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EN
Dynamics of the nonlinear spring pendulum is analysed using two asymptotic approaches. The multiple scale method is commonly applied with using two time scales. The purpose of the research is to justify the introduction of an additional third scale. Results of the analysis clearly show that introducing the third scale improve correctness of the approximate analytical solution. The obtained results allow for qualitative and quantitative analysis of the behavior of the studied system with a high accuracy. Calculations are made both in the neighbourhood of the resonance and also far from it.
EN
The aim of the study was to propose a relatively simple central pattern generator (CPG) model, which can be used to control a lower limb exoskeleton. The mentioned generator and the simulation model of the human gait were developed based on experimental observations of the healthy volunteer's gait recorded using a motion tracking system. In order to reproduce the correct movements of the exoskeleton segments, time series of angles in the joints corresponding to the hip and knee joints were calculated based on tracing the trajectories generated by the CPG and the inverse kinematic relations. The proposed model can be implemented to control the lower limb (extremity) exoskeleton and assist various types of gait abnormality in patients with different motor dysfunction by means of changing the parameters of the control system. The presented experimental data, the developed gait simulation model, and the results of numerical simulations can be treated as guidelines for further improvement of the proposed model and its application in the exoskeleton control system. Although the study is mainly focused on rehabilitation applications, the proposed model is general and can be used also for other purposes such as control of bipedal and multi-legged robots.
3
EN
In this paper we consider a 4-link model of a human for simulating a forward fall. The model implemented in Mathematica is constructed based on a planar mechanical system with a non-linear impact law modelling the wrist-ground contact. The segments of the human body are modelled as bodies connected by rotary elements which correspond to the human joints. Parameters and kinematic relations used in numerical analysis are obtained based on the 3D scanned model of the human body created in Inventor and experimental observation by the motion capture system. Validation of the model is conducted by means of comparing the simulation of the impact force with the experimental data obtained from the force platform. The obtained ground reaction forces can be useful for the finite element analysis of the numerical model of the human upper extremity.
EN
The paper presents dynamic simulation and experimental identification of a human forward fall model describing the process of “falling like a broomstick” on the outstretched arms. The model implemented in Mathematica allows one to estimate time histories of the ground reaction force in different scenarios of the fall process. These time series are applied as time-varying load conditions to the numerical analysis of the human radial bone model created from the computed tomography data. Finally, the obtained numerical results indicate that the strain criterion seems to be more useful for estimating the radius fracture site in comparison to the stress criterion.
EN
The dynamic vibration absorber is a kind of mechanical device with inertia, stiffness, and damping. Once connected to a given structure or machine, it is capable of absorbing vibratory energy. As a result, the primary system can be protected from excessively high vibration levels. In this paper, we deal with classical Den Hartog’s model to clarify the known results and improve the mathematical component of this approach. We suggest the optimal choice of absorber parameters, which is slightly different and more general analytical approach. The comparison of two methods of optimization is carried out, and the corresponding error of calculus is estimated.
EN
Recommendations for the optimal thickness of the cement mantle in cemented hip arthroplasty are outlined based on the results obtained with the finite element method. The investigations show that distal femur cement thickness higher than 2 mm positively affects mechanical behaviour of the cement mantle and can be useful in reducing stress-strain levels in the distal part of the femur what leads to prevention of development of a stress-shielding effect. The results of the study can contribute to the success of long-term implants.
7
Content available remote A two dimensional approach for modelling of pennate muscle behaviour
EN
The purpose of this study was to elaborate a two-dimensional approach for unipennate and bipennate striated skeletal muscle modelling. Behavior of chosen flat pennate muscle is modelled as a rheological system composed of serially linked passive and active fragments having different mechanical properties. Each fragment is composed of three elements: mass element, elastic element and viscous element. Each active fragment furthermore contains the contractile element. Proposed approach takes into consideration that muscle force depends on a planar arrangement of muscle fibers. Paper presents results of numerical simulations, conclusions deduced on the base of these results and a concept of experimental verification of proposed models.
EN
Vibration of two simple open systems (namely the linear mass-sprins oscillator and the mathematical pendulum) are investigated. During the motion, the body absorbs matter through its boundary. In both cases, mechanism of mass absorption is modeled as a perfectly 'inelastic' collision and constant rate of mass change is assumed. The paper is focused on the influence of mass change on the kinematic aspects of oscillations.
EN
In this paper the model of four degree-of-freedom mechanical sliding system with dry friction is considered. One of the components of the mentioned system rides on driving belt, which is driven at constant velocity. This model corresponds to a row of carriage laying on a guideway, which moves at constant velocity with respect to the guideway as a foundation. From a mathematical point of view the analyzed problem is governed by four second order differential equations of motion, and numerical analysis is performed in Mathematica software. Some interesting behaviors are detected and reported using Phase Portraits, Poincaré Maps and Lyapunov Exponents. Moreover, Power Spectral Densities obtained by the Fast Fourier Transform technique are reported. The presented results show different behaviors of the system, including periodic, quasi-periodic and chaotic orbits.
EN
This paper is devoted to human motion analysis and comparison of chosen kinematics parameters during normal gait with and without additional load in a form of backpack. A stability in both cases were compared in both frontal and sagittal planes, by applying a video tracking system. Experimental tests performed on treadmill, passive markers, placed on volunteers bare skin were used. Additionally, an infra-red camera was employed to evaluate muscle activity and its groups involved in the movement. The change of body temperature and distribution of the thermal maps were observed. Analysing these thermograms, loading of different muscle groups was evaluated. During the experiment, an attempt to correlate a results obtained from a thermal imaging camera and video tracking system were made. It is shown that thermal imaging can help to evaluate an asymmetry in muscle load and in some cases can help to detect pathological cases, what was confirmed with motion analysis. Advantages and disadvantages of this method were also described.
EN
The paper is devoted to the dynamical modelling of the hexapod robot walking on a flat and hard ground. The main goal is to determine time series of reaction forces acting on individual legs of the robot during tripod gait often used both by the six-legged insects as well as mobile walking robots found in engineering applications. The movement of the considered robot is realized by the kinematic excitation of its legs using the so-called Central Pattern Generator (CPG) method. The paper demonstrates that there are different contact forces and overload acting on the robot, resulting from different models working as a CPG. The mentioned forces belong to the important issues that should be taken into account when the robot locomotion on the unknown terrain is planned.
EN
A class of smooth approximations of the total friction force occurring on a plane finite contact surface is presented. It is assumed that the classical Coulomb friction law is valid on any infinitesimal element of the contact region. The models describe the stick phase, the fully developed sliding and the transition between these two modes. They take into account different values of static and dynamic friction coefficients. The models are applied in simulation of a dynamical system performing translational and rotational stick-slip oscillations, and then they are verified by comparison with the corresponding results in which an event-driven discontinuous model of friction is used.
EN
Nowadays, microcontrollers are commonly used in many fields of industrial applications previously dominated by other devices. Their strengths such as: processing power, low cost, and small sizes enable them to become substitutes for industrial PLC controllers, analog electronic circuits, and many more. In first part of this article an overview of the Atmel AVR microprocessor family can be found, alongside with many scientific and industrial applications. Second part of this article contains a detailed description of two implementations of ATmega644PA microprocessor. First one is a controller with PID regulation that supports a DC motor driver. Second one is a differential equation solver with 4-th order Runge-Kutta method implemented. It is used for solving a torsion pendulum dynamics. Finally, some general conclusions regarding the two presented implementations are made.
PL
W dzisiejszych czasach mikrokontrolery są często używane w miejscach poprzednio zdominowanych przez inne układy logiczne. Argumenty przemawiające za stosowaniem tych układów, takie jak: moc obliczeniowa, niski koszt i małe rozmiary, pozwalają na zastępowanie nimi przemysłowych sterowników PLC i innych elektronicznych układów analogowych. W pierwszej części artykułu przedstawiono przegląd dostępnych mikroprocesorów Atmel AVR, uwzględniając przykłady naukowych i przemysłowych zastosowań. Druga część zawiera szczegółowy opis dwóch implementacji procesora ATmega644PA, przeprowadzonych przez autorów pracy. Pierwsza przedstawia regulator PID silnika prądu stałego obciążonego zmiennym momentem. Kolejna przedstawia implementację metody Runge-Kutty czwartego rzędu, stosowanej często do rozwiązywania równań różniczkowych. Algorytm został zastosowany do rozwiązania zadania dynamiki ruchu obrotowego wahadła torsyjnego na mikrokontrolerze.
EN
The purpose of this paper is to investigate a double torsion pendulum with planar frictional contact. The single torsion pendulum with one-degree-of-freedom is an angular equivalent of the linear harmonic oscillator. The second degree of freedom has been obtained by adding a free body to the inverted single torsion pendulum. The free body’s angular displacement is caused by frictional forces appearing in the interface (contact zone) between the free body and the pendulum column’s head kinematically excited at its base by a mechanism with torsion spiral spring. An experimental station has been set up and run to find most unknown parameters of the pendulum from the time series of state variables taken as inputs to the Nelder-Mead method of identification. The obtained results proved significant usability of the identification method in the case of numerical simulation of the pendulum’s dynamical model. It has not been satisfactorily proved in the case of time characteristics coming from a real system that exhibits also some unrecognized physical effects.
15
Content available remote Dynamics of Mechanical Sliding System with Dry Friction
EN
In the paper we consider a four degree of freedom model of a mechanical system with dry friction, which can explain non-regular vibrations of mechanical sliding system. Stick-slip vibrations are studied for the case, where body is riding on a driving belt as a foundation that moves at a constant velocity. From a mathematical point of view, the analyzed problem is governed by a set of nonlinear ordinary second order differential equations of motion, obtained using the Lagrangian method. Numerical analysis is carried out with the qualitative and quantitative theories of nonlinear differential equations reduced to the non-dimensional form. The behavior of the mentioned system is monitored via standard phase portraits, bifurcation diagram as well as Lyapunov exponents. Some interesting numerical results (periodic, quasi-periodic, chaotic and hyper-chaotic orbits) are obtained and reported in the paper.
EN
A paralyzed and not fully functional part of human body can be supported by the properly designed exoskeleton system with motoric abilities. It can help in rehabilitation, or movement of a disabled/paralyzed limb. Both suitably selected geometry and specialized software are studied applying the MATLAB environment. A finger exoskeleton was the base for MATLAB/Simulink model. Specialized software, such as MATLAB/Simulink give us an opportunity to optimize calculation reaching precise results, which help in next steps of design process. The calculations carried out yield information regarding movement relation between three functionally connected actuators and showed distance and velocity changes during the whole simulation time.
EN
The problem of control and dynamical modeling of a unicycle-cyclist system treated as a double inverted pendulum with rolling friction and vibrating in the plane that is perpendicular to the direction of movement is studied. The object of analysis consists of two basic parts: the wheel and the double pendulum. The equations of motion have been derived using the Lagrange equation of the second kind. The kinematic excitation has been applied to the cyclist. The aim of control is to maintain the unicyclecyclist system in an unstable equilibrium around given angular position. Control moment of force has been applied to the wheel in a numerical procedure performed in Simulink. Kalman filtering problem has been solved basing on the feedback control system and functions included in Control System Toolbox of MATLAB. The proposed approach could be extended in future to solve some dynamical problem of transverse vibrations.
PL
Praca podejmuje rozwiązanie zagadnienia kontroli i modelowania dynamicznego układu monocykl-rowerzysta rozpatrzonego jako podwójne wahadło odwrócone z tarciem tocznym drgające w płaszczyźnie prostopadłej do kierunku ruchu. Analizowany obiekt składa się z dwóch podstawowych części, tzn. koła i podwójnego wahadła. Równania ruchu układu mechanicznego, w którym wymuszenie kinematyczne przyłożono do masy reprezentującej ciało rowerzysty wyprowadzono stosując równania Lagrange’a drugiego rodzaju. Zadaniem kontroli było utrzymanie modelu układu monocykl-rowerzysta w niestabilnym położeniu równowagi w pobliżu zadanej wartości kąta obrotu. W procedurze numerycznej zrealizowanej w Simulinku moment siły kontroli przyłożono do koła napędzającego układ modelowy. Zagadnienie doboru filtru Kalmana rozwiązano w układzie sterowania ze sprzężeniem zwrotnym przy użyciu wbudowanych funkcji numerycznych wchodzących w skład biblioteki Control System Toolbox pakietu MATLAB. Zaproponowane podejście można rozszerzyć w przyszłości w celu rozwiązania podobnego problemu dynamicznego uwzględniającego drgania poprzeczne.
EN
A prototype of arm, aimed to simulate human arm is presented. In the device following original constructions have been proposed: glenohumeral joint, elbow joint, and wrist joint with the possibility of ulna and radius rotation. Also special shape of radial bone and ulna bone has been proposed. In addition, pneumatic McKibben-type muscles and their control have been examined. The comparison of the range of motions of the prototype and a biological system in the meaning of the SFTR method is also presented.
PL
W artykule autorzy starali się pokazać problemy i ich rozwiązania, napotkane podczas konstrukcji modelu ludzkiego ramienia sterowanego pneumatycznie. W założeniu konstrukcyjnym prototyp miał posiadać pełną funkcjonalność konstrukcji biologicznej. Podczas realizacji przedsięwzięcia natrafiono na liczne problemy jak: odwzorowania kości, mięśni, stawów, ich skomplikowanych kształtów i działania. Zaproponowano następujące rozwiązania praktyczne: staw ramienny, staw promieniowo-łokciowy bliższy i dalszy wraz z możliwością obtaczania się specjalnie ukształtowanej kości promieniowej po kości łokciowej. Ponadto dobrano odpowiedni typ mięśni pneumatycznych wraz z ich sterowaniem zapewniając odpowiedni zakres ruchów i funkcjonalności układu. W pracy pokazano ponadto porównanie zakresu ruchów wspomnianej konstrukcji i układu biologicznego w rozumieniu metody SFTR oraz porównanie pewnych, wybranych parametrów mięsni biologicznych i pneumatycznych typu McKibben.
19
Content available Mechatronic eye: modeling and design
PL
W artykule autorzy prezentują mechatroniczny model oka. Celem budowy stanowiska było zasymulowanie i odtworzenie funkcji oka wraz z odwzorowaniem jego sterowania. Na podstawie budowy biologicznej, badań zarówno własnych, jak i innych autorów zaproponowano konstrukcję obejmującą budowę optyczną oka, funkcje i działanie źrenicy oraz sterowanie, które umożliwia wykrywanie i śledzenie źródła światła.
EN
In this paper both model and prototype of a human eye are developed. We are aimed on building and control of the simplified eye model, which is able to simulate some real eye biological functions. Control of the prototype has been motivated by monitoring the human eye behavior in different environment conditions. In addition, optical properties, functions and operation of the applied electrical control of the pupil (apple of the eye) and control of the prototype movement focused on detection and tracking a light source are also presented.
20
Content available remote On the human arm motion camera tracking system
EN
This paper presents results of research devoted to tracking human arm trajectories in sagittal plane by means of motion capture. One camera tracking system was developed. Co-ordinates of upper limb joints (distincted by light reflecting markers) were obtained via tracking software. Markers were illuminated coaxially to the optical axis of the lens to obtain maximum of reflectivity. Positions, linear velocities and accelerations of a shoulder, elbow, wrist and palm in a sagittal plane were presented. Obtained results in the form of points (in Cartesian co-ordinate system) can be adopted for control of mechanism and robots with kinematics similar to that of a human arm. The obtained results show that in studied biological systems there are no fixed trajectories. All movement co-ordinates (including velocities, accelerations and joints angles) are slightly different for each time selected until movement task is completed. Presented method is relatively inexpensive and noninvasive and can be adopted for other types of motion capture.
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