bkc said:
...The classic example is a girl that can't throw a ball effectively because they start with their elbow out front, and prevent the whipping motion from occuring.
Well I certainly understand my strokes. Unfortunately I don't agree with your response here. Taking your example above, the source of major power would be to get the shoulder more involved in the throwing of the ball. The girl has obviously shortened her length and time to generate sufficient arm speed (throwing from the elbow). Adding shoulder movement with an excellent range of motion will contribute more to power then pronation and supination.
Your example, indicates that you are wrong in another sense. If the arm were held still and the ball was in hand, pronating and supinating the arm would do nothing to generate HUGE sources or amounts of power as you incorrectly described. Placing the ball in her hand and just throwing the ball from her shoulder joint would generate more power!
The forearm does rotate rapidly in the acceleration phase of the serve. But the role of this pronation is to position the racquet head correctly in preparation for impact. It does not substantially contribute to racquet velocity.
Additionally, the role of the wrist does extend (extension) in the cocking phase (the so-called "backscratch" position with the sudden upward change in direction) and then rapidly flexes in the acceleration phase to what players call "snapping".
The flexion in the wrist has been reported to be a major contributor to racquet head speed and power.
Using the whole body in a fluid and integrated manner is really the only way to improve the power in a serve (see my wave analogy). A good stroke production begins at your feet, flows up through your knees and legs, uses the hips and body weight and then allows the upper body and arms to stroke the ball. This is called the efficient use of
all body parts in stroke production "the kinetic chain".
Braking mechanisms are also important to generate a quick source of stored power within a kinetic energy transfer. The stop and start motions of different body parts causes an acceleration of the latter. By the time energy reaches the arm a large amount of the energy coming through the arm is kinetic.
Flexibility and range of motion are two of the most important elements in generating and tranferring energy and far more contributing in generating power then pronation and supination.
Here is an article for you to read. The shoulder area and the ability to transfer flowing energy quickly through the body are the MAJOR SOURCES OF ENERGY.
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Tennis
Biomechanics of High-Velocity Tennis Serves and Variations between Different Styles and Gender
Elliott B, Fleisig, R, Nicholls R, Escamilla R. Technique effects on upper limb loading in the tennis serve. Journal of Science and Medicine in Sports 6(1):76-87, 2003
Fleisig GS, Nicholls RL, Elliott BC, Escamilla RF. Kinematics used by world class tennis players to produce high-velocity serves. Sports Biomechanics 2(1):17-30, 2003
Methods
Researchers from ASMI, the University of Western Australia, and Duke University worked together to study the high-velocity serve of elite tennis players. Singles matches were recorded at Centre Court of the 2000 Olympic Games in Sydney, Australia. Two electronically-synchronized high-speed (200 pictures per second) cameras were used. Three-dimensional kinematics (motions) and kinetics (joint forces and torques) were calculated using manual digitization and inverse dynamics.
Results
High-quality data were calculated for 20 Olympic athletes (8 male and 12 female). One of the key features noticed was that the shoulder rotated back into an extreme position (172º). From this cocked position there was a coordinated rapid sequence of angular velocities of the upper torso (870º/s), pelvis (440º/s), elbow (1510º/s), wrist (1950º/s), and shoulder (2080º/s). At impact, the trunk was 48º above horizontal, the arm was abducted 102º and the elbow, wrist, and lead knee were slightly flexed. Compared to female players, males produced greater ball velocity (183 v. 149 km/hr), shoulder internal rotation velocity (2420 v. 1370 º/s), and later upper torso angular velocity (0.05 v. 0.07 seconds before ball impact). These differences may be related to the fact that male players produced greater internal rotation torque and proximal force about the shoulder.
Minimal differences were seen between the full and abbreviated backswing techniques. Compared to players with minimal knee flexion (6º), players with larger knee flexion (16º) produced similar ball speed but generated less shoulder internal rotation torque and elbow varus torque. Thus, larger knee flexion was a more effective technique than minimal knee flexion.
To achieve a high-velocity serve, a tennis player should utilize strength, flexibility, and technique training programs developed for motions and forces similar to those reported in this study. An understanding of serve mechanics may also help in the development of surgical and rehabilitative treatment procedures for shoulder and elbow injuries in tennis.
Copyright © 2000, American Sports Medicine Institute
October 05, 2004
Going from supination to pronation (or vice versa) is forearm rotation around a longitudinal axis. As I said earlier, this rotation therefore causes the racquet to rotate and the head then travels a further distance. You also have rotation occuring at the shoulder, which also rotates the racquet head. These two rotations are compounded and that is what creates a whipping motion. I suppose there is another rotation created by the elbow straightening. 
