Biomechanical study of cross- country skiing Marie Lund

Department of Physics
Master’s Thesis 20p
Biomechanical study of crosscountry skiing
Marie Lund
Master’s thesis in Engineering Physics carried out at Mid Sweden University,
Department of Engineering, Physics and Mathematics, Östersund
Supervisor: Joakim Holmberg
Examiner: Svante Jonsell
This investigation is a biomechanical study of how the stiffness in pectoralis major (the big
chest muscle) affects the muscles in the upper back during the fourth gear in Cross-country
skiing free-style technique.
It is believed that cross-country skiers often have a stiff pectoralis major, which may result in
an increased work for the poling. Further, a stiff pectoralis major will limit the range of
motion for the backward pendulum (extension) of the arm, important in the fourth skiing gear.
The question to be answered in this report is what a person with a stiff pectoralis major can
do to be able to use the same technique as one with a normal pectoralis major. Should
stiffness in pectoralis major be decreased and/or should the upper back muscle forces be
increased, how much and which ones.
The investigation was performed in the inverse dynamics software The AnyBody Modelling
System. In inverse dynamics the movement is the input and the program calculates the muscle
forces for output.
First the resting length for pectoralis major was measured. This was needed for individual
calibration of the stiffness for this muscle. The motion of a skier was calculated from a
visualisation produced after a recording by a motion capture system (3-D video recording).
Thereafter several pectoralis major tendon lengths were tested for the skiing motion with the
AnyBody Modelling System. The pole forces and the mass of the poles were not included in
the skiing model.
From the motion recording it was not possible to calculate the motion of the shoulder;
therefore the shoulder was held fix in this investigation.
Since it is not known how to decrease the stiffness in a muscle the muscles in the upper back
(antagonists to pectoralis major) have to increase their forces to balance the motion. The
results of this investigation showed that forces of the outward rotators of the arm, the
adductors of scapula and the basin parts of latissimus dorsi have to be increased equally to
balance the motion. Stretching should be used to increase or maintain the range of motion for
pectoralis major. If the movement of the shoulder had been included in the model the results
would probably have been different.
This thesis was performed as a part of the DAVOS project, Computer-aided tools for
optimization and simulation at the department of Engineering, Physics and Mathematics, Mid
Sweden University, Östersund 2004.
The DAVOS project is financed by European Union Objective 1 programme.
Optimisation of biomechanical systems is one of the six subparts of the project DAVOS.
The project has in view to use optimisation methods and mechanical base principles with
computer-aided tools to describe situations within both cross-country and alpine skiing. The
situations to be described are those that are of importance for the performance or where there
are risks for injuries. The objective of the project is to build up knowledge that may increase
the competitiveness for Swedish athletes and reduce the number of injuries.
I gratefully acknowledge my supervisor PhD student Joakim Holmberg for very valuable
discussions and support. Without you this work would have been nothing.
I am also very grateful to all members in the AnyBody Research group for their excellent
support concerning The AnyBody Modelling System and other questions about inverse
My great acknowledge to Technical Licentiate Peter Rydesäter who has given me support
regarding the software Matlab and the perspective reduction calculations.
Other people who have helped me with this thesis;
- Hans-Crister Holmberg, Swedish Olympic committee, discussion about cross-country
- Professor Peter Magnusson, with ideas for measuring pectoralis major resting length
and knowledge about mechanical properties of muscles.
- Tech. Lic. Erica Johansson, with support and whipping.
- My father, Kaj Lund, with building of the measurement equipment for resting length
Thanks to all of you!
Introduction ...................................................................................................................... 1
Background ................................................................................................................ 1
Aim and Objective ..................................................................................................... 2
Limitations ................................................................................................................. 2
Disposition ................................................................................................................. 3
Theory ............................................................................................................................... 4
Physiology.................................................................................................................. 4
Preface................................................................................................................ 4
The skeletal parts................................................................................................ 4
The muscle ......................................................................................................... 7
The shoulder muscles ....................................................................................... 10
Movements ....................................................................................................... 17
Posture.............................................................................................................. 19
Stretching ......................................................................................................... 21
Biomechanics ........................................................................................................... 23
The AnyBody Modelling System..................................................................... 23
The Hill type muscle model ............................................................................. 26
The equations of equilibrium ........................................................................... 34
Interpreting the results...................................................................................... 36
Experimental method..................................................................................................... 39
Investigation method ................................................................................................ 39
The human model..................................................................................................... 40
Measuring pectoralis resting length ......................................................................... 42
The input motion ...................................................................................................... 44
Background ...................................................................................................... 44
Landmarks ........................................................................................................ 44
Perspective reduction ....................................................................................... 45
Joint angle calculations .................................................................................... 50
Results ............................................................................................................................. 56
Pectoralis major resting length................................................................................. 56
Motion of cross-country skiing 4th gear ................................................................... 61
Results from the AnyBody Modelling System ........................................................ 64
Discussion and conclusions............................................................................................ 76
The resting length measurement .............................................................................. 76
The input motion ...................................................................................................... 77
Results from the AnyBody Modelling System ........................................................ 78
Summarizing discussion........................................................................................... 79
References ....................................................................................................................... 82
Unpublished references ............................................................................................ 82
Published references................................................................................................. 82
Electronical references ............................................................................................. 84
1 Introduction
1.1 Background
Within cross-country skiing a shoulder posture called rounded shoulder is believed to be quite
common, HC Holmberg (personal communication). This posture appears as the shoulder is
pulled forward and downward. This posture can result in pain in the upper back and the neck;
because the muscles in the upper back are in lengthened position. One other reason for this
common posture among cross-country skiers might also depend on the monotone movement
for the shoulder girdle in skiing. During skiing the arms work with the poles during all the
gears in both free-style and classical technique (except the fifth1 in free-style technique). The
strongest muscles working in the poling is believed to be pectoralis major, teres major,
latissimus dorsi and triceps long head2. The three first of this muscles are all inward rotators
of the arm, and if they are stiff they can give rise to the rounded shoulder posture.
The reason for this kind of posture may be psychological; a cross-country skier seldom looks
as proud as for example a sprint runner. This reason should not be neglected as unimportant
since the mental health is of big importance for postures.
Today’s cross-country skiing technique is developing to be more and more focused on
frequency. To be able to ski with high frequency it is often important to for example in the
double-poling technique, make the time for the poling cycle short. However, the fourth3 gear
in free-style technique is a technique where the poling cycle should be large. The meaning of
a large poling cycle is using an arm pendulum with large extensive range. This is physical
important fact since there is a transformation of power from the angular momentum of the
arm into power in the leg if it is right performed. In Swedish is this timing often called
“träffen” (“the hit”).
In the fourth gear it is possible to pole either when standing on the left leg of or when standing
on the right leg. Poling when standing on the left leg is illustrated in Figure 1.1-1. “Träffen”
occurs twice in one cycle, phase 1 and phase 4, see Figure 1.1-1. First when the arm is on its
way forward, the arm passes the leg at the same time as the push from the right leg initialises.
The second time are the arms on their way backward and when they pass the legs the left leg
starts its push.
The different techniques in cross-country skiing free-style technique are named gear 1-5. The higher number
used the easier are the terrain. The fifth gear is used down the slopes.
The muscles will be described intensively in chapter 2.1.4.
The fourth gear is a high-speed gear used mainly in flat terrain. Double poling while standing on one leg.
Called single dance in Norway.
Figure 1.1-1. Illustration of the 4th gear in cross-country free style technique. Reference web page for Norwegian
ski federation.
The push from the leg should be directed vertical to the skiing direction and not backward
which is commonly assumed.
It is believed within cross-country skiing that an arm pendulum needs a good range of motion
in the pectoralis major to be performed properly. This is because the arm needs to pendulate
up a little bit behind the body to give time for the centre of mass to move from the poling ski
to the other ski (the right ski in Figure 1.1-1).
1.2 Aim and Objective
The object of this project is to examine how a stiffened pectoralis major changes the muscle
forces in the upper back during an arm pendulum in the fourth gear in cross-country skiing
free-style technique.
When pectoralis major becomes stiffer the shoulder posture might change. This change will
give rise to tension in other muscles, for example those in the upper back. This tension may
give rise to pain. The changing of the posture might also make the athlete use a less economic
skiing technique.
To be able to use the same skiing technique as with the original shoulder posture the stiffness
in pectoralis major has to be decreased or the produced forces in the upper back has to be
increased. If an athlete has high stiffness in pectoralis major what should the
recommendations to her be? How should the stiffness be decreased, which muscle forces
should be increased and how much should they be increased?
1.3 Limitations
This investigation is going to be performed with a program that uses inverse dynamics.
Shortly described, in inverse dynamics the movement are input to the program and the muscle
forces are output.
The input movement in this investigation are not satisfying. In April 2003 VICON made
recordings of cross-country skiing motions in Östersund only for demonstration purposes. The
idea for this project was to perform a new recording. Unfortunately I have not managed to
come in contact to any company in Sweden that could or wanted to perform the recording of
this skiing motion.
Since the recording is old all information are not saved. The information left from recording
of the fourth gear free-style technique is a visualisation of the motion. Neither the accuracy of
the recorded motion nor if the athlete is focusing on his skiing technique is known. Since the
recording only was done for demonstration purposes the motion does not include all
information needed to drive a shoulder motion. It is therefore the shoulder are held fix during
the motion.
1.4 Disposition
This report is first describing the theory about human physiology and thereafter theory about
the inverse dynamic software The AnyBody Modelling System. After this is done the
experimental method will be described. The plan for the way the project was carried out is
shortly described here in four steps:
Step 1: Statical measurement.
Calibrating the stiffness of the muscle for a specific individual. The joint angles is measured
when the muscle are in its resting length.
Step 2: Dynamical measurement
The upper body movement of the fourth gear in cross-country skiing is measured. From these
measurements the joint angles are calculated for all involved joints.
Step 3: Calibration of pectoralis major resting length in the artificial body.
Implementing the joint angles when the muscle is in its resting length. Calculating the
artificial muscle length in the AnyBody Modelling System.
Step 4: Implementing the movement
Implementing the movement in the AnyBody Modelling System and evaluating the muscle
forces for several different resting lengths.
After this follows the results and discussion with conclusions.
This master’s thesis should according to the instructions from the Department of Physics at
Umeå University be written so an average student in physics will understand it. Since this
thesis contains lots of physiology an attempt has been made to cover enough theory to achieve
2 Theory
2.1 Physiology
2.1.1 Preface
To be able to understand this thesis it is important to have some knowledge about the
This chapter uses terms that are common in physiology. These are necessary to be familiar
with to understand the text. The words used in the text are listed in Table 2.1-1. When these
terms are used for the first time in the text there will a reference to this table.
Table 2.1-1 Physiological terms describing positions.
Towards the middle
Away from the middle
Part closer to the attachment of the limb
Opposite to proximal
The end of the muscle were it “starts” from
(often the proximal part)
The other end of the muscle
Muscles which have opposite tasks
Muscles which cooperate to accomplish the
same task
The first eight terms in the table defines positions. Especially used for describing the muscles´
positions. The terms origin and insertion are important because a muscles task depends on the
positions of the origin/origins and insertion/insertions. The last two terms in the table are used
when describing the tasks for a muscle. For example are the upper back musculature
antagonists to pectoralis major.
2.1.2 The skeletal parts
The shoulder is one of the most complex skeletal parts in the body and as a result of that the
arm is the most movable limb in the body. The skeletal parts involved in moving the limb
include parts from the basin (pelvis) to the skull (cranium), see Figure 2.1-1. The reason why
so many skeletal parts are involved is that the muscles involved in shoulder movements
origins from these bones.
Figure 2.1-1. Skeletal parts involved in shoulder movement, reference Budowick (1993).
Several shoulder muscles origins from the spine. The spine of the human body consists of
vertebrae. These are named Cervical, Thoracic, Lumbar and Sacrum and are numbered with
the lowest number closest to the head. An illustration of the spine is shown in Figure 2.1-2.
Figure 2.1-2. Spine with names of all vertebrae shown, reference Netter (1997).
The spine has in normal cases a curvature. The curvature for the thoracic part is called
kyphosis and for the lumbar part is called lordosis.
The shoulder has a central role for the human being. When man started walking on two legs
instead of four the forelegs became its arms and hands. To put the hand in a functional
position the shoulder needed greater mobility. This mobility has developed on expense of
stability. Due to the lack of stability the shoulder is quite fragile, thus may pain and
malfunction occur (Caillet 1981). Only by observing the skeletal parts of the shoulder in
Figure 2.1-3 one can understand that it is fragile. The only bony connection the arm has to the
trunk is the little thin bone clavicula.
There are seven joints stabilizing the arm to the trunk. Four of these are not real joints named
functional joints, one of them is the gliding of scapula (the shoulder blade) over the ribs, the
second one is the binding between the ribs and the sternum, the third one is the connection
between the ribs and the vertebrae and the last one is a stabilizer for the glenohumeral joint
called suprahumeral joint. The three real joints will be described more intensively; these ones
bind the arm together with the trunk and are underlined in Figure 2.1-3. The real joints are
articulum humeroscapularis often called glenohumeral GH, art. Acromioclavicularis, AC and
art. Sternoclavicularis, SC.
Figure 2.1-3. Close view of skeletal parts of the shoulder, reference Budowick (1993).
The first joint connecting the arm in view from the trunk is the SC joint. This joint connects
the proximal part of clavicula with sternum, (explanation for distal and proximal see Table
2.1-1). This joint is an irregular joint. That means that the joint functions like a ball and socket
joint (spherical joint) but the rotation centre is not consistent throughout the movement (Putz
et al., 2001 p.166). The rotation centre is not consistent since there are gliding present
between the surfaces. Gliding occurs since the joint surfaces are somewhat plane, thus not
completely in ball-socket relation. To compensate for the plane joint surfaces there is an
articular disc present that makes the joint work like a spherical joint. The SC joint is
participating in all motions of the shoulder complex (Caillet, 1981 p.32).
The second joint, AC, connects the distal
part of clavicula with the acromion part of
scapula. This joint function the same way
as SC, a spherical joint with gliding. The
AC joint has a weak capsule that is
reinforced with strong ligaments. Close to
the AC joint the clavicula is tightly
fastened to scapula by the
coracoclavicular ligament. This ligament
consists of three parts, the lateral
trapezoid, the conoid and the medial
coracoclavicular ligament. In Figure 2.1-4
two of the parts of the ligament are shown.
The third part is attached to coracoid
process medial and clavicula inferior
proximal to the conoid ligament (Caillet,
1981 p.28-31).
Figure 2.1-4. The coracoclavicular ligaments,
reference Kapandji (1982 p.51).
The last joint involved in shoulder movements is the GH joint. According to Putz et al. (2001
p.166) GH is a real spherical joint, however Caillet (1981 p.4) claims the opposite since the
joint rotation centre is not consistent through the movements of the arm. Due to that is GH an
incongruous joint. The incongruousness arises from the shallow cavity of the socket and the
spherical irregularities of the head of humerus. The incongruousness makes the shoulder very
movable, but the great mobility causes lack of stability. Since the joint surfaces do not by
themselves fit tightly together ligaments and muscles are present as stabilizers (Caillet, 1981
The co-work between SC, AC and GH and the incongruousness of GH gives the arm a big
range of motion (RoM).
2.1.3 The muscle
In the human body there are three types of muscles, heart muscles, smooth muscles and
skeletal muscles. Contraction of a muscle can either be active or passive. Active means that
you by yourself can initiate contraction of a specific muscle and passive means that you
cannot decide by yourself when to contract the muscle. Heart and smooth muscles can only be
contracted passively while skeletal muscles can both be contracted actively and passively
(Guyton, 1984 p. 40). Skeletal muscles will be described thoroughly.
Every skeletal muscle contains of fascicles. Every fascicle is a collection of around 100 fibres
(muscle fibre is the same as muscle cell). The muscle cell is huge compared to other cells in
the body; it may be more than 30 cm long but normally they are around a few centimetres
(Haug, 1993 p.235). A normal human muscle cell contains of 1000-2000 myofibrils. The
work produced in a muscle is performed in the myofibrils that consist of basic contractile
units, the sarcomeres. In Figure 2.1-5 the structure of a muscle and a sarcomere is shown
Figure 2.1-5. Structure of a skeletal muscle, reference Simons (1999) page 46.
A sarcomere is the contractile part of the fibril that is situated between the so-called Z-lines,
Figure 2.1-5. The sarcomere contains of many actin and myosin filaments (these are proteins)
that perform the contraction. On the myosin filaments there are small projections, these are
called cross-bridges and connects the actin and the myosin filaments (shown in the figure
above). To produce a contraction the actin and myosin filaments needs energy in the form of
ATP (adenosine triphosphate). The ATP creator, mitochondria, has a central role in the
muscle cells and are therefore plentiful represented.
Contraction of a muscle is a process that contains of several steps. A simplified explanation
will be presented here, for more intensive explanation Guyton (1984) is recommended. The
first thing that occurs in the chain of contraction is that ATP binds to the projections of
myosin, which causes the cross-bridge to break. A cross-bridge is the binding between actin
and myosin, it is shown in Figure 2.1-5. In the next step ATP splits into ADP (adenosine
diphosphate) and phosphate and gives the energy to the projections, which tightens as a
spring. When a signal from the central nervous system, CNS, to the fibre is generated calcium
ions are released. The high concentration of calcium makes it possible for myosin to form a
new connection to actin. Since the projections on myosin are tensed the z-lines can approach
each other. As long as there are presence of both calcium ions and ATP the contraction
continues until the sarcomeres cannot be shortened any more. During relaxing is the
concentration of calcium ions is so low that no bridges are formed between actin and myosin.
(Haug 1993 p.236-239).
Depending on which speed a muscle is going to be contracted the signal from CNS is
distributed among the muscle cells differently. If the muscle is going to be contracted with
higher speed more muscle cells are activated. This since muscle cells cannot be activated
partly, either they are activated fully or they are not activated at all (Bauer et al. 1982 p.14).
Skeletal muscles have different properties for example size, strength, reaction velocity and
appearance. Muscles that control the hand and finger movements are very precise in both
applied strength and position. Bigger muscles (like the thigh muscles) are stronger and cannot
therefore control the movement with the same as accuracy as the hand.
The appearance are also quite various for different muscles. In Figure 2.1-6 are various
appearances of human muscles shown.
Figure 2.1-6. Different appearances of skeletal muscles in the human body, reference Simons (1999 p. 51).
A muscle is connected to the bone by a tendon that is often both internal (tendon and muscle
integrated often called aponeurosis) and external (only tendon tissue). The fibres in a muscle
can be oriented parallel to the tendons pulling direction or they can be attached to the tendons
in an angle relative to parallel insertion. This angle is called pennation angle and are not
trivial for the pennated muscles shown in Figure 2.1-6.
The fibres themselves also have different internal properties. There are two different main
types of muscle fibres, fibres with fast contraction speed coloured white and with slow
contraction speed coloured red. The human muscles are a mixture of both types of fibres. The
mixture is different in different parts of the body, it also for differs between individuals and
changes during a lifetime.
The maximal force a muscle can produce depend on size of the muscle. The size for the
muscle is measured in its cross-section area PCSA (physiological cross-section area). The size
of the force per unit cross-section area varies from 30-200 N/cm2 in the literature (Rasmussen,
2004 personal communication). The size of the produced force is also dependent on how
much the muscle is stretched; Figure 2.1-7 shows this phenomenon. The lower curve shows
the force when stretching a relaxed muscle and the upper curve shows the maximal
contraction force for a muscle related to its length. The lower curve is the same as the passive
force the tendon in the muscle gives rise to. The upper curve can be explained as the sum of
the contraction force from the muscle and the passive resistive force from the tendon.
A muscle is strongest when it is in its resting length see Figure 2.1-7 (Brunnstrom 1972).
Literature is not unambiguous in this question; some claims that the muscle is strongest when
it is slightly stretched.
The velocity of the movement is also dependent of the created force. In Figure 2.1-8 the
force/velocity relation of a fully activated muscle in its resting length is shown. If the applied
load P0 is decreased to P1 the velocity becomes V1 and the muscle shortens (Brunnstrom,
1972 p.39-46).
Figure 2.1-7. Function of the tension depending on
the length for a muscle, reference Brunnstrom
(1972 p.40). In the upper curve is the muscle fully
activated and in the lower curve is the muscle not
activated at all.
Figure 2.1-8. Function of the force depending on
the velocity of a fully activated muscle, reference
Brunnstrom (1972 p.45).
2.1.4 The shoulder muscles
The muscles involved in the movements of the shoulder are quite many. They will all be
described here with origins, insertions and tasks. However to really understand the
explanations of the positions and the tasks there are a few thing that are important to explain
In physiology special terms are often used to describe rotations around axes. The set of terms
used for movements of humerus are shown in Figure 2.1-9. In starting position the arm is
relaxed and hanging vertical, thumb pointing outward. Moving the arm forward and upward is
called flexion and the opposite of flexion is called extension, e.g. arm moving backward and
upward. Moving the arm out from the body and upward is called abduction and the opposite is
called adduction. The arm can also be rotated outward (external/lateral) or inward
Figure 2.1-9. Physiological terms for the movements of humerus, reference Budowick (2000).
For the shoulder movements there are other physiological terms. Lifting the shoulder towards
the ear is named elevation and pushing the shoulder towards the floor is named depression.
Moving the shoulder backward so the medial border of scapula approaches the spine is called
retraction for the shoulder or adduction for the scapula. The opposite movement, the shoulder
is moved forward, is called protraction and for scapula abduction. Rotating the shoulder
girdle forward/downward is called anterior tilt, (Kapandji, 1982 p.4).
There are 15 muscles working with the movements of the shoulder and humerus, listed in
Table 2.1-2. The muscles can be divided into three groups, Brunnstrom 1972 page 143. Group
one includes the muscles connecting the shoulder girdle with the trunk, neck and skull. These
ones are serratus anterior, trapezius, rhomboideus, pectoralis minor, levator scapulae and
subclavius. The second group are the muscles connecting scapula with humerus namely
deltoideus, supraspinatus, infraspinatus, teres minor, subscapularis, teres major and
coracobrachialis. The third and last group is the muscles that have direct connection between
the trunk and humerus. There are only two muscles in this group: latissimus dorsi and
pectoralis major.
Some of the muscles are large and take care of the more loaded movements while muscles
smaller in size and those that lies closer to the joints take care of the precision and the stability
of the movements. The muscles closest to the GH joint are called the “rotator cuff muscles”.
The rotator cuff includes supraspinatus, infraspinatus, teres minor, teres major and
Before reading Table 2.1-2 it is important to know that there are always deviations between
different human beings. When studies are made to find insertions and origins several cadavers
are examined and the result is not unambiguous.
Table 2.1-2. Muscles involved in shoulder movements1 with names, origins and insertions are listed, reference
Kendall (1993).
biceps brachii, long head
biceps brachii, short head
scapula, supraglenoid, tubercle of
scapula, coracoid process
coracoid process
deltoideus anterior
clavicula anterior lateral third
(acromion end)
scapula, acromion lateral
spine of scapula, inferior edge
scapula (posterior), infraspinous
spine, transverse processes C1-C4
deltoideus middle
deltoideus posterior
levator scapulae
latissimus dorsi
pectoralis major, upper portion
pectoralis major, lower portion
spinous processes T6-T12.
dorso lumbar fascia
posterior crest of ilium2
ribs posterior lowest ones
clavicula (anterior) medial half
pectoralis minor
sternum anterior alongside ribs 2nd
to 7th
costal cartilage of rib 1-6
aponeurosis of abdominal muscles
ribs 2nd to 5th, anterior surface
rhomboideus major
spine, thoracic vertebrae, T2-T5
rhomboideus minor
spine, ligamentum nuchae and
spinous processes on C7 and T1
ribs anterolateral 1st to 9th
serratus anterior
teres major
teres minor
trapezius upper
anterior surface of first rib
scapula anterior, subscapularis
scapula supraspinous fossa
scapula posterior, inferior, inferior
scapula posterior, lateral border
two areas
skull (posterior inferior), supeior
nuchal line
occipital protuberance
ligamentum nuchae (posterior neck
radius, tubercle
radius, tubercle.
fascia of forearm, bicipital
humerus, at the same height as
deltoid tuberosity but medial
humerus lateral, deltoid tuberosity
humerus lateral, deltoid tuberosity
humerus lateral, deltoid tuberosity
humerus, posterior on greater
scapula, medial border superior part
humerus proximal lesser tubercular
humerus proximal anterior, crest of
greater tubercular
humerus proximal anterior, crest of
greater tubercular
coracoid process on scapula, medial
scapula, medial border below spine
of scapula
scapula, medial border alongside
spine of scapula
scapula medial border anterior
clavicula inferior
humerus proximal anterior, lesser
humerus greater tubercular
humerus proximal anterior on lesser
humerus, greater tubercular
clavicula, lateral third (posterior).
Sternocleidomastoid muscle is not involved in movements of the shoulder even though it origins on the skull
and inserts on clavicula. This because it mainly moves the skull and not clavicula.
The big flat bone on top of pelvis often called hipbone.
trapezius middle
spine, C7 and T1-3, spinous
trapezius lower
triceps brachii, long head
spine,T4-12, spinous processes.
scapula, infraglenoid turbercle of
scapula, acromion process medial
spine of scapula, superior border.
spine of scapula, inferior border
ulna proximal posterior, olecranon
The pictures Figure 2.1-10, Figure 2.1-11 and Figure 2.1-12 show the muscles with their
origins and insertions illustratively.
Figure 2.1-10. Muscles of the shoulder complex, reference Netter (1997).
Figure 2.1-11. Anterior view of the skeletal parts in the shoulder, reference Netter (1997). Areas of origins and
insertions of the muscles are shown.
Figure 2.1-12. Posterior view of the skeletal parts in the shoulder, reference Netter (1997). Areas of origins and
insertions of the muscles are shown.
Pectoralis major consists of several layers, the main ones are the clavicular, the sternal, the
costal and the abdominal parts (Simons, 1999 p. 819). Since the parts of pectoralis major
have different origins they also have different tasks. The muscle parts have different arms of
momentum (lever arm) that gives rise to different directions of the torque. In Figure 2.1-13
the pathway from origin to insertion are shown. The abdominal and the lower part of the
sternal layer are twisted a half revolution.
Figure 2.1-13. All layers of pectoralis major with their orientations, reference Simons (1997).
2.1.5 Movements
This part will explain the movements the arm is able to perform and which muscles that
perform the movements. For the more interested reader Kapandji (1982) is recommended.
As explained earlier the arm is very movable. These arm movements is a precise co-work
between the muscles in the shoulder. The movements in the shoulder are mainly statically
indeterminate, which means that there are more muscles present than there are directions of
the movements in the joints. If one muscle is not working properly other muscles can often
compensate for the lost work. This compensating makes the arm produce the same or almost
the same movement but for example can scapula be situated in another way. When scapula is
situated differently the load on the muscles connected to scapula is distributed in a different
way. This compensating is very helpful for us humans since the arm can move in almost the
same way even though a muscle is not working properly. However this compensating can
result in pain; a muscle, which is not strong enough for this increased load, can be overloaded
and that may eventually give rise to pain.
The arm has a great range of motion, RoM,
as earlier described. This RoM is shown in
Figure 2.1-14. Normal RoM for the
different movements of the shoulder are,
flexion 180°, extension 45°-50°, abduction
180°, adduction 40°, internal rotation 90°
and external rotation 90° (Kapandji, 1982
p.2-12). Starting position for the angles is
when the arm is hanging vertical beside the
body and the thumb is pointing laterally.
In Table 2.1-3 it is described how the
muscles are activated during shoulder
movements. It should be noted that the
literature for Table 2.1-3 are not
For an arm pendulum in 4th gear in crosscountry skiing the main movement for the
arm is roughly from flexion 90° to
extension 45°. There are also
abduction/adduction and rotation present
although these movements are smaller in
Figure 2.1-14. Range of motion for the arm. The
plane B are called frontal plane and the plane A are
called sagital plane (Kapandji, 1982 p.13).
Table 2.1-3. Muscles involved in different movements of the shoulder complex, references Kendall (1993)
complemented by Kapandji (1982) and Bojsen-Möller (2000).
Muscles moving humerus
Muscles moving scapula
Flexion (to 180°)
deltoideus anterior
pectoralis major, upper
serratus anterior
Outward rotator:
serratus anterior
Extension (to 45°)
Outward rotators:
teres minor
deltoideus posterior
deltoideus posterior
teres major
latissimus dorsi
triceps, long head
Anterior tilt of scapula:
pectoralis minor
Abduction (to 180°)
Strong extensor in front of the
pectoralis major.
biceps, long head
Outward rotators:
teres minor
deltoideus posterior
pectoralis major
teres major
latissimus dorsi
triceps, long head
Inward rotators:
deltoideus anterior
pectoralis major upper
teres major
latissimus dorsi
Outward rotators:
teres minor
deltoideus posterior
Outward rotators:
serratus anterior
Adduction (to 40°)
Inward rotation (to 90°)
Outward rotation (to 90°)
Adductors, internal rotator &
levator scapulae
trapezius, middle
serratus anterior
pectoralis minor
trapezius, middle
- During adduction works rhomboideus together with teres major and triceps long head together
with latissimus dorsi as synergists1.
Explained in Table 2.1-1.
Flexion and abduction is only possible to 180° with one arm at a time. The spinal muscles assists.
The “rotator cuff” muscles are activated in all movements to stabilize the GH joint.
Maximal attainable force is normally much larger for inward rotation than outward rotation.
2.1.6 Posture
In a dictionary the word posture is explained as “relative arrangement of different parts of
the body”. A good posture means that the muscle activities, joint and ligament reaction
forces are as small as possible. Muscle activity is the performed muscle force divided
with the maximal feasible force (dimensionless, measured in percent).
To understand the importance of good postures Figure 2.1-15 shows an example of a
“good” and a “bad” shoulder posture when abducting the arm (Elpinston, 2003 p. 14-16).
In the left illustration the shoulder is elevated unnecessary to achieve the location of the
hand, which exhausts the muscles upper trapezius, levator scapulae and deltoideus.
These muscles are small in size and will therefore use high activity. In the right
illustration the forces are distributed among stronger muscles on a larger area, upper,
middle trapezius and serratus anterior. The activity will be lower in these muscles since
they are stronger and they will therefore not be exhausted in the same way as the muscles
in the left illustration. Since the muscles in the right figure are distributed on a greater
area the stability of the shoulder and the hand position will be better than in the left
Figure 2.1-15. Left illustration showing a “bad” posture when raising the arm. The forces are sent up to the
head and neck, little area. Right illustration shows a better posture, the forces are distributed over a larger
area to upper, middle trapezius and serratus anterior. Reference Elpinston et al. (2003 p. 14)
When using the “good” posture described above the position gets stronger and more
stable. The posture improves the stabilisation of the GH joint since the “rotator cuff” has
better control of the position of humerus head in the socket (glenoid fossa), the shoulder
blade is situated closer to the ribs. One more advantage when using the better posture is
that the risk of pain and injuries in the joints and tendons in the neck is decreased
(Elpinston, 2003 p. 14-16).
The following question for this “bad” posture is why it occurred. It could be a mechanical
reason; a muscle might be tensed, damaged or paralysed somewhere. The reason might
be a faulty taught technique or it may be a faulty resting posture for the shoulder (when
the arm is hanging vertically). The faulty posture can have many different bases.
A “good” standing posture is shown in Figure 2.1-16.
Figure 2.1-16. A good posture related to landmarks on the body, Kendall (1982).
A “bad” resting posture for the shoulder has often the appearance of a rounded–shoulder,
head-forward posture and depressed chest/great kyphosis1. These appearances often
appear together since they are results of each other. For example is the head-forward
posture a compensation of great kyphosis. Therefore it is hard to look at one single cause
for a wrong posture.
The rounded shoulder is the interest of this report. A rounded shoulder is a protraction,
elevation and often also a forward tilt of the shoulder girdle (Kendall 1993 p. 106). This
posture often occurs together with a short pectoralis major. A short pectoralis major
inward rotates humerus, which secondarily results in abduction of scapula from the spine
and therefore a protraction of the shoulder girdle (Simons, 1999 p.819).
Protraction and elevation gives rise to tension in some of the muscles in the neck and the
interscapular part of the back, which may cause pain. The protraction gives rise to tension
in rhomboideus and trapezius middle fibre since they are in lengthened position (Simons,
1999 p.820). Elevation shortens serratus anterior, upper trapezius and levator scapulae
while lower trapezius is lengthened. Both the muscles that are shortened and those who
are lengthened may become overloaded. Since many of these muscles cooperate with
other muscles (synergists or antagonists) these may also become overloaded. For example
serratus anterior is antagonist to rhomboideus so if serratus anterior is tensed also
rhomboideus may become tensed.
2.1.7 Stretching
It is important to make the meaning of a short muscle clear. Muscles that have large
passive resistance when stretched are called stiff. This means that a stiff muscle needs a
large force to be stretched. The range a person can stretch a muscle is called stretch
tolerance. This knowledge is quite new. The earlier chapters in this report have references
that are older than 10 years and therefore are no difference made of low stretch tolerance
and large passive resistance. I will though assume that the older references means low
stretch tolerance since that is more easy to measure than passive resistance. Now on only
stretch tolerance and passive resistance will be used. The words shortened and lengthened
position means that a muscle length is less than respectively greater than its resting
Stretching is very common used today both among athletes but as well as among amateur
exercisers. Anderson (1993) and (1998) has a very positive attitude towards the practice
of stretching. Stretching releases tensions, relaxes, improves coordination, range of
motion and blood circulation, prevents ruptures in the muscle and gives an overall wellbeing (Andersson, 1993). Despite the fact that stretching is used a great deal the
knowledge about what really happens in the body during stretch exercises is not
completely analysed (Björklund, 2000).
Kyphosis is the curvature of the upper back. Great kyphosis is the same as humpback.
Team Danmark, test center with professor Peter Magnusson et al. have made several tests
on stretching training of the backside of the thigh. Here are two of them:
The first test examined how the passive force, the stiffness, in the backside of the thigh
changed after one single stretch exercise. Initially the passive force was first measured in
both legs. One of the legs was stretched for 90 seconds. Directly after the stretch the
passive force had decreased over all the range and the RoM was larger. However after
one hour after the stretch exercise the passive force and also RoM had returned to the
same values as before the stretch exercise. This means that one single stretch does not
change the mechanical properties long term (Magnusson, 1998).
The second test examined how the passive force in the backside of the thigh changed
after a three-week program of stretch training. As before the passive force was measured
in both legs. One leg was stretched twice a day in three weeks while the other leg served
as reference. After three weeks of stretch training was the RoM, the stretch tolerance,
increased for the stretched leg and unchanged for the reference leg. The passive force as
function of the hip flexion angle is quite similar for the stretched leg before and after the
stretch period up to the old RoM (Pre), see Figure 2.1-17. The stretch tolerance is
increased although stretching the leg to this new RoM (Post) needs more force than to the
old RoM (Pre). This shows that stretch tolerance is increased and the stiffness (the
passive resistance) is unchanged after this stretching period.
Figure 2.1-18 shows the passive force for different hip flexion angles for the reference
leg both before the training period and after (Magnusson et al., 1996).
Figure 2.1-18. The other leg that has not been
stretched during the period. No changing in
torque discovered, reference Magnusson et al.
Figure 2.1-17. The difference in torque before,
pre, and after, post, the training period of
stretching, reference Magnusson et al. (1996).
After stretch period are RoM increased and the
passive resistance unchanged.
There are also studies that show decreased muscle stiffness after stretch training (Björklund,
Increased muscle stiffness occurs plentiful. Our muscles are made for working, and the
working muscles will become stiffer so they are more sensitive and alert for the task,
(Björklund, 2000). Magnusson has also shown that strength training together with stretching
will increase the stiffness in the muscle even though the stretching feels relaxing (Magnusson,
2.2 Biomechanics
2.2.1 The AnyBody Modelling System
The AnyBody Modelling System is a simulation program for human bodies as well as
animals. Information about the program can be found on the web page for AnyBody
technology. The web page is also the main reference for this chapter; other references are
noted in the text.
Using the program is usually started with creating the body. The AnyBody Research group
has constructed a human body, which is free to be used. When creating a body the first thing
to do is to define segments (a segment is the part between two joints). The segment is not just
the bone; the segment includes the mass and inertia properties of the bones and everything
around it, muscles, fat, skin, etc. The segments are rigid and will therefore not change size or
inertia properties during the movement. That is actually the fact in real muscle movement.
This means that the effects of wobbly masses of the soft tissues are neglected. A segment can
also be a tool as for example a ski pole or a wheel on a wheelchair.
Next thing is to connect the segments to each other. Joints, muscles and ligaments connect the
segments together. When inserting a joint there are a few predefined choices and also
possibility of building new ones. For the muscles there are today three muscle models
implemented in the program. These muscles can be made either to push (non-physiological)
or to pull. All the muscles have no mass and involve no friction when sliding over surfaces. In
the simplest muscle model the contraction force is constant and the muscle contains of no
passive element properties (as tendon, parallel elastic element or series elastic element). The
second model consists of a 2 element Hill type model; see chapter 2.2.2 for the Hill model. It
includes the tendon and the contraction force is modelled linearly. The third one is modelled
as a 3 element Hill type muscle. This one includes both of the tendon and the parallel elastic
element. The contractile force is modelled non-linear.
The muscles may be implemented to pass certain points on their way or/and they can be made
to wrap around a surface. This is needed since the muscles cannot feel the bones or other
muscles unless it is specifically defined that there are things like that present.
If there are external forces working on the body they can be defined as a point force
somewhere on the segment.
The performed analyse in the program is an inverse dynamics analyse. This means that the
movement analysed has to be completely specified for input and the output are the muscle
forces and joint reaction forces as well as the momentums. The opposite of inverse dynamics
is forward dynamics. Forward dynamics needs the neural activity for the muscles as input and
calculates the movement for output see Figure 2.2-1.
Figure 2.2-1. A flow chart for inverse and forward dynamics for human body modelling. Reference web page of
international shoulder group, conference ISB2003 Dunedin, New Zealand.
Inverse dynamics has a great advantage since the computational time is much shorter than for
forward dynamics. This is because the optimisation is more efficient since there are
assumptions made about the kinematics. In forward dynamics there is not made any
assumptions regarding the kinematics and therefore is it a very time expensive optimisation.
To win both time and decrease the number of approximations it is possible to make a
combination of both inverse and forward dynamics. The international shoulder group has
made a model combining both inverse and forward dynamics; reference the web page of the
international shoulder group.
The human body has of more muscles than necessary to perform a given motion. This means
that there are more muscles than there are degrees of freedom in the system; the system is
statically indeterminate. For the human body the central nervous system, CNS, decides which
muscles that shall be activated to perform a certain movement.
It is believed that the human brain want to minimize the load on the muscles. This has led to
several suggestions for optimising algorithms for calculation the muscle forces.
Equation (2.2-1) shows the frame for the optimising algorithm in inverse dynamics,
G f (M )
subject to
Cf = d
f i ( M ) ≥ 0, i ∈ 1,..., n ( M )
The G is the objective function. The equation Cf = d in equation (2.2-1) are the equilibrium
equations where C = C ( M ) C ( R ) is a matrix of the coefficients depending on the current
positions of the segments and f = f ( M ) f ( R ) is the vector of the muscle (M) and the reaction
(R) forces in the system. The d consists of the external forces and the inertia forces. It is this
equation that is statically indeterminate; there are more rows in f than there are rows in C and
The last row in equation (2.2-1) means that no muscle force can be negative; muscle can only
pull not push. The numbers of muscles involved in the system are n(M).
The first line in equation (2.2-1) is the objective function; this is the function supposed to
describe how the brain through CNS is choosing the muscles to work. There are several
suggestions on how this equation should look like. A common approach to the problem is
using the equation named polynomial criteria,
(M )
⎛ f (M ) ⎞
= ∑ ⎜⎜ i ⎟⎟ .
i =1 ⎝ N i ⎠
n( M )
f i ( M ) is the muscle force for the i´th muscle in the system. Ni, is the normalisation factor for
the muscle force for the i´th muscle. It can be the maximum strength, the physiological cross
section area, PCSA, of the muscle or instant muscle strength computed when using the Hill
muscle model, see chapter 2.2.2. Investigations for several values have been made for the
superscript p, Rasmussen et al (2001). The AnyBody Research group has made a test that
showed that the polynomial criteria with p=100 gives the same result as equation (2.2-3),
⎛ f (M ) ⎞
G f ( M ) = max⎜⎜ i ⎟⎟, i ∈ 1,..., n ( M ) .
⎝ Ni ⎠
The value of p expresses how much the muscle will cooperate. When p=100 will the muscles
cooperate as much as possible, no muscle will get overloaded if other muscles can help. This
will delay the overall fatigue as far as possible.
Equation (2.2-3) is much easier to handle since it is linear. Unfortunately this equation is not
continuously differentiable which will complicate the calculations. A trick is made to simplify
the equation (named the bound formulation); an artificial variable β is introduced. The
optimisation problem gets transformed into,
subject to
fi (M )
≤ β,
i ∈ 1,..., n ( M ) .
Cf = d
f i ( M ) ≥ 0, i ∈ 1,..., n ( M )
The equation (2.2-4) shows an objective function that is both linear and differentiable. The
boundary conditions are linear, not differentiable and the side constraints are also linear. This
gives the optimisation problem used in the AnyBody Modelling System; it is quite quick and
stable to solve. Because of the linearity the common used algorithm in optimisation theory,
the simplex algorithm, can solve the optimisation problem.
2.2.2 The Hill type muscle model
This section will explain how the AnyBody Research group has approximated the muscle to a
mechanical model suitable for inverse dynamic studies. There are two main references for this
chapter, Tørholm et al (2002) and Dahlqvist (2002 p.24-31) other references are noted in the
text. The most common models used in muscle dynamic simulations are a combination of the
models developed in the first half of the 20th century by Hill et al. and Wilkie (Zajac, 1989
p.360). Very common in muscle modelling is the Hill type muscle model shown in Figure
Figure 2.2-2. Hill type muscle model.
This model consists of four parts. T represents the tendon part of the muscle, this part have
only linear elastic property. PE is the parallel elastic element that represents the passive
properties of the muscle; this part is also linear elastic. CE is the contractile element that is the
only active part in this model. The last part is SE, series elastic element. This part arises from
the elasticity of the cross-bridges. According to Zajac (1989 p.367) SE can be neglected for all
muscles except for the ones with short tendon; since the energy from SE is very small
compared to the energy from the tendon. The calculations become easier if SE is neglected.
Other notations from Figure 2.2-2 which needs to be explained:
γpennation angle,
fT- total force on the system,
lT- length of the tendon,
lM- length of the muscle,
lMT- length of the muscle and tendon system,
lPE- length of the PE element,
lCE- length of the CE element,
lSE- length of the SE element.
This model has approximated some issues. The normal procedure during a contraction is that
the muscle will increase its cross section area, in this muscle model the cross section area is
held constant. There are several muscles in the human body where the pennation angle is
different for diverse fibres in the same muscle; here all fibres in the same muscle have equal
angle. There is no damping included in the model from the contractile element. There is no
fatigue mechanism in the model; the muscle can repeat the same movement infinitely many
times. No activation dynamic is included in the model; activation is either on or off like a
heavy-side function, see Figure 2.2-3. Activation dynamics for a muscle are the same as
reaction speed. This is one reason why this software cannot be used for rapid movements as
for example whiplash injuries.
Figure 2.2-3. The activation dynamic of the muscle model; a heavy-side function.
AnyBody has neglected the SE element after several tests presented in a paper by Tørholm et
al (2002). These tests showed that the presence of the series elastic element contributes to a
very small extent to the total result. The AnyBody Modeling System´s most complex muscle
model (AnyMuscleModel3E) is shown in Figure 2.2-4.
Figure 2.2-4. This figure shows the 3-element muscle model implemented in the AnyBody software.
The optimisation problem as explained earlier was expressed as
subject to
f i (M )
≤ β,
i ∈ 1,..., n ( M ) .
Cf = d
f i ( M ) ≥ 0, i ∈ 1,..., n ( M )
The strength Ni for the simplest model AnyMuscleModelSimple is only the maximum
contraction force for the muscle. For the other two models in the software
AnyMuscleModel2Lin and AnyMuscleModel3E the strength are a little more complicated
and need an illustration for explanation, see Figure 2.2-5.
Since the muscle models AnyMuscleModelSimple and AnyMuscleModel2Lin are
simplifications of the AnyMuscleModel3E model only the last model will be explained
further. Figure 2.2-5 shows the muscle forces during loading with constant muscle length (lMT
is constant). When activation is zero the force in the muscle can be unequal to zero if the
muscle is stretched. The subscript 0 denotes force when activity are zero, f T 0 and f PE 0 . If the
muscle is stretched both the parallel elastic element and the tendon element experience a force
that are approximated to be equal in size, f PE 0 = f T 0 ≠ 0 . When the muscle gets activated the
parallel elastic element relaxes since the muscle shortens. The picture describes that the
muscle needs the strength N to be able to carry the load f T 1 − f T 0 and also keep the muscle
length lMT constant. f T 1 is tendon force at maximal activity.
Figure 2.2-5. Explanation for the strength N and the tendon force gradient H.
The strength N is defined as
N = f T 1 − f P1 .
This is followed by the definition for the activity,
ai =
f i (M )
The equilibrium equation from the optimisation problem Cf=d is transformed to yield this the
3-element muscle model. The muscle forces are rewritten in terms of activity and the right
hand side with the load vector d gets a contribution of the passive element,
i =1
i =1
∑ Cij H i ai = d i − ∑ Cij f PE 0i ,
this since f PE 0i = f T 0i .
New notations here: Hi the slope for the approximated tendon force curve and the design
variables ai, the activity. The subscript i is the row and j is the column.
The meaning of the following derivation is to find Hi and fT0i. When these are found they are
used in equation (2.2-8), which is the boundary equation for the optimisation problem
equation (2.2-5). The optimisation problem will then be possible use for calculating the
muscle activities, reaction forces and torques.
The length of the whole muscle, both tendon and muscle, lMT can be written as
lT = l MT − l PE cos(γ ) .
Since lPE= lCE the velocity of the tendon can be described as
l&T = l&MT − l&CE cos(γ ) − l CE sin (γ )γ& .
The derivation for γ& needs the assumption that k& = 0 ,
k = lCE sin (γ )
k& = l&CE sin (γ ) + lCE cos(γ )γ& = 0
γ& = −
l&CE sin (γ )
l CE cos(γ )
Inserting equation (2.2-13) into (2.2-10) the expression for the tendon velocity becomes,
l& sin (γ ) ⎞
l&T = l&MT − ⎜⎜ l&CE cos(γ ) + l CE sin (γ ) CE
cos 2 (γ ) l&CE sin (γ ) ⎞
l&T = l&MT − ⎜⎜ l&CE
l&T = l&MT − CE .
cos(γ )
As explained earlier all muscle elements are assumed mass less and there is no friction
involved. Therefore the equation of force equilibrium can be written as
fT = ( f PE + f CE )cos(γ ) .
The forces in equation (2.2-15) are all depending on the length of the element the force
represents, f T = f T (lT ) , f PE = f PE (l PE ) and f CE = f CE (l CE ) .
The force the contractile element produces can be expressed as
( )
f CE = F0 f l (lCE ) f v l&CE a .
The force depends on the maximum feasible force for the muscle, F0, the force-length relation
fl, the force-velocity relation fv and the activity a. The maximum feasible force F0 are often in
literature related to the so-called physiological cross section area, PCSA. The definition,
F0 = PCSA ⋅ σ 0 ,
means that the larger a muscle is the greater force it can produce. The constant σ 0 is the
muscle tension.
The definitions for the force-length and force-velocity relations used in AnyBody are from
papers of Daxner and Gföhler (Tørholm et al., 2002). The force-length relation is,
f l (lCE ) = e
⎛ (∈ +1)β F −1 ⎞
−⎜ F
lCE − l Fopt
, ∈F =
l Fopt
where the constant l opt
f most probably denotes the optimum muscle fibre length even though it
is not stated explicitly in the paper (Tørholm et al., 2002). Optimum length means the length
were the muscle is strongest.
The parameters in equation (2.2-18) are chosen according to a regression analyse of
experimental data for the relation. AnyBody has chosen to set the parameters to:
ρF = 2
ω F = 0.35327⎜⎜1 −
i A ⎟⎠
β F = 0.96343⎜⎜1 − ⎟⎟
⎝ iA ⎠
iA =
cos(γ )
The force-velocity relation is shown in equation (2.2-19),
⎛ l&CE max + l&CE
Hill ⎜
& ⎟
f v (l&CE ) = ⎨
& F + l& F A − l& A F
⎪⎜ CEexz Hill 0 CE Max CE Max Hill CE Hill 0
F0 l&CEexz AHill + l&CE
l&CE max = k1l opt
+ k 2 l opt
f C fast
F − F0
l&CEexz = l&CE max max
AHill = 0.1 + 0.4C fast
Fmax = 1.3F0
k1 = 2 ⋅ s −1
k 2 = 8 ⋅ s −1
l&CE < 0
l&CE ≥ 0
As explained earlier a muscle consists of different muscle fibres1. The constant Cfast is the
percentile of fast muscle fibres in the muscle. The constants k1 and k2 represents the
“velocity” for slow and fast fibres.
Now are fCE defined as f CE = f CE l CE , l&CE . Using the expression for l&CE from equation (2.2. The force relations for PE and T are
14) the relation transforms to f = f l , l& l&
( ))
defined as
l < l rest
⎛ l −l
f (l ) = ⎨ f 1 ⎜ J l1 −l rest
⎟ l ≥ l rest .
⎪e −1
This equation needs two points to be fitted, the first point is the resting length ( l rest ) where the
force is zero and the other point ( l1 ) is any other point chosen along the curve. For the PE
element respectively the T element the constants are;
l PE
= l opt
l PE1 = 1.5l opt
J PE = 3
f PE1 = F0
lTrest = ?
lT 1 = lTrest 1+ ∈Topt
JT = 3
f T 1 = F0
Where ∈Topt denote the optimal tendon strain for the particular muscle. lTrest (the resting length
of the tendon) is an user applied constant during the analysis.
The equation of equilibrium (2.2-15) can now be expressed as
f T (lT ) = f PE (lCE ) + f CE l CE , l&MT cos(γ ) .
Hi and fT0i needs to be calculated for every l MT , l&MT (these are given since it is an inverse
dynamic analysis) to be able to solve the optimisation problem. The first term fT0i are the
The inner properties for the muscle fibres are described in the chapter 2.1.3.
tendon length at zero activity for given l MT , l&MT . Zero activity gives f CE = 0 , which reduces
equation (2.2-21) to
f T (lT 0 ) = f PE (l PE 0 ) cos(γ ) .
The relation between the lengths for the elements in the muscle is shown in equation (2.2-9),
writing lPE explicit the equation transforms to
l PE =
l MT − lT
cos(γ )
Inserting equation (2.2-23) in (2.2-22) gives an implicit equation for lT0 for a given lMT ,
f T (lT 0 ) = f PE (l PE 0 (lT 0 , l MT )) cos(γ ) .
The tendon force gradient Hi is given by equation (2.2-25) where a1=1 and a0=0,
f T 1 (lT 1 ) − f T 0 (lT 0 )
a1 − a 0
The only unknown in the right side of equation (2.2-25) is lT 1 ; which can be found by first
calculating l CE1 . Rewriting equation (2.2-9) it transforms to
lT 1 = l MT − lCE1 cos(γ ) .
Combining the equation of equilibrium (2.2-21) with equation (2.2-26), the equilibrium
equation transforms to only have one unknown, l CE1 ,
f T 1 (l CE1 (lCE1 , l MT )) = f PE (l CE1 ) + f CE l CE1 , l&MT cos(γ ) .
Solving equation (2.2-27) for l CE1 makes it possible to calculate f T 1 (lT 1 ) and f PE1 (lCE1 ) with
(2.2-26). The strength N is calculated by equation (2.2-6) and the slope of the tendon force
curve, H, is calculated by equation (2.2.25). Everything is set for solving of the optimisation
problem, equation (2.2-5).
2.2.3 The equations of equilibrium
This part explains how the equations of equilibrium are found; references for this chapter are
Nikravesh (1988), Damsgaard (2001) and Michael Damsgaard personal communication
The basis for inverse dynamics is the equations of equilibrium. The equations of equilibrium
explain the segments position for each time step for the optimisation algorithm so that the
algorithm can calculate the muscle forces.
The position of the i’th segment is defined in Cartesian coordinates as
q i = ri p i
Here is ri the global position of the segment and p i are the four Euler parameters
describing the segments local position. The common way of describing the local coordinate
system for a body (segment) in space is by Euler angles. The Euler angles are only three and
can therefore give rise to something called “gimbal lock”. The gimbal lock is the
representation of a singularity. More thoroughly described is gimbal lock the phenomenon of
two rotational axis of an object pointing in the same direction. This can happen in AnyBody
since the first rotation is around an axis of the first segment and the other two axes are around
the second segment1. By using the Euler parameters, which are four, gimbal lock can be
avoided. There are only six degrees of freedom for a segment but according to the definition
(2.2-28) there will be seven coordinates. This problem is possible to solve since the transpose
is equal to the inverse for the Euler parameters, pT=p-1.
The velocity of the i’th segment is defined as
v i = r&i ω i 'T
Here is r&i the velocity of the segment in the global reference frame and ω i 'T is the angular
velocity of the segment where the apostrophe denotes that it is relative the local reference
frame. The acceleration of the i’th segment is the time-derivative of the velocity, v& i .
The entire set of segments is defined by both position and velocity. For n segments is
q = q 1T
v = v1
... q Tn
... v n
Joints connect the segments to each other; this information is collected in a constraint
equation together with the Euler parameter constraints (that states that they all are unit
vectors). This constraint equation is shown in (2.2-31),
First and second segment is user definable.
Φ (q ) = 0 ,
and contains of 7n non-linear equations.
In inverse dynamics, drivers are used to specify the motion of the system of segments. The
optimisation algorithm calculates the necessary forces in each muscle so that the system of
segments follows that specified motion. The drivers should also be included in the constraint
equation, making it transient,
Φ (q, t ) = 0 .
To obtain the velocity, (2.2-32) is differentiated with respect to time,
Φ q q& + Φ t = 0 .
And the acceleration is obtained by differentiating the velocity,
&& + (Φ q q& )q ⋅ q& + Φ tq q& + Φ tt + Φ qt q& = Φ q q
&& + (Φ q q& )q ⋅ q& + Φ tt = 0
Φ qq
&& = −ϕ (q, q& , t ) .
⇒ Φ qq
The velocity and the acceleration is required in terms of v i equation (2.2-33) and (2.2-34) are
transformed to
Φ q* v = − Φ t
[ ]
v = − Φ q*
Φ q* v& = ϕ (q, v, t )
[ ] ϕ (q, v, t )
v& = Φ q*
The * denotes that the Jacobian are transformed to fit the new equation with v.
For every mechanical system the equilibrium equations are defined. This means that the
system is in equilibrium only if the sum of all forces is zero and the sum of all torques is zero,
⎪∑ f i = m&r&i
⎪ i =1
⎪ M
= Jω& '+ω ' J 'ω '
⎪⎩∑ CoM
The equation above written in matrix form,
⎡mI 0 ⎤ ⎡ &r& ⎤
i =1
⎥ ⇔ Mv& = f ( ext )
⎢ 0 J '⎥ ⎢ω& '⎥
⎦ ⎣ ⎦ ⎢∑ M CoM − ω~ ' J 'ω '⎥
⎡ J xx
MCoM is the torque around the centre of mass, J = ⎢ J yx
⎢ J zx
J xy
J yy
J zy
J xz ⎤
J yz ⎥ is the inertia tensor, I is
J zz ⎥⎦
the unit matrix and ω~ ' is the skew matrix ( ω '× ), where the apostrophe denotes “with respect
to the local coordinate system” and f(ext) is the external forces working on the system.
This is the ordinary way of defining a mechanical system. In this case also muscle and
reaction forces are present. That transforms (2.2-37) to
C ( M ) f ( M ) + C ( R ) f ( R ) = Mv& − f ( ext ) = d .
f(M) is the muscle forces and f(R) are the reaction forces.
The coefficient matrix for the reaction forces is defined as
C ( R ) = (Φ q* ) .
The other coefficient matrix in (2.2-38) representing the muscle forces is related to the muscle
lengths according to
C ( M ) = l MT
... l MT
The subscript q* in (2.2-40) denotes that the muscle actuator length are differentiated with
respect to q*. The superscript n denotes which muscle this length belongs to. The muscle
actuator length is calculated from the positions of the segment geometrically.
2.2.4 Interpreting the results
The results from an inverse dynamics program are not so easy for the inexperienced to
interpret. Therefore, a short presentation of how to read the results is given. Reference for this
chapter is Rasmussen personal communication (2004).
First of all, the accelerations for all segments have to be checked so they do not exceed values
of 8-10 g ( g = 9.82 m s 2 ). If the acceleration exceeds these values for some segments two
methods can be used, either can the input (here the joint angles) be down-sampled or the data
can be filtered through a butterworth filter.
The collected results from all the subparts of one muscle might look quite strange for the
inexperienced. The result might not look so smooth as expected. When a muscle is starting to
activate it is called shifting in, and when the muscle is ending activation it is called shifting
out. This shifting is very common.
Figure 2.2-6 shows the activity as function of time for one subpart of a muscle while Figure
2.2-7 shows the activity for all the subparts of a muscle plotted in the same view.
Figure 2.2-6. The activity as function of time for one subpart of a muscle.
shifting out
shifting in
Figure 2.2-7. The activity as function of time for all subparts of a muscle plotted in the same view.
Common problems in numerical analysis are instabilities. In this software there are
parameters that can be adjusted to minimise these instabilities. Thus all instabilities are not
possible to reduce. Instabilities and muscles shifting in and out are shown in Figure 2.2-7.
Instabilities are recognised as irregularities. The instabilities mainly occur because there are
several solution possibilities that are almost equally good. Therefore, small deviations in the
numerical calculations can make the model to shift between different solutions.
3 Experimental method
3.1 Investigation method
The plan for this project was to start with a measurement of the joint angles when pectoralis
major was in its resting length. The reason for this is that the muscle model that includes
tendon properties needs tendon length calibration. Chapter 3.3 explains how the resting length
is measured.
Next, to get the input motion, the movement of the upper body in the fourth gear in crosscountry skiing free-style technique was measured. This was needed as input to the AnyBody
Modelling System.
These results were implemented in two models in the AnyBody Modelling System. The first
model calculated the resting length of pectoralis major from the measured joint angles. The
second model calculated the muscle forces with the skiing motion and the resting length of
pectoralis major as input. The ski model consisted only of the upper body and no external
reaction forces (for example the pole forces). The mass of the pole was not included either.
The solution scheme for the project is shown in Figure 3.1-1. A control unit was implemented
in the software Matlab. For certain joint angles (the 1st step in Figure 3.1-1) the control unit
initialises AnyBody to calculate the resting lengths for pectoralis major. The control unit
receives the results of the calculations (the 2nd step). In the next step (the 3rd) are the
calculations for the AnyBody ski model started with the resting lengths as arguments. In the
4th step the AnyBody ski model returns the activities for the muscles in the upper back to the
control unit.
These steps (1- 4) were performed 25 times, each time with a different horizontal flexion
angle (explained in chapter 3.3) in step 1 (from 45° to 21°). After these 25 loops were carried
out the muscle forces were plotted as function of time and horizontal flexion angle.
Control unit
1. Joint angles
2. Resting
Resting length
4. Muscle
3. Resting
Model of skier.
Muscle force
Figure 3.1-1. Flow chart over the implemented program
3.2 The human model
The AnyBody Research group has created a repository that contains body models and several
applications for these bodies. The models in the repository can be used under the reservation
that there is no guarantee that these models will work properly. Anyone is free to use or to
contribute something to the repository. The body used in this project is a human upper body
that the AnyBody Research group has created. Reference for this chapter are the web page for
AnyBody technology under the link The Model Repository.
The model used in this project consists of an upper body and two ski poles. The upper body
comprises a trunk that is fastened to ground (origin), two arms and a head. The trunk was
considered rigid. It is possible to drive the spine curvature in the model although that was not
done here because the input motion did not include such information.
The arm or the shoulder model, which was of interest for this model, consists of 118
“computer muscles”. A normal muscle, for example the pectoralis major is modelled with
several “computer muscles”; five parts origins from clavicula and five origins from the thorax
bone sternum. These computer muscles are spanning from one point to another; i.e. the
muscles’ origins and insertions are not areas. The arm model consists of six segments
scapula, clavicula, humerus, ulna, radius and the hand.
The joints in this model are approximated like this: GH, SC, AC are modelled by spherical
joints, the elbow joint FE by a hinge joint, the pronation/supination joint in the forearm, PS, is
modelled by a combination joint1, the wrist like a universal joint2 (2 degrees of freedom) and
the joint between the hand and the ski pole is modelled as a spherical joint.
For more information about this joint, web page of AnyBody technology, The Model Repository.
Universal joint has two degrees of freedom abduction/adduction and flexion/extension.
The functional joints that were explained in the chapter 2.1 are also modelled because they
have important functions just like a real joint. A segment is not able to feel that it is lying
beside other segments. For example the functional joint between scapula and the trunk is
important to model. If this joint is neglected, scapula will fall into the trunk when the muscles
around scapula are activated. The method for forcing scapula to be outside the trunk in this
model is by defining two artificial muscles. These two muscles only have pushing properties
not pulling properties as an ordinary muscle. In Figure 3.2-1 the landmarks TS and AI are
shown. The artificial muscles are situated from TS and AI to a point inside thorax. The
artificial muscles will force scapula to be outside the trunk while the other muscles will pull
scapula towards the ribs. The shoulder is also restrained by one ligament named the conoid
ligament shown in Figure 3.2-1. As explained in chapter 2.1 there are actually three parts of
this ligament. The conoid ligament will represent all three of these real ligaments.
The degrees of freedom, dof, in the shoulder are:
SC joint
AC joint
Scapula gliding
Conoid ligament
Total number of dof
3 dof
3 dof
-2 dof
-1 dof
3 dof
Three degrees of freedom that either can be driven in the SC joint or in the AC joint.
Figure 3.2-2. The green dots illustrate the artificial
rake restraining the deltoideus muscle.
Figure 3.2-1. Picture of the AnyBody shoulder
This investigation examined the muscle forces in the upper back when pectoralis major was
shortened. The only muscle model that includes passive forces is the advanced muscle model
AnyMuscleModel3E; this muscle model was used for pectoralis major. As explained in
chapter 2.2.2 the advanced muscle model needs calibration of the tendon length. The other
muscles in the model are modelled with the simple muscle model AnyMuscleModelSimple
because they do not need tendon properties. The advanced muscle model slows down the
Several of the muscles wraps around objects on their way from origin to insertion. For
example wraps pectoralis major around thorax and the muscle deltoideus wraps over
acromion and the head of humerus. For deltoideus the wrapping is modelled with an extra
artificial rake that restrains the “computer muscles” so that it is impossible for the parts of
deltoideus to slip off the head of humerus when the arm is moving. The real human deltoideus
is one muscle and when deltoideus is modelled into several computer muscles there is nothing
that will keep the muscle parts together. The artificial rake will hold the computer muscles
close together, Figure 3.2-2.
The ski poles were modelled as segments without mass or inertia properties and are present
for visualisation purposes only.
3.3 Measuring pectoralis resting length
Since the advanced muscle model, which is used for pecoralis major, needs calibration of the
resting length, a test is performed to obtain an approximate value of the resting length. The
arm was stretched as shown in Figure 3.3-1. The largest part of pectoralis major is stretched
when the arm is abducted 90° (Kendall, 1982 p. 63). Since pectoralis major is an inward
rotator of the arm should also be outward rotated for best effect when stretched (Caillet, 1981
p.24). The arm was also flexed approximately 90° to ensure that biceps long head were not
tensed. The elbow rested on a wagon and the joint angles for the shoulder (AC, SC) were held
fix by a frame.
Figure 3.3-1. Figure of the experimental set-up when measuring the resting length of pectoralis major.
The arrow in Figure 3.3-1 shows the stretching direction of pectoralis major. This direction is
called horizontal extension and the angle for measuring this is shown in Figure 3.3-2. The
angle α will from now on be called horizontal flexion angle.
Figure 3.3-2. The horizontal flexion angle.
Professor Peter Magnusson, Team Denmark test center, suggested a method for measuring
resting length of pectoralis major (Magnusson, 2004 personal communication). In this
method the elbow is pulled with a dynamometer in the direction of the stretch. When the force
start to increase the resting length is found and the horizontal flexion angle is measured.
This method needed a wagon that rolled with very little friction. Otherwise, the large friction
in the wagon hid the changes in the passive force of the muscle. Another problem is that the
wagon can only could be pulled in a linear direction and not circular, such as the path for the
elbow when the muscle is being stretched. Therefore, the arm rested on a lightweight support
and the support was fastened to the wagon with a rotational bearing.
When measuring the position for the resting length it was very hard to pull the wagon with a
dynamometer and get a clear result of the force. Instead the wagon was pulled backwards a
little bit to let the passive muscle force pull the wagon forward untilled it stopped. This was
the approximate resting length position.
The test person was a junior elite athlete in ski-orienteering. Before the resting length was
measured the curl of the upper back, the kyphosis, and the “whole body” posture was
measured to ensure that the kyphosis was normal. A normal kyphosis is between 20°-30°1.
Kyphosis is measured with an instrument called cyfometre and are commonly used for spine
measurements. The whole body posture was also controlled with Figure 2.1-16 as reference.
3.4 The input motion
3.4.1 Background
As described earlier the AnyBody Modelling System uses inverse dynamics. Since inverse
dynamics needs the motion as input argument some kind of recording of a motion is needed to
achieve the outputs, the muscle forces. In this investigation the idea was to make a new
optoelectronical measurement (motion capture). However, this failed since no company in
Sweden were able to perform this recording at the present time.
An optical measurement system is a system of several cameras, for example five2, which is
recording the motion of several markers in the area covered by the cameras. These markers
are usually placed on landmarks (explained in the following next chapter).
An optoelectronical measurement, recorded by VICON in Östersund April 2003, was used in
this investigation. This measurement was only recorded for demonstration purposes. The only
available data was a visualisation in 3-dimensions, Figure 3.4-2 shows one still of it.
3.4.2 Landmarks
A landmark is a place on the body on which measurements can be made. Some landmarks are
possible to observe with the eye, these are used in optical measurements. On these landmarks
is it possible to fasten an optical marker since there are very little tissue (muscles or fat)
present between the skin and the bone.
In Figure 3.4-1 landmarks on the trunk and the right shoulder/arm are shown. It should be
noted that C7 and T8 not are shown in the figure below; these are shown in Figure 2.1-2.
The size of the lower back curvature, lordosis, are also of importance for a normal kyphosis.
The SOL company in Lund are using five camera in their VICON system.
Figure 3.4-1. Landmarks on thorax for the right shoulder/arm, reference Helm (2004 p. 5).
From the positions of the landmarks it is possible to calculate the joint angles.
3.4.3 Perspective reduction
The visualisation used for input motion has perspective. The effect of the perspective was
reduced by a method explained in this chapter (Rydesäter, 2004 personal communication).
The perspective reduction will improve the data for the marker positions.
The landmarks shown in the visualisation were IJ, C7, AC-right, AC-left, EL-right, EL-left,
US-right, US-left, Pole-right, Pole-left and two points on the hip to approximate the upper
body movement (will be called Hip-right and Hip-left).
The positions of the points of interest in the visualisation were determined in relation to the
coordinate system of the pictures (red arrows). The coordinate systems for the visualisation
from the horizontal and vertical views are shown in Figure 3.4-2 and Figure 3.4-3
Figure 3.4-2. Figure of one still from the horizontal view of the visualisation. The analysed body is the yellow
(the bigger) one.
Figure 3.4-3. Figure of one still from the vertical view of the visualisation. The analysed body is the yellow (the
lower) one.
When observing the vertical view of the visualisation, Figure 3.4-3, the blue lines on the floor
looks like squares. However, when observing the horizontal view, Figure 3.4-2, the blue lines
are not rectangular with two equal sides (which they would have been if there was not any
perspective in the picture).
The origin for the perspective is the small white triangle in these pictures. In Figure 3.4-4 the
distance between every two vertical or horizontal blue lines is 1.0 length unit, lu, (assumed
value, only used as reference) and the distance between origin and the closest horizontal line
is 0.2 lu.
Figure 3.4-5. Measurements for perspective
calculations in the horizontal view.
Figure 3.4-4. Measurements for perspective
calculations in the vertical view.
As seen in the vertical views the magnitudes of each side of the blue square are the same.
In the horizontal view, Figure 3.4-5, the size of two horizontal lines 2a and 2b are measured.
It should be noted that the measurements are made in pictures with the equal zooming. The
perspective relation for the visualisation looks like Figure 3.4-6 illustratively.
Figure 3.4-6. The perspective relation.
The constants 2a and 2b should be equal in size when the perspective is reduced. The constant
R measures the magnitude of the perspective. The perspective relation gives the constant R to
R − 1.8 R + 0.2
0.2a + 1.8b
The perspective was calculated with the approximation that the perspective was equal in size
in both the horizontal and vertical views, this since the blue vertical lines in the horizontal
view intersect in origin.
The equation used for this perspective relation is a proportionality where 1 lu in the reference
plane, situated R lu from the focus, is proportional to x´ lu, the size of the measured horizontal
line situated y´ lu closer to the camera from the origin. Figure 3.4-7 shows this phenomenon.
Figure 3.4-7. The proportionality needed for calculating the magnitude of the perspective. The camera is
situated in y>0.
The equation for this proportionality is shown in equation (3.4-2),
R R + y'
Both the horizontal and vertical views have their own coordinate system x,y. The coordinate
system in the real room, which the 3-D coordinates are wanted in, are:
x3d = y vertical ,
y 3d = − y horizontal ,
z 3d = − xvertical = − x horizontal .
The corrected 3-D coordinates will from now on only be called x,y,z.
The perspective reduction uses the system of equations (3.4-3),
− z x horizontal
− y y horizontal
= vertical
R+ y
x y vertical
R R+ y
derived from the proportionality equation (3.4-2).
To make the system of equations more stable (3.4-3) are transformed into
− z (R + x ) = x side R
− y (R + x ) = y side R
− z (R + y ) = x above R
x(R + y ) = y above R
With this system of equations it is possible to find the perspective reduced coordinates for all
the points needed.
3.4.4 Joint angle calculations
The object of this chapter is to show how the rotations of the joints are calculated and the
approximations made. The reference systems shown in this chapter are not the reference
systems that are used in the body from the repository of the AnyBody Research group.
However, the results in chapter 4.2 correspond to the calculations.
Joint angles are easy to calculate when the joint for example is a hinge joint since it has only
one degree of freedom. For a spherical joint like the GH joint calculations are more
complicated. The joint has three degrees of freedom, three rotational directions. When three
rotational directions are present it is important to decide the order of rotation; which rotation
that comes first and which that comes second etc. The order of rotation is not only important
for the visualisation but also for the space of solutions. If the rotation order is incorrectly
chosen for the problem, gimbal lock can occur (also explained in chapter 2.2.3 page 34).
Some simplifications needed due to lack of data:
The landmark AC was assumed to be GH (the rotation centre of the arm).
EL was assumed to be in the elbow joint rotation centre.
US was assumed to be in the wrist joint rotation centre.
The wrist rotations were neglected (abduction/adduction and flexion/extension).
The hip was fixed to ground.
The motion of the back curl was neglected; the back was assumed stiff.
The joints calculated were:
Hand to pole joint called α Pole = α Pole
α Pole
α Pole
Elbow joint called α elb .
Glenohumeral, GH, the shoulder joint called α GH = α GH
Upper body relative to ground called α T = α Ty
α GH
α Tx′ α Ty′′ ].
y ′′
α GH
The reference systems for the shoulder and the trunk for these calculations are shown in
Figure 3.4-8.
Figure 3.4-8. The reference systems for the shoulder and the trunk.
The marker positions IJ, C7, AC, EL, US, Pole, HipLeft and HipRight are explained in chapter
The reference system for the trunk has its origin in IJ, the y-vector directed along the back
towards the head, the x-vector directed towards right shoulder and the z-vector orthogonal to x
and y pointing backwards. This was calculated for all time steps by
⎡Tx ⎤ ⎡
T y × C 7 − IJ
⎢ ⎥ ⎢
Te = ⎢T y ⎥ = ⎢C 7 − HipLeft + 1 2 HipRight − HipLeft
⎢Tz ⎥ ⎢
Tx × T y
⎣ ⎦ ⎣
The subscript e denotes that the positions are related to the basis vectors e x
e z , which
are the “ground” reference system from the visualisation (the red arrows in the pictures in the
chapter 3.4.3).
Next step was to calculate the rotations of the trunk. For the trunk, the orders of the rotation
axes are chosen to be [ y x' y ' '] . After the system has been rotated one time the local
coordinate systems axes have different positions. The “new” directions of the coordinate axes
are denoted with a ´. After two rotations the notation are ´´.
The rotation angles for the trunk were calculated according to
T y (x )
T y (x ) + T y (z ) ⎥
⎡ α Ty ⎤ ⎢
⎛ T (y)⎞
⎢ ⎥
⎜ y ⎟
α T = ⎢α Tx′ ⎥ = ⎢
⎢α Ty′′ ⎥ ⎢
⎝ y ⎠
⎣ ⎦ ⎢
The third rotation is a little more complicated and need more explanation. After the first two
rotations the x-vector , T x , points in the direction of ref. The x-vector is only affected by the
first rotation. The angle between the vector ref and T x is calculated by a dot product but the
sign for the angle needs an if- statement. The statement says that if the cross product of T x to
ref is parallel to T y the sign is negative,
( )
⎡ cos α Ty
ref = ⎢
⎢− sin α Ty
⎛ ref
α Ty′′ = arccos⎜⎜
⎜ ref
( )
( )⎤ ⎡1⎤
0 sin α Ty
0 cos α Ty
⎥⎢ ⎥
⎥ ⎢0 ⎥
⎥ ⎢⎣0⎥⎦
( )
• Tx ⎞⎟
⋅ Tx ⎟⎟
This gives the third rotation for the trunk,
y ′′
⎧− α Ty′′ if Tx × ref parallel to T y
= ⎨ y′′
⎩ αT
The flexion of the elbow joint was calculated by an ordinary dot product, equation (3.4-8).
The hinge joint between the humerus and forearm are defined to have 180 degrees when the
arm is fully extended.
α elb = arccos⎜⎜
(AC − EL)• (US − EL )⎞⎟
⎜ AC − EL ⋅ US − EL ⎟⎟
The GH joint is a spherical joint and just like the trunk the rotation axes and the orders of
those are needs to be decided. The reference system for humerus H : y-axis points along the
bone from the elbow to the GH joint, H y , x-axis points along the revolute axis in the elbow
outward (for the right arm) to the right, H x , and the z-axis pointing backward, H z , see
Figure 3.4-8. The rotations of humerus are only interesting relative to the trunk; this is why
the points AC, EL and US were transformed into the coordinate system of the trunk, (subscript
T). This was done by
⎡Tx ⎤
⎡e x ⎤
⎢ ⎥
⎢ ⎥
⎢T y ⎥ = P ⎢e y ⎥ ,
⎢Tz ⎥
⎢⎣ e z ⎥⎦
⎣ ⎦
AC T = P AC e ,
where the subscript e denotes that the points are related to the ground basis vectors
ex e y ez .
The rotation axes were chosen to be [ y
y ' '] for the GH rotations. The y-axis for the
reference system of humerus, H y , were calculated as
Hy =
Equation (3.4-10) shows how the first two rotations were calculated,
H y (z )
H y (x ) + H y (z ) ⎥
⎡α GH
⎤ ⎢
⎛ H (y)⎞
⎢ x′ ⎥
⎜ y ⎟
α GH = ⎢α GH
⎢α GH ⎥ ⎢
⎦ ⎢
The third rotation was calculated with an if-statement just like the trunk also was,
⎡ cos α GH
ref = ⎢
⎢− sin α GH
H x = US − EL × H y
y ′′
⎛ ref • H
= arccos⎜⎜
⎜ ref ⋅ H x
)⎤ ⎡1⎤
0 sin α GH
0 cos α GH
⎥⎢ ⎥
⎥ ⎢0 ⎥
⎥ ⎢⎣0⎥⎦
y ′′
⎧− α GH
if H x × ref parallel to H y
y ′′
α GH
y ′′
The last required rotations were the rotations between the forearm, denoted RU (radius and
ulna), and the pole. The hand was not included since the measurement did not include the
hand. Hence were the pole attached directly to the wrist. The position of the marker attached
to the pole had to be transformed into the reference system of the forearm, RU . The
reference system of the forearm was defined as
⎡ RU x ⎤ ⎡ RU y × H y ⎤
⎥ ⎢
RU = ⎢ RU y ⎥ = ⎢ US T − ELT ⎥ .
⎢ RU z ⎥ ⎢ RU x × RU y ⎥
⎦ ⎣
The position of the marker on the pole was transformed into the reference system RU by
⎡ RU x ⎤
⎡e x ⎤
⎢ ⎥
⎢ RU y ⎥ = Q ⎢e y ⎥
⎢ RU z ⎥
⎢⎣ e z ⎥⎦
Pole RU = Q Pole e .
The reference system for the pole was chosen as: z-vector pointing along the pole towards the
handle x and y orthogonal to z. In Figure 3.4-9 are the blue lines the arm, the black line the ski
pole and the red arrows the coordinate system for both the forearm and the pole.
Figure 3.4-9. The reference systems for both the pole and the forearm (RU) are illustrated with red arrows.
For the pole rotations, the y- rotation take place in the PS joint1 between radius and ulna. The
x rotation is approximated to take place in the joint between the hand and the pole. The orders
of these rotations are not important since they take place in two different joints. However,
these two rotation angles are collected in the same equation,
The pronation-supination joint for the hand is a joint between radius and ulna.
α Pole
⎛ Pole ( y ) ⎞
⎜ Pole RU ⎟⎟
⎡α Pole
⎤ ⎢
Pole RU ( x )
⎢ y ⎥ ⎢
= ⎢α Pole
⎥ ⎢
Pole RU ( x ) + Pole RU (z )
⎢α Pole
⎥ ⎢
⎟⎥ .
In the spherical joint between the hand and the pole are the other two rotations x and z held
4 Results
4.1 Pectoralis major resting length
The kyphosis was measured to 36º. This is regarded as a little bit above normal.
Figure 4.1-1. The posture of the person.
The posture for the test person is shown in Figure 4.1-1. The posture is good except for a
slight head-forward posture.
Figure 4.1-2 and Figure 4.1-3 shows the protraction and elevation angles for clavicula of the
test person in “normal” standing position. These measured angles were used in the simulation
of the skiing movement.
Figure 4.1-2. Protraction angles for clavicula.
Figure 4.1-3. Elevation angles for clavicula.
Figure 4.1-4, Figure 4.3-5 and Figure 4.1-7 to Figure 4.1-9 shows the measurements of all the
angles of interest when the test person was in supposed pectoralis major resting length
position. These angles were used in the AnyBody Modelling System when calculating the
resting length of pectoralis major.
Figure 4.1-4. Abduction angle for humerus.
Figure 4.1-5. Measured protraction angle when right arm is resting on the wagon.
The measurement of Figure 4.1-5 is only the measured angles. Assuming that Figure 4.1-2 is
the angles for the protraction of clavicula when the arms are resting beside the body, normal
standing position. When resting the right arm on the wagon left clavicula has the same
protraction angle while protraction for right clavicula are changed. The protraction for right
clavicula is calculated by (4.2-1). The result of the protraction for right clavicula is 29.4º.
180° − 23.16° − 22.28° = 134°
180° − 134.26° − 16.34° = 29.4°
Illustration of the calculation is shown in Figure 4.1-6.
Figure 4.1-6. Explanation for protraction angle calculations.
Figure 4.1-7. The elevation angles when right arm is resting on the wagon.
Figure 4.1-8. The horizontal flexion angle.
Figure 4.1-9. The outward rotation angle is 90º- 22.66º = 77.44º.
The outward rotation angle was 90 o − 22.66 o = 77.44 o .
The results of the angles for the resting length measuring are shown in Table 4.1-1.
Table 4.1-1. Measured joint angles for pectoralis major is in its resting length.
Protraction, arm beside
Protraction, arm on wagon
Elevation, arm beside
Elevation, arm on wagon
GH abduction
GH horizontal flexion
GH outward rotation
4.2 Motion of cross-country skiing 4th gear
The results from the joint angle calculations are presented in Figure 4.2-1 to Figure 4.2-4.
Figure 4.2-1. Joint angles for joint between the ground and the trunk.
Figure 4.2-2. Joint angles for the GH joint for both the left and right side. Observe that left side has inverted
signs relative to right side.
Figure 4.2-3. Joint angles for the elbow joint for both left and right side.
Figure 4.2-4. Joint angles for the joint between the hand and the pole for both left and right arm. For the second
rotation the left pole needs a sign shift to be compared to the right pole.
4.3 Results from the AnyBody Modelling System
The fixed values for the two first rotations for SC were measured in Figure 4.1-2 and Figure
4.1-3. The value of last rotation (the third) was only estimated from what illustratively looks
good in the visualisation from the AnyBody Modelling System.
Below follows some muscle forces of the right side from the simulation. In Figure 4.3-1 and
Figure 4.3-2 the passive forces for the ten parts of pectoralis major are shown.
Figure 4.3-1. The tendon forces for the parts of pectoralis major that origins from thorax.
Figure 4.3-2. The tendon forces for the parts of pectoralis major that origins from clavicula.
The activities for the other muscles that are involved in shoulder movements have similar
appearance. The activity for the parts of trapezius scapular are shown in three different
figures to give a full view of the plot, Figure 4.3-3, Figure 4.3-4 and Figure 4.3-5.
Figure 4.3-3. The activity for the parts of trapezius scapular plotted in the same figure. The activity is plotted in
relation to both the horizontal flexion angle and the time.
Figure 4.3-4. The activity for the parts of trapezius scapular plotted in the same figure. The activity is plotted in
relation to the horizontal flexion angle.
Figure 4.3-5. The activity for the parts of trapezius scapular plotted in the same figure. The activity is plotted in
relation to the time.
The presented muscle forces are divided into groups depending on their task.
Trapezius is not a rotator since it origins from the spine (neck to T12) and inserts on clavicula
and scapula. Trapezius is an adductor1 and an elevator of scapula. Trapezius clavicular are
shown in Figure 4.3-6
The activities of some outward rotators, infraspinatus, supraspinatus and deltoideus scapular
(deltoideus posterior), are shown in Figure 4.3-7, Figure 4.3-8 and Figure 4.3-9.
Pulls scapula closer to the spine.
Figure 4.3-6. Activities for the parts of trapezius clavicular shown in the same figure.
Figure 4.3-7. Activities for the parts of infraspinatus shown in the same figure.
Figure 4.3-8. Activities for the parts of supraspinatus shown in the same figure.
Figure 4.3-9. Activities for the parts of deltoideus scapular shown in the same figure.
The activities of some inward rotators, deltoideus clavicular (deltoideus anterior), latissimus
dorsi, teres major, and subscapularis, are shown in Figure 4.3-10 to Figure 4.3-13. Latissimus
dorsi consists of 5 parts; the higher number the further down and closer to the hip are the
origins. Latissimus dorsi only gets activated in part 3-5; the higher number the more
Figure 4.3-10. Activities for the parts of deltoideus clavicular shown in the same figure.
Figure 4.3-11. Activities for the parts of latissimus dorsi shown in the same figure.
Figure 4.3-12. The calculated activity is zero for all the parts of teres major.
Figure 4.3-13. Activities for the parts of subscapularis shown in the same figure.
Levator scapulae and rhomboideus are adductors of scapula. They are shown in Figure 4.3-14
and Figure 4.3-15.
Figure 4.3-14. Activities for the parts of levator scapulae shown in the same figure.
Figure 4.3-15. Activities for the parts of rhomboideus shown in the same figure.
The muscles shown here have different strength; the strength is linearly related to the PCSA
(physiological cross section area). In Table 4.3-1 the PCSA is shown for the muscles which
activities are plotted in this chapter shown.
Table 4.3-1. PSCA for the muscles which activities are plotted in this chapter.
Trapezius scapular
Trapezius clavicular
Deltoideus scapular
Deltoideus clavicular
Latissimus dorsi
Teres major
Levator scapulae
Total PCSA (mm2)
(Physiological cross section area)
5 Discussion and conclusions
5.1 The resting length measurement
The first recommended method for measuring the resting length was by palpating the muscle
and noticing when it starts to become tensed. This method was very hard to accomplish since
I have no experience about palpating muscles. Instead, the idea professor Magnusson
recommended was easier. This method had been tested in a similar manner on the hamstring
muscle in his laboratory.
The resting length of pectoralis major was measured to give the muscle tendon properties in
the simulation. The measurement gave a value of the stiffness of pectoralis major. The first
plan for this thesis was to make advisements to skiers with stiff pectoralis major of how much
they could decrease the total work produced if they decreased the stiffness in pectoralis
major. After a while I learned that the stiffness is an area in physiology that are not examined
thoroughly. The stiffness in a muscle will probably not change after stretch training (literature
is ambiguous, Björklund (2000), Magnusson (1996)). This reduced the resting length
measurements to be a test of how the stiffness can be measured and as estimation for the
stiffness for a set of shoulder joint angles.
Since the muscle is assumed strongest in its resting length the results here be can compared to
the results from Williams (1959). In this paper the joint angles for Scand AC were not
presented. The force as function of the horizontal flexion angle from Williams (1959) is
shown in Figure 5.1-1. The upper curve in the figure is for men and the lower is for women.
The maximum feasible force for men is attained between 30º and -30º. Compare the curve
with Figure 2.1-7 and it is possible to believe that the resting length is approximately at 30º.
Comparing Williams 30º of horizontal flexion to the 40º, found in my resting length
measurement, gives a hint that this method for measuring the resting length is working as
estimation for the horizontal angle. However this only works as a rough estimation and is not
suitable for investigating stiffness changes during a stretch training period.
Figure 5.1-1. The maximal feasible force as function of horizontal flexion angle. For men the upper curve and
for women the lower curve. Reference Williams (1959).
The stiffness of a muscle are as told above an area that needs more investigations. As
explained in chapter 2.1.7, the stiffness differs between individuals and during a lifetime and
ordinary stretching does not decrease the stiffness. However, for gymnasts who have as an
especially large range of motion it is possible to believe that their muscular stiffness are lower
than average. The gymnasts’ muscles have developed into having lower stiffness and this
have occurred by some reason. So it seems to be possible to change the stiffness of a muscle
although the exact procedure is not known (Magnusson,1998).
5.2 The input motion
The original plan was to order a measurement of the skiing motion from a laboratory that uses
optoelectronical system (motion capture). Unfortunately there was no laboratory in Sweden
that could make a shoulder measurement at the present time (various reasons). Instead were
data from an old motion capture measurement used made by VICON in Östersund April 2003.
These data were only produced for demonstration purposes.
There were many uncertainties for the input motion. First, the accuracy for visualisation was
not known. Also the measurements of the landmarks in the visualisation, the calculations of
the perspective reduction and the calculations of the joint rotations gave rise to uncertainties.
Although the output motion from the AnyBody Modelling System appear to be very similar to
the visualisation from VICON. This gives an indication that the calculations are not
completely wrong. One can also see that the output movement from the simulation are a
cross-country skiing movement.
When observing the results of the calculations in Figure 4.2-1 to Figure 4.2-4 it is possible to
see some similarities between left and right side of the body. Even though this skiing
technique is not symmetric it has some similarities between left and right side. The movement
of the poles are the most asymmetric, this since the poling in this skiing gear are only
performed on one side.
There is no doubt that a more accurate measurement of the input motion would improve the
results. At the present time I have not been able to construct a better input motion of the
skiing motion. I have been in contact with one company in Sweden that thinks it is impossible
to record shoulder motion with motion capture systems with enough accuracy. However,
VICON international were working with a validated model for the shoulder 2000 (Murray et
al., 2000), this has unfortunately not reached Sweden yet. Although three years before, 1997,
Helm claimed that it was impossible to record clavicular and scapular motion with an
optoelectronical system due to large bone-to-skin displacement (Helm, 1997). There are a few
other ways that have been used for 3-D motion recordings. Högfors et al. 1991, used a 3-D
roentgen technique with two roentgen cameras and implanted markers. This technique has
high accuracy and the possibility to record dynamic motions. The disadvantage is that
roentgen is not good for the health in too big amount and implanted markers might not be
In physiology, optical measurement systems are used frequently for gait training; after an
operation for example. I believe that motion capture systems can be used to simulate the
shoulder with inverse dynamics. At least for this application, where there is not the same high
demand of accuracy as within clinical1 tests.
The AnyBody Research group has just started developing interface methods for transforming
the data from the motion capture system VICON into the AnyBody Modelling System. This
will be very helpful for inverse dynamics investigations in the future.
This project is multidisciplinary which have caused several difficulties. The terminology is
different in different sciences, for example in mechanics one speaks about rotations among
axes while in physiology the terms flexion, extension, abduction, adduction are more
common. Since the terminology is different, communication can be complicated.
Multidisciplinary projects are although a great advantage since there is different knowledge in
every science area. I believe reciprocal progresses can be made if different science areas
5.3 Results from the AnyBody Modelling System
The plot of the muscle force for trapezius scapular is shown in several views. This is done
because when the muscles were activated, they were activated similarly. The reason why
trapezius scapular is used as example is that the plot shows a smooth behaviour over time and
it is a large muscle. In Figure 4.3-4 was the activity plotted as function of the horizontal
flexion angle. This was done to show that the maximal activity was decreased when the
horizontal flexion angle was decreased. The Figure 4.3-5 shows the activity as function of
time. This figure shows that the activity was decreased equally over the whole time interval.
When first interpreting the results I thought it was strange that the activity for several muscles
was exact the same. After a while I understood that this was the meaning of the optimisation
algorithm, recall from chapter 2.2.1 “the muscles cooperate as much as possible, no muscle
will get overloaded if other muscle can help”. The muscles that could help the movement
were helping.
The inward rotators were activated very little. The inward rotators in the “rotator cuff”, teres
major and subscapularis were almost not activated at all. Latissimus dorsi are also regarded
as an inward rotator in literature, see chapter 2.1.5. This muscle has both the task as inward
rotator and the task as extensor. The upper origins of latissimus dorsi (origins at the spine)
functions as inward rotators while the parts that origins from the basin functions more like
extensors. The parts of latissimus dorsi that functions like extensors were activated.
Note that this investigation did not include the pole force or the mass of the pole. If these
things were included the inward rotators would be much more activated, according to the
three-stage rocket in cross-country skiing (Holmberg, 2004 personal communication).
The outward rotators, supraspinatus and the greater muscle infraspinatus, see Table 4.3-1,
origins from scapula. These outward rotators cannot work alone since they need support from
the muscles that keeps scapula in position, levator scapulae, rhomboideus, trapezius and
serratus anterior. Since the shoulder is held fix during the motion the muscles in the upper
back only works statically during the motion. The activation for levator scapulae and
rhomboideus are in the same size as trapezius when activated.
The muscle forces in the upper back, which were the object of this report to determine, are
hard to discuss. This investigation shows that the muscles in the upper back will all decrease
their work equally when pectoralis major is lengthened. The maximal value of the muscle
activity for trapezius scapular, rhomboideus, levator scapulae and deltoideus posterior is
almost exact the same. Since the shoulder is held fix (SC and AC) during the motion this is
not strange. I also believe that it is therefore the activity of the muscles that origins from
clavicula are less smooth; the result is more unnatural. If the SC rotations and the position of
scapula were included the result would have been different.
How can we really know that these results are correct? This answer is stated on the web page
of AnyBody technology:
The fact of the matter is that the simulation result of AnyBody as all other numerical analysis
is inaccurate to a certain extent. But this does not mean that it is without value. You will find
when you use AnyBody that detailed models of the musculoskeletal system can provide you
with much, much more information than you can find from qualitative or experimental
investigations alone.
The clinical way of measuring muscle activity is by using EMG, elektromyography. EMG
measures the electrical impulse from nervous system to the muscle. It is false to say that EMG
is the correct way of measuring activity in real-life. Although it would be interesting to see a
comparative study between EMG and an inverse dynamics study.
Since there is no fatigue criterion included in this model a muscle can perform the same
movement infinite many times. The muscle is stronger the bigger it is, which I did not accept
at once. However, since there is no fatigue criterion in the muscle this makes sense. A muscle
that is small and strong is often strong only for a short while. However, a muscle that is big
often needs a big amount of oxygen to perform the same task over and over again. When there
is no fatigue criterion the big muscle always produces more power than the small one. This
area will perhaps also be developed within a few years. However, if no approximations are
made it would be too hard to start investigate anything
5.4 Summarizing discussion
The object of this report was to determine how a stiff pectoralis major affects the muscles in
the upper back.
A muscle becomes stiffer if it is strengthened and frequently used. Stiffness also increases
with aging. Stretch training will probably not decrease the passive resistance in a short period
of time, ex. within three weeks (Magnusson (1998)). However, for example among gymnasts
is muscular stiffness assumed to be lower than average. So, it is possible to make a muscle
less stiff although the method is not completely investigated.
Since input movement is lacking in accuracy and because the shoulder is held fix there is hard
to draw clear conclusions. When pectoralis major is stiffened the outward rotators of the arm,
the adductors of scapula and the extension parts of latissimus dorsi are increasing their force
to balance the same skiing motion. The increasing of the force is very small for each one of
the muscles; this is shown in Figure 4.3-4. In the beginning of this work I thought the result
would show different increasing force in different upper back musculature. I believe the
reason why this did not occur is that the shoulders were held fix during the movement.
In cross-country skiing the poles are used in almost every skiing gear. The strongest muscles
in poling are pectoralis major, teres major, latissimus dorsi and triceps (Holmberg 2004,
personal communication). The first three of these muscles are inward rotators of the arm. As
explained earlier, a muscle that becomes stronger also becomes stiffer. If all the inward
rotators become stronger and stiffer they will all be able to contribute to a “bad” shoulder
posture: rounded shoulder, increased kyphosis and/or a head forward posture.If the antagonists
to pectoralis major, the shoulder adductors (pulls scapula closer to the spine) and the outward
rotators of the arm, are not strengthened it is possible that “bad” shoulder postures will arise.
The outward rotators are, infraspinatus, supraspinatus, and the adductors are, trapezius,
rhomboideus and levator scapulae. The strongest of these muscles are trapezius.
The ending conclusions of this work are that the body needs muscular balance in the shoulder
and the mind needs consciousness about bad postures. Muscle balance is especially important
for youth, while the skeletal still is growing; muscle imbalance can give rise to scoliosis1
(Bergstrøm et al. 2004). Even though the result of this study is inaccurate it gives a hint that
avoiding of a bad shoulder posture which origins from a stiff pectoralis major should be
treated by both stretching and strengthening. Stretching is used to increase or maintain range
of motion for pectoralis major. Strengthening is used to increase the passive resistance in the
muscles. Since the shoulders were held fix in this study all the adductors, outward rotators and
the extending parts of latissimus dorsi should be strengthen equally if pectoralis major
becomes stiffer.
There is no study made of increased kyphosis among cross-country skiers, although this issue
is well known (Bergstrøm 2005 personal communication). When kyphosis appears for young
people, the form of the vertebrae might grow to be wedge-formed, this may give rise to
intravertebral disc herniation2 (slipped disc).
Literature agrees that a good posture prevents injuries and makes the muscles relax as much
as possible. But how can we change our posture? It is important to know how a good posture
feels and looks like so that you can change the posture by yourself. Kendall et al. (1993 p.
106) suggest that stretching and strengthening of different muscles can treat a faulty head and
shoulder posture. This is their suggestion: (Note that short here probably means low stretch
Stretch cervical spine extensors, if short, by trying to flatten the cervical spine. Strengthen
cervical spine flexors, if weak. Strengthen the thoracic spine extensors. Do deep breathing
exercises to help stretch the intercostals and the upper parts of abdominal muscles. Stretch
pectoralis minor. Stretch shoulder adductors and internal rotators, if short. Strengthen middle
and lower trapezius. Use shoulder support when indicated, to help stretch pectoralis minor
and relieve strain on middle and lower trapezius.
Scolioses is when the spine has got a curvature in the frontal plane (definition for frontal plane see Figure
In swedish: Kyphos i tillväxtåren kan göra att kotorna i ryggen växer till så de blir kil-formade, detta kan ge
upphov till diskbråck.
Not only for skiers need to realize the importance of the shoulder posture. This is also
important to think about for everyone everyday and especially women and girls who normally
have less strength in the upper back (Kelley, 2000).
Even though this science today makes many approximations the results, as the AnyBody
Research group states, provides much more information than it is possible in any other way.
This science is under development and it makes progress all the time. When one system is
working properly, fewer approximations can be made and the system develops. For example,
I have used three different versions of the AnyBody Modelling System during this
Biomechanics are under development; within a few years I believe that the approximations
are fewer and the results more reliable.
6 References
6.1 Unpublished references
Bergstrøm Kjell Arne, Doctor medicinae, University in Oslo, Oslo.
Personal communication January (2005) electronical.
HC Holmberg, Swedish Olympic Committee.
Personal communication June 5, 2004,electronical several times during 2004.
Rasmussen John, Professor Aalborg University, Institute for Mechanical Engineering.
Personal communication several times during 2004.
Damsgaard Michael, Professor Aalborg University, Institute for Mechanical Engineering.
Personal communication Maj 2004.
Rydesäter Peter, Technical Licenciate Umeå University, Department of Applied Physics and
Personal communication fall 2004.
Tørholm Christensen Søren, Damsgaard Michael, Rasmussen John & De Zee Mark
Muscle model for inverse dynamic musculo-skeletal system.
Manuscript 2002 from the Institute of Mechanical Engineering, Aalborg University.
6.2 Published references
Anderson Bob (1998). Stretching vid datorn. Borås, Centraltryckeriet AB. ISBN 91-3232232-1
Anderson Bob (1993). Stretching, för ökad rörlighet och smidighet. Borås, Centraltryckeriet
AB. ISBN 91-32-31746-8
Bauer Mats, Persson Per-Lennart & Söder Kjell-Erik (1982). Grundstyrketräning för
harmonisk muskelutveckling. Östersund: Kopiering och tryck. ISBN 91-970145-0-8
Bergstrøm Kjell Arne, Brandsteh Kjell, Fretheim Sigurd, Tvilde Kjartan & Ekeland Arne
(2004). Back injuries and pain in adolescents attending a ski high school. Knee Surg Sports
Traumatol Arthrosc. 2004 Jan;12(1):80-5.
Brunnstrom Signe (1972). Clinical Kinesiology. Philadelphia: F.A. Davis Company. ISBN 08036-1301-6
Budowick Michael, Bjålie Jan G., Rolstad Bent & Toverud Kari C. Swedish translation
Bjerneroth Gunnel & Svensson Björn A (1993). Anatomisk atlas Stockholm : Liber utbildning
AB. ISBN 91-634-0051-0
Dahlqvist Johan (2002).Biomechanical study of the forearm. Master Dissertion. Division of
Solid Machanics, Lund. ISRN LUTFD/TFHF—01/5097—SE(1-67)
Damsgaard Michael, Rasmussen John & Søren Christensen (2001). Inverse dynamics of
musculo skeletal systems using an efficient min/max muscle recruitment model.
In: ASME 2001 Design Engineering Technical Conferences and Computors and Information
in Engineering ConferenceK, Pittsburgh, Pennsylvania, September 9-12, 2001.
Cailliet, René (1981). Shoulder pain. 2nd edition. Philadelphia F.A. Davis Company. ISBN 08036-1613-9
Elpinston, Joanne & Pook, Paul (2003). Bålstabilitet, fakta och övningar på balansboll.
Farsta: SISU 2003. ISBN 91-88941-65-5
Guyton Arthur C. (1984). Physiology of the Human Body. 6th edition. Philadelphia: Sauders
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Haug E. & Sand O. & V. Sjaastad Ø. (1993). Männsikans fysiologi. Stockholm: Liber
Universitets förlaget. ISBN 91-47-04806-9
Kapandji I.A. (1982). The Physiology of the Joints. Volume 1 Upper Limb. 5th edition
Edinburgh: Churchill Livingstone. ISBN 0-443-02504-5
Kelley, Lee A (2000). In neck to neck are women more fragile?. Clinical Orthopaedics and
related research 2000 March (372):123-130
Kendall, F.P. , Kendall, McCreary E.K & Provance P.G. (1993). Muscles, Testing and
Function. 4th edition. Baltimore Williams & Wilkins. ISBN 0-683-04576-8
Magnusson Peter, Simonsen Erik B., Aagaard Per & Sørenson Henrik, Kjæ r Michael (1996).
A mechanism for altered flexibility in human skeletal muscle. Journal of Physiology 497.1
Magnusson Peter. Passive properties of the human skeletal muscle during stretch maneuvers.
A review. Scandinavian journal of medicine & science in sports 1998, 8, 65-77.
Murray Ingram & Johnson Garth (2000). Definition of marker positions and technical frames
for studying the kinematics of the shoulder. In: Proceedings of the third conference of
international shoulder group, Newcastle upon Tyne, September 4-6, 2000.
Netter Frank H. (1997). Atlas of Human Anatomy. East Hanover, N.J: Novartis. ISBN 0914168-81-9
Nikravesh, Parvis E. (1988). Computer-aided analysis of mechanical systems. Englewood
Cliffs, N.J.: Prentice-Hall. ISBN 0-13-164220-0
Putz R. & Pabst R. (2001). Sobotta, Atlas of Human Anatomy. 13th English edition
Lippincott: Williams &Wilkins. ISBN 07817-3173-9
Rasmussen John, Damsgaard Michael & Voigt Michael (2001). Muscle recruitment by the
min/max criterion – a comparative study. Journals of biomechanics 34 409-415
Simons, David G., Travell, Janet G. & Simons, Lois S. (1999). Travell & Simons´
Myofascicle Pain and Dysfunction: The Trigger Point Manual. Volume 1, Upper Half of
Body. 2nd edition. Baltimore: Williams &Wilkins. ISBN 0-683-08363-5
Bojsen-Møller, Finn (2000). Rörelseapparatens anatomi. Stockholm: Liber AB. ISBN 91-4704884-0
Van der Helm, Frans C.T. (1997). A standardized protocol for motion recordings of the
shoulder. In: Proceedings of the first conference of international shoulder group, Delft
University of Technology, August 26-27, 1997.
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Zajac Felix E (1989). Muscle and tendon: Properties, models, scaling, and application to
biomechanics and motor control. Critical Reviews in biomechanical Engineering Volume 17
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6.3 Electronical references
AnyBody Technology
Retrieved several times during 2004 from the World Wide Web:
International Shoulder Group
Retrieved several times during 2004 from the World Wide Web:
Norweigian Ski Federation
Retreived fall 2004 from the World Wide Web: