In the video below Coach Moore, an MMA instructor, is experimenting with what I would like to call a horizontal (sine) wave motion with the hip. The renowned self-defence instructor Peter Conserdine is known for teaching this "double hip" punch. It is not his own invention; rather, it is a rediscovery of an old Karate technique. We do something similar in ITF Taekwon-Do and usually refer to it as "hip rotation" or "hip jerk." It derives from the section on "Mass" in ITF Taekwon-Do's Theory of Power.
While watching the video, notice Coach Moore's legs. Particularly notice how he bends the front knee, lifts the back heel of the ground, and then slams the back heel back to the floor at the end of the technique to absorb any rebound energy. This is practically the same mechanics we employ in ITF Taekwon-Do when we do our peculiar "sine wave motion." Notice the similar mechanics between what he is doing and what we do when perform, what is sometimes known as, the "D"-formation -- i.e. the rolling of the knees, the lifting of the body in a slight arc, and then the drop of the body while thrusting the hip forward.
Of course it is not exactly the same, but there are similarities. Particularly as far as the horizontal wave, in other words, the hip rotation is concerned; although in recent years we do not perform such an exaggerated hip rotation any more. We often find ourselves with one hip already in a forward position and therefore negating the need for a "double hip" as Coach Moore is demonstrating in the video. Usually we are standing in a guarded position or in a blocking posture, which requires that we be "half facing" the opponent; this means that one hip is already rotated forward. To do a reverse punch from such a position we merely need to thrust the opposite -- rear -- hip forward. Attempting a "double hip" when the hips are not squared, when one is already pulled back, would just waste time. Coach Moore, on the other hand, is not starting off in a half facing position. He starts off full facing -- hips squared, face forward -- and then as he starts the punch (by rolling the front knee) he turns in to a half facing. This causes the leading hip to thrust forward, then followed by thrusting the rear hip forward -- hence the name "double hip" punch.
The principle is in effect the same as we do in ITF Taekwon-Do. The way he rolls his knees are also similar to what we achieve with our sine wave motion. However, in ITF Taekwon-Do we would not swivel the front knee as much. We tend to roll the knee in a vertical circle -- forward, up, and down; we do not rotate the knee horizontally as much. Our hip thrust is also a little less. Peter Conserdine's method creates actually more forward thrust, I believe, but it also creates lots of side ways forces that my hamper ones balance, especially when stepping forward. It would be very difficult to do the "double hip" punch as Coach Moore is demonstrating while stepping forward. For this reason we tone down the technique somewhat in ITF Taekwon-Do. Although we do lose some of the power, we keep more of our dynamic balance, which is very important for stepping.
What I'd like to point out in this post is that the mechanics of the sine wave motion does not merely contributed to vertical forces -- in other words dropping the body weight behind a punch -- but also contributes to the horizontal force of hip rotation. Both requires a rolling of the knees. What we cannot see in the video clearly is what he is doing with his back heel, but one can deduce some things. We know that he is lifting up the back heel. This means that he is pivoting on the ball of his foot as he is thrusting his rear hip forward. We do the same thing in ITF Taekwon-Do -- never do we pivot the rear foot while it's completely flat on the ground, as this puts a lot of strain on the knee joint. In this way we are different from many Karate systems which will actually keep the back foot flat, while rotating the hips; a potentially unsafe practise. One of my friends (she used to be a Karateka) has injured her knees this way.