MIKE GEORGE says: Inertia mechanisms are driven by the recoil of the first barrel being fired. A typical inertia mechanism consists of a small steel weight attached to the end of a vertical lever within the mechanism.
When the first barrel fires, the whole gun recoils backwards, until this movement is arrested by the shooter’s shoulder. When the gun stops, the inertia weight tends to keep going, moving the lever to which it is attached. This movement of the lever transfers the trigger to the firing mechanism of the second barrel.
The system usually works very well. Failures can be caused by over-lubrication of the mechanism, so the movement of the lever is prevented by gummy oil. Its efficiency also demands the shooter fully releases the trigger between shots. A rarer failure can be caused by the shooter pulling the trigger with the gun not mounted firmly to the shoulder.
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