Dismount the barbell using a pronated (overhand), shoulder-width grip and hold the barbell over your forehead so that your arms are slightly slanted backwards.
Execution
Keeping your upper arms still, inhale as you lower the barbell toward your forehead in a smooth, semicircular motion by flexing your elbows.
Exhale as you reverse the movement and push the barbell back up to the starting position by extending your elbows.
Repeat for the prescribed number of repetitions.
Comments and tips
Keep your shoulders and upper arms fixed. All of the movement should be in your elbows.
Do not allow your elbows to flare out, as this will allow your pectoralis major and anterior deltoid to get involved, which will take the emphasis away from your triceps brachii.
The point of holding the bar over your forehead in the starting position is to ensure that your arms are slightly slanted backwards, which will ensure that tension is kept on your triceps throughout the movement.
For obvious reasons the barbell skull crusher can be dangerous. Start light, add weight gradually, and always keep the movement under full control.
