There have been "single" (i.e. twin-bore) and "twin" (i.e. four-bore) models and several important internal developments, the last of them being obvious externally too, with the carburettor (uniquely amongst motorcycles) moving to the front of the engine under the exhaust.
Principle of Operation 
The split-single system sends the intake fuel-air mixture up one bore to the combustion chamber, sweeping the exhaust gases down the other bore and out of the exposed exhaust port. The split-single two-stroke thus delivers better economy than the common forms of two-stroke and runs better at small throttle openings, at the cost of a heavier engine.
In the 60-year history of this arrangement there were two important variants, earlier versions have a single, Y-shaped or V-shaped connecting rod and these look much like a regular single-cylinder two-stroke engine with a single exhaust, a single carburettor in the usual place behind the cylinders and a single sparkplug. Racing versions of this design can be mistaken for a regular twin-cylinder, since they had two exhausts or two carburettors but these are actually connected to a single bore in an engine with a single combustion chamber. Some models, including those in mass-production, used two spark-plugs igniting one combustion chamber.
After World War II, more sophisticated internal mechanisms improved mechanical reliability and led to the carburetor being placed in front of the barrel, tucked under and to the side of the exhaust. This is the arrangement which was used on the Puch 250 SGS and sold in the United Stated by Sears from the 1950s through the early 1970s under their own Allstate brand, with the engine being referred to in Sears literature as the Twingle.
Garelli invented 1912 
The first split-single engine was patented in 1912 by Italian engineer Alberto Garelli. His company, Garelli Motorcycles, produced a 346 cc version for use in motorcycles for road use and for racing. Production continued until 1926, by which time Garelli was increasingly concentrating on the military market. Garelli motorcycles remained in business until the late 1990s, but they did not further develop or produce these engines.
Trojan invented 1913 
The Trojan two-stroke, as used from 1913 in the Trojan car in the UK was independently invented but would now be described as a split-single. Photos of a 1927 "twin" model at the London Science Museum show the internals. The "fore-and-aft" layout of the cylinders means that the V-shaped connecting rod has to flex slightly with each revolution. Unlike the German/Austrian motorcycle engines, this engine was water-cooled.
Puch 1923-1970 
After the First World War ended, Austrian engineering industry struggled to recover. Italian engineer Giovanni Marcellino arrived at the main factory of Puch in Graz to wind up operations. Instead of liquidating the factory, however, he settled in the town and, in 1923, designed and began production of a new split-single with asymmetric port timing, taking inspiration from industrial opposed-piston engines. As arranged on a typical motorcycle, Marcellino's design had the pistons one behind the other, unlike Garelli's pistons, which were side-by-side. The new system allowed better cylinder filling and a longer power stroke. To avoid flexing of the connecting rod, the small-end bearing of the cooler intake piston was arranged to slide slightly fore-and-aft in the piston. In 1931 Puch won the German Grand Prix with a supercharged split-single, though in subsequent years they were overshadowed by the split-singles of DKW.
After the Second World War, Puch split-single production and racing were restarted in 1949 with an improved system of one connecting rod hinged on the back of the other. These engines typically use the forward piston to control both intake and exhaust ports, with the interesting result that the carburettor is at the front of the engine, under and to the side of the exhaust. The rear piston controls the transfer port from the crankshaft to the cylinder. Increasingly, these models were fitted with an early two-stroke oil mixing pump, fed from a reservoir incorporated in the petrol tank. Some also have a twin-spark plug ignition system firing an almost figure-eight shaped combustion chamber. Sears marketed considerable numbers of the Puch SGS split-single fitted with both these innovations as the "Allstate 250" or "Twingle" in the US. The improvements tamed, if not virtually eliminated, the previously notorious problem of two-stroke plug fouling. A total of 38,584 Puch 250 SGS motorcycles were produced between 1953 and 1970. Puch gave up racing in the 1950s, and split-single production ended around 1970, but the machines themselves remain well-regarded and collectable.
DKW 1931-1939 
TWN 1946-1957 
The German TWN motorcycle company (originally part of Triumph Motorcycles in the UK) experimented with split-singles in 1939 and started producing two models when production resumed in 1946. They used mostly Garelli's original Y-shaped connecting rod, so the pistons are "side-by-side", making the engine little different visually from a regular two-stroke, with the carburettor in the usual place behind the inlet cylinder bore.
The BDG125 125 cc was made from 1946 to 1957, the BDG250 250 cc from 1946 to 1957, the Cornet 200 cc from 1954 to 1957 (12v electrics and no kickstart), the Boss 350 cc from 1953 to 1957 and the Contessa scooter 200 cc from 1954 to 1957. The bulbous shape of the exhaust of the Cornet and Boss is a two-stroke TWN feature, not linked to the split-single-engine. All TWN motorcycle production ceased in 1957.
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Regulation implications 
For modern vehicle taxation purposes the split-single suffers no penalty and offers no advantage, as only the swept volume is considered, not the number of cylinders or spark plugs. This remains true even if the two pistons are not the same size and have different strokes (mechanically possible, if rarely used). This simple calculation was not always the case (see Tax horsepower, as used in the UK and some European countries in the 1920s and 1930s).
Lubrication weaknesses of the early "side-by-side" versions with the carburettor in the "normal" place behind the cylinder, were substantially the same as with all other two-strokes running on the same "petro-oil" mixture. However, they were greatly eased in the later ones, since the cool, lubricated mixture is delivered straight onto the hot (exhaust side) of the hotter, exhaust piston from the carburettor at the front of the engine under the exhaust.
Pollution from the original 1920s and 1930s total-loss lubrication versions was similar to other forms of two-stroke - however, the post-war split-singles from Puch (marketed in the US by Sears, Roebuck and Co.) were amongst the first to be fitted with pumped oil injection, making them substantially cleaner.
- Diagramatic split-single Fuel-air circulation and the Y-shaped connecting rod.
- Sammy Miller Museum Split-single torque and economy rival that of a four-stroke.
- The Garelli 350 cc split-single stayed in production until 1926 and made a major impact in racing.
- Trojan Two-stroke 1927 Science Museum photo of split-single with V-shaped Connecting Rod.
- Puch's two-stroke double-piston engines asymmetric port opening of 1923 Puch Marcellino design, inspired by industrial opposed-piston engines.
- Walker, Mick (2000), Mick Walker's European Racing Motorcycles, retrieved 2011-08-28
- "Allstate 250" 1966 from Sears. Note the mistake in this diagram, labelling of the "front" and "rear" pistons has been reversed.
- Friedrich F. Ehn: Das große Puch-Buch. Weishaupt, Graz 1993, ISBN 3-900310-49-1 (German). 38,584 Puch 250 SGS were produced from 1953 to 1970.
- Allstate "Twingle" Sears sold tons of them ... survived better than almost any other bike of that era.
- Adopted by Ing Zoller in 1931 the concept [of the Split Single Engine] was to make DKW the dominant racing motorcycle in the Lightweight and Junior classes during the pre war years.
- TWN split-single BDG250 A radical two stroker in 1953? Business Standard Motoring, Aug 2008.
- TWN Bike Review includes sketch of split-single "side-by-side" piston layout.
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- "Cylinder With Two Pistons Used In Motorcycle Engine" Popular Mechanics, December 1935 pg. 843 bottom left side.