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.
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.