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I predict these won't ever be smaller, lighter and cheaper than traditional design with an rotating engine and separate generator.

In general, the generator weighs and costs more than the engine for the same power level. In the linear design, the generator is used inefficiently because the magnets are moving in a sinusoid instead of a constant velocity past the windings, and the maximum speed of a piston is lower than the optimum speed of a generator. So you'll need more magnet & wire for the same power level, increasing total weight and cost.

>I predict these won't ever be smaller, lighter and cheaper than traditional design with an rotating engine and separate generator.

it most possibly will. The reason is that traditional design was built for actual mechanical spinning of the wheels with all the trade-offs coming from it. Generating engine has completely different requirements which would drive trade-offs and optimizations. For example, you can run free-piston at much higher rpm, thus mitigating the inefficiency of magnet/wire usage. Higher rpm would lead to less weight for the same power. The pressure/volume curve can also be optimized and shaped instead of the sinusoid forced by the rotating movement. Etc...

Much higher frequency, not RPM! (there is no flywheel to go around...)
Oscillating piston generators have been around for a long time, they're nothing new and based on the same principle of operation as those shake-to-recharge flashlights; note the date on this one in particular:

http://www.google.com/patents/US2900592

AFAIK they were briefly used in very limited amounts by the Germans in highly-space-constrained applications like missiles, but otherwise they were quite inefficient.

Whatever happened to the Mueller wave disc motor? Does anyone know? It seemed very well-suited as a range extender motor in a series hybrid. Surely there's a Chevy Volt driving around with one somewhere...

EDITED to add: they seem to have run out of funding without producing anything commercializable: http://newenergyandfuel.com/http:/newenergyandfuel/com/2013/...

Interesting. Presumably there will still be just piston rings in the normal place, although I would like to see more on how they are going to lubricate it. You don't want the gas spring chamber to fill up with oil. My guess for how they are going to get it started is by driving the permanent magnets with the coils. Also, why is it 2 stroke? I'd always assumed that 2 strokes were smaller and cheaper, but had less power. Possibly because there is no momentum to do 2 of the 4 strokes. Toyota definitely has the technology to make it a modern EFI 4 stroke, though. For the fuel intake and compression strokes, the coils could be disconnected from the load and driven so that the strokes complete.
Two stroke engines are actually smaller, cheaper, and more powerful than four stroke engines of equal displacement. The issue with two stroke engines is cleanliness. Because there isn't a spare cycle to push all the extra unburned particles out of the chamber and let only clean air/fuel into the chamber, there is some loss of power efficiency due to the attempted combusting of leftover particles. This is more than mitigated by having double the amount of power strokes per equivalent displacement. There's actually some really interesting design techniques that have been used to "coax" the waste particles out of the chamber, take a look at MotoGP technology circa early 2000's if you want to learn more.
All the two stroke engines I have used (light aviation) have been terribly unreliable and painful to maintain. Won't start, often fires just on one cylinder, stops randomly, leaks oil everywhere. Is this a "shitty design" problem rather than an inherent problem with two-stroke engines?
Probably a combo of both. You know how I said above that there are some cool design techniques to get the old waste gases out of the cylinder? Well those techniques only work over a very narrow band of RPMs, under very specific air/fuel ratios. Your problem is even worse because you're in an aviation setting. Your engines are experiencing very different air densities, and this is causing the air/fuel ratio to change drastically compared to what they've been tuned for. If they get too rich, they stall. Too lean, they explode.

The leaky oil? Yeah, that's probably just a two stroke being a two stroke. Due to the design, they aren't "oiled" like a car, you instead shoot the oil in with the gasoline in the injection cycle, and it just kinda seeps in and around the engine. That's the main reason why they're dirty - both literally and environmentally.

Diesel engines have less problems when inlet air goes to the exhaust, since in a diesel, inlet air doesn't contain any fuel. A two stroke diesel has thus some synergistic advantages.

A direct injection otto engine could also work very well as a two stroke.

My bet would be that using a two-stroke cycle allows the piston to stay lubricated without using a sump for oil.