The spiral is done from high to low (ue kara shita made). For tai jutsu, your hand must go between aite's hands.
Rotate 180º. The feeling here is identical to kokyu. That's what bring aite in his forward imbalance.
In the cutting phase, one must now step back with the right leg which must "disappear".
For tai jutsu, the rotation of your right hand on aite's right wrist forces him to release his grip with the right hand.
For the sword technique, the same result is achieved with the cut on the abdomen.
Cut the abdomen
Keep cutting backward with the ken now held with the sole right hand.
Open the body with the left leg so you can enter in aite's backward imbalance.
... by stepping in with the right leg.
Control the elbow for aite's rotation.
Aite's arm being in extension, push in the angle toward his face.
Aikido is not a sport, it is a martial art which laws (takemusu) are in harmony with the laws of the universe. Studying them allows the practitioner to understand his place in the universe. Aikido was born in Iwama, O sensei achieved in that village the synthesis of tai jutsu, aiki ken and aiki jo.
The International Takemusu Aikido Federation (ITAF) brings to the practitioner the structure he needs in order to work as close as possible to the reality O sensei MU defined. The official national representations are the guarantee of a teaching faithful to the Founder's.
In modern Aikido, weapons are hardly taught, if taught at all. In O sensei's Aikido, on the contrary, aiki ken, aiki jo and tai jutsu are unified and form together a riai, a family of harmonious techniques stemming from one unique principle. Each techniques helps understand all the others.
Peace is a balance between a human being and the world around him. The true martial art's goal is not to become stronger than one's opponent but to find in that opponent a way to realize harmony. There is no enemy anymore as such, but an opportunity offered to reach unified ki.