A member recently asked me to dig up the pictures from my previous arch threads, so I figured I'd repost them so newer members could get a chance to see them.
Arch Exercises:
Rest your foot (try to keep your toes off the ground so that you use your arch to point your foot, and not your scrunched up toes) and slowly try to straighten your knee, keeping the ball of your foot as close to the floor as possible. When you've straightened your knee, try to push the ball of your foot as close to the floor using only your muscles. I find this useful, because it helps me gain the strength to actually point my foot to the fullest.
Point your foot as much as you can, and then flex ONLY your toes, and THEN point your foot (but don't use your toes). I used to scrunch up my toes to make my point look nicer, and this helped a lot, because I learned to stretch the arch. Also, when leaving your toes flexed, stretch your knee to its fullest using all the muscles in your leg, its given me a good and stable demi-pointe when on flats.
I think this is pretty much the same as the tennis ball exercise, you wrap your foot around something round, trying hard to point your foot around it much as you can, and then lifting it away from the object, to see if you can hold that position.
My previous teacher would have very slow tondues as part of the warm up, the challenge is keeping your foot stuck to the ground as much as possible without shifting your weight. (2nd pic) It's a great stretch for the thigh muscles, and you also gain a lot of strength from going from demi-pointe to pointing your foot (last two pics).
Working with Hyperextension:
In this picture, I'm locking my knee instead of tightening my muscles. This is wrong for various reasons. Not only does it throw off your placement, but it forces you to curve your lower back, and centers your weight not on your whole foot, but on your heel, as the arrow is showing. This throws off your balance when on demi-pointe and pointe, forcing you to lean forward to counter the center of mass being slighty behind you. On pointe, it makes it all that much harder to go over the box and keep your balance.
Internally, it wreaks havoc on your knee; if you don't correct this wrong placement, it can cause inflammation to certain tissues surrounding the kneecap, and further pain by having the tissues getting pinched (yes, pinched, I can't describe the pain as anything else) between the tibia and femur.
This is the correct placement, the center of mass is centered on your foot, I've circled the muscles that you have to use to pull up. It's not about stretching the knee, you have to avoid sinking into your hip, and the only way to do that is by using the muscles around and ABOVE your knee, not behind it. If you haven't strengthened the necessary muscles however, it will take time to gain enough strength to pull this off.
Winging Your Foot:
How to wing your foot and at the same time maintain your arch stretched and your foot pointed? I figure a picture explains it better, so here goes:
Stand with one knee bent and your foot in demi-pointe (DON'T put weight on it, this is merely a way of gaining flexibility in your ankle, if you rest your weight on it, you'll injure yourself because this is NOT how you should be standing).
Go up as high as you can on demi-pointe on that ONE foot, (without resting your weight on it). Try changing where you've centered your foot; sickling your foot (first picture) would mean resting your weight on your pinkie, while winging your foot (third picture) would mean resting your weight on your big toe and lifting your pinkie. While you're doing this, try to maintain your demi-pointe, as in, don't wing your foot so far that your foot is almost flat. At first, you might be able to wing your foot only slightly, but as you increase your flexibility, you'll find it gets easier to wing your foot farther without sacrificing your pointe.
This is obviously not how one should stand on demi-pointe, I'm just using this as a way to show you how to find the muscles needed to wing the foot, and to get a feel of what winging the foot is.