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IMPORTANCE OF BIOMECHANICAL MODELLING FOR TECHNICAL PREPARATION OF A GYMNAST

Authors:
  • Faculty of Sport and Physical Education, University of Niš

Abstract and Figures

The aim of this paper has been to present the importance of biomechanical modelling in designing the methodology of physical movement learning process and in the implementation of learning process of elements in artistic gymnastics. Gymnastics is a conventional sports discipline which is characterized by the fact that success depends primarily on the knowledge and the successful presentation of the elements at the highest difficulty level in competitions. Therefore, it is the selection of elements for each individual athlete and the type of elements learning process which guide and determine the integrated process of an athlete‘s preparation for competition. Consistently with its objectives the article presents the model of biomechanical modelling and the implementation process of identifying fundamental kinematic and dynamic characteristics of movements that represent the foundation to understanding of the movement techniques in the selected elements. The whole model is designed in four successive phases, wherein the last phase of modelling mainly depends on the purpose of modelling. The applicability of the model is presented on the cases in gymnastics, whereby its usefulness can be extended to all sports disciplines in which the technical knowledge is an important segment of athletes‘ successful performance.
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IMPORTANCE OF BIOMECHANICAL MODELLING FOR TECHNICAL
PREPARATION OF A GYMNAST
Kolar E.1, Samardžija Pavleč M.1 & Veličković S.2
1University of Primorska, Science and Research Centre, Instut for Kinesiology Research, Koper,Slovenia
2University of Niš, Faculty of Sport and Physical Educaon, Niš, Serbia
ABSTRACT
The aim of this paper has been to present the importance of biomechanical modelling in designing the
methodology of physical movement learning process and in the implementaon of learning process of
elements in arsc gymnascs. Gymnascs is a convenonal sports discipline which is characterized
by the fact that success depends primarily on the knowledge and the successful presentaon of the
elements at the highest diculty level in compeons. Therefore, it is the selecon of elements for each
individual athlete and the type of elements learning process which guide and determine the integrated
process of an athlete‘s preparaon for compeon.
Consistently with its objecves the arcle presents the model of biomechanical modelling and the
implementaon process of idenfying fundamental kinemac and dynamic characteriscs of movements
that represent the foundaon to understanding of the movement techniques in the selected elements.
The whole model is designed in four successive phases, wherein the last phase of modelling mainly
depends on the purpose of modelling.
The applicability of the model is presented on the cases in gymnascs, whereby its usefulness can be
extended to all sports disciplines in which the technical knowledge is an important segment of athletes‘
successful performance.
Key words: arsc gymnascs, technical preparaon, biomechanical modelling.
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INITIAL PREMISE
The rapid development of top level sport urgently requires from pracce to be associated with science in
all its areas of acvies. Without proper guidance, and conducng training process, based on the latest
scienc and theorecal ndings, it is dicult to achieve the highest compeon results. The concept
of training, which is based on the enthusiasm of coaches and athletes, is today almost always doomed
to failure. Such approach to work in elite sport may produce a top level result, but this sort of training
should not become a system because it is oen associated with failures and successes. The imperave
in the realizaon of the aspiraons of the top sporng outcome is denitely a structured system based
on a scienc basis and muldisciplinary approach in dealing with athletes (Kolar, Farrier & Pileč, 2006,
p. 12).
In general, gymnascs is classied among individual sports. However, in sport science there are three
basic types of sports disciplines classicaon. Each of these types of classicaon uses dierent criteria
to classify sports. Based on the structural complexity of movements (Matveev, 1977) in individual sport
disciplines, gymnascs is ranked among convenonal sports, which are characterized by aesthec and
physically determined cyclical sets of structures to be carried out either in standard or in variable external
condions. Depending on the prevailing energy processes in the organism (Bravničar - Lasan, 1996) it is
a sports discipline, which is dominated by anaerobic energy processes, since compeve composions
do not last longer than one minute and a half. Among the dominant motor abilies (Milanović, 1997)
determining the success in arsc gymnascs belong relave strength, coordinaon, exibility and
balance.
And the convenonal character of arsc gymnascs denes the process of dealing with an athlete in
gymnascs. Convenonality of sport discipline means that all moon/movements must be performed
in the context of a parcular motoric model (prescribed by the experts - convenon), which could be
called the ideal model of movement (hereinaer IMM). IMM is determined by the biomechanical model
of movement and is prescribed in the regulaons for the assessment prescribed by the Internaonal
Gymnascs Federaon or some other organizaons (naonal sports federaon). Any deviaon from this
model constutes an oense against the rules or an error in the movement, which can be of technical or
aesthec nature. Movement contents are in the regulaons divided into diculty classes regarding the
complexity and the entanglement of the movement.
Evaluang the performance of athletes in convenonal sports takes place in terms of evaluang the
performance of moon content athletes demonstrate in compeons. They are assessed by specially
trained judges. The criterion of evaluaon is based on comparison between the prescribed model of
movement (IMM) and actually performed movement by each athlete. Performance in convenonal
sports is therefore dened primarily by the number and the complexity of the exercise content –the
elementswhich the athlete masters and is able to successfully (in accordance with regulaons) perform
at the compeon. Due to the above said, we can therefore claim that the motoric elements and
movement contents that are trained during the technical preparaon of athletes are the key aspect
of atraining process, which dene the process of planning, implementaon and control of training in
arsc gymnascs (Kolar, 2007, p. 380).
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TEHNICAL PREPARATION OF AN ATHLETE IN ARTISTIC GYMNASTICS
In sports training theory we know the technique of motor structures performance and the methodology
of motor structures training under the concept - technical preparaon of an athlete.
The word technique comes from the Greek word “techne”, which means - the skill or knowledge. The
term “technique” in sport represents a certain form of moon, which is standardized and idened by
name. Moon technique and ideal movement model in the performance of elements in gymnascs is
determined by the biomechanical model of movement and by its kinemac and dynamic characteris-
cs. The kinemac characteriscs are as follows:
The path drawn by the centre of gravity of the body (hereinaer CG) or individual segments of
the body;
Time that CG or individual segments need to perform a movement;
The velocity by which the CG or individual segments travel during the movement performance;
Acceleraon, which indicates a change in velocity of CG movement or individual segments on a
certain path;
The angles between segments of the body or body segments and the grounds; and
Angular velocity and angular acceleraon in circular movements.
And the dynamic and kinec characteriscs are as follows:
Forces, which are divided into internal (muscular force)and external forces (gravity, the force of
air resistance, fricon ...);
torque and momentum, which are important in rotaon movements; and
work done, when the body operates under a certain force on a certain path.
The word methodology also comes from Greek, namely the word “methodos”, which means - a way of
focused performance of an acvity or the way how to achieve the target objecve. Methodology in
sport is oen associated with the methods and principles as well as acvies related to the preparaon
of an athlete for a compeon. However, we shall in this case be limited to the methodology of training
elements in arsc gymnascs. In training elements in arsc gymnascs methodical procedures are
used. Methodical procedures consist of methodical steps that follow each other in the exact sequence
that is formed on the basis of the most important didacc principles, namely, the principle of gradualism,
formed by the following rules (Kolar, Pileč & Veličković, 2005, p. 12-13):
from easy to more demanding,
from familiar to unknown and
from simple to complex.
Learning elements in arsc gymnascs is a very complex process involving many dierent aspects. Each
aspect separately has a certain inuence on the successful compleon of the transformaon process, the
aim of which is in our case a successful performance of the required element. The training methodology
of individual elements of movement is based on the theory of motor learning. There are several dierent
theories of motor learning but they all have in common that the process of learning elements is a mental
process that takes place in certain successive stages. The speed of the transion between phases is
largely dependent on the number of successful repeons of the whole or parts of each movement. The
end result should be automated movement, which enables a successful implementaon of individual
element in dierent condions and under stress and fague (Kolar, Farrier & Marinšek, 2006, p. 57).
Elements performed by top athletes in gymnascs are, as a rule, an upgrade of basic elements that
are taught in the training process in the younger categories. Technically correct performance of the
basic elements allows the contestants’ advancement and development in the youth and later the senior
category. Points that disnguish top athletes from others are elements of the highest diculty levels,
which are usually extremely complex by their motor structures and where the possibility of error or injury
during the performance is extremely high. Therefore, in the construcon of methodical procedures we
implement the biomechanical analyses that in terms of kinemacs and dynamics allow us to construct
biomechanical models of movement, and to explain the important parts of the movement performance.
In the selected element learning process this enables us to stay limited through individual methodical
steps on the special part of the movement, which is for the nal performance of the element presented
as a whole, the most important.
Based on the aforesaid, the model of learning element may therefore be dened, which envisages that
the planning of an individual element training is based on the knowledge of the element’s technique and
its kinemac and dynamic characteriscs that dene biomechanical model of movement in the selected
element (Figure 1). The model of training elements in arsc gymnascs (Figure 1) provides that, within
the designed process of training of arsc gymnascs elements it is necessary to dene the following:
methodical procedure for element training,
necessary prior technical knowledge,
detecon and correcon of errors,
system of help and security during training, where special importance is aached to health -
prevenve aspect, which further inuences:
physical preparaons planning, divided into:
ogeneral or basic physical preparaons and
ospecial physical preparaons.
Figure 1: Model of training elements in arsc gymnascs.
BIOMECHANICAL MODELLING
By biomechanical modelling we want to nd a relevant physical - biomechanical model for the selected
element or movement in order to describe the movement and dene technology of movement in
individual elements with physical values. The physical descripon of moon is needed for arbitrarily
selected data to mathemacally predict the movement and the numerical values of its quanty –velocity,
acceleraon, force, etc. Biomechanical models for the elements can be used for the following purposes:
analysis of movement techniques of an element,
planning methodical training of an element,
planning special physical preparaons,
evaluaon of methodical procedures,
detecon of movement errors,
detecon of variability in successful movements and
evoluon of new elements.
Kinemac and dynamic structure of complex movements can be objecvely and accurately determined
only by veried and licensed biomechanical methods and techniques. Preference is given to non-invasive
methods and techniques, because they allow the capture of large amounts of feedback, and data capture
does not interfere with the athlete, training process and compeons. The opportunity to explore the
situaonal condions allows kinemac method with manual labelling of anatomical points - APAS, PEAK
and SIMI Moon. These kinemac models and techniques are currently the most raonal and most
topical. All of these systems can produce a large amount of raw informaon to be processed, reduced
and synthesized later on. The results obtained by measuring these methods are primarily suitable for
interpretaon in its original form. They also can be transformed into a more suitable form and thus can
be used as the input of complex systems such as mathemacal models. It is possible to make a selecon
from the measured parameters which will later funcon as the so-called direct criteria. These criteria can
be reached via biological and stochasc models, which does not exclude the synergy of these methods.
Below we show a dra model for raonal and general denion of the model of biomechanical modelling
techniques in performing complex gymnasc elements, which covers most of the procedures used in
previous studies (Čuk, 1996; Kolar, 2005; Veličković et al., 2006).
DEFINITION OF PROCEDURE FORBIOMECHANICAL MODELING OF MOVEMENT TECHNIQUES
IN COMPLEX GYMNASTIC ELEMENTS
The process of biomechanical modelling of movement techniques in complex gymnasc elements consist
of sequenal set of phases, where each phase is dened by the objecves associated with the desired
data that we want to acquire by the model, or with the purpose of each type of biomechanical modelling,
which we have menoned in the previous secon. The enre procedure consists of four phases, where
it is signicant that the rst three procedure phases, regardless of the purpose of movement modelling
techniques are always the same, while the fourth phase of the procedure will depend largely on the
purpose of biomechanical modelling of movement techniques for each movement. The amount of
informaon necessary to successfully dene a biomechanical model of each movement grows from
phase to phase, which enables more and more accurate denion of the movement and the realizaon
of the underlying purpose of modelling. The model, of course, also allows us to stop proceedings, given
that the informaon gathered meets the needs of experts in dening the model of performing a certain
movement technique. This mainly depends on the complexity of the elements and the selected purpose
of modelling.
The whole process will be presented in the connuaon of the paper (Figure 2), and also the acvies
that have to be carried out in each phase of the procedure. In some phases concrete examples of phase
performance will be presented.
Figure 2: The procedure of biomechanical modelling of movement techniques in complex gymnasc elements.
PHASE 1: Recording of movement techniques in the selected element
Phase 1 (Figure 3) is a standard part of the procedure when making a video recording of all these
biomechanical systems for the kinemac analysis. First, a selecon of the most suitable posions for the
cameras is envisaged (at least two) and their synchronizaon. This is followed by recording of reference
frames (1m3) for precise calibraon of space. The number of reference frames and places where the
frames are going to be posioned depends on the movement that we intend to record and invesgate,
as well as on the apparatuses where the elements will be performed.
Depending on the purpose of introducing the procedure the number and the amount of elements that
will be covered at this phase of the procedure has to be idened already in the research plan. Most of
the researches done so far have been related to the recording of one representave (reference) successful
aempt of element performance that may be sucient for the analysis of the element performance
technique, for planning of the methodology of learning/training elements, for the calculaon of kinemac
and dynamic parameters when developing new element or for the planning of physical preparaon
for the performance of the selected element. However, if the purpose of biomechanical modelling is
evaluaon of methodical procedures, to idenfy errors in movement or to determine the variability in
technique in the performance of successful movements, it is necessary to determine the appropriate
paern of movements, which will be analysed in subsequent phases of the process. It is also important
that simultaneously with the recording also the evaluaon of the quality performance of the elements
takes place, done by the experts - gymnascs judges, because the judge’s assessment is an important
qualitave informaon for further analysis of movement.
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Figure 3: Steps in the implementaon of the phase 1 of the procedure of biomechanical modelling of movement
techniques.
Step 1
Posioning and
synchronisaon o f
cameras.
Step 2 Determinaon of space to be
measured.
Step 3 Recording and expert
assessment of movements.
Data obtained in this phase or the acquired video material allow establishment of a clear idea about the
movement being studied. A researcher or coach as well as the athlete get the rst rough, but important
informaon. Should we make a stop in the procedure in this phase, many hidden details in the technique
of performance might escape, such as the exact rao of body segments in space during the element
performance, the posion and route of the centre of gravity of the body, the speed of reference (body)
points, the size of the angles and angular velocies of the body segments. In addion, the occurrences
of certain biomechanical principles might be overlooked (e.g. start of reacve transmission of swing
from one part of the body to another) as well as the causes for the incidence of errors in movement and
others.
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PHASE 2: Biomechanical (expert) modelling of movement
In this phase, we produce the basis of expert knowledge on the relevant theorecal biomechanical and
physical movement models of the selected element. When making a theorecal biomechanical model of
the movement we need to take into account those movements which are by experts (judges, coaches)
considered as relevant and technically awless (consistent with IMM). For such movements it is necessary
to dene the important movement segments and posions of the body in moon (Figure 4).
Figure 4: Acvies in the execuon of phase 2 of biomechanical modelling of movement.
In the process of producing a theorecal biomechanical model of movement we become beer
acquainted with the selected movement and understand its physical backgrounds. Such model makes it
easier for us to disnguish the important segments of each movement and on this basis makes it easier
to choose the parameters for the analysis of movement and posion of the body during movement
which we have to be focused on, when making the analysis. To construct these models, it is important to
have a good - expert knowledge on the element techniques in arsc gymnascs, as well as a sasfactory
knowledge of physics and mechanics. In order to construct the model we use dierent models of division
of the enre element movement and the corresponding descripons.
Below, the model of Smolevskij (1992) will be presented, which provides a relavely accurate and
suciently detailed construcon of biomechanical models for all the stated purposes of biomechanical
modelling.
Smolevskij (1992) has divided elements according to the following criteria:
1. posion of the athlete according to the apparatus or the surface during the performance of
movements,
2. acon of forces during the performance of movements and
3. borderline posions during the performance of movements.
The rst criterion for the division of movement is the posion of the athlete in reference to the apparatus
or the surface. During the performance of gymnasc elements athlete is in two specic posions in
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relaon to his surroundings: supporve and non-supporve. The supporve part of the movement is
the part where the athlete is in contact with the ground or apparatus.A special example of supporve
part of movement is landing. And the non-supporve part of movement is the part when the athlete
is not in contact with the ground or the apparatus or when the athlete is in the air. The movements
containing the phase of ight can thus be divided into three parts: supporve part, non-supporve part
and landing. In this kind of division, there are three systems: “gymnast-apparatus”, “gymnast in free fall”
and “gymnast-landing area”.
The second criterion is the acvity of forces during the performance of movements. The forces acng
on the athlete’s body during the performance of movements can be divided into external and internal
forces:
internal forces:
omuscular acvity,
external forces:
omass force (gravitaon force),
oapparatus and ground exibility force (acon-reacon),
ofricon force,
oair resistance force.
When doing analyses in arsc gymnascs most oen the friconal force and the force of air resistance
are neglected. According to the established criteria the elements can be divided into four parts, called
phases of movement.
During the rotaon movements from above downward the force of gravity accelerates the speed of
gymnasts’ body and acts as a posive acceleraon which is in the rotaonal moon as follows:
α=dω/dt, where »α« stands for: change in angular velocity (dω) within certain me (dt).
When body is traveling from top to boom the internal forces (muscular acvity), and the force of
gravity are acng in the same direcon, and this phase is called the “accumulaon phase”. In the case,
however, when the athlete’s body moves from the boom up, the internal forces and the mass force
oppose to each other and the force of gravity acts as a negave acceleraon. This phase is called the
“phase of work”.
During the ight (non-supporve part) the gravitaon force is pulling the gymnast’s body to the ground,
rst by reducing the speed of the body’s centre of gravity (during the ight up) then by the acceleraon
(during ight downwards). But this does not aect his/her rotaon. Gymnast uses the accumulated
energy(Es) to perform the necessary movement during ight. This part of the movement is called
“performance phase” (Figure 3).
With the forces (F) and torques (M) the momentum (G) and angular momentum (Γ) of the body are
connected.
G=(F/a)*v Γ=(M/α)*ω
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The angular momentum is parcularly important parameter that describes the rotang movement of
the body in non-supporve phase and in the performance phase of movement. The angular momentum
of the enre body is the algebraic sum of the angular momentum of individual segments. Among
the various segments of the body internal forces act (muscular acvity), which can vary the angular
momentum of individual segments, yet, they do not change the total angular momentum of the body.
This alter only due to shock torques of external forces. If there are no shock torques of external forces
(which is typical for the performance phase, as we do not take into account the force of air resistance),
the angular momentum of the body retains. The size of angular momentum can also be expressed by the
following equaon:
Γ=J*ω
Angular momentum is thus the product of the body moment of inera (J) and angular velocity (ω). The
moment of inera of the body is the equivalent to inera of the body in linear moon and is a measure
of the body mass distribuon about the axis of rotaon. The magnitude of the moment of inera of the
body determines how dicult it is to start or stop the circular (rotaonal) movement, which is one of the
fundamental characteriscs of moon in the performance of gymnasc elements. Unlike the linear inera
of the moving body (G) the moment of inera of a rotang body (Γ) depends on the posion of the body
(stretched, bent, shrunken) and on the angles between segments (e.g. the trunk and legs). The moment of
inera is a product of body mass (m) and the square of its distance from the axis of rotaon (r2).
J=m*r2
By changing the body posion (shrinking, stretching, bringing hands to the body, etc.) in the performance
phase we change the lever size (bringing body closer or further away from the rotaon axis) and thus
increase or decrease by square the moment of inera of the body at a constant mass (the mass of
an athlete does not change during the movement).Thus we do not change the angular momentum by
changing the moment of inera, which is by denion in non-supporve phase (performance phase)
constant (not changing its value) and is the result of inera and angular velocity, however, the angular
velocity does change, which manifests itself as faster or slower rotaon of the body around the diagonal
(salto) or longitudinal (twists) axis. Therefore, the athlete by increasing or decreasing the momentum
of inera of the body, decreases or increases his angular velocity, at a constant angular momentum. This
allows controlling the angular velocity in the performance of saltos and twists (Petrov & Gagin, 1974). All
the above stated ndings apply only for non-supporve part (performance phase) of movements and in
the absence of shock torques of external forces. If the angular momentum of the non-supporve part of
the movement does not change its value, therefore, the performance of movements in the performance
phase depends on the size of angular momentum an athlete produces in the supporve part (push o on
the ground oor, whip and swing on the high bar, etc.).The aim of every athlete is to provide the greatest
possible amount of rotaonal movement in the supporve part, to enable him to carry out movements
in the non-supporve part.
During landing aer dismount, the force of gravity has similar eect as in case of supporve part of the
movement. The force of gravity opposes the athlete’s acvies to keep him from remaining at the site
(landing), so an athlete aempts to neutralise the accumulated energy in order to sck. This phase of the
movement is called amorsaon phase.
The third criterion is a division of phases into the borderline posions. This criterion includes changing
the type of movement. For example, at the moment when gymnast begins a “whip acon” in dismount
from the high bar, his body passes from stooping posion of the body into strong arched (extension in the
shoulder and hip joints). It is important to learn and to understand any such borderline posion because
they have a signicant impact on the nal performance of movement.
Figure 5: Example of division of double stretched somersault with two turns from the bar, according to the criteria
of Smolevskij (1992).
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DOUBLE OUTSTRETCHED SOMERSAULT FROM THE BAR WITH DOUBLEROTATION ARROUND THE LONGITUDINAL AXIS
DIVISION CRITERIA (Smolevskij, 1992)
PRIKAZ
1. Athlete‘s
posion 2. Acon of forces 3. Borderline posion
SUPPORTIVE PART 1
Phase of work 1
Transion from arch into stoop:
Movement from 1 to 3
Phase of accumulaon
Transion from body’s stoop
into archedposion (beginning
of »whip«):
Movement from 4 to 6
Phase of work 2
Transion from arch
into the gymnasc dish
posion(»swing«):
Movement from 7to 9
NON-SUPPORTIVE PART
Phase of performance
Arms closing in towards the
body and persistence in dish
posion
Movement from 10 to 20
Stretching and shiing hands
away from the body and body
stretching with preparaons for
landing
Movements from 21 to 22
SUPPORTIVE PART 2
Phase of amorzaon
Bending in hip and knee joint
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Thus, divided elements (Figure 5) are suitable for the descripon of technical structures and biomechanical
parameters for any gymnasc movement.
Figure 6: An example of a theorecal biomechanical model of movements in separate phases of movement (Figure
5) during the performance of the double stretched somersault with two turns/ plants from the bar.
DOUBLE OUTSTRETCHED SOMERSAULT FROM THE BAR WITH DOUBLE ROTATION ARROUND THE
LONGITUDINAL AXIS
DIVISION CRITERIA Theorecal biomechanical model of movement
(physical quanty used for descripon of movement)
1. Athlete’s
posion 2. Acon of forces
SUPPORTIVE PART 1
Phase of work 1
The rst phase of work begins with a pronounced swinging of legs
over the bar (me, acceleraon, angular velocity). The consequence
is bending of the body in the hip and shoulder joint (angle). The
angle between the trunk and the thighs may also be more than 90
degrees (angle).The competor is trying to minimize radial force and
maximize tangenal force (force). This phase of the movement ends
in a stooped handstand posion (path, me, angle). At that me, the
potenal energy reaches maximum, and kinec energy is supposed
to be maximized (energy).
Phase of
accumulaon
This phase begins in the stooped handstand when the potenal
energy is at its maximum (path, me, angle, energy). Aer passing
from handstand in stooped posion, the athlete starts strong
stretching backwards and down (me, path, angle). Extension of the
body must be sucient that the angle in the shoulder and hip joint
exceeds 200 degrees (path, angle).The athlete is under the eect of
the sum of external forces and torques/moments, which is greater
than zero, since the movement is accelerated along the circumference
(force, speed, acceleraon). In this phase, the competor is trying to
maximize the radial force and minimize the tangenal force (force).
The phase ends in a posion of hang when the potenal energy is
minimum, and the kinec energy is maximum (path, me, energy).
Phase of work2
The second phase of work begins in a posion of hang (path, me,
angle). In this posion, the competor must achieve a maximum
extension in the hip and shoulder joint (me, angle). Hips are far
ahead of the shoulders (path, angle). At the end of this phase the
athlete must have the highest possible movement and angular
momentum. Therefore, the sum of all shock torques from external
forces should be as high as possible (force).During the swing the
circular moon connues (me, path, angular velocity), when
a contestant tries to maximize the tangenal force (force). This
condion ends at the moment when the athlete releases the bar
(path/route, me). At the me, his potenal energy is lower than
later on in the highest posion non-supporve part (energy).
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DOUBLE STRETCHED SOMERSAULT FROM THE BAR WITH DOUBLE ROTATION ARROUND THE LONGITUDINAL AXIS
DIVISION CRITERIA
(Smolevskij, 1992) Theorecal biomechanical model of movement
(physical quanty used for descripon of movement)
1. Athlete‘s
posion 2. Acon of forces
NON-SUPPORTIVE PART
Phase of performance
In the performance phase the contestant performs double stretched
somersault (double rotaon around the transverse axis of the body) and
double rotaon around the longitudinal axis (angle, path). The movement of
the centre of gravity of the body is a parabola, which depends on the take-o
angle and the speed of the centre of gravity of the body (path, angle, speed).
Upon releasing the bar the body has certain inera. When the athlete releases
the bar the axis of rotaon is transferred to the centre of gravity of the body,
therefore, the moment of inera reduces, and the angular speed increases.
The athlete‘s performs air movements in a gymnasc dish posion (strong
muscle tension in the front part of the body gives the body a slightly concave
shape) (angle).Quickly aer leaving the apparatus the competor starts to
perform the rotaon about the longitudinal axis (path, angle). By strongly
and unevenly pulling his hands towards his body in the direcon of rotaon
around the longitudinal axis, he changes the moment of inera of the body
and increases the angular velocity of the body about the longitudinal axis.
In the performance phase the contestant performs biaxial rotaon (rotang
around two axes at the same me).At the moment of leaving the bar the
gymnast has from zero up kinec energy, and the potenal energy is lower
than in the highest point of the ight (path). In the highest point of the ight
the potenal energy of the body‘s the highest (path). Before landing the
competor stretches the body and opens his arms outwards (path, angle,
me). This increases the inera moments of the two rotary movements and
reduces the angular speeds. This enables him to control the movement and
prepare for landing (me).
SUPPORTIVE PART 2
Phase of amorsaon
At the me of landing the shock torques of external forces on the athlete
must be equal to his angular momentum during the ight. At the end of
landing the body has less potenal energy than in the inial posion, and
the kinec energy is zero.
Findings obtained in the second phase, allow us to answer the queson why the body moves during the
performance of the element like it does. A researcher, trainer and athlete gain important informaon
about the physical (biomechanical) laws that aect movement and make it possible. This phase allows us
to have a detailed theorecal insight into the analysed movement and to idenfy those biomechanical
laws, which are important for the performance of the movement and the important informaon on
what are those parameters throughout the enre movement or a parcular segment of the movement,
which in the subsequent steps of the analysis are necessary and worth observing. It also allows a
precise idencaon of movement techniques in each element. Of course, at this stage we do not know
anything about the actual amounts of recognized physical laws and their changes during the movement
performance. Therefore, we recognize and dene them with the modern technology in the subsequent
steps or phases of the model which allows us to have a direct and detailed insight into the whole
movement and its important segments.
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Notwithstanding the aforemenoned, the theorecal biomechanical model of movement in accordance
with the Figure 1 allows us (especially in the less complex movements) to design methodical procedures
for learning the elements, to idenfy technical errors in the movement performance, to establish relevant
procedures of safety protecon and assistance in learning the elements and to see certain aspects of
planning physical preparaon.
PHASE 3: Kinemac and dynamic (kinec) moon analysis
The third phase of the model represents the data transfer from the video recording of quantave values,
thus determining the value of kinemac and dynamic (kinec) parameters for the selected reference
points and segments. Although one can use systems such as the APAS (Ariel Performance Analysis
System) to calculate values of kinemac parameters for each selected item in skimmed area, it is the task
of experts to carry out, on the basis of theorecal biomechanical model of the movement, the selecon
and chose only those points and segments of movement that are relevant for achieving the objecve of
the analysis. This is followed by digizaon of selected segment of movement and the reference points
(step 1, Figure 7), which enables the producon of kinogram (Step 2, Figure 7), and a graphical display
of the values of kinemac parameters of reference points (step 3, Figure 7), which enables accurate
quantave and qualitave kinemac analysis of the analysed movement. This enables us to pinpoint
phases and sub-phases in the movement, as well as signicant changes in kinemac parameters in the
movement performance.
The nal step in the phase of biomechanical model is dynamic and kinec analysis of movement which
is carried out if we are implemenng the fundamental objecves of the planned analysis. In the dynamic
analysis of movement the point is to idenfy the forces and torques generated by the movement.
Dynamic moon analysis can be performed by direct measurement of forces on the apparatus (Krug,
1992; Bruggemann, 1994; Marinšek, 2011) or on the ground or with the procedure of calculaon of forces
derived from the kinemac parameters by the method of inverse mechanics (Kolar, 1996; Čuk, 1996).The
method of inverse mechanics is a non-invasive method that is performed on the basis of the calculated
kinemac moon parameters (Colja, 1994). The calculaon is only possible if there is a ground support
with one segment, thus calculaons can be carried out only unl leaving the apparatus and the grounds
push o (analysed possible only in supporve part). The inverse mechanics allows the calculaon of net
forces and torques on the basis of kinemac parameters.
Equally, in this phase the hypothecal funconal anatomical moon analysis can be carried out (Čuk,
1996). The analysis of angles between segments (kinemac analysis) and the forces generated in a
parcular part of the movement (dynamic analysis) may point at the type of movement in a parcular
joint, as well as at the acve muscle group, the size of the angular velocity and at the type of muscle
contracon. This analysis largely facilitates the producon plan for special physical preparaon as well as
the process of successful acquision of certain elements.
Upon terminaon of this phase of biomechanical modelling we have enough data to be able to make an
accurate descripon of the movement technique, which enables us to make a very accurate determinaon
of changes in the physical characteriscs of the selected movement. And this enables us to idenfy those
segments of movement performance, which are crucial for the successful performance and a direct
guideline for the coach and athlete regarding where they should focus their aenon in learning and in
the performance of the movement.
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Figure 7: Display the steps of the Phase 3 in the biomechanical modelling of selected movement.
Step 1
Selecon of reference
points and digizaon of
movement.
Step 2 Producon of kinogram.
Step 3
Calculaon and display of
kinemac parameters of
reference points.
Step 4
Calculaon of dynamic
parameters with the method
of universal mechanics.
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PHASE 4: Analysis of selectedparametersand interpretaon
This phase of biomechanical modelling primarily depends on the very purpose of the analysis. If it is
only for the sake of analysis and descripon of moon it is required to properly interpret and describe
the calculated kinemac and dynamic parameters to allow their applicaon in planning the methodical
procedures or in the planning of physical preparaon (Manon, De Leo &Carvelli Mallozzi, 1992; Bedenik,
1995; Cuk, 1995; 1996; Prassas& Ariel, 2005; Marinšek et al., 2006; Veličković et al., 2011; Bango, Sillero-
Quintana & Grande, 2013).And, if it is a queson of evaluaon of methodical procedures, then it is
necessary to adequately explain why each methodical step is more adequate than another and why, for
example, the methodical process may be shortened by oming individual methodical steps (Manon, De
Leo & Carvelli Mallozzi, 1992b; Kolar, Kolar Andlovec & Štuhec, 2002; Veličković, Kugovnik, Kolar, Bubanj,
Madić & Supej, 2005).When dealing with errors idencaon during movements or with detecon of
possible variability in the performance of one of the elements it is, of course, necessary to cover a larger
number of element performances. In order to detect errors in the movements performance it is worth
comparing the kinemac and dynamic parameters between successful and unsuccessful performances
of each movement, whereas to detect the variability of individual parameters in the same movement,
we usually analyse a larger number of successful aempts od movement (Kolar, Pileč, Kugovnik, Kolar
Andlovec & Štuhec, 2005 Veličković, 2005).When trying to introduce new elements it is usually a queson
of mathemacal modelling of already accomplished movements, for which a dierent posion of the
body is envisaged in the movement performance (e.g . instead contracted we envisage stretched) or add
rotaons to separate movements around the longitudinal or transverse axis (Čuk, 1996; Čuk, Aković &
Tabaković, 2009).
Figure 8: Examples of interpretaons of movement techniques analyses by applying biomechanical modeling, given
the purpose of the applicaon of this method.
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Purpose Research Main stresses in the interpretaon given the purpose of the
research
Analysis and
movement
descripon
Kolar, E. (1996).
Technique and
methodology
of dismount
form the bar
(double stretched
somersault
backwards with two
rotaons).
From the graph, showing the movement of the body centre of
gravity in the x axis, we can see that a contestant in the rst half
of the accumulaon phase reached the maximum distance of the
centre of gravity of the body from the bar, which allows to develop
large tangenal forces later on in this phase of the movement.
Aerwards the center of gravity of the body in the x axis steadily
moves away from the bar, which allows to move away from it when
leaving the apparatus. The graph of movement of the center of
gravity of the body in the y axis indicates that the center of gravity
of the body in the accumulaon phase rapidly decreases, and that
it is growing rapidly in the phase of work. It reaches its maximum in
the performance phase (4.02m).
The graph of body‘s gravity centre speed shows two peaks. The rst
peak coincides with the start of the third boundary posion while
others coincide with the point before leaving the apparatus. The
feature of this movement is actually present in all methodical steps.
From the graphs of forces and moments we see that the curve has
two peaks, both low and high. The rst coincides with the start
of the third boundary posion and the second with the point just
before leaving the bar. Since the torque and the force have a decisive
inuence on the angular momentum of the body, and the laer on
the performance of rotaons around the transverse axis of the body,
it is extremely important that they are as high as possible just before
to leaving the apparatus.
Given the fact that the law of conservaon movement and angular
momentum respecvely, provides, that angular momentum is
preserved if it is not aected by any external force or if the vector
sum of torques of all the external forces is zero (which is enrely
appropriate to exercise double salto with double rotaon), we
can argue that the success of dismount mainly depends on the
performance in the supporve part of the element.
Planning of
methodical
procedures
Kolar, E. (1996).
Technique and
methodology
of dismount
form the bar
(double stretched
somersault
backwards with two
rotaons).
Based on biomechanical model of double stretched salto back with
double rotaon from the bar, the author has proposed the following
methodical procedure for the training/learning of selected element:
Giant swing back with acceleraon on the high bar,
stretched somersault backward with landing on the back with
emphasized bending down in backswing from the bar,
from the giant to „whip“ with a swing towards front swing without
releasing the bar,
double stretched somersault backwards with landing from the bar,
double stretched somersault with 1/1 rotaon around the
longitudinal axis, with landing on feet, from the bar,
double stretched somersault with 2/1 rotaon around the
longitudinal axis, with landing on feet, from the bar.
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Planning
of physical
preparaons
Veličković, S.
(2005). Dening of
kinemac model
of performance
technique of most
complex gymnascs
exercises.
The author developed the models of special physical preparaon for
the element swing and swing with rotaon for 1800 on the parallel bars
by using three sequenal steps (phases) for exploring the following
elements:
producing kinograms of successful performances of these elements
and the calculaon of kinemac variables (angles and angular
velocity) of movement between selected body segments,
making hypothecal funconal anatomical analysis of body
movement and body segments in the element performance for
each phase of elements separately and
selecon of exercises for physical preparaon for each phase of the
movement, according to the ndings from funconal anatomical
analysis of body movement and the regime of movement of
selected segments of the body, in each phase of movement in
element performance (kinemac analysis).
Example: Physical preparaon for the implementaon of the
second phase of the element movement (transion from support
at the hands towards inverted hang piked - accumulaon phase
named by the author as SPAD):
prevenon exercises for strength of exors of the neck and
hands (ngers),
exercises to increase exibility of hip joint extensors,
exercises to develop strength exors of back muscles and
exors of the hip joint.
Identification
of errors in
movement
Kolar, E., Pileč,
S., Kugovnik, O.,
Andlovic Kolar, K. &
Štuhec, S. (2005).
Comparison of
kinemac variables
of good and bad
performances of
dismount from the
parallel bars.
The results of t-test shows that good and bad (with error)
performances of the double piked somersault backwards from the
parallel bars is stascally signicantly dierent in two kinemac
variables, which are located in non-supporve part (the me when
the tested person reached the maximum bend of the body in the hip
joint) and in amorsaon phase (as in the hip joint at amorsaon
of landing).
Within the matrix of connecons (Pearson correlaon coecient),
we found that the criterion (dismount without judge‘s deducon)
was stascally signicantly associated only with the angle of the
hip joint in amorsaon of landing. This variable was stascally
signicantly associated with some kinemac variables in the
supporve part of the element.
Therefore, the aenon should be devoted also to the analysis of
the supporve part of the elemenn the processof learning these
elements or error correcon when landing.
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Detecon of
of possible
variability in
performances
Veličković, S.
(2005).. Dening
of kinemac model
of performance
technique of most
complex gymnascs
exercises.
The author has invesgated the variability of kinemac parameters on
the basis of ranges between the minimum and maximum values by
taking into account the standard deviaons for each of the selected
kinemac variables during the enre movement. The analysis covered
15 successful aempts of the element from swing to stand on the
parallel bars. The analysis sought to answer the following research
quesons:
What are the boundary values of selected kinemac parameters
that sll enable a successful performance of selected elements?
Where are the opportunies for correcon of movements big (high
variability)?, and where they are small (low variability)?
The author has found that the variability of kinemac variables in the
performance of the element swing on the parallel bars is the lowest
in the phase of transion of the body through inverted piked hang
and in the rst part of front swing in the inverted piked hang. Based
on the ndings he concluded that when performing the element
it is necessary to be more aenve parcularly to this part of the
element, since each minor deviaon from the intended movement
in this part of the element may result in ineecve performance of
the enre element. The rest of the element movement was marked by
greater variability of kinemac variables, which had no inuence on the
successful performance of the enre element. The stated recognion is
also a direct guidance for coaches on which part of the elements should
they be especially aenve in the element training/learning process
and in the process of correcng errors.
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Development
of new skills
Čuk, I., Atiković,
A. & Tabaković, M.
(2009). Tkachev
somersault on high
bar.
The high demands of performing a Tkachev somersault can be
achieved by excellent gymnasts who can perform straight Tkachev
with a very high amplitude. However, the new element is extremely
dicult to perform as its basic condions are:
posion of release requires very good exibility of the arms and
trunk(angle x axis – arms 43, arms-trunk 223, trunk -legs 200);
a very good physical preparaon as a tucking me of 0.24s can
only be performed by the best prepared gymnast;
the me of ight has to be at least 0.68s which should not be a
problem for the gymnasts who can perform a straight Tkachev;
vercal velocity should be as high as possible, but minimum safe
velocity is2.77 ms-1, as this gives the gymnast more airborne
me and a higher distance from the high bar (in this case the
gymnast‘s posion can also be more open);
a problem which has yet to be analysed is how to preserve
angular momentum during release.
All the calculated data for a safe Tkachev somersault;
me of ight;
vercal, horizontal and total velocity at release;
body angles at release and re-grasp;
angular momentum during ight and
the distance of the gymnast from the high bar,
are equal to or lower than other comparave researches. As
maximum known load to apparatus (at rings, at the gymnasts
vercal posion in hang performing triple somersault backward
tucked) is 13G (Čuk, Karacsony, 2002), we can conclude that the
producon and preservaon of angular momentum during the
preparaon phase unl the release phase should be solved.
As gymnast scan produce even higher biomechanical values than
those needed for a Tkachev somersault, we can conclude that a
Tkachev somersault can be accomplished, and will probably, in the
near future, be performed at compeons.
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CONCLUSIONS
The arcle deals with the importance of biomechanical modelling for eecve and ecient
implementaon of the process of learning of elements (especially the most complex) in gymnascs. Given
that the gymnascs is a convenonal sport and that the performance of each athlete depends primarily
on the amount and diculty of elements that they are able to successfully perform at the compeon,
it is therefore true that their performance decisively and crucially depends on the successfully carried
out process of elements learning and training. Thus, the learning of elements in gymnascs is the basis
for the planning of the enre training process, and consequently all other aspects of training should
be subordinate to this process. Parcularly the process of biomechanical modelling of movements is
a fundamental process of learning about the techniques of moon for each element, and thus a sine
qua non of understanding the element and establishing a methodical path for its learning. From this
perspecve, the importance of biomechanical modelling of movements in learning the elements is
essenal for the successful planning, implementaon and control of the learning process of elements in
gymnascs.
This paper presents a model of biomechanical modelling as a framework that can help every researcher
or manager to detect technical structures of movement of each element. The complete model consists of
four consecuve phases. For each phase it is signicant that both, the researcher as well as the coach or
athlete may obtain a certain amount of informaon about each of individual movement. The amount and
the accuracy of the informaon from phase to phase increases and further illuminates the mechanisms
that aect the successful performance of each movement. The number of phases of a presented
model, that an individual will be using in the planning process of learning individual elements or for
the correcon of errors in the performance of elements depends on the complexity of the elements,
required informaon and, in parcular, on the purpose of biomechanical modelling.
We, the authors, believe that understanding the biomechanical characteriscs of the movements in
individual element is the key factor of eecve and ecient learning and the subsequent performance
of the elements. We therefore consider that the presented model can be an important and welcome
tool for all who parcipate in that process. The applicability of the model is presented on the example of
gymnascs but its usefulness can be extended, in parcular, to the group of convenonal sports, as well
as into the area of other sports, because a correct and eecve movement technique is an important
component of successful performance in all sports.
2nd INTERNATIONAL SCIENTIFIC CONGRESS ORGANIZED BY SLOVENIAN GYMNASTICS FEDERATION
30
VIRI
Bango, B., Sillero-Quintana, M. & Grande, i. (2013). New apparatus to assess the force producon in the swallow.
Science ofGymnascsJurnal, 5 (3): 47-59.
Bedenik, K (1995). Vpliv Biomehanskih parametrov na oceno plovke čez konja. Diplomsko delo. Ljubljana: Fakultetaza
Šport.
Brüeggmann, G.P., Cheetam, P., Arampatzis, D. (1994). Approach to a Biomechanical Prole of Dismounts and
Release-Regrasp Skills ohe High Bar. Olympic Scienc Projects, Journal of Applied Biomechanics, 10 (3): 291-312.
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Čuk, I. (1995): Kolman and Pegan saltos on high bar. V Jošt, B. (Ur.) Kinemačna analiza gibanj v izabranih športnih
panogah (str. 195-198). Ljubljana: Univerza v Ljubljani, Fakultet za šport.
Čuk, I. (1996). The development and analysis of a new gymnastics exercise – dropshoot with a forward somersalto
tucked from the parallel bars (Unpublished Doctoral dissertaon thesis). Universityof Ljubljana, Faculty of Sport,
Slovenia, Ljubljana.
Čuk, I., Atiković, A. &Tabaković, M. (2009). Tkachev salto on high bar. Science ofGymnascsJurnal, 1 (1): 5-15.
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meri otrok in mladostnikov : pedagoško-psihološki in biološki vidiki kondicijske vadbe mladih. Ljubljana: Fakulteta
za šport, Inštut za šport, str. 380-391.
Kolar, E., Andlovic-Kolar, K., Štuhec, S. (2002). Comparave analysis of selected Biomechanic characteriscs between
a support backward swing and support swing forthe 1 - 1/4 straddle-piked forward salto on the parallel bars. Sports
Biomechanics, 1 (1): 69-78.
Kolar, E., Pileč, S., Kugovnik, O., Andlovic-Kolar, K. & Stuhec, S. (2005). Primerjava kinemačnih spremenljivk
dobrih in slabih izvedb seskoka z bradlje. V E. Kolar & S. Pileč (Ur.) Gimnaska za trenerje in pedagoge 1. Ljubljana:
Gimnasčna zveza Slovenije, str. 34-44.
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forward saltos at the parallel bars. Biomechanics in Gimnascs: Cologne: 487-497.
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Veličković, S. (2005). Denisanje kinemačkog modela tehnike izvođenja najsloženijih gimnasčkih vežbi.
(Unpublished Doctoral dissertaon hesis). Novi Sad: Fakultet zičke kulture.
Veličković, S., Kugovnik, O., Kolar, E., Bubanj, R., Madić, D. & Supej, M. (2005) Primerjava nekaterih kinemačnih
spremenljivk med točem in točem z obratom na bradlji. Šport, 53 (1), 59-65.
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ResearchGate has not been able to resolve any citations for this publication.
Article
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With the new FIG Code of Points for men (2006) based on the philosophy of open ended difficulty score, point advantages have been given, again, to those who are in search for and willing to perform new elements. Each element in the Code of Points can be developed by changing its start and its final position, the start and the final grip with the apparatus, the body position during the element, by adding a flight phase or a rotation around the frontal, the longitudinal or the sagital axis. The Tkachev is quite an old release element (approximately 40 years old) on high bar. In line with the knowledge available to us today, we have been looking into the possibility of performing the Tkachev salto. Following series of biomechanical analysis with consideration of the gymnast's safety, we calculated that the Tkachev salto could be performed by those gymnasts who can perform the straight Tkachev with a high amplitude. Gymnast who will be able to perform the Tkachev salto at a major competition will enter the gymnastics history and have huge chances of wining the most prestigious competitions.
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8 men artistic gymnasts were evaluated with a new test protocol in order to assess isometric strength in an specific hold position on still rings. The proposed test protocol measures the force applied the gymnast on the rings from an initial lying prone position on a force platform while he is trying to achieve the Swallow (or Hirondelle) position. The vertical force (FZ) from the forcetime curve registered (100 Hz) was used and it showed a descent from the initial body weight level caused by the gymnast force on the rings and, later, a maximal isometric force period. Fundamental and derivate variables to extract from the evolution of Fz were defined. Results showed significant statistical differences between gymnasts that could perform the Swallow (P) from those that could not (NP) (p<0.05). Performer gymnasts were characterized by a higher percentage of body weight descent and higher strength in relation to body mass (p<0.05). The practical application of this tool could be to provide coaches with information about how close the gymnast is to perform the Swallow.
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The aim of our research was to study the relationships between performance variables in a support backward swing (SBS), which was used as a progressive step in the learning procedure for a 1 1/4 straddle-piked front somersault and the swing prior to a 1 1/4 straddle-piked front somersault from support to bent arm support on the parallel bars (5/4S). Mitja Petkovsek, parallel bars gold medallist at the 2000 EC in Bremen, performed these elements. Kinematic analysis involved CMAS software (Praha, 1993), and the Suskana body segment model that has 17 points and 15 segments. Kinetic variables were estimated using 2D IMGIM software, which has 8 points and 6 segments (Colja and Cuk, 1994). The results indicated that some kinematic aspects of the two types of swings were similar but there were important differences in kinetic aspects of the motion. During the swing for the 5/4S, force and torque were higher than in the SBS.
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At the 1992 Barcelona Olympic Games, 70 dismounts and release-regrasp movements on the high bar were selected from films gathered with three synchronized cameras during the compulsory and the optional men's high bar competition. The skills were classified into 10 groups depending on the direction of rotation, body configuration, and flight projection. Kinematic variables were used to profile the movement groups. Statistically significant differences between the groups were identified by ANOVA. Three groups with significant differences in terms of the maximum values and the locations of the maxima could be differentiated. These were (a) backward rotating swings with an increase of rotation (e.g., overgrip giant swing—triple backward tuck somersault dismount), (b) backward rotating swings with a change of the direction of rotation (e.g., overgrip giant—Tkatchov straddle), and (c) forward rotating swings with an increase or a decrease of rotation (e.g., undergrip giant swing—Jaeger somersault).
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RESULTS AND DISCUSSION: Mean kinematic results for all 8 giants are shown in Table 1. Since the height of the cast varied between gymnasts, results are presented commencing with each gymnast's center of mass positioned 45 degrees above the bars. Bar levels I/II represent the instant when the gymnast's center of mass (CM) was level with the bars in the downswings/upswings, respectively. Bottom represents the point below the bars where the CM vertical velocity changed from negative to positive. Vertical represents the point above the bar where theCM is vertically aligned with the gymnast's hands . Data in Table 1 show that gymnasts perform giants on the parallel bars in a similar fashion as in apparatuses such as the high bar and uneven bars with a noticeable exception regarding knee joint motion.
Vpliv Biomehanskih parametrov na oceno plovke čez konja. Diplomsko delo
  • K Bedenik
Bedenik, K (1995). Vpliv Biomehanskih parametrov na oceno plovke čez konja. Diplomsko delo. Ljubljana: Fakultetaza Šport.
Računalniški program za izračun sil pri kroženju. Ljubljana: Fakulteta za šport
  • I Colja
Colja, I. (1994). Računalniški program za izračun sil pri kroženju. Ljubljana: Fakulteta za šport.
Kolman and Pegan saltos on high bar Kinematična analiza gibanj v izabranih športnih panogah (str. 195-198)
  • I Čuk
Čuk, I. (1995): Kolman and Pegan saltos on high bar. V Jošt, B. (Ur.) Kinematična analiza gibanj v izabranih športnih panogah (str. 195-198). Ljubljana: Univerza v Ljubljani, Fakultet za šport.
The development and analysis of a new gymnastics exercise -dropshoot with a forward somersalto tucked from the parallel bars (Unpublished Doctoral dissertation thesis)
  • I Čuk
Čuk, I. (1996). The development and analysis of a new gymnastics exercise -dropshoot with a forward somersalto tucked from the parallel bars (Unpublished Doctoral dissertation thesis). Universityof Ljubljana, Faculty of Sport, Slovenia, Ljubljana.
Proces treninga v športni gimnastiki v obdobju od 11. do 14. leta starosti Šport po meri otrok in mladostnikov : pedagoško-psihološki in biološki vidiki kondicijske vadbe mladih
  • E Kolar
Kolar, E. (2007). Proces treninga v športni gimnastiki v obdobju od 11. do 14. leta starosti. V Škof, B. (ur.). Šport po meri otrok in mladostnikov : pedagoško-psihološki in biološki vidiki kondicijske vadbe mladih. Ljubljana: Fakulteta za šport, Inštitut za šport, str. 380-391.