TOWARDS UNDERSTANDING HUMAN BALANCE -ANALYZING STICK BALANCING

In this study stick balancing serves as a role model for more demanding balancing tasks. The purpose is to detect the movement parameters important for stick balancing and their interrelations. Two tilt angles were defined and the relations with the stick coordinates and their derivations analyzed. The correlation between tilt angle and acceleration of the lower coordinate, the angular velocity and the same acceleration of the lower coordinate proved to be the most important relations. The relations were identified to serve as a guideline for establishing a computer simulation of stick balancing which is presented in a separate study. Four parameters were identified and the values determined for comparison with the results of a computer simulation

INVERSE DYNAMICS IN SPORTS BIOMECHANICS

The aim of this paper is to illustrate developments in inverse dynamics using selected examples. It will give a description of the method with emphasis on the critical parts. Results are discussed for several examples and the methodological difficulties are specified. It is shown how hidden parameters can be uncovered with the help of inverse dynamics. The quantification of sports performance is demonstrated, and the applicability of inverse dynamics in the training process is illustrated

TOWARDS UNDERSTANDING HUMAN BALANCE – SIMULATING STICK BALANCING

The purpose of this study was to develop a simulation model for stick balancing. Experimental result served as a guide for the developing progress. The progress started with a deterministic approach. We solved the Euler-Langrange equation and received the equation of motion. The controlling variable within this equation is the acceleration of the lower end of the stick. This parameter depends on the balancing strategy and ability of the human subject. We chose the van der Pol equation as an ansatz for describing it. A second attempt included the incorporation of a time delayed parameter. The third form included additional stochastic noise. We found close similarity between the measured and the calculated parameters tilt angle at reversal points, frequency expectation value, and others

TRIPLE F (F³) FILTERING OF KINEMATIC DATA

Raw data in biomechanical studies usually require filtering. Depending on the used filter there exist some drawbacks as “signal shifted relative to the raw data”, “instability or degradation”, “endpoint problem”, “oscillations”. A filter called triple F or F³ based on the Fourier transformation is presented that is not crippled by these drawbacks. It consist of a transformation of the original data into the frequency spectrum followed by eliminating the unwanted frequencies (windowing) and an inverse Fourier transformation back to the data as a function of time. This procedure is stable and does not shift the data. It is shown how to dampen additional oscillation on the filtered data and how to avoid the endpoint problem completely. A comparison with a Butterworth filter and an application completes the presentation

A Mathematical Model of Human Dynamic Locomotion: Theoretical Bases of the Model

The most current models of dynamic locomotion involve the use of a simple or damped spring-mass system (McMahon and Green, 1979 and Blickhan, 1989). Each of these models uses rather simple approximations (point-like mass, and massless spring) of the complex human anatomy. They use the dynamic variables but neglect the control process completely. These models do not describe a realistic behavior of the system at some instant in time. For example, previous models have kept the system stiffness k, as a constant during the support phase. In reality, however, a complicated process depending on anatomy, posture, and muscle control gives rise to a wide variation in system stiffness as the takeoff leg moves over the support foot. Therefore, the problem faced in developing an analytical approach for coaching is to develop a mathematical model that accurately describes support phase mechanisms. The purpose of this study is to create a mathematical model that reflects all features that determine jump distance. In order to create a more realistic model, it has been necessary to derive equations of motion in a spring-mass system with stiffness k, as a function of time and posture. System stiffness k(t) was calculated from jump data collected using a Bertec force plate. Jump data was also used to test the accuracy of the model by comparing calculations to measurements of a 3D Motion Analysis System. The input parameters used for our model were the touchdown angle, the velocity at touchdown, the mass of the subject, the leg and foot length, and the system stiffness kW. We found the actual jump distance and the calculated distance in agreement. Also the calculated coordinates and velocities as functions of time match the measured data. The very first tests suggest a relative deviation of less than 5%. This refined model is more accurate than previous models of dynamic locomotion. It contains all the features necessary to accurately predict flight distance as a function of initial value parameters and support phase parameters. This model now becomes a tool for coaches to design individual performance in a heuristic manner

THE INFLUENCE OF TIMING IN MOVEMENT EFFICIENCY

INTRODUCTION The vertical movement of the human body is visible in almost all sports. Even in the case of sports like running, cycling, and long jumping where the aim is to achieve horizontal distance, vertical motion is obvious and highly essential in performing the movement. Components of vertical motion contribute to the total energy needed for the movement. In this study we analyze efficiency of the vertical motion components and discuss timing as one of the factors influencing the energy consumption of the movement. Efficiency is defined as the quotient of the work output divided by the energy needed to perform and given as η= Wout / Ein where Wout is work per formed on a mass. In both the ascending or descending motions. Ein is energy produced by muscles to do so. In classical mechanics efficiency is calculated as positive for ascent and negative for descent. METHOD A computer simulation of human motion beginning in a standing position, moving down to a squatting position and vice versa was performed. The motion was constructed symmetrically for upward and downward movements, so that a downward movement can be described as an upward movement with time reversed (t -> -t). For this simulation we used the commercial software SDS Version 3.5 of Solid Dynamics. The human body is approximated by the Hanavan model using anthropometric data of a male person. Similar simulations are also done in the following movements: a) raising the body off the ground with one leg on a bench b) alternate stepping with one leg then the other, keeping the same foot position when on the ground C) lifting weights with the arms flexed In the second stage of the study we obtained real movement data using 3 cameras and a 3D Peak Performance digitizing system. This data and the anthropometry of our subjects were included into an inverse dynamics analysis, using SDS to calculate the efficiency. RESULTS Figure 1 represents the efficiency simulation for a squatting motion at difference timings. The graph shows for a downward or upward movement with a duration of 0.75 seconds, which result in an efficiency of 0.674. For slower movements η Coverges below 0.9. Our experiment shows efficiencies in the same range as the simulation. A detailed analysis of the various simulations demonstrates that efficiency is dependent on timing. Conclusion The above results suggest that the optimizing of efficiency helps to reduce energy consumption of the vertical motion. This subsequently provides more energy needed for the horizontal motion and thus the complete performance. Such effects seem unimportant for a single movement, but with thousands of repetitions in a cyclic motion the minute energy conservation adds up to a substantial amount and consequently influences the performance

THE ROTATIONAL ABILITY OF 'THE HUMAN BODY

In sports like gymnastics, trampolining and diving, attention is focussed on control and good execution. Like all general movements, the movements involved in such sports are motions that consist of translation and rotation. However in this case, proficiency depends dominantly on the rotational ability of the athlete while performing the movement. We analyze such a movement using parameters from anthropometry, dynamics, and posture. We recorded anthropometric data of top athletes in trampolining and compared them with those of ordinary people. With a computer program based on the Hanavan model together with mass density values given by Dempster, we use the data to calculate the inertia tensor. Further data pertaining to dynamics, timing and coordination are derived by video-cinematographic methods. With the aid of two cameras, we filmed simultaneously various trampoline performances during the international competition held in Dillenburg, Germany in 1991. The videos were then digitized and the data processed by computer. We obtain the results for momentum, body orientation, posture and the center of gravity of the trampolinists during a jump. We demonstrate how strongly body structure, dynamics, timing and coordination contribute to the ability of the human body to rotate. The important parameters are the inertia tensor and the momentum, the combination of which determines the rotating. While momentum remains constant during a jump, the inertia tensor may vary in time due to different postures. Our findings show what momentum is necessary and which posture have to be in sequence for athletes to excel

A Mathematical Model of Human Dynamic Locomotion: The Development and Application of the Model

Human walking is characterized by a progression of steps such that contact with the ground is never broken. More dynamic activities such as running, hopping, and jumping are characterized by a cycle that includes a phase of support as well as a ballistic flight phase. The objective of individuals engaged in dynamic locomotor activities is to produce and control desired movements in order to achieve a determined performance goal. The problem confronted by teachers, coaches, and trainers is to devise a systematic procedure based on scientific principles which can be used to evaluate motor skills. One solution to this problem is the traditional trial and error approach used by most coaches. In this study the authors have developed a systematic analytical approach using mathematical modelling as the tool. This tool permits the coach to systematically vary the input parameters thus moving toward an ideal technique for that individual without continually stressing the athlete. More specifically, the purposes of this presentation are to: 1) highlight the coaching demands that a realistic mathematical model of dynamic locomotion must meet and 2) show the development of a model that meets all features necessary to calculate the flight distance correctly given various input parameters. Therefore, the presentation will focus on: 1) features necessary for a realistic model of dynamic locomotion, which are anatomy, posture, dynamic variables, control processes, and stochastic, 2) the advantages and disadvantages of existing models, 3) the steps taken in developing our model, and 4) how our model can be used as a tool for coaches to evaluate and design individual performance in a heuristic manner

THE ATTRACTOR METHOD – A TECHNIQUE TO QUANTIFY DIFFERENCES OF CYCLIC PROCESSES AND THEIR VARIABILITY

The purpose of this study is to introduce a new, very sensitive method to quantify differences of movement pattern and the variability of cyclic processes. While the method is applicable to practically all cyclic processes, we restrict ourselves to an example of walking under various conditions