Obviously, mounting the hammer below the receiver, where it swings upward to the barrel, offers several logical advantages over the side-mounted hammer. The shooter’s view of both the sights and the target is not interrupted by the distraction of a hammer protruding into the shooter’s field of view. Likewise, the percussion underhammer system keeps the flash and the shrapnel of the cap from the eye and provides a greater margin of protection to the face. It was, after all, the distracting flash of powder in the priming pan that inspired the first flint underhammer designs by Germanic gunmakers back in the 18th century (that's the 1700s for those who didn't pay attention in History class).
Clicking in the center of the photo above will enlarge it to provide a better idea of just how much flame and distraction is created by the flintlock. Remember, that when firing a flintlock rifle the flare seen here is much closer to the shooter's face than with a pistol held at arms length. By the way it is at this precise moment that you're supposed to be focusing on breathing, sight alignment, and trigger squeeze...
Yeah, right. They weren't nicknamed "flinchlocks" for nothing.
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Most underhammer designs feature a trigger that is in direct engagement with its hammer, thus eliminating the need for extra parts such as the sear, tumbler, fly, and bridle, as well as their attendant small screws and spring. A correctly designed hammer and trigger directly engaged, as in better underhammer designs, also eliminates the need of a set trigger mechanism to achieve a crisp pull of the trigger, although there are a few examples of older underhammer target rifles that were so equipped.