arXiv:1206.1471v1  [cs.RO]  7 Jun 2012
A new approach to muscle fatigue evaluation
for Push/Pull task
Ruina Ma ‡, Damien Chablat ‡ and Fouad Bennis ‡
‡ 44321 France (corresponding author: +33240376963; fax: +33240376930;
e-mail: Ruina.Ma@irccyn.ec-nantes.fr).
Abstract Pushing/Pulling tasks is an important part of work in
many industries.
Usually, most researchers study the Push/Pull
tasks by analyzing different posture conditions, force requirements,
velocity factors, etc. However few studies have reported the effects
of fatigue. Fatigue caused by physical loading is one of the main
reasons responsible for MusculoSkeletal Disorders (MSD). In this
paper, muscle groups of articulation is considered and from joint
level a new approach is proposed for muscle fatigue evaluation in
the arms Push/Pull operations. The objective of this work is to pre-
dict the muscle fatigue situation in the Push/Pull tasks in order to
reduce the probability of MSD problems for workers. A case study
is presented to use this new approach for analyzing arm fatigue in
Pushing/Pulling.
1
Introduction
Approximately 20% of over-exertion injuries have been associated with push
and pull acts (National Institute for Occupational Safety and Health. Division of Biomedical and Behavioral Scien
1981). Nearly 8% of all back injuries and 9% of all back strains and sprains
are also associated with pushing and pulling (Klein et al., 1984).
Thus,
there is a need to understand push and pull activities in industry since
many over-exertion and fall injuries appear to be related to such activities.
However, unlike other operations, push/pull capabilities have been studied
only within a very limited scope. Most studies describe a laboratory exper-
iment designed to mimic a working condition. For example: Mital did the
research of push and pull isokinetic strengths from moving speed and arm
angle changes (Mital et al., 1995). Badi did an experiment of one handed
pushing and pulling strength at different handle heights in the vertical di-
rection (Badi and Boushaala, 2008).
In industry a number of push/pull operations are causing the MSD prob-
lems. From the report of Health, Safety and Executive and report of Wash-
ington State Department of Labor and Industries, over 50% of workers in
1
industry have suffered from MSD, especially for manual handling jobs. Ac-
cording to the analysis in Occupational Biomechanics, muscle fatigue is
an essential factor in MSD problems (Chaffin et al., 1999). Several muscle
fatigue models have been proposed in the literature. In Wexler et al., a
muscle fatigue model is proposed based on Ca2+ cross-bridge mechanism
and verified the model with simulation experiments (Wexler et al., 1997).
In Liu et al., a dynamic muscle model is proposed based on motor units
pattern of muscle from the biophysical point of view (Liu et al., 2002). It
demonstrates the relationship among muscle activation, fatigue and recov-
ery. Another muscle fatigue model is developed by Giat based on force-pH
relationship (Giat et al., 1993). This fatigue model was obtained by curve
fitting of the pH level with time t in the course of stimulation and recovery.
In Ma et al., a muscle fatigue model is proposed from the macroscopic point
of view (Ma et al., 2009). External physical factors and personal factors
are taken into consideration to construct the model from joint level. The
existing muscle fatigue models consider the muscle fatigue problem from
different scientific domain perspectives and each with its own advantages
and disadvantages.
We note from the above investigation that few people consider the fatigue
factor in the push/pull operation. Therefore, it is necessary to combine the
fatigue factor with push/pull operation. The objective of this paper is to
introduce a new approach for muscle fatigue evaluation in push and pull
operation and it is illustrated by using Push/Pull arm motion.
Firstly,
we extend the existing static muscle fatigue model in dynamic situation.
Secondly, we give some hypothesis of arm muscle activities in push/pull op-
eration. Thirdly, a new approach for muscle fatigue evaluation is proposed.
Finally, a case-study is discussed to explain the two articulation push/pull
operation of the arm fatigue situation in both shoulder and elbow joints.
2
A New Approach for Push/Pull Arm Fatigue
Evaluation
2.1
Human muscle fatigue model
Ma proposed a muscle fatigue model from a macroscopic point of view
(Ma et al., 2009). This muscle fatigue model is expressed as follows.
Fcem(t) = MVC · e
R t
0 −k Fload(u)
MVC
du
(1)
where MVC is the maximum voluntary contraction, Fcem is the current
exertable maximum force, Fload(u) is the external load and k is a constant
parameter.
Since Ma et al.
consider only a static situation, Fload(u) is
2
assumed as a constant.
This muscle fatigue model was validated in the
context of an industrial by an experimental procedure.
In dynamic situation the value of Fload is not a constant. According to
robotic dynamic model (Khalil and Dombre, 2002), Fload can be modeled
by a variable depending on the angle, the velocity, the acceleration and the
duration of activities.
Fload
def
= F(u, θ, ˙θ, ¨θ)
(2)
This way, Eq. (1) can be further simplified in the form.
Fcem(t) = MVC · e−
k
MVC
R t
0 F(u,θ, ˙θ,¨θ)du
(3)
Eq. (3) defines the muscle fatigue model in dynamic situation. The model
takes consideration of the motion by the variations of the force Fjoint from
joint level.
This dynamic factor can be computed using Newton-Euler
method or Lagrange method.
2.2
Push/Pull muscles activity hypothesis
When a human performs a simple motion, nearly all aspects in the body
change. However, from a macroscopic point of view, when a human per-
forms a push/pull operation the related muscle groups of triceps, biceps and
deltoid, subscapularis are activated differently. For elbow, when a person
does the push operation, the triceps muscle groups are mainly used. In-
versely, when a person does the pull operation, the biceps muscle groups
are mainly used. For shoulder, the movement is more complex. Generally
when a person does the push operation, we can see that the deltoid related
muscle groups are mainly used and inversely in the pull state the subscapu-
laris and other related muscles are mainly used. Based on this, we suppose
that every articulation is controlled by two groups muscles: Push muscles
group and Pull muscles group. Furthermore, we suppose that during the
push phase the push muscles group is in an active state and the pull mus-
cles group is in an inactive state. The opposite would occur if the activity
is inversed. Here we do not take consideration of the co-contraction factor.
We can use Fig. 1(a) to illustrate the activity of push/pull muscles groups.
This supposition provides the basis of the new muscle fatigue evaluation
approach for push/pull tasks.
2.3
Push/Pull muscle fatigue evaluation approach
From the muscle fatigue model we can see that when a muscle is in an
active state, the force generated by muscle decreases with time. In a dy-
namic push/pull task, the push and pull muscles groups will also experience
3
Time (s)
Muscle groups
Push Muscles
Pull Muscles
Phase_Pull
Phase_Push
(a)
Time (s)
Muscle groups
Push Muscles
Pull Muscles
Phase_Pull
Phase_Push
F_Push
F_Pull
(b)
Figure 1. (a) Activity of muscle Push/Pull groups (b) Activity of muscle
Push/Pull groups with fatigue
the fatigue procedure. Based on the muscle fatigue model we introduced
before, for a push muscles group, the force exerted trend with time is:
Fpush cem(t) = MVCpush · e
−
k
MVCpush
R t
0 Fpush(u,θ, ˙θ,¨θ)du
(4)
Meanwhile for a pull muscles group, the force exerted trend with time is:
Fpull cem(t) = MVCpull · e
−
k
MVCpull
R t
0 Fpull(u,θ, ˙θ,¨θ)du
(5)
Push/Pull task is an alternating activity. In this situation, the arm fatigue
in push/pull task can be expressed by a piecewise function, as follows:
Fpush / pull(t) =
(
Fpush cem(t),
t ∈Phase Push
Fpull cem(t),
t ∈Phase Pull
(6)
Figure 1(b) shows the arm fatigue situation in push/pull task.
As for the arm fatigue from a joint-based point of view, we can cal-
culate the force of every articulation (shoulder, elbow) by using a robotic
method where every external push and pull force is known. According to
the Push/Pull muscle fatigue evaluation approach, when we know the ex-
ternal push/pull force and with other arm biomechanic parameters we can
know the arm fatigue trends at both the shoulder and elbow levels.
3
Case study: two articulation push/pull operation
In this case study we discuss the fatigue situation of a two articulation arm
in the push/pull operation. From the joint-based view, the arm fatigue can
depend on the shoulder fatigue and elbow fatigue. Below are the detailed
explanations.
4
3.1
Arm model
According to the biomechanical structure, we present a geometric model
of the arm. We simplify the human arm to 5 revolute joints. The geometric
model is shown on Fig. 2(a).
1
D1
D2
Q
2
Q
3
Q
4
Q
5
Q
(a)
0
5
10
15
20
0
5
10
15
20
30
40
50
60
70
80
90
MVC of Shoulder for man and women
Strength(N)
Q4
Q1
MVC of Male
MVC of Female
(b)
0
5
10
15
20
0
5
10
15
20
30
40
50
60
70
80
Q1
MVC of Elbow for man and women
Q4
Strength(N)
MVC of Male
MVC of Female
(c)
Figure 2. (a) Arm geometric model (b) Shoulder MVC of male and female
(c) Elbow MVC of male and female (Chaffin et al., 1999)
3.2
Shoulder and elbow maximum strength
In the muscle fatigue equation we should pay attention especially to the
MVC parameter. MVC means the maximum force that muscles generate.
In static situation the MVC value is a constant, because it is decided by arm
posture. Obviously, in a dynamic situation the MVC value changes with
different arm postures. Using the previously researched strength model of
Chaffin (Chaffin et al., 1999), we can get the maximum arm force in different
postures. The strength model can be expressed by Eq. (7), where αe = θ1
and αs = 180 −θ4. G is the parameter for gender adjustment. Fig. 2(b,c)
shows the strength of elbow and shoulder in different arm angles both for
man and women.
Strengthelbow
= (336.29 + 1.544αe −0.0085α2
s) · G
Strengthshoulder
= (227.338 + 0.525αe −0.296αs) · G
(7)
3.3
Fatigue risk force
When people do some tasks, at what point will they risk fatigue? A
subjective measure of fatigue is not appropriate to quantify fatigue. We
need an objective parameter to measure the fatigue risk. The Maximum
Endurance Time (MET) is an important concept in ergonomics. It describes
the duration from the start to the instant at which the strength decreases to
below the torque demand resulting from external load. Once the external
load exceeds the current force capacity, potential physical risks might occur
5
to the body tissues. So the fatigue risk force, noted Ffatigue risk is reached
when the external load equals the current force capacity,
Ffatigue risk = Fexternal = Fjoint.
(8)
For a static posture, Ffatigue risk is a constant value, because in the static
situation the external force is a constant. Meanwhile, in dynamic situa-
tion, Ffatigue risk is non-linear function; it changes according to different
postures. According to the arm geometric model, the force of every joint
can be represented by Fjoint ∈{Fθ1, . . . , Fθ5}. For example, Ffatigue risk of
shoulder is Fshoulder = Fθ1 and Ffatigue risk of elbow is Felbow = Fθ4. When
the arm does the horizontal push and pull operation and the hand move
alone x axis between (0.3, 0.4) meter, the shoulder angle changes between
(-49.3, -42.3) degrees and the elbow angle changes between (124.1, 101.3)
degrees. The force changes of shoulder and elbow were shown on Fig. 3.
This also represents the fatigue risk force trends in the push/pull oper-
ations.
Forces of shoulder and elbow are computed using Newton-Euler
method (Khalil and Dombre, 2002).
0
0.2
0.4
0.6
0.8
1
0
5
10
15
20
25
30
time (Minutes)
Force (N)
Shoulder force
Elbow force
(a)
0
0.2
0.4
0.6
0.8
1
0
5
10
15
20
25
30
time (Minutes)
Force (N)
Shoulder force
Elbow force
(b)
Figure 3. (a) Push Operation (b) Pull Operation
3.4
Dynamic push/pull simulation
Suppose the weight of the object is 2Kg, and a person (Sex: man,
Height: 188cm, Weight: 90kg) uses 10N to push and 10N to pull this object.
In reality the push/pull task time may not be exactly the same, here we
simplify the situation and consider that the two operations use the same
time (Tpush = Tpull = 1 minute). Fatigue rate parameter k depends on the
subject and experiment measures are needed to determine it. Here for this
specific case we choose k = 1 for both push and pull operations. In different
postures, according to the estimated arm’s strength we know the MVC of
the shoulder and elbow at every moment; according to the push force and
6
pull force we can calculate the force of elbow and shoulder at every mo-
ment. Furthermore we can know the fatigue risk line of the shoulder and
elbow. Based on these initial conditions, and using our approach, we can
determine the fatigue trends in shoulder and elbow separately. Fig. 4 shows
the simulation of arm fatigue in both shoulder and elbow level.
0
0.1
0.2
0.3
0.4
-0.3
-0.2
-0.1
0
horizontal position (meter)
vertical position (meter)
Upper arm
Lower arm
(a)
0
5
10
15
20
0
10
20
30
40
50
60
70
80
time (Minutes)
Force (N)
Shoulder force with fatigue
Elbow force with fatigue
Shoulder fatigue risk line
Elbow fatigue risk line
(b)
Figure 4. (a) Arm Push/Pull Operation (b) Fatigue simulation of arm
Push/Pull Operation
3.5
Discussion
From the simulation result we can see that in push/pull task, the shoul-
der exerted force reaches Ffatigue risk in about 5 minutes and the elbow
exerted force reaches Ffatigue risk in about 11 minutes. This explains why
many workers have problems with shoulder rather than elbow from push-
ing/pulling. These results support the idea that when workers do this kind
of work, it is better to have a rest or to change the working posture every
5 minutes to avoid fatigue. The simulation here is a general case; the spe-
cific prediction is decided by the individual person, the working posture,
the weight of the object and the single push/pull operation time. In fu-
ture work we will use experimental data to verify this fatigue evaluation
approach. The experiment would also consider more muscles and joints,
female subjects and changing external loads.
4
Conclusions
In this paper, we took into consideration the muscle groups of articulation
in push and pull operations and from joint level proposed a new approach to
muscle fatigue evaluation for push/pull tasks. From simulation results we
can see that in a push/pull process, the arm fatigue trends appear in both
shoulder and elbow level and it is decided by the parameters MV C, Fload, k,
7
and working postures. The case study shows that our new fatigue evaluation
approach has a potential to provide information to help people prevent
fatigue risk and estimate the safe working periods for pushing/pulling. Our
work enlarges the vision of push/pull operation research. The final goal
of our work is to use this model in ergonomic evaluation procedures, to
enhance work efficiency and reduce MSD risks.
Bibliography
T. H. Badi and A. A. Boushaala. Effect of one-handed pushing and pulling
strength at different handle heights in vertical direction. Engineering
and Technology, page 47, 2008.
D. B. Chaffin, G. B. J. Andersson, and B. J. Martin. Occupational Biome-
chanics. John Wiley and Sons, Inc, third edition, 1999.
Y. Giat, J. Mizrahi, and M. Levy. A musculotendon model of the fatigue
profiles of paralyzed quadriceps muscle under fes. IEEE transactions on
biomedical engineering, 40(7):664–674, 1993.
W Khalil and E Dombre. Modelling, identification and control of robots.
Hermes Science Publications, 2002.
B. P. Klein, R. C. Jensen, and L. M. Sanderson. Assessment of workers’
compensation claims for back strains/sprains. Journal of Occupational
Medicine, 26(6):443–448, 1984.
J. Z. Liu, R. W. Brown, and G.H. Yue.
A dynamical model of muscle
activation, fatigue, and recovery. Biophysical journal, 82(5):2344–2359,
May 2002. ISSN 0006-3495.
L. Ma, D. Chablat, F. Bennis, and W. Zhang. A new simple dynamic muscle
fatigue model and its validation.
International Journal of Industrial
Ergonomics, 39(1):211 – 220, 2009. ISSN 0169-8141.
A. Mital, P. Kopardekar, and A. Motorwala. Isokinetic pull strengths in
the vertical plane: effects of speed and arm angle. Clinic Biomechanics,
10(2):110–112, 1995.
National Institute for Occupational Safety and Health. Division of Biomed-
ical and Behavioral Science. Work practices guide for manual lifting.
DHHS publication, no. (NIOSH) 81-122, 1981.
A. S. Wexler, J. Ding, and S. A. Binder-Macleod. A mathematical model
that predicts skeletal muscle force.
IEEE transactions on biomedical
engineering, 44(5):337–348, 1997.
8
arXiv:1206.1471v1  [cs.RO]  7 Jun 2012
A new approach to muscle fatigue evaluation
for Push/Pull task
Ruina Ma ‡, Damien Chablat ‡ and Fouad Bennis ‡
‡ 44321 France (corresponding author: +33240376963; fax: +33240376930;
e-mail: Ruina.Ma@irccyn.ec-nantes.fr).
Abstract Pushing/Pulling tasks is an important part of work in
many industries.
Usually, most researchers study the Push/Pull
tasks by analyzing different posture conditions, force requirements,
velocity factors, etc. However few studies have reported the effects
of fatigue. Fatigue caused by physical loading is one of the main
reasons responsible for MusculoSkeletal Disorders (MSD). In this
paper, muscle groups of articulation is considered and from joint
level a new approach is proposed for muscle fatigue evaluation in
the arms Push/Pull operations. The objective of this work is to pre-
dict the muscle fatigue situation in the Push/Pull tasks in order to
reduce the probability of MSD problems for workers. A case study
is presented to use this new approach for analyzing arm fatigue in
Pushing/Pulling.
1
Introduction
Approximately 20% of over-exertion injuries have been associated with push
and pull acts (National Institute for Occupational Safety and Health. Division of Biomedical and Behavioral Scien
1981). Nearly 8% of all back injuries and 9% of all back strains and sprains
are also associated with pushing and pulling (Klein et al., 1984).
Thus,
there is a need to understand push and pull activities in industry since
many over-exertion and fall injuries appear to be related to such activities.
However, unlike other operations, push/pull capabilities have been studied
only within a very limited scope. Most studies describe a laboratory exper-
iment designed to mimic a working condition. For example: Mital did the
research of push and pull isokinetic strengths from moving speed and arm
angle changes (Mital et al., 1995). Badi did an experiment of one handed
pushing and pulling strength at different handle heights in the vertical di-
rection (Badi and Boushaala, 2008).
In industry a number of push/pull operations are causing the MSD prob-
lems. From the report of Health, Safety and Executive and report of Wash-
ington State Department of Labor and Industries, over 50% of workers in
1
industry have suffered from MSD, especially for manual handling jobs. Ac-
cording to the analysis in Occupational Biomechanics, muscle fatigue is
an essential factor in MSD problems (Chaffin et al., 1999). Several muscle
fatigue models have been proposed in the literature. In Wexler et al., a
muscle fatigue model is proposed based on Ca2+ cross-bridge mechanism
and verified the model with simulation experiments (Wexler et al., 1997).
In Liu et al., a dynamic muscle model is proposed based on motor units
pattern of muscle from the biophysical point of view (Liu et al., 2002). It
demonstrates the relationship among muscle activation, fatigue and recov-
ery. Another muscle fatigue model is developed by Giat based on force-pH
relationship (Giat et al., 1993). This fatigue model was obtained by curve
fitting of the pH level with time t in the course of stimulation and recovery.
In Ma et al., a muscle fatigue model is proposed from the macroscopic point
of view (Ma et al., 2009). External physical factors and personal factors
are taken into consideration to construct the model from joint level. The
existing muscle fatigue models consider the muscle fatigue problem from
different scientific domain perspectives and each with its own advantages
and disadvantages.
We note from the above investigation that few people consider the fatigue
factor in the push/pull operation. Therefore, it is necessary to combine the
fatigue factor with push/pull operation. The objective of this paper is to
introduce a new approach for muscle fatigue evaluation in push and pull
operation and it is illustrated by using Push/Pull arm motion.
Firstly,
we extend the existing static muscle fatigue model in dynamic situation.
Secondly, we give some hypothesis of arm muscle activities in push/pull op-
eration. Thirdly, a new approach for muscle fatigue evaluation is proposed.
Finally, a case-study is discussed to explain the two articulation push/pull
operation of the arm fatigue situation in both shoulder and elbow joints.
2
A New Approach for Push/Pull Arm Fatigue
Evaluation
2.1
Human muscle fatigue model
Ma proposed a muscle fatigue model from a macroscopic point of view
(Ma et al., 2009). This muscle fatigue model is expressed as follows.
Fcem(t) = MVC · e
R t
0 −k Fload(u)
MVC
du
(1)
where MVC is the maximum voluntary contraction, Fcem is the current
exertable maximum force, Fload(u) is the external load and k is a constant
parameter.
Since Ma et al.
consider only a static situation, Fload(u) is
2
assumed as a constant.
This muscle fatigue model was validated in the
context of an industrial by an experimental procedure.
In dynamic situation the value of Fload is not a constant. According to
robotic dynamic model (Khalil and Dombre, 2002), Fload can be modeled
by a variable depending on the angle, the velocity, the acceleration and the
duration of activities.
Fload
def
= F(u, θ, ˙θ, ¨θ)
(2)
This way, Eq. (1) can be further simplified in the form.
Fcem(t) = MVC · e−
k
MVC
R t
0 F(u,θ, ˙θ,¨θ)du
(3)
Eq. (3) defines the muscle fatigue model in dynamic situation. The model
takes consideration of the motion by the variations of the force Fjoint from
joint level.
This dynamic factor can be computed using Newton-Euler
method or Lagrange method.
2.2
Push/Pull muscles activity hypothesis
When a human performs a simple motion, nearly all aspects in the body
change. However, from a macroscopic point of view, when a human per-
forms a push/pull operation the related muscle groups of triceps, biceps and
deltoid, subscapularis are activated differently. For elbow, when a person
does the push operation, the triceps muscle groups are mainly used. In-
versely, when a person does the pull operation, the biceps muscle groups
are mainly used. For shoulder, the movement is more complex. Generally
when a person does the push operation, we can see that the deltoid related
muscle groups are mainly used and inversely in the pull state the subscapu-
laris and other related muscles are mainly used. Based on this, we suppose
that every articulation is controlled by two groups muscles: Push muscles
group and Pull muscles group. Furthermore, we suppose that during the
push phase the push muscles group is in an active state and the pull mus-
cles group is in an inactive state. The opposite would occur if the activity
is inversed. Here we do not take consideration of the co-contraction factor.
We can use Fig. 1(a) to illustrate the activity of push/pull muscles groups.
This supposition provides the basis of the new muscle fatigue evaluation
approach for push/pull tasks.
2.3
Push/Pull muscle fatigue evaluation approach
From the muscle fatigue model we can see that when a muscle is in an
active state, the force generated by muscle decreases with time. In a dy-
namic push/pull task, the push and pull muscles groups will also experience
3
Time (s)
Muscle groups
Push Muscles
Pull Muscles
Phase_Pull
Phase_Push
(a)
Time (s)
Muscle groups
Push Muscles
Pull Muscles
Phase_Pull
Phase_Push
F_Push
F_Pull
(b)
Figure 1. (a) Activity of muscle Push/Pull groups (b) Activity of muscle
Push/Pull groups with fatigue
the fatigue procedure. Based on the muscle fatigue model we introduced
before, for a push muscles group, the force exerted trend with time is:
Fpush cem(t) = MVCpush · e
−
k
MVCpush
R t
0 Fpush(u,θ, ˙θ,¨θ)du
(4)
Meanwhile for a pull muscles group, the force exerted trend with time is:
Fpull cem(t) = MVCpull · e
−
k
MVCpull
R t
0 Fpull(u,θ, ˙θ,¨θ)du
(5)
Push/Pull task is an alternating activity. In this situation, the arm fatigue
in push/pull task can be expressed by a piecewise function, as follows:
Fpush / pull(t) =
(
Fpush cem(t),
t ∈Phase Push
Fpull cem(t),
t ∈Phase Pull
(6)
Figure 1(b) shows the arm fatigue situation in push/pull task.
As for the arm fatigue from a joint-based point of view, we can cal-
culate the force of every articulation (shoulder, elbow) by using a robotic
method where every external push and pull force is known. According to
the Push/Pull muscle fatigue evaluation approach, when we know the ex-
ternal push/pull force and with other arm biomechanic parameters we can
know the arm fatigue trends at both the shoulder and elbow levels.
3
Case study: two articulation push/pull operation
In this case study we discuss the fatigue situation of a two articulation arm
in the push/pull operation. From the joint-based view, the arm fatigue can
depend on the shoulder fatigue and elbow fatigue. Below are the detailed
explanations.
4
3.1
Arm model
According to the biomechanical structure, we present a geometric model
of the arm. We simplify the human arm to 5 revolute joints. The geometric
model is shown on Fig. 2(a).
1
D1
D2
Q
2
Q
3
Q
4
Q
5
Q
(a)
0
5
10
15
20
0
5
10
15
20
30
40
50
60
70
80
90
MVC of Shoulder for man and women
Strength(N)
Q4
Q1
MVC of Male
MVC of Female
(b)
0
5
10
15
20
0
5
10
15
20
30
40
50
60
70
80
Q1
MVC of Elbow for man and women
Q4
Strength(N)
MVC of Male
MVC of Female
(c)
Figure 2. (a) Arm geometric model (b) Shoulder MVC of male and female
(c) Elbow MVC of male and female (Chaffin et al., 1999)
3.2
Shoulder and elbow maximum strength
In the muscle fatigue equation we should pay attention especially to the
MVC parameter. MVC means the maximum force that muscles generate.
In static situation the MVC value is a constant, because it is decided by arm
posture. Obviously, in a dynamic situation the MVC value changes with
different arm postures. Using the previously researched strength model of
Chaffin (Chaffin et al., 1999), we can get the maximum arm force in different
postures. The strength model can be expressed by Eq. (7), where αe = θ1
and αs = 180 −θ4. G is the parameter for gender adjustment. Fig. 2(b,c)
shows the strength of elbow and shoulder in different arm angles both for
man and women.
Strengthelbow
= (336.29 + 1.544αe −0.0085α2
s) · G
Strengthshoulder
= (227.338 + 0.525αe −0.296αs) · G
(7)
3.3
Fatigue risk force
When people do some tasks, at what point will they risk fatigue? A
subjective measure of fatigue is not appropriate to quantify fatigue. We
need an objective parameter to measure the fatigue risk. The Maximum
Endurance Time (MET) is an important concept in ergonomics. It describes
the duration from the start to the instant at which the strength decreases to
below the torque demand resulting from external load. Once the external
load exceeds the current force capacity, potential physical risks might occur
5
to the body tissues. So the fatigue risk force, noted Ffatigue risk is reached
when the external load equals the current force capacity,
Ffatigue risk = Fexternal = Fjoint.
(8)
For a static posture, Ffatigue risk is a constant value, because in the static
situation the external force is a constant. Meanwhile, in dynamic situa-
tion, Ffatigue risk is non-linear function; it changes according to different
postures. According to the arm geometric model, the force of every joint
can be represented by Fjoint ∈{Fθ1, . . . , Fθ5}. For example, Ffatigue risk of
shoulder is Fshoulder = Fθ1 and Ffatigue risk of elbow is Felbow = Fθ4. When
the arm does the horizontal push and pull operation and the hand move
alone x axis between (0.3, 0.4) meter, the shoulder angle changes between
(-49.3, -42.3) degrees and the elbow angle changes between (124.1, 101.3)
degrees. The force changes of shoulder and elbow were shown on Fig. 3.
This also represents the fatigue risk force trends in the push/pull oper-
ations.
Forces of shoulder and elbow are computed using Newton-Euler
method (Khalil and Dombre, 2002).
0
0.2
0.4
0.6
0.8
1
0
5
10
15
20
25
30
time (Minutes)
Force (N)
Shoulder force
Elbow force
(a)
0
0.2
0.4
0.6
0.8
1
0
5
10
15
20
25
30
time (Minutes)
Force (N)
Shoulder force
Elbow force
(b)
Figure 3. (a) Push Operation (b) Pull Operation
3.4
Dynamic push/pull simulation
Suppose the weight of the object is 2Kg, and a person (Sex: man,
Height: 188cm, Weight: 90kg) uses 10N to push and 10N to pull this object.
In reality the push/pull task time may not be exactly the same, here we
simplify the situation and consider that the two operations use the same
time (Tpush = Tpull = 1 minute). Fatigue rate parameter k depends on the
subject and experiment measures are needed to determine it. Here for this
specific case we choose k = 1 for both push and pull operations. In different
postures, according to the estimated arm’s strength we know the MVC of
the shoulder and elbow at every moment; according to the push force and
6
pull force we can calculate the force of elbow and shoulder at every mo-
ment. Furthermore we can know the fatigue risk line of the shoulder and
elbow. Based on these initial conditions, and using our approach, we can
determine the fatigue trends in shoulder and elbow separately. Fig. 4 shows
the simulation of arm fatigue in both shoulder and elbow level.
0
0.1
0.2
0.3
0.4
-0.3
-0.2
-0.1
0
horizontal position (meter)
vertical position (meter)
Upper arm
Lower arm
(a)
0
5
10
15
20
0
10
20
30
40
50
60
70
80
time (Minutes)
Force (N)
Shoulder force with fatigue
Elbow force with fatigue
Shoulder fatigue risk line
Elbow fatigue risk line
(b)
Figure 4. (a) Arm Push/Pull Operation (b) Fatigue simulation of arm
Push/Pull Operation
3.5
Discussion
From the simulation result we can see that in push/pull task, the shoul-
der exerted force reaches Ffatigue risk in about 5 minutes and the elbow
exerted force reaches Ffatigue risk in about 11 minutes. This explains why
many workers have problems with shoulder rather than elbow from push-
ing/pulling. These results support the idea that when workers do this kind
of work, it is better to have a rest or to change the working posture every
5 minutes to avoid fatigue. The simulation here is a general case; the spe-
cific prediction is decided by the individual person, the working posture,
the weight of the object and the single push/pull operation time. In fu-
ture work we will use experimental data to verify this fatigue evaluation
approach. The experiment would also consider more muscles and joints,
female subjects and changing external loads.
4
Conclusions
In this paper, we took into consideration the muscle groups of articulation
in push and pull operations and from joint level proposed a new approach to
muscle fatigue evaluation for push/pull tasks. From simulation results we
can see that in a push/pull process, the arm fatigue trends appear in both
shoulder and elbow level and it is decided by the parameters MV C, Fload, k,
7
and working postures. The case study shows that our new fatigue evaluation
approach has a potential to provide information to help people prevent
fatigue risk and estimate the safe working periods for pushing/pulling. Our
work enlarges the vision of push/pull operation research. The final goal
of our work is to use this model in ergonomic evaluation procedures, to
enhance work efficiency and reduce MSD risks.
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