• F. Casolo
  • B. Zappa


Modern athletics and gymnastics are characterized by very complex exercises whose mechanics Is very often difficult to understand by intuition so t h a t some problems may arise in teaching ,and coaching. Moreover, many exercises include an aerial phase composed of different sub-phases; while learning, they are experimented separately by the athlete who rebuilds the whole exercise afterwards: a difficult coaching item concerns. for example. the variations of the movements which allow t o obtain the same sub-phases once they are linked in the full exercise, since the initial conditions of each sub-phase are in fact different. This kind of reasons gave recently impulse t o the development of computer simulation systems, especially oriented to sport biomechanics for teachers and coaches. BACKGROUND Starting from the Denavit(l975) approach to the kinematics of multi-body chains. which is based on the adoption of 4x4 matrices to define the relative position of bodies in 3D space. we introduced a set of six 4x4 special matrices. Our main goal is to face coherently. with the same matrix approach, the whole question of the mathematical analysis and synthesis of human motion: from the position analysis to the direct and inverse dynamics. Three out of those matrices are related t o kinematics (generalized position, velocity and acceleration matrices). while the other ones deal with dynamics (generalized action, momentum and Inertia matrices); all of them feature both linear and rotational components (eg.:linear and angular velocity; forces and couples; momentum and angular momentum). The structure and the properties of those matrices easily allow t o build computer programs for 3D direct and inverse dynamics of human motion. in which the equation structure is quite simple and clear. and efficient for computer handling. APPLICATIONS The system of programs f o r the simulation of sport exercises developed in our Department in connection with the University of Brescia. consists of a set of cooperating modules, each performing a particular task; the basic modules are: SPACE-LIB: a library of routines to perform the operations Involving the described matrices; ANTHROPM: to compute geometrical parameters and to build the Inertia matrix from as many data as they are available; DY-MAN: the main module. for the solution of the direct dynamic problem: from the knowledge of the relative motion of body segments and the external forces applied it calculates the athlete's body trajectory and orientation during an hypothetical exercise; GRAPIIMAN: a graphic 3D post-processor for dy_man output. This kind of software can help to solve some of the teaching problems described in the introduction, showing for instance to the athlete the effect of hypothetical variations of limbs’ movement on the whole body motion. It can also be very useful to plan complex athletic exercises without exposing the athlete to the danger of the preliminary set-up phase.




Coaching and Sports Activities