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Über dieses Buch

This book presents versatile, modern and creative applications of graph theory in mechanical engineering, robotics and computer networks. Topics related to mechanical engineering include e.g. machine and mechanism science, mechatronics, robotics, gearing and transmissions, design theory and production processes. The graphs treated are simple graphs, weighted and mixed graphs, bond graphs, Petri nets, logical trees etc. The authors represent several countries in Europe and America, and their contributions show how different, elegant, useful and fruitful the utilization of graphs in modelling of engineering systems can be.

Inhaltsverzeichnis

Frontmatter

Basics and Theoretical Aspects of Graph and Network Modelling

Frontmatter

Bond Graphs in System Modelling

The paper focuses on the presentation of a graphical modeling method named a bond graph method that is applicable to various dynamic systems such as mechanical, electrical, hydraulic, thermal, chemical and magnetic or a combination of these named hybrid systems or multidisciplinary systems. The method is based on an analysis of the power flow in a system from the power sources to its working elements. A brief presentation of the method illustrates its basic concepts and intends to outline the ease and the benefits of using it and its huge potential for multidisciplinary systems modelling, as well.
R. Ibănescu

Structural Importance and Local Importance in Network Reliability

Network reliability analysis has interesting applications in areas such as computer and mobile networks. However, the computation of many important reliability measures (all-terminal reliability, reachability) turns out to be NP-hard. This statement applies to the computation of relevant reliability importance measures, too. In this paper we introduce local importance measures that describe the importance of an edge or vertex of the network in its local network neighborhood. Suitable scaling of the local neighborhood renders the computation of generally intractable reliability measures possible.
P. Tittmann, S. Kischnick

Access Distribution Scheme to the Computer System Based on Fuzzy Logic

This paper presents access distribution at computer system transmission of client-server data type. In order to enhance information protection fuzzy logic is applied to select the data encryption method. A server block diagram of such computer system has been developed based on the proposed fuzzy distribution of system access.
A. Shaikhanova, A. Zolotov, L. Dubchak, M. Karpinski, V. Karpinskyi

Problem of Medicines Distribution on the Example of Pharmaceutical Wholesale

The paper presents the task of determining the optimal route for the transport of medicines to pharmacies (i.e. traveling salesman problem) with two methods. The first one is a branch and bound method, the second is an artificial immune system. The calculations were performed with a TSPSG computer application for the first method and their own program for the other. In this way it was possible to conduct a comparative analysis of the ideal state, the optimum from the point of view of the results obtained, with the state of the current routing of medicines to pharmacies. This allowed us to verify the existing distribution channels in the logistics distribution of medicines.
M. Cieśla, B. Mrówczyńska

Modelling of Mechanical Systems

Frontmatter

Bond Graph Model of a Robot Leg

In the paper, we present the bond-graph model of a 12-legged robot. The robot was built within the framework of a master thesis. The system of control was designed and performed by the authors. There are versatile control options e.g. via a PC-type computer as well as commercial mobile devices such as tablets or mobile phones. Various tests of the robot were performed. The bond-graph model allows for versatile simulations that help a designer in finding the most efficient solution. The bond graph schemes are discussed in the paper.
B. Gola, J. Kopec, J. Rysiński, S. Zawislak

Kinematical Analysis of Variants of Wind Turbine Drive by Means of Graphs

Variants of a wind turbine drive are discussed in the paper. The drive should be adjustable. The control tools should be reliable and simple. Several variants of drive system based upon a compound planetary gear accompanied by a friction gear are analysed and compared. Graph models had been used for analysis of the gear itself. The analysis of the whole system using graphs is proposed via modification of known approaches. The analysis of results shows their full compatibility.
J. Drewniak, J. Kopeć, S. Zawiślak

Graph-Based Algorithm for the Evaluation of the Mechanical Efficiency of Epicyclic Gear Drive in Hybrid Scooters

Efficiency in transportation of goods and people are crucial objectives for the sustainability of society and the protection of its environment. In the particular case of urban mobility, the current trend is toward the applications of hybrid propulsion, if not purely electric. The growing dimensions of urban areas suggest that a particular attention needs to be addressed to vehicles’ energy requirements, air quality and noise pollution. Hybrid technology satisfies the needs of small engines, with low emissions and high energy-efficiency. Therefore, for efficient power management of small internal combustion engines and electric sources, reduced costs and energy efficient gear transmission systems are required. A scheme of hybrid gear transmission, proposed by Sheu, with the aim of minimizing the emissions and fuel consumption, will be herein analysed to estimate the overall mechanical efficiency. In particular, we will discuss an application of a methodology based on graph theory for a systematic and unified analysis of the gear train mechanical efficiency, in all six driving modes. The phases of the proposed analysis are summarized in Table 1.
Table 1
Phases of the proposed mechanical efficiency analysis procedure
https://static-content.springer.com/image/chp%3A10.1007%2F978-3-319-39020-8_7/MediaObjects/328580_1_En_7_Tab1_HTML.gif
P. Coaccioli, E. Pennestrì

Graph-Theoretic Modelling and Sensitivity Analysis of Dynamic Systems

In this paper, a graph-theoretic formulation is presented that can be used to generate governing equations for dynamic systems in a flexible, automated and efficient fashion. Furthermore, a modified formulation is presented to demonstrate the applicability of graph-theoretic methods to generate the sensitivity equations for dynamic systems. An example is provided, in which the new graph-theoretic formulation is used to generate the governing and sensitivity equations simultaneously from the linear graph representation of the systems.
J. Banerjee, J. McPhee

Three-Dimensional Analysis of Vehicle Stability Using Graph Theory

Vehicle stability is a widely studied topic today. It is crucial that we develop a better understanding of one of the main problems of vehicular accident rate problems throughout the world: the rollover accident. The main goal for researchers is to determine a way to predict vehicle behaviour under a variety of circumstances. Davies method is a mathematical tool that allows the static and kinematic analysis of any kind of mechanisms, as well as we can find in vehicle suspensions. This method uses the Graph theory that enables kinematic chain representation by means of a graph for later analysis. In this paper we present the vehicle stability kinematic analysis using Graph theory, Screw theory and the Davies method.
G. G. Moreno, R. L. P. Barreto, R. S. Vieira, L. Nicolazzi, D. Martins

Analysis of the Kinematics of Planar Link Mechanism with Non-stationary Motion of Crank

The article presents an example of using contour graphs to analyse the velocities and accelerations of components of the complex link mechanism without the use of decomposition of mechanism approach. The active link mechanism carries out the non-stationary motion, i.e. starting, stationary motion and stopping braking. The resulting system of algebraic linear equations solved for a given distribution of velocity and acceleration of the active link mechanism has been derived using the contour graph assigned to the considered mechanism.
J. Drewniak, P. Garlicka, B. Borowik

Modeling of Production Processes

Frontmatter

Petri Nets for Computer Aided Group Technology

An increasing number of various versions of Petri nets and the tools for modeling them raises a question: which variant is the most suitable? What are its capabilities and limitations for solving a particular problem? This work presents a chosen Petri net class as a tool for modeling group manufacturing processes, verifying their completeness and coherence as far as optimization of the machined parts flow through the manufacturing cell. A timed priority Petri net has been proposed. The modules of the manufacturing process model have been presented. A tested genetic algorithm with a chromosome in form of an ordered set of priorities of the chosen events has been used for the manufacturing cell performance scheduling. The work includes an example in the form of CNC lathe machining process.
R. Stryczek

Graph Theory in Product Development Planning

Development of process planning methods is an important research area. Product development planning takes into consideration lead-times of tasks and activities, bill of materials, quality plans, and risk analysis. Production process planning can be supported by graph theory. Methods such as CPM, PERT, GERT are useful in product development planning. In this article, a methodology of risk identification and assessment is combined with the GERT method.
I. Kutschenreiter-Praszkiewicz

A Digital Pattern Approach to 3D CAD Modelling of Automotive Car Door Assembly by Using Directed Graphs

The present paper deals with methods for product development aimed to support designing activities and to re-use company know-how. The work is addressed to complex products i.e. products characterized by several components and dependencies among them. Then, the paper presents both the methodological approach and the application to the 3D CAD modelling of an automotive car door assembly. The work uses directed graphs and a series of algorithms to provide a Graphical User Interface (GUI) able to support a designer by reducing the development time of new car door assemblies and increasing the accuracy of the design activities. According to a digital pattern approach, the GUI is used to determine the set of changes to 3D CAD models that typically occur in the automotive field, during the development of new car door assemblies.
S. Patalano, F. Vitolo, A. Lanzotti

Graph-Based Aid and Modelling of Design Tasks

Frontmatter

Application of Game Graphs to Describe the Inverse Problem in the Designing of Mechatronic Vibrating Systems

Dependence graphs and parametric game trees can be applied to describe dynamic properties of machine systems. Discrete mechatronic systems are understood as a combination of mechanical discrete models with piezoelectric elements and external electrical circuits LRC. An application of game graphs to describe the inverse problem on the basis of an example of a mechatronic vibrating system has been presented in the paper, focusing on mechanic subsystems of concentrated parameters and an external LRC system.
A. Deptuła

Graphic Matrix Formalization of Logical Decision Trees in the Optimization of Machine Systems

Multi-valued logical decision trees indicate the importance rank of construction and/or exploitation parameters. There is an isomorphic interpretation of logical transformations, thus the Quine−Mc Cluskey algorithm of the minimization of individual multi-valued logical functions can be considered by taking into account the graphic matrix formalization in the optimization of machine systems.
A. Deptuła, M. A. Partyka

The Class of Objects Graph Model as Dataware of Structural Synthesis System

The article is devoted to a graph method of dataware that will form a system of construction spiroid gearboxes, based on search algorithms. Stages of the data are considered that form, from existing structures, an analysis to generalize graph structure synthesis. It is an informational base for further synthesis of new structures.
O. V. Malina, E. G. Zarifullina

Miscellaneous

Frontmatter

Search Module as a Tool for Improvement of Classifier

The article is dedicated to the approach of information search realization as part of a configuring system of engineering products. Effectiveness of a search depends on algorithm quality, trained on a database of the configuration system and base of linguistic rules, some of which are cited as examples in the article. Additionally, an algorithm is given for building a classifier and rules of data used for constructing the most optimal variants of search according to wishes of a user. From such a point of view, a search for information is a replenishment tool of the configurator database. It makes the system more open.
E. G. Zarifullina, O. V. Malina, I. M. Nekipelova

Kazimierz Kuratowski—Biography and Genesis of the Theorem on Planar Graphs

The present paper discusses Professor Kazimierz Kuratowski’s achievements, especially proving his theorem on planar graphs in 1930. Some facts of the biography are analysed, aiming for explanations of how it was possible for him to do this and to delineate the background of such success. The general situation of mathematics in Poland (especially in Lvov) in the 1920s and 1930s is roughly described. The way of proving the theorem is also analysed i.e., transformation of the problem from the graph theory field into the field of topology.
J. Wojnarowski, S. Zawiślak

Backmatter

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