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CHAPTER3
Developmental biodynamics
e development of coordination
James Watkins
Introduction
Human movement is brought about by the musculoskeletal system
under the control of the nervous system. e skeletal muscles pull
on the bones to control the movements of the joints and, in doing
so, control the movement of the body as a whole. By coordination
of the various muscle groups, the forces generated by the muscles
are transmitted by the bones and joints to enable the application of
forces to the external environment, usually via the hands and feet,
so that humans can adopt upright postures (counteract the constant
tendency of body weight to collapse the body), transport the body,
and manipulate objects, oen simultaneously.1 e forces gener-
ated and transmitted by the musculoskeletal system are referred to
as internal forces. Body weight and the forces that are applied to the
external environment are referred to as external forces. At any point
in time body weight cannot be changed, and as such body weight is a
passive external force. e external forces that are actively generated
are active external forces. e magnitude, duration, and timing of
the active external forces are determined by the magnitude, duration,
and timing of the internal forces. Biomechanics is the study of the
forces that act on and within living organisms and the eect of the
forces on the size, shape, structure, and movement of the organisms.2
e brain coordinates and controls movement via muscu-
lar activity.3 Coordination refers to the timing of relative motion
between body segments and control refers to the optimization of
relative motion between body segments, i.e. the extent to which the
kinematics of segmental motion and, consequently, the motion of
the whole body centre of gravity (CG), matches the demands of
the task.4 For example, the mature form of coordination of the leg
action in a countermovement vertical jump, as shown in Figure3.1,
is characterized by simultaneous exion of the hips, knees, and
ankles in the countermovement phase (Figure3.1a– c), followed
by simultaneous extension of the hips, knees, and ankles in the
propulsion phase (Figure3.1c– e). is pattern of coordination
normally occurs between three and four years of age.4 However,
whereas most mature individuals exhibit similar coordination in
the countermovement vertical jump (and other whole body move-
ments), there are considerable dierences in the extent to which
individuals can control the movement, that is, optimize the relative
motion of the body segments in order to match the task demands.4
If the objective in performing a countermovement vertical jump
is to maximize height jumped (upward vertical displacement of
the whole body CG measured from the oor) then control of the
movement is concerned with maximizing the height of the CG at
take- o (h1) and maximizing the upward vertical displacement of
the CG aer take- o (h2) (Figure3.1e and f). e height of the CG
at take- o (h1) is determined by body position which, in turn, is
determined by the range of motion in the joints and the extent to
which the available range of motion is used. e upward vertical
displacement of the CG aer take- o (h2) is determined by the ver-
tical velocity of the CG at take- o, and therefore the greater the
vertical component of take- o velocity, the greater h2. e verti-
cal component of take- o velocity is determined by the impulse
of the vertical component of the resultant ground reaction force
(the force exerted between the feet and the oor) prior to take- o,
so the larger the impulse the greater the velocity. e impulse F · t
of the vertical component of the resultant ground reaction force F
is determined by the magnitude of F and its duration t; the larger
the force and the longer its duration the larger the impulse. e
magnitude of F will depend upon the strength of the jumper’s mus-
cles, especially the extensor muscles of the hips, knees, and ankles.
e duration of F will depend upon the ranges of motion in the
jumper’s hips, knees, and ankles and the extent to which the avail-
able ranges of motion are used. Clearly, restricted ranges of motion
in any of the joints, especially hips, knees, and ankles, and lack of
strength in any of the muscles, especially the extensor muscles of
the hips, knees, and ankles, will adversely aect the jumper’s abil-
ity to control the movement and, consequently, result in less- than-
optimal performance.
ere are numerous studies of jumping performance in adults,
especially elite athletes.5,6 However, there are relatively few stud-
ies on the development of coordination and control of jumping in
young children. Jensen etal.4 investigated coordination and control
in the countermovement vertical jump in two groups of young chil-
dren (mean ± standard deviation (SD) age=3.4 ± 0.5years) and a
group of skilled adults. e two groups of children (n1=n2=nine)
were selected from a larger group (n=32) on the basis of their
take- o angle (angle of velocity vector of the whole body CG at
take- o) into a high take- o group (HT0) and low take- o group
(LT0). Take- o angle is a key control variable, since to maximize
vertical displacement aer take- o, the take- o angle should be 90°
(with respect to the horizontal). e criterion for inclusion in the
HT0 and LT0 groups was a take- o angle at least one SD greater or
less than the total group mean, respectively. All jumps were per-
formed on a force platform to measure the ground reaction force.
To encourage maximum eort, a suspended ball, just out of reach,
was used as a visual target. Coordination was assessed by exam-
ining the timing of reversals (between the countermovement and
PART 1 26
propulsion phases of the jump) of the hip, knee, and ankle joints
and the timing of the peak extension velocities of the hip, knee, and
ankle joints. Control was assessed by examining the body position
(hip, knee, and ankle joint angles) at three events during the jump;
the time of maximum acceleration downward (minimum vertical
ground reaction force), the time of maximum acceleration upward
(maximum vertical ground reaction force), and take- o.
No signicant dierences were found between the three groups
with regard to the coordination variables. is nding is consistent
with the results of a study by Clark etal.7 of three, ve, seven, and
nine- year- old children involving the same task and methodology.
e mean take- o angles for the adults, HT0, and LT0 groups—
91.8° ± 3.8°, 82.0° ± 3.5°, and 61.2° ± 5.6° respectively— were sig-
nicantly dierent from each other and the mean of the adult
group was closest to the theoretically desired angle of 90°. ere
were also signicant dierences between the groups in some of the
other control variables (hip, knee, and ankle angles) at one or more
of the three events, in particular, the ankle angle between adults
and both child groups at take- o and the knee angle between all
three groups at take- o. e small mean angle of take- o of the
LT0 group was found to be associated with a large (relative to the
adults and HT0 groups) forward displacement of the CG during
the countermovement and propulsion phases, that is, the trajec-
tory of the CG was V- shaped, downward and forward then upward
and forward. In contrast, the trajectory of the CG of the adults was
U- shaped, downward, and very slightly forward then upward and
very slightly forward. e trajectory of the CG of the HT0 group
was in between those of the adult and LT0 groups. In general, the
smaller the forward displacement of the CG, the greater the take- o
angle and vice versa. Whereas the HT0 and LT0 groups had smaller
take- o angles than the adult group, the HT0 and LT0 groups still
accomplished a clearly recognizable vertical jump, although the
jumps were simply not optimized for maximum vertical displace-
ment of the CG. Jensen etal.4 concluded that the performances of
the children were coordinated but poorly controlled, due perhaps
to inadequate strength of the leg extensor muscles, especially dur-
ing the braking period of the countermovement phase (the period
when the downward velocity of the CG is reduced tozero).
Development ofcoordination and control
e human neuromusculoskeletal system consists of approximately
1011 neurons, 103 muscles, and 102 moveable joints.3,8 e way
that the nervous system organizes movement in the face of such
complexity has been viewed historically from two viewpoints:the
neuromaturational perspective and the information- processing
perspective.8
e neuromaturational perspective has been used primarily
to explain motor development in infants and children. e neu-
romaturational perspective arose from the work of Gesell and
ompson,9 and McGraw10 who observed and described the grad-
ual and sequential development of motor skills in infants from
apparently unintentional reex movements through the develop-
ment of intentional movements like crawling, sitting, standing, and
walking. e legacy of Gesell and McGraw was twofold:rst, the
assumption that motor development was sequential and inevitable,
and, second, that progress directly reected the gradual maturation
of the nervous system.11 is view became widely held and the
age norms for the emergence of motor skills in infants and chil-
dren produced by Gesell and McGraw became, and still are, widely
used.11 Whereas neuromaturation is undeniably a major deter-
minant of motor development in infants and children, it does not
explain skill acquisition in adults where the nervous system is con-
sidered to be fully mature.12
Traditionally, the information- processing perspective has
dominated theories of skill acquisition in adults.13 From the
information- processing perspective, the brain is regarded rather
like a computer with a very large number of motor programmes
G
G
h2
h1
ab cd ef
Figure3.1 Stick figure sequence of a countermovement vertical jump from a standing position:
a = standing position.
a to c = countermovement or dip phase.
c to e = propulsion phases.
G=whole body centre of gravity.
h1=height of G above thefloor.
h2=upward vertical displacement fo G after take- off.
CHAPTER3 : 27
which can be executed at will to match the specic demands of
each movement task as dened by the available sensory informa-
tion. However, similar to the neuromaturational perspective, the
information- processing perspective does not account for the great
exibility demonstrated by individuals in accommodating rapidly
changing task demands, especially in the context of sports.14
e deciencies of the neuromaturational and information-
processing perspectives were pointed out by Bernstein.15 He argued
that the complexity of the neuromusculoskeletal system was such
that a one- to- one relationship between activity in the nervous sys-
tem and actual movements was not possible, i.e. that the nervous
system cannot simultaneously directly control the activity of every
nerve cell. Consequently, it then cannot simultaneously directly
control the activity of every muscle cell. He also pointed out that
a particular set of muscular contractions is not always associated
with the same movement pattern, and that not all movements are
controlled by the nervous system. For example, if you raise your
arm to the side by using the shoulder abductor muscles and then
relax the muscles, the arm will fall down under its own weight with-
out any involvement of the nervous system. Similarly, if you hold
your arm with the upper arm horizontal, the lower arm vertical,
and the wrist relaxed, and then alternately slightly ex and extend
the elbow fairly rapidly, the hand will ail about the wrist due to
its own inertia and the force exerted on the hand at the wrist by
the movement of the lower arm; again this happens without any
involvement of the nervous system. At any particular point in time
each body segment may be acted on by ve kinds of forces, which
can be classied in two ways16; internal (muscle, articular, inertial)
and external (gravitational, contact) forces, and active (muscle) and
passive (articular, inertial, gravitational, contact) forces. Muscle
forces are the forces exerted by active muscles. Articular forces arise
from passive deformations of inactive muscles, tendons, ligaments
and other connective tissues. Inertial forces are the forces exerted
on one segment arising from the motion of other segments linked
to it. Gravitational force is the weight of the segment. Contact
forces are forces acting on the segment that result from contact of
the segment with the physical environment, such as theoor.
Reference axes and degrees offreedom
It is useful to refer to three mutually perpendicular axes—
anteroposterior, transverse, and vertical— when describing the
movement of a joint (Figure 3.2). With respect to the three refer-
ence axes there are six possible directions, called degrees of free-
dom, in which a joint, depending upon its structure, may be able to
move. e six directions consist of three linear directions (along the
axes) and three angular directions (around the axes). Most of the
joints in the body have between one and three degrees of freedom.
Most movements of the body involve simultaneous movement in
a number of joints, and the degrees of freedom of the whole seg-
mental chain is the sum of the degrees of freedom of the individual
joints in the chain. For example, if the wrist (comprised of eight
small irregular shaped bones) is regarded as a single joint with two
degrees of freedom (exion- extension and abduction- adduction)
then the arm has approximately 25 joints (joints of the shoulder,
elbow, wrist, and ngers) and approximately 35 degrees of freedom.
Coordination and degrees offreedom
Bernstein15 pointed out that in any motor skill (purposeful task-
oriented movement) that involves a part of or the whole body, like
reaching with an arm from a seated position, the total number of
degrees of freedom of the joints involved normally greatly exceeds
the number of degrees of freedom that are minimally necessary to
accomplish the task. Consequently, when learning a new or unfa-
miliar motor skill, Bernstein described the problem for the learner
as ‘the process of mastering redundant degrees of freedom’15(p.127),
i.e. reducing the number of degrees of freedom to a manageable
number. He suggested that there are essentially three stages in the
development of motor skill. In the rst stage, the inuence of the
many degrees of freedom is restricted by i) minimizing the ranges
of motion in the joints and ii) forming temporary strong couplings
between the joints e.g. moving multiple joints in close phase rela-
tions. e latter is likely to compress the many degrees of freedom
into a much smaller number of virtual degrees of freedom which,
in turn, is likely to simplify neuromuscular control. e second
stage is characterized by the establishment of relatively stable phase
relations between the movements of the joints, in association with
changes in joint kinematics (ranges of motion and angular veloci-
ties). e notion of a functional assembly of relatively stable phase
relations has been referred to as a ‘coordinative structure’17 and a
‘coordinative mode’.18 e third stage is characterized by an increase
in economy of movement (reduction in energy expenditure)
by exploitation of the passive forces in a manner that minimizes
the active forces i.e. the work done by muscles, and maximizes
mechanical energy conservation i.e. facilitating mechanical energy
exchanges, potential to kinetic and vice- versa, and energy transfer
between segments.
Most of the muscles (muscle- tendon units) of the body cross
over more than one joint. ese muscles, such as the rectus femoris
and hamstrings, are usually referred to as biarticular muscles, since
muscles which cross over more than two joints function in the
same way as muscles that cross over just two joints.19 Biarticular
muscles are too short to fully ex or fully extend all the joints that
X
AY
LY
Z
LX
AX
Y
AZ
L
Z
Figure3.2 Linear and angular degrees of freedom with respect to the
shoulderjoint.
X=anteroposterioraxis.
Y=verticalaxis.
Z=Transverseaxis.
Lx = linear motion alongXaxis.
Ly=linear motion alongYaxis.
Lz=linear motion alongZaxis.
Ax=angular motion aboutXaxis.
Ay=linear motion alongYaxis.
Az=linear motion alongZaxis.
PART 1 28
they cross over simultaneously. For example, the hamstrings are too
short to fully extend the hip and fully ex the knee at the same time;
indeed, hip extension is usually associated with knee extension and
hip exion is usually associated with knee exion, as in a counter-
movement vertical jump20,21 (Figure 3.3). Consequently, anatom-
ical constraints, like biarticular muscles, tend to reduce the range
of movements that are possible in a segmental chain such that the
apparent degrees of freedom in the segmental chain may be lower
than initially appears. For example, Valero- Cuevas22 demonstrated
that biarticular muscles and their specialized aponeuroses in the
human hand couple the degrees of freedom of the corresponding
joints and constrain possible patterns of use. Such contraints are
likely to simplify neuromuscular control.
Bernstein’s three stages of motor skill development are now
generally accepted23,24 and supported by an increasing volume
of empirical data.25,26,27,28 Recent technological improvements,
including multi- camera systems allied to subject- mounted wireless
accelerometers, have facilitated more ecological (real- world) stud-
ies of the biomechanics of coordination.29,30 However, there still
appear to be few studies which have clearly related kinematics to
kinetics, investigated the eects of practice, or involved children.
Kinematics ofcoordination
Whereas control of movement is essential to maximize perfor-
mance, the development of coordination is a necessary precursor
to the development of control. is was demonstrated by Anderson
and Sidaway26 in a study of the eects of practice on performance in
kicking. Anovice group of right foot dominant subjects, ve males
and one female (mean age 20.3years, age range 18– 22years) was
selected on the basis of no previous experience of organized soc-
cer or soccer training. An expert group of three males (mean age
25.2years, age range 22– 30years), each with more than 10years
experience of organized soccer, was included in the study in order
to determine whether the coordination of the three experts was
similar, and to compare the pre- and post- practice coordination of
the novices with the experts. e task to be learned (only the novice
group took part in the practice sessions) was a right- footed instep
drive at a 2 m2 target placed 5 m from the ball following a two step
approach. e primary goal was to maximize the velocity of the
ball while trying to hit the target. e subjects practised twice a
week for ten weeks and had between 15 and 20 trials during each
session. Prior to and aer the practice period, three trials of each
subject were videotaped with a single camera placed perpendicular
to the plane of motion on the right side of the subject. By using
markers on the right shoulder, right hip, right knee, right ankle, and
right small toe (Figure 3.4), the angular displacement and angular
velocity of the hip and knee and linear velocity of the foot (toe) was
found for each subject at 60 Hz throughout each trial. From the
linear and angular velocity data and the angular displacement data,
three velocity measures, three timing measures, and two ranges of
motion were derived for each subject in each trial (see Table 3.1).
R
H
G
Figure3.3 Coupling of the trunk, upper leg and lower leg by the rectus femoris,
hamstrings and gastrocnemius. e trunk is linked to the lower leg by the
hamstrings (H)and the rectus femoris (R ) and the upper leg is linked to the foot
by the gastrocnemius (G). If the length of H, R and G are approximately set, hip
extension will result in simultaneous knee extension and ankle plantar flexion
Adapted from Ingen Schenau GJV. From translation to rotation:constraints on multijoint
movements and the unique action of biarticular muscles. Hum Mov Sci. 1989; 8:301– 337..
200
S = Shoulder jointHip angle
S
H
K
AAnkle angl
e
Knee angle
H = hip joint
K = knee joint
A = ankle joint
• approximate ball contact
180
160
140
Knee (°)
120
100
80
60
40
120 140 160 180 200 220
Hip (°)
Expert
Novice: post
Novice: pre
240 260 280
Figure3.4 Kicking a soccer ball:hip angle- knee angle diagrams for one
representative novice's performance, pre and postpractice, and one representative
expert’s performance.
Adapted from Anderson DI, Sidaway B. Coordination changes associated with practice of a
soccer kick. Res Q Exerc Sport. 1994; 65:93– 99.
CHAPTER3 : 29
As each subject exhibited a high degree of consistency with regard
to the eight variables, the data were averaged across the three trials.
Table 3.1 shows the group means and standard deviations for the
eight variables for the novices, pre- and post- practice, and the experts,
together with percentage changes pre- and post- practice for the nov-
ices, and percentage comparison of the novices, pre- and post- practice,
with the experts. It is clear that the performance of the novices, in
terms of maximum foot linear velocity (which reects ball velocity)
improved considerably with practice (47%) but was still well below that
of the experts (85%) post- practice. However, the 47% increase in max-
imum foot linear velocity was associated with much smaller increases
in maximum hip angular velocity (2.1%), maximum knee angular vel-
ocity (12.3%), hip range of motion (19.8%), and knee range of motion
(14.5%). ese changes, especially the angular velocity changes, sug-
gest that improvement in performance resulted largely from a change
in coordination rather than from an increase in the speed of execution
of the pre- practice movement pattern. is interpretation is supported
by the change in the timing variables which were much closer to those
of the experts post- practice than pre- practice (see Table 3.1). It is also
supported by the change in relative motion of the thigh and lower
leg as reected in the representative knee angle— hip angle diagrams
shown in Figure 3.4. e post- practice pattern was similar to that of
the experts, which suggests that the novices had developed coordin-
ation. However, comparison of the novice post- practice and expert lin-
ear and angular velocities and ranges of motion in Table 3.1 indicates
that control was less than optimal. e results of the study provide sup-
port for Bernstein’s theory of motor skill acquisition, i.e. development
of coordination (establishment of a coordinative structure) followed by
development of control (changes in joint kinematics).
Kinetics ofcoordination
A kinematic analysis describes the way an object moves, that is,
the changes in linear and/ or angular displacement, velocity, and
acceleration of the object with respect to time. To understand why
an object moves the way that it does, it is necessary to carry out a
kinetic analysis, i.e. an analysis of the impulses and timing of the
impulses of the forces acting on the object during the movement.
With regard to human movement this involves analysis of the active
and passive forces acting on each body segment.
Modelling
Each body segment is comprised of hard and so tissues. Whereas the
segment may deform to a certain extent during movement, the amount
of deformation is usually very small and, as such, for the purpose of
biomechanical analysis, the body segments may be regarded as rigid.31
Consequently, the human body may be regarded as a system of rigid
segments with the main segments (head, trunk, upper arms, forearms,
hands, thighs, lower legs, and feet) linked by freely moveable joints.
Free body diagram
Kamm etal.32 carried out kinetic analyses of spontaneous leg move-
ments in infants while reclined at 45°, as shown in Figure 3.5a.
Figures3.5b and 3.5c show free body diagrams of the thigh and the
combined lower leg and foot of the right leg, that is, sketches of the
segments showing all of the forces acting on them. It is assumed that
the movement of the legs takes place in the sagittal plane (X- Y plane
with respect to Figure 3.5). ere are no contact forces acting on the
segments and, as such, the only forces shown are the weights of the seg-
ments acting at the segmental CGs, and the force distributions around
the hip and knee joints. It can be shown that any force distribution is
equivalent to the resultant force R acting at an arbitrary point P together
with a couple C equal to the resultant moment of the force distribu-
tion about P.31 e combination of R (acting at P) and C is referred
to as the equipollent of the force distribution. In a kinetic analysis of
human movement, it is usual to show the force distribution around a
joint as the equipollent with respect to the joint centre. In Figures3.5b
and 3.5c, the equipollent of the force distribution around the hip joint
is shown as FH and MH, and the equipollent of the force distribution
around the knee joint is shown as FK and MK. In Figures3.5d and 3.5e,
the resultant forces through the hip and knee joint centres are replaced
by their horizontal (FHX, FKX) and vertical (FHY, FKY) components.
Table3.1 Kicking a soccer ball:means, standard deviations, and comparative data forfoot linear velocity, hip and knee angular velocity, timing*,
and hip joint and knee joint ranges ofmotion fornovice and expert subjects
NoviceExpert
Pre- practice Post- practice
Mean SD %E Mean SD %E %pp Mean SD
MFLV (m · s–1) 14.9 1.7 58 21.9 1.5 85 47 25.6 1.1
MHAV (deg · s–1) 671 77 78 685 168 79 2.1 864 49
MKAV (deg · s–1) 1146 213 77 1287 251 86 12.3 1494 115
SKE/ IMHAV 1.02 0.06 117 0.89 0.05 102 –13 0.87 0.03
IMHAV/ IMKAV 0.61 0.1 77 0.69 0.03 87 13 0.79 0.01
IMKAV/ IMFLV 1.14 0.06 109 1.04 0.05 100 –8.7 1.04 0.03
Hip ROM (deg) 86 14 64 103 21 77 19.8 135 9.5
Knee ROM (deg) 90 16 75 104 13 86 14.5 121 5.7
MFLV: maximum foot linear velocity; MHAV: maximum hip angular velocity; MKAV: maximum knee angular velocity; SKE: start of knee extension; I: Instant of; %E: percent of expert value;
%pp: percent difference between pre- and post-practice.
* e ratios of the durations of the events (SKE, IMHAV, IMKAV, IMFLV) measured from the start of the backswing of the right leg. A ratio greater than 1.0 indicates that the numerator
event occurred after the denominator event, and vice-versa.
Adapted from Anderson and Sidaway.
PART 1 30
Components ofnet jointmoment
Each segment will move in accordance with Newton’s laws of motion.
Consequently, with respect to the lower leg and foot segment:
FmaxX=
(3.1)
FmayY=
(3.2)
MI
Z=
α
(3.3)
where FX=resultant of horizontal forces acting on the segment;
FY= resultant of vertical forces acting on the segment; m=mass
of the lower leg and foot; ax=horizontal component of the lin-
ear acceleration of the CG of the segment; ay=vertical component
of the linear acceleration of the CG of the segment; MZ=result-
ant moment about the Z axis through the CG of the segment;
I=moment of inertia of the segment about the Z axis through the
CG of the segment; α=angular acceleration of the segment about
the Z axis through the CG of the segment.
From Equations (3.1), (3.2), and (3.3)it followsthat:
FmaxKX =
(3.4)
FWmayKY S
−=
(3.5)
MFdFdI
KKXKY
−− =
12
α
(3.6)
From equation(3.5),
Fma W
yKY S
=+
(3.7)
By substitution of FKX from Eqn (3.4)and FKY from Eqn (3.7)
into Eqn(3.6),
Mmad ma Wd I
x yKS
−−+=
12
( )
α
Mmad ma dWdI
x yKS
−− −=
122
α
Mmad ma dWdI
x y sK−+ −=()
122
α
MK=Generalized Muscle Moment (MUS):the moment aris-
ing from active muscles and passive deformations of inactive
muscles, tendons, ligaments, and other connective tissues about
the Z axis through the knee joint centre, that is, the moment
exerted by active muscles and articular forces about the joint.
(maxd1+ mayd2)= Motion Dependent Moment (MDM) (also
Y
(a)
(b)
MH
GT
GS
WS
WT
MKMK
FK
FKY
MK
MH
MKFKX
GS
WS
FKX
FKY
FHX
FHY
IFH = force distribution (muscle and articular) about the hip joint
IFK = force distribution (muscle and articular) about the knee joint
MH = moment of IFH about the Z axis through the hip joint centre
MK = moment of IFK about the Z axis through the knee joint centre
FH = resultant of IFH acting through the hip joint centre
FHX = horizontal component of FH
FHY = vertical component of FH
FK = resultant of IFK acting through the knee joint centre
FKX = horizontal component of FK
FKY = horizontal component of FK
GT = centre of gravity of the upper leg
WT = weight of upper leg
WS = weight of combined lower leg and foot
d1 = moment arm of FKX about the Z axis through Gs
d
2
= moment arm of F
KY
about the Z axis through G
s
GS = centre of gravity of the combined lower leg and foot
WT
GT
FK
FH
(c)
(d) (e)
X
Z
Figure3.5 Free body diagrams of the thigh and combined lower leg and foot of the right leg of a three month old infant inclined at 45°:(a)infant inclined at 45°;
(b)free body diagram of right upper leg; (c)free body diagram of combined right lower leg and foot; (d)free body diagram of right upper leg with resultant joint forces
replaced by horizontal and vertical components; (e)free body diagram of combined right lower leg and foot with resultant joint forces replaced by horizontal and
vertical components.
AQ: IFH, IFK, d1,
d2 these labels
are not noted
in gure. Please
check and let
me know your
comments.
CHAPTER3 : 31
referred to as the inertial moment):the moment acting on the
segment as a result of the motion of adjacent segments, that is,
the thigh. WSd2=Gravitational Moment (G R AV ):the moment
acting on the segment due to its weight. Iα=Net Joint Moment
(NET):the resultant of MUS, MDM, and GR AV moments acting
on the segment.
In this example, there is no external contact force, such as the
ground reaction force in walking or running acting on the lower
leg and foot segment. However, when there are contact forces,
these must be included in the analysis of the components of joint
moment. Consequently, the general equation relating the compo-
nents of joint moment may be expressedas:
NET MUSGRAVMDM EXT=+ ++
(3.8)
EXT represents the moments about the joint exerted by one
or more contact forces. e NET moment is the joint moment
required to accomplish the task; it is clear from Eqn (3.8)that the
NET moment may be inuenced by each of the four component
moments. e actual signs of the components in Eqn (3.8)would
depend upon the directions of the components. e relationship
between MUS, GRAV, MDM, and EXT is usually referred to as the
biodynamics of joint movement.15
Bernstein15 referred to the MDM component as ‘reactive phe-
nomena’ when statingthat,
e secret of coordination lies not only in not wasting superuous
force on extinguishing reactive phenomena but, on the contrary, in
employing the latter in such a way as to employ active muscle forces
only in the capacity of complementary forces. In this case the same
movement (in the nal analysis) demands less expenditure of active
force.15(p.109)
With current technology it is not possible to directly measure
the forces which contribute to MUS or, therefore, to measure
the separate contributions of muscle and articular forces to the
MUS. However, since the MUS includes the only active (muscle)
component of the NET, the MUS is particularly important for
understanding coordination. Whereas MUS cannot be measured
directly, it can be determined indirectly, i.e. MUS=NET- MDM-
GRAV- EXT. EXT can usually be measured. For example, ground
reaction force can be measured by a force platform. NET, MDM, and
G R AV can be calculated directly by kinematic analysis of the move-
ment of the body segments. is indirect method of determining
MUS is referred to as indirect dynamics or inverse dynamics.33 e
converse of indirect dynamics, that is, determination of kinematics
from directly measured kinetic (forces and moments of force) data
is referred to as direct dynamics.33
In the study by Kamm etal.32 of spontaneous leg movements
in children reclined at 45°, it was found that the infants naturally
produced kicks of varying degrees of vigour and range of motion.
In general, the infants exhibited a consistent pattern of relative
motion between trunk, thigh, and lower leg segments, suggesting
a high level of coordination. e relationship between the MUS,
MDM, and G R AV proles was similar at the hip and knee joints. At
slow speeds of movement the MDM were very small and the MUS
served mainly to counteract the G R AV (Figure3.6a). e G R AV
prole, as expected, was similar at all kicking speeds. However, at
fast speeds the MUS and MDM proles were sinusoidal and out
of phase by approximately 180°, suggesting that as speed of move-
ment increased the main function of the MUS was to counter-
act the MDM (Figure6b). e MUS prole was also found to be
approximately 180° out of phase with the change in joint angle,
i.e. the peaks of the MUS prole corresponded to changes in dir-
ection of movement of the segment. Since change in direction of
movement is associated with eccentric muscle activity during the
deceleration phase, the correspondence between the proles of
joint angle, MUS, and MDM suggest that coordinated movement
tends to exploit the capacity of muscle- tendon units to store energy
(in the elastic components during eccentric contractions) which,
in turn, is likely to enhance energy conservation and reduce the
1.0
(a) (b)
2.8 1.0
0.5
0
–0.5
–1.0
0 0.1 0.2 0.3 0.4
Time (S)
Angle (RAD)
2.6
2.4
2.2
2.0
1.8
2.8
2.6
2.4
2.2
2.0
1.8
1.6
0.5
0
Moment (Nm)
–0.5
–1.0
0 0.4 0.8 1.2
Time (S)
1.6 2.0
Angle (RAD)
Moment (Nm)
GRAV MUSMDM HIP JOINT ANGLE
Figure3.6 Profiles of generalized muscle moments (MUS), motion dependent moments (MDM), and gravitational moments (GR AV) about the hip joint in relation to
hip joint angle for an infant performing a spontaneous nonvigorous kick (a)and a vigorous kick(b).
Adapted from Kamm K, elen E, Jensen J L. A dynamical systems approach to motor development. Phys er, 1990; 70:763– 775.
PART 1 32
energy expenditure of the muscles. Schneider etal.34 found simi-
lar correspondence between the proles of joint angle (shoulder,
elbow, and wrist), MUS, and MDM in adults performing a rapid
reciprocal precision hand- placement task. e studies by Kamm
etal.32 and Schneider etal.34 support the now generally- held view
that the development of coordination and control involves a pro-
cess of optimization of the passive and active components of joint
moment around each joint in order to maximize the use of pas-
sive moments. is, in turn, decreases the contribution of active
moments and, therefore, decreases energy expenditure. Lockman
and elen35 introduced the term ‘developmental biodynamics’ to
describe the development of coordination and control in infants, or
how infants learn to coordinate joint biodynamics.
Dynamical systems approach
todevelopment ofcoordination
Studies of spontaneous kicking,32 reaching,36 and stepping37,38
clearly indicate that infants have a high level of coordination in
spontaneous (non- task oriented, non- intentional) multi- joint limb
movements, which suggests an intrinsic ability of the body seg-
ments to self- organize their relative motion.39 Self- organization is
a key feature of complex dynamical systems which, like the human
body, have many degrees of freedom and are subject to a range of
constraints.40 Dynamical systems theory was developed nearly
a century ago as an attempt to explain the way physical systems
change over time.8 Dynamical systems theory was rst applied to
coordination of human movement by Kugler etal.,41 and since then
concepts from dynamical systems have been increasingly used to
explain the development of coordination.42,43
Self- organization and constraints
From a neuromaturational perspective, motor development in
children is considered to result directly from the gradual matur-
ation of the nervous system; the more mature the nervous sys-
tem, the higher the level of motor skill displayed. Similarly, from
an information- processing perspective, motor learning in adults
is assumed to result from the triggering of established motor pro-
grammes. In contrast to these two perspectives, from a dynamical
systems perspective, motor learning at any age (in humans and in
all other animals) is regarded as a dynamic process whereby motor
ability (the ability to perform motor skills) emerges from the intrin-
sic self- organizing properties of the dynamical system consisting of
the individual, the task, and the environment.7,44,45
Self- organization refers to the spontaneous integration of the
dynamical properties of the subsystems that comprise a system and
results in the spontaneous establishment of a pattern of activity.46
e actual pattern that emerges is dependent upon the constraints
on the system. With regard to human movement, a constraint is
any inuence that serves to decrease the number of degrees of
freedom that need to be controlled, that is, the constraints acting
on the system limit the types of movement that can emerge.18,22,47
Constraints can be broadly classied into three groups:individual,
task, and environmental.48
Individual constraints, also referred to as organismic constraints,
refer to the limitations imposed by the current status of the individ-
ual in terms of all aspects of physical, cognitive, and aective func-
tions. ere are essentially two types of task constraints:extrinsic
and intrinsic.47 Extrinsic task constraints refer to the mechanical
requirements of the task which may include, for example, the speed
(e.g. running for a bus) and/ or precision (e.g. threading a needle)
needed to successfully complete the task. Intrinsic task constraints
refer to the individual’s perception of the potential costs (e.g. energy
expenditure and risk of injury) of particular types of movement
that could be used to complete the task. ere is clear evidence that
individuals normally move in ways that tend to minimize energy
expenditure (e.g. walk rather than run) and risk of injury (e.g. walk
slowly rather than quickly on a slippery surface). Environmental
constraints arise from the physical and socio- cultural environ-
ment.8 Physical environmental constraints include, for example,
weather conditions, conditions of light and heat, surface condi-
tions, and the availability of protective clothing (e.g. in industry
and sport). Socio- cultural environmental constraints include peer
pressure and the pressure to behave in culturally acceptableways.
All organisms within a species share a common gene pool (the
sum total of all the genes in a species).49 However, the genome
of each individual organism (the genes and assembly of genes) is
slightly dierent to all of the other organisms within the species.
e genome determines ontogenesis, which is the innate pro-
cess of development of the individual from zygote to maturity.50
Ontogenesis is similar for all organisms within a species, but not
identical because ontogenesis imposes individual constraints on
development. Development is simultaneously inuenced by envi-
ronmental constraints; dierent environments tend to result in
dierent rates of development.42 Consequently, the actual devel-
opment of an organism, referred to as epigenesis,50 is the result of
the interaction of individual and environmental constraints (see
Chapter32).
A main feature of the ontogeny of motor development is the pro-
pensity of infants to develop those behaviours that enable them
to explore and interact with the environment (locomotion and
manipulation skills).42,51 Most normally developing infants experi-
ence similar motor development outcomes in terms of the timing
and types of motor skills that emerge. From a dynamical systems
perspective, these predictable early milestones emerge as the result
of species- similar constraints.7,42 From this perspective, the mat-
urational status of the nervous system is regarded as a major indi-
vidual constraint, but only one of many individual constraints that,
together with task and environmental constraints, determine the
form of movement that emerges. For example, while infants nor-
mally learn to crawl and then stand before walking,51 there is no
pre- determined programme for crawling. Crawling emerges as the
best available solution to a particular motor problem (to travel in
a particular direction), which is later replaced by the more eect-
ive and ecient solution of walking, which comes about as a result
of changes in individual constraints.42,51 Furthermore, as the
constraints are continually changing, the system as a whole is in
a constant state of ux. erefore, no two movements are exactly
thesame.
e appropriateness of the dynamical systems approach to
understanding motor development was clearly shown by elen
and her colleagues in a series of studies on infant locomotion.52– 57
elen monitored the spontaneous behaviours of infants and
found that certain behaviours appeared, disappeared and then re-
appeared some time later.53 For example, she found that infants
exhibit from birth kicking movements when lying on their backs
and stepping movements when they are held upright. She also
observed that stepping disappeared within the rst three months,
CHAPTER3 : 33
only to re- appear a few weeks later, while kicking continued and
increased in frequency over the same period. She also observed that
infants who gained weight fastest were the rst to stop stepping.
elen reasoned that if the appearance and disappearance of step-
ping was due solely to nervous system maturation, then changing
the prevailing environmental constraints, such as the eect of grav-
ity, should not aect the behaviour. She tested the hypothesis by
articially increasing and decreasing the weight of the legs of the
infants. She found that stepping behaviour disappeared when the
weight of the infants’ legs was increased by attaching small weights
to the ankles; conversely, removing the weights restored the step-
ping behaviour. Furthermore, she found that the stepping behav-
iour could also be restored by submerging the infants’ legs in water.
e buoyancy provided by the water articially reduced the weight
of the infants’ legs which, in turn, increases the strength:weight
ratio of the leg to a level that restores the stepping behaviour. ese
observations clearly indicate that the strength:weight ratio is an
important individual constraint that inuences the motor behav-
iour of infants (see Chapter4).
Most researchers agree that the development of strength and pos-
tural control are major inuences on infants’ rate of development
of walking, and that body growth, neural maturation, and practice
of walking determine strength and postural control.58 However,
there is less agreement and little empirical research on the rela-
tive importance of body growth, neural maturation, and walking
practice on the development of strength and postural control. e
lack of empirical research would appear to be due, at least in part,
to methodological diculties associated with assessing neural
development and practice and in separating out the eects of body
growth, neural maturation, and walking practice, which are all
constantly changing. Adolph etal.59 investigated the relative con-
tribution to improvements in walking skill of body growth (height,
weight, leg length, head circumference, crown- rump length, and
ponderal index), neural maturation (assumed to be reected in
chronological age), and practice in walking (assumed to be reected
in the number of days since the onset of walking, dened as the
rst day that the infant could walk at least 3 m independently) in a
part- longitudinal and part cross- sectional study. e subjects were
210 infants (101 girls, 109 boys) aged nine to 17months and, for
comparison, 15 children (eight girls, seven boys) aged ve to six
years and 13 adults (ten women, three men). Walking skill was
assessed by changes in step length, step width, foot angle (toe- in
or toe- out), and dynamic base (the angle formed by three consecu-
tive steps). Using robust statistical methods based on hierarchical
regression analyses, the results showed that body growth did not
explain improvements in walking skill independent of neural mat-
uration and walking practice. Similarly, neural maturation did not
explain improvements in walking skill independent of body growth
and walking practice. In contrast, walking practice played the sin-
gle most important role in the improvements in walking skill. It was
concluded that the magnitude, distributed nature, and variability of
infants’ walking experience facilitate exploration of passive forces
and dierentiation of perceptual information which, in turn, pro-
mote the development of strength and postural control.
In a subsequent study, Adolph etal.60 quantied the amount of
walking practice engaged in by infants by analysing video tapes
of infants playing freely under caregivers’ supervision in a labora-
tory playroom. To simulate the infants’ home environments while
eliminating dierences in their home environments, the laboratory
playroom was equipped with furniture, varied ground surfaces, and
a variety of large and smalltoys.
Fieen to 60 minutes of continuous spontaneous activity was
recorded for each of 151 infants aged 12– 19months. e results
showed that the infants took an average of 2,368 steps · h–1, trav-
elled an average distance of 701 m · h–1, and fell an average of 17
times · h–1. Based on these data, and assuming a walking infant is
active for 6 h · day–1 (approximately half of an infant’s waking day),
walking infants may complete approximately 14,000 steps · day–1
and travel approximately 4,200 m · day–1 (2.61 miles). Adolph
etal.60 suggest that such a large amount of walking practice (involv-
ing forward, backward, and sideways steps) reects the diculty of
learning to walk (maintenance of an asymmetric upright posture
while moving forward, backward, and sideways) and is comparable
to the amount of daily practice required by concert musicians and
athletes to achieve expert performance. e transition from crawl-
ing to walking results in a greater number of falls, but the cost of
this intrinsic task constraint would appear to be outweighed by the
ability of the learner to cover more space more quickly, experience
more varied visual input, access and play with more distant objects,
and interact in qualitatively new ways with caregivers.51
In accordance with the dynamical systems approach, Clark8
pointed out that motor skill acquisition takes place throughout the
whole of the life of the individual and that the process underly-
ing the emergence of new skills is basically the same at any age.
Consequently, to describe the process of children learning to walk
as motor development and that of adults learning a new sports
technique as motor learning is to make an unnecessary articial
distinction between the way that children and adults learn new
motor skills (see Chapter4).
Coordinative structures, control parameters,
andorder parameters
According to the principles of dynamical systems, the movement
pattern of the human body that emerges in response to the need to
solve a particular movement task, such as reaching, pointing, walk-
ing, running, hopping, skipping, jumping, and landing, is the result
of self- organization of the individual constraints in relation to the
task and environmental constraints on the system. For a particular
movement task, self- organization assembles the muscles/ joints of
the body into functional groups (referred to by Bernstein15 as func-
tional synergies) that together form a coordinate structure for the
whole body41 (Figure 3.7). e muscles/ joints in each functional
group move together (e.g. extend simultaneously or ex simultan-
eously) which reduces the number of degrees of freedom within
the functional group and, in turn, reduces the number of degrees
of freedom in the coordinate structure. e smaller the number
of degrees of freedom in the coordinate structure, the lower the
demand on the nervous system. e coordinate structure sets the
timing (relative phasing) of the movements of the body segments.
Dierent task constraints give rise to dierent coordinative struc-
tures. For example, for speeds of locomotion up to about 2.0 m · s–1
most humans naturally adopt a walking pattern (bipedal alternate
right- le- right- le stepping) rather than another form of loco-
motion such as running or hopping. e coordinate structure for
walking is characterized by two double support phases (both feet
in contact with the ground at the same time) and separate single
support and swing phases of each leg during each stride. Dierent
forms of locomotion, such as walking, running, hopping, skipping,
PART 1 34
and jumping have dierent coordinative structures. Acoordina-
tive structure is stable over particular ranges (or scaling) of certain
constraints (referred to as control parameters) so that the observed
movement pattern may change qualitatively (reected in changes
in order parameters) while the coordinate structure remains
the same.61 For example, as walking speed (control parameter)
increases up to about 2.0 m · s–1, the movement pattern changes
qualitatively (change in the order parameters of stride length and
stride frequency), but the coordinative structure (walking) remains
the same. However, as the speed of walking increases above 2 m · s–1,
the walking pattern becomes increasingly unstable, reected in
increasing variability of the relative phasing of the body segments
and increasing asymmetry between the movements of the le and
right sides of the body. At about 2.3 m · s–1 there is an abrupt change
from walking to running, which is a new coordinative structure
characterized by two ight phases (instead of two double support
phases as in walking) and separate single support and swing phases
of each leg during each stride. is coordinate structure remains
stable over most of the 2.3 m · s–1 to maximum speedrange.
e abrupt change from walking to running illustrates a major
characteristic of dynamical systems. Changes in coordinative struc-
ture are triggered by instability resulting from a change in the scal-
ing of one or more control parameters.42 In the case of bipedal
locomotion, speed is a control parameter that determines the most
appropriate coordinative structure, either walking or running, for
a givenspeed.
Patterns, attractors, and stability
Coordinate structures result in stable patterns of activity which are
likely to be reected in the activity of the system as a whole and/
or in the activity of the subsystems. In human movement, the pat-
tern of activity resulting from a particular coordinative structure
is likely to be manifest in a very wide range of kinematic (e.g. the
movement of each body segment), kinetic (e.g. peak force at heel
strike, rate of loading during the passive phase of ground contact),
physiological (e.g. tidal volume, breathing rate, stroke volume,
heart rate, and rate of oxygen consumption), and neuromusculo-
skeletal (e.g. intensity and duration of contractions of individual
muscles) indicators. Kinematic indicators are likely to show highly
repeatable whole body movement patterns (movement of the CG),
highly repeatable movement patterns of individual body segments,
and low variability in the relative phasing (coordination) of the
movement of body segments.
e stability of a movement pattern can be illustrated and quanti-
ed in a number of ways.62 One of the most frequently used dynami-
cal systems techniques for illustrating the stability of the movement
pattern of a body segment is the phase plane (also referred to as
phase portrait, phase plane trajectory, and parametric phase plot).
Aphase plane captures the space- time pattern of the movement of
the segment by plotting the velocity (linear or angular) of the seg-
ment as a function of the displacement of the segment.63 For exam-
ple, Figure 3.8 shows a phase plane of the movement of the shank
of an infant in the sagittal plane four weeks aer starting to walk.64
It shows the angular velocity- angular displacement trajectory of
the shank in three successive stride cycles. It is clear that there is
some overlap between the trajectories, but no direct mapping of
one trajectory onto the next. In dynamical systems terminology, the
phase plane exhibited by the shank occupies a region in the state
space.65 e state space encompasses all possible trajectories of the
shank in the state space. e state space is dened by the relevant
state variables. In this example, the state variables are the angular
velocity and angular displacement of the shank which dene a two-
dimensional statespace.
e trajectories of the shank dene a region in the state space
referred to as the attractor, which is the region of the state space in
which the movement of the shank is most stable. e stability of the
phase plane of the shank from cycle to cycle is reected in the band-
width of the attractor. e narrower the bandwidth, the more stable
the attractor. e standard deviation of the length of the angular
velocity- angular displacement vectors, which are determined at
the same frequency as the data used to plot the phase plane, over a
Environmental
Task Individual
Coordinative
structure
Figure3.7 e emergence of a coordinate structure from self- organisation of the
individual, task and environmental constraints.
500
400
300
200
Angular velocity (°/s)
100
Angular displacement (°)
–100
40 50 60 70 80 90
HS
TO
100
–200
0
30
Figure3.8 Phase plane of the sagittal plane movement of the shank in three
successive stride cycles of an infant four weeks after starting towalk.
HS:heel strike, TO:toeoff.
Adapted from Clark JE, Phillips SJ. A longitudinal study of intralimb coordination in the first
year of independent walking:a dynamical systems analysis. Child Dev. 1993; 64:1143– 1157.
CHAPTER3 : 35
number of cycles provides an estimate of the bandwidth; the lower
the standard deviation, the more stable the attractor.
Another frequently used dynamical systems technique for esti-
mating the stability of a movement pattern is the variability of the
relative phase between two events in the movement pattern over
a number of trials or cycles. For example, in running, the relative
phasing of the movement of the knee and ankle joints of each leg
could be determined by the time dierence between peak knee ex-
ion and peak ankle dorsi- exion during the ground contact phase
expressed as a proportion of ground contact time (Figure 3.9).
Asimilar measure of relative phase could be obtained for any pair
of joints in the same leg during each ground contact phase (hip/
knee, knee/ ankle, and hip/ ankle) or for corresponding joints in the
le and right legs during each stride (le hip/ right hip, le knee/
right knee, and le ankle/ right ankle). e stability of each measure
of relative phase is reected in the standard deviation of the relative
phase over a number of cycles; the smaller the standard deviation,
the more closely coupled is the movement of the two joints and,
therefore, the more stable is the movement pattern.
Cyclicity inbiological systems
e dynamical systems approach emphasizes the thermodynamic
nature (patterns of changes in energy) of biological systems and
how thermodynamic laws guide behaviour.63 Biological systems
obey the second law of thermodynamics, which is that all systems
tend toward instability and disorder. In the case of a living organ-
ism, this culminates in death. However, during life a biological
system can maintain an ordered state by a cyclical process of gen-
eration, transformation, and dissipation of energy which occurs at
all levels of the system. ese include circadian rhythms, cardiac
rhythms, respiratory rhythms, and locomotion.66 It is believed that
the oscillatory nature of biological systems is analogous to inani-
mate self- organizing oscillatory systems.40,67 is viewpoint has led
to the application of the physics of pendulums to such systems.40
Any object that is free to oscillate about a horizontal axis is a
pendulum. For example, a pendulum in a clock usually consists of a
long light bar or rod that supports a small dense mass. e idealized
form of this type of pendulum, referred to as a simple pendulum,
consists of a mass- less rod of length L that supports a point mass m.
As the rod has no mass, the centre of mass of a simple pendulum is
at the centre of mass of the point mass. Consequently, the distance
D from the axis of rotation to the centre of mass of the pendulum
is equal to L. e moment of inertia I of the pendulum about the
axis of rotation through its point of support is given by I=mL2
where L=the radius of gyration of the pendulum about the axis
of rotation. Areal pendulum is usually referred to as a compound
pendulum. In a compound pendulum, L is always longer thanD.
If a pendulum (simple or compound) is displaced from its vertical
resting position and then released, it will oscillate about the vertical
rest position with a constant period, which means that the duration
of each cycle of movement will be constant even though the amp-
litude of movement will gradually decrease. is decrease is due to
friction around its axis of rotation and, to a lesser extent, airresist-
ance. e period τ of a simple pendulum is given by τ=2π(L/ g)½.68
An oscillator that has a constant period, like a swinging pendulum,
is referred to as a harmonic oscillator.68
e period (seconds per cycle) of a pendulum is entirely deter-
mined by its physical properties, in particular the distribution of
the mass of the pendulum. For a given mass, a change in the distri-
bution of mass will result in a change in the moment of inertia of
the pendulum with respect to its axis of rotation. In other words,
a change in L, will result in a change in the period. e reciprocal
of the period is the frequency of oscillation (cycles per second). As
the period of a pendulum is constant, its frequency of oscillation is
referred to as natural frequency or resonant frequency.68
If there was no friction around the axis of rotation of a pendulum
and no air resistance, the pendulum would oscillate with constant
amplitude and the energy of the system would be entirely conserved
at the level it had at the point of release. In practice, there would be
some friction around the axis of rotation and some air resistance
such that a certain amount of energy would be dissipated (lost to
the pendulum in the form of heat and movement of the air) during
each oscillation. Consequently, the amplitude of oscillation would
gradually decrease and the pendulum would eventually come to
rest and hang vertically. Apendulum is a very simple example of
a dynamical system. e movement of the system aer release is
self- organized (amplitude and frequency of oscillation), entirely
predictable, and energy is conserved (to a level determined by fric-
tion and air resistance). Similarly, if a metal spring is stretched or
compressed and then released, the spring will oscillate in a predict-
able manner and come to rest at its equilibrium position; there is no
brain controlling its movement, which is instead determined com-
pletely by its physical properties of stiness and damping. Just as
the physical properties of a pendulum and a spring determine their
movement when allowed to oscillate freely, it is reasonable to infer
that the movement of the arms and legs might be determined in a
similar manner in certain movements. For example, in walking, if
the stiness and damping levels of the legs are set by the muscles
that control the hips, knees, and ankles, the oscillation of the legs
will be determined to a certain extent by their physical properties,
which is likely to simplify neural control of the movement.40
Force- driven harmonic oscillators
If a child’s swing is set in motion, its swing amplitude will gradually
decrease due to friction around its axis of rotation and to air resist-
ance. In order to maintain a constant swing amplitude, the swing
must receive a brief push at the start of each swing to replace the
energy lost due to friction and air resistance in the preceding swing.
Aharmonic oscillator that requires energy input at the start of each
Time
rrr
Knee
Ankle
Angle
Figure3.9 Determination of the relative phase (r) between peak knee flexion
and peak ankle dorsi- flexion during the ground contact phase in running.
Holt KG, Hamill J, and Adapted from Andres RO. Predicting the minimal energy costs of
human walking. Med Sci Sport Exerc. 1991; 23:491– 498.
PART 1 36
oscillation in order to maintain a constant amplitude of oscillation,
which is like a child’s swing, is referred to as a force driven har-
monic oscillator (FDHO).69
e motion of the legs in constant speed walking is quasi-
periodic (alternate oscillation of the legs with similar swing time
and similar swing amplitude). However, the body as a whole loses
energy in each step due to damping, where kinetic energy trans-
formed into strain energy during the period of double support as
a result of eccentric muscle contraction is partially dissipated as
heat. Unless replenished, the loss of energy during each step would
quickly bring the body to rest. e continued oscillation of the legs
is maintained by a burst of muscular activity just prior to the start
of each leg swing (to replace the energy lost in the previous step).
Consequently, the motion of the legs in constant speed walking is
similar to that of an FDHO.69
In an FDHO, there is a particular frequency, referred to as the
resonant frequency, which requires minimal impulse (intensity of
force multiplied by the duration of the force) to maintain oscilla-
tions. In human movement, muscle forces (intensity, duration, and
frequency of muscular activity) determine energy expenditure.
ere is considerable evidence that adults and children naturally
adopt a step frequency and step length in walking that minimizes
energy expenditure and maximizes stability.69–73 Furthermore, the
preferred step frequency can be predicted from the resonant fre-
quency of an FDHO model of the leg swing69,71 where the period
τ=2π(L/ 2g)½.40 Similarly, Ledebt and Breniere74 found that in
four- to eight- year- old children, gait initiation (from the start of
movement to maximum horizontal velocity in the rst step) can be
closely predicted from the resonant frequency of an FDHO model
of the movement of the body over the grounded foot. Even very
young children appear to adopt movement patterns at resonant fre-
quency in certain situations. For example, Goldeld etal.75 showed
that infants bouncing up and down in a jumper device tend to adopt
resonant frequency as modelled by an FDHO mass- spring system.
Self- optimization ofcoordinative structures
e observation that cyclic human movement like walking tends to
be performed at resonant frequency has led to the suggestion that
coordination is self- optimized in relation to so- called optimality
criteria to which the individual is sensitive in adopting a particular
movement pattern.69,70 e optimality criteria reect the prevail-
ing intrinsic task constraints and result in movement patterns that
minimize the ‘costs’ to the system.47 e main optimality criterion
would appear to be energy expenditure, but others have been sug-
gested, including stability, bilateral symmetry, and shock absorp-
tion at foot- strike.71,76 For example, at a particular walking speed,
minimal expenditure usually occurs at preferred step frequency in
children and adults and is usually associated with high stability and
high bilateral symmetry.70,71
With regard to symmetry, Clark etal.72 investigated coordina-
tion in walking in a cross- sectional study involving seven groups of
subjects:new walkers (capable of three consecutive steps) with sup-
port, new walkers without support, children who had been walking
for two weeks, one month, three months, and six months, and a
group of adults. ere were ve subjects in each group. e aver-
age age of onset of walking in the infant subjects was 11.2months.
Interlimb coordination, at preferred speed of walking, was assessed
by measuring the step time:stride time ratio (temporal phase) and
the step length:stride length ratio (distance phase). It was expected
that in a mature walking gait, the temporal phase and the distance
phase would be close to 50% and that a low variability (measured
as the standard deviation of each phase) would indicate a stable
coordinative structure. e results showed that there was no sig-
nicant dierence in mean temporal phase or mean distance phase
(all close to 50%) across all age groups. Additionally, variability
decreased with age with no signicant dierence in variability
between the three months, six months, and adult groups. e vari-
ability of the supported new walkers (two- handed support by a par-
ent) was not signicantly dierent from the two weeks, one month,
and three months groups in temporal phase and not signicantly
dierent from the three months and six months groups in distance
phase. Clark etal.72 concluded that i) the coordinative structure for
interlimb coordination used by new walkers is similar to, but not as
tightly coupled as, that used by adults, and ii) the practice of walk-
ing increases postural stability which, in turn, increases the stability
of the coordinative structure. e results of the study suggested that
bilateral symmetry is a feature of coordination in walking.
Jeng etal.71 investigated energy expenditure, stability, and sym-
metry in walking in three- to 12- year- old children and adults. ere
were six groups of subjects with nine subjects in each group:three
to four years, ve to six years, seven to eight years, nine to ten years,
11– 12years, and 20– 21years. e subjects were carefully selected
to represent the full range of body sizes in each age group. Aer
familiarization, each subject was required to walk for eight min on
a treadmill at preferred walking speed (established in overground
walking) at three dierent step frequencies in time with a metro-
nome:preferred step frequency (PSF), PSF— 25% and PSF + 25%.
Energy expenditure during steady- state walking was assessed at
each step frequency by the physiological cost index (in beats · m–1),
which is the dierence between resting heart rate and walking heart
rate (in beats · min–1) divided by walking speed (in m · min–1).
Coordination was assessed at each step frequency via symmetry
and relative phase. Bilateral symmetry was assessed by the ratio of
the durations of the stance phases of each leg in each stride, the
ratio of the durations of the swing phases of each leg in each stride,
and the ratio of the duration of the right step to the stride dura-
tion in each stride. e mean of each ratio was calculated over ten
consecutive stride cycles during steady- state walking. e relative
phase (time dierence between the occurrences of the maximum
angles of each pair of joints in each stride as a percentage of stride
time) was determined for the hip/ knee, knee/ ankle, and hip/ ankle
joint couplings. e mean of each relative phase was calculated over
ten consecutive stride cycles during steady- state walking. Stability
was assessed as the standard deviation of each of the symmetry and
relative phase measures.
e results clearly indicated that energy expenditure, symmetry,
and stability were all optimal at preferred step frequency for all age
groups and that preferred step frequency was consistent with reso-
nant frequency as predicted by an FDHO model of the leg swing.40
Seven of the three- to four- year- olds and four of the ve- to six-
year- olds had diculty in modulating their step frequency at the
non- preferred step frequencies. All of the other subjects were able
to modulate their step frequency at the non- preferred step frequen-
cies. Jeng etal.77 concluded that the ability to self- optimize walk-
ing appears to be established by seven years of age and seems to
involve three stages. Stage 1 (one to four years of age) is character-
ized by early sensitivity to resonance and diculty in modulating
step frequency to non- preferred frequencies. Stage 2 (four to six
CHAPTER3 : 37
years of age) is characterized by a progressive increase in the ability
to modulate step frequency and a decrease in stability which may
be due to the need to adapt to marked changes in body composi-
tion that are characteristic of this period. Stage 3 (six to seven years
of age) is characterized by the ability to consistently modulate step
frequency.
Jeng et al.77 suggested that sensitivity to resonance (an aware-
ness of how to minimize energy expenditure by maximizing energy
conservation in energy exchanges between and within body seg-
ments) may be a mechanism underlying the development of self-
optimization in walking. ey also suggested that sensitivity to
resonance is a function of the individual’s sensitivity to the physi-
cal properties of her/ his body and to the environment. Sensitivity
to personal physical properties would suggest awareness of the
anthropometric (size and shape), inertial (mass and distribution
of mass), viscoelastic (stiness and damping), and gravitational
(weight) properties of body segments and combinations of body
segments. Sensitivity to the environment would suggest awareness
of what movements are possible in a given environment, for exam-
ple, negotiating an obstacle or moving through a conned space.
Awareness of the possibilities aorded by a particular environment
has been referred to by Gibson78 as aordance. Figure 3.10 pre-
sents a model of the emergence of motor behaviour based on the
dynamical systems approach.
Dynamic resources
As shown by Adolph etal.,59,60 the rapid improvement in walk-
ing ability in the rst month following the onset of walking would
appear to be largely due to the eects of practice. According to
Fonseca etal.79 and Holt etal.,80 the practice of walking enables
toddlers to explore the sources of energy available to them to
maintain upright posture and forward progression. ese dynamic
resources available may be categorized as i) energy generation by
concentric muscle contractions, ii) conservation of energy in so
tissues, which is the potential to store and then release strain energy
in muscle- tendon units (spring dynamics) and iii) conservation of
energy by interchange of kinetic energy and gravitational poten-
tial energy within and between body segments (pendulum dynam-
ics).80 e gait (walking movement pattern) that emerges will
reect the relative contribution of the three sources of energy.
ere are potentially a number of ways of using these resources
to maintain upright posture and forward progression. For example,
pendulum dynamics is more evident in walking than in running
and spring dynamics is more evident in running than in walk-
ing81,82 (Figure3.11).
Figure 3.12 shows a picture sequence of a young boy walking
at preferred speed from just aer heel- strike of the right foot to
just aer heel- strike of the le foot. From toe- o of the le foot
(TOL) to heel- strike of the le foot (HSL) (single support phase
of the right leg, approximately 40% of the stride cycle) the body
rotates forward over the right foot similar to an inverted pendulum
(Figure3.11a and Figure3.12a– e). During the period TOL to mid-
stance (Figure3.12a– c), kinetic energy is converted to gravitational
potential energy (as the CG moves upward) and during the period
from mid- stance to HSL (Figure3.12c– e), gravitational potential
energy is converted to kinetic energy (as the CG moves downward).
ere will be some loss of energy during these phases due to damp-
ing in so tissues (dissipated as heat inside the body and then to
the surrounding air), but energy will be largely conserved due to
pendulum dynamics.83
Individual
constraints
Environmental
constraints
Self-organization
Coordinative structure
Sensitivity to
resonanceSelf-optimization Intrinsic task
constraints
Movement pattern
Extrinisic task
constraints
Figure3.10 Adynamical systems- based model of motor learning.
CG
(a)
(b)
CG
Figure3.11 Pendulum dynamics (a)is the predominant form of energy
conservation in walking. Spring dynamics (b)is the predominant form of energy
conservation in running.
CG:whole body centre of gravity.
Adapted from Farley CT, Ferris DP. Biomechanics of walking and running:Center of mass
movements to muscle action. Exerc Sport Sci Rev. 1998; 26:253– 285.
PART 1 38
During the period HSR to TOL (Figure 3.12a and b) (double
support phase prior to le swing phase, approximately 10% of
the stride cycle), kinetic energy is converted to strain energy in
the right leg (i.e. the leg is compressed like a spring). Most of the
strain energy will be immediately returned as kinetic energy and
gravitational potential energy, but some of the strain energy will
be lost due to damping in the so tissues. Simultaneous to the stor-
age and release of strain energy in the right leg, active plantar ex-
ion of the le ankle (the push- o of the le foot) generates new
energy (kinetic and gravitational). To maintain forward progres-
sion, the new energy generated by the push- o must be sucient
to replace the energy that was lost due to damping in so tissues.83
e energy changes between HS and TO of each foot are illustrated
in Figure3.13.
Walking at resonant frequency will result in minimal loss of
energy and therefore minimal energy expenditure. As in any
FDHO, correct timing of the push- o (referred to by Holt etal.80 as
the escapement force) is necessary to produce resonant frequency
in walking. To produce resonance, the push- o should begin as, or
just before, the landing foot strikes the ground at the start of the
double support phase, which means that the period of generation
of new energy should correspond to the period when energy is lost
due to compression of the leadleg.83
Holt et al.80 investigated the use of pendulum dynamics and
spring dynamics in new walkers. e subjects were seven infants
who were encouraged to walk on a walkway in a laboratory while
being video- taped from the side. e infants were video- taped on
seven visits to the laboratory at one- month intervals. e rst video-
taping of each infant occurred as soon as possible aer the infant
could perform three to six independent steps. e mean age of the
infants was 11months at the rst visit and 17months at the last
visit. e timing of the push- o (referred to as escapement timing)
was assessed in terms of the time dierence (tc– ta) between foot-
strike (tc) and peak forward acceleration of the whole body centre
of gravity (ta). Anegative escapement time indicates that ta occurs
aer tc, which means that it occurs during double support when the
push- o would be most eective (correspondence between the new
energy generation phase of the rear leg and the energy loss phase
of the lead leg). However, a positive escapement time indicates that
ta occurs before tc, indicating lack of correspondence between the
energy generation phase and the energy loss phase of the lead leg.
At visit one, mean escapement time was positive with high vari-
ability. At visit two, mean escapement time was negative with high
variability. In visits three to seven, the mean escapement time was
consistently negative with much lower variability than in visits one
and two. Consequently, in contrast to visit one, escapement time in
visits two to seven was consistent with resonant frequency.
e changes in the eectiveness of escapement over visits one to
seven were reected in changes in walking speed, step length, and
step frequency. ere were signicant increases in speed of walk-
ing (0.18 m · s–1 to 0.59 m · s–1), step length (0.10 m to 0.21 m), and
step frequency (1.83 to 2.87 Hz) between visits one and two, but
no signicant changes in any of the three variables over visits two
to seven. ere were no signicant dierences in weight, stand-
ing height, or sitting height of the subjects between visits one and
two, but there were signicant increases in all three variables over
(a) (b) (c) (d) (e)
Figure3.12 Ayoung boy walking at preferred speed from just after heel- strike of the right foot to just after heel- strike of the leftfoot.
AQ: Alphabets
a to e not
dened in
caption?
A
CG
D
BE
F
C
Figure3.13 e energy changes between heel strike and toe- off of each foot
during walking.
A:conversion of kinetic energy to gravitational potential energy; B:storage of strain energy
in the muscle- tendon units and other soft tissues; C:loss of some strain energy as heat;
D:conversion of gravitational potential energy to kinetic energy; E:release of strain energy;
F:push- off; CG:whole body centre of gravity.
Adapted from Holt KG, Obusek JP, Fonseca ST. Constraints on disordered locomotion:a
dynamical systems perspective on spastic cerebral palsy. Hum Mov Sci. 1996; 15:177– 202.
CHAPTER3 : 39
visits two to seven. e results suggested that in the early stages of
walking (within the rst month aer the onset of walking) infants
rapidly learn to provide active force (via appropriate escapement
timing) in a way that is consistent with the utilization of pendulum
and spring dynamics to optimize energy expenditure.
A dynamical systems perspective ofwalking
inchildren withcerebralpalsy
e major task constraints in walking are the maintenance of
an upright posture and continued oscillation of the legs despite
energy losses.79 As a result of weakness in the calf muscles (ankle
plantar- exors), children with spastic diplegia, a condition of cere-
bral palsy, are unable to generate the same amount of new energy
during push- o in walking as normally- developing children. e
reduced new energy available from the push- o makes the use of a
pendulum gait pattern almost impossible.79 As energy generation
(concentric muscle contractions), pendulum dynamics, and spring
dynamics are the only dynamic resources that are potentially avail-
able, and energy generation and pendulum dynamics are severely
restricted, it follows that forward progression can only be main-
tained by increasing the amount of energy available from spring
dynamics. Consequently, it should be no surprise that children
with spastic diplegia tend to adopt a gait that is more similar to
running (a bouncing pattern) than walking as spring dynamics are
predominant in running whereas pendulum dynamics are predom-
inant in walking.
e increase in energy available via spring dynamics is the result
of increased stiness of the legs due to co- contraction of the exors
and extensors of the hips, knees, and ankles and an equinus foot
position (plantar exed ankles). e increase in energy available via
spring dynamics is the result of the body being projected upwards
following each bounce which increases the amount of gravitational
potential energy available at mid- stance (relative to normal walk-
ing) and, even allowing for loss of strain energy as heat during the
subsequent compression phase of the lead leg, results in sucient
energy being returned to maintain forward progression. e boun-
cing gait requires a higher level of energy expenditure than normal
walking, but it is reasonable to assume that such a gait is optimal in
relation to the dynamic resources available. ere is evidence that
the eciency of the bouncing gait is increased over time by adap-
tive morphological changes that increase the tendon length:muscle
length ratio in the leg extensor muscles which, in turn, increases
the resilience of the muscle- tendon units and, therefore, reduces
the amount of energy that is lost.84
Traditional therapy for such gait abnormalities has been directed
at normalizing the abnormal kinematics. For example, attempts
have been made to reduce the equinus foot position in children
with spastic diplegia by electrical stimulation of the tibialis anter-
ior (to dorsiex the ankle), but such intervention has been largely
unsuccessful.44,85 From a dynamical systems perspective, the lack of
success of traditional therapy is not surprising; all of the abnormal
joint movements in an abnormal gait will be the result of a particu-
lar coordinative structure and, consequently, all of the abnormal
joint movements will be symptoms of the abnormal individual
constraints in the form of abnormal dynamic resources. e corol-
lary is that therapy directed at normalizing the abnormal dynamic
resources is likely to be more eective than therapy directed at nor-
malizing the abnormal kinematics. ere is evidence in support of
this view. For example, electrical stimulation of the gastrocnemius-
soleus group to improve the push- o in children with spastic diple-
gia (which might have been expected to worsen the equinus gait)
has been shown to result in a more normal gait that included a nor-
mal heel strike.86,87 e implication of these ndings is that normal-
izing the dynamic resources results in a more normal coordinative
structure which, in turn, produces a more normalgait.
Conclusions
From a dynamical systems perspective, coordination of human
movement emerges from the intrinsic self- organizing properties
of the dynamical system consisting of the individual, the task, and
the environment. Self- organization refers to the spontaneous inte-
gration of the dynamical properties of the subsystems (individual,
task, and environment) and results in the spontaneous establish-
ment of a coordinative structure, which is a relatively stable pattern
of phase relations and joint kinematics when performing the task.
ere is considerable evidence that coordinative structures are self-
optimized in relation to optimality criteria to which the individual
is sensitive. e main optimality criterion would appear to be a pro-
pensity to minimize energy expenditure in such a way that a well-
practised pattern of movement that appears abnormal is likely to
be optimal in relation to the dynamic (energy) resources available
to the individual. Consequently, therapy directed at normalizing
the abnormal dynamic resources is likely to be more eective than
therapy directed at normalizing joint kinematics.
Summary
◆ e brain coordinates and controls movement via muscular
activity. Coordination refers to the timing of relative motion
between body segments, and control refers to the optimization of
relative motion between body segments.
◆ e development of coordination has been viewed historically
from two viewpoints: the neuromaturational perspective (in
relation to motor development in children) and the information-
processing perspective (in relation to motor learning in adults).
However, these approaches fail to account for the great exibility
demonstrated by individuals in accommodating rapidly chang-
ing task demands.
◆ e deciencies of the neuromaturational and information-
processing perspectives were highlighted by Bernstein.15 He
pointed out that all joint movements are the result of active (mus-
cle) and passive (motion dependent, gravitational, and external)
components of joint moments (collectively referred to as joint
biodynamics), and that coordination results in utilization of the
passive components to minimize energy expenditure.
◆ Bernstein’s biodynamical approach was a major inuence on the
increasingly widely held dynamical systems view of the devel-
opment of coordination. From a dynamical systems perspective,
coordination of human movement emerges from the intrinsic
self- organizing properties of the dynamical system consisting of
the individual, the environment, and thetask.
◆ Self- organization refers to the spontaneous integration of the
dynamical properties of the subsystems (individual, environ-
ment, and task) and results in the spontaneous establishment
of a coordinative structure within and between the subsystems.
PART 1 40
is, in turn, results in a pattern of movement. e actual pat-
tern of movement that emerges depends upon the state of the
subsystems that impose constraints on the types of movement
that may emerge; the constraints arise from the anthropometry
and functional ability of the individual (individual constraints),
the requirements of the task (task constraints), and the prevail-
ing environmental conditions (environmental constraints). Each
type of constraint inuences the movement pattern that emerges
by encouraging certain types of movement and discouraging
others.
◆ ere is considerable evidence that coordination is self- optimized
in relation to optimality criteria to which the individual is sen-
sitive. e main optimality criteria would appear to be energy
expenditure and injury risk, but there is clear evidence of others,
including, for example, stability, bilateral symmetry, and shock
absorption at foot- strike in walking.
◆ Traditional therapy for gait abnormalities has been directed at
normalizing the abnormal kinematics. However, such interven-
tion has been largely unsuccessful. From a dynamical systems
perspective, the lack of success of traditional therapy is not sur-
prising; all of the abnormal joint movements in an abnormal gait
will be the result of a particular coordinative structure and, con-
sequently, all of the abnormal joint movements will be symptoms
of the underlying cause, that is, abnormal individual constraints
in the form of abnormal dynamic resources. e corollary is that
therapy directed at normalizing the abnormal dynamic resources
is likely to be more eective than therapy directed at normalizing
the abnormal kinematics. ere is increasing evidence in support
of thisview.
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