Koichi Tohei

The application of Aiki in the technique demonstrated by Koichi Tohei is analysed below

In this video, at the time of 2.36, Tori is threatened with a knife. Tori pivots about his front foot and induces Uke to apply Aiki, to unbalance himself, by pressing downwards on Uke's  knife arm. This induces Uke to push upwards by reversing the muscle torque about his front foot joint, so his heel rises, causing him to become unbalanced to the front due to his forward momentum. 

The application of Aiki in the technique demonstrated by Koichi Tohei is analysed below

In this video, at the time of 15.07, Tori is held by his jacket. Tori bends at the waist which induces Uke to pull upwards by lifting his heel(s) to resist Tori's downward movement.  This causes Uke to apply Aiki, to unbalance himself, by reversing the muscle torque about his foot joint(s), as he resists being pulled forward as Tori steps back.

Tori applies the atemi to deter Uke from stepping forward with his left leg to regain his balance.

In this video, at the time of 7.33, Uke holds Tori's wrists. Prior to stepping to the side, to unbalance Uke, Tori quickly lowers his wrists/body inducing Uke to follow Tori's wrists by bending at the waist and relaxing his arms to avoid becoming unbalanced to the front. Tori then induces Uke to apply Aiki, to unbalance himself, by turning his wrists to the side which Uke's hands can only follow by reversing the muscle torque about his foot joint, so as to lift his heel, as he pulls.