Ugoki isn't something you add to your movement. It's already there. Watch someone walk. One shoulder dips, the other rises, then they trade. Nobody taught him or her that. He's been doing it since he was a toddler. That down-up flow, the "U," is just how the body moves when nothing is jamming it up. Now watch what happens when the same guy gets scared or tense. He climbs instead of flows. Rises high, collapses, rises high again. Over "N" movement. It's what shows up when people fight instead of move. It burns energy fast, breaks down the second real pressure hits, and it isn't sustainable for more than a few seconds. This is the whole problem with most training. Many are drilling technique on top of Over "N" movement and wondering why it falls apart against resistance. You can't fix bad structure with more reps. You fix it by going back to the thing your body already knows how to do. Ugoki doesn't fight gravity, it uses it. It doesn't fight your structure, it comes from your structure. This is why it adapts in any direction and why it never runs out of gas. This is the foundation everything else in Budo Taijutsu sits on top of. Not a technique. Not a stance. The way the body moves when you stop interfering with it. Natural, efficient, and unfakeable.

Note the "u" shaped shoulder movements & the coil. How would an "n" shaped shoulder movement change things? U for Ugoki also reveals the walking foundation of taijutsu. https://youtu.be/jPSpHZF2y6A?is=QwZss0tEVOW3cTA2