THEOREI'ICAL MODEL AND EXPERIMENTAL TESTS FOR TENNIS IMPACT DYNAMICS

Only the very short phase of the ball-net Impact, lasting few hundreds of seconds, is here analyzed. This critical phase is influenced by the dynamic characteristics of ball and racket and obviously by the initial conditions, such as position and velocity, of racket and ball right before their contact. Aim of this research is that of verifying a rather simple mathematical model recently developed, in order to highlight the influence of each single racket parameter on the impact and to set up correct procedures for experimental tests of rhckets and balls. BACKGROUND The forces transmitted from the ball to the hand. then to the arm and to the shoulder, cause a displacement of the involved body segment which is proportional to their Impulse; they result to be at least one order of magnitude as high as any other force acting during the impact. Therefore, in the mathematical model. any muscular action is neglected and the racket is considered as freely hinged to the forearm. Writing the equation of dynamic equilibrium it is possible to calculate the equivalent mass. that can be substituted to the athlete's body during the Impact phase. This mass depends on the subject's anthropometry and approximates to 1 kg. This means that the racket which is free in the space with 1 kg fixed to the handle responds exactly like the one which is handled by the tennis player. if their position and speed before the impact are equal. I In order to formulate the equation of the bail's motion during its sinking in the net. it is required to know the racket's Inertial parameters, as well as other parameters quite simply obtainable, e.g. from the diagram force deflection. for both racket and ball. This system of equations can be useful for example to determine, in relation to the racket's features, the rebound speed of the ball or the force transmitted to the athlete. 5 An experimental device has been built to validate the theoretical results and to test different rackets in various play conditions. This apparatus consists of: a special "tennis bail gun", a frame allowing the automatic release of the racket during the impact and a system oflaser barriers to measure ball's and racket's speed before and after the impact. Other simple mechanical systems have been used for static measures of racket strings and ball properties. Different handle constraints have been tested with and without the equivalent mass and held by the player as well. Various rackets and string tension have been tested. The preliminary results are in good agreement with the mathematical approach. Some interesting deductions can be easily Inferred from a combined theoretical and experimental approach. The rebound coefficient of the racket, for instance, is mainly affected by the ball characteristics and by the inertia of the racket; a higher string tension does not increase the rebound speed; or else, the player's wrist stiffness has no influence on the impact; and so forth

Spin coupling around a carbon atom vacancy in graphene

We investigate the details of the electronic structure in the neighborhoods of a carbon atom vacancy in graphene by employing magnetization-constrained density-functional theory on periodic slabs, and spin-exact, multi-reference, second-order perturbation theory on a finite cluster. The picture that emerges is that of two local magnetic moments (one \pi-like and one \sigma-like) decoupled from the \pi- band and coupled to each other. We find that the ground state is a triplet with a planar equilibrium geometry where an apical C atom opposes a pentagonal ring. This state lies ~0.2 eV lower in energy than the open-shell singlet with one spin flipped, which is a bistable system with two equivalent equilibrium lattice configurations (for the apical C atom above or below the lattice plane) and a barrier ~0.1 eV high separating them. Accordingly, a bare carbon-atom vacancy is predicted to be a spin-one paramagnetic species, but spin-half paramagnetism can be accommodated if binding to foreign species, ripples, coupling to a substrate, or doping are taken into account

COMPUTER SIMULATION IN SPORT DIDACTICS AND COACHING

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

On The Coefficient Of Restitution Of Tennis Rackets

The evolution of research on tennis equipment has recently introduced some parameters for the evaluation of the racket's efficiency. Among them, the most used in current practice is the coefficient of restitution of the racket (COR), that is simply defined as "the ratio of the rebound speed to the incident speed of the ball for orthogonal impact". Remarkable differences between values of COR reported in the tennis literature are mainly due to the various test conditions adopted. In order to compare different results, some important test parameters must be imposed for a better COR definition. Our recent laboratory tests show that the COR of the same racket is mainly affected by: - kind and conditions of balls kind and tension of strings impact velocity. Moreover, they show that the largest portion of energy is lost because of ball's deformation. Figure 1 shows the coefficient of restitution of a ball, at different impact velocities and on a rigid wall. Furthermore, in a tennis shot, ball deformation for a given velocity is affected by the other test parameters listed above. The augments of string's tension, for instance, increases the ball deformation and consequently decreases COR. This highlights that the traditional coefficient of restitution is not a direct measure of the racket frame efficiency, but it involves the behaviour of ball, strings, frame and grip restraint together. Therefore, in order to be compared by means of COR, rackets must be tested with the same kind of balls and the same kind of strings at equivalent string tension (i.e. tension that gives the same stiffness to the string plane). We suggest to test the racket at four different ball velocities in order to analyse different play conditions; thus we propose a new COR which should contain four values. Moreover, the knowledge of the influence of balls and strings allows to evaluate the portion of COR that is related only to the racket's frame characteristics

HIGH JUMP DIRECT DYNAMIC SIMULATION

INTRODUcrION High jumps are composed of a complex sequence of movements whose single contribution to the whole body motion cannot be intuitively predicted. While most of the movements are well learned by the elite athletes in order to reach the result, few are not effective or negative from the mechanical point of view and are probably performed for an erroneous feeling of their effects. The direct dynamic simulation of jumping can be useful in order to more fully understand the mechanics of high jump techniques; to explain to the athletes the consequences of some errors; and to test possible evolution of the exercise. When the external forces and the relative movements of the limbs are known, the calculation of the whole body trajectory and orientation is a direct dynamic problem

EVALUATION OF TRAINING METHODS BY MEANS OF KINEMATIC MEASUREMENTS

INTRODUCTIONAim of this work is the evaluation of different training techniques developed for increasing the hip joint range of motion.The standard technique has been comparedwith a training program based on PNF(Proprioceptive Neuromuscolar Facilitation).The experimental data were acquired by using an electrogoniometer system for its easy application in sport exercices, for its reduced dimensions and weight and for its high sample rate (up to 1000 Hz).The quality of the results has been critically analysed and compared with experimental tests made by using both electrogoniometer and optoelectronic system. MATERIAL AND METHODS The flexion extension movement of hip joint of101 male volunteer students, aged between19 and 23 years, was evaluated before and after a training with PNF. The subjects, fastened to an experimental table in supine position, were asked top erform the maximum hip flexion. The tests consist also on passive movements. Preliminary 'results seem to confirm the adequacy of the training technique but the high dispersion of the results leads the authors to analyse the possible causes related to the phenomena. With this aim further tests have been acquired both with electrogoniometer and with an automated optoelectronic system. The experimental analysis included both planar motion of two hinged bar and athletes movement during the standard test. For these analysis reflective markers where rigidly fixed on the electrogonio meter bases. From the 3Dmarker coordinates the angle (a*) between the electrogoniometer bases has been evaluated and compared with that one obtained by the electrogoniometer output. RESULTS The results of the training program showed that the range of motion of the subjects increases after the PNF technique both for passive and active movements The angle between the bases is evaluated in[1.11in which RCHA and RCHB are the electrogoniometer output data representing the two active channels, a and 8 the angles represented in Fig. I.Fig.I In the evaluation of athlete movements the analysis of the result differences of the two systems adopted leads to these following considerations. For the analysed movement the effect of the goniometer cable torsion seems to be negligible while an incorrect calibration procedure seems to be the main source of errors. In fact in the evaluation of athlete movement the gauges have been zeroed at the initial movement position and not with the basis perfectly aligned. This error can be easily corrected if the relative position of the bases is known by using the [ I .2]where k~ and k~ are the output of the electrogoniometer previously correctly calibrated and then placed on the subjects. Another source of errors may be due to the skin where the bases and consequently the markers are fixed. This effect can be partially solved by using rigid cluster linked to the moving body segment. CONCLUSION This study leads to consider new aspects of the movement evaluation by using electrogoniometer and suggest some practical rules to correct the electrogoniometer acquired data

A COMPOSITE MODEL FOR THE SIMULATION OF SKIING TECHNIQUES

INTRODUCTION In this work we present a model for skiing technique analysis and simulation: it consists of a man model, an equipment model and a contact (ski-snow) model. Such a model is the basis for a deeper understanding of the interaction between skier and equipment and its use will be profitable in various applications such as: equipment optimisation and technique improvement. Moreover this simulation technique can be profitably used for teaching the basic principles of skiing. MATERIAL AND METHODS To build our model we combined the methods used for multibody systems dynamic analysis (man model with finite element techniques (ski model). The human body model consists of 3D chains of rigid bodies: according to the "sophistication" of the simulation we use 16 segments, with 39'internal d.0.f (full man model), or 7 segments, with 6 internal d.0.f . To describe rigid body dynamics and kinematics (man model) we adopt a method based on homogeneous matrices (Casolo 1995): both the absolute and the relative position, velocity and acceleration are described by 4x4 matrices, as well as the inertial properties and the external loads. This approach allows to embed both the linear and angular terms in the same formalism. To derive the equation of motion a Lagrangian approach was adopted, leading to this expression: Mq+C(cf.q.t) = Fl(q.q,t) +Ft(q,q) where M is the mass matrix, C contain the weight, the centrifugal and Coriolis effect, Ft contains joint torques, F2 represent the action exchanged with ski through the bindings and the vector q contains joints laws of motion. The model can be used to perform direct and inverse dynamics analysis of skiing, since it allows the input of joint torques and/or joint relative movements, that can be experimental data or can be generated by scratch, by a law of motion preprocessor. Skis are modelled with Finite Element techniques. The internal structure of a ski is quite complex: different material, with complex arrangement, are employed giving rise to properties (stiffness, damping and mass) which can be determined by experimental measures or by complex FE analysis. These properties can be quite well reproduced by means of a simplified model consisting of 3D beam elements . Some geometrical features, such as camber and sidecut, can be easily reproduced. Ski equations of motion, in matrix form, are: M9+ q v r e l + Kq&f = F,,I +Fnlon-ski f F.+.ki - cn,,wn where M, C, K are, respectively, the ski mass, damping and stiffness matrices. The ski load consists of three terms: weight, action exerted by the skier through the bindings and the contact action exerted by the snow. A simple contact model has been also developed, based on the assumption that the snow reacts both to ski deepening, sliding and skidding. This simple model can take into account, for example, the effect of ski vibration on the ski-snow interaction. RESULTS Some simulations have been performed to test model capabilities: we analysed the effect of ski torsional stiffness, as well as the amount of sidecut, on skier trajectory during traverse and turns. The model is also used to simulate the aerial phase of a free-style jump and the following landing phase. In all of these cases simulation can be an useful tool for predicting the effect of changing joint movements (i.e varying skiing technique) and equipment characteristics. A sensitivity analysis can be a first step toward a technique and equipment optimisation. References Casolo F., Legnani G., Righettini P., Zappa B. "A homogeneous matrix approach to 3D kinematics and dynamics", TMM (in press)

Diagnostic work-up of arrhythmogenic right ventricular cardiomyopathy by cardiovascular magnetic resonance

Cardiovascular magnetic resonance (CMR) has become a widespread diagnostic tool. Since its introduction, CMR has been used to image patients with a known or suspected arrhythmogenic right ventricular cardiomyopathy (ARVC). Several abnormalities have been found and described by CMR and at present this diagnostic tool is considered very important for the diagnosis. However, the diagnosis of ARVC relies upon the fulfillment of both clinical and functional criteria and CMR can provide several but not all the information useful for the diagnosis. Furthermore, some findings such as evidence of right ventricular epicardial fat, once considered a peculiar marker of ARVC, have been shown to possess a low specificity. This document was prepared by representatives of the three Italian official Organizations involved in CMR. Its main scope is to highlight the problems encountered when studying patients with suspected ARVC at CMR, to indicate the basic technical equipment needed, to recommend a proper imaging protocol and to offer a consensus on the main features relevant for the diagnosis