There are generally eight methods for generating power in Shotokan karate. These methods, in the order easiest to learn, include: (1) hip vibration, (2) body shifting, (3) body rising, (4) body dropping, (5) hip rotation, (6) hip counter rotation, (7) hip pendulum, and (8) expansion and contraction.
Hip vibration is performed by firmly planting the feet on the ground while pulling strongly with one foot and then the other.
For example, if you were to throw a straight punch with the right hand, you would pull firmly with the right foot. As you pull backward with the right foot, the muscles in the right calf, hamstrings, and glutes will contract strongly. This contraction will cause your right hip to rotate forward of the left hip, with rotation occurring on the center axis. As the punch reaches the target, violently pull with the left foot to fire the same muscles while keeping those of the right side contracted. This action will draw the right hip back parallel to the left hip, creating a rotational “vibration” of the hips.
Remember that all hip action begins with the feet and travels up the legs to the glutes. The foot pull is linear but is converted to rotational force at the hips. That rotational force is then transferred up the spine (if the lumber spine is kept braced), then to the shoulders, where energy is sent to the arm (often becomes linear once again). Wiggling the hips without using the feet, legs, glutes, and posterior chain of the body is not karate; it’s dancing.
The best approach to mastering hip vibration is through three-time punching from ready position (yoi). Assume the ready position with left arm extended and right hand in pull-back position on the right hip. Pull with the right foot as you punch off-center to the left with the right arm. This will allow the right hip to rotate forward while the left hip rotates backwards. At the completion of the punch, the right leg, from the foot to the glutes will be contracted strongly. The left leg and glutes will be mostly relaxed. Now, the hard part. Instantly relax the right leg and glutes while simultaneously pulling with the left foot and tensing the left leg and glutes. This will rotate the hips on the center axis so the left hip is forward and the right hip is back. The left arm will punch off center to the right side. The right leg and glutes will be mostly relaxed. Finally, keep the left leg and glutes contracted while simultaneously pulling firmly with the right foot, contracting the right leg and glutes. This will center the body so the hips are square to the front with both legs and glutes contracted. Relax both legs and glutes. You will now have the right arm forward and left hand at the left hip, ready to repeat the drill in the opposite direction. At first, take your time to consciously pull with the correct foot and tense the leg and glutes while relaxing the opposing side. If your arms or upper body become tired at any time, you are holding too much tension above the lumbar spine. The upper body should be almost completely relaxed during this drill. The idea is to literally “throw’ the punches using the power of the feet and glutes generating energy up the spine. See my video on this exercise at Hip Vibration in Shotokan Karate - YouTube.
You must perform (at minimum) heavy deadlifts and hard-style kettlebell swings to improve posterior chain strength. Since heavy deadlifts wear out your nervous system, they can only be performed about once every two weeks (or more). Therefore, kettlebell swings are excellent in developing strength between heavy deadlift days.
Hip vibration is used mainly with shorter stances and, therefore, close to the opponent. As distance increases and stance length increases, hip rotation is more practical. Use body shifting to generate power at very long distances (beyond arm reach). Furthermore, use expansion and contraction, combined with other methods, with almost all karate techniques to generate power.
See also Eight Ways to Generate Power for other methods.