"...even motioncaptured movements seem unnatural and give no illusion of life."
I often agree with this. When digging deeper into the details of why this is the case, it's often because the motion captured data is played back on a model of different proportions than the actor. I think I first noticed this when a magazine article did a writeup on The Polar Express movie. There's a photo of Tom Hanks in a mocap suit beside a rendering of the train conductor in the same pose. The conductor's proportions were completely different from the real Mr. Hanks. I've also noticed this problem when ballet is mocapped and applied to computer models.
My opinion, since I'm no CGI expert nor hobbyist, is that actual natural movement has no place in a cartoon. You'll notice that each of Pixar's worlds maintains its own naturalness - Mr. Incredible moves the right way with respect to the 3D model in his own universe as do the other characters. Although they modeled Syndrome's swagger on a Pixar employee (or at least a real human if not a fellow Pixarite), that doesn't mean they applied an actual mocap session's data to the character model. Every time I've seen anything "behind the scenes" of a Pixar film, they're animating movement 'manually' and maintaining a 'natural' feeling within the context if the current project.
I agree about cartoons. The creation of movement is essential part of the uniqueness of given art piece. But I'm talking about endeavors that aim to create virtual version of reality, some games, movie fx etc.
Maybe simply sin(x) and cos(x) with some limitations on how much it can flex.
If you look at your arm joint from the elbow up, keep your elbow in a fixed point you move your arm in a circular motion on a plane. The same applies for your hand on your wrist joint.
Extending that your arm moves in 3 dimensions so fixed point elbow means you can move your arm in a sphere.
But you cant reach every point on the sphere, because of the way the muscles work, which is why you need to limit it. It's really hard to get those limits right, which is why the artificial characters dont look natural .. if their hand moves to a point where your subconscious mind see's that position would be painful or impossible, then it looks unnatural.
My old calculus teacher used to always tell us to flip the paper around when you're drawing a curve, so the curve you're trying to draw moves naturally with the arc of your arm .. you get a much sexier curve that way.
It depends how you move your hand, of course, but 'easeInOutQuint' from Robert Penner's easing equations[1] is a fairly good approximation of a hand, finger, or cursor moving quite quickly from one point to another in a straight line.
The movement is almost linear, except for the rapid acceleration when you hand begins to move and the rapid deceleration as it slows to focus on a point.
[1]: Example, with onion skinning: http://gizma.com/easing/ [requires Flash] (Check x and y under the "Qnt" column on the bottom row, then click anywhere in the box to move the ball.
I'm not sure why but for me even motioncaptured movements seem unnatural and give no illusion of life.