This is a LEGO version of the popular Hoberman Sphere toy.
Although the sphere is pretty stable, it can’t really take the repeated abuse of being handled by the public at a show. I built the spinner so that I didn’t have to hang around and open and close it myself, or keep putting it back together.
Update 10/18/2016: Instructions for building the stand are now available here.
It works really well when connected to a programmable controller to repeatedly start and stop it.