Dr.Hab., Professor V.I. Zagrevskiy^{1, 2}
Dr.Hab., Professor O.I. Zagrevskiy^2
1Mogilev State University named after A.A. Kuleshov, Mogilev
²National Research Tomsk State University, Tomsk

Keywords: exercise performance technique, simulation, biomechanical system, optimization

Introduction. Modern elite sports face many problems that need to be duly stated and solved [6, 4, 5, 1], including the problem of the best sport exercise performance technique model design individualized for every athlete [2, 3]. In case of a positive solution being found for this problem, it will open up the opportunities for: first of all, further competitive progress of the athletes; and, second, facilitate new competitive wins in the sport disciplines where success is largely determined by motor skills. Some latest studies of the sport exercise biomechanics performed for the last few years [2, 3] have made it possible to outline further research avenues for the optimal/ best sport exercise performance technique designing process. We believe that the problem may be successfully solved through its formalization (mathematical statement) procedure followed by the relevant computing experiments.

Objective of the study was to develop a heuristic software tool for the optimal sport exercise performance technique model design on a computer.

Methodology of the study was based on the human motor performance modelling software developed and applied for the heuristic computer design of an optimal sport exercise performance technique model.

Study results and discussion. System analysis of the mathematical model of the human motor performance integration system gave us the means to spell out the conceptual basics of the sport exercise performance technique designing methodology and apply them for a computing experiment. These conceptual basics may be listed as follows:

1. Human movements are purpose-driven.
2. A motor performance focused task may be efficiently solved by the software control tool that adequately simulates every aspect of the modelled system biomechanics in every system links, i.e. in the boundary points where transition of one movement phase to the other takes place.
3. An objective of the movement may be stated in terms of its content and senses and formalized by the relevant process-quality-rating criteria (with the mathematically stated sport exercise performance technique being viewed as a functional).
4. Both the purpose of movement and human movement as such may be mathematically stated by a system of equations, i.e. the human purpose-driven motor performance presenting equations.
5. The human motor performance synthesizing mathematical model must be designed being sensitive to the individual traits of the athletes as verified by the relevant anthropometric rates, i.e. the mass/ inertial characteristics of the body segments.
6. The software control tool may be formed on the following two tiers: (a) Kinematic tier that addresses the joint angle variations with time; and (b) Dynamic tier that presents the muscular force control mode variation regularities for the forces applied to the athlete’s joints over time.
7. Limitations of the kinematic component of the model are determined by the individual athlete’s joint flexibility and mobility rates.
8. Limitations of the dynamic component of the model are determined by the individual athlete’s strength rates.

The mathematical statement of a human motor performance process was assumed to include 11 conditions to set forth the following: design parameters for the biomechanical system motor qualities integration model; software control tools applicable to the whole trajectory of the subject bio-system; and the starting movement conditions and limitations of the executor's kinematic and dynamic resources.

The software operation controls were designed in the form of window menus (see Figure 1). Conditions for the subject exercise performance modelling task are set by the “Modelling parameters” button. Each of the conditions may include a few options for the optimal exercise performance modelling process control (see Figures 1, 2).

Figure 1. “Sport Exercise Performance Technique Modelling” Software: main menu

Many gymnastic exercises, for instance, are performed with different arm(s) and leg(s) being used for support. And it is the supporting element (arm or leg) that determines the values of computed coordinates in the BMC profiling equations (body mass centre) under the model, in the biomechanical system movement equations; and the support/ joint response equations. Therefore, the anthropometric input data of the subject will include both the relevant segmental mass-inertial rates (MIR, see Figure 1) and identify the segments that comprise the links of the model (Figure 2). Note that Link 1 operates as a support link in the case presented on Figure 2 hereunder.

Figure 2. Human body link structure formation procedure, with indication of the support link (Link 1 - arms)

Conditions for the heuristic software tool of the optimal sport exercise performance technique computer design are the following:

1. Number of the model links;
2. Mass/ inertial rates of the subject bio-system links, i.e. the individual anthropometric data of the athlete;
3. Limitations of the control moments of muscular forces applied to joints, i.e. the dynamic component of the athlete’s capacities;
4. Limitations of the flexion-extension movements in joints, i.e. the kinematic component of the athlete’s capacities;
5. Gravitational conditions for the modelling process, i.e. some specific gravity or zero gravity;
6. Modelling process finishing conditions, i.e. the modelling timeframe or some other biomechanical modelling process rate will be set;
7. Integration step for the biomechanical system movement modelling differential equations (equal or under 0.1 s);
8. Support friction force moment – that depends on the subject task and may equal zero for the whole movement trajectory;
9. Software control conditions (Figure 3) preset by the user for the whole movement trajectory of the modelled bio-system (with the joint angles being indicated on the kinematic tier of the software control tool);
10. Functional indicative of the subject sport exercise performance quality (any biomechanical movement rate that adequately describes the purpose of the movement); and
11. Starting conditions of the movement sequence, i.e. the generalized coordinates of the model links and their summarized speeds at the starting point of the movement.

The task conditions will be input to the memory. Each option of the computer modelling process will consider the functional variation rates: if the functional is found to decrease versus the previous best control iteration, the control model will be accepted as optimal.

Figure 3. Data input (joint angles) in matrix
 

The computing experiments under the study demonstrated that the most efficient form of the software control tool development task is the kinematics-focused design based on the joint angle variations with time presented in the form of a numerical sequence (value matrix). This way of task setting for the software control tool identifies changes in the biomechanical system configuration with every iteration step.

Conclusion. The study resulted in the “Sport Exercise Performance Technique Modelling” Software developed and applied for the optimal movement performance technique design in application to biomechanical systems with due account of the individual limitations of the kinematic and dynamic resources of the performers. 

References

1. Zagrevskaya A.I. Fizkulturno-sportivnoe obrazovanie studentov na osnove kineziologicheskogo podkhoda (Kinesiology-based physical education of students) / A.I. Zagrevskaya // Teoriya i praktika fiz. kultury. – 2014. – № 10. – P. 8-10.
2. Zagrevskiy V.I. Kompyuterny sintez tekhniki sportivnykh uprazhneniy na osnove formirovaniya zritel'nogo obraza biomekhanicheskoy sistemy v opornykh tochkakh dvigatel'noy metaprogrammy (Computer synthesis of exercise technique based on formation of visual image of biomechanical system in motor metaprogram reference points) / V.I. Zagrevskiy, V.O. Zagrevskiy, O.I. Zagrevskiy // Mater. tretey mezhdunar. nauch.-prakt. konf. «Zdorov'e dlya vsekh». – Pinsk: PolesSU, – 2011. – V. 3. – P. 66–70.
3. Zagrevskiy V.I. Komp'yuterny sintez dvigatel'nykh deystviy s upravleniem dvizheniem po kinematicheskomu sostoyaniyu biomekhanicheskoy sistemy (Computer synthesis of motor actions with motion control based on kinematic state of biomechanical system) / V.I. Zagrevskiy, O.I. Zagrevskiy // Teoriya i praktika fiz. kultury. – 2013. – № 7. – P. 10–15.
4. Kapilevich L.V. Fiziologicheskie mekhanizmy koordinatsii dvizheniy v bezopornom sostoyanii u sportsmenov (Physiological mechanisms of coordination of unsupported movements in athletes) / L.V. Kapilevich // Teoriya i praktika fiz. kultury. – 2012. – № 7. – P. 45-48.
5. Sharafeeva A.B. Tekhnologiya formirovaniya professionalnykh kompetentsiy v rekreatsionnoy deyatel'nosti budushchih spetsialistov po fizicheskoy kulture i sportu (Professional competence formation Technology in recreational activity of future physical culture and sports experts) / A.B. Sharafeeva, O.I. Zagrevskiy // Vestnik Tomskogo gosudarstvennogo universiteta (Bulletin of Tomsk State University). – 2012. – № 361. – P. 153-156.
6. Shil'ko V.G. Fizicheskoe vospitanie studentov na osnove lichnostno-orientirovannogo soderzhaniya fizkulturno-sportivnoy deyatelnosti (University physical education based on personality-centered physical culture and sports activity) / V.G. Shil'ko. – Tomsk. Tomsk State University, 2003. – 196 p.

Corresponding author: kapil@yandex.ru

Abstract
Subject matter under investigation by the authors is the best athletic exercise performance tech-nique designing procedure individualized for every athlete. The authors believe that the design problem may be successfully solved through its formalization (mathematical statement) procedure followed by computing experiments.
Objective of the study was to develop a heuristic software tool for the optimal sport exercise performance technique design on a computer.
System analysis of a mathematical model of the human motor performance simulation system gave us the means to spell out the conceptual basics of the sport exercise performance technique designing methodology and apply them to a computing experiment. The mathematical statement of a human motor performance process was assumed to include 11 basic conditions to set the following: design parameters for the biomechanical system motor qualities integration model; software control tools for the whole trajectory of the subject bio-system; starting movement con-ditions and limitations of the executor's kinematic and dynamic resources. We believe that the most efficient form of the software control tool development mission is the kinematics-focused design based on the joint angle variations with time presented in form of a numerical sequence (value matrix).