Download PS1-003 - IFToMM 2015

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. The result
is substantial fluctuation in the motion and stress curves of
the forearm (ulna and radius) and wrist (carpal bones) and
the muscle strength curves of the biceps brachii and triceps
brachii, meaning that the motions adopted in Path 4 can
also easily cause sports injuries.
Comparing the three different error paths, we conclude
that Path 3 is the most dangerous because the failure to
completely straighten the arm and the incorrect posture can
result in a squeezing phenomenon, leading potentially to
enhanced stress and muscle strength and an increased risk
of sports injuries.
Acknowledgments
Thanks for Dr. Lu Wen-jun of the ST. Joseph，s Hospital,
Huwei, Yunlin for his advice on constructing human bone
and muscle.
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