The first two stroke cycle was invented in 1878 by Dugald Clerk and patented in England in 1881 as the Clerk-cycle engine, which completes one thermodynamic cycle in two movements of the piston, unlike the four strokes found in most modern day cars. The genius of this design is that the beginning of the induction stroke and the end of the combustion stroke both perform intake of fuel and exhaust of waste gases simultaneously.
The above animation shows a two-stroke engine, in this case with a tuned expansion pipe illustrating the effect of a reflected pressure wave on the fuel charge. This feature is essential for maximum charge pressure (volumetric efficiency) and fuel efficiency. It is used on most high-performance engine designs.
These engines are very efficient for their size and fairly lightweight and have been put to use in all sorts of machinery, from mopeds and scooters to chainsaws and outboard boat motors. The two strokes most common use though is probably the motor-cycle. Manufacturers such as Saab made some two stroke cars along with a number of major automobile companies at the time, production of these ended in around the 1960's in Europe and America but some eastern block and asian countries still made them in the early 1990's, even Lotus of the UK has a prototype Exige based car called the Omnivore, which uses a two stroke engine with direct fuel injection systems.
Although the principles remain the same, the mechanical details of various two-stroke engines differ depending on the type. The design types of the two-stroke engine vary according to the method of introducing the charge to the cylinder, the method of scavenging the cylinder (exchanging burnt exhaust for fresh mixture) and the method of exhausting the cylinder.
There are various types of two stroke engines, each of which have varying features and for a more indepth research i suggest doing a quick google search of some of the terms below:
Rotary Inlet Valve
Reed Inlet Valve
Piston Controlled Inlet Port
Crossflow Scavenged
Loop Scavenged
Uniflow Scavenged
Stepped Piston Engine
notes on diesel two strokes:
Unlike a gasoline engine, which employs a spark plug to ignite the fuel/air charge in the combustion chamber, a Diesel engine relies solely on the heat of compression for ignition. Fuel is injected at high pressure into the superheated compressed air shortly before top dead center (TDC) and begins burning. Scavenging is performed with intake air alone; the combustion gases exit through conventional exhaust valves located in the cylinder head or Schneurle porting just above the piston at bottom dead center (BDC).