Ikkyo, Nikkyo, Sanyko, Yonko, etc... We all know them as "First technique, Second technique, etc". Or perhaps "First teaching, Second teaching..." But I recently watched a YouTube video in which they were referred to as "First principle, Second principle... etc."
This was an "aha" moment for me. There are a number of common principles in Aikido. Each school would have a different set of them -- each teacher, each person, even. I'm talking about things like centering, breathing, blending, "live blade," self-control, balance, extending Ki, weight under center, movement. There are so many.
I think that each technique we show, and even each variation we show, or attitude with which we show it, can focus on certain Aikido principles. Some techniques lend themselves better to certain principles over others.
I find myself, when I'm teaching, looking around the room and watching people train, noticing different things. Perhaps I'm seeing errors in simple mechanics.Those are easy. But I'm also looking, consciously or unconsciously, for certain principles.
For example, in our dojo we make a distinction between irimi-nage and kokyu-ho (or is it kokyu-nage?-- after 20 years I'm still not sure of the difference). Even though some of the mechanics of certain variations can be very similar, by focusing on a particular principle we can see some differences. Irimi is "entering," so we focus on entering, and the technique can become a bit more assertive, even aggressive. Kokyu is "breath," and so the technique can be more "opening" -- more "flowy." The basics of the variation can be very similar (say, from Ryote-dori or Katate--dori). Both techniques can be very effective. Each involves principles of the other. The emphasis might depend on the teacher, the Uke, the Nage, the particular attack, etc...
If we're Kose-dori doing Nikkyo, I might focus on finding a direct line to Uke's center (or even my own). If we're doing Yokomen-uchi Shihonage, however, all that motion might lend itself more to a focus on movement, or of maintaining center connection.
All principles apply all the time, probably, but some techniques lend themselves better to demonstrating certain principles more than others.