Robert M Watson Jr
Don't need much help there ...
I know. I was thinking of that when I wrote it. In general, it's a very vague relationship that comes down a vague flow from a very vague history. Even Mochizuki Sensei used Katori Shinto Ryu sword to explain how aikido is "base on kenjutsu" though Ueshiba did not use KSR in his sword. I'm given to believe that both Ueshiba and Takeda before him were considered extremely good swordsmen but very few after them could begin to understand anything about the sword. And it may be because of that that aikido mastery has declined in the following generations.
Even though I trained a long time with Mochizuki Sensei and his students, including Kyoichi Murai, in kenjutsu, I don't consider myself to understand much about sword. I just know that the intent is not to bang the swords together, but simply to cut the other guy.
Beyond that, based on a comment attributed to Morihei Ueshiba (translated, I think, by John Stevens), I concluded that the thrust is the primary technique of the sword and that the downward cut emerges from the forward thrust. Ueshiba's comment? "The essence of aikido is thrusting with the katana."
But as far as any vestigial reputation aikido has for roots in kenjutsu, I think Graham's Golden Center videos drive a big nail in the coffin...