Human multibody model used in athletics.

Burca, Ioan ; Tofan, Mihai ; Purcarea, Ramona 等

1. INTRODUCTION

The present paper aims to elaborate a mathematical model designed to clear up the technical perfecting in hurdle from its biomechanical point of view in order to improve the athletes' performances.

The biomechanical research of sports technique tends to become the most important way of improving performance (Burca, 1979), (Burca, 1981), opposing somehow to the biochemical methods used to serve this purpose, which are considered to be harmful to the human body.

The biomechanical research encourages the natural development of all athletic events' performances, including the hurdle (Burca, 1970) ,(Burca, 1985).

Coaches must be able to use the latest knowledge available in order to assist the sportsmen in one of the most important fields of their activity, namely the improvement of the athletic events' technique.

2. THE RUNNER'S MULTIBODY MODEL

(Burca et al., 2003) presents a mathematical model designed for the hurdle runner's movements kinematics. The model is made of 12 rigid elements, interconnected by spherical or cylindrical joints. For reporting of various segments, a noninertial reference system tied to the athlete's trunk was considered. For the dynamical analysis of the system the multibody system will be dismembered in its constitutive parts. The previous kinematic analysis allows to determine the couplings between the kinematic elements. Then the movement equations for every constitutive element of the athlete's body must be written. The constitutive elements of the system are connected through cylindrical and spherical joints. The forces occuring inside the system are internal and external forces. The interior forces are performed by the athlete's muscles that move the segments of the body in order to accomplish the various phases of running. For the four main phases of the hurdle they activate different groups of muscles that move the active segments. The dynamical analysis identifies the groups of muscles having the crucial influence on the movement. The exterior forces are the weights of the segments and if this influence is considered as significant, the air resistance force.

[FIGURE 1 OMITTED]

3. MOTION EQUATIONS

The moment he rises in order to pass the hurdle, the athlete will suffer only the influence of the weight, the position of his weight center will move in a determinate way within the gravitational field and the movement of the active segments during his passing the hurdle will generate a compensatory movement of the other segments in order to respect the mechanical theorems. Fig. 3 represents the cylindrical and spherical joints and the forces that appear within this type of couplings.

In order to write the movement equations the system has to be dismembered in its constitutive parts. Fig. 2 presents the constitutive parts of the athlete and the forces appearing within the couplings, without the representation of the forces given by the muscle groups and the weights. In each cylindrical joint appear two components of a reaction while in each spherical one, there are three reaction components.

These forces are joined by the ones due to various groups of muscles which depend on the segment relative position and the weights that operate within the segments weight centers. The connection betweeen two random segments of the body are made through spherical or cylindrical joints. The spherical joints suppress three movement possibilities of a rigid and equalizes the introduction of a reaction. The movement of the various segments will be related to the athlete's trunk movement. His position is unimportant, so it results that his position towards an inertial reference system can be defined using six scalar parameters. The number of freedom degrees defining the position of the entire system at a certain moment is 27.

[FIGURE 2 OMITTED]

[R] = [{i} {j} {k}] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

A limitative condition is the athlete's moving on a horizontal track which will decrease the number of system's freedom degrees.

The scalar parameters defining the position of a random segment will appear in second degree differential equation systems that, once solved, will reveal the trajectory and the movement rule. If [phi], [psi], [theta] are Euler' angles that describe the movement of the reference system attached to a segment tied to a spherical joint, then the attached rotation matrix will have the following shape:

[FIGURE 3 OMITTED]

The angular speed, reported to the global reference system, will be obtained from:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

And the angular acceleration from:

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4. CONCLUSIONS

In what the athelete's body model (Burca, 1979)--(Burca, 1985) using a multibody system is concerned, we obtain a set of differencial equations describing the movements of the various segments that form the system (Tofan, 1981), (Vlase, 1993). The unknown variables are the angular positions of the various segments of the body and the coupling forces appearing within the spherical and cylindrical joint type couplings. A mixed differential and algebrical system results from it, and after eliminating the unknown algebric variables we obtain a differential equation system in which the amount of unknown variables, generalized coordinates is equal to the amount of equations we get. Solving these differential equations for concrete situations in hurdle are the goals established for further research.

5. REFERENCES

Burca, I.; Tofan, M.; Vlase, S. & Modrea, A. (2003) Model multicorp al alergatorului de garduri. Conferinfa stiinfifica internafionald: COMPETIJIA (The multibody model of the runner of the fences. International scientific conference: COMPETITION), pp 40-46, Bucuresti (Bucharest), 24 octombrie 2003 (october 2003)

Burca, I. (1979) Atletism--Analiza tehnicii probelor de atletism (Athletics--The analysis of the athletics samples technique). Institutul de invatamant superior Targu-Muresection (The Institute for Higher Education Targu-Mures)

Burca, I. (1981), Atletism (Athletics). Curs optional (Optional course). Institutul de inva^amant superior Targu- Mures (The Institute for Higher Education Targu-Mures)

Burca, I. (1985) Relatia dintre pregatirea tehnica si cea fizica la nivelul grupei de avansati, alergatori de garduri, in cadrul Clubulul Sportiv Scolar (The relationship between technical and physical training at the advanced group level, runner fences, inside the Scholastic Sports Club). Lucrare, grad didactic I (Paper, 1st teaching grade)

Tofan, M. (1981) Mechanics. Kinematics. Transilvania University of Brasov

Vlase, S. (2008) Mechanics. Kinematics. Ed. Infomarket