Artemis BJJ (MYGYM Bristol), Can Sönmez, Bristol, UK - 11/09/2015
For the north south kimura, start in side control, controlling their far arm. This is made easier if they aren't careful and let you bump their arm up onto your shoulder. Often they'll put it there themselves, attempting to reach your head, enabling you to trap their arm by your shoulder. Another possibility is that they turn and try to get an underhook.
Whether they put it there or you do, the next step is to wrap your arm over theirs, aiming to get just under their elbow to kill mobility in the limb. Ideally, also pull them up by that arm, so they're rolled onto their side. To lock it in place, grab your own collar, or just somewhere on your gi if you can't reach far enough. You'll also want to use you head, clamping your skull against their forearm. Braulio advises following their arm with your head: e.g., if they try to fling it down to the mat or something like that. Don't let them work their arm past your head.
You're also going to move round to north-south, so again you need to block their legs from running after you by putting a hand on the mat, near their bum (although it should be a bit harder for them to turn if you've locked up that arm). As you move around, you want to jam your knee into the armpit of their free arm, swivelling your lower leg under that arm as you move around. That makes it harder for them to escape. If you can't manage that, slide your knee over their free arm once you've got to north south. It is useful to maintain some kind of control on that free arm, as otherwise they can use it to try and create some space to escape.
You essentially end up sitting on their head, so in drilling, be aware that you don't want to squish your partner. You can take a bit of the weight off by transferring it to your knees: obviously in competition, that's less of a concern. As you sit up, make sure their elbow is glued to your chest.
The next important step is to establish a figure four on their trapped arm, which can be easier said than done. One simple method Kev showed me is to put your free hand in place, ready to grab their wrist. Next, turn your head away from their arm: this will push your shoulder forwards, which will then also knock their arm forwards, putting the wrist right into your waiting hand. It's then simple to complete the figure four grip.
To finish the kimura, simply turn back in the other direction, pushing their wrist towards the side their elbow is pointing . Alternatively, you can also bring the elbow of your non-clamping arm to their trapped arm side. Turn your body so you're facing their head, then apply the kimura from that lower position.
If you make a mistake while looking to apply the kimura from that upright position, or they simply defend well, you might find that they are able to grab their own belt or gi. This will make it tough to complete the submission. You can try pulling in the direction their knuckles are pointing, or Roy Dean's option of using rhythm to break that grip. Push their arm towards them twice, as if you are really trying to break their grip, then yank hard in the other direction (aiming for the direction in which their fingers are weakest). Lovato Jr suggests adjusting your grip so that you're holding the meat of their hand rather than their wrist. He then does two quick jerks to yank their hand free.
Should none of that work, you can instead switch to an armbar. Bring your knee up on their trapped arm side. This will enable you to put your whole body into it when you turn towards their other side, which should break their grip. Make sure you keep that figure four grip, as it is about to prove useful. If possible, you also want to try and slip your foot into the armpit of their free arm, which should help prevent their escape attempt.
Pinch your knees together to control their arm, in what is sometimes called a 'Japanese armbar' position (I'm not sure why: something from Japan, I guess? Or maybe Pancrase? Leave a comment if you know). You don't have both your legs over their body, which means that the hitchhiker escape is a possibility. It's called that because they lead with their thumb pointing the way out, turning their body and walking around.
However, because you have that figure-four grip, they can't use it anymore. If they try to turn away, you can just apply the kimura. In order to relieve the pressure, they'll have to turn back. You can then drop to the mat, switching your grip to finish the armbar as normal. Another option is to grab their leg, wrapping underneath it ideally. That will prevent them turning, because they need to swivel that leg down: they can't if your arm is in the way.
Teaching Notes: I'm still going with the 'they make a mistake' version, wrapping their arm around your head, which means you have to switch arms for the figure-four grip. The other version, where you trap their elbow straight from their defensive frame, could be better as there isn't that arm switch? I showed it briefly, but it felt awkward, so I need to try it more myself. Something to emphasise even more next time is locking their arm into your chest, as some people having trouble with that. Having said that, Ryan Hall has a different method on his Open Elbow DVD, trapping it against his bicep, so there are other options I could consider.