Makkikomi-shutō uchi, the winding knife-hand strike, is a "karate chop" variant, mainly used to strike the neck or throat of an opponent who is beside you. Despite a deceiving appearance, makkikomi-shutō strikes are linear techniques.
Winding knife-hand strikes are chambered like a downward-fist block. Raise the striking hand to your opposite-side ear, with your palm facing inward. Place your open, opposite-side hand underneath the elbow of your striking arm, to cover your exposed ribs. The picture below will make things clear:
[photos of makkikomi shuto ready position, from the front and from the side.]
From here, pull your elbow straight backwards, so that the striking hand is by its shoulder. Then extend and straighten the striking arm outward by pulling your elbow forward. This will drive your shutō into your opponent’s neck or throat. Do not swing the striking arm out in a large arc; this can hyperextend your elbow. The correct motion is like a scissor jack, and not like a windshield wiper, or a folding pocket knife. As you extend, grab the opponent’s arm or clothing with your opposite side-hand, and pull it to your opposite-side shoulder, to drag your opponent into the technique.
Finish by immediately returning the striking hand to the shoulder, by bending the elbow. The correct retracting motion is just like a pocket knife.
This is a complex move. So, once again, practice slowly, until winding knife-hand strikes become one fluid motion. Then, gradually perform that one fluid motion faster, and faster. Slow is smooth, smooth is fast. Do not try to put a lot of strength or muscle behind this technique, as the resulting tension will only slow you down. Winding knife-hand strikes should have the same crack-the-whip/wet-towel-snapping feel that backfist strikes have.
[videos of makkikomi shutos, fast and slow, from the front and from the side. Show from above if possible; get a ladder.]