Web Technologies for Modelling and Visualization in Mechanical Engineering

Transcription

1 Web Technologies for Modelling and Visalization in Mechanical Engineering 1 X 1 Web Technologies for Modelling and Visalization in Mechanical Engineering Mihai Dpac and Cladi-Ionţ Popîrlan Uniersity of Craioa Romania 1. Introdction Modeling and isalization techniqes are indispensable tools for the nderstanding of mechanical systems, mechanism generation and isalization being a challenging sbject in order to interpret the data and to hae a better nderstanding of system dynamics. The importance of shape modeling in comptational ision, CAD/CAM or irtal prototyping has been recognized for a long time. The idea of fnction-based approach to shape modeling is that complex geometric shapes can be prodced from a small formla rather than thosands of polygons. Parametric, implicit or explicit fnctions and their combinations may be sed to define the shapes. Parametric representations of shapes hae been discssed in (Metaxas, 1996, and are ery appropriate selections when handling complex shapes in three dimensional dimensions. Implicit srfaces remain difficlt to isalize and maniplate interactiely becase they reqire root-finding to locate the srface (Sarti & Tbaro, 001. A standard method for isalizing and interacting with implicit srfaces can be fond in (Lorensen & Cline, Other standard methods for isalizing implicit srfaces are ray-tracing (Leoy, 1990 and olme rendering (Drebin et al., Implicit srfaces hae also been isalized sing dynamic particle systems (Witkin & Heckbert, The idea of the hybrid fnction-based approach (Li & Sorin, 006a; Li & Sorin, 006b is to se different mathematical fnctions to modeling shapes. Based on this approach, the Fnction-based Extension Virtal Reality was proposed in (Li & Sorin, 005a. Following this, Li and Sorin (Li & Sorin, 005b extended FVRML to defining time dependent objects by analytical formlas as well as with a scripting langage. A similar approach for shapes modeling applied to mechanical components generation and isalization was discssed in (Dpac, 007. Li and Sorin (Li & Sorin, 006b proposed a fnction-based extension of Extensible 3D (X3D. The extension allows the se of analytical fnctions to define geometry, color, 3D textre and operations on 3D shapes, or time-dependent metamorphosis. Chen et al. (Chen et al., 004 ses 3D representations to isalize a web strctre. The athors reslts pertains to geographical systems and proides information on maps. Cartwright et al. (Cartwright et. al., 005 presents a project to deeloping an open system architectre and Web-based shape modeling sing HyperFn, a high-leel programming langage for specifying implicit srfaces and objects. Another approach for

2 Modeling, Simlation and Optimization Tolerance and Optimal Control shape modeling was proposed in (Fayolle et. al., 005, where a web-based system implementation for modeling shapes sing real distance fnctions hae been sed. Some general aspects of the WEB technology that may hae important effects on modelling, simlation and isalization and the role of Jaa and Web technologies for modelling and simlation, and sggested approaches and applications are discssed. For the modeling and isalization in mechanical engineering a ariety of mechanical components will be discssed, together with their fndamental concepts and description. Mechanical components sch as screws, rolling bearings, sliding bearings, gears, mechanical springs, and flexible belts will be presented. The web-base approach presented here is intended for mechanism components modeling and isalization sing object oriented programming (Jaa (Eckel, 006. A Jaa Applet which sed an XML (Extensible Markp Langage format to specifying shapes for Jaa objects is deeloped. The web-application component is responsible for sering p the object data to the Applet for rendering and to handle serer-side processing of actions triggered by the ser. Different parametric, implicit or combination between implicit and parametric fnctions, hae been sed for the modeling of the mechanical components shapes. Shapes sch as gears, springs, chains and corkscrews hae been generated on the XML file format and iewed as Jaa objects on the graphical interface. Sophisticated shapes hae been generated withot increasing the application size, and with a ery good comptational time. It was demonstrated that simple mathematical fnctions represent sefl tools for shape modeling and isalization.. Actal WEB Technologies.1 Introdction The emergence of the World-Wide Web (WWW has prodced a new compting enironment. This has motiated researchers in many disciplines to re-ealate their approaches and techniqes in light of the new facilities proided and the new frontiers allowed by the new WWW technology. Web-based simlation is one sch new concept that has eoled in the new web era and that has attracted the interest of many researchers and practitioners in the compter simlation field. The appearance of the network-oriented programming langage, Jaa, and of distribted object technologies like the Common Object Reqest Broker Architectre (CORBA has had major effects on the state of simlation practice. These technologies hae the potential to significantly alter the way we think of, deelop, and apply simlation as a problem soling techniqe and a decision spport tool. In this way, modeling and isalization software for the fields of mechanical engineering, chemistry, biology etc. helps to connect high school learners with the kinds of real scholarly inqiry practiced daily by professional scientists. Cstom software for scaffolding inqiry learning helps the teams deelop classroom lesson topics and connect distribted commnities of learners. Scientists want to condct hands on analysis in an attempt to gain a better nderstanding of otpt data. The size of applications poses a significant problem for accessibility and analysis. The soltion is to deelop the web-based applications where scientists can download the data and are able to create cstom isalizations oer the web directly from srface data. Simlation modeling methodology deals with the creation of models and the se and maintenance of these models. Oer the fast fie decades simlation modeling spport has

3 Web Technologies for Modelling and Visalization in Mechanical Engineering 3 eoled from the adent era to the era of simlation programming langages to the era of simlation spport enironments to the modern era (Page, 1998; Fishwick, The adent era began with the inception of digital compters and is marked by early theories of model representation and exection. Later on, simlation programming langages like Simla, Simscript and GPSS started to appear. The research done dring the deelopment of these langages has led to both refining the nderlying simlation concepts and defining new conceptal frameworks or world iews. The third era was marked by the interest in integrated simlation enironments where the focs is on the broader life cycle of a simlation stdy. Also, a great interest emerged dring this era in interoperability of heterogeneos simlators. Crrently, most actiities are focsed on the simlation enironments and langages, with some emphasis on simlation methodology deelopment and parallel exection of simlations in academia. The combination of WWW and Jaa offers a set of niqe capabilities for compting (Chn et. al., The World Wide Web proides important infrastrctre for scientific and engineering comptation. The distribted compting hardware of the Web has remarkable potential compte performance times that of the largest spercompter.. Web Spport for Modelling and Visalization Web technology has the potential to significantly alter the ways in which simlation models are deeloped, docmented, and analyzed. The web represents a new way for both pblishing and deliering mltimedia information to the world. Web technologies that cold be leeraged in a simlation spport role are nmeros. For example, the Hypertext Markp Langage (HTML proides both docment formatting and direct linkage to other docments. This capability can significantly improe the information acqisition and presentation process for model deelopers. Moreoer, the power of hypermedia aailable on the web can also inflence the way models are deeloped and sed. The forms capability of HTML proides a simple mechanism to constrct a graphical ser interface that cold be sed in web-based simlation modeling enironments. The WWW can also act as a software deliery mechanism and distribted comptation engine. Recent efforts like CORBA are enhancing the mechanisms throgh which a ser can inoke and tilize serices resident on remote machines. Jaa also enables safe and efficient exection of serice software on the client machine. Three approaches for web-based can be identified in the literatre (Whitman et. al., Serer-hosted simlation allows existing simlation tools to be hosted on a web serer and accessed by clients ia normal HTML pages. This approach has the adantage of sing a familiar tool and enables the rese of existing models. The disadantage is that the commnication power proided by animation in these tools is not isible oer the web. Client-side simlation allows simlation tools to se an applets-based approach that minimizes the learning cre, bt on the expense of power and flexibility. The performance of this type of simlation is also limited by the client machine capabilities. Jaa is an example of programming langages that may be sed to deelop simlation applications that may be exected on the client machine. Seeral Jaa based simlation packages and langages hae been deeloped. For example, Simjaa (McNab & Howell, 1996 ses a basic discrete eent simlation engine and extends this with Jaa s graphical ser interface featres. JSIM is a Jaa-based simlation and animation enironment based on both the process interaction and eent schedling approaches to simlation. It incldes a graphical

4 4 Modeling, Simlation and Optimization Tolerance and Optimal Control designer that allows for graphical model constrction on the web (Nair et. al., Silk (Healy & Kilgore, 1997 is a process-based mltithreaded simlation langage bilt in Jaa. Hybrid client/serer simlation attempts to combine the adantages of serer hosted and client exected simlations. The approach relies on hosting the simlation engine on the serer and sing Jaa for isalization of the animation to proide a dynamic iew on the client machine. Nmeros relationships between the web and modelling are eident. A reiew of the crrent literatre sggests seeral areas of potential impact of the web on modelling. Modelling and simlation research methodology, for example, can be affected by the ability to rapidly disseminate models, reslts and pblications on the web. Remote exection of legacy simlations from a web browser throgh HTML forms and CGI scripts is another area most commonly associated with the term web-based simlation. This also incldes the deelopment of mobile-code simlations sing applets that rn on client machines. Distribted simlation is an area that incldes actiities that deal with the se of the WWW and new distribted compting standards and techniqes (e.g. CORBA, Jaa RMI and HLA to proide an infrastrctre to spport distribted simlation exection. Finally, the natre of the WWW enables the prodction of hypermedia docments containing text, images, adio, ideo, and simlation..3 Web Technolgies Description The LAMP Technologies (Linx, Apache, MY-SQL, Peal/PHP/Python is refers to a soltion stack of software, sally free and open sorce software, sed to rn dynamic Web sites or serers. The original expansion is as follows: Linx - an operating system; Apache, for Web serer; MySQL, for database management system; Perl, Python, and PHP, for the programming langage. The combination of these technologies is sed primarily to define a web serer infrastrctre, define a programming paradigm of deeloping software, and establish a software distribtion package for any application. The most commonly sed Operating System for this prpose is Linx - it's Open Sorce too, and it's based on Unix which was and is an operating systems designed from the grond p for a mltiser enironment and for proiding all the facilities a compter geek cold possibly need to do his job well, with secrity and withot limitations at the Operating System leel. Where job of Apache's is to handle reqests, interpret it, and proide responses. In order for it to access the basic facilities on the serer compter, it makes operating system calls on that compter. In order for Apache to be able to rn yor (serer side application, it needs to be told how that's to be done - it needs to be programmed. Open Sorce langages sch as Perl, PHP and Python are sed to do programming for applications. The MySQL database has become the "de facto" standard for many Linx - Apache - Perl / PHP / Python web applications making p the acronym LAMP. By combining these tools yo can rapidly deelop and delier applications. Each of these tools is the best in its class and a wealth of information is aailable for the beginner. Becase LAMP is easy to get started with yet capable of deliering enterprise scale applications the LAMP software model jst might be the way to go for yor next, or yor first application. Adantages of LAMP: Seamless integration with Linx, Apache and MySQL to ensre the highest leels of aailability for websites rnning on LAMP. Fll 3bit and 64bit spport for Xeon, Itanim and Opteron-based systems Rns on enterprise Linx distribtions from Red Hat and SSE.

5 Web Technologies for Modelling and Visalization in Mechanical Engineering 5 Spports Actie/Actie and Actie/Standby LAMP Configrations of p to 3 nodes. Data can reside on shared SCSI, Fiber Channel, Network Attached Storage deices or on replicated olmes. Atomated aailability monitoring, failoer recoery, and failback of all LAMP application and IT-infrastrctre resorces. Intitie JAVA-based web interface proides at-a-glance LAMP stats and simple administration. Easily adapted to sites rnning Oracle, DB, and PostgreSQL. Many web-based application ses LAMP (Linx, Apache, MySQL, PHP and Jaa technology for web middle-ware and on the back-end compte side relies on specialized programs to fetch data from the archie, isalize, composite, annotate and make it aailable to client browser. Technologies on the client side: 1. Actie X Controls: Deeloped by Microsoft these are only flly fnctional on the Internet Explorer web browser. This eliminates them from being cross platform, and ths eliminates them from being a webmasters nmber one technology choice for the ftre. Disabling Actie X Controls on the Internet Explorer web browser is something many people do for secrity, as the platform has been sed by many for nethical and harmfl things.. Jaa Applets: are programs that are written in the Jaa Langage. They are self contained and are spported on cross platform web browsers. While not all browsers work with Jaa Applets, many do. These can be inclded in web pages in almost the same way images can. 3. DHTML and Client-Side Scripting: DHTML, JaaScript, and VBScript. They all hae in common the fact that all the code is transmitted with the original webpage and the web browser translates the code and creates pages that are mch more dynamic than static html pages. VBScript is only spported by Internet Explorer. That again makes for a bad choice for the web designer wanting to create cross platform web pages. Of all the client side options aailable JaaScript has proed to be the most poplar and most widely sed. Technologies on the serer side: 1. CGI: This stands for Common Gateway Interface. It wasn't all that long ago that the only dynamic soltion for webmasters was CGI. Almost eery web serer in se today spports CGI in one form or another. The most widely sed CGI langage is Perl. Python, C, and C++ can also be sed as CGI programming langages, bt are not nearly as poplar as Perl. The biggest disadantage to CGI for the serer side is in it's lack of scalability.. ASP: Another of Microsoft's attempt's to "improe" things. ASP is a proprietary scripting langage. Performance is best on Microsoft's own serers of corse, and the lack of widespread COM spport has redced the nmber of webmasters willing to bet the farm on another one of Microsoft's siler bllets. 3. Jaa Serer Pages and Jaa Serlets: Serer side JaaScript is Netscapes answer to Microsoft's ASP technology. Since this technology is spported almost exclsiely on the Netscape Enterprise Seer, the likelyhood that this will eer become a serios contender in the battle for the webmaster's attention is highly nlikely.

6 6 Modeling, Simlation and Optimization Tolerance and Optimal Control 4. PHP: PHP is the most poplar scripting langage for deeloping dynamic web based applications. Originally deeloped by Rasms Lerdorf as a way of gathering web form data withot sing CGI it has qickly grown and gathered a large collection of modles and featres. The beaty of PHP is that it is easy to get started with yet it is capable of extremely robst and complicated applications. As an embedded scripting langage PHP code is simply inserted into an html docment and when the page is deliered the PHP code is parsed and replaced with the otpt of the embedded PHP commands. PHP is easier to learn and generally faster than PERL based CGI. Howeer, qite nlike ASP, PHP is totally platform independent and there are ersions for most operating systems and serers. Serlet technology has become the leading web deelopment technology in the recent years de to its safety, portability, efficiency and elegance in design. The serlets are specialized in browsing the web (web docments and arios databases for data mining, information extraction and meaningfl presentation inside the web browser. More important, their power is in online analysis, filtering and strctring of the retrieed information. The serlets are object-oriented and therefore highly modlar and mltifnctional. We are crrently inestigating their efficiency for classification and meaningfl representation of arios aspects of web docments, inclding modelling and isalization. BEA WebLogic Serer contains Jaa Platform, Enterprise Edition (JEE technologies. JEE is the standard platform for deeloping mltitier enterprise applications based on the Jaa programming langage. The technologies that make p JEE were deeloped collaboratiely by Sn Microsystems and other software endors, inclding BEA Systems. JEE applications are based on standardized, modlar components. WebLogic Serer proides a complete set of serices for those components and handles many details of application behaior atomatically, withot reqiring programming. WebLogic Serer consolidates Extensible Markp Langage (XML technologies applicable to WebLogic Serer and XML applications based on WebLogic Serer. A simplified ersion of the Standard Generalized Markp Langage (SGML markp langage, XML describes the content and strctre of data in a docment and is an indstry standard for deliering content on the Internet. Typically, XML is sed as the data exchange format between JEE applications and client applications, or between components of a JEE application. The WebLogic Serer XML sbsystem spports the se of standard parsers, the WebLogic FastParser, XSLT transformers, and DTDs and XML schemas to process and conert XML files. WebLogic Serer is an application serer: a platform for deeloping and deploying mltitier distribted enterprise applications. WebLogic Serer centralizes application serices sch as Web serer fnctionality, bsiness components, and access to backend enterprise systems. It ses technologies sch as caching and connection pooling to improe resorce se and application performance. WebLogic Serer also proides enterprise-leel secrity and powerfl administration facilities. WebLogic Serer operates in the middle tier of a mltitier (or n-tier architectre. The software components of a mltitier architectre consist of three tiers: 1. The client tier contains programs exected by sers, inclding Web browsers and network-capable application programs. These programs can be written in irtally any programming langage.. The middle tier contains WebLogic Serer and other serers that are addressed directly by clients, sch as existing Web serers or proxy serers.

7 Web Technologies for Modelling and Visalization in Mechanical Engineering 7 3. The backend tier contains enterprise resorces, sch as database systems, mainframe and legacy applications, and packaged enterprise resorce planning (ERP applications. Fig. 1. The Three Tiers of the WebLogic Serer Architectre Client applications access WebLogic Serer directly (Fig. 1, or throgh another Web serer or proxy serer. WebLogic Serer generally connects with backend serices on behalf of clients. Howeer, clients may directly access backend serices sing a mltitier JDBC drier. WebLogic Serer has complete Web serer fnctionality, so a Web browser can reqest pages from WebLogic Serer sing the Web s standard HTTP protocol. WebLogic Serer serlets and JaaSerer Pages (JSPs prodce the dynamic, personalized Web pages reqired for adanced e-commerce Web applications. Client programs written in Jaa may inclde highly interactie graphical ser interfaces bilt with Jaa Swing classes. They can also access WebLogic Serer serices sing standard JEE APIs. All these serices are also aailable to Web browser clients by deploying serlets and JSP pages in WebLogic Serer. CORBA-enabled client programs written in Visal Basic, C++, Jaa, and other programming langages can execte WebLogic Serer Enterprise JaaBeans and RMI (Remote Method Inocation classes sing WebLogic RMI-IIOP. Client applications written in any langage with spport for the HTTP protocol can access any WebLogic Serer serice throgh a serlet. The middle tier incldes WebLogic Serer and other Web serers, firewalls, and proxy serers that mediate traffic between clients and WebLogic Serer. Applications based on a mltitier architectre reqire reliability, scalability, and high performance in the middle tier. The application serer yo select for the middle tier is, therefore, critical to the sccess of yor system. The WebLogic Serer clster option allows yo to distribte client reqests and back-end serices among mltiple cooperating WebLogic Serers. Programs in the client tier access the clster as if it were a single WebLogic Serer. As the workload increases, yo can add WebLogic Serers to the clster to share the work. The clster ses a selectable load-balancing algorithm to choose a WebLogic Serer in the clster that is capable of handling the reqest. When a reqest fails, another WebLogic Serer that proides the reqested serice can take oer. Failoer is transparent wheneer possible, which minimizes the amont of code that mst be written to recoer from failres. For example, serlet session state can be replicated on a secondary WebLogic Serer so that if the WebLogic Serer that is handling a reqest fails, the client s session can resme

8 8 Modeling, Simlation and Optimization Tolerance and Optimal Control ninterrpted on the secondary serer. WebLogic EJB, JMS, JDBC, and RMI serices are all implemented with clstering capabilities. The backend tier contains serices that are accessible to clients only throgh WebLogic Serer. Applications in the backend tier tend to be the most alable and mission-critical enterprise resorces. WebLogic Serer protects them by restricting direct access by end sers. With technologies sch as connection pools and caching, WebLogic Serer ses backend resorces efficiently and improes application response. Backend serices inclde databases, enterprise resorce planning (ERP systems, mainframe applications, legacy enterprise applications, and transaction monitors. Existing enterprise applications can be integrated into the backend tier sing the Jaa Connector Architectre (JCA specification from Sn Microsystems. WebLogic Serer makes it easy to add a Web interface to an integrated backend application. A database management system is the most common backend serice, reqired by nearly all WebLogic Serer applications. WebLogic EJB and WebLogic JMS typically store persistent data in a database in the backend tier. A JDBC connection pool, defined in WebLogic Serer, opens a predefined nmber of database connections. Once opened, database connections are shared by all WebLogic Serer applications that need database access. The expensie oerhead associated with establishing a connection is incrred only once for each connection in the pool, instead of once per client reqest. WebLogic Serer monitors database connections, refreshing them as needed and ensring reliable database serices for applications. 3. A Basic Mechanical Components Description 3.1 Screws A screw may be defined as a shaft with a helical grooe formed on its srface. Screws are sed to translate torqe into linear force, to hold objects together or to moe loads. A screw is part of a large category of threaded fastener, with the fasteners classified also as fixed, locking and threaded. Fixed fasteners category inclde riets, welds, brazing, and solders, while locking fasteners inclde pins, keys, springs and washers. Fig.. Two Examples of Screws A screw thread may be thoght as a helical strctre, an inclined plane wrapped arond the internal or external srface of a cylinder/cone. If the srface is a cylinder one hae a straight thread, if the srface is a cone one hae a taper thread. A screw is sed to conert between linear moement and rotational moement, and so, the pitch of the screw (the distance between corresponding points on adjacent thread forms haing niform spacing is chosen

9 Web Technologies for Modelling and Visalization in Mechanical Engineering 9 in a way to preent the screw to slip. By conention (both, Unified-inch series, or ISO-metric International Standards Organization, all threads are considered to be right-hand. 3. Rolling Bearings A rolling bearing may be defined as a connector which carries rond elements (balls, rollers, or needles between two parts (sally a fixed part and a moing part, parts that moes/rotates relatie to one another. In the relatie motion of the two parts, the rond elements rolls/slides with a ery little rolling/sliding resistance, based on a ery low friction (ery small contact area. To frther minimize the sliding resistence, contacting srfaces are separated by a liqid (sally oil or gas or a film, or materials (bronze allows with a ery low coefficient of friction are sed. The important parts of rolling bearings are the oter and the inner ring, the rolling element and the retainer (separator. The main adantages of rolling bearings are: drability in time, easy replacement in case of failre, accracy for a long time period, ability to operate at ery low friction leels, and good trade-off between cost, size and weight. Fig. 3. Side View of a Rolling Bearing Rolling bearings can be classified by the: 1. rolling element shape: ball bearings (se spheres instead of cylinders, roller bearings (se cylinders of slightly greater length than diameter, needle bearings (se ery long and thin cylinders;. direction of the principal force: radial bearings, thrst bearings (sed to spport axial loads, sch as ertical shafts, radial-thrst bearings, or thrst-radial bearings; 3. the nmber rolling bearing rows: rolling bearings with one row, with two rows. 3.3 Gears A gear may be defined as a toothed element within a transmission deice that transmit rotary motion (force to another deice. A gear allows force to be transferred/transmitted (at different speeds, torqes, or in a different direction withot slippage with a transmission efficiency as high as 98 percent. The most important featre for a gear is the meshing possibility with another gear (sally of neqal diameter, in order to prodce a different rotational speed and torqe of the second gear. The constant anglar elocity ratios condition, i.e., the anglar elocity ratio (between a 30-tooth and a 90-tooth gear to be 3, represents the gear-tooth geometry main reqirement.

10 10 Modeling, Simlation and Optimization Tolerance and Optimal Control Fig. 4. Two Classical Gears The main difference between internal and external gears is where the teeth are formed (on the inner or on the oter srface, an internal gear form the teeth on the inner srface (of a cylinder or cone, while an external gear form the teeth on the oter srface (of a cylinder or cone. Gears can be classified as: Spr gears - (the most common type of gear hae a general form of a cylinder or disk with the teeth parallel to the shaft, are sed to transfer motion between parallel shafts. Helical gears hae the leading edge set at an angle (non-parallel with the axis of rotation, allowing a smoothly and qietly motion, and the possibility of sing nonparallel shafts. Doble helical gears (herringbone gears has a general form as a two helical gears mirror image. Beel gears are conically shaped gears. The beels are called miter gears if they hae an eqal nmbers of teeth and the shaft axes at 90 degrees. Crown gear (contrate gear - are a particlar beel gear with the teeth at right angles to the plane of the wheel. Hypoid gears (sally designed to operate with shafts at 90 degrees - are spiral beel gears with a not intersecting shaft axes and with a conical pitch srface. Worm gear - is a species of helical gear that resembles a screw, with his helix angle sally close to 90 degrees and a long body in the axial direction. 3.4 Mechanical Springs A spring is a mechanical element sed to store mechanical energy and to exert forces or torqes. Springs are sally made ot of metal (annealed steel hardened after fabrication, plain carbon steels, alloy steels, or corrosion-resisting steels, and for small loads or minimm mass, by plastics or composite materials. Depending on the reqirements, almost any material haing the right combination of elasticity and rigidity may be sed to constrct a mechanical spring. A spring rate (stiffness is defined as the change in the force, diided by the change in spring deflection. The inerse of spring rate is the compliance.

11 Web Technologies for Modelling and Visalization in Mechanical Engineering 11 Fig. 5. Three Types of Mechanical Springs: a simple, b conical, c doble Depending on load springs may be classified as: Tension/Extension spring, Compression spring, Torsional spring. Depending on material spring can be classified as: Wire/Coil spring, Flat spring. The most common types of spring are: Cantileer spring - a spring which is fixed only at one end. Coil spring (helical spring - a helical spring arond a cylinder or a cone. These are in trn of two types: Compression springs (designed to become shorter when loaded, and tension springs (designed to become longer when loaded and for maintaining the torsional stress in the wire. Hairspring (balance spring - a type of spiral torsion spring Leaf spring - a flat springy sheet (can be simple cantileer or semi elliptic leaf V-spring - antiqe type of springs 3.5 Flexible Belts A Belt may be defined as a looped strip of flexible material (sally fabric or rbber. The most important featre of a belt is the efficiently to transmit power as a sorce of motion. A flexible belt mechanically link two or more rotating shafts sch as plleys or coneyors. In sch systems the belt can drie the plleys in the same or in an opposite direction. In the design of belts and band brakes the slippage of flexible cables, belts, and ropes oer sheaes and drms represents a ery important aspect. Fig. 6. A Classical Belt 3. Chains A chain may be defined a series of connected links sally made of metal. Chains are made in two styles: designed with tors shaped links for lifting or plling designed with links made to mesh with the teeth of a machine for transferring power

12 1 Modeling, Simlation and Optimization Tolerance and Optimal Control Specific ses for chain inclde: Bicycle chain - to transfers power from the pedals to the drie-wheel Chain pmps - type of water pmp Chainsaw - portable mechanical, motorized saw Roller chain - type of chain sed for transmission of mechanical power in indstrial or/and agricltral machinery Snow chains - sed to improe traction in snow High-tensile chain - sed for towing or secring loads. Anchor chain cable - as sed by ships and boats 4. A Web Application Strctre for Shape Modeling and Visalization For the design of the mechanism components, a web-base approach for shape modeling and isalization sing object oriented programming (Jaa is proposed. A Jaa Applet which se an XML format to specify 3D implicit or parametric srfaces for Jaa objects is sed. The Jaa objects are defined sing implicit or parametric fnctions, or their combinations. The Jaa objects sed in the Applet and defined on the graphic interface (Jaa 3D iew spport allow the ser to rotate, scale and translate the associated shapes (mechanism components on screen. In order to create a more complex mechanical component shape, a mating process in which two or more shapes are combined is sed. The mating process, that allows a great degree of interactiity, is described in detail in the next section. In the mating process, the shapes iewed as Jaa objects are stored in predefined objects classes. The predefined classes are based on the classical object oriented programming (OOP and se the inheritance and part off concepts in the mating process. The inheritance concept allows a new created object to take oer (or inherit attribtes and behaior of the preexisting classes. The part off concept creates a new object sing parts of the pre-existing classes. The objects not yet inclded on a pre-existing classes, are stored in new classes and referred as pickable objects. The web application consist of two components, an Applet concordant to the standard Jaa Application Programming Interfaces (API and a serer/web-application written against the most recent ersion of the SDK and JEE API s, and rnning in a common web application serer (in this case a Tomcat web serer was sed. The web application is responsible for sending the Jaa objects to the Applet (Popîrlan & Popîrlan, 007; Bamann, 000 for rendering and handling serer side processing (eents of actions triggered by ser clicks. The Jaa Applet allows to send a ser-initiated action that contains the defalt orientation (matrix transform of the object in the iewer. The interface between the client and the serer is occrring ia Hypertext Transfer Protocol (HTTP to minimize the impact of the firewall between the Applet and the serer. The Jaa 3D iew spport is sed in the interface to incorporate head tracking directly, ths proiding the sers with the illsion that they actally exist inside a irtal world. Using the standard Jaa 3D iew spport we constrcted and maniplated Jaa 3D objects inside a Web application to make isible shapes within the irtal world. The Web application strctre that inclde the related components is described below and can be isalized in Fig. 7.

13 Web Technologies for Modelling and Visalization in Mechanical Engineering 13 Fig. 7. The WEB Application Strctre The roles of the iew-related components are as follows: The Virtal Unierse represents the domain where the mathematical fnctions are defined in a XML format. The View- Platform (VP represents the drawing srface (inclded in the graphical interface for the Jaa objects. The ViewPlatform s parents as shown in Fig. 7 specify its location, orientation, and scale within the irtal nierse. The View component represents the main iew Jaa object. The Local Objects component represents the 3D ersion of the AbstractWindowing Toolkit (AWT Canas object, i.e., a window in which Jaa 3D draws images. It contains a reference to a Shape3D object (described below and information of the Shape3D s size and location. The Shape3D Nodes (S component represents an Jaa object that reslt from the defined mathematical fnction and contains information describing the display properties. By sing the Jaa 3D iew spport the Jaa objects are placed on the display as separate components, preenting the dplication of screen information within eery Local Object. The BrancheGrop Nodes (BG component represents an Jaa object that contains information describing the physical world, mainly the associated six-degrees-of freedom screen and scale (iew capabilities. The Transition (T component represents the Jaa object state from implementation to isalization. The User Code and Data component represents the XML file format sed for fnction representation. The Other Objects component represents the final shape representation. The iewer of Applet is capable of rendering objects in the XML file format. XML format is sed to define the mathematical fnctions and spport predefined tags.

14 14 Modeling, Simlation and Optimization Tolerance and Optimal Control 4.1 The Web Application Components Implementation Regarding the implementation of the application components which are sed by the ser to generate shapes, the next classes representing the basic strctre of the Jaa Applet and described below hae been sed. It is to be mentioned one more time, that the Applet has the role to take the representation of mathematical fnctions from XML format and to transform them to Jaa objects, which allows the ser to mate and to generate a final shape. The class strctre of the Jaa Applet is as follow: MainApplet: The Applet class which parses the <param> tags and creates a ShapePanel object. ShapePanel: This is the class that actally corresponds to the panel inclded in the MainApplet class, panel that display the shapes. The ShapePanel contains a thin horizontal ControlPanel (main men of the ser at the top, and a large ShapeCanas nderneath it. The ShapePanel object also seres as the main controller for the Applet. ControlPanel: The thin horizontal panel at the top of the ShapePanel containing the control widgets. ShapeCanas: The drawing area of the generated shapes. KeyCommandHandler: The object which translates keystroke eents into actions. This cold probably be jst a part of the ShapePanel class, bt it s defined as a different class object for modlarity sake. Drag3D, Drag3DOrbit, Drag3DRotate, Drag3DScale, Drag3DTranslate, DragConstants: These class objects handle mose dragging eents in order to translate, rotate, and scale the generated shapes in the ShapeCanas window. ShapeMatrix3D: This class defines the coordinates of the new generated shapes iewed as Jaa Objects. Camera3D: This class incorporates the implicit and parametric mathematical fnctions sed to generate the shapes. 4. The Shape Generation Process Defining shapes sing mathematical fnctions is the most straightforward method of fnction-based shape modeling. Some shapes can easily be defined with implicit and explicit formlas, while others can be defined better by sing a parametric representation. Besides these methods, there are many other ways to define shapes. For example, skeleton modeling and blending fnctions (Blinn, 198 describe how two primities can be merged into one shape. In addition to defining geometry, fnctions can also be sed to create sophisticated colors and textres. Parametric fnctions for mapping textre images, or simple textre mapping, is a common approach implemented in many software and hardware systems (Peachey, 1985; Wyill et al., Distortion of shape geometries (Lewis, 1989 can also be done by other techniqes sed for coloring shapes. Implicit srfaces are well-sited for simlating physically based deformations (Terzopolos & Metaxas, 1991 and for objects modeling (Trk & O Brien, Like parametric representation, implicit representation codes the shape information in a higher dimensional space. The coding process is referred as embedding, which reqires decoding to obtain the object shape. The embedding in higher dimensional space makes it possible to model topologically complex shapes as ones with simple s topology. The implicitly defined objects are objects described by an implicit fnction. Implicit fnctions define an implicit srface or

15 Web Technologies for Modelling and Visalization in Mechanical Engineering 15 shape. The implicit representation of a cre has the form F(x, y = 0. An implicit fnction F representing a shape is a continos scalar-aled fnction oer the domain R 3, where F=F(x, y, z and x, y, z, are Cartesian coordinates, i.e. the dependent ariable is not isolated on one side of the eqation. The implicit srface of sch a fnction is the locs of points at which the fnction takes the zero ale, i.e., F(p=0, where p = x,y,z, i.e., the eqation is satisfied by the all points in the srface. The fnction eqals to zero for the points located on the srface of a shape. An implicit srface is a set of points p sch that F(p = 0, where F is a triariate fnction (i.e., p R 3. In many cases, F partitions space into an inside and otside 0 if p is on the interior of the object F( p 0 if p is on the bondary of the object 0 if p is on the exterior of the object This ability to enclose olmes and the ability to represent blends of olmes endow implicit srfaces with inherent adantages in geometric srface design. An explicit shape representation describes the points that belong to the object explicitly which makes it the most intitie of representations. The most simple explicit fnctions are defined as g = f(x, and for this case represents an explicit representation of a cre. An explicit representation is not a general representation, since for each x ale, only a single y ale is compted by the fnction. Explicit more general fnction are defined as g=f(x,y,z=0, where x, y, z are Cartesian coordinates, i.e., the dependent ariable are written explicitly in terms of the independent ariable(s. The fnction eqals to zero for the points located on the srface of a shape, and so the explicit srface is as an image of the fnction defined on a domain of a plane. Positie ales indicate points inside the shape and negatie ales are for the points otside the shape. In short, explicit srface representations are well sited for graphics prposes bt less sited for fitting and atomated modeling. The reerse can be said for implicit srface representations. Parametric shape generation and isalization is ery poplar in compter graphics mainly becase of their easy mathematical maniplation and simple ealation. Using parametric representation, the shape information is transpose into ariables by creating mapping fnctions. The types of information hae to be kept when sing the parametric representation, are the co-ordinates and topological information which relate the geometric shapes to each other. For defining geometry of shapes (srfaces and solid objects with parametric fnctions, one can se the following form, x = f 1 (,,w, y = f (,,w, z = f 3 (,,w (1 where x, y and z are the Cartesian coordinates of the points, and, and w are the parametric coordinates. For modeling srfaces, parametric fnctions with two parameters are sed. Solid objects are defined sing parametric fnctions with three parameters and operations, sch as nion, intersection, complement, etc., operations that add flexibility in creating complex shapes. Parametric fnctions may also define color ales. In the graphical ser interface (Shape3D class, a three dimensional shape (a final mechanism component is generated sing combinations between the defined shapes created sing implicit, and/or parametric fnctions. The mating process between the shapes

16 16 Modeling, Simlation and Optimization Tolerance and Optimal Control is shown in Fig. 8 and Fig. 9, and is relatiely similar with the one described by Li and Sorin (Li & Sorin, 006a. Mating is the process by which two or more shapes are combined to create a new complex shape. Fig. 8. Fnction-based Shape Modeling Representation The obtained final shape is a combination of the defined fnctions f i, where each of these fnctions represents the shapes geometry generated sing implicit and/or parametric fnctions. Using the mating process complex shapes (from an initial pool of basic shapes are created sing a predetermined set of rles that are a priori defined and programmed. Once the new object (the final shape as illstrated in Fig. 8 is created, it is added to the library. Fig. 9. Fnction-Based Shape Modeling Process

17 Web Technologies for Modelling and Visalization in Mechanical Engineering 17 The fnctions nobj i, where i =, 3,..., k shown in Fig. 9 represent the i th generated shape geometry as a combination of implicit and/or parametric fnctions (the m th generated shape nobj m is obtained from nobj m-1 and obj m. The fnctions obj i where i = 1,, 3,..., k are simple basic shapes sed to obtain the final shape. It is to be mentioned that one of the adantages of the model is the simplicity and easiness of deeloping the final geometry by combining seeral basic shapes. 5. Reslts The reslts from the web-base approach for shape modeling and isalization sing object oriented programming (Jaa is presented. The Jaa Applet specify the parametric srfaces iewed as Jaa objects, allowing the ser to rotate, scale and translate the objects on the screen. The isalization of different mechanism components has been tested sing different mathematical fnctions and has proen to prodce iable shapes. The important criteria of the application hae been considered the easy implementation, fnctionality and a good rnning time. A ery good comptational time has been obtained per each mechanical component generation. Sophisticated shapes hae been generated withot increasing the file size, as it happens when polygon models based on a complicated meshing process are sed. The Web graphical interface of the application is sed to represent the shapes, shown as 3D srfaces. The Web graphical interface proide arios interactie featres, containing a toolbar, a panel describing the properties of the 3D shapes, and a small window for the final shape representation, as shown in Fig. 10. (a Fig. 10. (a Spring Srface, (b Corkscrew Srface (b In the graphical interface different mechanical component hae been generated and isalized. A spring srface, shown in Fig. 10 (a, was generated sing the next parametric fnction

18 Modeling, Simlation and Optimization Tolerance and Optimal Control 18 sin( cos( sin( cos( cos( sin( sin( sin( sin( cos( cos( cos(, ( b a r b b a b a b a b a f, ( where a, b R, and, [0, ]. Two types of seashell srfaces hae been generated sing two different kinds of parametric fnctions gien by sin( sin( 1 cos sin( 1 cos cos( 1, ( e e e e f k k k k, (3 and 1 sin( sin( cos( 1 1 cos( cos( 1 1, ( a b n c n c f, (4 where k N and, [0, ]. The isalization of the seashell srface gien by Eq.(3 is shown in Fig. 10 (b. The mating process has been illstrated sing a seashell type srface generated by a parametric fnction, a cylinder and a handle (ellipsoidal type shape. Two operations hae been applied for the mating of the preios defined parts, and the new reslting shape after each mating hae been isalized inside the Web graphical interface.

19 Web Technologies for Modelling and Visalization in Mechanical Engineering 19 (a Fig. 11. (a Seashell Srface, (b Corkscrew Cylinder (b More specifically the seashell type srface shown in Fig. 11 (a is mate with the cylinder shown in Fig. 11 (b to obtain the shape in Fig. 1 (a. (a Fig. 1. (a First Corkscrew Mating Process, (b Corkscrew Handle (b The reslting shape shown in Fig. 1 (a is mate with handle preiewed in Fig. 1(b to obtain the final shape as shown in Fig. 13. Another example is a chain generation that was accomplished sing the next two parametric fnctions and n kn0 n cos( sin(, (5 f k (, n1 cos( cos( n1 sin(

20 0 Modeling, Simlation and Optimization Tolerance and Optimal Control sn0 n cos( sin(, (6 f s (, n1 sin( n1 n cos( cos( where, [0, ], k = 1, 3, 5,..., n + 1, s =, 4, 6,..., n, and n N. The chain in Fig. 14 (a was obtained sing Eq.(5 and the parameters n 0 = n 1 = 4 and n = 3. Fig. 13. Corkscrew Final Shape (a (b Fig. 14. (a A Chain Obtained Using Eq.(5, (b A Chain Obtained Using Eq.(6 The chain in Fig. 14 (b was obtained sing Eq.(6 and the parameters n 0 n 1, n 0 = 6, n 1 = 4 and n = 3. It is to obsere that a link of the chain shown in Fig. 14 (a has a elliptical shape beside the link of the chain shown in Fig. 14 (b that hae a circlar shape. Two types of gears hae been obtained sing the mating process preiosly mentioned. The 3D isalization of two types of gears, a classical type and a conical one, are shown in Fig. 15 (a and Fig. 15(b.

21 Web Technologies for Modelling and Visalization in Mechanical Engineering 1 (a Fig. 15. (a A Classical Gear Type, (b A Conical Gear (b The gears hae been obtained mating a cylinder and a frstm of a cone with the gear tooth srface. In order to generate the gears tooth geometry the following Forier series (a ery sefl tool for generating periodic fnctions as a sm of sinsoidal components nx nx F( x 0 n cos n sin, (7 n1 k k has been sed to approximate the trapezoidal shape. The 3D trapezoidal geometry was obtained sing n = -n and n = n, with the fnction F extended in the z direction to 3 obtain the gear tooth srface. A classical cylinder is shown in Fig. 16 (a, a connector is shown Fig. 16 (b, and a cred cylinder is shown in Fig. 17 (a. (a Fig. 16. (a A Classical Cylinder, (b A Connector (b

22 Modeling, Simlation and Optimization Tolerance and Optimal Control The reslting shape shown in Fig. 17 (b is the mate obtained sing the shapes shown in Fig. 16 (a, Fig. 16 (b and Fig. 16 (c. (a Fig. 17. (a A Cred Cylinder, (b Obtained Final Shape (b 6. Conclsions In this work a web-base approach for mechanism components modeling and isalization sing object oriented programming (Jaa is proposed. A Jaa Applet which se an XML format for specifying 3D shapes (Jaa objects was deeloped. Parametric, implicit or combination between implicit and parametric fnctions defined on the graphic interface and iewed as Jaa objects, hae been sed to generate the mechanical components shapes. Different mechanism components sch as gears, springs, chains, and corkscrews, hae been generated and isalized. Simple geometry as well as the combination of the 3D shapes (sing a mating process is proided. It was demonstrated that simple mathematical fnctions represent sefl tools for shape modeling and isalization, with no increase of the application size and with a ery good comptational time. To learn, nderstand and dissect a complex mechanical system in order to perform analysis and design a 3D isalization of the mechanical components is essential. Frthermore the presented models do not indicate the limit in shape (mechanism components generation. 7. References Metaxas, D. (1996. Physics-Based Deformable Models, Klwer Academic Pblishers Sarti, A. & Tbaro, S. (001. Mltiresoltion Implicit Object Modeling, Proceedings of the Vision Modeling and Visalization, pp Lorensen, W. & Cline H. E. (1987. Marching Cbes: A High Resoltion 3-D Srface Constrction Algorithm. Compter Graphics (SIGGRAPH 87, Vol. 1, No. 4, pp Leoy M. (1990. Efficient Ray-Tracing of Volme Data, ACM Transactions on Graphics, Vol. 9, No. 3, pp Drebin, R. A.; Carpenter, L. & Hanrahan P. (1988. Volme Rendering, Compter Graphics Proceedings (SIGGRAPH 88, pp