First, for those readers who don't know what a rotary
engine is, or whose first thought when reading the
phrase "rotary engine," is "Wankel engine," please go
visit Wikipedia's Rotary engine page [link].
Next, take a look at Wikipedia's Radial piston pump
page [link], and observe how a rotary
engine is very
much like an outside impinged radial piston pump --
notably, the part which pushes the pistons is on the
inside, and the working space of each piston is on the
outside.
This idea is to make an engine which resembles an
inside impinged radial piston pump, with the working
space of each cylinder located between the cylinder's
piston and the (stationary) hollow shaft. The shaft
acts as the engine head.
Intake and exhaust are accomplished through ports in
the shaft, which the cylinders slide over; similarly,
there is a fuel injector and spark plug on the shaft,
which the cylinders move past. (Or a fuel injector
and glow plug, in the case we want to use a diesel
cycle).
Sealing can be done using the same kind of sliding
seals and apex seals that are used by Wankel engines.
The simplest design of cycle would of course be a two
stroke, since intake and exhaust can be timed entirely
by the movement of the cylinders past the ports.
A split cycle two stroke is also quite doable...
By not having valves poking into the cylinder, we
have a huge advantage compared to earlier split cycle
engines -- namely, the clearance between the
compression piston and the ported shaft can be very
tiny, thus forcing the entirety of the compressed air
charge into the crossover passage, improving
volumetric efficiency.
A double rotor version of the split cycle two stroke
might be a good idea (with one rotor doing
compression and the other expansion), because if the
rotors spun in opposite directions from one another, it
could minimize unwanted gyroscopic effects... plus it
would look cool.
A four stroke version should be possible, though it
would be more complicated. If the piston rods are
pushed in by a ring to which they are attached, or a
circular cam which they slide along, it would require
actual valves, not just ports, since each cylinder
would need to whole revolutions per cycle. If the
pistons are pushed in by a two lobed cam, then simple
ports could still work, but the piston motions will be
complicated.
It's probably not worthwhile to make a four stroke
version of this engine layout.