Having an efficient Kip on the rig is a staple element for improving all gymnastic movements. Spending some time just focusing on and understanding the Kip Swing to become stronger in this movement will be so beneficial in the long run when it comes to linking pull-ups, toes to bar and bar muscle-ups. Even if you can already perform these exercises, working specifically on your Kip swing separately will help a lot!
Understanding Hollow & Arch positions:
Having a good understanding of the Hollow and Arch shapes is the 1st step to improving your Kip. Being able to move well from one shape to the other is a great place to start. The more you can practice these shapes on the floor the better.
Shoulder mobility will play a factor in your range of motion when it comes to jumping up on the rig to Kip. Being able to hang well and comfortably on the rig 1st, and then from there, you can start to activate the shoulders and the lats and press down on the bar (with straight arms) to create a hollow shape. Repeat this movement until it feels natural. From there we can then start to introduce the Arch into it.
The movement of the Hollow and Arch all comes from the shoulders and not the back or hips. So there should be no hinging at the hip. Think about squeezing your glutes and your core, keep your legs straight, your feet together and let your shoulders and lats do the work. Having a nice tight Arch shape will act like an elastic band does when you stretch it, it should feel like a spring and ping you back into that hollow shape again.
Lat strength is important when it comes to feeling that press down on the bar I mentioned earlier. The more you can press down at the back in the Hollow shape the better. Your pull-ups/toes to bar/muscle-ups will feel a lot more efficient if you can create this big press down.
Banded Lat press downs are a great exercise to add in to your training to build up those muscles needed to create that press down in your Kip.
Get practising and get your kip on!