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1
EN
The paper focuses on a winch drum winding a heavy rope to present the variety of issues related to the dynamics of systems with rotating parts of time-varying mass. The dynamic motion equations for such systems are frequently either incorrect or derived under the assumption of mass constancy. When the mass variability is taken into account, simpler cases are discussed. The considerations on the angular momentum theorem enables formulating a new two time parameters form of the rotational motion equation for the system with time varying mass. Four cases are considered and different approaches of motion equations derivation are applied. The assumptions and solution methods of the analyzed systems as well as ambiguities and possible contradictions that may arise as a result of the trial of the problem formulation on the grounds of rigid body mechanics are discussed. The numerical simulations are presented.
EN
The paper presents the method for the optimal synthesis of four-link mechanism generating open/closed paths with time prescription. Although the method is suitable for both closed and open paths, it enables decreasing the number of design parameters describing dimensions, orientation and position of a path generator. Compared to the methods presented in the references, this is a one-phase synthesis method; although the number of design parameters is reduced, the method does not require affine transformations to be performed on the synthesised mechanism. The effectiveness of the method is discussed based on examples of three paths, with two taken from the literature.
PL
Celem endoprotezoplastyki jest przywrócenie mobilności oraz zniesienie bólu w uszkodzonym stawie. Dokonano analizy literatury dotyczącej problematyki oraz skuteczności implantacji endoprotezy stawu ramiennego w organizmie człowieka wraz z przeglądem dostępnych na rynku endoprotez o budowie modułowej. Przeanalizowano także wpływ poszczególnych parametrów endoprotezy na jakość implantacji. Na podstawie tej wiedzy zaproponowano własną konstrukcję endoprotezy hybrydowej stawu ramiennego. Wymagało to rozwiązania wielu problemów dotyczących projektowania poszczególnych elementów endoprotezy o nastawnych parametrach zapewniającej warunki geometryczne i kinematyczne zbliżone do naturalnych.
EN
The purpose of arthroplasty is to restore the mobility and soften pain in an injured joint. The literature dealing with problems and efectiveness of the shoulder joint implantation was analyzed. The overview of available modular endoprothesis was performed. The influence of the endoprothesis geometric parameters on the quality of arthroplasty was summarized and presented. The literature studies were employed to design the hybrid shoulder endoprothesis with adjustable components. The main problem was to propose the structure of the adjustable components to reproduce geometric and kinematic conditions of the anatomical joint.
4
Content available A specific problem of mechanism synthesis
EN
A technique for path synthesis is employed to design a feeder for carrying products between two points. The feeder is assumed to be a one degree of freedom system of six links connected by means of revolute joints. The mathematical basis of the concept is presented. An exemplary solution is presented and discussed.
5
Content available remote Dynamic model of the drum of the washing machine SAMSUNG WF0804
EN
The paper deals with vibrations of the washing machine Samsung WF0804. The motion equations of the washing machine drum were derived. The vibration of the drum caused by the unbalanced mass was examined. The presented analysis will make up the basis for experimental studies aimed at validating the theoretical model and finding the most effective way of balancing of the drum vibration.
6
Content available remote Optimal synthesis of quick return mechanism as a path generator
EN
The paper deals with an optimal synthesis of planar mechanisms as path generators. The technique verified in the synthesis of four bar linkages and crank slider mechanisms was successfully applied to a quick return mechanism with prismatic joints. The main idea of the method consists in decreasing the number of the design parameters. The problem was formulated as an optimisation task. The mathematical foundations were presented. An objective function was constructed and minimised in searching for generators of test paths using an evolutionary algorithm. The exemplary solutions were presented and discussed.
7
Content available remote Numerical and experimental vibration analysis of domestic washing machine drum
EN
The vibration of a drum of the washing machine Samsung WF0804 caused by the unbalanced mass attached to the rotating unit was examined. The motion equations of the washing machine drum were derived. The stand for experimental measurement was presented. The numerical results were compared with experimental measurements. General conclusions were mode. The analysis will make up the basis for experimental studies aimed at finding the most effective way of balancing drum vibrations.
PL
W pracy zaprezentowano metodę syntezy generatorów krzywych otwartych. Przedstawiono ogólne założenia i na tej podstawie wyprowadzono matematyczne formuły umożliwiające rozwiązanie zadań syntezy czworoboku przegubowego oraz mechanizmu korbowo-wodzikowego. Metoda może być rozwinięta na pozostałe płaskie mechanizmy dźwigniowe z trzema ogniwami ruchowymi. Zaprezentowano wyniki testów numerycznych dla wybranych krzywych.
EN
The synthesis method of planar mechanisms generating open paths was presented. On the base of taken assumptions mathematical formulas for the synthesis of four-bar linkage and crank-slider mechanism were derived. The method can be adopted to the other planar mechanisms with three moving links. The results of the numerical experiments for chosen curves were presented and discussed.
EN
A curve description invariant under affine transformations allows to minimize the design space in optimal synthesis of a planar mechanism. The paper introduces new curve descriptions and confronts them with functions developed for purposes of pattern recognition in computer image processing. Distance norms in the sense of the similarity of shapes are introduced. The norms are used as objective functions in the optimal synthesis of 1-DOF geared five bar linkage and minimized using the evolutionary algorithm. The mechanisms generating a wide variety of shapes are searched for, and the general conclusion are put forward.
PL
Opis krzywej niezmienniczy względem transformacji afmicznych pozwala zminimalizować przestrzeń rozwiązań w optymalnej syntezie mechanizmów. W pracy zaproponowano nowe opisy i skonfrontowano je z funkcjami wypracowanymi na potrzeby jej obróbki kształtu. Wprowadzono normy odległości w sensie podobieństwa kształtu i zastosowano je jako funkcje celu w optymalnej syntezie pięcioboku przegubowego lego z przekładnią zębatą. Funkcje celu zminimalizowano przy użyciu algorytmu ewolucyjnego. Wnioski sformułowano na podstawie syntezy wybranych krzywych.
EN
The paper presents the solution of a chosen dynamic problem, i.e. determination of the engine power to drive a mechanism, by means of the Mathematica environment for numerical and symbolic computations. It was done on the example of a third class mechanism. The author’s intention is to show the advantages of replacing the classes on “Mechanism Theory” with the computer laboratory.
11
Content available remote Determining of stresses in unpropperly curved cervical spine
EN
The paper presents the method of determining the stresses in cervical spine vertebrae. It is based on techniques known from strength of materials – the theory of strongly curved beams. It allows to determine normal stresses in vertebrae of cervical part of spine with known characteristic dimensions. The method was tested on three different cases of cervical spine conformation: one properly and two improperly curved spinal line. Obtained information about influence of spine geometry on character and value of stresses could be useful in clinical practice.
15
Content available remote Non-Uniform Torque Transmitted by a Non-Circular Belt Gear
EN
The present article deals with the process of non-uniform transmission of the torque in non-circular variable speed belt gear systems. Geometric characteristic and kinematic analysis of a selected variable speed toothed belt gear system are presented. The gear in question has been described in such a way as to show the relation between the torque on the driving wheel and the torque on the driven wheel. Differences in dynamics between circular gear systems and the studied gear system have been shown. Salutions to the derived equations are presented, and on their basis, general proposals are put forward.
PL
Przedmiotem pracy jest analiza procesu przenoszenia momentu obrotowego w nierównobieżnej przekładni cięgnowej o nieokrągłej obwiedni koła. Podano cechy geometryczne oraz przedstawiono analizę kinematyczną wybranej nierównobieżnej przekładni cięgnowej. Dla podanej przekładni wprowadzono zależności wiążące moment obrotowy na kole czynnym z momentem obrotowym na kole biernym. Pokazano różnice w zakresie dynamiki między przekładniami o kołach okrągłych a analizowanymi przekładniami. Przedstawiono rozwiązania numeryczne otrzymanych równań i na ich podstawie sformułowano ogólne wnioski.
PL
Przedmiotem artykułu jest analiza warunków zachodzących podczas rozruchu niewyważonej tarczy kołowej osadzonej na sprężystym pionowym wale. Zakłada się, że środek masy tarczy zbacza o pewną małą odległość od jej środka geometrycznego, czyli od osi obrotu tarczy. Podano założenia, przy których następnie wyprowadzono równania ruchu oraz sformułowano warunki początkowe. Zbadano zachowanie się wału w trakcie przechodzenia przez zakres rezonansu. Przedstawiono rozwiązania numerycznie równań ruchu.
EN
This paper is aimed at analysis the conditions occurring at starting an unbalanced circular disk attached to an elastic, vertical shaft. It is assumed that the centre of mass of the disk deviates from its geometrical midpoint, i.e. from the axes of rotation of the disk, by a small distance. Appropriate assumptions are provided, serving for purposes of formulating the equations of motion and initial conditions. Behaviour of the shaft during its transition through resonance range was studied. The numerical solutions were presented and discussed for several cases.
PL
Przedstawiono przebieg prac zmierzających do ograniczenia drgań ciężkiego ubijaka do zagęszczania podłoża. Opisano dynamikę wewnętrzną bijaka - elementu roboczego ubijaka.
EN
The course of researches aimed to limit the vibration of a heavy rammer for ground compacting is presented. The internal dynamics of the ram - main part of the rammer - is discussed.
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