Measuring Leg Stiffness During Vertical Jumps : Theory and Methods

145 Pages·2019·2.593 MB·English

by  Artur Struzik

Artur  Struzik
Measuring
Leg Stiffness
During Vertical
Jumps
Theory and Methods
Measuring Leg Stiffness During Vertical Jumps
Artur Struzik
Measuring Leg Stiffness
During Vertical Jumps
Theory and Methods
Artur Struzik
University School of Physical Education
Wrocław, Poland
ISBN 978-3-030-31793-5 ISBN 978-3-030-31794-2 (eBook)
https://doi.org/10.1007/978-3-030-31794-2
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To my beloved little dragon, I love you my
son.
Preface
“Everything has been said before, but since nobody listens we have to keep going
back and beginning all over again”. Although these words were spoken of the
French writer and Nobel laureate André Gide, they also seem to be relevant (at least
in part) to exact sciences.
Biomechanics is quite a young field of science and is developing rapidly.
Currently, many conferences in the field of biomechanics research are organized.
Also, a large number of international journals (including those interdisciplinary)
willingly publish articles in the field of biomechanics. I think I can be tempted to
say that biomechanics and its research methods have become trendy in some way.
Biomechanics mainly operate with terms borrowed from classical mechanics.
However, biomechanics combines the knowledge of anatomy, biology, physics,
physiology, medicine and sport science, among others. Therefore, the subject matter
of biomechanics is very broad. What may be an advantage of the above situation can
also be a disadvantage. Mechanics (or physics) terms have been precisely defined
only for a limited set of objects or phenomena. Unfortunately, due to the interdisci-
plinary nature of biomechanics, many terms are used imprecisely and with different
meanings. This leads to the loss of the original meaning of terms and to use them as
jargon. In some cases, new definitions are necessary. In other cases, application of
notions from classical mechanics needs some refinement. Stiffness is an example of
such a term.
An example of the interpretation of stiffness inconsistent with its mechanical
definition is leg stiffness. Leg stiffness is a quantitative measure of elastic properties
and determines the ability to accumulate potential elastic energy. Due to the sub-
stantial roles of inertia and damping on force-displacement relationships, especially
during transient states, leg stiffness is not stiffness viewed in strict terms. Therefore,
leg stiffness in terms of human continuous movement should be considered as
“quasi-stiffness”. The conceptual and methodological confusion regarding the term
of leg stiffness has made it difficult to organize and compare the results obtained by
the different authors. Thus, problems arise concerning both what stiffness is (or
what it is not, because its definition is quite strict) and how to measure it. This situ-
ation slows down progress in this field.
vii
viii Preface
The main purposes of this book are attempts to standardize the concepts about
leg stiffness found in the literature and present a methodology for determining leg
stiffness during vertical jumps based on the measurements of the slope of the ground
reaction force curve with respect to length changes. This method accurately reflects
the nature of quasi-stiffness. This book presents a thorough description and critical
discussion of different approaches to measuring leg stiffness during vertical jumps.
Various topics covered include the applicability of the spring-mass model, leg stiff-
ness controversies and interpretations and computational and measuring methods of
leg stiffness. Additionally, a description of a research project performed expressly
for inclusion in this book is given. This research project aims to determine norma-
tive values for leg stiffness for young, healthy, nonathletes during single vertical
jumps to maximal and specific heights. A final chapter covers additional perspec-
tives, enabling to acquire different perspectives on measuring leg stiffness across a
breadth of information and interpretations.
I would like to thank Professor Jerzy Zawadzki (Department of Biomechanics,
University School of Physical Education in Wrocław, Poland) for all scientific con-
sultations regarding this book.
Wrocław, Poland Artur Struzik
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction to the Subject . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Human Muscle Properties: Elasticity . . . . . . . . . . . . . . . . . . . . . . . . 3
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Biomechanical Characteristics of the Countermovement Jump . . . . . 9
2.1 Description of the Movement and Proper Performance
Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 The Concept of Performing a Vertical Jump to a Specific
Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Energy Balance During the Countermovement Jump . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 L eg Stiffness and Quasi-Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 The Concept of Leg Stiffness and Applicability
of Spring-Mass Model to a Human Motion System . . . . . . . . . . . . 19
3.2 Asymmetry of Leg Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3 Different Interpretations of “Stiffness” . . . . . . . . . . . . . . . . . . . . . . 22
3.4 Contribution of Leg Stiffness During Vertical Jumps . . . . . . . . . . . 26
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 Research Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.1 Assumptions and Aim of the Study . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2 Material and Research Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.1 Research Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.2.2 Research Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.1 Leg Stiffness During Vertical Jumps to Specific
Heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3.2 Potential Elastic Energy during Vertical Jumps
to Specific Heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
ix
x Contents
4.3.3 Other Variables Describing Vertical Jumps to Specific
Heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.4 Variables Describing Vertical Jumps to Specific
Heights from the Intraindividual Standpoint . . . . . . . . . . . . 77
4.3.5 Inter-Limb Stiffness Asymmetry . . . . . . . . . . . . . . . . . . . . . 80
4.3.6 Normative Values of Leg Stiffness During Vertical
Jumps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.4.1 Leg Stiffness Value During Vertical Jump . . . . . . . . . . . . . . 82
4.4.2 Leg Stiffness and Phases of the Vertical Jump . . . . . . . . . . . 84
4.4.3 Leg Stiffness and Sex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4.4 Effect of Arm Swing on Leg Stiffness . . . . . . . . . . . . . . . . . 86
4.4.5 Leg Stiffness and Inter-Limb Asymmetry . . . . . . . . . . . . . . 88
4.4.6 The Accuracy of Performing a Vertical Jump
to Specific Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4.7 Relationship Between Leg Stiffness and Vertical
Jump Height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4.8 Relationship Between Leg Stiffness and the Ability to
Accumulate Potential Elastic Energy . . . . . . . . . . . . . . . . . . 95
4.4.9 Relationship Between Vertical Jump Height and
Ability to Accumulate Potential Elastic Energy . . . . . . . . . 98
4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.6 Practical Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5 L eg Stiffness Controversies and Interpretations . . . . . . . . . . . . . . . . . . 107
5.1 C ritical Discussion of Different Approaches to Measure Leg
Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 Additional Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
List of Abbreviations
ACMJ – akimbo countermovement jump, vertical jump preceded by the counter-
movement with hands resting on the hips,
a – acceleration
α – value of the joint angle
α – maximum knee joint flexion angle, approximating the boundary between
max
the countermovement and take-off phases,
b – viscosity
CMJ – countermovement jump, vertical jump preceded by the countermove-
ment and arm swing
COM – a general centre of human body mass
DJ – drop jump, vertical jump after landing from a specific height
Δ – increase, change in value
δ – relative error of measurement of quantity x
x
E – kinetic energy
k
E – potential gravitational energy
p
E – potential elastic energy
pe
f – frequency
F – force
F – maximum instantaneous value of the ground reaction force in the take-
max
off phase
g – acceleration due to gravity
h – vertical jump height determined based on the equation of free fall of
f
bodies
h – maximal vertical jump height
max
h – vertical jump height determined based on vertical component of the
v
take-off velocity
K – longitudinal stiffness
K – torsional stiffness
α
K – leg (quasi-)stiffness
l
K – leg (quasi-)stiffness related to body mass
r
L – lower limb length
xi