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The advantage was compactness. In the nineteenth century there was a need for the smallest powerplant with the highest power, usually in the shipbuilding trades. The less space the engine took, the more space you had for cargo.

It may have been a military ship, but the engine that powered the USS Monitor, is fascinating. It's strange motions was a result of the constraints of space. (I believe it was 300 horsepower).

http://youtu.be/VWn8gQ9Ykpk

...Ved.
 
I agree the Monitor engine is more compact than an equivalent conventional design. But the overcranked does not seem to deliver an improvement is size.
Given the same con-rod length there is no gain in placing the con-rod after the crank, but there is an increase in width to place the sliders which basically replace the cross head. The cross head take no more length than the stroke and the width is contained in the general envelope of the cylinder.

If this is a creative model then no justification is needed but if it is a model of a real engine there must be some other explanation.

I can see that the design is more compact if we consider only the cylinder+flywheel section. That part has a large envelope and the reduced length may be valuable in a hull, for example. The skinny extension of the con-rod and slides may be not a penalty.

In other words I am considering the volume of a rectangular box enclosing the engine versus a closely fitted shaped box volume.
 
For the overcrank engine, one possible place for that design would be in the hull of a small ship, where you need to have the propellor shaft in the middle - this design would fit the engine into a narrower hull than a normal one while keeping the output shaft centered. I dont know if that was the reason in this particular engine, but considerations like that were common reasons for an uncommon shape.
 
That make a lot of sense. The main power shaft is roughly in the middle of the total extension. Could use a vertical cylinder arrangement but that raises the center of gravity, risky for a small ship.
 

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