This straight up pull-up exercise with hands on the handles to the side trains the shoulders and back more along with the biceps. It will also work out the chest, core and glutes. By changing the angle at which you pull yourself up (how you grasp the handles with your hands), you can focus on different upper body muscles, and on each of them slightly differently, thus creating exercise variation.
Using a more forward pull-up with your hands on the handles more in front of you, you can perform the pull-up exercise to focus more on your chest, as a chest exercise.
I prefer to do this exercise using bars that offer a variety of handles with different angles such as the Hammer Strength workstation shown in this video. I will do this straight up pull-up using a wide and medium grip. You can also do a close-grip as well.
Method of Performance
Wide Pull-Up
Find a convenient way to reach the handles. I like to use the removable side bars to stand on and then reach for the handles very easily and safely.
Grab the widest handles for the wide grip with your palms facing away from you as well as keep your hands on the handles and your arms at your sides or as close as you can. This will allow you to pull yourself straight up. Having the hands more in front of you will pull you up more from the front and that is not what you should be doing for this exercise.
Pull yourself straight up as far up as you can go then lower yourself as far down as you can while still maintaining a slight bend in your elbow.
Repeat for the desired number of sets. I like to do 4 sets of 10 to 12 repetitions. For the later sets 8 -10 reps are fine.
Remember to breathe. Breathe out as you pull up and breathe in as you lower yourself.
Medium Pull-Up
Same way to do this exercise as the wide pull-up except the palms of the hands will face at an angle towards each other or more inwards.
TIPS
Stretch the lats and shoulders in between sets to maintain flexibility and prevent the “next day muscle soreness”.
By slowing down your pull-ups you can add in increased resistance