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Ashi guruma is a throw where tori off-balances uke to the front and tori spins to wheel uke over the fulcrum of tori's outstretched leg (and not a reap, like harai goshi). I find it easiest to execute ashi guruma in using the inner-outer circle principle where you occupy the center and move opponent around the outside, rather than with a static uke. I think I understand ashi guruma well.

In Kyuzo Mifune's Canon of Judo, Mifune states that he as a small person developed o-guruma to throw larger people using the inner-outer principle.

My understanding of o-guruma is that the off-balancing and entry are quite similar to ashi guruma, but the key distinction is in the placement of the tori's leg near uke's hip rather than near uke's knee. This placement makes very little sense to me as an alteration to ashi guruma; the fulcrum is moved closer to uke's center of mass, which results in uke's forward motion being blocked rather than rotation about the leg fulcrum into a successful throw.

Kodokan Judo Throwing Techniques by Toshiro Daigo, Kodansha International, Tokyo 2005, p. 184:

The difference between o-guruma and ashi-guruma lies in the area of tori's leg that he uses to press with, and the part of uke's body that is pressed. The technique will be classified according to the function of these parts.

What am I missing that makes o-guruma successful? Is there a different setup entirely?

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The principles as I learned them (or had to make sense of by myself) are pretty different.

While in ashi-guruma you really block his leg, having to apply your force mainly backwards, o-guruma is a throw that works the following way:

It is applied from quite some distance, standing outside of your partner, but nevertheless applying force in the center of the partner (inner-outer-principle). You are attacking the hips from underneath, lifting it ever so slightly. You achieve this by turning your heel up, sliding along the thighs (already applying force), and locking in at the hip, as the partner should (similar to ashi-guruma) stand bent forwards in this moment already (Mifune: "It is also important that the leg stretched out must sweep up in a rolling way", Canon of Judo, p. 112). Sometimes, the upwards pressure on the thighs is enough already. This little "bump" is all you should need. It is a bit similar to how harai-goshi should be thrown, especially in nage no kata: only a very short, explosive lifting movement by the leg - but here the partner is pivoting around the hip, therefore harai-goshi is koshi waza albeit the leg is seemingly doing most of the work.

This means that the pivotal axis is completely different: In ashi-guruma it is in line with the side of your whole body, diagonally to the ground when looking from the front; you twist uke's body around the side of your body. In o-guruma, uke tilts frontwards around your leg, which is parallel to the ground. You apply the inner-outer-principle to push uke over your leg as it were. This brings o-guruma regarding the mechanism of uke's movement closer to hip and shoulder throws. While the inner-outer-principle of how to apply the force to the upper body is similar to ashi-guruma, the directions of force are different.

And this explains why it favours smaller persons: Being taller, it is virtually impossible to apply the upwards, lifting movement in the centre of uke's body and much easier to twist a smaller uke around you. Lifting, which enables you to tilt/push over your opponent in the first place, is possible only by bending the standing leg to get low enough, which obviously screws stability. This is not very realistic, especially considering that the inner-outer-principle requires much stability in the standing leg to apply force.

I think keeping this in mind, you can see that the gifs quite well depict the differences. Just look at how the legs are moving and the heels are turned.

Regarding the application I would say the smaller you are in comparison and the more the partner is bent over already, the more sense it makes to do o-guruma rather than ashi-guruma, because ashi-guruma needs quite a lot of twisting uke's body around your leg (which you can't do when you are smaller and/or weaker), whereas o-guruma just needs a little bump from underneath, which of course is even easier with a partner that is bent over.

Mifune himself wrote about it:

A big player is naturally higher in center than a small player. It is comparatively easier to float and break the opponent in a circle by utilizing the center. So, I came to think it wise to snatch the big opponent's exterior circle: this this technique I contrived. (The Canon of Judo, p. 111)

You can see the moment when to apply it here, executed by Mifune himself

Therefore, it really comes down to being forced to and having advantages in it because of being small.

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