How round are your ball bearings?

Did you know that ball bearings don't need to be spherical to roll smoothly?  Really.  You can make pointy versions that will roll just as well as the round ones.  They just need to have constant diameter, or constant width as they call it since non-circular shapes don't really have a diameter.  The video below shows a fascinating little glimpse into a world of math and physics that kind of intrigued me.  Apparently there are 3-D shapes that are constant width that are not round.  They roll around like ball bearings.  The only reason that we don't make wheels this way is that there is no stationary place to put an axel in the center of the shape.  Take a look at the video to see what I mean.

I think the non-symmetrical shapes are really interesting.  For every sharp pointedness on one side there must be an equivalent flatness to the opposite side in order for it to all balance out.  This allows you to create objects that roll smoothly, but do not have equal weight distribution.  They won't roll away on their own, but they are smooth when used as ball bearings.

It seems to me that this is a great opportunity for playing with a CAD program and a 3D-printer.  You should be able to design all sorts of surfaces of constant width.

For more information, see How Round is Your Circle or buy the book, How Round is your Circle on Amazon.