The origin of this rifle can be traced back to the final years of World War II when Mauser engineers at the Light Weapon Development Group (Abteilung 37) at Oberndorf am Neckar designed the MKb Gerät 06 (Maschinenkarabiner Gerät 06 or "machine carbine instrument 06") prototype assault rifle chambered for the intermediate 7.92×33mm Kurz cartridge, first with the Gerät 06 model using a roller-locked mechanism which was unique for being gas operated, as opposed to recoil operation, originally adapted from the MG 42 machine gun, but with a fixed barrel and conventional gas-actuated piston rod.
After observing bolt-bounce during firing trails of the roller locked Gerät 03 prototype semi-automatic rifle Dr. Karl Maier, one of Mauser's scientists at the time, realized that with careful attention to the mechanical ratios, the gas system could be omitted.
The resultant weapon, the Gerät 06H (the "H" suffix is an abbreviation for halbverriegelt or "half-locked") was assigned the designation StG 45(M) (Sturmgewehr 45(M)).

Though appearing simple, developing the roller-delayed blowback firearm action was a hard technical and personal effort, as German engineering, mathematical and other scientists had to work together on a like-it-or-not basis led by Ott-Helmuth von Lossnitzer, the director of Mauser Werke's Weapons Research Institute and Weapons Development Group.
Experiments showed roller-delayed blowback firearms exhibited bolt-bounce.
To counter bolt- bounce the perfect angle choice on the nose of the bolt head had to be found.
Mathematician Dr. Karl Maier provided analysis of the components, assemblies in the development project.
In December 1943 Maier came up with an equation that engineers used to change the angles in the receiver to 45° and 27° on the locking piece relative to the longitudinal axis solving the bolt-bounce problem.
With these angles the geometrical transmission ratio of the boltcarrier to the bolthead became 3:1, so the rear boltcarrier was forced to move three times faster than the bolthead.
The rearward forces on the boltcarrier and receiver were 2:1.
The force and impulse transmitted to the receiver increases with the force and impulse transmitted to the boltcarrier.
Making the boltcarrier heavier lessens the recoil velocity.
For Mausers Gerät 06H/StG 45(M) project Maier assumed a 120 g bolthead and 360 g boltcarrier (1 to 3 ratio).
However, the design required that the bolt started moving while the bullet was still in the barrel and the spent case fully pressurized.
Using traditionally cut chambers resulted in separated cartridge case heads during testing.
This problem was solved by cutting 18 longitudinal gas relief flutes in the chamber.
Fluting the end of the chamber allowed combustion gasses to float the neck and front of the cartridge case providing pressure equalization between the front outer surface of the cartridge case and its interior.
During the process, the front cartridge case would typically show blackened, longitudinal scorch marks around the diameter of the case which was characteristic for later roller-delayed blowback-operated small arms, which also used the fluted chamber principle.

The roller-delayed blowback firearm action was patented by Mauser’s Wilhelm Stähle and Ludwig Vorgrimler.

Like the German FG 42 battle rifle/automatic rifle and Sturmgewehr 44 assault rifle the StG 45(M) was one of the first inline firearms incorporating a "straight-line" recoil configuration.
This layout places both the center of gravity and the position of the shoulder stock nearly in line with the longitudinal axis of the barrel bore, a feature increasing controllability by reducing muzzle rise during burst or automatic fire.

The elevated sight line over the bore axis layout was also adopted from these designs as it helps to extend the "battle zero" range.
The current trend for elevated sights and flatter shooting higher-velocity intermediate cartridges in assault rifles is in part due to a desire to further extend the maximum point-blank range, which makes such a rifle easier to use.

The StG 45(M) was
The origin of this rifle can be traced back to the final years of World War II when Mauser engineers at the Light Weapon Development Group (Abteilung 37) at Oberndorf am Neckar designed the MKb Gerät 06 (Maschinenkarabiner Gerät 06 or "machine carbine instrument 06") prototype assault rifle chambered for the intermediate 7.92×33mm Kurz cartridge, first with the Gerät 06 model using a roller-locked mechanism which was unique for being gas operated, as opposed to recoil operation, originally adapted from the MG 42 machine gun, but with a fixed barrel and conventional gas-actuated piston rod. After observing bolt-bounce during firing trails of the roller locked Gerät 03 prototype semi-automatic rifle Dr. Karl Maier, one of Mauser's scientists at the time, realized that with careful attention to the mechanical ratios, the gas system could be omitted. The resultant weapon, the Gerät 06H (the "H" suffix is an abbreviation for halbverriegelt or "half-locked") was assigned the designation StG 45(M) (Sturmgewehr 45(M)).
Though appearing simple, developing the roller-delayed blowback firearm action was a hard technical and personal effort, as German engineering, mathematical and other scientists had to work together on a like-it-or-not basis led by Ott-Helmuth von Lossnitzer, the director of Mauser Werke's Weapons Research Institute and Weapons Development Group. Experiments showed roller-delayed blowback firearms exhibited bolt-bounce. To counter bolt- bounce the perfect angle choice on the nose of the bolt head had to be found. Mathematician Dr. Karl Maier provided analysis of the components, assemblies in the development project. In December 1943 Maier came up with an equation that engineers used to change the angles in the receiver to 45° and 27° on the locking piece relative to the longitudinal axis solving the bolt-bounce problem. With these angles the geometrical transmission ratio of the boltcarrier to the bolthead became 3:1, so the rear boltcarrier was forced to move three times faster than the bolthead. The rearward forces on the boltcarrier and receiver were 2:1. The force and impulse transmitted to the receiver increases with the force and impulse transmitted to the boltcarrier. Making the boltcarrier heavier lessens the recoil velocity. For Mausers Gerät 06H/StG 45(M) project Maier assumed a 120 g bolthead and 360 g boltcarrier (1 to 3 ratio). However, the design required that the bolt started moving while the bullet was still in the barrel and the spent case fully pressurized. Using traditionally cut chambers resulted in separated cartridge case heads during testing. This problem was solved by cutting 18 longitudinal gas relief flutes in the chamber. Fluting the end of the chamber allowed combustion gasses to float the neck and front of the cartridge case providing pressure equalization between the front outer surface of the cartridge case and its interior. During the process, the front cartridge case would typically show blackened, longitudinal scorch marks around the diameter of the case which was characteristic for later roller-delayed blowback-operated small arms, which also used the fluted chamber principle.
The roller-delayed blowback firearm action was patented by Mauser’s Wilhelm Stähle and Ludwig Vorgrimler.
Like the German FG 42 battle rifle/automatic rifle and Sturmgewehr 44 assault rifle the StG 45(M) was one of the first inline firearms incorporating a "straight-line" recoil configuration. This layout places both the center of gravity and the position of the shoulder stock nearly in line with the longitudinal axis of the barrel bore, a feature increasing controllability by reducing muzzle rise during burst or automatic fire.
The elevated sight line over the bore axis layout was also adopted from these designs as it helps to extend the "battle zero" range. The current trend for elevated sights and flatter shooting higher-velocity intermediate cartridges in assault rifles is in part due to a desire to further extend the maximum point-blank range, which makes such a rifle easier to use. 
The StG 45(M) was 
StG 45(M)