Dear Label_Name,

Greetings! I hope you are well.

I am writing on behalf of an international publishing house, Science and Education Publishing, USA (http://www.sciepub.com).

Science and Education Publishing (SciEP) is a multidisciplinary open access publisher of Journals covering the fields of Science, Technology and Medicine. All SciEP publications are subject to high-quality peer review, editorial and production processes and are freely available online.

Welcome to the April, 2013 edition of SciEP newsletter, providing monthly summaries of articles on science & education related topics of interest to scientist and professionals. The mission of our journals is to provide an open access forum for publishing new findings on issues pertinent to scientific and academic field. We also invite you to submit original research papers, review articles, short reports, or case studies are considered for publication in our Multidisciplinary Journals.

American Journal of Public Health Research
DOI: 10.12691/ajphr-1-1-3

The Implementation of a Tele-Homecare System with Service Oriented Architecture and HL7 Message Transmission Standard
Ching-Sung Wang

American Journal of Medical and Biological Research
DOI: 10.12691/ajmbr-1-1-2

The Influence of Ethanol on Pyruvate Kinases Activity in Vivo, in Vitro, in Silico
Lelevich Sergey Vladimirovich, Khrustalev Vladislav Victorovich, Barkovsky Eugene Victorovich, Shedogubova Tatyana Aleksandrovna

American Journal of Medical Sciences and Medicine
DOI: 10.12691/ajmsm-1-1-1

Clinical and Histological Features in Wegener Granulomatosis
Li Cavoli Gioacchino, Passantino Rita, Bono Luisa, Tortorici Calogera, Ferrantelli Angelo, Giammarresi Carlo, Rotolo Ugo

American Journal of Infectious Diseases and Microbiology
DOI: 10.12691/ajidm-1-1-2

The Curse of Lymphatic Filariasis: Would the Continual Use of Diethylcarbamazine Eliminate this Scourge in Papua New Guinea?
Anne Lanham, Lillian Mwanri

We have released issues of some journals on February 2013.
American Journal of Public Health Research
American Journal of Medical Sciences and Medicine
American Journal of Medical and Biological Research
American Journal of Pharmacological Sciences
American Journal of Clinical Medicine Research
American Journal of Nursing Research
American Journal of Cancer Prevention
American Journal of Medicine Studies
American Journal of Infectious Diseases and Microbiology
American Journal of Cardiovascular Disease Research
American Journal of Biomedical Research
American Journal of Mechanical Engineering
American Journal of Microbiological Research
Journal of Preventive Medicine
American Journal of Food and Nutrition
American Journal of Hypertension Research
American Journal of Sports Science and Medicine
Journal of Cancer Research and Treatment
American Journal of Zoological Research
Journal of Biomedical Engineering and Technology
American Journal of Microbiological Research
Biomedical Science and Engineering

We are pleased to announce that submissions are now being accepted for peer review for all the journals across all our subject areas in SciEP.

Please submit your manuscript via our online submission system:
http://www.sciepub.com/author/signin

To unsubscribe from our mailing list, please click on the following link: unsubscribe

I am looking forward to hearing from you.

Kind regards,

David Rain
Email:join@sciepub.com
Science and Education Publishing (http://www.sciepub.com)

Geometric Transformations in the Design of Assembly Systems

Milan Fiľo, Jaromír Markovič, Gabriela Ižaríková, Peter Trebuňa*

Department of Industrial engineering and management, Faculty of Mechanical Engineering, Technical University of Košice, Košice, Slovakia

Abstract: The design of the assembly systems is an important role optimizing the spatial resolution. An important tool for the problem solving is approaches to mathematics based modeling. The article presents the basic geometric transformations to identify the location.

Keywords: modeling, assembly systems, scaling

Received October 24, 2013; Revised November 04, 2013; Accepted November 20, 2013

Citation: Milan Fiľo, Jaromír Markovič, Gabriela Ižaríková, Peter Trebuňa, Geometric Transformations in the Design of Assembly Systems. American Journal of Mechanical Engineering, 1 (7). 434-437. January 2013. doi:10.12691/ajme-1-7-56

1. Introduction

The optimization of the spatial resolution is very important in the design of assembly systems. An important tool for the problem solving approaches is based on the mathematical modeling. For the creation and design assembly systems is significant systemic approach.

When exploring a systems approach involves the modeling of object decomposition into elemental components, examine their functional interaction and integration in the structure of the system [1,2].

The system approach is promising for identification of complex, interrelated functions of system elements, the elements of the system are treated as parts of an integrated whole system approach is an effective method for analysis and design solutions to complex problems. There are applied two basic strategies for addressing of the problem in the systems approach: analysis and synthesis [3].

The analysis process is thought to spread to the whole or part of its conceptual distinction between the individual properties.

The system is divided into subsystems. In the process of fusion is to merge components phenomena objects, their properties and relations, solving partial problems are compiled into a functional whole [4]. Analysis and synthesis of integration allow you to create interfaces with various disciplines.

The current mathematics has developed a rich description of the apparatus for quantitative and qualitative relationships between variables. In addressing placement relationship is most often used mathematical theories listed in Table 1.

Table 1. The mathematical theory

The creating geometric models of technical objects are based of the basic geometric elements and their mathematical expression.

Topology is a branch of geometry that studies the properties of geometric shapes which are retained for each unique two-sided continuous mapping. The examining topological relationships of structural elements assembly systems can be advantageously used tools of the analytic geometry.

The analytic geometry using algebraic tools defines and studies different types of spaces (Euclidean space E, the affine space A, projective space P), which approximates the different meaning of actual physical space. The analytical geometry examines particular geometric properties of the spatial units of the analysis method, i.e. the spatial units expressed mathematically means (eg by coordinates).

2. Basic Geometric Transformations

Translation - characterized by a vector displacement, displacement of point X is the displacement vector (x, y),

for new coordinates valid:

expression of matrix transformation:

[picture] | (1.1)

Figure 1. Translation

Figure 2. Rotation

Rotation - given center of the rotation and the angle of the rotation (increasing counterclockwise),

for new coordinates valid:

expression of matrix transformation:

[picture] | (1.2)

(* - matrix multiplication)

If we want to implement the rotation around any point, then we have to do the moving to the point O, then turning and pushing back into the original center of the rotation.

Scale - the scaling factors given in the direction of the axes coordinate system and the reference point (the point whose position relative to the beginning of the coordinate system remains unchanged),

m - giving a constant size scaling

for new coordinates valid:

expression of matrix transformation:

[picture] | (1.3)

Figure 3. Scale

Figure 4. Reflections

Reflections - mirror point X can be carried out with respect to the axis of respect to the axis of or with respect to the beginning of the coordinate system,

for new coordinates valid:

- with regard to o: ,

- with regard to o: ,

- with regard to the center: ,

transformation matrix representation with regard to

[picture] | (1.4)

transformation matrix representation with regard to

[picture] | (1.5)

[picture] | (1.6)

Figure 5. Slope

Slope - skewing point X is the coefficient of skew S,

new coordinates for the skew in the x-axis applies:

new coordinates for the skew in the y-axis applies:

expression of matrix transformation:

[picture] | (1.7)

The combination of that elementary transformation can be expressed mathematically or any change in position scale geometric object.

When combined transformation does not apply to matrix multiplication commutative law. For example:

Translation and rotation:

expression of matrix transformation:

Rotation and translation:

expression of matrix transformation:

Translation and scale:

expression of matrix transformation:

Scale and translation:

expression of matrix transformation:

3. Summary

The designing assembly systems are a great emphasis on the initial technical work associated with the graphical representation of the process. The selection of the appropriate mathematical tools to solve placement and the zonal problems is usually influenced by the chosen design method and concept solutions [5,6]. The advantage of using a mathematical expression that position leads to a shortening of the time needed to conclusively establish the location of places of the assembly machinery.

The methodical progresses of automated designing are based on the utilizing of topological models of constructed equipments of assembled systems. These progresses go out these assumptions:

Ÿ  The model of raster grid is assigned to reference area for location assembled system. This system is laid out capacitive calculation of required surface (volume).

Ÿ  Reference area of assembled system is located to the reference area by the assembled activity.

Ÿ  The models of topological relations of the constructed equipments of assembled models are solved in the individual zones.

Ÿ  The calculation-interactive mode of the solution of topological relations is based on the utilizing 2D or 3D models of constructed equipments of topological relations.

Ÿ  The concrete 2D and 3D models are chosen from graphic database and inserted into calculated reference points.

Ÿ  The optimal variant of structure of the assembled model is chosen on the base of interactive decision progress.

Acknowledgement

This article was created by implementation of the grant project KEGA: Intensification of modeling in education of II. and III. degree in the field of study 05/02/52 Industrial Engineering

References

[1]   | Trebuňa P.: Projektovanie výroby integrované optimálnym systémom hmotných tokov. In: Transfer inovácií. č. 11 (2008), s. 184-186.Internet: <http://www.sjf.tuke.sk/transferinova cii/pages/archiv/transfer/11-2008/pdf/184-186.pdf>.
[2]   | IŽARÍKová, G.: Modely pre automatizované projektovanie montážnych systémov, Dizertačná práca, SjF TU v Košiciach, 2008.
[3]   | TAKALA,J. - MALINDŽÁK,D. - STRAKA,M.: Manufacturing strategy: Applying the logistics models / - Vaasa : Vaasan yliopisto - University of Vaasa, - 2007. - 206 p.
[4]   | ŠÍPOŠ, Ľ., BEŇO, P.: Počítačom podporované konštruovanie. TU Zvolen, 2006.
[5]   | DURKÁČOVÁ, M., LAVIN, J., KARJUST, K.: KPI optimization for product development process In: Annals of DAAAM for 2012: proceedings of the 23rd International DAAAM Symposium: 24. - 27.October, 2012, Zadar, Croatia. Vienna: DAAAM International, 2012 P. 1079-1084.
[6]   | DURKÁČOVÁ, M.: Performance monitoring system / Michaela Durkáčová. In: Collaborative Engineering v inovačním cyklu: sborník přednášek z mezinárodní konference: Zlín, 29. - 30.11.2012. Liberec: Technická univerzita v Liberci, 2012 P. 197-204.