There is a 3-D object that is very tipsy but will always return to upright. Dan Bollinger suggested in a message thread in the news group rec.woodworking Where Do Ideas Come From? "for intentional, and very wobbly shapes, turn a Super Egg. This is the 3D version of the 2D super ellipse by Danish mathematician Piet Hein.
http://en.wikipedia.org/wiki/Piet_Hein_(Denmark)

Now if you look at the collage of some of the turned lidded boxes I've been doing you'll notice that they're trending towards just this shape. I was stumbling towards it out of frugality - getting the largest diameter box from a square blank. Rounding the top towards almost a hemisphere was a simple way to get a pleasing top that would lend itself to adding a finial.

Early on, I'd accidently made a tipsy lidded box when I left the bottom of one slightly convex rather than concave. Found it interesting but didn't pursue the idea of a dynamic piece at that time. But now, since I was playing with the ball and socket swivel joint and moving parts, why not combine "tipsy" with a counter balanced, swivel jointed, finial? SYNTHESIS!

Because the finial has a ball at the bottom and the box has the socket at the top, the two can move somewhat independently of each other while remaining connected. To keep the finial upright I merely added a counter weight to it inside the box.

So here's the first of probably many Hyper Ellipsoids with Articulated Counter Balanced Finials. Not real elegant but hey - it's the prototype. Still shots can only give you an idea of what this thing can do but they give you the idea.

Here's the inside. Could probably have made the acorn counterweight a bit smaller, but hey, this is a prototype.

Note: the black thing on the steel wire between the finial and the acorn counter weight is a flat rubber disk - with a hole poked in it smaller than the steel shaft's diameter. It slides up to the underside of the hole in the lid of this box, holding the finial to the box while still allowing it to pendulum in the socket/cup in the box lid.

Pretty simple to make, doesn't use a whole lot of wood and things move. So when are you going to make one?

more to come