From Road & Track:
No crankshaft, no problem: Toyota's free piston engine is brilliant
Let's get one thing straight: The variable-valve-timing, direct-injection, turbo-wonderful powerplant in your new car is not cutting-edge. Despite the complexity of the modern engine, the fundamentals haven't changed since Grover Cleveland was in office. Pistons turn a crankshaft that eventually spins your car's wheels.
Yawn.
Electrically driven cars are the future. But until we have cheap, 1000-mile batteries, we still need range-extending fossil-fuel engines. Those devices don't need to turn wheels, just generate juice. The simple solution is to strap a generator to a piston engine, as BMW did with the two-cylinder range extender in its i3 EV. But if the engine never turns a wheel, there's no need for it to rotate anything. Why not cut out the middleman and use the piston's reciprocating motion to generate electricity? That obviates camshafts and most other rotating parts, too.
This is one of those ideas that you know, some engineer somewhere woke up at 3:00AM reaching for a pencil and some paper. Much simpler and efficient. This would be great for stand-alone generators too.
Also, do not denigrate the two-stroke cycle. Two-stroke engines are not just for cheap weed-whackers and chain saws. The power to weight ratio is great and many of your larger diesel engines run a two-stroke cycle. More here and here.