Set up at the pull-up bar with a medicine ball beneath you, then hop up and clamp the ball between your legs. You should feel an automatic core response. By squeezing your adductors, your abs will light up, creating a much safer position from which to execute your pull-ups. This will look almost like the foundational "hollow body" position in gymnastics.
Start with a heavy ball and have a lighter one nearby. Do as many reps as possible with the heavy ball, drop to the lighter one and attempt a few more reps, then finish up with as many unweighted reps as possible. Do 3 sets. This is much easier than having to unbuckle a chained dipping belt.
And, as seen in the video, the same method works great for dips too.