This is a particular type of tank tread, that looks to the ground like a very big wheel. It would do well on uneven but flat ground because it rolls over small obstacles easily. Hills are a problem, because the same principle means it would be hard to block it from rolling down the hill. The same sort of tread could be scaled up for handcarts, wheelbarrows, rickshaws, Mars rovers, pedal-powered whales, all sorts of vehicles that want to roll over uneven surfaces and small obstacles easily.
For a lawnmower, the tread pieces are 1 inch high by 2 inch wide by 2 inches long, where the 2 inches long is really 1 inch long plus a 1 inch lip extending under the next piece. They are hinged together. A chain of 25 of them fit together to form a 60-degree arc of a 4-foot-diameter circle. That arc is 2 feet long and 3 inches high. The pieces can rotate on their hinges to form a smaller 1-foot-diameter circle. They curve like that on either end, then the bottom arc is repeated on top, forming sort of an ellipse. On the top and bottom the lip of one piece is flush with the next piece, but on the ends with the tighter curves the lips stick out slightly.
A frame would support the ellipse, and two such ellipses would be connected to act as big flattened wheels on either side of a lawnmower. A 4-foot-diameter circle (which is essentially what is touching the ground) can roll over rocks and roots easily. Turning in place is relatively easy, the two wheels would rotate independently in opposite diretions. On a soft surface like grass the tracks would put very little pressure on any one spot.
These treads can fold into tight circles fairly easily, but the overlapping lip makes it resist unfolding into a straight line or a circle any bigger than a certain radius. You can see the same principle by spreading out a deck of cards and taping one edge of each card to the top center of the next card. When the tape is on top, force is spread across all cards, but when the tape is on the bottom it folds together easily.
This has reached the point where further progress requires making prototypes. A prototype would be two ellipses consisting of about 70 treads each, along with some supporting wheels and casters. Software to simulate that is both too expensive and inadequate (the bending of the material and stress on joints and behavior when pebbles get between plates are important questions). Paying to have a prototype done is too expensive too, especially since I'd probably get it wrong and have to do many such prototypes. Right now the easiest path seems to be BRL-CAD (free) to produce 3d models, followed by buying a cheap 3D printer and a roll of plastic filament. Given that, it would cost about $10 and a day or two of time per prototype. Once a scaled-down plastic prototype works, a larger metal prototype might make sense.
Here is a later sketch of the same design, with some refinements
like the cross section is a straight-lined U instead of a rounded
sideways C. Ideally the bottom of the U would be rounded up, so
that combined with the gradual curve of the large circle the
material is saddle-shaped, to resist bending. The innards of the
frame vary with what is being supported. The two side wheels should
be sprung, not quite fixed, to keep the tread under tension. If you
lose a segment you could hook the remaining treads up again and keep
going. Only the bottom arc bears weight, the rest of the oval is just
recirculating the tread back around. It would probably all be
within a rubber tread to keep dirt from getting in when the segments
open up around the side wheels.
