Right- what they are calling a 'wobble' plate is a swash plate as used on helicopter rotors, hydraulic pumps, etc.
There are some problems with that design, the first of which is that the port timing is interrelated and not independant from each other as nail valves are. In other words, one cannot control the timing as well but especially not the valve (port in this case) opening rate; a simple fact of life is that mushroom valves open and close very quickly and so spend most of their 'open' time very much open. Ports like this, also used in a Wankle design, are opened and closed at the rate the plate under them can pass by and the rates themselves are fixed. The second problem is that there must be some type of sliding plate, or metal seal above each piston; this is fine for intake but suffers on the exhaust stroke where there is zero lubricant on that seal. Again, a common problem that is shared with the Wankle and shows up as short seal life, and excessive oil consumption.
There really are sound physical reasons why a mushroom valved, reciprocating piston engine has been chosen as the powerplant of choice. Others certainly have specific benefits (two cycle engines are simpler and rev. higher, Wankles have an extremely high power to weight ratio, etc.) but in the end, the best overall performing engine is the one that goes back over two centuries. I know a lot of people think it is a conspiracy by someone / some entity, or that that really clever guy has not come along yet but physics really does rule the day here and what we have is about as good as it is likely to get for internal combustion engines.
Brian
Actually, very different than an aircraft radial. Radials have a conventional crankshaft with a single (for a single-row engine or more for multiple rows) crankpin and the conn rods are connected to the master rod knuckle so they all go around at the same time. (Not to be confused with the original rotary engines that had the crankshaft bolted to the airframe and the whole engine rotated around it.)
http://en.wikipedia.org/wiki/Rotary_engine#Distinction_between_.22rotary.22_and_.22radial.22_engines
This Duke "axial engine" is actually a form of "wobble-plate" engine, the design of which has been around for decades. Very simple, very powerful for size.
Their difference seems to be that the pistons circle around inside the case, where a regular wobble plate engine, the cylinders/pistons are in fixed bores and just go up and down.
https://www.google.com/#q=wobble+plate+engine
https://www.google.com/#q=dynacam+engine&revid=469752981