FACULTEIT GENEESKUNDE EN
GEZONDHEIDSWETENSCHAPPEN
Vakgroep Bewegings- en Sportwetenschappen
2004
Movement adaptations for maximal and submaximal execution of a vertical jump from stance
(Aanpassingen in bewegingscoördinatie bij maximale en submaximale uitvoeringen
van een verticale hoogtesprong uit stand)
Jos Vanrenterghem
Proefschrift ingediend tot het behalen van de graad van
Doctor in de Lichamelijke Opvoeding
Supervisor
Prof. Dr. D. De Clercq
Process supervisory board
Prof. Dr. D. De Clercq
Prof. Dr. M. Lenoir
Prof. Dr. P. Aerts
Collaborating expert in sport sciences
Prof. Dr. A. Lees
Examination board
Prof. Dr. G. Vanderstraeten
Dr. M. Bobbert
Prof. Dr. A. Lees
Prof. Dr. M. Van Leemputte
Prof. Dr. E. Witvrouw
Prof. Dr. R. Philippaerts
Prof. Dr. P. Aerts
Prof. Dr. M. Lenoir
Prof. Dr. D. De Clercq
Dedicated to Bart
The following manuscripts were the result of research that contributed to the
development of the present dissertation, and were published, accepted for
publication or submitted for publication:
Vanrenterghem, J., De Clercq, D. and Van Cleven P. (2001) Necessary precautions
in measuring correct vertical jumping height by means of force plate measurements.
Ergonomics, 44, 814-818.
Vanrenterghem, J., Lees, A., Lenoir, M., Aerts, P. and De Clercq D. (2004)
Performing the vertical jump: movement adaptations for submaximal jumping. Human
Movement Science, 22, 713-727.
Vanrenterghem, J., Lees, A. and De Clercq D. The effect of trunk inclination on
coordination in the vertical jump. Journal of Applied Biomechanics, submitted.
Vanrenterghem, J. Lees, A. and De Clercq D. Movement adaptations in the vertical
jump from sub-maximal to maximal performance when using an arm swing. Journal
of Sports Sciences, accepted for re-submission.
Lees, A., Vanrenterghem, J., and De Clercq D. Understanding how an arm swing
enhances performance in the vertical jump. Journal of Biomechanics, In Press.
Lees, A. Vanrenterghem, J., and De Clercq D. The benefit and energetics of an arm
swing on maximal and sub-maximal vertical jump performance. Journal of Sports
Sciences, Accepted for publication.
Lees, A., Vanrenterghem, J. and De Clercq D. The maximal and sub-maximal vertical
jump: implications for strength and conditioning. Journal of Strength and Conditioning
Research, In Press.
Contents
v
Preface
vi
Chapter 1
General introduction
1
Chapter 2
Necessary precautions in measuring correct vertical
jumping height by means of force plate measurements
15
Chapter 3
Performing the vertical jump: Movement adaptations for
sub-maximal jumping
23
Chapter 4
The effect of trunk inclination on coordination in the
vertical jump
39
Chapter 5
Movement adaptations in the vertical jump from submaximal to maximal performance when using an arm
swing
57
Chapter 6
Summary and epilogue
71
Chapter 7
Nederlandse samenvatting
85
Chapter 8
Appendices
91
Acknowledgements / Dankwoord
95
Preface
vi
Dear reader,
Prior to the reading of this preface, you as reader opened this dissertation without
having to think about how to do so. A large number of body segments were involved
in this movement. Each segment has its own mass distribution, density and inertia
and each joint has a certain freedom of movement. The whole is held together and
also moved by ligaments and skeletal muscles. Thinking of each muscle as an
employee, it is easy to understand that organising the collaboration between muscles
requires a major managing task.
Reading this might slowly convince you that the human body has an unknown
complexity. Also movements of this body are limited due to some specific features.
One such feature is that movements of the body are mainly caused by the rotation of
segments, whereas most of the movements pursue translation. These rotations have
a specific set of degrees of freedom at each joint, leading to an endless number of
possibilities for moving the system. As such, all the above demonstrates the
wonderful ease and precision with which humans execute highly complex skills like
opening the first page of this book.
The vertical jump is another such movement which any healthy human can execute
and at first sight seems very simple. However, the vertical jump requires balancing on
the forefoot and at the same time pushing the body upward with high effort. The
simulation of such vertical jump takes hours of calculations with the present
knowledge on the ‘moving human body’. This might be reflected in months of practice
by a child to gain the necessary coordination for a vertical jump. However, the
comparison fades when the initial condition of the target of the movement is
changed. For each change, the simulation asks for all calculations to be re-done
whereas the human succeeds in immediate adaptations – and with apparent ease –
to counteract or implement the alteration.
The way in which these movement adaptations occur has not been clarified until now
and this issue forms the main theme of this dissertation.
Chapter 1
General introduction
General introduction
1
Chapter 1
General introduction
2
1. Aim of the present study
It is fascinating how humans are able to execute a wide variety of movements with
high precision and efficiency. We can execute very refined tasks like writing
(Hollerbach, 1978 ; Viviani and Terzuolo, 1980) or throwing (Chowdhary and Challis,
1999 & 2001 ; Jöris et al., 1985 ; Neal et al., 1991) with the utmost precision and
speed. We can also execute gross-motor tasks like walking or jumping (AragonVargas and Gross, 1997b) in a controlled way. However, humans are usually not the
specialists in individual disciplines when compared with other animals but are in most
cases average performers (many other predators run faster, jump higher or are better
swimmers). It is the huge diversity of refined and gross-motor abilities – that is, being
a generalist (Van Damme et al., 2002) – that seems to be of benefit and helps us
organise life satisfactorily (putting aside the inability to fly). Investigating these
qualities was, and still is, the driving force for numerous scientific studies.
Like walking and running, the vertical jump is part of the overall motor development of
the child (Jensen et al., 1994). It is a movement that is executed in many sports
activities without depending on particular sports techniques. Therefore, jump
movements are commonly used as a part of the sports-medical support to measure
overall power of the lower extremities (Bosco and Komi, 1979 ; Dowling and Vamos,
1993 ; Hunter and Marshall, 2002 ; Sayers et al., 1999) and as a training component
for improving that power (Bobbert et al., 1987b ; Bobbert, 1990).
Despite the ease with which a vertical jump is executed, it is a movement consisting
of a complex interaction of the lower extremities by extension in mainly three joints,
that is, hip, knees and ankles, and involving the activity of large muscle groups like
glutei, quadriceps, hamstrings and ankle plantar flexors (Bobbert and van Ingen
Schenau, 1988 ; Bobbert and van Soest, 2001). That interaction has been explicitly
studied through many variations of the maximal vertical jump, such as:
• the vertical jump with and without a countermovement (Anderson and Pandy,
1993 ; Bobbert et al., 1996 ; Bosco and Komi, 1979 ; Fukashiro and Komi,
1987 ; Gollhofer and Kyröläinen, 1991 ; Harman et al., 1990 ; Kubo et al.,
1999);
• the vertical jump with and without extra weights (Eloranta, 1996 ; Gollhofer
and Kyröläinen, 1991 ; Gollhofer et al., 1992);
• the vertical jump with and without the use of an arm swing aiding the
enhancement of jump height (Feltner et al., 1999 ; Harman et al., 1990 ; Lees
et al., accepted for publication);
• the vertical jump of adults compared with children (Jensen et al., 1994);
• good performance compared with weak performance (Aragon-Vargas and
Gross, 1997a ; Dowling and Vamos, 1993), and,
• comparison between sports related variations of the jump (Coutts, 1982 ; Ravn
et al., 1999).
Chapter 1
General introduction
3
Knowledge regarding mainly the maximal performance in the human vertical jump
has been gathered through these investigations. This knowledge describes how
specific body-related and movement-related properties produce maximal
performance through optimal interaction.
The most important body-related properties within the context of maximal vertical
jumping are the number of joints that a muscle spans (van Ingen Schenau et al, 1987
; van Ingen Schenau, 1989 ; van Soest et al., 1993), length and velocity of muscle
contraction (Hill, 1938 ; Bobbert et al., 1987 ; Fukashiro et al., 1995 & 2001 ; Huijing,
1998), muscle-tendon length ratio (Finni et al., 2000 ; Gollhofer et al., 1992),
physiological cross section of a muscle (van Soest and Bobbert, 1993) and the inertia
of individual segments (Jöris et al., 1985 ; van Ingen Schenau, 1989). Movementrelated properties are the geometric and anatomical limitations of segments
transferring rotation into translation (van Ingen Schenau, 1989), the large number of
degrees of freedom in the jumping movement (Bernstein, 1967) and the necessary
occurrence of ineffective movement in order to reach a certain performance goal.
Maximal jump coordination depends on, and seems to be weighed down by, the
above properties. Previous investigations on maximal vertical jumping have
demonstrated segmental motions that seem to deal with each of these properties and
result in the most optimal coordination. Experimental research does not allow the
conclusion that it actually is the most optimal coordination. Therefore, physical
models (Bobbert et al., 1987a ; Vanrenterghem and De Clercq, 1997) and computer
models (Anderson and Pandy, 1993 & 1999 ; Pandy et al., 1990 ; Pandy and Zajac,
1991 ; Spägele et al., 1999a & b ; van Soest et al., 1993) were developed to gain
more insight into the role of each of these factors. This type of research reported that
the influence of each factor on the movement was optimally accounted for in order to
achieve maximal performance. Movement control and coordination approximate the
mathematical optimum pattern by a characteristic proximo-distal movement
sequence.
This proximo-distal sequence consists of an earlier extension of more proximal
segments (e.g., trunk segment) than more distal segments (e.g., foot segment) and
has been found in jumping, running and throwing movements (Jöris et al., 1985;
Bobbert and van Ingen Schenau, 1988). Despite the differences between these
movements, each involves a ballistic task in which the body or another object is to be
accelerated from a low to a high velocity. In order to achieve this mechanical goal the
proximo-distal movement sequence has the advantage of (i) optimal use of biarticular muscles by accelerating the extension of distal segments through
decelerating the extension of proximal segments, (ii) optimal lengths and low
velocities of muscle fibre contractions, (iii) optimal use of the long tendons in distal
muscles by a pre-loading which is built up through slow contractions in proximal
muscles having short tendons, (iv) slow rotations of proximal segments with a high
inertia and fast rotations of distal segments with a low inertia and (v) maximal
movement effectiveness by achieving the mechanical goal (as potential and vertical
kinetic energy) through effective muscle work. Summarized, the proximo-distal
movement sequence results in a longer ground contact phase, advantageous muscle
activation for force- and work-production, and the reduction of ineffective movements
(Bobbert and van Soest, 2001).
Chapter 1
General introduction
4
In particular, this reduction of ineffective movements through the proximo-distal
movement sequence is an intriguing result and can be approached from two points of
view. From a purely mechanical approach, ineffective movements are movements
that do not contribute to the goal of the task. In a vertical jump, these ineffective
movements contain rotation of segments, horizontal translation of segments, and
opposite movements of segments relative to the vertical position of the body center of
mass. It is wishful that at the time of take off ineffective movements are minimised
and effective movements (vertical translation) are maximised. Therefore, the ratio
between effective movement and the sum of the effective and ineffective movement
has been used as the efficacy ratio in order to quantify this mechanical effectiveness
of a vertical jump (Bobbert and van Soest, 2001). This approach, however, has the
limitation that the energetic changes of the system prior to the energetic state at take
off are strictly not taken into account. Such, similar efficacy ratios at take off can be
reached, regardless of the size of the countermovement amplitude preceding the
push off. Nevertheless, the muscle work in order to perform a deep
countermovement is expected to exceed that of a minimal countermovement,
because elastic energy storage in the downward phase is not accompanied by full
recovery in the upward phase and replacing the dissipated energy by extra muscle
work is then required. Also, muscle architecture is expected to influence muscle work
when different strategies are used to reach a certain energetic state at take off. The
most important architectural characteristic of leg muscles is the difference in
contractile component length and tendon length between proximal and distal
muscles, such that proximal muscles have relatively short tendons while distal
muscles have long elastic tendons. A number of studies have estimated that using
distal muscles in a movement like the vertical jump requires less muscle work –
consequently less ATP hydrolysis and therefore less physiological input – than using
proximal muscles (Alexander and Ker, 1990). It has been suggested that the
observed movement strategies generally correspond to the strategy that optimises
the use of this advantageous muscle architecture in distal muscles (e.g. running,
hopping, walking).
This leads to the second approach to study ineffective movements, namely the
physiological approach. In physiological literature, the term efficiency has been used
to express the amount of mechanical output from a system (e.g. distance travelled,
movement speed) relative to the amount of physiological input that has been fed into
that system (e.g. oxygen uptake). According to Winter (1990), reduced efficiency can
be caused by (i) superfluous co-contractions of antagonists countering contractions
of agonists, (ii) isometric contraction against gravity, (iii) energy production in one
joint while energy is absorbed in another joint and (iv) jerky or unsmooth movements.
Modern techniques have allowed scientists to estimate both these factors as well as
oxygen uptake in order to quantify this efficiency in cyclic movements like walking,
running or cycling. However, for a discrete movement like the single vertical jump –
which only takes one breath – this has not yet been possible.
Returning to our single vertical jump, it was thought that by using a specific
coordination – i.e. a proximo-distal movement sequence – maximal effectiveness and
maximal performance are both pursued, if not achieved. However, it has never been
investigated whether maximal effectiveness has the same role in determining the
coordination of a vertical jump in which maximal performance is not pursued, i.e., in a
sub-maximal jump.
Chapter 1
General introduction
5
Besides effectiveness, another mechanism has been put forward in the literature.
This mechanism consists of performing the movement in a slow motion of the
maximal execution by reducing the muscle activation levels and increasing the time
duration. Such a mechanism is attractive on the control level and has been found in
swimming motions of Lamprae larvae (Boyd and McClellan, 2002). However, it
seems rather difficult in vertical jumping, considering the presence of gravitational
forces acting on the body on land compared to underwater swimming. Van Zandwijk
et al. (2000) compared muscular control in maximal vertical jumps and in jumps at
80% of maximal intensity and found differences in relative timing of muscle
activations. Such differences in relative timing confirmed that neuromuscular control
in submaximal jumping is not determined through a simple slowing down of motion.
The quest is open.
2. The research
The aim of the present research was to gain insight into movement adaptations for
sub-maximal performance in vertical jumping from stance. Specifically, the goal of the
movement, i.e., jump height, served as the independent variable. Therefore, the first
objective of this study was to accurately determine jump height to allow correct
interpretation of the data.
2.1. Methodology for accurate determination of jump height.
The methodology of numerical integration of acceleration signals from ground
reaction force measurements has, due to its high level of accuracy, become the
standard methodology for determination of jump height in scientific investigations. As
such, the numerical integration method has been used as a reference procedure for
the evaluation of other methods like the ergometer contact mat and kinematic
techniques according to Winter, 1990 (Hatze, 1998 ; Kibele, 1998). The method of
numerical integration allows the calculation of both contact height1 and flight height2
(see figure 1.1) in the most accurate way.
1
Contact height describes the vertical displacement of the centre of mass from initial stance preceding
the jump until take off.
2
Flight height describes vertical displacement of the centre of mass from take off until the apex of the
flight.
Chapter 1
General introduction
6
Figure 1.1. Jump variables which can be calculated with the numerical integration methodology.
Despite the accuracy of this method, some uncertainties noted in the literature and
personal experiences in the laboratory have identified varying sources of error that
can lead to erroneous calculation of variables. These sources of error are (i) the
determination of body mass, (ii) the determination of moment of take off, (iii) the
integration frequency and (iv) the initial conditions and their consequences for the
determination of the start of the movement. In experimental measures, these sources
of error cannot be isolated as each one has its influence on others, e.g., integration
frequency influences the precision of determination of the instant of take off. It was
therefore found necessary to develop a theoretical model. This model was a
succession of both sinusoidal and linear equations representing a realistic ground
reaction force pattern for the standing countermovement jumps. Subsequently, the
resulting pattern could be integrated analytically and numerically to calculate jump
height variables (figure 1.1). Comparison between both integration methods,
combined with the theoretical introduction of sources of error allows the analysis of
isolated sources of error. This analysis would lead to the development of a method in
which the influence of each source of errors on the calculation of jump height
variables is minimized. The most accurate measurement of jump height was to be the
goal.
2.2. Insights into movement adaptations for maximal and sub-maximal jumps
A correct determination of jump height allows the investigation of movement
adaptations in maximal and sub-maximal vertical jumps. In a sub-maximal jump, the
interaction between segments could theoretically result in an indefinite number of co-
Chapter 1
General introduction
7
ordination patterns. This leads to a crucial question in biomechanics, and to the
second objective of this study: How does the neuromuscular system control a submaximal vertical jump?
A first possibility is that the neuromuscular system performs a slow motion version of
maximal execution, i.e. by reducing the amplitude of muscle stimulation and
increasing its duration. However, as was described above, neuromuscular control in
sub-maximal jumping is not determined through a simple slowing down of motion.
A second possibility is that the neuromuscular system takes into account the criterion
of minimising the energy requirements relative to the achieved performance. This
criterion is referred to by using the term ‘movement effectiveness’. The muscular
system directly profits from high movement effectiveness, and several hypotheses
can be formulated to explain how. These hypotheses are related to the properties
inherent in the human musculo-skeletal system. One of these properties is the
preferred use of a countermovement prior to extension. The countermovement is
required to build up kinetic energy during the contact phase, but a larger
countermovement causes a greater potential energy reduction before a rise of the
centre of mass position above that at stance can occur. Jumping for a low height is
therefore hypothesised to involve a smaller countermovement than when jumping for
maximal height. Another property of the human musculo-skeletal system is the high
rotational inertia of proximal segments compared with that of distal segments. The
angular velocity of segments determines, and is indispensable for, the translational
velocity of the centre of mass. Nevertheless, rotation of proximal segments involves
higher rotational energies than that of distal segments, therefore reducing rotation of
proximal segments when jumping for a low height would minimise the ineffective
energy expenditure. Thus, it is hypothesised that for low jumps rotation of proximal
segments is reduced to a minimum. A third property of the musculo-skeletal system
that can influence movement effectiveness is the horizontal orientation of the foot
segment in the anatomical position, as in standing still prior to the jump. This is
advantageous as the ankle is already partially flexed in the initial stance phase. The
necessary flexion prior to extension is therefore required less than in the knee and
hip joints (the hip can hyperextend from the anatomical position but this would not
lead to a rise of the centre of mass). It is hypothesised that work done in ankle
extension is an important contributor to the jump at all heights.
2.3. The role of forward inclination of the trunk
Different theories were proposed to explain the true origin of the proximo-distal
movement sequence. The earliest theory explained that all muscles are activated
simultaneously, and that the downward inertial forces from proximal segments on
distal segments mechanically impose the sequential extensions (Hudson, 1986). This
theory was refuted by Bobbert and van Ingen Schenau (1988) and later by Pandy
and Zajac (1991). The latter authors observed a sequenced movement strategy
originating from an intrinsic proximo-distal activation pattern and stated that due to
the forward inclination of the trunk at the start of the propulsive phase, only a
proximo-distal movement strategy would prevent the body from achieving an
undesirable ventral rotation. The orientation of the trunk at the start of the upward
movement seems to play a crucial role for the coordination of the jump. It is expected
to cause the typical proximo-distal movement sequence, but also would it cause a
Chapter 1
General introduction
8
limited contribution of the knee joint due to its postponed extension awaiting the
initiation of hip extension.
The purpose of this part of the research – and third objective of the study – was to
gain more insight into the relationship between the forward inclination of the trunk
and the mechanical output in the lower limb joint during a vertical jump. It was
hypothesised that restricting the forward inclination of the trunk in a maximal vertical
jump will adversely affect performance due to restricted hip action, but involve
adaptations to the coordination of the movement such that knee extension is no
longer restricted. Thus, it was also hypothesised that in sub-maximal jumping with
restricted trunk inclination the knee rather than the ankle would take over the role of
the restricted hip in controlling jump height. Namely, the ankle joint was expected to
remain maximal in its contribution, based on the advantageous functional morphology
of the ankle joint.
2.4. Influence of using an arm swing on movement adaptations in the vertical jump
from sub-maximal to maximal performance
The investigation of criteria that determine movement adaptations in maximal and
sub-maximal vertical jumps can provide insights in the control of a discrete ballistic
movement, as explained above. However, the results from such investigations do not
allow immediate extrapolation to the control of other similar movements, even if it
was an alteration of the vertical jump. Such alteration is the vertical jump with using
an arm swing to enhance performance.
The arm swing is a natural part of many jump activities in sports and although the
arms influence performance by about 10% in maximal jumping, the mechanisms
explaining how this might occur have only recently been given attention (Lees et al.,
accepted for publication). In that study it was shown that the complex interaction
between the arms and the rest of the body when using an arm swing consists of
several phases in which energy is exchanged between the arms and the rest of the
body. However, it is not known to what extent the arm swing is used to aid submaximal jumps. Also, given the large energy transfers which occur when using an
arm swing to aid jump performance, it is not known if previously found movement
adaptations for sub-maximal jumping without using an arm swing continue to be
used. The fourth objective of the study, then, was to investigate to what extent
subjects use an arm swing in sub-maximal vertical jumping and to test whether
movement adaptations in sub-maximal jumps without an arm swing still hold in this
more natural execution of the movement with arm swing.
3. Summary
The main aim of the present study was to investigate movement adaptations for submaximal and maximal executions of a discrete ballistic movement. Due to several
reasons, the vertical jump was found appropriate for this. To allow for an accurate
determination of the goal of the jumping movement – i.e., jump height – the first
objective was to conduct an error analysis to validate and further develop the most
advanced measuring method for jump height determination (Chapter 2). While
utilising this new method, the second objective was to study movement adaptations
for sub-maximal and maximal vertical jumping (Chapter 3). Then, the third objective
Chapter 1
General introduction
9
of the study was to gain more insight into the role of the forward inclination of the
trunk in vertical jumping and in movement adaptations for sub-maximal jumping
(Chapter 4). Finally, the fourth objective was to investigate to what extent subjects
use an arm swing in sub-maximal vertical jumping and to test whether movement
adaptations in sub-maximal jumps without an arm swing still hold in this more natural
execution of the movement with arm swing (Chapter 5).
Chapter 1
General introduction
10
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General introduction
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Chapter 2
Correct measurement of vertical jump height
15
Necessary precautions in measuring correct vertical jumping height by means
of force plate measurements.
J. Vanrenterghem, D. De Clercq and P. Van Cleven
Ergonomics, 2001, 44(8), 814-818
Chapter 2
Correct measurement of vertical jump height
16
Abstract:
The present study was designed to investigate the determination of vertical jumping
height by means of force plate measurements. Four different sources of error
influence this determination: the measurement of body mass, the determination of
take off, the integration frequency, and the assessment of the initial conditions
influencing the determination of the start of the movement. A theoretical model was
utilized to simulate the vertical ground reaction forces in vertical jumping and to
compare the outcome of analytical and numerical double integration of the vertical
acceleration of the body centre of mass. A high integration frequency and an
optimizing loop for body mass determination were found to be important and should
be taken into account when determining jumping height parameters.
Chapter 2
Correct measurement of vertical jump height
17
1. Introduction
Due to their high measuring accuracy, force plates have currently become well
established for the determination of vertical jumping height. This is commonly used
for the representation of explosive strength in sports and ergonomics applications.
The numerical integration method has been the reference procedure for the
validation of other methods like the ergometer contact mat or Dempster-like methods
(Hatze, 1998 ; Kibele, 1998). In the numerical integration method, both contact height
and flight height are jump describing parameters that can be calculated in a more
accurate way than in any other method. These parameters are defined as follows:
(a) Preceding variables to be calculated are
• vertical acceleration ay of centre of mass
ay = Fry . mB – g
•
with Fry the resulting ground reaction force, mB body mass and
g = 9.81 m.s-2, and,
respectively vertical velocity vy and vertical position y of centre of mass
calculated by numerical integration (trapezoidal rule).
(b) Contact height: the change in y from the upright standing posture to y at take off.
(c) Flight height: vy02 . (2g)-1
(vy0 = vy at take off).
2. Problem
Extensive laboratory practice and uncertainties in the literature have resulted in a
more critical view on jump describing parameters and have yielded insight into
possible sources of error. These sources of error can theoretically be divided into:
• determination of body mass (mB);
• determination of instant of take off;
• integration frequency, and,
• initial conditions and their consequences for the determination of the start of the
movement.
In experimental measures, these sources of error cannot be isolated as each one has
its influence on others, for example, integration frequency influences the precision of
determination of the instant of take off. A theoretical model was therefore developed
(see figure 2.1). A succession of both sinusoidal and linear equations represent a
realistic ground reaction force pattern for the standing countermovement jumps found
in the literature (Dowling and Vamos, 1993: pg. 98, figure 1; Bobbert and van Ingen
Schenau, 1988: pg. 255, figure 7). This theoretical model allows a straightforward
analytical double integration and a separate analysis of each source of error.
Validation of the model primarily consisted of calculating hcontact and hflight (see a-c),
respectively measuring 10 and 41.5 cm. Secondly, the comparison of integrating the
derived acceleration signals both analytically and numerically (1000 Hz) revealed
differences in parameter outcomes of less than 0.1 mm. The precision of 1000 Hz
numerical integration was assured by this validation. Therefore this analytical
Chapter 2
Correct measurement of vertical jump height
18
GRF (N)
integration of combined first degree equations was used as a golden standard
procedure to analyse isolated sources of error.
2000
1500
1000
500
0
0
0.5
1
1.5
2
Time (s)
Figure 2.1. Theoretical shape of ground reaction forces,
approximated by combined sinusoidal and linear curve intervals
(stance phase duration is not representative for the experimental
measures).
Prior to this analysis, the size of realistic – that is, frequently occurring - errors was
estimated in order to provide functional feedback.
2.1. The determination of mB
Determining body mass was based on the difference between the force levels prior to
the countermovement (average of 500 values) and during the airborne phase (Kibele,
1998). Firstly, the mB variability within one trial was estimated for 10 stance phases of
1 second by 1 subject. Averaging 500 values at shifted time steps (1000 Hz),
revealed maximally 0.3 kg – that is, 0.5% of mB – intra trial variability. In contrast, the
inter variability (between trials) was 1.3 kg or 1.7% of mB.
2.2. Instant of take off determination
Kibele (1998) reported an error of 2-3 milliseconds, whereas Hatze (1998)
determined take off with 1 millisecond accuracy. This last author sampled signals at
2000 Hz. This might explain the higher accuracy (Kibele, 1998 used 1000 Hz). For
1000 Hz measurements, an error of 3 milliseconds seems appropriate.
2.3. Integration frequency
Most contemporary laboratories measure at high frequencies, however, sampling
rates from 100 to 2000 Hz appear in the last decade’s literature (Dowling and Vamos,
1993; Aragon-Vargas and Gross, 1997; Kibele, 1998; Hatze 1998). Therefore the
influence of low measuring frequency on the results of vertical jumping height
determination was examined.
2.4. Initial conditions and start of movement determination
The assumption that both integrands (vy and y) are zero at the start of movement is
fundamental for the numerical integration method. However, defining the start of
movement in experimental measurements is less obvious than it sounds. Changes in
vy and subsequent fluctuations in y (see mB determination) preceding the start of
Chapter 2
Correct measurement of vertical jump height
19
actual jumping movement induce an obviously unclear cut off. Thereby previous
literature (Kibele, 1998; Hatze, 1998) referred to software routines without description
of the procedure. These procedures can be very complex and somehow ‘exclusively’
correct. However, a basic method with objective criteria should help the researcher in
correctly analysing start of the movement. An efficient method was proposed in this
study.
3. Methods and results
In order to take into account variability between vertical ground reaction forces of
different jumps, 10 different simulations, which all represent realistic ground reaction
force curves of standing vertical jumps, were used for the analysis of errors. Further
results show the overall test outcomes of these 10 simulations. Parameters hcontact,
hflight and htotal (= hcontact + hflight) of these 10 simulations averaged, respectively, 11.7 ±
8.0, 44.4 ± 6.9, and 56 ± 16.7 cm when analytically determined. Subsequently the
influence of each source of error was isolated and tested:
3.1. Determination of mB
Maximal deviation in htotal was 1 cm for 0.5% mB change (variability within trials). On
the other hand, when integrating over a 2 second stance phase, the correct mB
results in null displacement after 2 seconds, whereas slight deviations in mB induce
artificial displacements at the end of the 2 second period.
This observation leads to the fact that optimisation of mB to achieve null displacement
during the stance phase results in the best possible correct jump height parameters.
3.2. Initial conditions and determination of start of the movement
An optimising loop during the stance phase prior to the vertical jump was utilized,
after considering the above results concerning the determination of mB. This
optimisation results in null displacement from the start of the stance phase until after
2 seconds standing still. The initial conditions of null position and null velocity are
thereby fulfilled. Nevertheless, a criterion for start of the movement is necessary to
achieve jump time duration and other dependent parameters. Fundamental for the
time shifting criterion (1 millisecond time step) is the mean of five subsequent ground
reaction force values. This criterion shifts forward in time until the average value
exceeds the range specified by (1) the maximum + 1 SD and (2) the minimum – 1 SD
of all GRF values in the 2 second stance phase. This criterion has been used widely
in the author’s laboratory (Excel program routines can be obtained at: Kinesiology
lab, Department of Movement and Sports Sciences, Watersportlaan 2, 9000-Gent,
BELGIUM ; [email protected]).
3.3. Instant of take off determination
Both hcontact and hflight deviated 0.9 cm for a 3 millisecond misplacement of take off.
Longer jump time duration involved increased hcontact with decreased hflight measures,
offsetting each other largely and resulting in a htotal deviation of only 0.02 cm.
Chapter 2
Correct measurement of vertical jump height
20
3.4. Integration frequency
50Hz
hflight
100Hz
500Hz
hcontact
200Hz
0.04
0.04
0.03
0.03
0.02
0.02
0.01
0.01
0.00
1000Hz
Absolute difference (cm)
Figure 2.2 depicts the comparison of numerical integration at different integration
frequencies with the analytical results in the 10 simulations of the theoretical model. It
shows a high accuracy for integration frequencies higher than 100 Hz. More
variability in errors is shown at 100 Hz integration, whereas 50 Hz integration shows
considerably higher errors.
Integration Frequency (Hz)
Figure 2.2. Mean ± SD of absolute differences in hcontact and
hflight between analytical integration and integration at differing
data frequencies of 10 simulations.
4. Discussion
The theoretical model utilized in this study was appropriate for the investigation of the
role of isolated sources of error in the numerical method for jumping height
determination. The analytical double integration is insensitive to error, enabling the
comparison with differing numerical solutions or with analytical solutions when
isolated input variables are changed.
Firstly, the numerical double integration method is very sensitive to a correct body
mass determination. Even with a sound technical equipment, mB values need to be
optimised and therefore a feasible “optimisation loop” – based upon zero
displacement during stance phase – was proposed. Additionally, if more trials of the
same subject are needed – for instance when testing for a maximal performance – a
single mB value should never be used through all trials. In this study, a 1.7% mB
variability between trials was found (Kibele 1998 found less than 1% mB variability).
This variability resulted in 4.5 cm deviation in htotal, which is unacceptable for
research aims.
Secondly, an incorrect determination of instant of take off showed a large effect on
hcontact and hflight. On the other hand, scarcely any influence was found in htotal.
Moreover, this source of error is strongly related to integration frequency in
experimental measures, that is, the accuracy of determining the instant of take off
decreases – and the possibility of errors in the latter parameters grows – with lower
sampling/integration frequencies.
Finally, the algorithm for determining the start of integration needs a critical view. The
algorithm has already proved its use in numerous experimental and simulated trials,
Chapter 2
Correct measurement of vertical jump height
21
but its use could not be tested through the theoretical model. Comparing existing
methods in further mathematically and statistically based research should lead to the
development of a standard method and enable researchers to learn and understand
this one standard method.
Chapter 2
Correct measurement of vertical jump height
22
5. References
Aragon-Vargas, L.F. and Gross, M.M. 1997, Kinesiological factors in vertical jump
performance: Differences among individuals. Journal of Applied Biomechanics, 13,
24-44.
Bobbert, M.F. and van Ingen Schenau, G.J. 1988, Coordination in vertical jumping.
Journal of Biomechanics, 12, 249-262.
Dowling, J.J. and Vamos L. 1993, Identification of kinetic and temporal factors related
to vertical jump performance, Journal of Applied Biomechanics, 16, 95-110.
Hatze, H. 1998, Validity and reliability of methods for testing vertical jumping
performance. Journal of Applied Biomechanics, 14, 127-140.
Kibele, A. 1998, Possibilities and limitations in the biomechanical analysis of
countermovement jumps: A methodological study. Journal of Applied Biomechanics,
14, 105-117.
Chapter 3
Maximal and sub-maximal jumping
23
Performing the vertical jump: Movement adaptations for sub-maximal jumping
J. Vanrenterghem, A. Lees, M. Lenoir, P. Aerts and D. De Clercq
Human Movement Science, 2004, 22, 713-727
Chapter 3
Maximal and sub-maximal jumping
24
Abstract:
The purpose of this study was to gain insight into the kinematics and kinetics of the
vertical jump when jumping for different heights and to investigate movement
effectiveness as a criterion for movement control in sub-maximal jumping. In order to
jump high a countermovement is used and large body segments are rotated, both of
which consume energy which is not directly used to gain extra jump height. It was
hypothesised that the energy used to reach a specified jump height is minimised by
limiting the ineffective energy consumed. Standing vertical jumps attempting 25%,
50%, 75%, and 100% of maximal height were performed by a group of 10 subjects.
Force and motion data were recorded simultaneously during each performance. We
found that jump height increased due to increasing vertical velocity at take off. This
was primarily related to an increase in countermovement amplitude. As such, flexion
amplitude of the hip joint increased with jump height whereas ankle and knee joint
flexion did not. These findings revealed that for sub-maximal jumping a consistent
strategy was used of maximising the contribution of distal joints and minimising the
contribution of proximal joints, thus supporting the hypothesis. Taking into account
the high inertia of proximal segments, the potential energy deficit due to
countermovement prior to joint extension, the advantageous horizontal orientation of
the foot segment during stance and the tendon lengths in distal muscles, it was
concluded that movement effectiveness is a likely candidate for the driving criterion of
this strategy.
Chapter 3
Maximal and sub-maximal jumping
25
1. Introduction
The coordination of a maximal vertical jump from stance is very similar among
individuals. This stereotyped execution of a maximal vertical jump is purported to be
the result of optimising neuromuscular control through which one optimal solution for
maximal jump height is reached (Bobbert and van Ingen Schenau, 1988; Hatze,
1998). This optimal solution typically shows a proximal-to-distal sequence of
segmental motions (Bobbert and van Ingen Schenau, 1988) and as a consequence:
(a) the subject is able to keep contact with the ground until hip and knee joints are
nearly extended (van Ingen Schenau, 1989), (b) mono- and bi-articular muscles have
an optimal interaction throughout the movement (Bobbert and van Soest, 2001; van
Ingen Schenau et al., 1987), (c) restrictions of both geometrical and anatomical
constraints are minimised (van Ingen Schenau, 1989), and (d) the amount of
ineffective energy at take off is kept low (Bobbert and van Soest, 2001).
However, the control of a sub-maximal performance theoretically allows for infinitely
many solutions and a basic question arises: How does the neuromuscular system
control a sub-maximal vertical jump? A first possibility would be that the
neuromuscular system performs a slow motion version of maximal execution, that is,
by reducing the amplitude of muscle stimulation and increasing its duration. This type
of strategy is attractive on the control level and has been found in swimming of
lamprey larvae (Boyd and McClellan, 2002). However, it seems rather difficult in
vertical jumping, considering the nature of the gravitational forces acting on the body.
Van Zandwijk et al. (2000) compared muscular control in maximal vertical jumps and
in jumps at 80% of maximal intensity and found differences in the relative timing of
muscle activations. Such differences in relative timing confirmed that neuromuscular
control in sub-maximal jumping is not determined through simple slowing down of
motion.
Another possibility is that the neuromuscular system takes into account a certain
control criterion. One such criterion is that the energy requirements relative to the
achieved performance are kept minimal. We refer to this criterion using the term
‘movement effectiveness’. The muscular system directly profits from a high
movement effectiveness, and several hypotheses exist that explain how. These
hypotheses are related to the properties inherent in the human musculo-skeletal
system. One of these properties is the requirement of a countermovement prior to
extension. The countermovement is required to build up kinetic energy during the
contact phase, but a larger countermovement causes a greater potential energy
reduction before a rise of the centre of mass position above that at stance can occur.
Jumping for a low height is therefore hypothesised to involve a smaller
countermovement than when jumping for maximal height. Another property of the
human musculo-skeletal system is the high rotational inertia of proximal segments
compared to that of distal segments. The angular velocity of segments determines
and is indispensable for the translational velocity of the centre of mass. Nevertheless,
rotation of proximal segments involves higher rotational energies than that of distal
Chapter 3
Maximal and sub-maximal jumping
26
segments, and therefore reducing rotation of proximal segments when jumping for a
low height would minimise ineffective energy expenditure. Thus, it is hypothesised
that for low jumps rotation of proximal segments is reduced to a minimum. A third
property of the musculo-skeletal system that can influence movement effectiveness is
the horizontal orientation of the foot segment in the anatomical position, as in
standing still prior to the jump. This is advantageous as the ankle is already partially
flexed in the initial stance phase. The necessary flexion prior to extension is therefore
required less than in the knee and hip joints (the hip can hyperextend from the
anatomical position but this would not lead to an elevation of the centre of mass). It is
hypothesised that work done in ankle extension is an important contributor to jump
height.
The first purpose of this study was to gain insight into the kinematics and kinetics of
jumps ranging from a minor hop to a maximal jump. A purely mechanical analysis in
terms of work done by net joint moments and segment energies was expected to
provide this insight. Such analysis knows some limitations (e.g., it is not possible to
detect storage of energy during countermovement, it is not possible to provide
information on the metabolic energy consumption…) but was expected to provide
data for the second purpose of this study. The second purpose of this study was to
test several hypotheses which propose movement effectiveness as a criterion for the
observed movement control. It was hypothesised that in sub-maximal jumping an
increase of jump height involves: (1) an increase of the countermovement, (2) an
increase of the rotation of proximal segments and (3) a high contribution from the
ankle joints in all jump conditions. The authors believe that such movement
adaptations would likely involve metabolic consequences. However, practically the
assessment of metabolic energy in single jumps is impossible with currently available
knowledge.
2. Methods
2.1. Participants and test procedures
Ten proficient male volleyball players (age 22.8 ± 3 y, height 1.84 ± 0.04 m and body
mass 77.9 ± 6.5 kg) participated in this study. All were fit and injury free and each
gave informed consent according to the ethical guidelines laid down by the University
Ethics Committee. Prior to the tests, all participants were accustomed to performing
arms akimbo countermovement jumps at maximal and sub-maximal intensities. A
standard warm-up routine, consisting of moderate jumping and stretching, preceded
the actual tests. The actual tests consisted of executing three countermovement
vertical jumps from stance (arms akimbo) at maximal intensity. The trial with highest
total jump height (determined according to Vanrenterghem et al., 2001) represented
maximal performance. Subsequently, sub-maximal jump conditions were set at 75%,
50% and 25% height of the latter reference height. A thin rope placed above the
head of the participant served to accurately guide each jump for each specific submaximal condition by jumping until a slight touch of the rope was felt with the top of
the head. The participants performed three jumps for each sub-maximal condition.
Two jumps per condition were selected for analysis, based on (i) closest achievement
of the specific jump height and (ii) balanced landing on the force platform. The data
set thus existed of 10 (participants) x 4 (conditions) x 2 (trials). For brevity, a jump
Chapter 3
Maximal and sub-maximal jumping
27
condition with higher jump performance will be indicated below as the ‘higher jump
condition’.
2.2. Data collection
Landmarks were placed on the skin according to Bobbert and van Ingen Schenau
(1988). These landmarks defined the two-dimensional position of proximal and distal
extremities of four body segments: feet, lower legs, upper legs (left and right
members were taken as one segment), and head-arms-trunk (referred to as HAT).
Inertial properties for each segment were used as in Plagenhoef et al. (1983). The
jumps were filmed sagittally from one side with a NAC High Speed video camera
operating at 200 Hz. All jumps were performed from standing with both feet on a
calibrated Kistler force platform (type 9281 B11). Vertical and horizontal components,
and point of application of the summed ground reaction force were recorded and
sampled at 1000 Hz.
2.3. Data reduction
Position data were digitised with APAS system (Ariel Performance Analysis System,
USA), and smoothed using a Butterworth fourth order recursive filter with padded end
points (Winter, 1990). Cut-off frequency was based on a residual analysis and
qualitative evaluation of the data, and set at 5 Hz for shoulder, hip and calculated
HAT positions and at 8 Hz for other positional data. Derivatives were attained
numerically. The vertical ground reaction force component was analysed according to
Vanrenterghem et al. (2001), giving spatial and temporal characteristics of the jumps
as defined in figure 3.1. Subsequently ground reaction force signals were reduced to
200 Hz and synchronised in time with kinematic data, based on a flash light placed in
the camera view and simultaneously sending out an electronic pulse.
Figure 3.1. Sketch of discrete variables describing general characteristics of the
standing vertical jump.
Chapter 3
Maximal and sub-maximal jumping
28
2.4. Kinematics and kinetics
Mean diagrams of joint angles, joint moments and segmental energies as a function
of time were calculated after synchronisation of individual data on the instant of take
off. We respected the absolute time scale of curves because changes in jump height
induced changes in time duration. Net joint moments and powers were calculated
using standard inverse dynamics procedures (Winter, 1990). Joint powers were
integrated relative to time during the ascent phase – i.e., from deepest position of the
centre of mass until take off – to calculate the positive work done at each joint.
The segmental energy analysis consisted of the calculation of the four energy
components of each segment throughout the jump:
Esegment = m g h + ½ m vz2 + ½ m vy2 + ½ I ω2
with respectively potential energy, linear vertical kinetic energy, linear horizontal
kinetic energy and rotational kinetic energy: m = segment mass; I = segment moment
of inertia; g = acceleration due to gravity; h = vertical distance of segment centre of
mass relative to the initial position of body centre of mass; vz, vy = velocity of
segment centre of mass respectively in vertical and fore-aft direction; and ω =
segment angular velocity. Energy components out of the sagittal plane were
assumed to be negligible compared to those in the sagittal plane.
2.5. Statistics
One-way ANOVA, complemented with post-hoc Tukey tests, was used for
establishing differences between conditions (significance level p<0.05). When
differences were found, these were then tested to identify whether changes of
variables were related to changes in jump height: both variable and jump height were
first normalised relative to its maximal value (i.e., average of trials in the maximal
jump condition) and then a paired students’ t-test (two-tailed) determined differences
between normalised variable and normalised jump height. This revealed a linear
relation when no difference was found (significance level p<0.05). Greater
understanding was then gained through closer interpretation of the linear regression
between the normalised variable and normalised jump height.
3. Results
3.1. General insights in sub-maximal jumping
Changes in jump height (htotal) mainly resulted from a change in flight height (hflight)
rather than by a change in upward displacement at take off (∆hcontact). The ∆hcontact
mainly represented ankle plantar flexion at take off (Figure 3.2b) and differed
significantly between conditions (Table 3.1), but post-hoc tests revealed that this was
only between the 25% and 100% conditions. The hflight – caused by higher vertical
velocities at take off – increased with increasing htotal ([ Nhtotal = 0.77 Nhflight + 0.23 ];
R² = 0.991, N = normalised relative to its maximal value). Therefore hflight was used
as the independent variable to test whether variables change in relation to the height
Chapter 3
Maximal and sub-maximal jumping
29
jumped.
Table 3.1. Mean and standard deviation of body centre of mass displacement for countermovement (hcountermovement), contact
height (∆hcontact), flight height (hflight), and the sum of the latter two (htotal) and mean and standard deviation of time duration of
descent phase (tdescent), ascent phase (tascent) and the sum of the latter two (ttotal) in the four jump conditions. P-values indicate
differences between jump conditions (One-way ANOVA, level of significance at 0.05).
25%
50%
75%
100%
hcountermovement (m)* -0.05 ± 0.02 -0.13 ± 0.04 -0.21 ± 0.04 -0.32 ± 0.06
0.10 ± 0.02 0.12 ± 0.01 0.12 ± 0.02 0.12 ± 0.02
∆hcontact (m)*
hflight (m)
0.03 ± 0.01 0.14 ± 0.02 0.25 ± 0.03 0.34 ± 0.04
htotal (m)
0.13 ± 0.02 0.25 ± 0.03 0.36 ± 0.03 0.46 ± 0.03
ttotal (s)
0.51 ± 0.13 0.78 ± 0.16 0.79 ± 0.11 0.92 ± 0.16
0.31 ± 0.15 0.56 ± 0.13 0.57 ± 0.09 0.64 ± 0.10
tdescent (s)
tascent (s)
0.20 ± 0.04 0.21 ± 0.04 0.23 ± 0.04 0.28 ± 0.06
* relative to standing height
P
<0.001
0.013
<0.001
<0.001
<0.001
<0.001
<0.001
The increased hflight in the higher jump conditions was built up through an increase of
countermovement excursion (hcountermovement: t-test for comparison of normalised
values: t(9)= -0.06, p = 0.955; linear regression between normalised values: R² =
0.811). The entire contact phase (ttotal) lengthened with hflight (linear regression: R² =
0.637), and when divided into tdown (descent) and tup (ascent), both phases
lengthened with hflight (R² = 0.621 and R² = 0.430, respectively), but none of these
timing variables showed a linear relation to hflight (t-tests: p < 0.001).
a
b
Figure 3.2. Stick figures representing body configurations at (a) time of
deepest position of the body centre of mass and (b) at time of take off. Thicker
lines represent higher jump conditions, defining 25%, 50%, 75% and 100%
jump conditions, respectively.
Chapter 3
Maximal and sub-maximal jumping
30
3.2. Detailed exploration of kinematic and kinetic adaptations
Figures 3.3, 3.4 and 3.5 represent a selection of kinematic and kinetic curves. Figure
3.3 starts from stance, the other figures start from the beginning of the ascent phase
– i.e., the lowest position of body centre of mass. From the neutral standing position,
each joint flexed during descent and extended during ascent (Figure 3.3). Variability
of joint flexion excursion, expressed through coefficient of variation, describes
consistency of inter-limb coordination and was 12.1%, 11.0% and 20.5% in the
maximal jump condition for hip, knee and ankle flexion excursion, respectively. This
was similar in the 75% and 50% jump conditions. It was higher in the 25% jump
condition (33.0%, 47.6%, 53.9%) but standard errors approximated those in the
higher jump conditions and still indicated a certain consistency in inter-limb
coordination. This consistency was also found in the variations of curves that are
presented further in this study, but variations were omitted from the figures to aid
clarity. Flexion amplitudes of joints offer an indirect exploration of the
countermovement excursion (see above). The hip flexion amplitude increased with
hflight (t(9) = -1.12, p = 0.268, clearly observed in figure 3.2a, R² = 0.823). Knee and
ankle flexion amplitudes did not increase with hflight (t(9) = -8.85 and -8.52,
respectively, p < 0.001, R² = 0.695 and 0.307, respectively) but were significantly
smaller in the 25% condition compared to the other conditions (post-hoc Tukey tests
of one-way ANOVA, p < 0.001). No significant differences were found between the
other conditions, except for significantly smaller knee flexion amplitude in the 50%
condition compared to the 100% condition (p < 0.001). Body configurations at stance
and at take off were similar in all four conditions, except that the HAT segment at
take off was less upright in higher jump conditions (Figure 3.2b; HAT angle values at
take off were 1.51 rad, 1.46 rad, 1.41 rad, and 1.35 rad, respectively, for the 25%,
50%, 75% and 100% jump conditions, F(3,10) = 31.16, p < 0.001).
Maximal and sub-maximal jumping
75%
75%
4
3
25%
2
1
-1
-0.5
50%
angle (rad)
50%
25%
-0.3
0
-0.2
knee
knee
100%
4
3
2
1
50%
25%
-1
-0.5
75%
angle (rad)
75%
-1.5
50%
25%
0
-0.3
-0.2
Time (s)
25%
-0.5
75%
angle (rad)
4
3
2
1
50%
-1
0
5
4
3
2
1
0
-1
hip
100%
75%
-1.5
-0.1
5
4
3
2
1
0
-1
Time (s)
hip
100%
0
Time (s)
Time (s)
100%
-0.1
5
4
3
2
1
0
-1
torque (N.m/kg)
-1.5
ankle
100%
torque (N.m/kg)
ankle
100%
31
torque (N.m/kg)
Chapter 3
50%
25%
0
-0.3
-0.2
Time (s)
-0.1
0
Time (s)
Figure 3.3. Averaged time curves for hip, knee and
ankle joint angles for the entire jump movement.
Thicker lines represent higher jump conditions, defining
25%, 50%, 75% and 100% jump conditions,
respectively. Evolutions of the ankle angle in the 50%,
75% and 100% strongly overlap.
Figure 3.4. Averaged time curves for hip, knee and
ankle joint moments for the upward phase of the jump.
Thicker lines represent higher jump conditions, defining
25%, 50%, 75% and 100% jump conditions,
respectively.
The amplitude of resultant joint moments (Figure 3.4) showed interesting patterns.
The peak hip joint moment increased with increasing jump height. The knee joint
moment also increased with increasing jump height, but was highest in the 75%
condition. The highest ankle joint moment occurred in the 50% condition.
Table 3.2. Mean and standard deviation of positive work done at individual joints during the ascent phase of the jump,
expressed per kg body mass. P-values indicate differences between jump conditions (One-way ANOVA, level of significance at
0.05)
W+ at ankle
W+ at knee
W+ at hip
Total
25%
1.23 ± 0.19
0.26 ± 0.21
0.09 ± 0.11
1.58
50%
1.71 ± 0.20
1.36 ± 0.36
0.60 ± 0.38
3.67
75%
1.87 ± 0.36
1.75 ± 0.65
1.84 ± 1.07
5.46
100%
1.80 ± 0.58
1.90 ± 0.56
4.05 ± 1.19
7.75
P
<0.001
<0.001
<0.001
Observation of the positive work done at each joint (Table 3.2) nicely summarized the
kinetic adaptations in sub-maximal jumping, such that with increasing jump height a
sequence of increased work output occurred (F(3,10) = 73.37, 37.06 and 9.06 for hip,
knee and ankle joint work output respectively, p < 0.001). Work output was relatively
Chapter 3
Maximal and sub-maximal jumping
32
low in all joints in the 25% condition. When having to jump the 50% condition, all
joints delivered increased work (post-hoc tests:- p < 0.001). However, increasing
jump height to the 75% condition only induced further increased work output at the
knee and hip joints, whereas the ankle joint already seemed to have reached its
maximal work output (no difference between 50% and 75% conditions; p = 0.598).
Jumping the maximal 100% condition only involved a further increase in hip joint
work output (p < 0.001), whereas both ankle and knee joints remained at their
presumed maximal work production (no differences between 75% and 100%
conditions; knee:- p = 0.951 and ankle:- p = 0.797). Increasing jump height clearly
involved increased hip joint work output. In the present study, this resulted in greater
movement excursion and faster rotation of proximal segments, which is inherently
accompanied by increased levels of rotational and linear horizontal kinetic energy
(Figure 3.5).
100%
75%
2
25%
0
-0.3
-0.2
-0.1
0 -2
75%
Energy (J/kg)
4
50%
Y Kin En Trunk
0
-0.3
6
4
2
0
25%
-0.1
Time (s)
0
Energy (J/kg)
100%
50%
-0.2
0.2
25%
-0.2
-0.1
0
Time (s)
75%
-0.3
0.4
50%
Time (s)
100%
Rot En Trunk
Energy (J/kg)
Pot En Trunk
X Kin En Trunk
75%
0.1
50%
25%
0
-0.3
-0.2
-0.1
0
Energy (J/kg)
100%
Time (s)
Figure 3.5. Averaged time curves of the four energy components of the head-arms-trunk segment: (a)
potential, (b) rotational, (c) vertical kinetic and (d) horizontal kinetic energy. Thicker lines represent
higher jump conditions, defining 25%, 50%, 75% and 100% jump conditions, respectively.
4. Discussion
Changes in coordination were studied in vertical jumps with different jump height
requirements, ranging from a minor hop to a maximal vertical jump. Theoretically, an
infinite number of strategies is possible to perform a sub-maximal jump. However,
this study showed consistency among participants suggesting that a certain criterion
drives jumping strategy into a consistent pattern. Our results revealed that
countermovement amplitude increased with height jumped, and that this was mainly
due to increased hip flexion amplitude. This involved increased work output at joints
with increasing height jumped. However, the contribution from the ankle and knee
joints reached a maximum before the 100% jump condition, namely around the 50%
and 75% conditions, respectively. Subsequently, the hypothesis of movement
effectiveness as a criterion for the control of sub-maximal jumps is discussed from
Chapter 3
Maximal and sub-maximal jumping
33
the perspective of these findings. But first our data are inspected for limitations and
for compatibility with data from previous research.
4.1. Quality of the data
Our analysis was based on two-dimensional measurements and this needs some
critical consideration. In the countermovement vertical jump, motion primarily occurs
in the sagittal plane and this is assumed to be symmetrical in left and right body
segments. The possibility of asymmetry was assumed to be negligible in the present
study, as the participants were highly skilled jumpers, the task was not expected to
be influenced by lateral dominancy, and movements of joints out of the sagittal plane
were neither expected nor observed. The assumption of a rigid HAT segment is a
major simplification as movements of the arms and head relative to the trunk as well
as flexion-extension of the trunk segment are neglected. Estimation of the effect of
such movements could not be done with the present data set but these movements
were expected to only cause slightly increased values of kinetic energies of the HAT,
and not contradict the line of reasoning throughout this study.
Amplitudes and time curves of our dataset were very similar to those reported in
previous studies. The kinematics and kinetics of the maximal jump condition, that is,
joint angular displacements and net joint moments, showed good agreement with
those found by Bobbert and van Ingen Schenau (1988). Also, our data on positive
joint work in the maximal and 25% conditions showed good agreement with the data
of a maximal countermovement jump and a hopping movement in a study by
Fukashiro and Komi (1987). Total positive work output in the latter study was 8.89
J/kg and 2.14 J/kg for countermovement jump and for hopping, respectively, whereas
we found 7.43 J/kg and 1.58 J/kg for the 100% and 25% jump conditions in this
study. Also, amplitude and time curves of net joint moments showed a strong
similarity between the two studies. Therefore, our data were within the range of
expectations which provided the foundation for the above mentioned hypotheses.
4.2. Musculo-skeletal properties related to movement effectiveness
Our results showed that increased performance involved a deeper countermovement
prior to take off. Without a countermovement one would have to build up all of the
kinetic energy during the period from the initial stance until take off, having a working
distance of only approximately 10 cm due to ankle extension. However, ankle
extensor muscles are not able to produce all the necessary work output for a
maximal vertical jump. Therefore, a countermovement is required to enable kinetic
energy to be built up towards take off but a deeper countermovement involves a
larger potential energy reduction of the centre of mass relative to that at stance. The
work done to regain the body’s potential energy accounted for 28%, 34%, 37%, and
41% of the total vertical work done (from the deepest position until take off) in the
25%, 50%, 75% and 100% conditions, respectively. Or in other words, in the 25%
condition, 28% of the vertical work was done to regain the initial position and 72%
resulted in jump height, where the former increased and the latter decreased with
increasing height of jump.
Previous studies have demonstrated that in maximal jumping the optimal
Chapter 3
Maximal and sub-maximal jumping
34
coordination generally implies a strong reduction of ineffective rotational energies
towards take off (Bobbert and van Soest, 2001). This was also found in this study
(Figure 3.5), having a decrease in rotational energy towards take off (0.15 s until
0.075 s before take off). Nevertheless, rotational energy of the HAT segment showed
an extra rise just prior to take off in the maximal condition. This probably pointed to
the participants’ ultimate effort to reach the highest possible jump height. However,
due to the vertical orientation of the HAT segment just prior to take off, this effort did
not result in substantially improved vertical kinetic energy. In sub-maximal jumping
such extra increase of rotational energy just prior to take off was not found. In other
words, the remaining rotational energy at take off increased with increasing height
jumped. This increased rotational energy and the geometrical constraint of segmental
rotation near extension of a segment (detailed explanation in van Ingen Schenau,
1989) probably resulted in the significantly decreasing completion of extension of the
HAT segment at take off with increasing jump height (Figure 3.2b). In other words,
contact with the ground was forced to be lost earlier in the extension of the HAT
segment in higher jumps. Besides these considerations on rotational energy, another
energy loss which has not yet been considered is the linear horizontal kinetic energy.
These values were small relative to vertical kinetic energy (3.0%, 0.7%, 0.7% and
1.8% for 25%, 50%, 75% and 100% conditions, respectively). To finally demonstrate
the total remainder of ineffective energy at take off, we calculated the ratio between
ineffective energy at take off (rotational and linear horizontal kinetic) and the total
energy at take off (including the gained potential and vertical kinetic energy). This
ratio was 0.97, 0.95, 0.92 and 0.86 for the 25%, 50%, 75% and 100% jump
conditions, respectively. The latter is similar to the ratio of 0.87 in a maximal squat
jump reported by Bobbert and van Soest (2001). From these ratios it can be
concluded that the ineffective energy waste increases relatively with increasing jump
height, that is, from 3% up to 14%.
Another musculo-skeletal property related to movement effectiveness is the initial
foot segment orientation. The initially dorsi-flexed position of the ankle joint has an
advantage compared to the knee and hip joints, as less flexion – and thus less
countermovement – is required before the joint is able to extend. In other words, the
working distance of approximately 10 cm from stance to take off (∆hcontact) – mainly
as a result of ankle plantar flexion – occurs without requiring a preliminary potential
energy reduction and is considered to be advantageous compared to when work is
done in knee and hip joints. Therefore, in the 25% condition 78% of the total work
was done in the ankle joint (Table 3.2). In the 50% condition, this was still 47%.
However, as the ankle muscles are limited, higher jump conditions involved
increasing knee and hip contribution (ankle contribution accounted for 34% and 23%
in the 75% and 100% conditions, respectively).
Summarizing the reasoning above, results showed that the data are compatible with
the hypothesis that movement effectiveness serves as an optimisation criterion for
the control of sub-maximal jumping. Firstly, the musculo-skeletal system requires an
explicit countermovement to achieve maximal jump height. The resulting increasing
potential energy deficit with increasing jump height, points to a less effective
movement in higher jump conditions. A second property of the musculo-skeletal
design is that segments need to rotate towards extension in order to develop vertical
energy of the body from the deepest position until take off. This involves rotational
energies, especially in the proximal HAT segment. The accompanying energy levels
Chapter 3
Maximal and sub-maximal jumping
35
at take off were negligible in the 25% jump condition but increased with increasing
jump height, again leading to reduced movement effectiveness. A third property is the
optimal initially horizontal foot segment orientation. The ankle was used maximally in
sub-maximal jumping, which led to high movement effectiveness in sub-maximal
jumps.
Another property of the musculo-skeletal system which could influence the control of
jumping is the fact that the distal muscles have shorter muscle fibres and longer
tendons compared to the proximal muscles (Yamaguchi et al., 1990 and summarised
in Voigt et al., 1995). For a tendon of given stiffness, these longer tendons allow for
storing more energy in a stretch-shorten cycle. Studies on muscle mechanics (Voigt
et al., 1995 ; Hof, 2003) have found that this has important consequences regarding
the effect of muscular work on the musculo-skeletal system, and especially in springlike muscle actions (e.g., running and squat jumps in Hof, 2003). The results of our
study showed that lower jumps are mainly performed by extending actions of the
distal ankle joints, and consequently stretch-shortening of the distal muscle-tendon
complexes. To quantify this we calculated the force-length profiles of the muscletendon complex of soleus and gastrocnemius. According to the linear regressions in
Hof et al. (2002), muscle lengths were derived from joint angle profiles and muscle
forces were derived from joint moment profiles. A 1:2 ratio was assumed for dividing
force of the triceps surae muscle into the forces of the gastrocnemius and soleus
muscles, respectively. The force-length profile of the soleus muscle in the maximal
condition of our study (Figure 3.6) was similar to that in a maximal squat jump in Hof
et al. (2002). First the muscle-tendon complex is lengthened while force is built up
(Figure 3.6, A to B). Then the muscle-tendon complex shortens with decreasing
force, as if it was a spring (Figure 3.6, linear slope from B to C). According to
calculations by Hof (2003), such a profile indicates that the contractile component of
the muscle probably acts in a favourably slow concentric way while the apparently
eccentric action of the musculo-tendon complex is enabled by the stretching of the
series elastic component, allowing energy to be stored for later utilization.
Surprisingly, this characteristic profile is equally present in the 75% and 50%
conditions, showing even higher forces than in the 100% condition. This would
promote the storage of higher amounts of energy in the lower jump height conditions,
leading to greater effectiveness. The 25% condition shows a smaller range of stretchshortening, involving lower forces, but still shows the typical profile. These data
suggest that the longer tendons in the distal muscles promote the maximal use of the
distal joints in sub-maximal jumps, and therefore are compatible with movement
effectiveness as a control criterion for sub-maximal jumping.
Chapter 3
Maximal and sub-maximal jumping
36
Force (N)
3000
100%
75%
50%
25%
2000
B
1000
A
C
0
0
0.02
0.04
0.06
0.08
0.1
Length
Figure 3.6. Averaged force-length curves of the soleus muscle, determined and
presented according to Hof (2002). Length of the muscle-tendon complex is
expressed as the total muscle-tendon length relative to the slack length of the series
elastic component, i.e., 0.25 m for soleus and 0.35 m for gastrocnemius according to
average values in Hof (2002). Thicker lines represent higher jump conditions, defining
25%, 50%, 75% and 100% jump conditions, respectively.
4.3. Concluding remarks
The coordination of sub-maximal jumping appears to be controlled by a strategy that
is related to several specific properties of the musculo-skeletal system. These
properties are the obligatory countermovement prior to joint extension, the high
inertia of proximal segments compared to distal segments, the initial horizontal
orientation of the foot segment, and the properties of muscle-complexes spanning
distal joints compared to those spanning proximal joints. The observed changes in
control and consequently in movement coordination from a minor hop to a maximal
jump are compatible with the hypotheses that (1) countermovement and (2) rotation
of proximal segments increased with increasing jump height and that (3) contribution
from the ankle joints was maximised throughout all jump conditions. It was concluded
that for sub-maximal jumping the maximisation of movement effectiveness is a likely
candidate to explain the underlying control criterion for these adaptations. Whether or
not this is related to effectiveness on a metabolic level is an area for future studies to
address.
5. Acknowledgements
The authors would like to express their thanks to At Hof for his helpful comments.
Chapter 3
Maximal and sub-maximal jumping
37
6. References
Bobbert,M.F. and van Ingen Schenau, G.J. (1988) Co-ordination in vertical jumping
[published erratum appears in J Biomech 1988;21(9):784]. Journal of Biomechanics
21, 249-262.
Bobbert,M.F. and van Soest,A.J. (2001) Why do people jump the way they do?
Exercise and Sport Science Reviews 29, 95-102.
Boyd, M.R. and McLellan, A.D. (2002) Changes in locomotor parameters with
variations in cycle time in larval lamprey. The Journal of Experimental Biology 205,
3707-3716.
Fukashiro, S. and Komi, P.V. (1987) Joint moment and mechanical power flow of the
lower limb during vertical jump. International Journal of Sports Medicine 8, Suppl 1,
15-21.
Hatze, H. (1998) Validity and reliability of methods for testing vertical jumping
performance. Journal of Applied Biomechanics 14, 127-140.
Hof, A.L., van Zandwijk, J.P. and Bobbert, M.F. (2002) Mechanics of human triceps
surae muscle in walking, running and jumping. Acta Physiologica Scandinavia 174,
17-30.
Hof, A.L. (2003) Muscle mechanics and neuromuscular control. Journal of
Biomechanics 36, 1031-1038.
Plagenhoef, S., Evans, F.G. and Abdelnour, T. (1983) Anatomical data for analyzing
human motion. Research Quarterly for Exercise and Sport 54, 169-178.
van Ingen Schenau, G.J. (1989) From rotation to translation - Constraints on multijoint movements and the unique action of bi-articular muscles. Human Movement
Science 8, 301-337.
van Ingen Schenau, G.J., Bobbert, M.F. and Rozendal, R.H. (1987) The unique
action of bi-articular muscles in complex movements. Journal of Anatomy 155, 1-5.
van Zandwijk, J.P., Bobbert, M.F., Munneke, M. and Pas, P. (2000) Control of
maximal and submaximal vertical jumps. Medicine and Science in Sports and
Exercise 32, 477-485.
Vanrenterghem, J., De Clercq, D. and Van Cleven, P. (2001) Necessary precautions
in measuring correct vertical jumping height by means of force plate measurements.
Ergonomics 44, 814-818.
Voigt, M., Simonsen, E.B., Dyhre-Poulsen, P. and Klausen, K. (1995) Mechanical
and muscular factors influencing the performance in maximal vertical jumping after
different prestretch loads. Journal of Biomechanics 28, 293-307.
Chapter 3
Maximal and sub-maximal jumping
38
Yamaguchi, G.T., Sawa, A.G.U., Moran, D.W., Fessler, M.J. and Winters, M. (1990)
A survey of human musculotendon actuator parameters. In Winters and Woo (Eds.),
Multiple muscle systems (pp. 717-773). New York: Springer.
Winter, D. (1990) Biomechanics and motor control of human movement. New York:
John Wiley.
Chapter 4
Effect of trunk inclination in vertical jumping
The effect of trunk inclination on coordination in the vertical jump
J. Vanrenterghem, A. Lees, M. Lenoir and D. De Clercq
Submitted to Journal of Applied Biomechanics, January 2004
39
Chapter 4
Effect of trunk inclination in vertical jumping
40
Abstract:
The purpose of this study was to gain more insight into the role of forward inclination
of the trunk in vertical jumping. Twenty subjects performed maximal and sub-maximal
countermovement jumps, both with and without being allowed a forward inclination of
the trunk. Kinematic and kinetic data were recorded as well as electromyographic
signals from four muscles spanning the knee. In a maximal jump, subjects jumped
10% lower when the trunk was held in an upright orientation compared to when using
a normal forward inclination of the trunk. This led to a reduced work output about the
hip and ankle joints but was partially compensated for by an increased knee joint
work output. In sub-maximal jumping subjects automatically reduced the trunk
inclination. This resulted in reduced hip joint contribution, whereas contribution of the
knee and ankle joints was constant for the different jump heights. In sub-maximal
jumping with restricted trunk inclination the same was found, but knee contribution
increased as jump height increased. Electromyographic signals showed adaptations
to the muscle activation in bi-articular muscles. It was concluded that forward
inclination of the trunk enhances performance in maximal jumping due to improved
hip contribution but has a negative effect on knee joint contribution. In the case of
maximal jumping with restricted trunk inclination, the knee was able to produce more
work due to changes in the inertial effects of the trunk and changes in muscular
activity. In sub-maximal jumping with restricted trunk inclination, the restricted role of
the hip in controlling jump height was compensated by an increased role of the knee
and not by the ankle.
Chapter 4
Effect of trunk inclination in vertical jumping
41
1. Introduction
Jumping for height is part of many sports activities like field games play, gymnastics
or athletics. As these sports activities mostly require maximal performance,
numerous studies have tried to explain how maximal performance is achieved.
However, jumps are executed for both maximal and sub-maximal performances
during the learning and training of these sports activities. Only recently has research
been undertaken to understand the movement adaptations that occur when
performing the vertical jumping movement at different intensities.
Vanrenterghem et al. (in press) have shown that the movement adaptations for the
execution of sub-maximal jumps are not a strict miniature version of the maximal
jump. Movement adaptations are influenced for a large part by the high inertia of the
trunk segment. Fully inclining the trunk segment in a sub-maximal jump would involve
(i) a large reduction of potential energy due to the countermovement prior to push off
and (ii) high levels of ineffective rotational energy during the upward extension
phase. As a result, it was found that in sub-maximal jumps the hip joint contribution
progressively increased as jump height increased whereas the knee joints, and in
particular the ankle joints, had a contribution that is largely independent of jump
height. Other criteria that seemed to support the observed movement adaptations
were (iii) the horizontal orientation of the foot segment in the initial stance that allows
plantar flexion without preliminary dorsal flexion and (iv) the advantageous tendonlengths of distal muscles over proximal muscles. The latter two criteria are indicated
as the advantageous functional morphology of the ankle joint. All of these criteria (i –
iv) were related to the maximising of movement effectiveness throughout all jump
heights, that is, minimising the mechanical energy produced to achieve a certain
jump height.
The high inertia of the trunk segment also has an important role in the coordination of
maximal jumps. Previous studies have shown that the maximal vertical jump is
characterized by a proximo-distal (P-D) sequence in the extension of segments
(Bobbert et al., 1996; Hudson, 1986; van Ingen Schenau, 1989). This P-D sequence
implies an earlier extension in the proximal region than in the distal region. Several
theories have been proposed to explain how this P-D sequence originates. The
earliest theory explained that all muscles are activated simultaneously, and that the
downward inertial forces from proximal segments on distal segments mechanically
impose the sequential extensions (Hudson, 1986). This theory was refuted by
Bobbert and van Ingen Schenau (1988) and later by Pandy and Zajac (1991). The
latter authors observed a sequenced movement strategy originating from an intrinsic
P-D muscle activation pattern and stated that due to the forward inclination of the
trunk at the start of the propulsive phase, only a P-D movement strategy would
prevent the body from achieving an undesirable ventral rotation. Thus, the orientation
of the trunk at the start of the upward movement appeared to be crucial in the
coordination of the maximal vertical jump, resulting in the typical P-D movement
sequence. In particular, it was believed that the contribution of knee joint extension to
Chapter 4
Effect of trunk inclination in vertical jumping
42
performance was restricted due to delayed knee joint extension relative to hip joint
extension.
Presently, the above observations regarding the importance of the “heavy” trunk
segment on coordination in vertical jumping have not been substantiated by
paradigms that interfere with the forward inclination of the trunk while executing a
vertical jump. Therefore, the purpose of this study was to gain more insight into the
relationship between the forward inclination of the trunk and the mechanical output in
the lower limb joints during a vertical jump. It was hypothesised that restricting the
forward inclination of the trunk in a maximal vertical jump will adversely affect
performance due to restricted hip action, but involve adaptations to the coordination
of the movement such that knee extension is not further restricted. It was also
hypothesised that in sub-maximal jumping with restricted trunk inclination the knee
rather than the ankle would take over the restricted role of the hip in controlling jump
height. The ankle joint was expected to remain maximal in its contribution, based on
the advantageous functional morphology of the ankle joint.
2. Methods
Twenty athletic male adults (mean ± SD: age=19.9 ± 3.9 years; height = 180.0 ± 6.5
cm; mass = 75.4 ± 13.3 kg) participated in the study. All of the participants were
competitively active in sports which ranged from field games play to gymnastics. All
were fit and injury free and each gave written informed consent as required by the
Liverpool John Moores University Ethics Committee. Participants were given the
opportunity to warm up with light exercise and stretching, and practised a couple of
normal jumps and jumps with restricted forward inclination of the trunk prior to the
tests.
First, each participant performed three repetitions of a normal (N) maximal (MAX)
countermovement vertical jump from stance, arms held akimbo with the thumbs in a
belt around the waist to prevent use of the arms. In order to investigate the influence
of restricted forward inclination of the trunk, participants were then required to
perform three repetitions of a maximal jump while keeping the head-arms-trunk
segment as upright as possible throughout the entire jump (U). The participants felt
comfortable in executing the upright jumps after only one or two practise jumps prior
to the tests, regardless of the fact that this type of jump only occurs in certain ballet
jumps (Ravn et al., 1999) – which none of the participants had ever practised. Then,
in order to investigate movement adaptations for sub-maximal performances,
participants were required to perform three repetitions of both N and U conditions at a
given sub-maximal height (HIGH) and again at a lower sub-maximal height (LOW).
These sub-maximal conditions were determined by a target mounted above the head
of the participant and were randomised in order. Due to the differences in jump height
between UMAX and NMAX conditions (see results), target heights for HIGH and
LOW conditions were also different between the U and N conditions. Analysis of
another three repetitions of an NMAX jump at the end of the test session revealed no
differences in performance compared to the NMAX jumps at the start of the test
session and excluded a fatigue effect.
Each jump was performed on a force platform (Kistler, Winterthur, Switzerland). For
the definition of a 12 segment biomechanical model, reflective markers were placed
Chapter 4
Effect of trunk inclination in vertical jumping
43
over the 2nd metatarsal-phalangeal joint, lateral maleolus, lateral collateral ligament,
trochanter major, lateral epicondylus of the humerus, processus styloideus of the
ulna, acromion process, C7 and on the vertex of the head using a marker placed on
top of a cap worn on the head. The three dimensional position of each marker was
recorded using a 6 camera opto-electronic motion capture system (Proreflex,
Qualisys, Savedalen, Sweden). Electromyographical (EMG) recordings were made
from the rectus femoris, vastus lateralis, biceps femoris and gastrocnemius muscles
(TEL 100, Bio Pac Systems, Goleta, CA, USA). After degreasing the skin and lightly
abrading to reduce skin resistance to below 5,000 ohms, electrodes were placed 20
mm apart on the central portion of each muscle belly when contracted. Earth
electrodes were placed on the bony prominences of the tibia and superior iliac crest
as appropriate. Data were collected for a period of 6 seconds which allowed
approximately 2 seconds of quiet standing before the jump commenced. The motion
data were collected at 240 Hz while the force and EMG data were collected at 960
Hz. All data were electronically synchronized in time and force and EMG data were
later reduced to 240 Hz by averaging over 4 adjacent points.
As vertical jumping is essentially a sagittal plane activity, data were projected onto
the sagittal plane in order to compute linear and angular kinematic variables.
Therefore, the original 12 segment biomechanical model was reduced to a two
dimensional 4 segment model – consisting of feet, lower legs, thighs, and the headarms-trunk segment. The segmental data, proposed by Dempster (1955) for adult
males, were used to calculate segment and whole body centre of mass locations.
Segment orientations and joint angles were computed from segment end points. The
angle of the head-arms-trunk segment was defined as the angle made by the trunk to
the horizontal (trunk segment was determined by hip and shoulder markers). All
kinematic data were smoothed using a Butterworth fourth order zero-lag filter with
padded end points (Winter, 1990) and a cut off frequency of 7 Hz based on a residual
analysis and qualitative evaluation of the data. A link segment model was used to
obtain instantaneous net joint torques about the hip, knee, and ankle joints
(presented for two legs combined). Net joint torques having a hip extending, knee
extending and ankle plantar flexing influence were defined as positive. Work done
about each joint was calculated based on integration of joint powers over time
(Winter, 1990). Total movement time was taken from the first movement initiation
after stance phase until toe-off (Vanrenterghem et al., 2001), and was normalised to
101 data points having 0% and 100% as start and end of the jump phase,
respectively.
The raw EMG signal was high pass filtered using a critically-damped high pass filter
(Murphy and Robertson, 1994) at 10 Hz and low pass filtered at 350 Hz using a
Butterworth fourth order zero-lag filter with padded end points (Winter, 1990). The
data were then rectified and further low pass filtered at 10 Hz.
Besides movement time, other discrete variables were countermovement amplitude
(maximal reduction of vertical position of the whole body centre of mass from that at
stance), jump height (maximal increase of vertical position of the whole body centre
of mass from that at stance) and trunk inclination (maximal forward angular
inclination of the trunk segment from that at stance). These variables were averaged
over 3 trials per subject per condition for statistical analysis. Table 4.1 shows
Cronbach Alpha reliability scores over 3 trials for variables describing the jump. Testretest reliability was high for all variables and was as high in the UMAX condition as
Chapter 4
Effect of trunk inclination in vertical jumping
44
in the NMAX condition. This confirmed the participants’ notion that it felt comfortable
executing the jumps after only a couple of practice jumps and that jumps were
executed consistently. Paired-sample student’s t-tests were used for establishing
differences between NMAX and UMAX conditions. One-way ANOVA analysis was
used to establish differences between NMAX, NHIGH and NLOW conditions and
between UMAX, UHIGH and ULOW conditions, accompanied by post-hoc Tukey
tests to specify individual differences. The P-value was set at 0.05, and where
necessary the Bonferroni correction was applied to balance between type 1 and type
2 errors for multi-testing on correlated variables.
Table 4.1. Test-retest reliability measures (Cronbach’s Alpha) for 20 participants
performing 3 trials.
Countermovement amplitude
Jump height
Movement time
Forward inclination of the trunk
NMAX
0.9565
0.7263
0.8518
0.9735
UMAX
0.9665
0.9175
0.9084
0.8804
3. Results
3.1. Upright jumps
Table 4.2. Descriptive variables (mean ± SD) of the six jump conditions: countermovement amplitude, jump height, movement
time and maximal forward inclination of the trunk. The F- and P-values in the final column indicate differences between LOW,
HIGH and MAX conditions (One-way ANOVA). The t- and P-values below the MAX condition indicate differences between
NMAX and UMAX conditions (Paired t-test).
LOW
-16.4 ± 1.0
-14.9 ± 3.5
HIGH
-22.1 ± 3.9
-19.8 ± 4.0
MAX
-28.7 ± 6.3
-25.9 ± 6.5
-2.3 (0.031)
F
P
37.9 <0.001
27.5 <0.001
29.2 ± 4.6
26.5 ± 4.2
38.0 ± 3.8
34.6 ± 3.8
44.4 ± 0.049
39.8 ± 0.039
7.4 (<0.001)
82.4 <0.001
68.6 <0.001
Movement time
(s)
0.84 ± 0.19
N
0.84 ± 0.22
U
t (P)
0.92 ± 0.15
0.95 ± 0.18
1.01 ± 0.17
1.03 ± 0.23
-0.5 (0.623)
6.8
4.9
Trunk inclination
(Deg)
N
U
t (P)
17.3 ± 8.9
8.3 ± 5.9
30.2 ± 7.7
14.9 ± 7.3
44.2 ± 10.4
21.4 ± 8.3
11.4 (<0.001)
Countermovement
amplitude (cm)
N
U
t (P)
Jump height
(cm)
N
U
t (P)
0.002
0.011
43.9 <0.001
16.4 <0.001
Chapter 4
Effect of trunk inclination in vertical jumping
45
Participants were not able to fully eliminate forward trunk inclination in the upright
jump conditions (Figure 4.1), but maximal forward trunk inclination in the UMAX
condition was reduced to 48.4% of that in the NMAX condition (Table 4.2). This
produced a 4.6 cm reduction of jump height (Table 4.2). The upright condition
involved 2.8 cm (9.7%) less countermovement but this did not lead to a changed
movement time. In both conditions, the lowest position of the centre of mass was
reached at approximately 74% movement time. The reduced maximal forward
inclination of the trunk involved a reduction of range of motion of the hip joint,
accompanied by reduced net joint torques at the hip (Figure 4.2c). This resulted in
halved (51.4%) positive work output at the hip (Table 4.3). In the knee joint, the
UMAX condition involved increased range of motion and net joint torques (Figure
4.2b), resulting in 31.4% increased positive work output (Table 4.3). Positive work
output about the ankle joint was 8.6% lower in the UMAX condition due to reduced
joint moments (Figure 4.2a). All these differences were significant.
(b) upright
100
100
90
90
Segment angle (deg)
Segment angle (deg)
(a) normal
80
70
NLOW
60
NHIGH
50
NMAX
40
80
70
ULOW
60
UHIGH
50
UMAX
40
0
20
40
60
% movement time
80
100
0
20
40
60
% movement time
80
100
Figure 4.1. Time histories of angular displacement of the trunk segment for (a) normal and (b) upright conditions. Time is
expressed as percentage of movement time.
Table 4.3. Joint work output during the ascent phase for the six jump conditions (mean ± SD). The F- and P-values in the most
right column indicate differences between LOW, HIGH and MAX conditions (One-way ANOVA). The t- and P-values below the
MAX condition indicate differences between NMAX and UMAX conditions (Paired t-test).
LOW
128 ± 50
129 ± 26
HIGH
145 ± 27
140 ± 29
MAX
152 ± 28
139 ± 28
3.9 (0.001)
F
2.7
1.1
P
0.074
0.326
W+ at ankle
N
U
t (P)
W+ at knee
N
U
t (P)
116 ± 35
121 ± 38
130 ± 34
155 ± 38
140 ± 40
184 ± 45
-6.2 (<0.001)
2.3
13.6
0.106
<0.001
W+ at hip
N
U
t (P)
64 ± 33
36 ± 21
128 ± 40
68 ± 33
210 ± 88
108 ± 54
7.6 (<0.001)
33.7
21.0
<0.001
<0.001
Chapter 4
Effect of trunk inclination in vertical jumping
300
(a)
Joint torque (Nm)
250
200
150
NMAX
100
UMAX
50
0
-50
50
100
150
200
Joint angle (deg)
300
(b)
Joint torque (Nm)
250
200
150
NMAX
100
UMAX
50
0
-50
50
100
150
200
Joint angle (deg)
300
(c)
Joint torque (Nm)
250
200
150
NMAX
100
UMAX
50
0
-50
50
100
150
200
Joint angle (deg)
Figure 4.2. Net joint torques as a function of joint angles for (a) ankle, (b) knee
and (c) hip joints in the normal and upright MAX conditions.
46
Chapter 4
Effect of trunk inclination in vertical jumping
47
Figure 4.3 shows mean curves for muscle activation levels of four muscles, that is,
gastrocnemius, vastus lateralis, rectus femoris, and biceps femoris muscles. A
qualitative analysis of these graphs suggests that one mono-articular muscle among
these (i.e., vastus lateralis) showed equal activation levels throughout the entire jump
for both normal and upright conditions (Figure 4.3f). Activation levels of bi-articular
muscles showed minor differences between conditions. The rectus femoris activation
seemed higher in the descent phase of the upright condition (figure 4.3g). The
gastrocnemius and biceps femoris showed reduced levels of activation in the ascent
phase of the upright condition (figure 4.3e, 4.3h).
3.2. Sub-maximal jumps
Jump heights in the LOW and HIGH jumps were approximately 66% and 86% of the
MAX jumps, respectively, in both the upright and normal conditions (Table 4.2). As in
maximal jumps, in sub-maximal jumps upright jumping involved halved maximal
forward trunk inclination (47.9% and 49.3%, respectively, in LOW and HIGH
conditions), reduced countermovement (9.1% and 10.4%, respectively, in LOW and
HIGH conditions), similar movement time and the deepest position of the centre of
mass was reached at approximately 74% movement time.
Movement adaptations for sub-maximal performances revealed that positive work
output about the hip increased as jump height increased (Table 4.3) due to increased
range of motion and increased joint torques (Figure 4.4c, 4.4f). Positive work output
in the knee joint did not differ for jump height in the normal condition, but increased
as jump height increased in the upright condition (Table 4.3). The latter increase was
due to increased range of motion as jump height increased (Figure 4.4e), whereas in
the normal condition this increased range of motion was compensated by reduced
joint torques (Figure 4.4b). Positive work output about the ankle joint did not change
with jump height.
EMG levels did not systematically change as jump height changed in the normal
condition. However, in the upright condition there was a tendency towards higher
activation of the knee extensors towards the end of the descent phase (vastus
lateralis and rectus femoris muscles) as jump height increased (Figure 4.5).
Chapter 4
Effect of trunk inclination in vertical jumping
(a) m. Gastrocnemius
(e) normal - upright
arbitrary units
1,4
0,2
1,2
normal
1
upright
0,1
0,8
0,6
0
0,4
0
0,2
0
-0,2 0
20
20
40
60
80
100
80
100
80
100
80
100
80
100
% movement time
(b) m. Vastus Lateralis
(f) normal - upright
1,4
arbitrary units
60
normal - upright
-0,2
% movement time
0,2
1,2
normal
1
upright
0,1
0,8
0,6
0
0,4
0
0,2
-0,2 0
20
40
60
-0,1
0
20
40
60
80
100
-0,4
normal - upright
-0,2
% movement time
% movement time
(c) m. Rectus Femoris
(g) normal - upright
1,4
arbitrary units
40
-0,1
-0,4
0,2
1,2
normal
1
upright
0,1
0,8
0,6
0
0,4
0
0,2
0
-0,2 0
20
40
60
-0,1
20
40
60
80
100
-0,4
normal - upright
-0,2
% movement time
% movement time
(d) m. Biceps Femoris
(h) normal - upright
1,4
arbitrary units
48
0,2
1,2
normal
1
upright
0,1
0,8
0,6
0
0,4
0
0,2
0
-0,2 0
20
40
60
-0,1
20
40
60
-0,4
80
100
-0,2
% movement time
normal - upright
% movement time
Figure 4.3. Time histories of EMG signals of (a) gastrocnemius, (b) vastus lateralis, (c) rectus femoris, and (d)
biceps femoris for the normal and upright MAX conditions. Time histories of differences between conditions are
given in curves (e) – (h). Time is expressed as a percentage of movement time.
Chapter 4
Effect of trunk inclination in vertical jumping
300
300
(a)
(a)
250
200
NLOW
NHIGH
NMAX
150
100
50
Joint torque (Nm)
Joint torque (Nm)
250
0
-50
200
ULOW
UHIGH
UMAX
150
100
50
0
50
100
150
200
-50
50
Joint angle (deg)
(b)
200
NLOW
NHIGH
150
100
NMAX
50
Joint torque (Nm)
Joint torque (Nm)
200
(b)
250
0
200
ULOW
UHIGH
150
100
UMAX
50
0
50
100
150
200
-50
50
Joint angle (deg)
100
150
200
Joint angle (deg)
300
300
(c)
(c)
250
200
150
NLOW
100
NHIGH
NMAX
50
0
Joint torque (Nm)
250
Joint torque (Nm)
150
300
250
-50
100
Joint angle (deg)
300
-50
49
200
150
ULOW
100
UHIGH
UMAX
50
0
50
100
150
Joint angle (deg)
200
-50
50
100
150
200
Joint angle (deg)
Figure 4.4. Net joint torques as a function of joint angles for ankle (top), knee (middle) and hip (bottom) joints for MAX, HIGH
and LOW jump heights for the normal (left) and upright (right) conditions.
Chapter 4
Effect of trunk inclination in vertical jumping
(a) m. Gastrocnemius
1,4
NMAX
1,4
UMAX
1,2
NHIGH
1,2
UHIGH
1
NLOW
1
ULOW
arbitrary units
arbitrary units
(a) m. Gastrocnemius
0,8
0,6
0,4
0,2
0,8
0,6
0,4
0,2
0
0
0
20
40
60
80
100
0
20
% movement time
1
NMAX
UMAX
NHIGH
1,2
UHIGH
NLOW
1
ULOW
0,8
0,6
0,4
0,2
100
80
100
80
100
80
100
0,8
0,6
0,4
0
0
20
40
60
80
100
0
20
% movement time
40
60
% movement time
(c) m. Rectus Femoris
1,4
(c) m. Rectus Femoris
1,4
NMAX
UMAX
1,2
NHIGH
1,2
UHIGH
1
NLOW
1
ULOW
arbitrary units
arbitrary units
80
0,2
0
0,8
0,6
0,4
0,2
0,8
0,6
0,4
0,2
0
0
0
20
40
60
80
100
0
20
% movement time
40
60
% movement time
(d) m. Biceps Femoris
1,4
(d) m. Biceps Femoris
1,4
NMAX
UMAX
1,2
NHIGH
1,2
UHIGH
1
NLOW
1
ULOW
arbitrary units
arbitrary units
60
(b) m. Vastus Lateralis
1,4
arbitrary units
arbitrary units
1,2
40
% movement time
(b) m. Vastus Lateralis
1,4
50
0,8
0,6
0,4
0,2
0,8
0,6
0,4
0,2
0
0
0
20
40
60
% movement time
80
100
0
20
40
60
% movement time
Figure 4.5. Time histories of EMG signals of (a) gastrocnemius, (b) vastus lateralis, (c) rectus femoris, and (d) biceps femoris
for the normal (left) and upright (right) conditions for MAX, HIGH and LOW jump heights. Time is expressed as a percentage of
movement time.
Chapter 4
Effect of trunk inclination in vertical jumping
51
4. Discussion
Participants systematically inclined the trunk segment when asked to perform a
normal maximal standing vertical jump. Instructing participants to jump without
forward inclination of the trunk led to a reduced trunk inclination and consequently
reduced jump height compared to the normal condition. Adaptations were observed
by which the knee joint contribution increased to compensate for a strongly reduced
hip joint contribution. For sub-maximal jumping, the major role of the hip in the
regulation of jump height was present both with and without restricted trunk
inclination. However, the knee contribution became more important as trunk
inclination was restricted.
4.1. Upright versus normal
Results for jumping performance in the present study are comparable with findings
from previous vertical jump investigations. According to Luhtanen and Komi (1978)
rotation of the trunk segment accounted for approximately 10% of the performance
and Ravn et al. (1999) reported a 7.6% reduced performance when comparing a
ballet specific jump with a normal vertical jump with arm swing. These results are
similar to the 10% difference between normal and upright jumping found in the
present study. Joint kinematics and kinetics for the normal condition in terms of
amplitude resembled data presented by Anderson and Pandy (1993), by Bobbert et
al. (1996) and by Bobbert and van Ingen Schenau (1988).
Reducing trunk inclination in the MAX condition had an important effect on the knee
joint in that the knee joint work output increased through increased knee joint
torques. There are three possible explanations for this changed knee function. The
first is that the reduced trunk motion in the upright condition allowed the knee to
extend earlier and faster (Pandy and Zajac, 1991). Second, from a quasi static
analysis it is obvious that jumping with a more vertical trunk increases the horizontal
distance between body centre of mass and the axis of the knee joint. As a result, the
knee joint torque required to overcome the effect of gravity is higher in the upright
condition. The third explanation for the changed knee function involves active
neuromuscular changes. Both biceps femoris and gastrocnemius appeared to be
activated less in the case of upright jumping whereas rectus femoris appeared to
show higher activation. These changes in muscular activity of bi-articular muscles are
in support of the increased knee joint torques (Figure 4.3b).
4.2. Sub-maximal jumping
Movement adaptations for normal sub-maximal jumping were similar to that found in
Vanrenterghem et al. (in press) and consisted of a constant contribution of ankle and
knee work throughout jump heights and increased contribution of hip joint work as
jump height increased. In the latter study an increased knee joint contribution as jump
height increased was found in the lowest jump conditions (25%, 50%) but these jump
conditions were lower than the lowest jump condition in the present study (66%). The
constant knee contribution in the present study was due to a combination of
increased range of motion and reduced joint torques at the knee as jump height
increased. It is expected that the reduced knee joint torques with increasing jump
height resulted from the same mechanism as was explained above, that is, the
increasing influence of forward inclination of the trunk. This influence was expected to
Chapter 4
Effect of trunk inclination in vertical jumping
52
be less in upright sub-maximal jumps compared to normal sub-maximal jumps, which
was confirmed as knee joint torques in the upright condition were not reduced as
jump height increased. Combining similar knee joint torques with increased range of
motion led to increased joint work about the knee and indicated the higher
importance of the knee joint for the regulation of jump height in the case of upright
jumping.
Observation of EMG signals in sub-maximal jumping revealed no systematic changes
for normal sub-maximal jumping. Only the biceps femoris muscle revealed the
tendency of increased activity in the ascent phase as jump height increases, which is
necessary to counteract increasing forward inclination of the trunk in higher jumps.
Such increased biceps femoris muscle activity was not found in upright sub-maximal
jumping, which supported the influence of forward inclination of the trunk on biceps
femoris muscle activation. Whereas no other differences in muscle activation were
observed in normal sub-maximal jumping, upright sub-maximal jumping revealed the
tendency of increased activity of knee extensors (mono-articular vastus lateralis and
bi-articular rectus femoris) as jump height increased. Stronger activation of monoarticular knee extensors was expected to be possible as knee joint extension was
less restricted by the oppressing influence of forward inclination of the trunk.
Increased activity of the bi-articular rectus femoris would lead to reduced extension
torques at the hip joint, as observed, and would also allow for greater use of the
rectus femoris to contribute to the increased knee torque. Due to technical limitations
it was impossible to measure more than four muscles, and knowledge about the
activity of the mono-articular gluteus maximus muscle would be required for a correct
interpretation of muscle function about the hip joint.
The criterion of movement effectiveness – that is, minimised forward inclination of the
trunk and maximised ankle joint contribution – was suggested to explain the
movement adaptations in sub-maximal jumping (Vanrenterghem et al., in press). This
was found in the normal condition and in the upright condition of the present study,
supporting movement effectiveness as a criterion for movement adaptations in submaximal jumping. If this criterion was the sole criterion explaining movement
adaptations in normal sub-maximal jumping, it would be impossible to achieve the
same jump height with less forward inclination of the trunk than was observed.
However, jump height in the UMAX condition was 1.8 cm higher than in the NHIGH
condition, whereas forward inclination of the trunk was less. This interesting finding
revealed that minimising forward inclination of the trunk is not the sole criterion
explaining movement adaptations in normal sub-maximal jumping. A trade off with
alternative criteria is suggested, as it is still believed that movement effectiveness
plays an important role. One such alternative criterion could be that the maximal
activation of a small number of muscles (mainly distal in this case) requires more
muscular effort than the sub-maximal activation of a higher number of muscles
(balanced activation of proximal and distal muscles), based on the inversely
nonlinear relationship of muscle force exerted by an individual muscle and
contraction endurance (Crowninshield and Brand, 1981). However, the investigation
of such alternative criterion was beyond the scope of the present study, and further
investigations would be required to validate this suggestion.
Chapter 4
Effect of trunk inclination in vertical jumping
53
4.3. General conclusions
Movement adaptations due to keeping the trunk upright indicated that a rapid
adaptation is possible for performing vertical jumps under the altered movement
requirement. Performance in the upright condition was limited due to a reduced hip
extensor function, but this was compensated for by an increased knee extensor
function. This increased knee extensor function could be attributed to altered inertial
effects of the trunk and to altered muscle activations. In sub-maximal jumping with
restricted trunk inclination, the restricted role of the hip in controlling jump height was
compensated by an increased role of the knee and not by the ankle.
Chapter 4
Effect of trunk inclination in vertical jumping
54
5. References
Anderson, F.C. and Pandy, M.G. (1993) Storage and utilization of elastic strain
energy during jumping. Journal of Biomechanics, 26,1413-1427.
Bobbert, M.F., Gerritsen, K.G., Litjens, M.C. and van Soest, A.J. (1996) Why is
countermovement jump height greater than squat jump height? Medicine and
Science in Sports and Exercise, 28, 1402-1412.
Bobbert, M.F. and van Ingen Schenau, G.J. (1988) Coordination in vertical jumping
[published erratum appears in Journal of Biomechanics 1988;21(9):784]. Journal of
Biomechanics, 21, 249-262.
Crowninshield, R.D. and Brand, R.A. (1981) A physiologically based criterion of
muscle force prediction in locomotion. Journal of Biomechanics, 14, 793-801.
Dempster, W.T. (1955) Space requirements of the seated operator. WADS technical
report, 55-159, Wright-Patterson Air Force Base, OH.
Hudson, J.L. (1986) Coordination of segments in the vertical jump. Medicine and
Science in Sports and Exercise, 18, 242-251.
Jacobs, R. and van Ingen Schenau, G.J. (1992) Control of an external force in leg
extensions in humans. Journal of Physiology, 457, 611-626.
Luhtanen, P. and Komi, P.V. (1978) Segmental contribution to forces in vertical
jumps. European Journal of Applied Physiology and Occupational Physiology, 38,
181-188.
Murphy, S.D. and Robertson, D.G.E. (1994) Construction of a high pass digital filter
from a low pass digital filter. Journal of Applied Biomechanics, 10, 374-381.
Pandy, M.G. and Zajac, F.E. (1991) Optimal muscular coordination strategies for
jumping [see comments]. Journal of Biomechanics, 24, 1-10.
Ravn, S., Voigt, M., Simonsen, E.B., Alkjaer, T., Bojsen-Moller, F., and Klausen, K.
(1999) Choice of jumping strategy in two standard jumps, squat and
countermovement jump – effect of training background or inherited preference?
Scandinavian Journal of Medicine and Science in Sports, 9, 201-208.
van Ingen Schenau, G.J. (1989) From rotation to translation - Constraints on multijoint movements and the unique action of bi-articular muscles. Human Movement
Science, 8, 301-337.
Vanrenterghem, J., De Clercq, D. and Van Cleven, P. (2001) Necessary precautions
in measuring correct vertical jumping height by means of force plate measurements.
Ergonomics, 44, 814-818.
Chapter 4
Effect of trunk inclination in vertical jumping
55
Vanrenterghem, J., Lees, A., Lenoir, M., Aerts, P. and De Clercq, D. (in press)
Performing the vertical jump: Movement adaptations for sub-maximal jumping.
Human Movement Science.
Winter, D.A. (1990) Biomechanics and motor control of human movement (2nd Ed.).
New York: Wiley Interscience.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
Movement adaptations in the vertical jump from sub-maximal to maximal
performance when using an arm swing
J. Vanrenterghem, A. Lees and D. De Clercq
Submitted to Journal of Sports Sciences, December 2003
57
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
58
Abstract:
The purpose of this study was to investigate to what extent subjects use an arm
swing in sub-maximal vertical jumping, and to test whether previously observed
movement adaptations in sub-maximal jumps without an arm swing still hold in this
more natural execution of the movement with an arm swing. Twenty adult males were
asked to perform a series of low, high and maximal vertical jumps while allowed to
use an arm swing. Force, motion and EMG data were recorded during each jump.
Movement adaptations of the lower limb joints for sub-maximal jumps were similar to
those previously found in jumps without an arm swing. The ankle and knee joint
contributions to performance were largely independent of jump height. An increasing
hip joint contribution was found as jump height increased. The shoulder and elbow
contributions due to the arm swing were in line with that at the hip joint, increasing as
jump height increased. The increasing forward inclination of the trunk provided a
possible explanation for how both hip joint contribution and the contribution from the
shoulders and elbows changed with jump performance. It was concluded that the arm
swing contribution progressively increased as performance increased and that
movement adaptations previously observed when jumping without an arm swing
were not perturbed by the arm swing.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
59
1. Introduction
The knowledge of whether sub-maximal movements involving multiple joints
represent a miniature version of the maximal performance is important for the
learning and training of complex sports skills. In particular, jumping for height at
maximal or sub-maximal intensities is part of many sports activities like field games
play, gymnastics or athletics. However, little research has been undertaken to
understand the movement adaptations that occur when performing the same jumping
movement at different intensities. A first exploration of sub-maximal vertical jumping
was reported for squat jumps without the use of an arm swing to aid the jump (van
Zandwijk et al., 2000). That study compared the control of maximal and 80% maximal
jumps and although similarities in the overall muscle activation patterns were found
between the two conditions, dissimilarities were found in the relative timing of muscle
activity.
Importantly, no criterion for the movement adaptations was discovered based on the
observed coordination and control. In our own investigations (Vanrenterghem et al.,
in press) a wider range of performance levels was studied, covering 25%, 50%, 75%
and 100% of the maximal jump performance. Again, participants were asked to jump
without the use of an arm swing but the push off phase was preceded by a
countermovement from upright standing. It was shown that contributions of lower limb
joints did not all continuously increase as jump height increased. Specifically, the
knee and ankle joints reached their maximal contribution for sub-maximal jumps and
it was only the hip joint that continuously increased in line with increased jump height.
This finding suggested that jump height is primarily controlled by the hip joint
contribution, whereas knee and ankle contributions are largely independent of jump
height.
In Vanrenterghem et al. (in press), it was suggested that criteria related to the term
‘movement effectiveness’ determined the strategy of movement adaptation for submaximal jumping which implies a minimisation of the energy consuming mechanisms.
Specifically, this means (i) minimising the potential energy deficit resulting from the
lowering of the centre of mass due to the counter movement and (ii) minimising the
rotational energy required by segments during joint extension. In particular, the high
inertia of the upper body segment (head-arms-trunk) plays an important role in this,
because fully inclining the upper body segment in low height jumps would involve a
large reduction of potential energy as well as the need for high rotational kinetic
energies during the extension phase.
These criteria related to movement effectiveness have only been investigated for
jumps without the use of an arm swing to aid the jump and it is not known whether
they hold true for a more complex jump in which the arms are allowed to be used
freely to contribute to jump performance. The arm swing is a natural part of many
jump activities in sports and although the arms influence performance by about 10%
in maximal jumping, the mechanisms explaining how this might occur have only
recently been identified (Lees et al., accepted for publication). In that study, it was
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
60
shown that the complex interaction between the arms and the rest of the body when
using an arm swing consists of several phases in which energy is exchanged
between the arms and the rest of the body. First, as the arms are swung forward from
their retracted position, downward vertical energy is built up in the arms, primarily as
kinetic energy. Then, in the second part of the forward swing (as the arms are
elevated from the downward vertical to the forward horizontal) some of this energy is
transmitted to the rest of the body and stored in the muscles and tendons of the lower
body. A third phase from this forward horizontal position until take off involves the
transfer of energy from the arms to the rest of the body due to the pull of the arms on
the body, the raising of the arms against gravity and the release of previously stored
energy from muscles and tendons of the lower body. It was found that the enhanced
performance through using an arm swing can largely be explained by the work done
by the muscles of the shoulder and elbow joints together with extra work done at the
hip joint (Lees et al., accepted for publication).
It is not known to what extent the arm swing is used to aid sub-maximal jumps. Also,
given the large energy transfers which occur when using an arm swing to aid jump
performance, it is not known if previously found movement adaptations for submaximal jumping without using an arm swing continue to be used. The purpose of the
present study, then, was to investigate to what extent participants use an arm swing
in sub-maximal vertical jumping and to test whether previously observed movement
adaptations in sub-maximal jumps without an arm swing (Vanrenterghem et al., in
press) still hold in this more natural execution of the movement with arm swing.
2. Methods
The test protocol required participants to jump at a given sub-maximal height (termed
LOW), then again at a greater height (termed HIGH) and then finally for maximal
height (termed MAX), using a natural jumping technique in which the use of an arm
swing was allowed. Twenty athletic adult males (mean ± SD: age=19.9 ± 3.9 years;
height=180.0 ± 6.5 cm; mass=75.4 ± 13.3 kg) participated in this investigation. All of
the participants were competitively active in sports which ranged from field games
play to gymnastics. All were fit and injury free and each gave informed consent as
required by the University Ethics Committee.
2.1. Data collection
Participants were given the opportunity to warm up and to practice the three types of
jump prior to performing three repetitions of each condition. They performed each
jump on a force platform (Kistler, Winterthur, Switzerland). Reflective markers were
placed over the 2nd metatarsal-phalangeal joint, lateral malleolis, lateral collateral
ligament, trochanter major, lateral epicondylus of the humerus, processus styloideus
of the ulna, acromion process, C7 and on the vertex of the head using a marker
placed on the top of a cap worn on the head. The three dimensional position of each
marker was recorded using a 6 camera opto-electronic motion capture system
(Proreflex, Qualysis, Savedalen, Sweden). Electromyographical (EMG) recordings
(TEL100, Bio Pac Systems, Goleta, CA, USA) were made from the Rectus Femoris,
Vastus Lateralis, Biceps Femoris and Gastrocnemius muscles. Data were collected
for a period of 6 s which allowed approximately 2 s of quiet standing before the jump
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
61
commenced. The motion data were collected at 240 Hz while the force and EMG
data were collected at 960 Hz. All data were electronically synchronised in time.
2.2. Data reduction
(i) Kinematic analysis procedures
The 3D motion data from the 16 markers were used to define a 2D sagittal plane
projection of a 6 segment biomechanical model (feet, lower legs, thighs, trunk+head,
upper arms, forearms) using segmental data for adult males (Dempster, 1955).
These data were used to calculate the segment and whole body centre of mass
locations, segment orientations and joint flexion angles. All kinematic data were then
smoothed using a Butterworth fourth order zero-lag filter with padded end points
(Smith, 1989) and a cut-off frequency of 7 Hz based on a residual analysis and
qualitative evaluation of the data. Derivatives were calculated by simple
differentiation (Winter, 1990).
(ii) Kinetic analysis procedures
Through numerical integration procedures (Vanrenterghem et al., 2001) the force
data were used to calculate the height jumped, movement time (movement initiation
until take off), deepest position of the centre of mass (relative to the position in initial
stance) and time of this deepest position. The force data were then averaged over 4
adjacent points so that each force value corresponded to each motion data value at
240 Hz. Inverse dynamics using standard procedures (Miller and Nelson, 1973;
Winter, 1990) was used to compute the segment proximal and distal net joint forces
and net joint torques at the ankle, knee, hip, shoulder and elbow joints. Joint power
(the product of net joint torque and joint angular velocity) and work done (the time
integral of the power production at a joint between specified time points) were
calculated based on standard procedures (de Koning and van Ingen Schenau, 1994).
Positive work done in all joints was calculated to indicate the contribution of joints to
jump performance.
(iii) EMG analysis procedures
The raw EMG signal was high pass filtered (Murphy and Robertson, 1994) at 10 Hz
and low pass filtered (Winter, 1990) at 350 Hz using Butterworth fourth order zero-lag
filters with padded end points. The data were then rectified and further smoothed
using a 10 Hz low pass Butterworth fourth order zero-lag filter.
2.3. Statistical analysis
Differences between conditions were calculated through a one-way ANOVA with
post-hoc Tukey tests for individual comparisons. Pearson correlation coefficients (r)
were calculated to establish the relation between two sets of variables and two-tailed
t-tests were used to validate the correlation. Similarly, a multiple regression analysis
with jump height as dependent variable and work done at the individual joints as
independent variables was undertaken to determine the degree to which joint work
output predicts jump height. The P-value was set at 0.05. However, for repeated
analyses the P-value was reduced according to the Bonferroni correction to balance
between type 1 and type 2 errors for multi-testing on correlated variables.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
62
3. Results
Jump height (difference in vertical position of the centre of mass between stance and
apex of the jump) for each jump condition is given in Table 5.1, and was 65% and
83% of MAX for the LOW and HIGH conditions, respectively. This involved an
increased jump duration (initiation of counter movement until take off) and increased
countermovement amplitude of the body’s centre of mass (Table 5.1) as jump height
increased. The body configurations at maximal retraction of the arms shown in Figure
5.1 give a good picture of how this countermovement occurs. There is flexion in the
hip, ankle and knee joints and the arms are retracted at the shoulder joint. These
body configurations show that the increased countermovement is mainly due to the
increased inclination of the trunk (Table 5.1). The countermovement of the centre of
mass took approximately 70% of the movement duration for each jump condition
(Table 5.1).
Table 5.1. Kinematic and work variables (mean ± SD) for the LOW, HIGH and MAX jump conditions.
F- and P-values for one-way ANOVA analyses are given in the right hand column.
Jump height (m) a
Jump duration (s)
Deepest point (m) a
Time of deepest point
Trunk flexion angle
(deg)
+ Work elbows b
+ Work shoulders b
+ Work hips b
+ Work knees b
+ Work ankles b
a
b
LOW
0.346 ± 0.027
0.729 ± 0.104
-0.171 ± 0.022
72%
14.4 ± 7.1
HIGH
0.442 ± 0.030
0.812 ± 0.126
-0.216 ± 0.038
71%
25.8 ± 7.2
MAX
0.533 ± 0.043
0.962 ± 0.144
-0.297 ± 0.057
69%
44.8 ± 9.5
F
152.1
17.7
47.1
P
<0.001
<0.001
<0.001
73.5
<0.001
0.11 ± 0.08
0.20 ± 0.17
1.03 ± 0.28
1.62 ± 0.63
1.80 ± 0.33
0.22 ± 0.14
0.41 ± 0.23
1.84 ± 0.47
1.77 ± 0.58
1.97 ± 0.28
0.30 ± 0.20
0.63 ± 0.27
3.24 ± 0.60
1.94 ± 0.47
2.06 ± 0.35
8.9
17.3
110.1
1.4
3.6
<0.001
<0.001
<0.001
0.234
0.034
relative to standing height
Unit = J.kg-1
The net joint torques (Figure 5.2) in the ankle slightly increased with jump
performance (Table 5.2). The net joint torques in the knee decreased as jump height
increased, while net joint torques in the hip strongly increased. This inverse relation
between hip and knee joint torques was demonstrated in Figure 5.3, showing the
negative correlation between maximal net joint torques in the hip and knee joints (r =
-0.406, P = 0.001). Joint torques in shoulder and elbow joints were not only smaller
than those for extension of lower limb joints but also differed in pattern (Figure 5.2, de). Negative torques accompanying the retraction of the arms were followed by
positive torques during the first part of the forward arm swing. In the last part of the
arm swing, net joint torques in shoulder and elbow became negative to counteract
the upward movement of the arms. The amplitudes of torques in the shoulder and
elbow joints increased as jump height increased, showing a similarity to the
increased hip joint torques.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
63
Table 5.2. Pearson Correlation Coefficients (r) for jump height related
to variables describing individual joint action (+ work = positive work).
Peak elbow torque
+ work elbows
Peak shoulder torque
+ work shoulders
Peak hip torque
+ work hips
Peak knee torque
+ work knees
Peak ankle torque
+ work ankles
Jump height
r
P(2-tailed)
0.609
< 0.001
0.621
< 0.001
0.566
< 0.001
0.626
< 0.001
0.859
< 0.001
0.820
< 0.001
-0.454
<0.001
0.018
0.890
0.218
0.094
0.304
0.018
Values of positive work output at all joints were used to indicate the contribution of
each joint to jump performance and are given in Table 5.1. Work output at the elbow,
shoulder, and hip increased in line with increasing jump height. Work output at the
knee joint did not differ between conditions, and work output at the ankle only slightly
increased. A multiple linear regression predicting jump height from work output at the
individual joints confirmed these findings (F = 37.7, P < 0.001) and revealed that
jump height was significantly predicted by work output at the hip joint (t = 7.513, P <
0.001) but also by that at the elbow (t = 3.532, P < 0.001). Jump height was not
significantly predicted by work output at the knee and ankle joints (t = -0.668, P =
0.507 and t = 0.670, P = 0.506, respectively). The analysis initially indicated shoulder
joint work output as a poor predictor of jump height (t = 0.900, P = 0.372), but further
analysis revealed that this was due to co-linearity between elbow, shoulder and hip
work output (Table 5.3). Excluding the smaller elbow work values revealed that
shoulder joint work output was in fact a significant predictor of performance (t =
3.028, P = 0.004). Interpretation of Pearson correlation coefficients between jump
height and work output at individual joints confirmed the findings of this multiple
regression and revealed significant correlations between work output at hip, shoulder
and elbow joints and jump height (Table 5.2). Overall, the hip joint contribution was
the most significant and, of all the joints, increased the most throughout the three
jump conditions.
Table 5.3. Pearson Correlation Coefficients (r) describing interaction between positive work output values for
ankle, knee, hip, shoulder and elbow joints. Two-tailed reliability test was described by the P-values between
brackets.
+ work shoulders
+ work hips
+ work knees
+ work ankle
+ work elbows
0.590 (<0.001)
0.407 (0.001)
-0.081(0.539)
0.162 (0.216)
+ work shoulders
+ work hips
+ work knees
0.586 (<0.001)
0.271 (0.036)
0.028 (0.831)
0.118 (0.369)
0.307 (0.025)
-0.198 (0.129)
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
64
Figure 5.1. Typical ground reaction forces for each jump type (MAX, HIGH, LOW). Body configurations are given at initial
stance, maximal retraction of the arms, take off and apex of the jump. The marker at the proximal end of the foot segment
might suggest an initial plantar flexion, but as it represents the ankle joint (not the heel) it should be noted that the heels are
on the ground in the initial stance phase.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
(d)
4
LOW
3
HIGH
2
MAX
1
0
20
40
60
80
100
joint torque (Nm·kg -1)
joint torque (Nm·kg -1)
(a)
-1 0
1
LOW
0.5
HIGH
MAX
0
-0.5
0
20
60
80
10 0
80
10 0
% time
(e)
4
LOW
3
HIGH
2
MAX
1
0
20
40
60
80
100
joint torque (Nm·kg -1)
(b)
joint torque (Nm·kg -1)
40
-1
% time
-1 0
65
1
LOW
0.5
HIGH
MAX
0
-0.5
0
20
40
60
-1
% time
% time
joint torque (Nm·kg -1)
(c)
4
LOW
3
HIGH
2
MAX
1
0
-1 0
20
40
60
80
100
% time
Figure 5.2. Averaged time-normalized graphs for joint torques for (a) ankle, (b) knee, (c) hip, (d) shoulder and (e)
elbow joints for each jump type (LOW, HIGH, MAX).
Max moment knee (Nm/kg
6
5
4
3
2
1
0
0
1
2
3
4
5
6
Max moment hip (Nm/kg)
Figure 5.3. Scatter plot relating maximal joint moment at hip and
knee. The inverse interaction between both variables is indicated by
the linear trend line.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
66
Relations between work done at the elbow and shoulder with work done at the lower
limb joints are shown in Table 5.3. The interaction between work done at the elbow
and shoulder and work done at the lower limb joints revealed a significant interaction
with the work done at the hip joint but no significant interaction with work done at the
knee or ankle. The strong link between hip joint and arm swing contribution (i.e. work
done at shoulder and elbow joints) was primarily related to the forward inclination of
the trunk. A high correlation was found between trunk inclination and hip, shoulder
and elbow work (r = 0.918, P < 0.001; r = 0.447, P < 0.001; r = 0.593, P <0.001,
respectively). Figure 5.4 shows that forward inclination of the trunk allowed the arms
to retract without energy input and this might be an important feature explaining the
latter high correlations with trunk inclination (see discussion below).
3.5
LOW
energy (J.kg-1)
3
2.5
HIGH
2
MAX
1.5
1
0.5
0
0
20
40
60
% movement time
80
100
Figure 5.4. Averaged curves of variation of the total energy of the
arms, relative to a fixed reference point in the laboratory.
A qualitative interpretation of EMG data (Figure 5.5) revealed overall similarity in
muscle activation over jump conditions. One difference in EMG activity between
conditions was the earlier peak for the MAX condition in the Biceps Femoris muscle
(Figure 5.5d). This earlier muscle activity would be associated with an earlier onset of
muscle force which served to increase the hip extension torque while at the same
time reduced the knee torque. Another difference between conditions was the
reduced Rectus Femoris muscle activity as jump height increased (Figure 5.5c). This
reduced activity would also allow for an increased hip extension torque and reduced
knee extension torque.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
(b) vastus lateralis
EMG (arbitrary units)
EMG (arbitrary units)
(a) gastrocnemius
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
LOW
HIGH
MAX
0
20
40
60
% movement time
80
0.8
LOW
0.6
HIGH
MAX
0.4
0.2
0
100
0
LOW
HIGH
0.6
MAX
0.4
0.2
0
0
20
40
60
% movement time
20
40
60
% movement time
80
100
80
100
(d) biceps femoris
EMG (arbitrary units)
EMG (arbitrary units)
(c) rectus femoris
1
0.8
67
80
100
0.4
LOW
0.3
HIGH
MAX
0.2
0.1
0
0
20
40
60
% movement time
Figure 5.5. Averaged time normalized graphs for each jump type for muscle EMG for (a) Gastrocnemius, (b) Vastus
Lateralis, (c) Rectus Femoris and (d) Biceps Femoris.
4. Discussion
The present study was designed to investigate to what extent individuals use an arm
swing in sub-maximal vertical jumping, and to test whether previously observed
movement adaptations in sub-maximal jumps without an arm swing still hold in a
more natural execution with arm swing. Results showed that the arms were
progressively used more forcefully as jump height increased. The use of the arm
swing was strongly related to the work done at the hip joint but did not influence the
superior role of the hip in controlling the jump height.
For comparison of the present results (with arm swing) with results from our previous
investigations (without arm swing, Vanrenterghem et al., in press) one should note
that the present sub-maximal jumps ranged from 65% to 100% whereas in the other
investigation jumps ranged from 25% through 50% and 75% to 100%. Results from
the latter 25% jump condition cannot be compared to those in the present study. The
higher jump conditions, though, showed that with increasing jump height the
movement time and countermovement amplitude increased, similar to the results
found in the present study with arm swing. In both studies, the primary role of the hip
was demonstrated by increasing hip joint torques as jump height increased. Knee
joint torques in the present study with arm swing showed a reduction from 65% to
100% jump heights and in the study without arm swing a reduction was found from
the 75% to 100% jump heights. The ankle joint torques were similar throughout
conditions both with and without the use of an arm swing to enhance performance.
Joint work output also revealed similar results, confirming the major role of the hip
joint in determining jump height whereas knee and ankle joint contributions were
largely independent of jump height. This comparison revealed that the arm swing
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
68
does not have a structurally important effect on the movement adaptations for submaximal jumping observed in the lower limb segments.
Results of the present study revealed that in jumps with an arm swing, performance
is also related to work output at elbow and shoulder joints. Work output at these two
joints, together with work output at the hip joint, seemed to interact with each other
such that increased hip contribution involved increased contribution from the shoulder
and elbow joints. This increased contribution was found to be due to an increased
range of motion and increased torques about the shoulder joint. These were related
to an increased forward inclination of the trunk as jump height increased, suggesting
that trunk inclination is a key variable determining the contribution of both hip and
arms to performance.
To indicate the important role of trunk inclination, it was shown that inclining the trunk
has advantages when using an arm swing. The joint torques for retracting the arms
(Figure 5.2, d-e) were low, showing that little muscle activity is required for the
retraction of the arms. The arms practically rotate around their centre of mass such
that the amount of energy required to bring them to their retracted position was
negligible (Figure 5.4). This shows that the extent of forward inclination of the trunk
plays a crucial role in that it determines the amount of work which can be done at the
hip joint and allows retraction of the arms with minor work input, providing the initial
state for an optimal arm swing contribution. The role of trunk inclination has already
been found to be crucial for movement adaptations in sub-maximal jumps without the
use of an arm swing (Vanrenterghem et al., in press), suggesting that the amount of
trunk inclination determines the amount of arm swing contribution rather than the
other way around.
Another important feature in the interaction of segments is the inverse correlation
found between peak joint torques at the hip and knee. The mechanism of increased
muscle forces through lower muscle contraction velocities (Hill, 1938) cannot explain
this as increased hip joint torques are expected to cause a greater downward force
on the knee joint through increased vertical acceleration of the trunk segment. This
should cause reduced knee extension velocity and increased knee joint torques due
to the lower velocities of the muscle contraction. However, the mechanism that might
explain the inverse relation between torques at the hip and knee joints is the
presence of bi-articular muscles. When the bi-articular hamstring muscles produce
more power at the hip, that is, increasing the net joint torques at the hip, its biarticular structure at the same time reduces the net joint torques at the knee.
Similarly, when the bi-articular Rectus Femoris muscle activation is less, this would
lead to increased net joint torques at the hip and decreased net joint torques at the
knee. A qualitative interpretation of EMG results seemed to confirm this hypothesis,
and therefore it is suggested that altered activity of bi-articular muscles caused the
combined reduction of knee action and increase of hip action as jump height
increases.
The observation of increased hip action as jump height increased, and in particular
the increased inclination of the trunk segment, supports movement effectiveness as a
criterion for the movement adaptations. A strong reduction of trunk flexion found in
sub-maximal jumping indicated (i) reduction of the potential energy deficit resulting
from the lowering of the centre of mass due to the countermovement and (ii) reduced
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
69
kinetic rotational energies of the trunk segment during joint extension. Besides these,
energetic advantages of the retraction of the arms were demonstrated. The
increasing trunk inclination as jump height increased enabled the arms to be
retracted by a rotation of the arms around their own centre of mass rather than
having to lift them against gravity. This required minimal energy input from the
shoulder muscles and was an extra argument supporting movement effectiveness as
a criterion for movement adaptations in view of the strong coupling between trunk
inclination and arm action.
5. Conclusions
The present study was designed to investigate the influence of using an arm swing
on movement adaptations for sub-maximal jumps. It was found that previously
reported movement adaptations in the vertical jump from sub-maximal to maximal
performance without using an arm swing, were not perturbed when using an arm
swing. The arm swing contribution was related to the dominant role that the hip plays
through an increased forward inclination of the trunk. This enabled a work free
retraction of the arms and allowed increased shoulder and elbow contributions as
jump height increased. In general, this confirmed that a criterion like movement
effectiveness is a likely candidate to explain movement adaptations in complex tasks
at sub-maximal intensities.
Chapter 5
Arm swing in maximal and sub-maximal vertical jumps
70
6. References
Dempster, W.T. (1955). Space requirements of the seated operator. WADC technical
report, 55-159, Wright-Patterson Air Force Base, OH
Hill, A.V. (1938). The heat of shortening and the dynamic constants of muscle.
Proceedings of the Royal Society of London B, 126, 136-195.
de Koning, J.J. and van Ingen Schenau, G.J. (1994). On the estimation of
mechanical power in endurance sports. Sports Science Review, 3, 34-54.
Lees, A., Vanrenterghem, J. and De Clercq, D. (2004) Understanding how an arm
swing enhances performance in the vertical jump. Journal of Biomechanics (accepted
for publication).
Miller, D.I. and Nelson, R.C. (1973). Biomechanics of Sport. Philadelphia, Lea and
Febiger, pp. 39-88.
Murphy, S.D. and Robertson, D.G.E. (1994). Construction of a high pass digital filter
from a low pass digital filter. Journal of Applied Biomechanics, 10, 374-381.
Smith, G. (1989). Padding point extrapolation techniques for the Butterworth digital
filter. Journal of Biomechanics, 22, 967-971.
Vanrenterghem, J., De Clercq, D. and Van Cleven, P. (2001). Necessary precautions
in measuring correct vertical jumping height by means of force plate measurements.
Ergonomics, 44(8), 814-818.
Vanrenterghem, J., Lees, A., Lenoir, M., Aerts, P. and De Clercq D. (2004).
Performing the vertical jump: Movement adaptations for submaximal jumping. Human
Movement Sciences (In Press)
van Zandwijk, J.P., Bobbert, M.F., Munneke, M. and Pas, P. (2000) Control of
maximal and submaximal vertical jumps. Medicine and Science in Sports and
Exercise, 32 (2), 477-485.
Winter, D.A. (1990). Biomechanics and motor control of human movement. New
York: John Wiley.
Chapter 6
Summary and epilogue
Summary and epilogue
71
Chapter 6
Summary and epilogue
72
1. Summary
The research described in this dissertation was designed to gain more insight into
movement adaptations for maximal and sub-maximal executions of a ballistic task, in
particular a vertical jump from stance.
Prior to the main investigation, in Chapter 2, a methodological investigation was
undertaken to quantify the sources of error that limit the measurement of jump height.
The quality of the research heavily depended on correct jump height determination
and therefore the method of numerical integration of vertical acceleration signals
from measured ground reaction forces was analysed. This methodological
investigation revealed that under optimal testing circumstances, the numerical
integration method still suffered from three major sources of error. Firstly, the method
was found very sensitive to the determination of body mass. Even with sound
technical equipment, body mass values need to be optimized and therefore a
feasible optimization loop was proposed. Also, body mass should be determined for
each individual jump trial because of the high variability between trials. A second
source of error was the determination of the instant of take off, but with a sampling
frequency higher than 200 Hz this did not have consequences on jump height.
Finally, the algorithm for determining the start of integration needed critical
consideration. Its use could not be tested through the theoretical model that was
employed, but the algorithm has proven its use in numerous experimental and
simulated trials. It was concluded that the methodological analysis of the numerical
integration method provided sufficient insight into the strengths and weaknesses of
the method. Despite the weaknesses of the method it allows a correct jump height
determination when measurements and calculations are carried out with good care.
This knowledge provided the necessary methodological background to investigate
movement adaptations in maximal and sub-maximal vertical jumps. The research,
described in Chapter 3, revealed consistency among individuals in these movement
adaptations, suggesting that a certain criterion drives jumping strategy into a
consistent pattern. Results revealed that for jumps at different sub-maximal
intensities a consistent strategy was used of maximizing the contribution of distal
joints and minimizing the contribution of proximal joints. Taking into account (i) the
high inertia of proximal segments, (ii) the potential energy deficit due to
countermovement prior to extension, (iii) the advantageous horizontal orientation of
the foot segment during stance and (iv) the optimal tendon lengths in distal muscles,
it was concluded that movement effectiveness is a likely candidate for the driving
criterion of this strategy.
It was believed that through the high inertia of proximal segments, the rotation of
these segments involves high ineffective energy values relative to the effective
energy (resulting in jump height). In Chapter 4, this role of the high inertia of proximal
segments, in particular that of the trunk segment, was isolated by comparison of
Chapter 6
Summary and epilogue
73
jumps with and without restricted forward inclination of the trunk. Results revealed
that ankle joint contribution remained maximal throughout the different jump heights
and that the knee joint contribution was less restricted and had partly overtaken the
major role of the hip joint. This confirmed the likelihood of movement effectiveness as
a criterion for movement adaptations in sub-maximal vertical jumping as the ankle
joint contribution remained maximal.
The transfer of this criterion to explain movement adaptations in other movements
was by no means conclusive. Even in a variation of the vertical jumping movement
this criterion still needed to be tested. Therefore, in Chapter 5, its validity was further
tested in the more natural execution of the vertical jump, that is, with an arm swing
aiding jump performance. Results revealed that the arm swing increased as jump
height increased and this was in line with increased hip joint contribution. The
amount of forward inclination of the trunk explained how hip joint contribution and the
contribution of the arm swing changed with jump performance. This, together with the
fact that the ankle and knee joint contributions were largely independent of jump
height, led to the conclusion that movement adaptations observed in jumping without
an arm swing were not perturbed by the arm swing. In particular, the criterion of
movement effectiveness was still a likely candidate to explain the movement
adaptations for maximal and sub-maximal vertical jumping.
In conclusion, movement effectiveness was accepted as a criterion to explain the
observed movement adaptations for maximal and sub-maximal executions of a
vertical jump from stance. This was characterised by a maximised contribution of the
ankle joint due to its advantageous functional morphology and by minimised trunk
inclination due to the energetically disadvantageous high inertia of the trunk segment.
2. Constraints of the experimental protocol
In interpreting the data presented here, the reader must be aware of some limiting
aspects of this research. First, always to be considered in biomechanical analyses, is
the limitation of the methodology.
In the methodological investigation preceding the main research of this dissertation,
technical limitations of measuring ground reaction forces have been previously
discussed.
Also kinematic data have limitations, such as sampling frequency and measuring
accuracy. The present advances in technology have made it possible to measure at
high frequencies and filtering techniques have been developed to increase
measuring accuracy and represent smooth kinematic data. General knowledge about
these aspects is required to apply these techniques correctly and interpret the data
within the boundaries of the technology (Winter, 1990). Also, the reduction of the
data poses some limitations. A segmental analysis requires a model of the human
effector system, and this can vary from a very simple two-segment model to a
complex model with more than 20 segments. Both types of models have advantages,
for example, simple models are easier to interpret whereas complex models are a
better representation of the real system. In the present investigations, a 4 to 6
segment two-dimensional model was chosen to represent the human body. This
involved the assumptions that the vertical jump is basically a movement in the
sagittal plane and that joints between segments were hinge-based joints. The
Chapter 6
Summary and epilogue
74
combination of kinematic and kinetic data again involves certain limitations.
Calculating joint torques, joint powers and eventually joint work output requires the
combined use of kinetic and kinematic data. Therefore, all previous limitations apply
to this methodology, added with the summation of errors by calculating values based
on previously calculated values (Winter, 1990).
A third methodology used was electromyography. The preparation of the skin prior to
attaching the electrodes, the movement of skin tissue, movement of sub-cutaneous
tissues, movement of the wires to which the electrodes are attached, the presence of
electrical fields in the environment, filtering techniques applied to analyse the signals
and numerous other factors make it difficult to interpret measures of minimal
electrical currents in the muscle from the surface of the skin.
Standard procedures, based on a thorough study of the available literature, were
used in the present research and critical considerations were taken when interpreting
kinematic, kinetic or electromyographic data (see Winter (1990) and de Luca (1997)
for an overview). Nevertheless, one inconsistency repeatedly occurred throughout
the different data sets (in different laboratories, with different processing routines),
that is, summed joint work output was consistently lower than the mechanical work
done to raise the centre of mass. One would expect the work done by the joints to
exceed the work done in raising the centre of mass. Namely, besides the work done
to raise the centre of mass – that is, to increase effective energy – part of the work
done by the joints results in rotational or horizontal kinetic energy and energy due to
the velocity of segmental mass centres relative to the body centre of mass (Bobbert
and van Soest, 2001). The latter ineffective energies are approximately 3% of the
total energetic change in a vertical jump (Hatze, 1998). As such, results in the study
by Hatze (1998) were in line with the physical laws, but the inconsistency found in the
present research has also been found in other studies (Hubley and Wells, 1983,
individual trials; Nagano et al., 1998; Nagano et al., 2000; Fukashiro and Komi,
1987). Until now, it has not been possible to find the true reason of this
inconsistency. Suggested sources of error were: (i) the elevation of the shoulder
joints, (ii) the extension of metatarsal joints, (iii) additional articulations in lumbar,
thoracic and cervical inter-vertebral joints, (iv) deficiencies in spatial synchronisation
of the force platform and kinematic coordinate systems, (v) calculation noises due to
the numerical differentiation and integration processes (< 0.8% reported in Nagano et
al., 2000), (vi) the use of mass distributions and rotational inertia of the body
segments for standard populations, (vii) a systematic underestimation of joint work
output due to low-pass over-filtering of high frequent signals in kinematic data.
Further methodological investigations beyond the scope of this dissertation are
required to find the true reason for this anomaly. However, this inconsistency was
thought not to undermine the interpretation of data to test the outlined hypotheses.
The interpretation of experimental results has the advantage of observing reality as it
occurs. The disadvantage, however, is that interpreting experimental data in order to
investigate certain aspects of that movement inherently induces alterations of other
than the investigated aspects. The investigator makes the assumption that
throughout the altered conditions aspects other than the ones investigated do not
change or at least that the investigated aspects are not influenced by changes in
other aspects. Examples of such aspects are differences in storage and re-utilisation
of elastic energy, differences in pre-stimulation of muscles, or differences in
activation-loading dynamics – i.e., force-length-velocity conditions – of the muscles’
contractions. These aspects have been addressed in Chapter 3, showing that force-
Chapter 6
Summary and epilogue
75
length curves of the triceps surae muscle-tendon complex were optimal throughout
sub-maximal and maximal executions of the vertical jump. Due to similarity of ankle
joint torques and joint angular evolutions, it is the author’s opinion that this line of
reasoning continues for the other studies regarding jumping with restricted trunk
inclination (Chapter 4) or jumping with an arm swing (Chapter 5). However, in
Chapter 4, changed hip joint angular displacements (smaller range of motion in
jumps with restricted trunk inclination) may influence the activation-loading dynamics
of proximal muscles spanning the hip joint. Distal muscles have long tendons and
strongly depend on the mechanical properties (i.e., Youngs modulus) of these
tendons (Voigt et al., 1995; Kubo et al., 1999), but proximal muscles have short and
stiff tendons and are mainly dependent on the activation-loading dynamics (e.g.
force-length-velocity properties) of their contractile components. Therefore, it makes
sense to estimate muscle-tendon length changes of proximal muscles throughout the
jump movement, in particular when comparing jumps with and without restricted trunk
inclination. Figure 6.1 shows these length estimates for the rectus femoris and biceps
femoris muscles.
1.25
(a) rectus femoris (long head)
NM
1.2
normalised muscle length
normalised muscle length
1.25
UM
1.15
1.1
1.05
1
(b) biceps femoris
NM
1.2
UM
1.15
1.1
1.05
1
0
20
40
60
% movement time
80
100
0
20
40
60
% movement time
80
100
Figure 6.1. Normalised muscle lengths for (a) rectus femoris and (b) biceps femoris muscles in the normal maximal (NM) and
upright maximal (UM) conditions (described in Chapter 4). Lengths were calculated according to the regression equations in the
study of Hawkins and Hull (1990). The vertical line indicates the time of deepest position of the body centre of mass.
There were clear differences in muscle-tendon length changes between the
conditions (maximal vertical jumps with and without restricted trunk inclination). The
normal condition involved a minor stretch of the rectus femoris muscle-tendon
complex in the upward phase of the jump. The upright condition, on the other hand,
involved an immediate stretch of the rectus femoris muscle-tendon complex in the
downward phase, resulting in a more pronounced and slower stretch-shortening
cycle. The biceps femoris muscle-tendon complex was stretched in the normal
condition but had a constant length throughout the upright condition. Therefore, the
activation-loading dynamics were obviously different between both conditions due to
the different evolutions in muscle-tendon length, even when assuming that both
muscles are activated maximally in both conditions. Numerous challenging
interpretations of these findings are possible, among which the most favourite one
addresses the fact that the rectus femoris muscle had a more pronounced excentric
working load in the upright condition, meaning that higher forces might have been
possible due to a shift in the force-length relation of contractile components (if
activation levels are similar). These higher forces in the rectus femoris muscle would
then induce stronger knee extension, supporting the notion of higher knee joint
torques in the upward condition and adding to the previously stated hypotheses (see
Chapter 6
Summary and epilogue
76
Chapter 4). However, EMG levels were not similar between both conditions (see
Figure 4.3), having consequences for the above reasoning. Also changes in activity
of the gluteus muscles (which is not known), gastrocnemius and biceps femoris
muscles (see Figure 4.3), etc., would again have consequences for these
interpretations. Therefore, one can feel that the interpretation and further
investigation of such findings would exceed the timeframe of the present dissertation,
but that it would take us into another intriguing area within biomechanics and
neurophysiology, namely that of muscle dynamics (reviews in Hof, 2003; Huijing,
1998).
3. Further implications
The research described in this dissertation was designed to test a number of theories
and hypotheses. However, the present research has also resulted in additional
findings beyond the initial scope of the research.
3.1. Implications for power training regimens
A first implication of our findings was evident in the ankle and knee joint
contributions. The ankle and knee joint contributions in a sub-maximal jump are as
high as in the maximal jump, and largely independent of jump height. Therefore,
vertical jump type movements in training require high levels of effort by the ankle and
knee muscles when using only moderate height jumps (over 60% of maximal jump
height). This has several implications for the planning of training regimens. When a
training regimen is designed to train muscle groups about the ankle and knee joints,
sub-maximal jumping is a sufficient stimulus. If the training regimen is targeted at the
hip extensor muscles, then only maximal jumping will stimulate maximal activity in
these muscles.
Also, when additional loads are used in a training regimen targeting the hip extensor
muscles, the loads should be carried in a way that enables forward inclination of the
trunk. A weighted vest or belt may be more appropriate than a bar bell held across
the shoulders. If the trunk inclination is prevented, the full engagement of the hip
extensor muscles will be limited with, consequentially, a reduced training effect.
These findings also have implications for injury prevention during training. The
constantly high joint torques in the knee and ankle joints induce similar stress in the
knee and ankle regions in sub-maximal and maximal jumps. Therefore, training at
sub-maximal intensity does not reduce stress in the ankle and knee regions. Whether
or not as a consequence, injuries like patellar tendinopathy – commonly known as
‘jumper’s knee’ – have a high incidence in sports activities involving repeated
jumping (Archambault et al., 1995; Bahr and Reeser, 2003; Stanish, 1984).
Rehabilitation regimens regarding injuries at the level of ankle or knee joints should
take into account these high joint torques when jumping higher than 60% of maximal
performance. When trunk inclination is restricted, for instance when training with a
bar bell held across the shoulders, sub-maximal jumps might even induce higher
stress than in the maximal condition with normal trunk inclination (deduced from the
results in Chapter 4). A detailed description of these implications is under second
review for the Journal of Strength and Conditioning Research (abstract in Appendix
1).
Chapter 6
Summary and epilogue
77
3.2. Implications for motor control research
An alternative approach to interpret the movement adaptations found in maximal and
sub-maximal vertical jumping lies within the motor control and motor learning
research. Since the early 1970s, a lot of work has been done to search for internal
representations explaining the movement patterns as they were observed externally
(Gentner, 1987; Schmidt, 1985). In the early 1970s, Schmidt (1975) developed the
Generalised Motor Program (GMP) theory. This theory suggests that movements can
be categorized into movement classes, solving the ‘storage capacity problem’.
Summarized, the GMP theory hypothesized that changing the amplitude or speed of
a movement is based on changes in the amplitude or duration of muscle activation
but the sequence of these muscle activations is invariant within the so called
movement class. This temporal invariance has been tested in discrete skills like
handling a lever or catching a ball (Heuer et al., 1995 ; Lenoir and Musch, 1999) and
results supported the existence of a GMP. Temporal invariance was also tested in
cyclic movements like walking and running (Shapiro et al., 1981; Rosenrot et al.,
1980; Whitall and Caldwell, 1992) and again data were in line with the existence of a
GMP. Besides temporal invariance, spatial proportionality has been related to the
existence of a GMP. In particular, spatial variables were proven proportional to
accelerations of the movement in handwriting (Hollerbach, 1978) and Schmidt (1999)
agreed with the latter author that accelerations are strongly related to the force
delivered by muscle groups. Therefore, it was believed that the presence of spatial
proportionality supports the credibility of the existence of a GMP.
The existence of a GMP in a non-cyclic, but balanced gross motor task – for
instance, the standing vertical jump in everyday sports situations – has not been
investigated before. The tasks in earlier studies were either tasks that do not
immediately relate to daily life, or were cyclic by nature. A first exploration of our data
within this motor control approach is shown in Figure 6.2, re-interpreting data that
were collected for Chapter 3 of this dissertation. Temporal invariance was
demonstrated for the entire movement duration of the jump in the 50%, 75% and
100% jump conditions. However, the upward phase of the 25% condition showed a
significantly different temporal evolution, highlighting that the extension generally
occurred earlier in the jump.
Chapter 6
Summary and epilogue
78
100
100
100%
*
50%
25%
*
50
*
25
0
0
20
40
*
60
80
75
50
25
Normalized displacement
(% hcountermovement + hcontact)
normalized displacement
(% hcountermovement)
75%
75
0
100
% Movement time
Figure 6.2. Averaged time-normalized graphs of whole body centre of
mass vertical displacement, in the four jump conditions as described in
Chapter 3. Displacement values were normalised to countermovement
amplitude in the descent phase and to countermovement amplitude
added with contact height in the ascent phase. (* indicates that timing
of the 25% jump condition differed significantly from all other conditions
[ANOVA, post hoc Tukey test, p < .05])
The same approach was used to interpret data regarding individual joints, that is, hip,
knee and ankle joints, in Figure 6.3. The same difference of the upward phase in the
25% jump condition was found compared with the other conditions for all joints. This
demonstrated (i) that the observations were in line with the GMP theory for the 50%,
75% and 100% jump conditions but (ii) that an earlier upward phase in the 25% jump
conditions was found. This fitted with the theory that a GMP controls the standing
vertical jump movement, but to a limited extent.
Chapter 6
Summary and epilogue
79
normalized angular displacement
(% range of motion)
(a)100
100%
75%
50%
25%
75
*
50
*
25
*
0
0
20
40
60
% movement time
80
100
100
normalized angular displacement
(% range of motion)
(b)
100%
75%
50%
25%
75
*
50
*
25
*
*
0
0
20
40
60
80
100
% movement time
100
normalized angular displacement
(% range of motion)
(c)
100%
75%
50%
25%
75
*
50
*
25
*
0
0
20
40
60
80
100
% movement time
Figure 6.3. Time-normalised graphs of joint angles of (a)
hip, (b) knee, and (c) ankle, respectively. Angular
displacement values were normalised to amplitude in the
descent phase and in the ascent phase, respectively (A *
indicates that timing of 25% condition differs significantly
from all other conditions [ANOVA, post hoc Tukey tests, p <
0.05]).
Spatial proportionality was also investigated. Table 6.1 shows data regarding the
displacement of the body centre of mass and joint flexion amplitudes of hip, knee and
ankle joints for the counter movement (relative to the stance phase). This showed an
increased countermovement amplitude and increased hip and knee joint flexion as
jump height increased, whereas ankle joint flexion was similar throughout all jump
Chapter 6
Summary and epilogue
80
conditions. Strictly, these data did not support the GMP theory, although overall
scaling of the movement and scaling in hip and knee joint flexion was found. The
similarity in ankle joint flexion throughout all jump conditions could not be explained
through interpretation of the GMP theory.
Table 6.1. Spatial variables (mean ± SD) describing the amplitude of counter movement through the vertical displacement
of the body centre of mass (hcountermovement) and through joint flexion amplitudes (θ). The correlation of each variable
with jump height was described by R².
hcountermovement
θHip
θKnee
θAnkle
25%
50%
75%
-0.04 ± 0.02 -0.13 ± 0.03 -0.21 ± 0.04
151.4 ± 7.3 124.8 ± 12.1 98.8 ± 16.9
129.2 ± 7.5 104.9 ± 6.5
96.5 ± 9.7
96.7 ± 6.1
90.6 ± 8.6
90.2 ± 7.5
100%
-0.32 ± 0.05
58.6 ± 15.7
89.0 ± 6.9
90.3 ± 6.6
R2
0.839
0.883
0.725
0.056
The author believes that the biomechanical approach used in Chapter 3 revealed
insights that are necessary to conduct the type of analysis described above.
Therefore, the author would encourage motor control and motor learning scientists to
undertake a more detailed investigation of this type of data. Currently the underlying
motor control mechanisms remain inconclusive.
3.3. Implications for arm swing technique
The present investigations involved the examination of the extent to which an arm
swing is used in maximal vertical jumping. In the past, several theories had been
proposed to explain the effect that an arm swing has on performance (Payne et al.,
1968; Harman et al., 1990; Feltner et al., 1999). The analysis of data from the
present investigations revealed that the increased performance stems from a
complex series of events which allowed the arms to build up energy early in the jump
and transfer it to the rest of the body during the later stages of the jump (Lees et al.,
accepted for publication). These events were described as (i) increased kinetic and
potential energy of the arms at take-off, (ii) storage and re-utilisation of energy from
the muscles and tendons around the ankle, knee and hip joint, and (iii) ‘pull’ on the
body through an upward force acting on the trunk at the shoulder.
The present results showed that the extent of using an arm swing in sub-maximal
jumps increased as performance increased. Therefore, it was questioned whether
these mechanisms operate in the same way as was found in maximal jumping. A
better knowledge of how these mechanisms act and interact as performance
increases enables a deeper understanding of how an arm swing enhances
performance and may provide some insight into which of these mechanisms may be
most worthy of developing within athlete training programmes. This separate
investigation was undertaken and revealed the continued existence of the three
mechanisms explaining enhanced performance in the maximal jump. The storage
and return of energy from the lower limbs and the ‘pull’ on the rest of the body
became more important as jump height increased. It was concluded that an arm
swing contributes to jump performance at sub-maximal as well as maximal jumping
through the same mechanisms, but that the energy generation and dissipation
sources change as performance approaches maximum. A detailed description of this
has been submitted to the Journal of Sports Sciences (abstract in Appendix 2).
Chapter 6
Summary and epilogue
81
4. Future research
Experimental research can serve to investigate many research questions and
hypotheses can often be accurately tested within an experimental approach.
However, recent developments of computer simulations allow new opportunities to
test hypotheses that are difficult or even impossible to test within an experimental
approach. The author of the present dissertation had limited experience with
computer simulations, but previous literature describing simulations of vertical
jumping have shown numerous applications for the investigation of isolated aspects
of the control and coordination. Previous literature described one simulation study
trying to demonstrate the control of sub-maximal jumps from the known muscle
activations in a maximal jump (van Zandwijk et al., 2000). A similar study, starting
from the criterion movement effectiveness, would be suggested. This could enable (i)
further testing of movement effectiveness as a criterion for sub-maximal jumping and
(ii) testing whether the human system uses criteria other than the ones investigated
in this study.
The author encourages future investigations that go beyond the vertical jump
paradigms. Conclusions made in the present study regarding the standing vertical
jump cannot be directly transferred to other movements. The outcome of the present
research prompts the investigation of movement effectiveness as a criterion for
movement adaptations in movement in general. In particular, the analogy of a
standing broad jump (Ridderikhoff, 1999) with the vertical jump allows a similar
analysis of kinematic, kinetic and electromyographic data. The quantification of
performance in the standing broad jump – i.e., jumping distance – differs from that in
the vertical jump. It is expected that the observed movement adaptations still apply
for this movement, but future research is needed to confirm this. Also, other
analogies could be found in the animal world. Several investigators have tried to
explain the confounding jumping capacities of certain animals (Aerts, 1998; BennetClark and Lucey, 1967; Kargo et al., 2002), and similarly movement effectiveness
could be tested as a criterion to explain how animals execute sub-maximal
performances.
Chapter 6
Summary and epilogue
82
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influence of tendon youngs modulus, dimensions and instantaneous moment arms
on the efficiency of human movement. Journal of Biomechanics,
Whitall, J. and Caldwell, G.E. (1992). Coordination of symmetrical and asymmetrical
human gait. Journal of Motor Behavior, 24, 339-353.
Winter, D. (1990) Biomechanics and motor control of human movement. John Wiley,
New York.
Chapter 7
Nederlandse samenvatting
Nederlandse samenvatting
85
Chapter 7
Nederlandse samenvatting
86
1. Doelstelling van het onderzoek
De mogelijkheid van de mens om een uitgebreid gamma aan bewegingen met grote
precisie en efficiëntie uit te voeren is fascinerend. Het is bewonderenswaardig hoe de
mens in staat is een uitgebreid arsenaal van activiteiten gecontroleerd en met de
grootste precisie uit te voeren, gaande van kleinmotorische taken (zoals schrijven of
naaien) tot grootmotorische taken (zoals stappen of springen). Het doorgronden van
deze kwaliteiten was en is nog steeds de aanzet tot menig wetenschappelijk
onderzoek.
Naast stappen en lopen is ook springen een basisvaardigheid die deel uitmaakt van
de algemene motorische ontwikkeling van het kind. Springen is een grootmotorische
taak die bij tal van sportactiviteiten voorkomt, zonder dat deze taak afhankelijk is van
specifieke sporttechnische vaardigheden. Zo dient de verticale hoogtesprong als
maatstaf (in heel wat sporten en in sportmedische begeleiding) om de algemene
explosiviteit van de onderste ledematen te evalueren en is het een eenvoudig in te
lassen trainingscomponent om die explosiviteit te verbeteren.
Ondanks het grote gemak waarmee een hoogtesprong wordt uitgevoerd, blijkt dat de
hoogtesprong het resultaat is van een complexe interactie van de onderste
ledematen. Dit is reeds uitvoerig bestudeerd vanuit een groot aantal varianten van de
maximale hoogtesprong. Dergelijk onderzoek heeft geleid tot een ruime kennis over
de manier waarop de mens maximaal presteert, of hoe specifieke lichaams- en
bewegings-gerelateerde eigenschappen interageren om maximaal te presteren. De
belangrijkste lichaamsgerelateerde eigenschappen in het licht van de huidige
context, zijn:
• het aantal gewrichten dat een spier overspant,
• de optimale lengte en snelheid van een spiercontractie,
• de spier-pees lengteverhouding,
• de fysiologische doorsnede van de spier,
• de inertie van individuele segmenten.
Als bewegingsgerelateerde eigenschappen zijn er:
• de geometrische en anatomische beperkingen in het omzetten van rotatie
naar translatie door segmenten,
• het grote aantal vrijheidsgraden,
• de noodzakelijke niet-effectieve energielevering om effectieve energie te
produceren.
De sprongbeweging is onderhevig aan deze eigenschappen. Voor het bereiken van
een maximale prestatie is uit voorgaand onderzoek gebleken dat elk van deze
eigenschappen schijnbaar optimaal in rekening gebracht wordt. Deze optimale
coördinatie wordt gekenmerkt door een proximo-distale bewegingssequentie.
Chapter 7
Nederlandse samenvatting
87
De proximo-distale bewegingssequentie bestaat uit het vroeger strekken van
proximale segmenten (bijvoorbeeld het rompsegment) ten opzichte van distale
segmenten (bijvoorbeeld het voetsegment). Dit werd onder andere gevonden in
werpen, hardlopen en springen. Ondanks het uiteenlopend karakter van deze
bewegingen gaat het hier om ballistische bewegingen waarin het lichaam of een
voorwerp vanaf lage snelheid in een bepaalde richting tot een hoge snelheid
versneld wordt. Voor het nastreven van dit doel gaat de proximo-distale
bewegingssequentie gepaard met:
(i)
optimaal gebruik van bi-articulaire spieren door afremming van de
strekking van proximale segmenten om te zetten in versnelling van de
strekking van distale segmenten,
(ii)
optimale lengte en trage snelheid bij de contractie van spiervezels,
(iii)
optimaal gebruik van lange spierpezen in distale spieren door
voorspanning die is opgebouwd vanuit trage contracties in proximale
spieren met korte spierpezen,
(iv)
trage rotaties van proximale segmenten met grote inertie en snelle rotaties
van distale segmenten met lage inertie,
(v)
maximale effectiviteit van bewegen door effectief gebruik van spierarbeid
om het mechanisch doel te bereiken (in de vorm van potentiële en verticaal
kinetische energie).
Betreffende de enkelvoudige hoogtesprong, werd dus gesteld dat door de proximodistale bewegingssequentie maximale effectiviteit bereikt wordt en resulteert in de
maximale prestatie van het bewegingssysteem. Maar gaan dezelfde wetmatigheden
op bij een submaximale hoogtesprong? Is effectiviteit bepalend voor de coördinatie
van de submaximale hoogtesprong? Een mogelijke strategie die zich meteen
opdringt als criterium voor bewegingsaanpassingen in submaximaal springen is het
vertraagd uitvoeren van de maximale beweging, namelijk door de sterkte van
spieractivatie te reduceren en de duur ervan te laten toenemen. Deze strategie is
aantrekkelijk op neuronaal niveau en werd geobserveerd bij het zwemmen van
bepaalde larven, maar in de verticale hoogtesprong lijkt dit onwaarschijnlijk vanwege
de grote inwerking van de gravitatiekracht op het lichaam (welke slechts erg beperkt
aanwezig is onder water). Zo werd in voorgaand onderzoek het spieractivatie-patroon
in een maximale sprong vergeleken met dat van een sprong naar 80% van die
maximale hoogte. Duidelijke verschillen in relatieve timing van spieractivatie werden
vastgesteld. Dit bevestigt dat neuromusculaire controle van een submaximale
hoogtesprong niet door eenvoudige slow motion gestuurd wordt. De zoektocht naar
een criterium voor bewegingsaanpassingen in submaximaal springen was dus
geopend.
2. Het onderzoek
Het doel van huidig onderzoek was inzicht te krijgen in de aanpassing van het
bewegingspatroon van de verticale hoogtesprong bij het variëren van het
prestatieniveau.
De
spronghoogte
fungeert
hier
als
onafhankelijke
onderzoeksvariabele en het correct bepalen van spronghoogte was dan ook een
eerste vereiste voor juiste interpretatie van onderzoeksgegevens.
Chapter 7
Nederlandse samenvatting
88
2.1. Correcte bepaling spronghoogte.
De numerieke integratie van versnellingssignalen vanuit grondreactiekracht-meting
is, wegens de hoge precisie van deze meting, bij wetenschappelijk onderzoek de
standaard geworden om correct de spronghoogte te bepalen. Ondanks de grote
precisie van deze methode hebben onzekerheden in literatuur en een ruime
praktijkervaring op verschillende foutenbronnen gewezen die aanleiding kunnen
geven tot het foutief berekenen van beide variabelen. Deze foutenbronnen zijn:
(i)
de bepaling van lichaamsmassa
(ii)
de bepaling van het ogenblik van loskomen van de grond
(iii)
de integratie frequentie
(iv)
de integratieconstanten en de consequenties voor het bepalen van de start
van de sprongbeweging.
In het huidige onderzoek werd een theoretisch model ontwikkeld en is het mogelijk
gebleken om de invloed van deze foutenbronnen op de berekeningen te meten. Uit
de vergelijking van analytische en numerieke integratie-methoden werd de methode
geoptimaliseerd en werd aangetoond dat een accurate bepaling van
spronghoogtevariabelen mogelijk is indien de metingen en berekeningen met zorg
worden uitgevoerd.
2.2. Beschrijving van aanpassingen in bewegingscoördinatie in maximale en submaximale hoogtesprong
Met een accurate bepaling van spronghoogte was het mogelijk om aanpassingen in
bewegingscoördinatie in submaximale tot maximale hoogtesprongen te bestuderen.
Voor dit onderdeel werden hoogtesprongen uit stand naar 25%, 50%, 75% en 100%
van maximale prestatie geanalyseerd. Er werd een hoge consistentie in
bewegingsuitvoering gevonden, suggererend dat een bepaald criterium het
bewegingspatroon bepaalt. De bewegingsuitvoering voor variërende spronghoogten
werd gekenmerkt door maximale bijdrage van de distale gewrichten en minimale
bijdrage van proximale gewrichten. De effectiviteit van bewegen werd op die manier
als aannemelijk criterium aanvaard, rekening houdend met (i) de grote inertie van
proximale segmenten, (ii) het verlies aan potentiële energie door de inveerbeweging,
(iii) de voordelige horizontale oriëntatie van het voetsegment bij de uitgangshouding
en (iv) de optimale peeslengtes in distale spieren vergeleken met die van proximale
spieren.
2.3. De rol van voorwaartse inclinatie van het rompsegment
De belangrijke rol van proximale segmenten heeft geleid tot onderzoek met als
doelstelling het verwerven van inzicht in de relatie tussen voorwaartse inclinatie van
de romp en de bijdrage van individuele gewrichten tot spronghoogte. Dit inzicht werd
verwacht uit een vergelijking van de sprongbeweging met en zonder toegelaten
voorwaartse inclinatie van de romp, en dit voor submaximale tot maximale
hoogtesprongen. Resultaten toonden aan dat de bijdrage van het enkelgewricht tot
de sprong maximaal bleef voor de verschillende sprongcondities en dat in sprongen
met beperkte rompinclinatie de kniebijdrage sterker was, en zo gedeeltelijk de rol van
het heupgewricht overnam. Deze resultaten bevestigden de hypothese dat de
effectiviteit van bewegen een criterium is voor de bewegingsaanpassingen in
submaximale tot maximale hoogtesprongen.
Chapter 7
Nederlandse samenvatting
89
2.4. Invloed van de armzwaai op bewegingsaanpassingen bij maximale en submaximale hoogtesprong
Het onderzoek naar criteria die instaan voor de bewegingsaanpassingen van
submaximale tot maximale hoogtesprongen heeft inzicht verschaft in hoe een
ballistische enkelvoudige beweging zoals de hoogtesprong gestuurd wordt. De
resultaten uit ons onderzoek konden echter niet rechtstreeks doorgetrokken worden
naar andere bewegingen, laat staan naar een variante op de onderzochte
sprongbeweging. In een volgend onderzoek werd daarom nagegaan in hoeverre
bewegingsaanpassingen voor submaximale en maximale hoogtesprongen zonder
armzwaai ook in de hoogtesprongen met armzwaai gelden. Hierin werd gevonden
dat de bijdrage van de armzwaai toeneemt naargelang spronghoogte toeneemt, en
dit ging gepaard met een toenemende heupbijdrage. Het verband tussen beide
bevindingen werd verklaard door de mate van voorwaartse inclinatie van de romp.
De bijdrage van knie- en enkel-gewricht was echter grotendeels onafhankelijk van
spronghoogte. Uit dit alles werd geconcludeerd dat bewegingsaanpassingen voor
submaximale tot maximale hoogtesprongen nog steeds aanwezig zijn bij sprongen
met gebruik van de armzwaai.
3. Conclusie
De effectiviteit van bewegen werd aanvaard als een criterium voor
bewegingsaanpassingen in submaximale tot maximale uitvoeringen van een verticale
hoogtesprong uit stand. Dit criterium werd in hoofdzaak bepaald door het
maximaliseren van de bijdrage van het enkelgewricht omwille van de voordelige
functionele morfologie en door het minimaliseren van de bijdrage van proximale
gewrichten omwille van de energetisch nadelige hoge inertie van proximale
segmenten zoals het rompsegment.
Chapter 8
Appendices
Appendices
91
Chapter 8
Appendix 1
92
THE MAXIMAL AND SUB-MAXIMAL VERTICAL JUMP: IMPLICATONS FOR
STRENGTH AND CONDITIONING
Adrian Lees1, Jos Vanrenterghem2 and Dirk De Clercq2
1
Research Institute for Sport and Exercise Sciences, Liverpool John Moores
University, United Kingdom.
2
Department of Movement and Sports Sciences, Ghent University, Belgium.
Abstract
The vertical jump is a widely used activity to develop explosive strength, particularly
in plyometric and maximal power training programs. It is a multi-joint action which
requires substantial muscular effort from primarily the ankle, knee and hip joints. It is
not known if sub-maximal performances of a vertical jump have a proportional or
differential training effect on the major lower limb muscles compared to maximal jump
performance. Therefore, the purpose of this study was to investigate the contribution
that each of the major lower limb joints makes to vertical jump performance as jump
height increases, and to comment on the above uncertainty. Adult males (N=20)
were asked to perform a series of sub-maximal (LOW and HIGH) and maximal (MAX)
vertical jumps while using an arm swing. Force, motion and EMG data were recorded
during each performance and used to compute a range of kinematic and kinetic data
including ankle, knee and hip joint torques, powers and work done. It was found that
the contribution to jump height made by the ankle and knee joints remains largely
unchanged as jump height increases (work done at the ankle: - LOW =1.80,
HIGH=1.97 , MAX=2.06, J.kg-1, F= 3.596, p= 0.034; knee:- LOW =1.62, HIGH=1.77,
MAX=1.94, J.kg-1, F= 1.492, p = 0.234) and that superior performance in the vertical
jump is achieved by a greater effort of the hip extensor muscles (work done at the
hip:- LOW =1.03, HIGH=1.84, MAX=3.24, J.kg-1, F=110.143, p<0.001 ). It was
concluded that the role of sub-maximal and maximal jumps can be differentiated in
terms of their effect on ankle, knee and hip joint muscles, and may be of some
importance to training regimens in which these muscles need to be differentially
trained.
The full manuscript was submitted to the Journal of Strength and Conditioning
Research (July 2003) and re-submitted after positive recommendations (January
2004).
Chapter 8
Appendix 2
93
THE BENEFIT AND ENERGETICS OF AN ARM SWING ON MAXIMAL AND SUBMAXIMAL VERTICAL JUMP PERFORMANCE
Adrian Lees1, Jos Vanrenterghem2 and Dirk De Clercq2
1
Research Institute for Sport and Exercise Sciences, Liverpool John Moores
University, UK.
2
Department of Movement and Sports Sciences, Ghent University, Belgium.
Abstract
The purpose of this study was to investigate the benefit of an arm swing in submaximal and maximal vertical jumping and to establish the energy build up and
dissipation mechanisms associated with this benefit. Twenty adult males were asked
to perform a series of sub-maximal and maximal vertical jumps while using an arm
swing. Force, motion and EMG data were recorded during each performance and
used to compute a range of kinematic and kinetic data including ankle, knee, hip
shoulder and elbow joint powers and work done. It was found that the energy benefit
of using an arm swing appears to be closely related to the maximum kinetic energy of
the arms during their downswing and increases as jump height increases. As jump
height increases, energy in the arms is built up by a greater range of motion at the
shoulder and greater effort of the shoulder and elbow muscles but, as jump height
approaches maximum, these sources are supplemented by energy supplied by the
trunk due to its earlier extension in the movement. The energy of the arms is used to
increase their potential energy at take-off but also to store and return energy from the
lower limbs and to ‘pull’ on the rest of the body. These latter two mechanisms
become more important as jump height increases with the pull being the more
important of the two. It was concluded that an arm swing contributes to jump
performance at sub-maximal as well as maximal jumping but the energy generation
and dissipation sources change as performance approaches maximum.
The full manuscript was submitted to the Journal of Sports Sciences (December
2003)
Acknowledgements / Dankwoord
Acknowledgements / Dankwoord
95
Acknowledgements
96
“Science is organised knowledge. Wisdom is organised life.”
Back in May 1997, the author of this dissertation undertook the
challenge to simulate a vertical jump by using a relatively simple model. This physical
model consisted of a hinged wooden skeleton that was moved by elastic bands and
controlled by strings. The success of this experiment – that is, the first jumps of
Jumping George – and the rather unexpected international recognition, were the start
of a thrilling adventure in the small world of biomechanics and movement analysis.
This adventure led to the production of numerous rejected manuscripts, but with
perseverance close to an obstinate attitude it also led to the submission of this
dissertation. The ‘antics’ with which it all started originally had only a limited purpose,
but with the help of some good-natured individuals who shared the challenge and
gave an occasional push towards the tracks, a proper direction and cruising speed
were reached for the years to come.
So, where it all started, dad and uncle Romain helped Jumping George through a
very ‘woodenly’ boarding school. Their skills and true inventions often exceeded
perfection. Also Dirk De Clercq was there at that time to help uncork the Champagne,
and Dirk undertook the role of supervisor in the following six years (what two glasses
can do…). Through these years, our collaboration became one of fluent interaction,
mutual trust and respect, and often U-turns on both professional as well as personal
levels. Dirk, I’ve always enjoyed working with you, and hopefully the future offers
more full sails to sail with and high peaks to climb on!
Thus, gradually a world traveller started exploring new horizons. After a fascinating
intermezzo in Amsterdam – for which I still wish to thank the entire research group of
the late Gerrit Jan van Ingen Schenau – it came to Antwerp as its first stop. This is
where Peter Aerts continuously demonstrates how experimental data are brought to
life. As a true magician, Peter shows what it is all about, and proves how humans,
like all animals, have to live in line with the laws of physics. Peter provided my first
abacus, and through his patience against my often stubborn attitude I have the
greatest respect for this biologist.
Continuing the journey, it brought me to Canada, where I first met Adrian Lees.
Adrian invited me to visit his home-grounds in Liverpool, and soon I turned into a
Liverpudlian in order to withstand pouring rain and occupy the Henry Cotton Campus
on a regular basis (where I was banned to the basement). Working with Adrian
stands for that scientific stimulus through intriguing conversations, supersonic
scientific writing and a good old pint of lager! Besides Flanders’ fields, in particular
Gent, Liverpool has become an indispensable part of my life. And Adrian, can I order
new cod liver oil tablets…?
Acknowledgements
97
It remains that the author wishes to thank everyone who provided all the good
memories over these years, especially my family, friends and colleagues. I will
always praise all of you for tolerating my impulsiveness, poor memory and frequent
absence! Randomly, I call up…
… mom, dad and Kris, for living with a hyperactive son and brother, and for the
everlasting support in which ever choice I make.
… Pierre, Veke, An’leen, Davy, Christoph, Frederik, Matthieu and Liesbeth, for the
fantastic atmosphere in and around ‘our’ lab.
… An, Wim, Miek, Michel, Liesbeth, Ina, Karla, Pascale, and all of your companions,
for the good old days and the better future.
… Myrke, Ine, Anneleen, Annemie, for the numerous moments of joy and for helping
demolish brain cells!
… Cherd, Rach, Knot, Jae, Yok, Yingying and the rest of the Thai Society, for the
Thai oasis in St. Andrews Gardens in Liverpool. Hopefully I’ll visit you soon in
Thailand! And to everyone that soon graduates: congratulations!
… Ben, Neil,… for being who you are and allowing me to intrude into your lives!
… Adolf, for introducing me into the fine arts of computer programming.
… Kat, for the enjoyable moments that we shared throughout the past years, and for
the beautiful design of the cover of this dissertation.
… Rhys and Joanne, Willem, for the time you’ve spent to conquer reading this entire
dissertation and providing helpful comments.
… The ones that I would forget here, for forgiving me over a pint…
And, finally, remember that the beginning is always today!
Walk on,
Jos
Dankwoord
98
“Science is organised knowledge. Wisdom is organised life.”
Zeven jaar terug, in mei 1997, ondernam ik een poging om een
hoogtesprong na te bootsen aan de hand van een relatief eenvoudige constructie.
Deze constructie, gebaseerd op een scharnierend houtskelet, werd bewogen door
elastieken en gecontroleerd door touwtjes. Na weken van reken- en knutselwerk, was
er plots die vroege ochtend met de eerste beelden waarop het geheel amper twee
millimeter opveerde, maar die het bewijs leverden dat het allemaal niet voor niets
was geweest. Met deze eerste sprongen was Jumping George geboren en slaagde
ik op de valreep in m’n opzet. De onverwachte internationale erkenning die in
Kopenhagen volgde, werd de aanzet tot mijn groeiende interesse in het kleine
wereldje van de biomechanica en bewegingsanalyse. De “bokkesprongen” waarmee
dit alles begon waren oorspronkelijk weinig doelgericht, maar met de hulp van enkele
goedmoedigen, die me met raad en daad bijstonden, vond ik de juiste richting en een
aangename kruissnelheid om op verkenning te gaan in de fascinerende wereld van
de wetenschap.
Bij het vertrek in Gent waren daar pa en nonkel Romain, die George doorheen z’n
zware kostschool hielpen. Ook Dirk De Clercq hielp toen om de champagne te
ontkurken, en ging de uitdaging aan om me onder zijn vleugels om te scholen tot
wetenschappelijk avonturier (wat enkele glaasjes champagne al niet kunnen
doen…). Doorheen de jaren is onze samenwerking er één geworden van flitsende
interacties, wederzijds vertrouwen en respect, en van ingrijpende wendingen zowel
op professioneel als op persoonlijk vlak. Hopelijk brengt de toekomst nog veel goeie
wind in de zeilen en hoge bergtoppen om te beklimmen.
Vanuit Gent ging de reis naar Amsterdam. Daar leerde ik vooral dat er nog heel veel
te leren valt, waarvoor ik de groep van wijlen Gerrit Jan van Ingen Schenau bijzonder
dankbaar ben. Antwerpen was de volgende tussenstop op het Europese vasteland,
waar Peter Aerts voor het eerst toonde hoe cijfermateriaal tot leven komt. Als een
gedreven kunstenaar toont Peter waar het allemaal om draait, en levert hij het bewijs
hoe mens en dier aan de wetten van de fysica onderhevig zijn. Hij bezorgde me als
het ware mijn eerste telraampje, en door z’n geduld tegenover mijn koppigheid betuig
ik groot respect voor deze badmintonner-bioloog.
Met de rugzak volgeladen met souvenirs uit Gent, Amsterdam en Antwerpen, werd
de grote overtocht gewaagd en het machtige Canada betreden. Daar ontmoette ik
Adrian Lees voor het eerst. Op een bijzonder hartige wijze nodigde Adrian me uit om
op regelmatige basis de Henry Cotton Campus in Liverpool te bezoeken (alwaar ik
prompt naar de kelder verwezen werd…). De samenwerking met Adrian stond en
staat steeds garant voor een wetenschappelijke prikkel, opgewekt door boeiende
discussies, supersonisch wetenschappelijk schrijven en een goeie pint engels bier.
Dankwoord
99
Naast de Vlaamse lage landen, met in het bijzonder Gent, is Liverpool nu een
onmisbaar deel van m’n leven geworden.
En zo wenst de auteur, nabij de aanvang van alweer een nieuw avontuur, alle
reisgenoten te bedanken om deel uit te maken van mijn leefwereld, met in het
bijzonder m’n familie, collega’s en vrienden. Ik zal jullie altijd dankbaar blijven voor
het tolereren van m’n impulsiviteit, slecht geheugen en frequente lichamelijke
afwezigheid. Zonder volgorde noem ik in het bijzonder…
… ma, pa en Kris, voor het samenleven met een hyperkinetische zoon of broer, en
het blijvend steunen van de keuzes die ik maak.
… Pierre, Veke, An’leen, Davy, Christoph, Frederik, Matthieu en Liesbeth, voor de
fantastische sfeer in en rond ‘ons’ labo.
… An, Wim, Miek, Liesbeth, Michel, Ina, Pascale, Birgitte, Karla en al jullie
metgezellen, voor fantastische tijden die we meemaakten, en gegarandeerd nog
zullen beleven.
… Myrke, Ine, Annemie en Anneleen, voor het plezier in den Albert, en voor het
helpen afbreken van hersencellen.
… Cherd, Rach, Knot, Jae, Yok, Yingying en de rest van de Thai Society, voor de
Thaise oase in St. Andrews Gardens in Liverpool. Hopelijk kan ik jullie gauw in
Thailand bezoeken! En zij die binnenkort afstuderen: proficiat!
… Ben, Neil, Phil,… om te zijn wie je bent, en om me te laten binnendringen in jullie
leven!
… Adolf, voor de introductie in de kunsten van het computer programmeren.
… Kat, voor de fijne momenten die we deelden doorheen de voorbije jaren, en in het
bijzonder voor het mooie ontwerp van de cover van dit eindwerk.
… Rhys en Joanne, Willem, voor de tijd die jullie doorbrachten om de strijd aan te
gaan met de inhoud van dit eindwerk en daarbij het nodige commentaar te bezorgen.
… hij of zij die ik hierbij zou vergeten, om me bij deze te vergeven…
En, ten laatste, onthoud dat het begin altijd vandaag is!
Walk on,
Jos