Source by: http://auto.howstuffworks.com/rotary-engine2.htm
The Parts of a Rotary Engine
A rotary engine has an ignition system and a fuel-delivery system that are similar to the ones on piston engines. If you've never seen the inside of a rotary engine, be prepared for a surprise, because you won't recognize much.
The rotor has three convex faces, each of which acts like a piston. Each face of the rotor has a pocket in it, which increases the displacement of the engine, allowing more space for air/fuel mixture.
At the apex of each face is a metal blade that forms a seal to the outside of the combustion chamber. There are also metal rings on each side of the rotor that seal to the sides of the combustion chamber.
The rotor has a set of internal gear teeth cut into the center of one side. These teeth mate with a gear that is fixed to the housing. This gear mating determines the path and direction the rotor takes through the housing.
The housing is roughly oval in shape (it's actually an epitrochoid -- check out this Java demonstration of how the shape is derived). The shape of the combustion chamber is designed so that the three tips of the rotor will always stay in contact with the wall of the chamber, forming three sealed volumes of gas.
Each part of the housing is dedicated to one part of the combustion process. The four sections are:
The intake and exhaust ports are located in the housing. There are no valves in these ports. The exhaust port connects directly to the exhaust, and the intake port connects directly to the throttle.
The output shaft has round lobes mounted eccentrically, meaning that they are offset from the centerline of the shaft. Each rotor fits over one of these lobes. The lobe acts sort of like the crankshaft in a piston engine. As the rotor follows its path around the housing, it pushes on the lobes. Since the lobes are mounted eccentric to the output shaft, the force that the rotor applies to the lobes creates torque in the shaft, causing it to spin.
The output shaft
(Note the eccentric lobes.)
Now let's take a look at how these parts are assembled and how it produces power.