Kanetsuka Sensei, as Peter notes, puts great stress on aikido having to work against a strong grip - I think this is partly a remnant of his initial training with Gozo Shioda, and partly the influence of Saito Sensei in the 1970s.
I really think that this emphasis on a "strong grip" is misplaced. Not that we didn't all train that way, back in the day, we did. But I have come to believe that this is a mistaken idea for several reasons.
a) it's bad martial arts - anyone ever win anything, UFC included, by grabbing someone, making his hand turn purple, and being immovable? The grabs we do come from attempts to keep an opponent from accessing a weapon. There would always have been either a strike with the other hand or a kick or both. Or the attack would have been designed to break the balance and the deliver atemi. You simply can't do that while you are tight. You lose speed. You create a direct channel for the other guy's power to hit your structure, etc It's actually easier to move someone who attacks like that than someone who grabs lightly and is has freedom to move because nothing is tight.
b) 50% of ones practice is in the role of uke. If we are striving for relaxed technique and complete freedom to move as needed, you do not want to be doing just the opposite half the time. Your body just gets confused. This is one of the things I appreciate about Endo Sensei is that he insists that the two roles be the same. He stresses connection and each partner is expected to connect to the others center and maintain that connection throughout the technique.
c) Sensitivity is far more important than strength in what we do. If you are tight, you are feeling you not the other fellow. I think part of having our teachers have us be "strong" in our ukemi was so we would eventually realize that it was a dumb way to attack. It certainly never worked with them...
What I now do with my students, starting right from the beginner level, is to teach them to grab and find the partner's center through the grab. We have the partner being grabbed throw an atemi with his other hand. The partner executing the grab should be able to prevent that strike from hitting just using the connection from his grab. He should also be able to prevent a kick from other foot, just through the grab. You can't actually do this if you are being "strong" unless you have a hundred pounds or so on your partner.
Next, we teach the attacker how to grab and achieve kuzushi via the grab and strike with the other hand. It is fluid, it is VERY fast, it is a light enough touch that the defender doesn't feel much until he is off balance and struck. To my mind, that is good martial arts. This whole thing about being strong and immovable is bad martial arts. It exists because the weapons basis of the art has been forgotten. Put edged weapons back into the equation and things change drastically.
Kevin Choate Sensei was having his students wear tanto in their belts when training. If you hunkered down and planted he'd either pull his own or your own tanto and stick you. You discovered that movement was necessary to protect your weapon and avoid the other fellow's. An attack needs to effect the other guy's center while you remain free to move and respond. That's a real attack and it's good martial arts. Anything that creates tension reduces your freedom to move and slows you down. That's bad martial arts.