Wydział Mechaniczny / Faculty of Mechanical Engineering / W1

Stały URI zbioruhttp://hdl.handle.net/11652/1

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201524

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Data zakończenia: 2024Tematsearch.filters.applied.operator.equals: search.filters.subject.dynamical systems - conference

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Teraz wyświetlane 1 - 10 z 24
  • Pozycja
    Study of dynamic forces in human upper limb in forward fall.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Biesiacki, Paweł; Mrozowski, Jerzy; Awrejcewicz, Jan
    Knowledge of dynamic forces acting on the upper limb is useful, and sometimes even necessary, in its treatment and rehabilitation after injuries, during prostheses designing, as well as in optimization of the sports training process. In this work an attempt to determine the quantity of the inertia forces generated in forward fall has been undertaken. For this purpose a simplified mechanical model of the human body biokinematic chain has been prepared. Geometric data and mass of each element have been taken from anthropometric atlas for the Polish population. Kinematic data necessary to perform the analysis was calculated using fundamental laws of Mechanics. In this way accelerations of the selected points necessary for the determination of inertia forces acting on the individual links of the model were yielded. For validation of the obtained results a numerical model was constructed using SimMechanic module of the Matlab Simulink software. It made possible to compare the results obtained in both simulation methods. To make joints model more realistic a values of the viscous friction were assumed.
  • Pozycja
    Power consumption analysis of different hexapod robot gaits.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Grzelczyk, Dariusz; Stańczyk, Bartosz; Awrejcewicz, Jan
    The paper is focused on the power consumption analysis of different gaits of our constructed hexapod robot controlled by different Central Pattern Generator (CPG) models. There are a lot of gait patterns in the literature constructed either by different CPG models or using a series of oscillations with adjustable phase lag. The mentioned models, as well as those proposed in our previous paper are used and compared from the viewpoint of energy demand. In general, power consumption of the constructed hexapod robot is experimentally analyzed based on the current consumption in the applied servo motors, which drive the robot limbs. For this purpose the suitable drivers allowing a simple measurement of electric energy consumption of servo motors are used. The obtained experimental results show different energy demand for different robot gaits. Because power consumption is one of the main operational restrictions imposed on autonomous walking robots, we show that the performed energy efficiency analysis and the choice of the appropriate robot gaits depending on the actual situation can reduce the energy costs.
  • Pozycja
    On the vibrations of a composite structure with hexagonal structure of a circular inclusions.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Andrianov, Igor V.; Awrejcewicz, Jan; Markert, Bernd; Starushenko, Galina A.
    One of the major advantages of homogenization is a possibility of the generalization of the obtained results. Namely, if a solution to the local problem is found, then without principal problems one may solve not only the analyzed problem, by also a series of related static and dynamic problems, including: linear, quasilinear, the eigenvalue problems, etc. The mentioned approach has been applied to the eigenvalue problems regarding the perforated structures and periodically nonhomogenous 2D constructions with a square mesh of inclusions. In this work we have used theory of averaging to solve the vibrations problem regarding stiffly clamped rectangular membrane with periodically located circular inclusions creating a hexagonal mesh. The relations governing eigenvalues (frequencies) and eigenfunctions have been derived. The derivation of analytical formulas governing membrane eigenforms and frequencies consists of three parts. In the first part the local problem regarding a cell (inclusion) of the composite is studied. Second part is focused on finding main terms of the averaged problem. The third part is aimed at an estimation of the first improvement term with respect to the membrane fundamental frequency.
  • Pozycja
    Mathematical model for two-dimensional dry friction modified by dither.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Wijata, Adam; Awrejcewicz, Jan; Matej, Jan; Makowski, Michał
    A new dynamic two-dimensional friction model is developed which is based on the bristle theory. Actually it is the Reset Integrator Model converted into a two-dimensional space. Usually two-dimensional friction models are indeed onedimensional models which are rotated into the slip velocity direction. However, this often used approach cannot be applied to the bristle model. That is why an idea of a two-dimensional bristle is presented. Bristle’s deformation is described using polar coordinates. The carried out numerical simulation of a planar oscillator has proved that the new model correctly captures the mechanism of smoothing dry friction by dither applied via perpendicular and co-linear way regarding the body velocity. Furthermore, the introduced mathematical model captures two-dimensional stick-slip behaviour. The Cartesian slip velocity components are the only inputs to the model. In addition, our proposed model allows to describe a friction anisotropy using the bristle parameters. The paper contains results of an experimental verification of the new friction model conducted on the special laboratory rig being used to investigate the two dimensional motion in the presence of dither as well as to validate our numerical results.
  • Pozycja
    Mathematical model of pennate muscle.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Wojnicz, Wiktoria; Zagrodny, Bartłomiej; Ludwicki, Michał; Awrejcewicz, Jan; Wittbrodt, Edmund
    The purpose of this study is to create a new mathematical model of pennate striated skeletal muscle. This new model describes behaviour of isolated flat pennate muscle in two dimensions (2D) by taking into account that rheological properties of muscle fibres depend on their planar arrangement. A new mathematical model is implemented in two types: 1) numerical model of unipennate muscle (unipennate model); 2) numerical model of bipennate muscle (bipennate model). Applying similar boundary conditions and similar load, proposed numerical models had been tested. Obtained results were compared with results of numerical researches by applying a Hill-Zajac muscle model (this is a Hill type muscle model, in which the angle of pennation is taken into consideration) and a fusiform muscle model (a muscle is treated as a structure composed of serially linked different mechanical properties parts).
  • Pozycja
    Mathematical model of a multi-parameter oscillator based on a core-less three-phase linear motor with skewed magnets.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Gajek, Jakub; Kępiński, Radosław; Awrejcewicz, Jan
    This paper uses the example of a three-phase core-less linear motor to create a mathematical model of single-dimension multi-parameter oscillator. The studied linear motor consists of: a stator, an U-shaped stationary guide-way with permanent magnets placed askew to the motor’s movement’s direction; and a forcer, a movable set of three rectangular coils subjected to alternating external electrical voltage. The system's parameters are both mechanical (number of magnets and coils, size of magnets, distances between magnets, size of coils) and electromagnetic (auxiliary magnetic field, permeability, coil’s resistance). Lorentz force allows for the transition from electromagnetic parameters to mechanical force and Faraday’s law of induction creates a feedback between the forcer’s speed and coils voltage. An Ampere’s model of permanent magnet is used to determine the simplified function of auxiliary magnetic field distribution throughout the stator. In the model the external voltage applied to each coil serves as the excitation while displacement of the forcer is the output parameter. The solution to the introduced mathematical model of the system is compared with the experimental results showing a good coincidence.
  • Pozycja
    Identification of a non-linear damping coefficient characteristics in the free decay test of a single pendulum with friction.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Awrejcewicz, Jan; Olejnik, Paweł
    A pendulum in form of an equal arms angle body being a part of a two degrees-of-freedom mechanical system with friction is identified with respect to the observed in uence of some resistance of its rotational motion in ball bearings. It is damped in a much more complex manner, what could be considered as a non-linear damping. There is supposed between others, that the effective non-linear damping characteristics depends on a few effects such as fluid friction caused by vibrations of the pendulum with two springs in the air, as well as unknown kinds of a frictional resistance existing in ball bearings. The model under investigation finds its real realization on a laboratory rig designed for experimental investigations of viscous and structural frictional effects. A transient response oscillations of the pendulum are described by the explicitly state-dependent free decay. A free decay test of the pendulum with the state dependent non-linear parameters of damping and stiffness has been performed in this paper. It provided interesting observations that led to elaboration of a method of the overall damping coefficient identification. Effects of application of the proposed semi-empirical method of identification of the overall damping and stiffness coefficients have been illustrated and discussed.
  • Pozycja
    Double pendulum colliding with a rough obstacle.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Sypniewska-Kamińska, Grażyna; Starosta, Roman; Awrejcewicz, Jan
    The externally excited and damped vibrations of the double pendulum in the vertical plane are considered. The pendulum can collide with a rough obstacle many times during its motion. The pendulum is modeled as a piecewise smooth system. The differential equations govern the motion of the system in the relatively long time between the collisions. When a contact with the obstacle occurs, the pendulum exhibits a discontinuous behaviour. The velocities of both parts of the pendulum and the reaction forces are changing stepwise. An important element of the solving algorithm is aimed on the continuous tracking of the position of the pendulum in order to detect the collision with the unilateral constraints and to determine the state vector of the pendulum at the impact time instant. A single collision is described by the Euler’s laws of motion in the integral form. The equations are supplemented by the Poisson's hypothesis and Coulomb’s law of friction. The friction law is formulated for the instantaneous values of the reaction forces. The values of their impulses depend on the existence of a slip between the contacting bodies. Furthermore, during the collision the dynamic behaviour may change. Therefore the Coulomb law cannot be generalized for the linear impulses of the forces in a simple way. We have applied the Routh method in order to solve the problem. The method has a simple geometrical interpretation in the impulse space.
  • Pozycja
    Modelling and numerical simulations of a pendulum elastically suspended and driven by frictional contact with rotating disk.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Kudra, Grzegorz; Awrejcewicz, Jan
    The work concerns modelling and numerical simulations of a special kind of physical pendulum frictionally driven. The pendulum’s joint is suspended elastically in the plane of the motion resulting in the full plane motion of the pendulum and in tree degrees of freedom of the analysed mechanical system. The pendulum is driven by frictional contact with a disk with a constant angular velocity. Examples of self-excited oscillations and bifurcation dynamics of the pendulum are presented. Majority of the work focuses on efficient approximate modelling of the resultant friction force and moment occurring on the contact surface.
  • Pozycja
    Mechanical systems with two nonlinear springs connected in series.
    (Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki., 2015) Starosta, Roman; Sypniewska-Kamińska, Grażyna; Awrejcewicz, Jan
    The aim of the paper is analysis of dynamical regular response of the nonlinear oscillator with two serially connected springs of cubic type nonlinearity. Behaviour of such systems is described by a set of differential-algebraic equations (DAEs). Two examples of systems are solved with the help of the asymptotic multiple scales method in time domain. The classical approach has been appropriately modified to solve the governing DAEs. The analytical approximated solution has been verified by numerical simulations.