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The kipping pull-up employs elastic loading of the shoulders and hip movement to unload bodyweight momentarily. Begin hanging from a bar with a pronated grip. Push the hips forward, creating an arch as you would in a bridge. Explosively reverse the arch into a hollow, initiating a pull-up with the arms as you reach the peak of the backward curve. After reaching the peak of the pull-up (chin over bar), push yourself back horizontally, creating a curved descent to load the next successive pull-up.
These should be performed only by individuals with good shoulder flexibility and whose shoulders and elbows have been well-conditioned to loading through traditional pull-ups. The kipping pull-up is NOT a substitute for the traditional strict pull-up.