In 1873, Runge (14) described in an article the etiology and treatment of the writer's cramp (Schreibekrampf), a painful elbow condition at the lateral epicondyle. The pain can radiate distally into the forearm and often results in a weak grasp. Despite a multitude of possible pathological entities, an overuse of the wrist extensors is often cited as the major factor for the epicondylalgia lateralis humeri. A statistical study on 2633 average tennis players by Priest et al.(13) showed that 31% experience elbow pain at some time during their playing career. Older age, frequency of play, years of play, a lower playing proficiency, and increased body weight were identified as risk factors for a higher incidence of tennis elbow. Age and frequency of play were the main factors for the likelihood of elbow pain. In young athletes and recreational players who only play once a week, the incidence of lateral epicondylitis is almost unknown. A typical patient is a recreational athlete older than 35 years who plays three or more times a week.
Much confusion exists about the pathology of tennis elbow. Many inconsistent results have been published. For example, the conditions that have been cited as etiologic theories for epicondylitis include the following: chronic irritation of the radiohumeral joint capsule, myositis of the wrist extensors, chondromalacia of the radiocapitellar joint, bursitis of the radiohumeral bursa, and radial nerve entrapment. The most popular explanation of tennis elbow, as described by Cyriax (2) in 1936, involves repeated stress and strain that cause macroscopic and microscopic tears between the common extensor tendon and the periosteum of the lateral humeral epicondyle. In studying a sample of 750 cases, Nirschl (12) found primary and secondary muscles for the pathoanatomy of tennis elbow that he defines as angiofibroblastic tendinosis. Extensor carpi radialis brevis was found to be the primary muscle; and extensor digitorum communis, the secondary muscle associated with lateral tennis elbow tendinosis. Pronator teres, flexor carpi radialis, and palmaris longus were the primary muscles; and flexor carpi ulnaris and flexor sublimis, the secondary muscles for the development of medial tennis elbow, which is less frequent. In the rare case of posterior tennis elbow tendinosis, triceps brachii was identified as the only primary muscle. Independent of different clinical findings and the various theories of the pathoanatomy of tennis elbow, most clinicians agree that the overuse of the wrist and finger extensor muscles is the most frequent cause of lateral tennis elbow. These muscles are primarily involved in backhand strokes in tennis. Therefore, the best preventive measure to avoid tennis elbow pain is to reduce the load on these muscles. Although the onset of pain may be triggered by a traumatic event like a blow onto the arm, pain usually arises unexpectedly during a game or even at rest.
The tennis racket has always been suspected to be an additional cause in the multifactorial etiology of lateral elbow pain. It is known that tennis players do not like vibrations in the racket, and Segesser (15) suggested that tennis racket oscillations in the range of 80 to 200 Hz are likely to contribute to the development of tennis elbow. The cause for developing a tennis elbow is the impact between racket and ball, which results in shock and vibrations that are transferred to the arm. As previously discussed, an overuse of the wrist and finger extensors is the most cited reason for causing lateral elbow pain. These muscles are primarily involved in backhand strokes. A reduction of the loads onto these muscles is the best preventive measure to avoid lateral tennis elbow pain. Tennis racket constructions are likely to have an influence on the shock transmission and vibration transfer to the body.
THE PHYSICS OF TENNIS RACKET PROPERTIES
Brody (1) provided a thorough description of the physics of tennis rackets. More recently, computer models have been used to predict the properties and behavior of tennis rackets (10). At ball contact, the racket creates a moment around the wrist that acts on the joint stabilizing wrist extensor muscles. The magnitude of this moment depends on the location of ball impact on the string area. Because the ball impact creates both translation and rotation of the racket, there is only one impact location (center of percussion) where the effect of translation and rotation partially cancel each other. For ball impacts at the center of percussion, the player will experience minimal initial shock at the grip.
The center of percussion is one of three sweet spots that are present in a tennis racket (1). The second sweet spot is defined by the location on the racket strings where the highest rebound velocity occurs. The third sweet spot (the node of the first harmonic oscillation of the racket) identifies an impact location that leads to low and smooth oscillations at the grip. Theoretically, it is not possible to construct a racket that causes all three sweet spots to coincide at a single location. However, specific construction features allow tennis racket designers to influence the relative locations of these three sweet spots. Very stiff rackets, for example, shift the second sweet spot (highest coefficient of restitution) closer to the racket head center. Tennis players generally identify a sweet spot that is located somewhere in the middle of the three sweet spots. At this location, the rebound speed of the ball, low shock, and low vibration amplitudes at the hand give the sensation of a good shot. For expert players who are able to hit the sweet spot of the racket consistently during play, the loads on wrist and arm are lower than those of a novice player. Beginners who experience frequent ball impacts close to the tip of the racket are subjected to considerably higher forces and vibrations.
Increased string tension is also likely to increase the shock associated with ball impact. Because of a "trampoline effect," the rebound velocity of a tennis ball will increase with a decrease of string tension, and the ball contact time on the strings will be longer. The advantage of an increased string tension is an improvement in hitting accuracy. However, to achieve a comparable rebound speed of the ball with higher string tensions, the racket head must have a higher velocity toward the ball. The increased impulse at ball impact will involve a shorter contact time and therefore leads to greater peak forces at the racket. Especially during off-center hits, the initial shock at the hand will be noticeably increased for rackets with high string tension.
VIBRATION TRANSFER FROM THE TENNIS RACKET TO THE ARM
All rackets vibrate after being struck by a ball, and this vibration will be transferred to the arm of the player. Segesser (15) suggested that tennis racket oscillations in the range of 80 to 200 Hz are likely to contribute to the development of tennis elbow. Accordingly, the advertisements of many tennis racket manufacturers promote the excellent damping qualities of their rackets and the likelihood that this property will minimize the occurrence of tennis elbow. Rackets with good damping qualities are believed to be superior to those that produce high-amplitude oscillations of long duration.
Our group investigated the influence of the mechanical characteristics of 23 different racket constructions on the vibration transfer to the human forearm (4). To determine the mechanical effect of racket vibrations on the human arm, a miniature accelerometer was attached to the wrist above the ulnar head. To improve the mechanical coupling with the bony structures, the accelerometer was additionally pressed against the bone by means of an elastic wristband. The vibration load on the arm was quantified as the integral of the rectified acceleration signal within a period of 100 milliseconds after impact. The acceleration integral of the vibration load combines the strength and the duration of the vibration signal in a single quantity. Because the dimension of the integrated rectified acceleration (m·s −1) can easily be confused with the quantity "velocity," the dimension of the acceleration integrals in this manuscript is given in arbitrary units or is normalized to a reference condition. The ball contacted the racket head at center and off-center locations, which influences the mechanical behavior of the ball-racket-arm system. A ball machine was placed at a distance of 1 m in front of the racket face to achieve a high accuracy in the location of the impact. A helium-neon laser, which produces a visible red light beam, was positioned at a location opposite the ball machine. The laser beam was used to guide the subject in positioning the racket at the desired location (Fig. 1). The point of impact was determined in a plane perpendicular to the floor, where the center of the impacting ball (velocity, 14 m·s −1) and the laser beam coincided.
Off-center ball impacts resulted in approximately threefold greater vibration magnitudes compared with center impacts. There were large differences in acceleration values between different racket constructions. Increased racket head size and a higher resonance frequency of the racket were found to reduce arm vibration. There was a strong inverse relation (r= −0.88) between the vibration of the arm after impact and the resonance frequencies of the tennis rackets. Because of the construction geometry, the wide body rackets generally had a higher stiffness, which increased the resonance frequency of the racket. To further examine the influence of resonance frequency on the vibration of the arm, four different tennis rackets were built with identical shape, equal mass (363 g), and the same center of gravity location at 32.7 cm from the grip end (5). Three of the rackets had the same carbon fiber construction material, and the only difference between these rackets was the distribution of material across the frame. For one racket, a carbon fiber material with a higher modulus of elasticity was used. The rackets were strung with an identical nylon material at the same string tensions (280 N/270 N). Racket stiffness was estimated from the resonance frequency of the rackets using a Fourier analysis of the free vibrating rackets; a higher resonance frequency corresponds to a stiffer racket. The experimental setup was almost identical to the one described in Figure 1. Rectified acceleration integrals were determined at the wrist for ball impacts at center and an off-center location on the racket head. Especially for the off-center location, there was a frequency-dependent transfer of vibration to the body. The vibration load at the wrist was reduced with an increase in racket stiffness (higher resonance frequency) (Fig. 2).
Stiffer rackets absorb less energy during tennis strokes, resulting in higher ball rebound velocities. Less energy absorption by the racket likely results in lower racket vibration amplitudes and thus less vibration transfer to the human body. Furthermore, the hand-arm system may function as a low-pass filter for higher vibration frequencies. From these studies, it can be concluded that stiffer tennis rackets reduce the vibration at the wrist and elbow and also increase ball rebound velocity.
THE INFLUENCE OF GRIP FORCE ON BALL VELOCITY AND ARM VIBRATION
The effect of grip force on ball rebound velocity has been the subject of many studies in the past. Whereas most studies found that ball velocity is independent of grip force magnitude, some authors reported increased ball speeds with higher grip forces (3). The effect of grip force on ball rebound velocity and the transfer of vibration on the arm of 15 subjects were investigated (6). A capacitive force transducer (11) measured the grip forces, and an accelerometer at the wrist measured the vibrations that were transferred from the racket to the body. The capacitive force transducer had a thickness of 3 mm and surrounded the grip completely. To compensate for the increase in circumference of the handle by the capacitive sensor, a racket with the smallest available grip size was chosen for the study. The subjects were required to maintain a predetermined force level, and both the target and actual forces were shown on an oscilloscope. Trials were performed at four different grip forces of 35, 70, 105, and 140 N. The dependent variable was the rebound velocity of the ball. Tennis balls were shot at a speed of 50 km·h −1from a ball machine to two center and off-center locations of the string area as subjects held the racket in a backhand stroke position. For both impact locations, higher grip forces on the racket handle resulted in substantial increases of arm vibration loads. However, ball rebound speed was not influenced by the magnitude of grip force (Fig. 3).
Reduced grip forces, which decrease the vibration load on the arm, may prevent tennis elbow without sacrificing ball velocity. In a follow-up study, the dynamic grip forces from 19 expert players were compared with those of 13 intermediate players (7). Although ball velocity was considerably higher and the vibration load on the arm was much lower for the expert players, grip forces did not differ between the groups. For both groups, the maximal grip forces occurred approximately 30 milliseconds before ball contact. The authors concluded that players reduce grip forces just before ball impact to protect the body from vibration loads.
BALL IMPACT LOCATION ON A TENNIS RACKET HEAD
To study the interaction of the player with the tennis racket, a racket was developed to electronically determine the point of ball impact on the strings (8). Very thin steel wires were woven around the strings of the racket. This resulted in a 14 by 18 wire matrix, covering a large area of the racket head. Each steel wire was electrically insulated and connected to a charge amplifier by a thin shielded cable. The thin cable bundle from the 32 sensors was guided along the racket handle to a small electronic unit, which was attached to a belt and carried by the subject. Although total racket weight was increased slightly by the wires, it was still well in the range of weights of commercially available tennis rackets. Through friction of the ball with the ground and during its flight in the air, the tennis ball was electrically charged before it made contact with the racket head. At ball contact, the electrostatic charge was detected by the steel wires and electronically processed by charge amplifiers (Fig. 4).
Each wire was sampled at a frequency of 5 kHz by a data acquisition system. Data were collected for a total of 12 milliseconds, beginning 4 milliseconds before initial charge detection on the sensors. Subsequent data collection produced a 14 by 18 charge magnitude matrix. Geometric averaging of all matrix values determined the point of contact on the string area. The matrix wire arrangement and the time resolution of 0.2 millisecond guaranteed an accurate determination of ball contact location and its movement across the string area. An accelerometer was fastened to the wrist to measure the transfer of shock and vibration from the racket to the arm. Ball velocity was measured by a laser array photocell arrangement. Eighteen expert, 18 intermediate, and 19 recreational male players performed 30 right-handed strokes in each of three conditions: straight serve, forehand stroke, and backhand stroke (9). The 36 expert and intermediate players also performed 30 strokes in three additional conditions: second serve, forehand topspin, and backhand slice. Across all players and playing conditions, 8190 ball contacts with the racket head were measured and evaluated. To minimize variability across playing conditions, a ball machine on the opposite side of the tennis court was used to serve the balls to the players. Ball impact variables are summarized for the six different stroke techniques from the advanced and expert players in Table 1. The mean values are based on all strokes performed by the 36 players. Highest ball velocities, lowest roll distances (positive y values), and the shortest contact time were recorded for the first serve condition. As expected, the greatest roll distances and lowest ball speeds were measured during forehand topspin and backhand slice strokes. Creating spin on the ball reduces translatory energy and thus the velocity of the ball.
Table 2summarizes the differences in hitting the ball by the three groups of players. The vibration load values in this table are expressed as a percentage of the highest load that occurred for the beginners' forehand strokes. Rebound ball velocities for the beginners were the lowest for all three strokes, but the vibration loads on the arm were the highest. The beginners also hit the ball closer to the hand (negative values along the longitudinal y axis). The intermediate and expert players exhibited similar impact locations for all stroke conditions.
To compare the results of our study with those predicted by Brody (1) based on racket characteristics, we selected the results of the 30 forehand and backhand strokes from the 19 expert players (9). As apparent in Table 3, neither the point of minimum shock nor the point of minimum vibration was found at those racket locations (center of percussion, node) predicted by Brody (1) for the forehand and backhand strokes.
Brody (1) also predicted that the point of maximal ball speed along the y axis would occur at locations lower than the center of the racket head. Our data showed the opposite; maximal ball velocity was achieved at a location slightly higher than the racket head center. Rotation of the racket during the swing increases the velocities for more distally located racket points. Apparently, this effect has more influence on ball speed than a lower coefficient of restitution for the racket at more distal locations. The results of our study did not confirm the sweet spot locations predicted by Brody (1) for minimum vibration, minimum shock, or maximum ball velocity. Mechanical coupling of the hand with the racket and the contribution of racket rotation during the swing seem to have a major effect on racket performance in gamelike situations.
Biomechanical experiments can quantify the loads on the body and describe the mechanical behavior of tennis rackets. Stiffer tennis rackets and lower grip forces reduce the mechanical loads on the arm, without impeding ball velocity. Beginners hit the ball too close to the hand and experience substantially higher vibrations at the wrist. The biomechanical measurements identified significant flaws in racket performance predicted by theoretical studies.
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