Boy & frog invent square wheel car
This blog on ZDNET provides links to video and a press release from Global Composites and Distributed Robotics, both in NY state. Here's a PDF press release. If you want a smoother ride, here's a video of an elliptical wheel version.
It's an interesting idea, but can spinning a weight around really be more efficient than driving round wheels? The inventors suggest using other forces instead of gravity; perhaps in special applications (where such a force normal to the plane of motion is available) might be very effective. All I can think of right now is the "screen door in a submarine" - where the flow of water perpendicular to the screen would provide a huge force which is easily tapped. So there you have it - the basic concept for a novel submarine screen door cleaner robot. If you make a million from this idea, please send me a check.
Similar ideas have been around for a while: driving a square-wheel vehicle over a road composed of inverted catenaries, as seen here.
Steering such a vehicle is a bit complicated, since it easily interferes with the synchronization of the wheels.