At the end of Okinawan parties or events, they often do a dance called kachashi. This is a very free and spirited dance. There is an example at YouTube at:
We sort of do a similar "dance" to teach koshi. We begin by teaching students to relax their arms (with their elbows close to their body) and wave them from side to side. We start in the gedan position but progress to chudan and jodan. Soon the students can wave their hands in all positions while moving their koshi from side to side (in a sort of rotary way).
When they can do this, we teach them to be able to throw Karate techniques from the rhythm of the kachashi-like movement. For example, the student might swing his arms in the gedan position and then throw a gedan barai. As he progresses, the student can learn to throw any movement. Essentially, all movements are either like a backhand or a forehand, and either directional movement is easily accessible from within the "dance."
More advanced students can "walk" while dancing -- and throw techniques while moving. Even more advanced students can learn to internalize the rhythm.
Sometimes we hear that there is Karate in Okinawan dances. Perhaps this is true, although I do not think that there is modern linear Karate in the dances. Any Ti techniques would probably be more flowing, like Aikido or Ju Jitsu.
I do know that koshi exercises can look a lot like some movements of Okinawan dances. Whether this is a coincidence or not, I cannot say.
Charles C. Goodin