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7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 7th BRAZILIAN CONGRESS ON MANUFACTURING ENGINEERING 20 a 24 de maio de 2013 – Penedo, Itatiaia – RJ - Brasil May 20th to 24th, 2013 – Penedo, Itatiaia – RJ – Brazil
DEVELOPMENT OF THE DIDACTIC SOFTWARE FOR NUMERICAL CONTROL GENERATION FROM 3D MODELS USING CAD PLATFORM AND RAPID PROTOTYPING CONCEPT Rafael Juan Costa de Miranda,
[email protected] Federal University of the Minas Gerais, Department of Mechanical Engineering 6627 Antônio Carlos Avenue, CEP 31270-901, Belo Horizonte, MG, Brazil.
Anderson Geraldo Alves de Oliveira,
[email protected] Federal University of the Minas Gerais, Department of Mechanical Engineering 6627 Antônio Carlos Avenue, CEP 31270-901, Belo Horizonte, MG, Brazil.
Helton de Freitas Cota,
[email protected] Federal University of the Minas Gerais, Department of Mechanical Engineering 6627 Antônio Carlos Avenue, CEP 31270-901, Belo Horizonte, MG, Brazil.
Paulo Roberto Cetlin,
[email protected]. Federal University of the Minas Gerais, Department of Mechanical Engineering 6627 Antônio Carlos Avenue, CEP 31270-901, Belo Horizonte, MG, Brazil.
Antônio Eustáquio de Melo Pertence,
[email protected]. Federal University of the Minas Gerais, Department of Mechanical Engineering 6627 Antônio Carlos Avenue, CEP 31270-901, Belo Horizonte, MG, Brazil.
Abstract. In this paper is presented a didactic software developed that promotes an automation for code applied in CNC machines (the G code) generation process; it is done by extracting data from 3D models created in some CAD platform. This software developed using the Visual Basic programming language is able to control the CAD system, AutoCAD®, externally by using an ActiveX type automation technology named VBA (Visual Basic for Applications). A 3D model and some user's parameters are the entries for this software and a CNC code directly applicable in CNC machines is generated as output. This code has an embedded strategy similar to that one used by the Rapid Prototyping method to build a part In this case, this part is built considering all the layers generated from the 3D model's direct slicing modeled in some CAD system. To validate the developed software; a free manufacturing process simulation software, named CNCSimulator® and physical prototype manufactured, by a CNC machine, using prototyping by material removal, were used. The developed software, the application and the used strategy to manufacture the designed part are considered the products of the present work. All the work validates the proposal to use the program as a tool in teaching subjects related to the mechanical design and manufacturing processes within the scope in the field of Engineering. The use of the AutoCAM software requires from the user the development of strategies that allow representing the geometry of a part using how many 3D models as needed to represent the external contours and cavities, such that the sum of these actions will result in the final prototype. Keywords: CAD; CAM; Rapid Prototyping; Didactic Software 1. INTRODUCTION The prototypes are study tools widely used in design activity. They provide a feedback used to decide something about the product, thus they can affect future stages in a project. They also provide some known benefits like rework cost and manufacturing startup reduction. A project financing can be ensured by showing a prototype to possible investors. This work interest object is the mechanical design. It is related to mechanical parts design. Hence the prototyping is treated as activities focused to manufacturing prototype technologies study and development. Considering prototypes like this can open a large amount of research opportunities like: virtual prototypes applications, prototyping materials, prototyping technologies, prototypes dimensional characteristics, prototypes physical properties, prototyping machines parameters optimization, path generation and so forth. Has being developing works in prototyping area, (Pertence et al., 2001) searching use the results as didactic engineering tools applied in mechanical design and manufacturing process teaching. The present work continues this LPM’s research line related to virtual prototypes applications, path generation and manufacturing technologies. Thus the didactic computational program, considered as a result, goes forward on prototyping studies applying proposed methodology for numerical code generation, directly applicable to numeric command machines. These codes describes tool path followed during manufacturing. The progress obtained in means of manufacturing technology is about the ©
Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
developed strategy to use the didactic software AutoCAM which considers the manufacturing process adopted to build a prototype. The AutoCAM software developed for didactic purposes, promotes automation code generation task used in CNC (computer numerical command) machines, the well known “G code”, by getting 3D models data obtained some CAD platform. This program developed in Visual Basic programming language, is capable to externally control CAD software, the AutoCAD® through an ActiveX’s automation technology type named VBA (Visual Basic for Applications). The general objective is to contribute to prototyping technology field manufacturing parts for support of education for Mechanical Engineering students related to subjects in the manufacturing processes and machine design areas. The CAD software control through graphical interfaces knowledge and the development of strategies for parts manufacturing considering the prototyping technique can also be considered as specific objectives. 2. DESIGN AND PROTOTYPE A prototype can be considered an object (virtual or physical) of study used in the recursive process of design whose goal is to provide a feedback on some characteristic (qualitative or quantitative) to be evaluated before taking any decision with respect to the final product. According Guangchun (2004) the need to reduce design time is a characteristic of new products design, which has successive iterations until the design of the final product; costs while increasing quality by precedence. The design can be considered as an activity or set of activities that disregard product’s user needs and taking this information as input, aiming to specify the characteristics of the product, the processes involving the manufacture, the sequence of these processes and the interaction between them. 2.1. Classification of prototypes Regarding its constitution, the prototypes can be classified as physical or virtual. The virtual models are threedimensional graphics, generated by CAD software. Currently the majority of CAD software in the market is able to emulate physical quantities as mass, force, temperature, among others used in numerical simulations such as the finite element method that is being increasingly used in the evaluation of physical properties such as deformation, mechanical stress, fluid flow and temperature. Considering the process of prototype manufacturing, also known as prototyping, can be defined as subtract and additional prototyping (rapid prototyping). 2.2. Direct slicing method The direct slicing, due to Jamieson and Hacker (1995), Dolenc and Makela (1996), Fadel and Kirschman (1996), Jurrens (1999), Chang (2004), Kumar and Choudhury (2005), Chakraborty and Choudhury ( 2007), is the direct data removal related to the tool path from 3D model, in contrast to using the STL format, developed for stereolithography material addition prototyping. The direct slicing method, applied in the AutoCAM software has the 3D model as input and a sort of 2D model sliced layers as output. This practice solves problems observed in the triangular surfaces mesh model representation, which STL is based on. 2.3. Numerical Command (NC) Numerical command is a system of numerical data interpretation that converts an abstract code intelligible to human in instructions to numerical command machine tool. A numerical command machine in turn, is nothing more than for the servo-actuator control number. The part machining program is a text file, prepared using specific syntax and format, which contains required machining instructions to build a part (ASM, 1999). The proposed methodology for numerical command code generation involves a computer program development that assists in machining planning. In means of syntax, there are DIN 66025, ISO 6983-1:1982 and ANSI (American National Standards Institute) / EIA (Electronic Industries Association) RS-274D standards for numerical control machines, which are adopted by majority manufacturers of numerical control machines although some of them have own syntax in their systems (Falck, 2008). 3. METHODOLOGY 3.1. CAD system selection There are several CAD platforms and solid modelers, in addition to AutoCAD®, capable of external control through graphical interface. The AutoCAD® software was chosen first because continuation and improvement a research carried out by Santos (2002)and Miranda (2009, 2010). It was considered that there is a well structured and developed technical literature about AutoCAD® automation technology in its various versions. So based on that literature (AutoDesk, 2003, 2006, 2012); Finkelstein, (2004 and 2007), the time required for the field of technology and thus the time for their application and obtain some results are reduced. ©
Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
Another important fact is that there are many discussion groups, forums, web sites, etc., with knowledge dissemination in terms of executable programs, source code, explanations on the functioning of controls, study cases and solutions for various applications developed. They helped the development of this research with the AutoCAD®. 3.2. The AutoCAM software Several studies were conducted in order to correctly use the syntax required, and so be able use available VBA resources in the implementation of procedures assigned to the computational program in development, from Santos (2002) results analysis and certain number of conditions established to guide AutoCAM software development. The 3D virtual model slicing method in layers was the first item studied. This method generates a series of twodimensional objects such as lines, arcs and circles, as intersection of planes with 3D model limits in the plan. The developed strategy aimed slice CAD model into equal thickness layers along an orthogonal axis to the chosen slicing plane along the whole model. The practice to slice the model in layer is similar to the one employed in rapid prototyping technologies in general, which can be observed in Park (2000), Morgan, (2001) Yang (2002), Bellini (2003) and Tong (2003). For the CAD model slicing implementation, those requests must be satisfied: know model dimensions and set location in virtual space, existence of the AutoCAD® tool (command) or set of tools to perform the slicing, and availability to perform operations in automated manner using the VBA programming environment. If there is a need to slice the virtual model into layers whose thicknesses are not equal, it is necessary to perform an initial division in different partial models of the virtual model, so this model can be sliced according to the strategy of equal layers. Prototypes with curved surfaces for example, possibly need a thickness reduction to improve physical prototype surface quality. The concepts in numerical command of part’s zero, indicated in Fig.1, a point of reference in the virtual model, and coordinate system origin, which is the reference for coordinate definition within the coordinate system adopted, were inserted in the logic of the AutoCAM software. The point set is one that has the lowest values for the model coordinates in X and Y axes, and the higher value of Z-axis coordinate of the coordinate system origin. Thus the AutoCAM software moves the reference point of the model for the origin of the coordinate system of the virtual space. The AutoCAM software also allows through its interface model translation in three axes, which by default has a zero located at the coordinate system origin, to any other point to be defined by the user. The choice of work piece (part) zero coordinates (the CAD model) was made considering the method of manufacture and used machine tool constructive characteristics to manufacture the prototype. The CAD model slicing paths for the XY, YZ and ZX planes are shown in Fig. 1. The slicing direction is the same that will be employed in the numerical code generation and therefore will be the order followed by the cutting tool to manufacture a physical prototype using this code generated by AutoCAM software. Part zero Coordinate system origin
Figure 1. Use of slicing routine implemented in AutoCAM software. (a) Virtual model example. (b) Slicing the model in XY plane example. (c) Slicing the model in YZ plane example. (d) Slicing the model in ZX plane example.
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Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
3.4. Development of AutoCAM software extraction, storage and data ordering procedures The graphical objects storage was determined by using dynamic memory allocation. At first a matrix stores a region, product of slicing model in a plane, a two-dimensional graphical structure which is endowed with certain interest properties. Part of the data ordering strategy is due to the observation of how the two-dimensional graphical objects data storage is made. It was evidenced by a series of tests slicing models of different geometries that the graphical objects data storage in variables (data structures) occurred in a random fashion. The objects form a closed contour and thus each object has a point defined by three coordinates that is common to only the other, and, each object has a point of beginning and an end. The only object of interest, such logic is not applicable is the circle. It is a closed contour by definition. Saying storage is random means the objects whose points are not coincident in consecutive positions stored inside variables means that AutoCAD VBA not necessarily consider if two objects with common coordinates, hence a point is an object’s beginning and other’s end. In data ordering process applied to AutoCAM software, the starting point is a disorderly “M” matrix of “n x 6” size, where “n” is the graphical objects number identified in the "exploded" cutting region. The two first columns correspond to the objects’ beginning coordinates. The third and fourth column; correspond to the two-dimensional graphical objects’ end coordinates. The fifth column refers to object’s position in the disordered matrix and the sixth column is reserved to indicate the beginning and end of the object. It should be noted that the process is likely to be applied to any of the categories deemed of objects (lines, arcs and circles). Ordering is made from the first identified graphical object data and details of its start and end are considered as showed Fig. 2. A column was created with "pointers" that indicate the graphical objects original positions (what is considered the beginning and what is the end). This is an important step to identify the order of each two-dimensional object and to order them and forward remove data of interest. The lines start and end coordinates are extracted, of the arc beyond the start and end coordinates, its radius and the center coordinates are extracted. Only circle radius and center coordinates are of interest. As part of the ordinance a flag (indicator element) was introduced to point orientation change (the need to change the identified graphical object start to its end to match coordinates of a close contour). In a next step, XY slicing plane, the objects are rearranged so that the element closest to the closed contour lower limit will be the first ordered matrix element. For YZ and ZX planes, a point of coordinates X or Y minimum and maximum Z was chosen to set the first ordered matrix element. In ordering does not matter if the path is clockwise or anti-clockwise, this will depend largely on what will be the first graphic object closest to, and what its first identified orientation.
Figure 2. Ordering process illustration. The direction issue during trajectory would be of interest if the program worked with models with cavities. The slicing of models with cavities generates more than one region (closed contour). Even without the sophistication to deal with internal contours to each others, will be seen later that is possible to introduce holes in the prototype using AutoCAM software. One of the ordering strategy goals is to prevent undesired tool collision with the work piece during its translation. This is accomplished by establishing a zero point in each layer, whose absolute coordinates were defined. Between one layer and another equally spaced no sudden change of geometry is observed. Regarding that a closed region end point coincides with its beginning can be said that there was a path optimization between a layer and another. To be more clear, as part is a continuous object, it is expected that the sections adjacent are not very different from each other, and therefore the vertex distance of the point set (the zero of the 3D model) is the nearest (to be matched depending on the geometry and model orientation). Another objective is the optimization of the trajectory of manufacturing of the prototype, which would reduce the time within which the tool moves but does not cut. Analyzing for example the trajectory performance in the XY plane, using the lower limit of the closed contour, there are not objects whose coordinates at X and Y are smaller than this. The most extreme case would be the coincidence X and Y coordinates. Therefore the linear tool path from minimum to the starting point in a layer is minimal or zero and not run through any graphical object closed contour. ©
Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
The balloon 1 in Fig. 3 points to the icon created for the AutoCAM software within the AutoCAD® interface. Clicking on this icon, it triggers a macro for AutoCAM software file initialization. The balloon 2 in Fig. 3 points to the first AutoCAM software feature after opening the CAD file. This feature is the model visual properties manipulation. The balloon 3 in Fig. 3, leads to the second AutoCAM software feature. This is an optional feature, the application of tool radius compensation, done via the correction of model faces. After passing by the procedures outlined by balloons 1, .2 and 3, the user must click on AutoCAM software button referring balloon 4, to the fourth procedure, also shown in Fig. 3. This action will open a new interface, pointed by balloon 5, within which parameters will be chosen and then entered to result in the numerical code generation. When using this interface (balloon 5), the first step is to extract the model main dimensions, which is so intuitive done through the button "extract dimensions". This practice provides data to the program, used in setting the model slicing in addition to returning to the user the model main dimensions. These dimensions are required by the user to determine the number of layers and therefore their thickness. Then the user must move the model’s zero for the desired point in the virtual space coordinate system. In principle, only when you click the button "change coordinates", thus the model’s zero is positioned at the coordinate system origin. In a next step the user selects the slicing plane and then sets the desired parameters to generate the numerical code. Basically the user defines the number of layers with which the model will be sliced and the number of decimal places to be used in the coordinates in the numerical code to be generated. There is also below this same interface a space for optional setting of basic machining parameters. Defining all the parameters remains the user to order AutoCAM software to generate the numerical code, which is done via the button "generate CNC code". When the program finishes it returns to a message to the user. After this message the code is available as a text file.
Figure 3. AutoCAM’s interface software 3.5. CNC Generated code validation Tests were performed in the program to verify the compliance of the generated code with the virtual model geometry and to verify the strategies implementation. The trajectory visualization was done through CNC Simulator software. The generated CNC codes are entries to the CNCSimulator® (2012) as illustrated Fig. 4. In this case, it’s no necessary the definition of the cutting parameters. From the code and the definition of some parameters as the size of a virtual block in which it promotes the view of machining evolution. 3.6. Strategy developed to use AutoCAM software in prototyping The AutoCAM software was designed to prototype by material removal, without removing filling strategy closed contours. This software is based on the virtual solid modeling in CAD as machining trajectory. Then, slicing the model into several layers, there are several closed contours. After machining completion, the final work piece is the part sum of all the layers closed contours. The program will not work with more than one single virtual model at same time as illustrated in Fig. 5. The codes are generated separately for each solid and the operations of intersection occur directly in the physical prototype in the generated codes implementation. ©
Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
#CODE START# G01 X0 Y0 G01 Z 5 G01 X 17.5 Y 30 G01 Z-5 G01 X 17.5 Y 50 G02 X 22.5 Y 50 I 2.5 J 0 G01 X 22.5 Y 30 G02 X 17.5 Y 30 I -2.5 J 0 G01 Z 5 G01 Z-5 G01 X 17.5 Y 30 G01 Z-10 G01 X 17.5 Y 50 G02 X 22.5 Y 50 I 2.5 J 0 G01 X 22.5 Y 30 G02 X 17.5 Y 30 I -2.5 J 0 G01 Z 5 G01 X 0Y 0 G01 Z 0 #CODE END#
Figure 4. Numerical code validation using the CNCSimulator® software
Figure 5. Strategy developed strategy to apply AutoCAM software in prototyping. 4. RESULTS A 3D model indicated in Fig. 6 was designed to explore AutoCAM software application by generating numerical codes and using the developed strategy to obtain a physical prototype. The physical prototype’s virtual model was divided in 13 partial models to be worked separately. Each geometry in partial models were designed with the same dimensional characteristics desired in the prototype, The models, which represent a settle of tool paths, could be designed with compensated dimensions, but intending to use the tool radius compensation, they were created with the physical prototype dimensions so its cavities and external contours. For physical prototype manufacturing the prototyping by material removal was adopted. A three- axes numerical command milling machine, developed by Silveira (2007). The AutoCAM software was developed intending its application for prototypes manufacturing for didactic purposes. As a machining operation do participate of this application, thus the available manufacturing resources, were regarded in AutoCAM software development. As the machined used has three axes, so it allow to machine in three orthogonal planes and regarding the rotation axes always been at vertical position. The physical prototype was made of expanded polystyrene (EPS). The work piece was prepared with external dimensions close to the desired ones in the end. An abrasive mounted stone (1B type, ASM, 1999, diameter 5 mm and height 25mm) was the used attached to a high speed rotary tool adapted at the CNC milling machine. The MaxNC software was used to milling machine step-motors control. The codes which were validated by using the CNCSimulator® software (2012) were executed following the designed operation machining sequence. To accelerate the prototype manufacturing, some codes were edited and grouped. Before start milling, the work piece was prepared by realizing some initial holes to avoid undesired material in the finished prototype. The milling sequence followed in physical prototype can be seen in Fig. 7 until obtain the finished physical prototyping showed in Fig. 8.
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Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
5. ACKNOWLEDGEMENTS The authors gratefully acknowledge the Postgraduate Program of Mechanical Engineering of UFMG, the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq).
(a)
(b)
Figure 6. (a) Virtual model created, to explore AutoCAM software application, (b) partial models.
Figure 7. Milling operations sequence of prototype manufacturing.
Figure 8. Finished physical prototyping.
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Associação Brasileira de Engenharia e Ciências Mecânicas 2013
7º CONGRESSO BRASILEIRO DE ENGENHARIA DE FABRICAÇÃO 15 a 19 de Abril de 2013. Penedo, Itatiaia - RJ
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Bellini,A., Güçeri,S.,2003, “Mechanical Characterization of Parts Fabricated Using Fused Deposition Modeling” Rapid Prototyping Journal, United Kingdom, v.9, n.4, p.252-264. Chang, C.C., 2004, “Rapid Prototyping Fabricated by UV Resin Spray Nozzles”, Rapid Prototyping Journal, United Kingdom, v.10, n.2, p.136-145. Chakraborty, D; Choudhury, A. R., 2007, “A Semi-Analytic Approach for Direct Slicing of Free Form Surfaces for Layered Manufacturing” Rapid Prototyping Journal, United Kingdom, v.13, n.4, p.256-264. CNCSimulator,2012 “Site oficial CNCSimulator”, 20/03/2012, Dolenc, A.; Mäkelä, I., 1996, “Rapid Prototyping From a Computer Scientist’s Point of View” Rapid Prototyping Journal, United Kingdom, v.2, n.2, p.18-25. Fadel, G. M.;Kirschman, C., 1996, “Accuracy Issues in CAD to RP translations”, Rapid Prototyping Journal, United Kingdom, v.2, n.2, p.41-48. Falck, D., “EMC Handbook G-Code Programming Basics”, 02/12/2008, . Finkelstein, E., 2004, “AutoCAD 2005 and AutoCAD 2005 LT Bible,” Ed. USA, Wiley Publishing, Inc., p.1-1251. Finkelstein, E., 2007, “AutoCAD 2008 and AutoCAD 2008 LT Bible“, Ed. USA, Wiley Publishing, Inc., p.1-1124. Guangchun, W., Huiping L., Yanjin G., Guoqun Z., 2004, “A Rapid Design and Manufacturing System for Product Development application”, Rapid Prototyping Journal, United Kingdom, v.10, n.3, p.200-206. Jamieson, R., Hacker, H., 1995, “Direct Slicing of CAD Models for Rapid Prototyping”, Rapid Prototyping Journal, United Kingdom, v.1, n.5, p.4-12. Jurrens, K. K., 1999, “Standards for the Rapid Prototyping Industry”, Rapid Prototyping Journal, United Kingdom, v.5, n.4, p.169-178. Kumar, C., Choudhury, R., 2005, “Volume Deviation in Direct Slicing”, Rapid Prototyping Journal, United Kingdom, v.11, n.3, p.174-184. Miranda, R. J. C., 2009, "Desenvolvimento de um Programa Didático Computacional Destinado à Geração de Códigos de Comando Numérico a Partir de Modelos 3D Obtidos em Plataforma CAD Considerando a Técnica Prototipagem Rápida", Dissertação (Mestrado em Engenharia Mecânica), Universidade Federal de Minas Gerais, Belo Horizonte. Miranda, R. J. C, 2010, Cetlin P. R., Pertence. A. E. M, Methodology for Spur Gears Manufacturing with Teeth Profile Modification through 3D Modeling, Journal of Manufacturing Technology Research, Volume 2, Issue 3, 4, p 1, 9. Morgan, R., Sutcliffe, C. J., O'Neill, W., 2001, “Experimental Investigation of Nanosecond Pulsed Nd:YAG Laser Remelted Pre-Placed Powder Beds”, Rapid Prototyping Journal, United Kingdom, v.7, n.3, p.159-172. Park, J., Tari, M. J., Hahn, H. T., 2000, “Characterization of the Laminated Object Manufacturing (LOM) Process”, Rapid Prototyping Journal, United Kingdom, v.6, n.1, p.36-49. Pertence, A. E. M., Santos, D. M. C., Jardim, H. V., 2001, “Desenvolvimento de Modelos Didáticos para o Ensino de Desenho Mecânico Utilizando o Conceito de Prototipagem Rápida”, In: XXIX Congresso Brasileiro de Ensino de Engenharia Mecânica, Gramado/ Rio Grande do Sul. Santos, D. M. C., 2002, “Desenvolvimento de um Programa Computacional para a Prototipagem Rápida por Retirada de Material”, Dissertação (Mestrado em Engenharia Mecânica) – Laboratório de Projetos Mecânicos, Programa de Pós-Graduação em Engenharia Mecânica, Belo Horizonte, Universidade Federal de Minas Gerais. Silveira, R. C. A., 2007, “Desenvolvimento de um Equipamento Mecânico com Controle Numérico Computadorizado para Produção de Protótipos em Escala”, Dissertação (Mestrado em Engenharia Mecânica) - Laboratório de Projetos Mecânicos, Programa de Pós-Graduação em Engenharia Mecânica, Belo Horizonte, Universidade Federal de Minas Gerais. Tong, K., Lehtihet, E. A, Joshi S., 2003, “Parametric Error Modeling and Software Error Compensation for Rapid Prototyping”, Rapid Prototyping Journal, United Kingdom, v.9, n.5, p.301-313. Yang, Y., Loh, H. T, Fuh, J. Y. H., Wang, Y. G.,2002, “Equidistant Path Generation for Improving Scanning Efficiency in Layered Manufacturing”, Rapid Prototyping Journal, United Kingdom, v.8, n.1, p.30-37. 7. RESPONSIBILITY NOTICE The authors are the only responsible for the printed material included in this paper.
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