This is a topic that's come up several times over the years on the Karate CyberDojo: in the classic karate punch, the hand moves from the chambered position, with the fist palm-up at the hip or beside to chest, out to the target, turning over so that at the end of the motion the palm is down. It is important to maintain proper body alignment throughout the movement, but I think many karateka do not understand the alignment of the elbow and shoulder here. This is from a post I made to the CyberDojo today:
Put your arm straight out in front of you, palm up, point of the elbow down. There are two motions you can make to turn your palm down:
1) Keeping the upper arm in place, rotate just the forearm -- "pronation of the forearm at the radioulnar joint", to get anatomically geeky about it. The shoulder doesn't move, nor does the elbow. If you bend your elbow after this rotation, your hand moves upward. This is, I think, the "correct" movement.
2) Allowing the upper arm to move, rotate the entire arm from the shoulder -- "medial rotation of the shoulder at the glenohumeral joint". As you do this, the elbow moves up and out (superiorly and laterally) away from your center line. If you bend your elbow after this rotation, your hand moves medially, toward your center line. This is the "incorrect" movement, because it puts the shoulder in a weaker position and moves the elbow out of line.
Of course we're not robots that move only one joint, and I think we all have a little bit of movement 2; trying not to move the shoulder at all probably is counter-productive. But most of the motion to turn the fist over should be movement 1, at the forearm.