Aside from being one of the more unfortunately-named early repeating pistols, the Schlegelmilch is also one of the earliest and more unusual mechanically. It also the only example I am familiar with of a pistol made entirely with square-headed bolts rather than slotted screws, for what it’s worth.
The gun was designed in (or about) 1891 by Louis Schlegelmilch, who was at the time the chief armorer at the Spandau Arsenal in Germany. It is chambered for a proprietary 7.5mm cartridge, and was built for a series of trials in 1891/2 to find a replacement for the 1884 Reichsrevolver. The trials failed to find a gun worthy of adoption, and the Schlegelmilch was never manufactured again.
In total less than 20 examples were made, of two different variations. Only one of each variation is known to survive today (the other one in the collection of the Koblenz museum). I am not familiar with how the other variation differed form this example, but the mechanics of this one are quite interesting enough on their own.
The Schlegelmilch is not actually a semiautomatic pistol, really, but rather a mechanical repeater. The difference being that in a semiauto, the mechanism is operated by energy from the firing, in the form of either gas or recoil. Mechanical repeaters have no system for utilizing the energy of a fired cartridge and instead rely on the shooter to provide all the input to cycle the action. Other examples of mechanical repeaters include the Volcanic, the Berger, and the Schulhof (among many others).
The Schlegelmilch can be used as a double action weapon by simply pulling the trigger or as a single action weapon by manually cocking the hammer and then releasing it with a shorter trigger pull. The James D Julia catalog entry from when this pistol sold a couple years ago has a good description of the mechanical action:
Bringing the hammer to half cock moves the bolt horizontally to the left, exposing the entire chamber, while simultaneously moving the extractor rearward to eject a fired cartridge case. The magazine is fed from above with a stripper clip. Continuing the hammer cock pushes a loading arm forward that feeds the next round into the chamber. Near the end of the hammer movement the bolt returns to the right into the closed position, aligning a freely moving pin in the frame with a concentric firing pin in the bolt. After pulling the trigger to drop the hammer, the trigger springs back to its original position during which time the loading arm retracts and the cycling arm repositions the bolt for the next operation phase. Mounted to the left frame is checkered safety lever that blocks the mechanism when moved up.
In short, pulling the trigger causes the bolt to move left, an extractor to pull out the fired round, a loading arm to load a new cartridge, the bolt to return to the right, and the firing pin to fall and fire the chambered round. How’s that for complicated? As with many of the other early repeating and automatic pistols, this design was technologically advanced but complex and ungainly enough to not actually be more effective in use than a standard old-fashioned revolver.