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The 14th IFToMM World Congress, Taipei, Taiwan, October 25-30, 2015 DOI Number: 10.6567/IFToMM.14TH.WC.PS1.003 Predicting the Biomechanics Effects on the Human Arm of the Badminton Forehand Smash Wen-Huang Lin 2 Jia-Sian Chen 1 Chiu-Fan Hsieh 1 Department of Mechanical and ComputerOffice of Physical Education, Department of Mechanical and Aided Engineering, National Formosa University, National Formosa University, Computer- Aided Engineering, National 64 Wunhua Road, Huwei, Yunlin, Taiwan, R.O.C 64 Wunhua Road, Huwei, Formosa University, 64 Wunhua Road, Huwei, Yunlin, Taiwan, R.O.C [email protected] Yunlin, Taiwan, R.O.C [email protected] [email protected] Abstract: In this paper, we investigate the kinematic and tensile variations in the upper extremities during the various phases of a badminton forehand smash movement, which if incorrectly performed may lead to sports injuries. Specifically, based on biological, kinematic, and dynamic concepts and principles, we develop a biomechanical model of arm swing paths whose feasibility is assessed using four types of motion paths: a correctly positioned badminton smash (Path 1), a smash recovery following a successful smash shot (Path 2), and two error motions that commonly occur during smash shots (Paths 3 and 4). We then conduct a motion analysis of these four paths to determine the kinetic chain of the forehand smash and the influence that stress and muscle strength exertion have on badminton players’ arms. We find that Path 2 easily induces sport injuries in the humerus and biceps brachii; Path 3 causes serious sport injuries in the forearm (ulna and radius), wrist (carpal bones), triceps brachii, flexor carpi ulnaris, and extensor carpi; and Path 4 poses greater risk of injury to the forearm (ulna and radius), wrist (carpal bones), biceps brachii, and triceps brachii muscles. The proposed model can therefore be used to predict post-motion exertion points, making it a useful reference tool for training and teaching. Keywords: Badminton, Arm, Biomechanics, Kinematics, Dynamics 1. Introduction The global popularity of badminton and the intensity of competition among badminton players have increased considerably in recent years. Because badminton players typically invest great effort in training to enhance performance, they must take care to avoid sport injuries during training sessions. Such avoidance is facilitated by the ability to predict whether the swinging motions used when playing badminton injure the arms, which information also serves as a useful teaching and training reference. Numerous scholars have provided valuable insights into badminton smash techniques. For example, Tsai, Huang, and Ji, after recording 3D kinematics data with a high-speed camera, reported that the center of gravity applied during a stroke shot (the stroke point) and the angular velocity of the elbow and wrist increase as shuttlecock velocity increases [1]. Chien et al. [2], by applying the 2D inverse dynamics law to calculate and analyze the extent of muscle injuries during various badminton moves, found that different actions require varying muscle strength and that training the extensor carpi regularly reduces the injury risk. Tsai, Huang, and Chang [3] then quantified the kinematic variations in badminton players’ forehand and backhand grips to show that the forehand grip velocity and the height of the stroke point in a forehand smash are higher than those in the backhand smash. They also demonstrated that the motion velocity of the wrist is the highest, followed by that of the elbow and shoulder. Subsequently, Tsai, Pan et al. [4] used an electromyography (EMG) system to analyze the EMG responses of the lower extremities (i.e., the hip and knee muscles) during the badminton kill smash. Noting considerable response in the quadriceps, they recommended enhancing quadriceps training to enhance kill smash performance. In a study of the Achilles tendons, the most injury-prone region for badminton players, Wang, Tu et al. [5] found that injuries typically occur when the ankle bends and withstands 45 to 75 s of body weight. Subsequently, Lin et al. [6], using a concentric muscle strength test at various velocities on the muscle groups of male badminton players’ upper extremities, identified the relation between muscle strength before and after a smash shot. They found that the muscle strength in the wrist and elbow area is significantly related to badminton smash performance. Comparing skilled and unskilled badminton players, Wang, Huang et al. [7] observed that during the preparing, stroking, and swinging phases, the former showed greater muscle activation than the latter in the biceps brachii, deltoid anterior, triceps brachii, musculus flexor carpi ulnaris, and extensor carpi. By using an infrared high-speed camera, Wang, Xue et al. [8] studied the variation in 3D kinetic upper-extremity parameters of badminton players during the serving phase of singles or doubles. Their results indicate that training to improve the biceps brachii, triceps brachii, and internal and external rotations of the forearm facilitate serving performance. Hsueh et al. [9] summarized the factors that influence badminton smash performance as follows: extremity rotation and kinetic chain principles influence the shuttlecock velocity; forehand and backhand strokes, gravity, and stroke point influence the smash performance; and activation of the arm muscles during various phases and stroke actions influence the smash performance. As suggested by the above review, recent badminton studies have typically employed the EMG system and high-speed cameras as analytic tools, rarely adopting mechanical methods to simulate an arm performing badminton smash motions. In this current study, therefore, we develop a biomechanical model of the relevant arm motions and then, by simulating various smash motion paths, identify different curves for the upper extremity and generate information on such factors as muscle strength and stress. Both these results and the biomechanical model developed can serve as a useful reference for predicting sport injuries, enhancing athletic competitiveness, and improving badminton training and teaching. 2. Materials and methods 2.1 Arm Model Design The biomechanical model, constructed using SolidWorks, consists of a titanium-based scapula, humerus, ulna and radius, and wrist, together with a carbon-fiber badminton racket, all developed based on biological, mechanical, and dynamic concepts. Fig 1(a) outlines the model, and Table 1 summarizes the mechanical properties of the titanium material. In line with the kinetic chain and muscle contact point concepts, four springs represent the following muscles: biceps brachii (connection from the tuberosity above the glenoid cavity to the area around the biceps aponeurosis), triceps brachii (connection from the tuberosity of the scapula to the olecranon of the ulna), extensor carpi (connection from the lateral condyle of the humerus to the metacarpus), and flexor carpi ulnaris (connection from the medial condyle of the humerus to the area around the palmar aponeurosis). This model, illustrated in Fig 1(b), can simulate the forces applied in the arm muscles as the arm performs different motions and identify the point at which force is applied for each motion. It can thus assist in the prevention of arm injuries and extend athletes’ sports careers. 2.2 Mathematical model of motion Because an arm motion is a spatial movement, the initial positions of the three joints can be expressed as JJK T P1Ji =⎡⎣x1Ji y1Ji z1Ji ⎤⎦ (1) where i =1~3. Because the joints are ball joints, simulating the arm movement requires that the rotation angles of the respective joints for the X, Y, and Z axes be determined by a coordinated transformation matrix: 0 0 ⎤ ⎡1 ⎢ (2) Rot ( X , α i ) = ⎢0 cos α i − sin α i ⎥⎥ ⎢⎣0 sin α i cos α i ⎥⎦ ⎡ cos βi 0 sin βi ⎤ (3) 1 0 ⎥⎥ Rot (Y , βi ) = ⎢⎢ 0 ⎢⎣ − sin βi 0 cos βi ⎥⎦ ⎡cos γ i Rot (Z , γ i ) = ⎢⎢ sin γ i ⎢⎣ 0 − sin γ i cos γ i 0 0⎤ 0⎥⎥ 1⎥⎦ (4) Each joint’s move to the next position can then be derived as follows: JJK JJK (5) P 2 Ji = Rot ( X , α i ) ⋅ Rot (Y , βi ) ⋅ Rot ( Z , γ i ) ⋅ P1Ji Operating this equation yields JJK T P2Ji =⎡⎣x2Ji y2Ji z2Ji ⎤⎦ ⎡ ⎤ x1Ji cosβi cosγi −y1Ji cosβi sinγi +z1Ji sinβi ⎢ ⎥ =⎢ x1Ji (cosγi sinβi sinαi +cosαi sinγi )+y1Ji (cosαi cosγi −sinαi sinβi sinγi)−z1Ji sinαi cosβi ⎥ ⎢ ⎥ ⎣⎢x1Ji (−cosγi sinβi cosαi +sinαi sinγi )+y1Ji (sinαi cosγi +cosαi sinβi sinγi )+z1Ji cosαi cosβi ⎦⎥ (6) Based on (6), the rotation angles of the three axes of each joint can be determined using various motion path designs. (a) Arm bones 3. Results Four motion paths are used for the simulation: accurate motions (Path 1), a smash recovery following a successful smash shot (Path 2), and two error motions (Paths 3 and 4). However, simulating the paths requires that motion curves be developed for the three arm joints (J1, J2, and J3) (Fig. 1(b)). As already explained, because the joints are ball joints, angles must be determined for the X, Y, and Z rotation axes of each joint. The Path 1 motion curves for J1, J2, and J3 are shown in Fig. 2(a), while Fig. 2(b) illustrates the trajectory of the badminton racket center. The smash motion is divided into four phases: preparing, swinging, stroking, and follow-up, represented as a, b, c, and d in Fig.2(c), which illustrates the isolated motion of each phase. The first 0.5 s of the motion is the preparing phase, between 0.5 and 1.6 s is the swinging phase, from 1.6 to 1.66 s is the stroking phase, and from 1.66 to 1.8 s is the follow-up phase. (b) Arm muscles Fig. 1. Arm structure Table 1. Material properties Material Elastic modulus Poisson ratio Shear modulus Tensile strength Yield strength Titanium 345000 (N/mm2) 0.32 44000 (N/mm2) 240 (N/mm2) 170 (N/mm2) Path1 Path2 3.00E+02 3.50E+02 J1-X J1-X J2-X J2-X J3-X J1-Y J2-Y 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 J3-Y J1-Z -1.50E+02 J2-Z J3-Z -3.00E+02 1.75E+02 Angle(deg) Angle(deg) 1.50E+02 J3-X J1-Y 0.00E+00 J2-Y 0 0.3 0.6 0.9 1.2 1.5 J3-Y 1.8 J1-Z -1.75E+02 J2-Z J3-Z -3.50E+02 Time(s) Time(s) (a) Accurate path (Path 1) motion curve (a) Path 2 motion curve (b) Accurate path (Path 1) motion locus (b) Path 2 motion locus (c) Accurate path (Path 1) and Path 2 movement points of difference (Red circle of dissimilarity) Fig. 3. Path 2 design (c) accurate path (Path 1) swing movement Fig. 2. Path 1 design Path3 3.00E+02 J1-X J2-X 1.50E+02 Angle(deg) Fig 3(a) displays the Path 2 motion curves, while Fig. 3(b) depicts the motion trajectory. In contrast to Path 1, Path 2 manifests the rapid motion of returning the racket to its initial position to prepare for the next stroke immediately after a smash shot. The difference between Path 1 and Path 2 is shown in Fig. 3(c). Path 3 reflects an error motion typical of badminton: the forearm and wrist preparing for a smash shot before the upper arm is not straightened. The curves, trajectory, and swing and stroke motion used in this path are graphed in Fig 4. The second common error motion, represented by Path 4, occurs when the player’s arm extends outward before a smash shot but fails to maintain a position parallel to the shoulder. The motion curve and trajectory for this path, as well as the decomposition of the motions for Path 4, are shown in Fig. 5. The motion and stress analyses of the arm are presented in Fig. 6 to 8. The analysis of muscle strength is in Fig. 9. The discussion is in the next section. J3-X J1-Y J2-Y 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 J3-Y J1-Z -1.50E+02 J2-Z J3-Z -3.00E+02 Time(s) Translational velocity of humerus (mm/sec) 4.38E+04 a c b d 3.28E+04 path1 2.19E+04 path2 path3 1.09E+04 path4 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (a) Translational velocity of humerus Translational acceleration of humerus Fig. 4. Path 3 design Path4 3.00E+02 J1-X (mm/sec^2) 3.00E+06 Angle(deg) c b d path1 path2 path3 path4 1.50E+06 7.50E+05 0.00E+00 J2-X 1.50E+02 a 2.25E+06 0 J3-X 0.3 0.6 J1-Y 0.9 1.2 1.5 1.8 Time(s) J2-Y 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 J3-Y (b) Translational acceleration of humerus J1-Z -1.50E+02 J2-Z J3-Z -3.00E+02 Translational acceleration of humerus 1.5~1.8(s) Time(s) (mm/sec^2) 3.00E+06 path1 2.25E+06 path2 path3 1.50E+06 7.50E+05 path4 0.00E+00 1.5 1.6 1.7 1.8 Time(s) (c) Translational acceleration of humerus 1.5~1.8(s) Stress of humerus Stress(N/mm^2) 1.20E+01 a c b d path1 path2 path3 9.00E+00 6.00E+00 3.00E+00 path4 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (d) Stress of humerus Stress of humerus 1.5~1.8(s) Fig. 5. Path 4 design 4. Discussion Fig 6 to 8 graph the motion and stress analyses of the four motion paths for the humerus, forearm (ulna and radius), and wrist (carpal bones). Fig 6 illustrates the motion analysis for the humerus, which during the follow-up phase of Path 2 is affected by a sudden halt and pulling motion that first increases its translational velocity and then decreases it instantaneously (Fig. 6(a)). Following the halt-pull motion, the translational acceleration of the humerus in Path 2 is lower than in Paths 1, 3, and 4 (Fig. 6(b) and (c)). According to the stress analysis (Fig. 6(d) and (e)), the stress exerted on the humerus during the follow-up phase of Path 2 is the greatest, indicating that the sudden pull motion of the arm following a smash shot generates inertia, increasing the risk of injury to the humerus. There is also a greater stress difference stage in Path 2, a stress variation illustrated by the stress diagram for each second given in Fig. 6 (f) and (g). Stress(N/mm^2) 1.20E+01 path1 path2 path3 path4 9.00E+00 6.00E+00 3.00E+00 0.00E+00 1.5 1.6 1.7 1.8 Time(s) (e) Stress of humerus 1.5~1.8(s) (f) Path 2 1.69 ~ 1.73 seconds of the motion diagram (g) Path 2 1.69 ~ 1.73 seconds humerus stress diagram Fig. 6. Motion and stress analysis of the humerus Stress of ulna & radius 6.00E+00 Stress(N/mm^2) Fig 7(b) and (d) show the changes in translational velocity and translational acceleration during the stroke phase in Path 3, which are minimal because the forearm is extended at an angle during the smash shot, Nonetheless, the translational velocity and translational acceleration in Path 3 fluctuate more than those in Path 1. Moreover, the stress analysis graphed in Fig. 7(e) and (f) indicates that maximal stress is applied during the stroke phase of Path 3, suggesting that the rapid forearm rotation increases the force and elevates the injury risk to the forearm. Likewise, in Path 4, the arm is extended at an angle during the smash shot exerting maximal stress and also increasing the injury risk to the forearm. Here, there is a greater stress difference stage in Path 3, a stress variation on the ulna and radius captured by the stress diagram for each second shown in Fig. 7(g) and (h). path1 4.50E+00 path2 3.00E+00 path3 1.50E+00 path4 0.00E+00 1.5 1.6 1.7 1.8 Time(s) (f) Stress of ulna and radius 1.5~1.8(s) (g) Path 3 1.65 ~ 1.69 seconds of the motion diagram Translational velocity of ulna & radius (mm/sec) 6.00E+04 a c b d path1 4.50E+04 path2 path3 3.00E+04 1.50E+04 path4 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 (h) Path 3 1.65 ~ 1.69 seconds ulna and radius stress diagram 1.8 Time(s) Fig. 7. Motion and stress analysis of the ulna and radius (a) Translational velocity of ulna and radius Translational velocity of ulna & radius 1.5~1.8(s) (mm/sec) 6.00E+04 4.50E+04 path1 3.00E+04 path2 path3 1.50E+04 path4 0.00E+00 1.5 1.6 1.7 1.8 Time(s) (b) Translational velocity of ulna and radius 1.5~1.8(s) Translational acceleration of ulna & radius (mm/sec^2) 7.00E+06 a c b d path1 5.25E+06 path2 path3 path4 3.50E+06 1.75E+06 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (c) Translational acceleration of ulna and radius Translational acceleration of ulna & radius 1.5~1.8(s) (mm/sec^2) 3.50E+06 path1 2.63E+06 As regards the swinging and stroke phases of Path 4, the translational velocity and translational acceleration curves (Fig. 8a, b, c and d) fluctuate considerably compared with those of Path 1, indicating that the carpus is indirectly affected when the smash shot is performed with the arm extended at an angle. This motion generates vibration, which increases the risk of carpal bone injury. The stress analysis (Fig. 8e and 8f) further shows that stress increases during the stroke phase of Path 3 and the swinging and stroke phase of Path 4, thereby increasing the sports injury risk to the carpus. This increase is related to the rapid rotational speed and the arm’s being extended at an angle to perform the smash shot. Once again, there is a greater stress difference stage in Path 3, a stress variation on the carpal bones captured by the stress diagram for each second given in Fig. 8(g) and (h). In fact, among the three different arm areas studied, the stress value of the carpus is the highest, implying that it is easily injured during incorrect hitting. In terms of muscle strength, the musculus flexor carpi ulnaris is the most used of the four muscles in hitting and so the most easily injured by faulty technique. path2 1.75E+06 path3 8.75E+05 path4 Translational velocity of carpus bone 0.00E+00 1.5 1.6 1.7 1.8 6.00E+04 a (d) Translational acceleration of ulna and radius 1.5~1.8(s) c b 4.50E+04 a path3 path4 1.50E+04 0 c b d 0.3 0.6 0.9 1.2 1.5 path1 4.50E+00 path2 3.00E+00 path3 1.50E+00 path4 0.00E+00 0 0.3 0.6 0.9 path1 path2 3.00E+04 Time(s) 6.00E+00 d 0.00E+00 Stress of ulna & radius Stress(N/mm^2) (mm/sec) Time(s) 1.2 Time(s) (e) Stress of ulna and radius 1.5 1.8 (a) Translational velocity of carpus bone 1.8 Translational velocity of carpus bone 1.5~1.8(s) (mm/sec) 6.00E+04 path1 4.50E+04 path2 3.00E+04 path3 1.50E+04 path4 0.00E+00 1.5 1.6 1.7 1.8 Time(s) (b) Translational velocity of carpus bone 1.5~1.8(s) Translational acceleration of carpus bone (mm/sec^2) 7.40E+06 a c b d path1 5.55E+06 path2 3.70E+06 path3 1.85E+06 path4 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (c) Translational acceleration of carpus bone Translational acceleration of carpus bone 1.5~1.8(S) (mm/sec^2) 3.70E+06 path1 2.78E+06 path2 path3 1.85E+06 9.25E+05 Fig 9(a) and (b) illustrate the muscle strength of the biceps brachii, showing increased curve fluctuations in the follow-up phase of Path 2 and the swinging and stroke phase of Path 4. These occur because of an overly rapid arm motion and excessively large angle, both of which increase muscle use and enhance the risk of injury. Figs. 9(c) and (d) graph the muscle strength analysis of the triceps brachii, which shows that the force exerted during the swinging and stroke phase of Path 3 is low because the stroke is performed before the arm is straightened, leading to low tensility in the triceps brachii. Conversely, the muscle strength and tensile force during the swinging and stroke phase of Path 4 is high because the arm and elbow extend outward during the stroke, which increases curve fluctuations and the risk of injury. Finally, Fig. 9(e) and (f) show a comparison of the flexor carpi ulnaris and extensor carpi in which excessive tensile force is generated during the swinging and stroke phases of Path 3 because the arm is extended before the smash shot. As a result, these two muscles are especially prone to injury. path4 Biceps brachii 0.00E+00 1.5 1.6 1.7 1.8 2.50E+02 Force(newton) Time(s) (d) Translational acceleration of carpus bone 1.5~1.8(s) a path1 path2 path3 6.25E+01 path4 0 Stress(N/mm^2) a c b 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) d path1 1.50E+02 path2 1.00E+02 (a) Biceps brachii path3 5.00E+01 path4 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 Biceps brachii 1.6~1.8(s) 1.8 Time(s) Force(newton) 2.50E+02 (e) Stress of carpus bone Stress of carpal bone 1.5~1.8(s) 1.88E+02 path1 path2 1.25E+02 path3 6.25E+01 path4 0.00E+00 1.6 1.7 2.00E+02 1.8 Time(s) path1 1.50E+02 path2 1.00E+02 (b) Biceps brachii 1.6~1.8(s) path3 5.00E+01 path4 0.00E+00 Triceps brachii 1.5 1.6 1.7 1.8 2.50E+02 (f) Stress of carpus bone 1.5~1.8(s) Force(newton) Time(s) a c b d path1 path2 path3 path4 1.88E+02 1.25E+02 6.25E+01 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (c) Triceps brachii Triceps brachii 1.6~1.8(s) 2.50E+02 Force(newton) Stress(N/mm^2) d 1.25E+02 0.00E+00 Stress of carpal bone 2.00E+02 c b 1.88E+02 (g) Path 4 1.63 ~ 1.67 seconds of the motion diagram path1 path2 path3 path4 1.88E+02 1.25E+02 6.25E+01 0.00E+00 1.6 1.7 Time(s) (d) Triceps brachii 1.6~1.8(s) (h) Path 4 1.63 ~ 1.67 seconds carpus bone stress diagram Fig. 8. Motion and stress analysis of the carpus bone 1.8 References Musculus flexor carpi ulnaris Force(newton) 6.00E+02 a c b d path1 4.50E+02 path2 3.00E+02 path3 path4 1.50E+02 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (e) Musculus flexor carpi ulnaris Musculus extensor carpi radialis Force(newton) 2.00E+02 a c b d path1 1.50E+02 path2 path3 1.00E+02 5.00E+01 path4 0.00E+00 0 0.3 0.6 0.9 1.2 1.5 1.8 Time(s) (f) Musculus extensor carpi radialis Fig. 9. Muscle strength analysis 5. Conclusions In this study, we developed a biomechanical model of badminton swing paths and arm motions for predicting sport injuries whose feasibility was tested using four different path designs. Based on the results, we draw the following conclusions about the three designs that represent faulty execution: 1. In Path 2, because of the excessively rapid halt-pull motion, the inertia exerted after the smash motion is unmitigated during the follow-up phase when the arm halts and pulls to prepare for the next move. As a result, the curves for the humerus motion and stress and the biceps brachii fluctuate considerably, which may increase the risk of sports injuries. 2. In Path 3, the arm is extended before the smash shot, an error that increases the motion velocity of the ulna, radius, and carpal bones, thereby increasing the variations in the motion and stress curve of the forearm (ulna and radius) and wrist (carpal bones) and the muscle strength curves of the triceps brachii, flexor carpi ulnaris, and extensor carpi. The motions used in Path 3, therefore, may also lead to sports injuries. 3. In Path 4, the arm is extended outward to perform the smash shot, which necessitates additional wrist muscle strength during the swinging and stroke phases. 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