget". [ I could also see this somehow being used for Steampunk decorations for those who are into that. ]
Rather than something that spins around a single point (as the fidget spinners do) the Wood Gear rings require two pieces that work in conjunction to rotate. 
Each gear is a ring that you wear adjacent to each other-- lock them together and when you turn one the other turns. Pretty simple mechanics and (if you have a laser cutter or access to one*) pretty easy to make. The only difficult part of this is figuring out your ring sizes for two adjacent fingers, and making sure to not make them too tight so you can spin it easily.
I use to sell these Gear Rings in my Etsy shop but I'm offering the design here for free. Just be sure to laser cut the sizes you need --or cut a bunch of different sizes and see which ones fit best. I cut them from bamboo but you could probably try other types of wood. I used to lightly sand then coat mine with a clear lacquer to make sure there weren't any loose splinters but if the cut is really clean you probably don't need that.
Download the PDF file here.
Download the EPS file here.
Check out some of my other laser cut bamboo items here:
Laser Cut Bamboo Earrings
And some of my other laser cut products in my shop:
iPhone/Smartphone Holder for Strollers and Personalized Leather Compact Mirror
* Most areas in the US and abroad have Maker Spaces that often have a laser cutter available for community use. If there isn't one where you live try a service like Ponoko which lets you upload your files, choose a material to cut from, and have it shipped to you for a fee.