We have a couple of robot vacuum cleaners, so my wife always puts the bar stools up on the kitchen bench to allow them to clean under there.
I first tried installing some brackets under the bench to hang the stools slightly off the floor. However, you hit them with you knees when sitting at the bench. So In decided to make the brackets swing up out of the way when not in use. These work well.

To install them, essentially you have to mount the brackets in the retracted position (as shown in the last photo). First take one bracket and install the link in place (refer to the pictures). Install the mount into the bracket and screw it to the underside of the bench, ensuring that the bracket is pushed up against the back wall of the bench which helps to stop the link from working its way out. Then take the bracket you just installed and swing it up against the bench underside. Attach the other bracket to the other end of the link in the retracted position also, then (ensuring both brackets are swung tight to the underside of the bench), screw on the second mount.
Mounting them in the retracted position ensures that the mounts are spaced the correct distance apart. If not, they will bind up as you try to swing them up.

UPDATE:
I accidentally walked into one of the stools when it hanging on the brackets and broke the shaft off the mount. I decided to re-print the mounts with a 12mm hole and use 12mm aluminium tube (from Bunnings in Australia) for the shaft. This has made them a lot stronger and swing smoother. I've uploaded the alternative mount STL (BarstoolBracket_AlumTubeMount.stl).

UPDATE 2:
I've updated the file for the bracket now that I've learnt a lot more about 3D drawing and printing. It is now printed in two parts (BarstoolBracket_upper and BarstoolBracket_lower) that finger joint together and only takes a little glue to keep them together. This gives the advantage of being printed in the correct orientation for strength and very little supports. Also the bracket can swing in either direction now where previously it could only swing to the left due to a flat spot on the top of the bracket for easier printing.

Note that I've also included the Sketchup files for those who want to customize it.