Artemis BJJ (MYGYM Bristol), Can Sönmez, Bristol, UK - 01/08/2016
For the escape to the knees, Roy Dean is a useful reference point, so I'll be drawing on his method from Blue Belt Requirements as usual. It begins in much the same way as the shrimp back to guard. First thing to note is that they will want to kill your near arm. This is bad for you, because it means you can't stop them shifting up towards your head. From there, they can make as much space as they want and pass to mount.
So, you need to get your arm inside, the forearm pressing against their hip: this is a bit more reliable that grabbing the gi material, as they can potentially still bring their body onto your hand and collapse it due to the loose material. The forearm into the hip will help block their movement, and initiate your attempts to create some space. It should also help you block them moving to north south, as if you clamp your arm by their side, your body will move with them if they try to switch position.
One thing to note is that having your forearm by their hip like that does leave you more open to the cross-face. So, you could potentially block inside their cross-facing arm instead, which will prevent their shoulder pressure. This is the Saulo method from his book, which has advantages, but personally I prefer to block the hip.
With your other hand, grab the gi material by their shoulder, close to their neck, then pull down. Twist that arm up into their neck, keeping the elbow in: you need to be tight here, as otherwise they will go for a figure four on that arm. Once you've got the forearm into their neck, they can't press down into you, as they'll essentially be choking themselves. Note that this is a block: you don't want to start pushing and reaching, as that may leave you vulnerable. Reach too far and they can shove your arm to one side and set up an arm triangle.
Next I moved on to the legs. Your legs have two main purposes here: first, blocking your opponent getting to mount. Raise your near knee and drive it into their side. The idea is to wedge them between your knee and the arm you have by their hip. Personally, I like to keep my knee floating, glued to their side.
Many people prefer to cross their foot over their knee, which is something I used to do in the past as well. However, as this long Sherdog thread discusses, that can leave you open to a footlock, and also limit your mobility. Then again, you can see it used at the highest levels, like here at the Mundials.
The second use for your legs is bridging. Marcelo Garcia has a handy tip for this (although the escape he is doing there is slightly different), related to increasing the power of your bridge. To do that, bring your heels right to your bum, then push up on your toes. That increases your range of motion, so you can really drive into them.
Make sure you turn into them as you bridge, rather than just straight up. This will help the next part, which is to shrimp out as you come back down. That's why you've created space in the first place: if you simply plopped back down, then you've wasted the opportunity.
After you bridge and shrimp, rotate the arm you have by their neck under their armpit, then reach for their legs or around their back. Roy Dean then shifts out to the side, ending up crouched next to them (as in the picture): I find that's the most intuitive method. At the same time, bring your bottom leg under your top leg, reaching further around their back as you fully turn to your knees. It's the same motion as the shrimp to knees drill I do during the warm-up.
From there, reach for the far knee and drive forward, moving to the top position. Another typical method leaves you square on, but I personally am not keen on that position as I find it is more awkward to crawl up into a strong base from there. However, again, it is a totally valid variation: experiment to see what works best for you.
Teaching Notes: The question of how high to come up when you go to your knees arose again today. I tend to recommend staying low, as I feel that the higher you go, the more space they have to spin back into guard. Something for me to think about though, perhaps I'm wrong and it's ok to go high. Lots of ways to execute any technique in BJJ after all, which is one of the things I like so much about it. :)