I do my Pullups but the Dip asks to have elbows higher and opposite so I do with a shoulder rotation in order to be above the bar. Now, my elbows touche the bar and then I have nothing in my hands.
I have no problem to lift my body. I do 40 pull-ups after 40 Dips each days and could do easily 80 pull-ups if I move faster without a complete extension but I do 1 seconds to lift up and 2 seconds to lift down. I push air when I lift up and omoplate closer. I use the same way with dumbbells.
Some gyms have a pulls up fitness machine. This is similar to the Power Tower with a pad under the knees which one pushes you up. I think it is much better. My problem is with a strict muscle-up between the Pull-up and Dip. I do a transition but my elbows touch the bar.