Kaiten Nage makes use of the Uke's arm as a lever to propel them past the Nage (performer of technique). Initially the Uke is charging more or less straight towards the nage with the intent to strike the head with an overhead strike. The nage steps to the side (to avoid the massive force of the charging Uke) while at the same touching the Uke's arm. This allows the Nage to use the entire arm as a lever. As in the diagram, the arm is helped along its forward path. Since an object (arm) is in motion, it will tend to want to continue in that path which is exactly what the Nage wants. As the arm follows is path around in a large circle, the Nage's other hand pushes the Uke's head forward and down while at the same time continuing the arc of the arm up and behind the Uke. So far the Nage has made no movements to oppose the Uke's forward motion, nor has the Nage changed the direction of movement of the Uke's center of mass.
The Uke is treated as a free body rotating around a point in space, namely his center of mass. The Nage seeks to maximize the amount of torque he can apply by using the head and arm, two parts of the body that are far from the center of mass, of the Uke as he passes. From the Torque Equation T = F*D, where D is the distance between the axis of rotation and the line of force. Applying this equation, the Nage can use less force with a greater D to gain the same torque needed to spin the Uke on his axis. Or, if the Nage so wished, he could apply a large F along with a large D to fling the Uke a fair distance and/or dislocate his shoulder.
The Uke will also lose his balance and fall down because he no longer has his feet under him. Though his body has not moved from its initial trajectory, the orientation has changed from the Nages manipulation of his body around a central axis of rotation.
See the whole thing in action with this nifty video (http://www.aikidofaq.com/multimedia.html).
Also available in the Nifty section.
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