There have been a couple of threads about tenkan recently. One technical discussion about morotedori - a two hand grip
http://www.aikiweb.com/forums/showthread.php?t=18086 was very interesting for all the different perspectives and insights.
There was some more good advice in another discussion about tenkan
http://www.aikiweb.com/forums/showthread.php?t=18240. Mark Murray and I disagreed about a specific technical point which could have been confusing for beginners but he was very polite and reasonable. We thought a more advanced technical discussion thread about tenkan, not an advice thread for beginners, could be useful. So there is no right or wrong. Any ideas or comments are welcome.
ten means turn or revolve or roll 転
kan means change 換
So tenkan means change with an idea of turning 転換
It doesn't even have to be a physical movement. It can be a change in the situation.
kibun tenkan means a change of mood or a change of pace 気分転換
In aikido a tenkan changes the situation from a confrontational and possibly dangerous state with two people (and their energies) facing each other to a relatively safe and (possibly) cooperative situation with the two people (and their energies) facing in the same direction.
There are going to be differences in the way different ryuha do tenkan and differences even within the same traditions so perhaps it's easiest if I just describe a couple of the different ways of doing tenkan and then everyone else can add their own ideas.
I do all my movements in basically the same way: the first part of my body to move is my face, then my hips, then my trunk and then my shoulders and arms. I move my hips as opposed to my centre because I want to use that hip turn to generate soft controlled centrifugal force. My body is completely relaxed but is natural and full of energy. My posture is straight and my chest and shoulders are open. My heart too hopefully!
It's perhaps also worth pointing out that even though we often do tenkan as a complete exercise that would not normally be the end. Something happens after that!
The orthodox way to do tenkan is a body turn with your back leg describing an arc to end up beside or behind the uke. In the basic movement your arms finish up with your hands extended palm up. Your body weight is transferred through your arms to control the uke.
A second way is similar but with your hips lower and a wrist turn in the opposite direction so that it ends with your palms facing down. The advantage of that method is that the uke is overbalanced upwards instead of downwards. Uke's arm becomes extended and vulnerable and easy to take.
A third way is not to move your back leg. You turn your body but you keep your feet roughly in the original position, just turning them in the other direction. This tenkan is especially effective for breaking the uke's balance. It is also a very effective method for showing you if you are using unnecessary power because if you are you will be blocked easily. I use this tenkan the most because if I want to go in a certain direction (which happens to be the direction the uke is already facing) it seems to me to be wasted motion to go in the wrong direction to get beside or behind the uke first.
A fourth way develops this third way by starting off just by drawing in your wrist to your own centre, keeping the connection to the uke and then continuing that movement by adding a hip turn.
I'm sure there are many other ways and many other approaches.
photo: Gandhi Statue by Brandon Doran (http://www.flickr.com/photos/brandondoran/) used under creative commons licence. The ultimate tenkan.