Factorial Analysis of Body Elements in Rhythmic Gymnastics

Gordana Furjan-Mandić

, Josipa Radaš

, Petra Zaletel

and Igor Gruić

Faculty of Kinesiology University of Zagreb, Horvacanski zavoj 15, 10000, Zagreb, Croatia

Faculty of Sport University of Ljubljana, Slovenia

Keywords: Rhythmic Gymnastics, Body Elements, Structure.

Abstract: The main goal of this research was to analyze body movements of rhythmic gymnastics techniques, groups A

and B, to classify them into homogeneous groups, to determine similarities between the obtained groups. The

sample of entities was comprised of 108 body movements (elements), pertaining to the difficulty groups A

and B, that were described by 33 variables. Reliability of the measuring instrument was determined on the

basis of obtained opinions, collected from eight experts in rhythmic gymnastics. Ten significant latent

dimensions were obtained by factor analysis under the component model with the Guttman-Kaiser criterion.

The latent dimensions were interpreted as: one-leg jumps, spine mobility, frontal flexibility, free leg

movements, the help of the arm-work, body rotation, two-leg jumps, forward bend, other jumps and specific

elements. It is feasible to state that the application of the sophisticated measuring instruments for the different

anthropological factors and biomechanical parameters determination could have provided more information

on the characteristics of and differences between the rhythmic gymnastics elements.

1 INTRODUCTION

As in every sport, sport employees in rhythmic

gymnastics have attempted to determine and classify

movement structures into logically encompassed

units. Sokal and Sneath (1963, prema Ferligoj, 1989.)

have tried to merge different viewpoints of grouping

(sorting), and that attempt evolved into an

independent discipline within multivariate analysis.

A. Spiessa (1810.-1858.) is considered as a first

systematizer of exercises on apparatus, with the

system described in the book ”Lehre der Turnkunst”

(1840/41.), and exercising material divided into:1)

freehand exercises: stances, walking, running, hops,

jumps, rotations and exercises during rotations; 2)

hanging exercises: by hands, by trunk, by legs,

swinging, climbing and crawling; 3) exercises while

holding position: while standing (balance), while

kneeling, in sitting position, balances on the foot,

holding position on hands, on head and combined exer-

cises, 4) group exercises: freehand group exercises,

group exercises in holding position, group exercises

while hanging, group exercising in lying position.

With the development of specific types of dancing

techniques, their classifications and instructions for

proper execution have been implemented (credited

dancers or coreographers that have developed their

own techniques of modern dancing that are

recognisable even today: F. del Sarte, E. J. Dalcroze,

R. Laban, L. Fuller, R. Saint-Denis, M. Graham, J.

Limon, M. Cuningham et al.) One of the most

advanced and transparent classifications in

development of rhythmic gymnastics was given by a

great pedagogue in that area J. Kramaršek (1952,

1959, 1961, 1964), as well as Jastrjembskaia, N., Y.

Titov (1998).

Elements without props, that is, elements

performed exclusively with the body are an essential

foundation for individual and group routines in

rhythmic gymnastics except in youngest competitive

categories, movements have to be executed in

harmony with how one of the following props is

handled: jump rope, hoop, ball, cones and ribbon.

Elements from different groups of elements need to

be represented equally when assembling individual

and group. Elements performed with the body need to

be chosen in regard to logical and specifical

techniques, which are unique for every apparatus. In

rhythmic gymnastics routines, elements performed

with the body need to be executed together with

handling of the apparatus, and their execution is one

of the criteria when judging: a) degree of difficulty of

the routine (selection of elements of A, B, C and D

scores) total number of elements in a routine and their

170

Furjan-Mandi

c, G., Radaš, J., Zaletel, P. and Grui

c, I.

Factorial Analysis of Body Elements in Rhythmic Gymnastics.

DOI: 10.5220/0007233201700179

In Proceedings of the 6th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2018), pages 170-179

ISBN: 978-989-758-325-4

combinations), and b) degree of quality of a routine

(manner of execution of elements in a routine,

synchronicity with music, total number of performed

errors…).

Determinants of competitive performance in

rhythmic gymnastics were analyzed by Bobo-Arce,

M., Méndez-Rial, B. (2013), groups routines of elite

rhythmic gymnastics Ávila-Carvalho L, Palomero M,

Da L, Lebre E. (2009), about the importance of the

"technical evolution" aspect Buarque Maag. (2003),

then feedback in rhythmic gymnastics as a process of

correcting technical mistakes Cristina-Elena M. Sport

& Society (2012) etc.

When executing elements, every gymnast has to

abide by the rules of execution, on which the height

of the score for technical value is dependant.

Common parameters on which the height of the score

relies are proper posture, movement amplitude,

balance control, controlled execution of footsteps...

Besides that, all elements executed with the body

must be performed without breaks, with constant

exchanges of contraction and relaxation, with a close

connection between dynamics, amplitude and speed

of execution, in harmony with the rhythm and tempo

of music. At the same time, they need to be executed

simultaneously with the whole body, including the

head and hands, which means that there should be no

isolated muscle groups.

For the purposes of this research, experts analized

108 elements which display a representative sample

of entities. Goal of this research was to conduct an

kinesiological analysis of elements of rhythmic

gymnastics. Because of a quantitative objective

analysis of technique elements, a new measuring

instrument needs to be assembled, and measuring

characteristics determined (reliability analysis and

factor validity). Description of analysed entities will

be executed with a mathemathical-statistical procedu-

re. For the purpose of differentiating of hypothetical

groups, descriptive biomechanical and functional

characteristics (criteria on which the groups should

significantly differ), have been set in advance.

2 METHODS

2.1 Sample of Entities

Sample of entities in this research consists of

mandatory elements of techniques of body

movements without apparatus in rhythmic

gymnastics. The research was conducted on a sample

that is comprised from 108 elements, from total of

132 elements of A and B score. Elements that form a

sample of entities have been chosen from the official

Code of Points (Rulebook of rhythmic gymnastics),

published by International gymnastics federation

(FIG), in the year 1997. Elements for which the

experts of rhythmic gymnastics agreed that are the

most used when assembling a free composition were

chosen. During the evaluation of execution of

technique of elements, it is important to be familliar

with all existing groups of elements of body

movement, which can be executed in different

directions, in every axis, interconnected with

footsteps or no, with one or both leg support, but,

during the whole execution, they need to be

connected with movement of arms.

With regard that elements which are sorted in the

group of other elements, are those that are used when

interconnecting basic elements, and in this research

they are not included in the sample of entities. All

analysed elements from basic groups are, according

to the Rulebook, divided into four groups and contain

the following characteristics( characteristics of

elements are listed in the Code of Points, 1997):

JUMPS (high takeoff and good height during flight,

defined and fixed form during the flight, large

amplitude during the flight phase), BALANCE

(executed on tip of toes, held for atleast one second,

defined and observable shape, satisfying amplitude in

forming of balance), PIROUETTES (executed on tip

of toes, held and defined shape during and when

finishing rotations, large amplitude of movement),

FLEXIBILITY / WAVES (MOBILITY)( executed on

one or both feet. or other parts of the body, well

defined and held form, large movement amplitude).

Rhythmic gymnastics elements are natural forms of

movement, as are their variations, and they are

formed in a way to meet the term of aesthetically

designed movements. Requirements during the

execution of elements of rhythmic gymnastics are

subordinated to anatomical constitution of the female

body, as to incorporate an aesthetic component during

their execution.

Every group of elements in rhythmic gymnastics

has specific phases. First phase is the so called

preparation phase, which can be achieved through a

running start, lunge, descending into a squat, or from

a static position. As many of the elements in a routine

are executed after a formerly executed element,

which can be different, way of preparation varies.

Because of that, elements executed with the body are

descriped without a preparation phase. That way,

every element, regardless of which group it belongs

and the most characteristic preparation phase, is

described starting from the standing position and not

from movement. In that way, the experts can more

Factorial Analysis of Body Elements in Rhythmic Gymnastics

171

easily determine the possibility of interconnection of

elements in a routine. The goal of analysis was to

describe specific movements of every element in

isolation.

2.2 Sample of Variables

Sample of selected elements in this research is

described with a set of characteristics, which are

divided into following subgroups: 1) descriptive

biomechanical characteristics: a) movement of center

of gravity in space; b) movement characteristics

(movement of individual segments of the body -

topological characteristics), c) support surface during

element execution, and 2) functional characteristics:

valence of binding the elements together.

Characteristics, evaluated with the stated description,

were treated ad binary variables.

2.3 Experimental Procedure

Quantification of characteristics on the sample of

entities was conducted by eight (8) experts in

rhythmic gymnastics, with a passed judge exam and

with an experience of atleast three competitions of

federal importance as a judge. All judges that have

evaluated characteristics of elements of rhythmic

gymnastics, have graduated on Faculty of

Kinesiology, or have passed the courses Rhythmic

gymnastics and Biomechanics. Collection of data was

done through a structured interview, in the presence

of the supervisor of experimental procedure. Surveys

have been handed to all the experts at once, with

guidelines and clarifications on how to fill out the

surveys. The experts had a task where they had to

evaluate if they agree or not with every of 59

statements that describe an element. The investigators

assessed the characteristics of the technical elements

by looking at the drawings of the elements from Code

of Points. The answers were transcribed into binary

values, where 1 is agreeing with the statement, and 0

is disagreeing with the statement.

2.4 Data Analysis Methods

For the purpose of verification of the measuring

instrument, the data were processed by the SPSS

program package for Windows.

Data analysis was conducted in several phases,

and the following statistical analysis have been

performed:

1. Correspondence of agreement of judges-experts

on the unique subject of measuring of

every element was determined through the

calculation of:

 number of significant main components of

correlation matrix of judges for all required

specifics of analysed movement structures

 Variance size of first main components of

judge scores for all analysed elements

 Ortogonal projection of judges on the first

main subject of measurement for every

observed characteristic of every individual

element

 Reliability of measurement (Cronbach's

alpha) for all applied variables

2. Condensation of results from all eight experts

was conducted, and further procuders were

executed on the basis of variables formed in that

way.

3. Following descriptive parameters were

calculated for all variables: MEAN – average

value of scores given by the experts, SKEWNESS

– asymmetry of score distribution, KURTOSIS –

sharpness of peak, ST.DEV. – standard deviation

Factor analysis was conducted to analyse latent

contents in the space of original variables.

Number of significant factors was determined by

the Guttman-Kaiser criteria. Final exploratory

factor structure was achieved by a skewed

oblimin rotation, and is displayed through

matrixes of ortogonal and parallel projections

(structure and assembly), as is displayed with a

matrix of correlations between factors

3 RESULTS & DISCUSSION

3.1 Metrical Characteristics of

Variables

Reliabilities of variables, an assumption for further

analysis, were evaluated on the basis of Cronbach α

coefficient (table 1.). Not all variables have achieved

satisfying reliability coefficients (alpha values ranged

from 0,37 as the lowest and 1,00 as the highest value),

primarily because of an unsatisfying degree of

agreement of experts about the real subject of measu-

rement. Only variables with a satisfying reliability and

where all experts participated in formation of the result

have been taken into account for further analysis. From

the total of 59 variables, 33 were selected for further

analysis and are displayed in table 1.

Reliability coefficients in mentioned variables

range from 0,73 as the lowest, to 0, 99 as the highest.

Variables 5, 12, 13 and 14 (table 1.) have alpha values

in the range of 0, 70 to 0,80. Although the coefficient

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172

Table 1: Descriptive statistics; cronbach α; values of main components and factors after oblimin rotation.

code VARIABLE description

AS SD a

Cron-

bach α

λ* PCT Factor λ

% o

Var

Cum

Commu-

nality

V4 ACTKRBOC

center of gravity is moving

non-lineary in lateral plane

2.35 2.70 -.26 1.04 0,9157 5,24 65,4 1 6.40 19.4 19.4 0.93

V5 ACTKRCEO

center of gravity is moving

non-lineary in frontal

plane

.94 1.59 2.02 1.67 0,7928 3,31 41,4 2 4.47 13.5 32.9 0.74

V8 ACTVISE

center of gravity is moving

in two or more planes

.87 1.61 2.77 1.93 0,8169 3,74 46,7 3 3.46 10.5 43.4 0.86

V9 BTPRET

trunk bends forward .92 2.14 4.73 2.44 0,9405 5,75 71,9 4 2.66 8.0 51.5 0.93

V10 BTOTKL

Trunk bends sideways .53 1.78 11.55 3.53 0,9638 6,42 80.3 5 2.27 6.9 58.3 0.92

V11 BTZAKL

Trunk bends backwards 1.61 2.87 .38 1.45 0,9628 6,36 79,4 6 2.19 6.6 65.0 0.94

V12 BTZASU

Trunk rotation 1.41 1.88 1.20 1.41 0,7885 3,94 49,2 7 1.84 5.6 70.5 0.87

V13 BTZSPR

Trunk rotation while

bending forward

.31 .96 12.44 3.53 0,7807 3,67 45,9 8 1.79 5.4 75.9 0.71

V14 BTZSZK

Trunk rotation while

bending backwards

.31 .91 11.32 3.35 0,7398 3,12 39,1 9 1.10 3.3 79.3 0.59

V15 BTNEKR

Trunk remains in starting

position

3.95 3.35 -1.79 -.07 0,9447 5,81 72,6 10 1.05 3.2 82.5 0.91

V16 BSLNZAPR

Movement of free leg:

extended leg swing

4.66 2.78 -.97 -.73 0,8908 4,68 58,5 11 .96 2.9 85.4 0.83

V17 BSTNZAPR

kretanje stojne (odrazne)

noge: extended leg swing

1.50 2.68 1.41 1.74 0,9525 6,32 79,0 12 .79 2.4 87.8 0.80

V18 BSLNKRPR

Movement of free leg:

extended leg circling

1.78 2.35 -1.24 .76 0,8831 4,44 55,5 13 .73 2.2 90.0 0.79

V20 BSLNZAGR

Movement of free leg:

flexed leg swing

.94 1.91 2.20 1.88 0,8885 4,52 56,5 14 .67 2.0 92.0 0.83

V21 BSTNZAGR

kretanje stojne (odrazne)

noge: flexed leg swing

.46 1.43 12.96 3.55 0,8698 4,05 57,9 15 .55 1.7 93.7 0.65

V22 BSLNIGR

Movement of free leg:

flexed leg elevation

.75 1.82 5.04 2.48 0,9099 4,97 62,1 16 .41 1.2 94.9 0.80

V30 B2RUSLN

One hand supports free leg .94 2.43 3.84 2.35 0,9810 7,09 88,6 17 .36 1.1 96.0 0.80

V31 BRUNESLN

Both hands support free

leg

6.30 2.59 1.44 -1.72 0,9403 6,17 77,2 18 .27 .8 96.8 0.83

V32 BGLPRET

Hands do not support free

leg

.66 1.67 6.65 2.72 0,8957 4,67 58,4 19 .22 .7 97.5 0.97

V33 BGLZAKL

Head bends forward 1.65 2.79 .05 1.34 0,9494 5,92 74,0 20 .20 .6 98.1 0.93

V34 BGLOTKL

Head bends backwards .41 1.48 14.97 3.95 0,9322 5,56 69,5 21 .12 .4 98.4 0.96

V35 BGLROTS

Head bends sideways 2.18 2.40 -1.39 .50 0,8583 4,21 52,6 22 .10 .3 98.8 0.91

V36 BGLMJES

Head rotates sideways 3.72 2.71 -1.14 .36 0,8553 4,06 50,8 23 .09 .3 99.0 0.86

V38 CPOCSTO2

Head stays in starting

position

1.91 1.64 .21 .67 0,6165 6,16 77,0 24 .08 .2 99.3 0.84

V39 CPOCSTO1

Element is performed on

both feet fully and on both

legs

.13 .87 68.42 8.02 0,9470 6,67 83,4 25 .06 .2 99.4 0.59

V47 COP1KLEK

Element is performed on

the foot of one leg

.66 2.00 7.75 3.03 0,9698 6.96 87,0 26 .05 .1 99.6 0.43

V49 COPSUODR

Element is performed in a

one-leg kneeling position

.47 1.74 13.29 3.83 0,9731 7,46 93,2 27 .03 .1 99.7 0.65

V50 COP1ODR

Element is performed with

takeoff from both feet

.57 1.99 10.32 3.45 0,9881 7,86 98,2 28 .03 .1 99.8 0.97

V51 COPIZMOD

Element is performed with

a one-legged takeoff

1.47 3.09 .77 1.65 0,9974 7,36 92,0 29 .03 .1 99.8 0.97

V52 CSUNDOS

Element is performed with

multiple alternating

takeoffs from foot to foot

.09 .78 101.44 9.95 0,9698 7,49 93,6 30 .02 .1 99.9 0.57

V53 CJEDDOS

Landing is on both feet .50 1.88 12.16 3.69 0,9895 7,60 95,0 31 .01 .0 100 0.97

V55 CDOSZAM

Landing is on one foot 1.46 3.03 .77 1.64 0,9925 6,31 78,9 32 .01 .0 100 0.98

*Number of significant main components (K=1), specific values of first main components (EIGENVALUE) and percentage of clarified

common variance of (PCT) of every variable for eight judges; Eigenvalue - specific values and Pct of Var - percentage of explained variance;

Communality - communality values of variables

Factorial Analysis of Body Elements in Rhythmic Gymnastics

173

is low, these variables were included as to have better

coverage in the group of descriptive variables. Eight

variables had satisfying reliability coefficients (alpha

0,80-0,90), and most of the variables were over the

range of alpha of 0,90, and it can be concluded that

the agreement of the experts around the real subject

of measuring is satisfying and high, having in mind

that rhythmic gymnastics is one of the sports with the

most developed Rulebook and judging criteria

because of the sensitivity of determining the score on

competitions.

Selected variables are supoorted by size of

acquired specific values of the first main components

of matrix correlation of experts in all criteria variables

(table 1.). Through the factorisation process, it was

determined that every variable of 33 selected has a

unique subject of measurement, which is also proven

by the size of variance of first main components

(K) for every expert in particular. Component values

of every expert in forming of the first main

component are located in the annex.

Specifical values of the first main components

(EIGENVALUE) and percentages of common

variance of measurement range from the lowest (40 -

60%), to highest (over 90%). With regard to current

research (Zagorc, 1993., Trninić, 1995.), it can be

concluded that there is similarity between results, and

therefore, further statistical analysis have been

conducted.

3.2 Factorial Analysis of Variables

Regardless of various procedures of factor analysis,

every technique extracts a specific group of important,

Table 2: Matrix of model.

Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 Factor 9 Factor10

.92818 .11697 -.02792 -.03244 -.04342 .15139 .09450 .02504 .03598 -.04062

.44590 .04817 .40852 -.14928 -.02116 -.28342 .16226 .23810 -.03464 .14002

.62143 .03341 .17243 -.03651 .00003 -.42421 .11827 .17706 .03007 .17721

-.06026 -.09567 -.15287 -.05305 -.03606 .14345 .02256 .99725 -.06612 -.08572

V10

-.06998 -.02709 .97312 .02560 -.04861 .07055 -.05474 -.05588 .04281 -.00118

V11

-.00307 .91905 -.15387 -.01664 -.04244 .19796 .05180 -.11767 -.05831 .10261

V12

.30484 -.04854 .07528 .12063 .06775 -.77662 .09487 .01351 -.01885 .16109

V13

-.01035 .16312 .14647 .17659 .02762 -.16004 -.10543 .63114 .21641 .11926

V14

.12590 .31535 .11858 .20700 .06747 -.34661 .10379 .06003 .12650 .38963

V15

-.11816 -.67369 -.26344 .03631 .04546 -.04693 -.10590 -.38556 .15807 -.00910

V16

.23777 -.09992 -.10773 -.82690 -.01615 .06282 -.13255 .02070 .01631 .16466

V17

.80001 -.05959 -.07045 -.13101 -.04002 .03794 .12302 -.01919 .27313 -.00182

V18

-.09734 -.03472 -.23274 -.37132 .05634 -.75440 -.13282 .00683 -.11198 -.15117

V20

.12703 -.05776 -.07104 .90062 .00907 .03393 -.04629 -.01467 -.12223 -.03374

V21

.53936 .07663 -.09422 .21417 -.06461 .06704 .08127 -.15489 -.49129 -.14833

V22

-.08274 -.07517 -.03691 .84618 -.04515 .09077 -.09506 .18094 .04236 .07451

V29

-.06808 -.02353 .01414 -.03387 .86129 -.00219 -.04124 -.08024 .00063 .02069

V30

-.04836 -.00693 -.13312 .06540 .89663 .01049 -.02676 .02097 .01812 .01544

V31

-.04075 -.04550 -.00742 .01571 -.99410 -.03096 -.01469 .01897 -.00125 .03647

V32

-.08226 -.02563 -.06734 .10537 -.06151 .09001 -.06619 .95916 -.01438 -.02745

V33

.02202 .93927 -.13017 .02233 -.02300 .15773 .05976 -.12390 -.02802 .07611

V34

-.08760 -.05668 .97228 .00788 -.06680 .07343 -.04556 -.11260 -.00751 -.03303

V35

-.16834 -.15900 -.06212 .05432 -.10253 -.91723 -.07998 -.14622 -.02543 -.10838

V36

.02755 -.70266 -.17813 .05933 .13562 .32288 .00794 -.23575 .13160 .14014

V38

-.07351 .47964 .04276 .02845 -.02749 .00872 -.11204 -.08673 .30139 -.51789

V39

-.05583 -.05433 .34097 -.21983 .18668 .21557 -.06608 .03934 -.29268 -.18000

V47

-.20064 .14601 -.08841 -.15122 -.15964 .23585 -.16733 -.14584 -.02771 .65528

V49

-.09137 .01550 -.06167 -.02439 -.03068 .06444 .99207 -.04665 -.01677 -.04806

V50

.99086 -.04107 -.03660 -.01570 -.04185 -.00730 -.17490 -.05411 .02170 -.00885

V51

.18579 -.11314 -.01519 -.05298 -.02219 .14335 -.00035 -.02997 .69219 -.12695

V52

-.10645 -.00698 -.04624 -.03013 -.03376 .03562 .99846 -.04515 .01823 -.02691

V53

.99024 -.03183 -.04649 -.00269 -.04811 -.00607 -.15806 -.07379 -.04739 -.01734

V55

.94574 .01800 -.04043 .00363 -.03589 -.01205 -.00608 -.06180 .01670 -.01556

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factors. Because the procedure of factor analysis is

applied on the matrix of intercorrelations of variables

it is necessary that the values are not zero or close to

zero. A procedure of factorisation under the

component model of Gutman-Kaiser criteria was

used in this research, which determines all main

components with specific value equal or above 1,00

as significant. ten significant factors have been

extracted in this research (table 1.). Without regard

for existing and other criteria, the criteria G-K was

chosen, because it excretes a larger number of

significant factors, which is important in this

example, as to get as much information as possible

about latent space.

Total size of variance that exhausts ten acquired

factors is 82,5%. On the basis of former studies

(Zagorc, 1993., Trninić, 1995., Vuleta, 1997.), it can

be said that latent space is described with a higher

percentage of common vairability and co-variability

of kept variables. First factor exhausts 19,4%, second

13,5%, third 10, 5%, fourth 8,0%, fifth 6,9%, sixth

6,6%, seventh 5,6%, eighth 5,4%, ninth 3,3% and

tenth 3,2% of total variance (table 1.).

Values of communality of variables are displayed

in table 1., which range from low (0,43), middle, and

in most cases, largest (0,98) values, which displays

that most of the variables carries a significant

variance in the space of kept latent dimensions.

Lowest communalities have been noticed in four

variables, which descripe execution on elements on

full feet V38 and V39, execution of movement

structures with multiple alternatig takeoffs V51, or

execution of backward bend with simultaneous trunk

rotations. Movement structures that incorporate those

Table 3: Matrix of structure.

Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 Factor 9 Factor10

.93320 .18659 -.00882 -.00319 -.20906 .02220 .26051 .00050 .06552 .03621

.52923 .16264 .49828 -.09098 -.10352 -.41701 .26133 .37186 -.02988 .20393

.71723 .12063 .25286 .01610 -.11940 -.56146 .25046 .28914 .05257 .26142

-.09173 -.02823 .05961 .06190 -.03753 .02600 .01526 .92188 -.05496 -.02718

V10

-.07348 .09803 .94676 -.00264 -.01193 .01605 -.04905 .16202 .01321 -.03475

V11

.03871 .91133 -.07469 .06717 -.23186 .24006 .18715 -.09347 -.05211 .13980

V12

.42998 -.01517 .13094 .14345 .01512 -.84246 .17539 .16220 -.00230 .22392

V13

.01471 .23740 .31241 .26413 -.05467 -.26889 -.04520 .73101 .22868 .17496

V14

.23412 .37922 .18833 .26932 -.07969 -.40709 .21644 .21865 .13339 .44156

V15

-.16797 -.77047 -.44616 -.08504 .19900 .02986 -.24860 -.49771 .15722 -.07780

V16

.21066 -.18627 -.11300 -.83980 .02434 .04409 -.18690 -.11683 .02590 .14745

V17

.82614 -.01146 -.08382 -.11524 -.16437 -.07208 .22273 -.05830 .29795 .06198

V18

-.04227 -.15978 -.16870 -.37876 .14983 -.70482 -.18864 -.00551 -.09864 -.13865

V20

.10757 .01531 -.09404 .88631 -.05822 .00799 .06046 .06405 -.10486 -.00718

V21

.53028 .11668 -.10451 .20902 -.13013 .03333 .21631 -.16709 -.47034 -.10574

V22

-.09876 .01357 -.03186 .85595 -.10061 .05792 -.02385 .26244 .05901 .09785

V29

-.19997 -.20798 .00972 -.12096 .88311 .00233 -.12775 -.11592 -.06112 -.08340

V30

-.18483 -.19589 -.11359 -.00674 .89505 .00597 -.10147 -.03825 -.03916 -.07630

V31

.10646 .14645 -.02982 .09532 -.98347 -.01228 .05418 .06077 .06814 .13653

V32

-.10574 .05780 .14142 .21722 -.08472 -.02895 -.04538 .94028 .00242 .03420

V33

.06865 .93471 -.04694 .10676 -.22171 .19535 .20324 -.08400 -.02249 .11730

V34

-.09282 .06376 .93091 -.02945 -.01216 .03215 -.04889 .09817 -.03830 -.07218

V35

-.05439 -.19952 -.05140 .03715 -.01142 -.86220 -.10802 -.04196 -.00536 -.08016

V36

-.06005 -.75071 -.35496 -.04628 .23846 .33844 -.11199 -.37164 .11880 .06638

V38

-.08945 .44046 .08369 .04181 -.06669 .06282 -.09231 -.06664 .29982 -.50546

V39

-.14942 -.08264 .34609 -.26156 .26931 .20914 -.11480 .03101 -.32395 -.23662

V47

-.18487 .13974 -.14109 -.14520 -.19931 .26917 -.15553 -.15816 -.01263 .62943

V49

.06686 .14829 -.05413 .07474 -.09038 .07062 .97290 -.04584 -.06265 -.00096

V50

.96640 -.01647 -.05048 -.03508 -.16284 -.13225 -.01669 -.07568 .06735 .05279

V51

.17738 -.10864 -.06512 -.06320 -.05954 .11638 -.03225 -.07134 .69512 -.11983

V52

.05900 .12884 -.04075 .06926 -.09073 .04037 .97370 -.03706 -.02814 .02019

V53

.96690 -.00607 -.06140 -.02228 -.16699 -.12604 .00509 -.09609 -.00191 .04468

V55

.95209 .06435 -.04469 .00578 -.17518 -.13195 .15457 -.07180 .05338 .05504

Factorial Analysis of Body Elements in Rhythmic Gymnastics

175

movement structures are obviously rare in rhythmic

gymnastics and are not in common with other

variables, which is probably the reasom of their low

positioning in the space of latent dimensions.

With analysis of matrix of model (table 2.) and matrix

of structure (table 3.), it can be concluded that both matrixes

carry almost identical informations about isolated latent

dimensions, that is, values of parallel and ortogonal

projections on oblimin factors are of equable values. The

reason for that is most probably in the relatively high

independence of isolated factors.

Generally, first eight factors are formed with a

larger number and higher values of projections of

variables, while the last two are defined by a smaller

number of variables and lower values.

First latent dimension was defined by the largest

number of variables. For the biggest part, it consists

of variables linked with descriptions of movement

structures which are incorporated into most of the

jumps:

 V50 – execution of elements with one-leg

takeoff,

 V53 – one-leg landing,

 V55 – landing on swing leg,

 V4 – movement of center of gravity in lateral

plane,

 V17 – movement of standing leg by swing

out,

and with following variables:

 V8 – movement of center of gravity in two

or more planes,

 V21 – takeoff foot moving flexed in a swing,

 V5 – movement of center of gravity in

frontal plane.

By visual analysis of jumps, phases that the trunk

and body segments go through are obvious. Most of

the jumps consists of preparation, which is performed

by swing of the leg, separation of other leg, with

which the center of gravity starts moving in one of the

planes (usually lateral), the flight phase itself, which

takes place in a parabolic manner, and one-legged or

two-legged landings. During the flight phase,

exercisers can add another movement structures

which define the type and difficulty of the jump. The

first latent dimension encompasses most of

movement structures specific for jumps, and it can be

named ONE-LEG JUMPS.

Second latent dimension was defined by two

positive and two negative projections. All four

variables describe the position of trunk and head

during the execution of element. Positively projected

variables:

 V33 – head bends backwards:

 V11 – trunk bends backwards;

negatively projected variables:

 V36 – head stays in place,

 V15 – trunk remains in starting position.

Mentioned positions of trunk and head are

present in a large number of elements of rhythmic

gymnastics and can be found in all groups. It can be

said that these variables divide elements into those

that do not require mobility of the spine, and those

that do. Flexibility is a motor ability which is

positioned at the very top of specification equation of

thythmic gymnastics. Although the elements for

which flexibility is a primary requierment for their

execution, are sorted in a group called MOBILITY,

flexibility is present and necessary for execution of

elements from the remaining three groups. However,

when holding trunk and head in the starting position,

as when performing bends, spine stabilisator muscles

are activated, and in that way, it can be concluded that

this latend dimension is of topological character and

divides elements according to demands in mobility of

the spine (trunk), and therefore can be named SPINE

MOBILITY.

Third latent dimension was determined by high

projections of two variables:

 V10 – trunk bends sideways,

 V34 – head bends sideways.

As in the second latent dimension, for execution

of elements in which the trunk bends sideways, high

flexibility of spine needs to be present. However, in

the example of sideway bends, there is a high demand

on flexibility of muscles of lateral sides of the trunk,

most of the bends are executed with heads extended

above head, where lateroflexors, rotators, retroflexors

and adductors are in a stretched position. Usually,

those types of movement are present in groups of

elements from the group of balance and flexibility.

According to the topologically specific factor, this

group can be named FRONTAL FLEXIBILITY.

Fourth latent dimension was determined by one

variable which is positively situated:

 V20 – free leg movement, flexed swing;

and with two negatively situated:

 V22 – free leg is lifted while flexed,

 V16 – free leg movement, extended swing.

K-BioS 2018 - Special Session on Kinesiology in Sport and Medicine: from Biomechanics to Sociodynamics

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It can be concluded that the positively situated

variable carries information about elements from the

group balance and pirouette, where the swing of

flexed leg is the first phase in execution of the

element. Two negatively situated variables describe

the execution of element in a more complex way,

from physiological and biomechanical viewpoint. It

can be determined without a doubt that the force that

muscle generates to overcome the distance that is

covered by the longer lever is much larger than the

force that needs to be generated to overcome the

movement of the shorter lever. The same situation is

when determining the force needed to execute a

swing with flexed leg. and the same swing with

extended leg. Another situation is observed in gradual

lifting of flexed leg when compared with swing of

flexed leg. When performing a swing with a flexed

leg, starting force of inertia enables a large amplitude

of movement, while, when gradually lifting a flexed

leg, the same work needs to be generated during the

whole movement, and executing that kind movement

is much harder for the exerciser. It can be said that

this latent dimension discriminates some of the

balance elements and pirouettes from easier to harder.

It can be called FREE LEG MOVEMENT

Fifth latent dimension was determined by three

variables of high parallel and ortogonal projections.

Two are with positive projections:

 V30 – describes execution of elements

where both hands support the free leg,

 V29 – describes execution of elements

where one hand supports free;

and one negatively projected variable:

 V31 – execution of elements without the arm

support for the free leg.

Elements described in this way belong to the

groups flexibility, balance and pirouettes, where one

leg is in a forward, backward or upside position. As

described before, in one case the element is executed

with the help of one or both hands, while in the other

case, there is no support with arms during the

execution of these demanding elements. As with the

fourth latent dimension, there is a differentiation

between less and more demanding elements. This

factor could be named with a title that comes out of

the very definition of the variable, HELP OF HANDS.

Sixth latent dimension is formed from negatively

positioned variables with same characteristics:

 V35 – head rotation,

 V12 – trunk rotation,

 V18 – circling with extended leg.

Common elements in rhythmic gymnastics are

those where the body and segments of the body

change their position. When executing such elements

(jumps with roration, flexibility and pirouettes) the

head leads the movement, and if the focus of the

subject are jumps or pirouettes, the leg follows the

movement of the body. From the anatomical

perspective, elements in this group are executed with

the help of rotator muscles of the body. In simple

terms, this latent dimension can be named BODY

ROTATIONS.

Seventh latent dimension is clearly defined with

two variables which describe starting and final phase

of two-legged jumps:

 V52 – landing is on both feet,

 V49 – takeoff is from both feet.

Classification of elements from the group of jumps,

on jumps that are executed with one-legged takeoff

and two-legged takeoff was given by Jastrembskaia

and Titov (1998.). Frequently, it can be the same

jump during flight phase, however, there are

differences in learning methodics. In methodic

learning in rhythmic gymnastics, there is no

difference when learning jumps based on the type of

landing. From this example, it is obvious that jumps

can be classified based on this characteristic. Seventh

latent dimension can be named TWO-LEGGED

JUMPS.

Eighth latent dimension is characterised with

variables that are defined by movement of the body

in lateral plane:

 V9 – forward body bend,

 V32 – forward head bend,

 V13 – trunk rotation with forward bend.

First two variables are highly projected in both

matrixes, while the third one has somewhat lower

parallel and ortogonal. This latent dimension

encompasses descriptions of elements of techniques

which execution carries a description of trunk and

head rotation, primarily while bending forward, and

backwards. That type of movement of trunk and head

can easily be observed in all four grops of elements

of technique. Movements where the trunk bends

forward can be a basic position in execution of

elements, but can also just be a phase through which

the body goes during execution. Regardless of the

main phase of elements which encompass this

characteristic, this factor clearly "recognizes" and

Factorial Analysis of Body Elements in Rhythmic Gymnastics

177

Table 4: Matrix of correlation of isolated factors.

Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 Factor 8 Factor 9 Factor10

1.00000

.05461 1.00000

.00841 .13212 1.00000

.00537 .09675 -.01602 1.00000

-.14611 -.19406 .02153 -.08207 1.00000

-.14102 .01950 -.07470 -.02134 -.01805 1.00000

.16782 .14888 .02069 .10419 -.07811 -.02245 1.00000

-.00496 .08784 .23233 .12348 -.03907 -.14303 .02811 1.00000

.03509 .00507 -.03205 .01184 -.06917 -.01795 -.04465 .01161 1.00000

F10

.07267 .05079 -.02319 .02939 -.10314 -.05440 .05647 .06957 .01183 1.00000

isolates from other positions. This segment of

movement is a natural motion, and does not require

special involvement of flexor and rotator muscles of

the body. Eighth latent dimension can be named

FORWARD BODY BEND.

Ninth latent dimension carries information about

a small group of elements and it is described with only

two variables with medium and low parallel and

ortogonal projections. It is positively determined:

 V51 – execution of elements with multiple

alternating takeoffs from foot to foot;

 V21 – movement of takeoff leg is performed

by swing of flexed leg.

It is clear that this dimension describes specific

jumps, which are, although low in number, significant

for description of the space of movement structures in

rhythmic gymnastics in general. Ninth latent

dimension can be named OTHER JUMPS.

Tenth latent dimension is determined by the rest

of low value variables. Two are positioned on the

positive end of factors:

 V47 – execution of elements in one-legged

kneeling position

 V14 – Trunk rotation with backward bend;

while the third is positioned on the negative side:

 V38 - execution of elements on full feet with

both legs.

Factor is determined with very rare movement

structures which are encompassed in elements

balance and flexibility. While observing the function

of dominant muscle groups, when executing all three

movement structures, trunk, front and back upper-leg

muscles are activated. What separates variable 38 is

the support surface of the exerciser. Only one element

from the flexibility group is executed with both legs

on full feet. This latent dimension can be called

SPECIFIC ELEMENTS.

It can be concluded that all chosen variables have

contributed to formation of described latent

dimension, with projection of lesser or greater

significance, and that they have been chosen well for

this purpose.

From the matrix of correlation of isolated factors

(table 4.), it can be concluded that excreted factors are

in a negative, null, or very weak correlation.

However, the largest correlation value was achieved

by factor 3, named FRONTAL FLEXIBILITY, and

factor 8, named FORWARD BODY BEND (0,23).

According to anatomical and visual inspection, those

two factors are the most similar, and also specific

enough on their own. It cannot be disputed that every

one of this factors carries specific information in

regard to describing movement structures in rhythmic

gymnastics.

4 CONCLUSION

It was concluded that the groups differed according to

the movements of the body and extremities through

various planes, further, according to the recruitment

of muscle groups, to the type of the support surface,

and according to the types of take-off from the

surface. Ten significant latent dimensions were

obtained by factor analysis under the component

model with the Guttman-Kaiser criterion. The latent

dimensions were interpreted as: one-leg jumps, spine

mobility, frontal flexibility, free leg movements, the

help of the arm-work, body rotation, two-leg jumps,

forward bend, other jumps and specific elements.

The results suggest that the determination of

homogeneous groups in rhythmic gymnastics is a

very demanding task, which can not be accomplished

on the basis of the parameters obtained in the

research. Nevertheless, this research revealed that

K-BioS 2018 - Special Session on Kinesiology in Sport and Medicine: from Biomechanics to Sociodynamics

178

there were several equally ranking criteria according

to which the rhythmic gymnastics technique elements

could be grouped. It is feasible to state that the

application of the sophisticated measuring

instruments for different anthropological factors and

biomechanical parameters determination could have

provided more information on the characteristics of,

and, differences between elements in rhythmic

gymnastics. If the former had been conducted, the

results could have been quite different and the model

would have, probably, been more in accordance. This

research is the first attempt on grouping of elements

at the initial experimental level, which should

facilitate further research on the observed issue.

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