(See related pages)
Three-dimensional modeling is a rapidly emerging area of CAD, revolutionizing the way industry integrates computers into the design process. Commercial 3-D modeling packages, available since the early 1980s, have slowly made inroads into a wide range of industries. Two-dimensional CAD has, in many ways, matured to the point where simply using a more powerful computer will not have much of an impact on how well a 2-D CAD program functions. Like traditional drafting methods, 2-D CAD programs attempt to represent objects in two dimensions; in fact, the packages were developed to be computer drafting tools, with the end product being a drawing on paper. In contrast, a 3-D computer model is more like a real object, not just a drawing of the object; 3-D CAD is considered a computer modeling tool.
3-D computer modeling is a relative newcomer to the world of engineering and technical graphics. Though, as this section points out, 3-D modeling dates back to the earliest days of CAD, it is only in the last few years that its presence has really expanded in industry. The engineering and technical graphics curriculum, by its very nature, needs to respond to changes in technology. Whereas the introduction of 2-D CAD to the curriculum largely meant shifting the methods used on the drafting boards to the computer screen, 3-D modeling demands a new set of tools and a new way of thinking of how graphics integrates into the engineering design process.
In the latest revision of this chapter, a particular focus is put on constraint-based modeling and its relationship to documentation, analysis, and manufacturing technologies.
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HISTORICAL OVERVIEW |
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| 7.1 The development of the SKETCHPAD system by Ivan Sutherland at the Massachusetts Institute of Technology (MIT) in 1962 can be considered the beginning of CAD. The revolutionary aspect of Sutherland’s system was that it allowed a user to interact graphically with the computer, via a visual display and light pen. The history of CAD software is closely linked to the development of computer hardware. The cost of mainframe computers in the 1960s and 1970s meant that only the Government and larger corporations could afford systems capable of supporting CAD software. During this period, most CAD software was developed in-house by large defense, auto, and aerospace companies, such as General Motors, Lockheed, and Boeing. In addition, because 3-D CAD is computationally much more intensive than 2-D CAD, the computational limits of even the largest mainframes of that period meant that 3-D computer modeling saw limited use. |
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WIREFRAME MODELING |
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| 7.2 Until recently, wireframe modeling was the only 3-D modeling capability available to most educational users. Though it does allow 3-D modeling concepts to be taught, it does have a number of drawbacks. Among them is the difficulty in visualizing wireframe models when the hidden edges are still visible. There is also the fact that constructing wireframe models often differs considerably from the techniques used in solid modeling. Teaching wireframe modeling can be useful for conveying a number of important concepts, though. Among them is how geometry and topology are kept separate in the database and differing types of manipulation of the model will affect these two parts of the database differently. Have students use the wireframe modeler to build an invalid model (e.g. have a face that is not closed or a dangling edge). Note to them how the wireframe modeler does not protect against this violation of topology. Section 7.4.3 on Boundary Representation modeling contains more relevant material on model validity which you may want to refer to. The use of children's construction kits such as Tinkertoys® or simply flexible wire may be useful to demonstrate the construction process in a wireframe modeler. You can also use this to demonstrate the difference between geometry (where the vertices are located) and topology (how the vertices are connected together). |
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SURFACE MODELING |
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| 7.3 One of the most important concepts is an understanding of the basic differences in how a surface modeling database is structured when compared to a wireframe or solids modeler. This affects both the types of objects which can be created and how the user interacts with the system. Many 2-D modelers use spline curve mathematics similar to that which is used in many surface modeling systems. Particularly those spline curve tools that let you interactively manipulate the control points are instructive to demonstrate to your students. You then need to explain how this technique can be expanded to create and manipulate 3-D surface patches. If you do have access to a surface modeling system, it may be useful to demonstrate (assuming the system will allow it) the problem of continuity between patches that are supposed to be part of a single surface. You can explain it as an expansion of the concept of tangency covered in Chapter 6, Engineering Geometry and Construction. In addition, you can demonstrate the problems that most surface systems have with attempting to simulate an operation like drilling a hole. These sorts of changes in topology are often difficult to execute. Even with the popularity of solid modeling systems, it is important to point out the unique capabilities which surface modeling systems have, especially when it comes to complex surface creation. |
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SOLID MODELING |
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| 7.4 Solid modeling is currently enjoying a considerable amount of popularity in the manufacturing industry and, for good reason, is making inroads in the educational setting. Solids modeling, because of the way it is designed, has the potential of providing a very intuitive interface to the user. Depending on the level of sophistication of the modeler, it also has the potential of allowing very complex models to be constructed. Even though wireframe models are constructed much as you would a 2-D drawing, a solid model is typically constructed much like you would the physical object. This fact can be used to allow physical models to be used to demonstrate a number of the principles of solid modeling. One of the requirements for the model tends to be that it be manifold. Working from the examples given in Figure 7.15, you can give the students other example objects and judge whether they are manifold. |
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| 7.4.1 Even if your modeler is capable of more, you may want to have the first lab limited to construction techniques available to a primitive modeler. Using the metaphor of 'building blocks' and demonstrations with physical geometric primitives, the concept of creating more sophisticated models through purely additive means can be demonstrated. Students can typically grasp this technique of visualizing the decomposition of more complex forms into primitives quite readily; an important skill for working with modelers of all levels of sophistication. Working with purely additive techniques with primitives also allows there to be some focus on manipulation and arrangement of objects in 3-D space. Working in 3-D space on a computer screen often takes some practice. Section 7.7 goes into more detail on some of the various viewing technques. Working with primitives also gives and opportunity to focus on construction techniques used in solid modelers. One tool that some primitive modelers have is parametric control over the geometry of the primitive. A number of the more powerful solids modelers more fully incorporate parametric techniques throughout their systems to allow for variational design capabilities. These techniques are covered in more detail in Section 7.6. |
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| 7.4.2 This section on constructive solid geometry (CSG) introduces Boolean operations, and central tool for most of the more capable 3-D modelers. A number of figures (Figures 7.20 - 7.23) are devoted to explaining Boolean operations. As is true with many concepts, the best way for students to come to understand Booleans is to do it themselves. If this is not possible, demonstrations with computer and physical models can also be effective. You may choose to begin with just union and difference and save the less used intersection operation for later. One use of demonstrating the intersection operation is that it helps drive home the fact that it is the overlap of the two bodies that is at the heart of Boolean operations. One way of demonstrating the binary tree data structure (and its unevaluated data structure) is to create a model through a series of Boolean operations and then undo them, stepping back through the tree. Just as you may have had students decompose objects into a series of primitives which could be 'glued together' to create the final model, you can now have them go through the same exercise but allow them to incorporate Boolean operations. |
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| 7.4.3 Both CSG and boundary representation (B-rep) modelers typically have similar construction tools and interfaces even if the underlying data structure is somewhat different. There all also similarities between the B-rep modeler datastructure and that used in wireframe modelers; both address the elemental geometric and topological elements of edges, vertices, and faces. One of the main differences in the fact that B-rep models understand the solidity of the models whereas the wireframe model doesn't. |
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CONSTRAINT-BASED MODELING |
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| 7.5 Among the key innovations which Pro/ENGINEER and other packages have brought to 3D modeling is the idea of having the model defined as a series of modifiable features. For example, a feature might be a hole bored through the model or a fillet added to an interior corner. Each of these features can be created independent of other features or linked so that modifications to one will update the others. The geometry of each of these features is controlled through modifiable constraints, creating a dynamic model that can be updated as the design requirements changed. |
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| 7.5.1 One of the critical early questions to ask before creating the model is where is the model data coming from and how is the model data going to be used – both in the short term and in the long run. Ideally, the model will be built so that the model behaves as expected when features are modified. This behavior should reflect the design intent of the product being modeled. That is, changes in geometry of a feature should create model feedback or further changes in the model which reflect design performance or manufacturing constraints of the product. |
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| 7.5.2 Though model data can come from many sources, it is best if you are able to re-use a model created in the same modeling system you are currently using. |
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| 7.5.3 Another important part of the planning process is understanding how the model data is going to be used once it is created. Depending on whether the model is being used for analysis, mold design, etc. will influence how the model is constructed. |
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| 7.5.4 Models should be built to reflect both the internal standards of your company and standards established by larger industry, trade, or government groups. |
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FEATURE ANALYSIS |
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| 7.6 Capturing design intent in a model is a process of defining features and the relation of features within a model. The goal is to make sure that information extracted from the model or modified versions of the model for use in other parts of the product development process accurately reflects (as much as is possible) the original intent of the designers and engineers who specified the requirements of the product. 3D modeling is a process of transforming product requirements into geometry. In a constraint-based model this geometry is dynamic, since the size and location of features in the model can easily be changed to alter model’s geometry. Figures in this section demonstrate how geometry is broken down into features and how these features can be constrained to represent the design intent of the product. The building of the model begins with the creation of the base feature. |
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FEATURE DEFINITION |
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| 7.7.1 Many features in a model can be made through the use of sweeping operations. Most CAD systems use methods of automating object generation. In a sweeping operation, a closed polygon, called a profile, is drawn on a plane and is moved or swept along a defined path for a defined length. Figures in this section give examples of how features can be swept along both linear and revolute paths. |
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| 7.7.2 All geometry in a model must be located and oriented relative to some 3D coordinate system. A workplane, is the most common type of construction geometry used to support the creation of part geometry relative to the world coordinate system. Construction geometry does not represent any of the final geometry representing the part, but instead provides a framework for guiding the construction of this part geometry. A workplane can be used in the same manner as a drawing surface. In a modeler, workplanes are typically used to orient the profile sketch used in feature generation. By adjusting the view of the model to be normal (perpendicular) to the workplane, the effect is that you can draw on the workplane as though you were looking directly down on a piece of paper. Once the base feature is created, workplanes are often oriented using geometry of the model being built. In addition to workplanes, construction axes and construction points can also be created. |
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| 7.7.3 Many features on a part model begin as a profile sketch on a workplane. This sketch will consist of a series of line elements such as straight lines, arcs, circles, or splines. Tools used for drawing this sketch will be very similar to the tools used for drawing such elements in a 2D CAD system. One important difference concerns the accuracy with which the sketch needs to be drawn. Unlike a 2D CAD drawing, the sketch does not need to be dimensionally accurate. Instead, the sketch represents the overall shape, the topology, of the profile. That is, the sketch should represent the total number of sides of the final profile, the basic shape of the elements (curved or straight), and the order in which the elements are connected together. The sketch should also represent the basic geometric relationships between the elements (parallel, tangent, etc.) within a reasonable level of accuracy. Depending on how the modeler used other characteristics of the profile, the sketch might be either a closed loop or an open loop. The definition of inside and outside is needed to specify how the profile is to interact with the existing geometry. |
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| 7.7.4 Going hand in hand with the sketching of the profile is applying constraints. Whereas the sketching defined the topology of the profile, constraining defines the geometry of the profile. This use of the word geometry refers to a more narrow definition of the term: the size, location, and orientation of geometric elements that give them an overall shape and form. The types of constraints applied to the sketch profile can be roughly divided into two categories: explicit and implicit. These two types of constraints differ as to whether the modeling system infers the constraint based on the way the sketch was drawn, or whether the operator has to explicitly apply the constraint to the sketch. Though the profile does not need to be sketched dimensionally accurate, how you sketch it will influence how implicit geometric constraints are applied. Explicit constraints, unlike implicit constraints, are applied by the user to the profile sketch. The application of explicit constraints is very much like applying dimensions in a 2D CAD system, yet they behave very differently. Figures in this section show examples of how explicit dimensional constraints can be used to drive changes in model geometry. Central to developing a strategy for constraining a profile is knowing when the profile is fully constrained, underconstrained, or overconstrained. A fully constrained profile has completely specified the geometry of a profile. Dimensional constraint parameters can be set to something other than a constant value. The ability to link constraint parameters through algebraic equations or to control values based on logic statements provides tremendous power to the modeler to both embed design intent and to automate modifications of the model. |
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| 7.7.5 With the sweep profile drawn and constrained, there remain a few more elements of the sweep which need to be defined: One part of the sweep definition that still needs to be defined is how the profile is going to be swept out to create a form in 3D space. Typically it is swept out as a linear or circular sweep. A less commonly used definition is a path-based sweep. With a path-based sweep, the profile is swept along a path defined either by an existing edge on the part model or by a path drawn by the operator. The distance that a profile is swept can be determined in a number of ways, including: blind, through all, or to next. The swept feature will either add or subtract material from the existing model depending on how the feature has been defined. Most constraint-based modelers have tools that speed up the definition of commonly used features. Rather than having to define every variable of every feature, options can be given for common design or manufactured features which either have pre-defined certain feature parameters, bundled variables together in easy to use dialogue boxes, or otherwise automated the feature definition process. |
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| 7.7.6 Though it is impossible to come up with a definitive list of ‘rules’ which should be followed when planning the modeling of every part, there are still certain characteristics of the part geometry which should be evaluated and decisions which have to be made for most parts during the planning process. One of the more important considerations is whether the parts contain lines of symmetry. Another decision, which usually has to be made, is how geometric features are distributed across part features of the model. Ultimately, the level of complexity of feature profile geometry comes down to what is a logical decomposition of the part geometry. This logic is driven by how features are defined in the design and manufacturing process. Finally, good modeling practice calls for the user to avoid certain types of feature operation in order to preserve the integrity of the model geometry and to allow for easier management of the model. |
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EDITING PART FEATURES |
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| 7.8.1 Most constraint-based modelers record the features created for a part in a tree. This tree may or may not be directly visible to the operator of the system. Features, as they are created, are placed at the bottom of the feature tree. If a new feature is created as a copy or instance of another feature in the part model, the new feature on the tree may reference the original feature. Because features can be moved to other locations up and down the feature tree, the tree cannot be considered a history of feature creation. With many modelers, however, the order in the tree is the order in which features are applied to the construction of the model. Each time a new feature is added to the model, the user explicitly rebuilds/regenerates the model, or the modeler is otherwise triggered to do a rebuild, the feature tree is traversed from top to bottom; modifying the part model with a succession of feature operations. Closely related to the idea of feature ordering is the concept of parent-child relationships between features. As in a real parent-child relationship, the child feature is dependent on the existence of its parent feature. Editing the order of features means moving features up or down in the feature tree. Dependencies between features means that features can’t be moved to every possible position on the feature tree. |
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| 7.8.2 In addition to changing the order of features within the feature tree, many of the parameters that initially defined the feature can be edited at a later time. Within the sketch profile, elements of the profile can be deleted or modified. Other parameters besides the sketch profile can also be altered. The possible parameters that might be modifiable are:
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DUPLICATING PART FEATURES |
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| 7.9 Constraint-based modelers typically allow the user to duplicate at the level of features. Whether all of the dimensional constraints are tied between the parent and the child copy is often determined by the options chosen. A common tool is an array option. With a linear array the parent feature is copied in one or two dimensions with specifications given for distances between copies and the total number of copies. With a radial array, an axis of revolution is specified along with a radius, angular displacement, and total number of copies. Another common copying process is a mirror. In this case a mirror plane is specified along with features to be copied/mirrored. |
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ASSEMBLY MODELING |
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| 7.10 More sophisticated modelers are able to create parts structures which considerably ease the process of managing assemblies. If your modeler is capable of creating a hierarchical and/or networked structure of parts, explore these capabilities. Late in the term when students might be working on final projects involving assemblies, you can introduce these techniques to your students and have them use them with their work. Most parts management tools are less than intuitive and some effort may have to be expended in explaining them to the students. When discussing instancing, comparisons can be made to 'blocks' or 'symbols' used in 2-D CAD systems. Note that one of the key advantages of using these in either 2-D or 3-D is that geometry is shared among all the instances and only new location, orientation, and scale information has to be saved. |
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ASSEMBLY MODELING |
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| 7.11 Solids can be modified in several ways. Reflection, translation, and rotation are rigid-body transformations; they do not distort the shape of the solid. Geometric transformations include:
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3-D VIEWING TECHNIQUES |
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| 7.12 The primary elements in creating a projection are the model (object), the viewer, and an image (view) plane. |
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| 7.12.1 The view camera is a metaphor used to describe the viewing process with respect to 3-D models in various CAD systems. There is a camera and an image plane onto which the model is projected. The broadcasted image is contained within a viewport on the screen, and viewports may be resizable and relocatable, or fixed, depending on the system. The image plane is oriented such that the viewing direction is perpendicular to the image plane, creating an orthographic projection. Active workplanes can be attached to the view plane of the camera, so that what you draw is seen on the screen port without distortion. With this arrangement, the u and v axes of the workplane correspond to the horizontal and vertical axes of the screen viewport, respectively. Each active workplane has its own local U,V coordinate system and its own orientation to the X,Y,Z world coordinate system. If you rotate the model, its orientation to the world coordinate system changes as will its geometry in the database. If you move the view camera, however, the camera has changed location relative to the world system, but the geometry of the model has remained untouched. Preserving the location and orientation of a model can be critical when multiple parts in an assembly are being coordinated. To get a new view of a part, rotate the camera and not the part. |
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| 7.12.2 Once a view camera has been oriented and a projection calculated, a number of auxiliary commands can be used to manipulate the view of the model. Most systems also default to setting the view camera infinitely far away from the model, creating a parallel projection. Changing a parallel projection to a perspective projection is usually a matter of setting the view camera distance to something other than infinite. |
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| 7.12.3 Many modeling systems have a default view setup depicting the three standard multiviews and a pictorial view. This setup allows viewing of many of the surfaces of the object in their true size and shape. Quite often, a student can do a majority of the model construction with just these views. The pictorial view allows for operations which span all three dimensions. To choose viewpoints for construction, or for viewing a completed model, use the same rules as for sketching or drawing, as follows: Avoid views that are close, but not quite a standard orthographic view. Such views would have the features along one primary dimension severely foreshortened and therefore very distorted. Clearly identify the features of interest, and orient the view camera to depict those features. If there are important features along all three primary dimensions, an isometric or near isometric view may be appropriate. If most of the features of interest are along only two of the three primary dimensions, chose a view that favors those two; however, retain the third dimension. If there are features on more than three sides of the model, another viewport with a view from the opposite side of the model may be required. For features that must be carefully analyzed, choose a view where the applicable faces can be seen in their true size and shape. |
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3-D MODELING AND THE DESIGN PROCESS |
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| 7.13 2-D CAD has largely been used as a direct replacement for mechanical drafting in the design and manufacture of products. 3-D modeling has the potential of effecting every facet of the design and manufacture of products. For example, by implementing centralized database built around 3-D model information, computer-integrated manufacturing (CIM) methods can be implemented. |
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| 7.13.1 Sketch modeling is the concept of using 3-D modeling early in the design process, before much of the geometry has been firmly established. Some modelers allow for the easy mockup of design alternatives through tools which support quick model construction. |
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| 7.13.2 Prototyping techniques allow physical models to be made directly from a 3-D database. In one approach, Virtual models can be created in the computer, without the time and effort necessary to build real-world equivalents. Another somewhat expensive technique, called stereo lithography, uses light beams to trace the surface, avoiding the limitations of mechanical cutter heads. |
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| 7.13.3 A hierarchical structure allows parts to be logically grouped together into sub-assemblies. In computer systems, files are stored in a hierarchical structure of directories and subdirectories. This means that the hierarchical structure of an assembly can easily be mapped to storage files on the computer. Another structure, layering, is a facility which allows the various graphics elements of a drawing to be grouped together in the database. This facility is used most often to control what is seen and/or editable on the screen and what is printed or plotted. Layering in most systems is nonhierarchical, that is, no one layer has precedence over another. This sharing across assemblies constitutes a networked hierarchy in which parts exist in several hierarchical trees. The basic geometries of standard parts are stored in a central database and are never changed. |
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| 7.13.4 As the design becomes finalized and moves towards production, changes to the design become increasingly expensive to implement. For that reason, analysis tools should be carefully chosen and used at the appropriate times during the design process. Visual inspection is an evaluation technique that is quick and easy, although very subjective. The visual inspection may involve making sure all the necessary parts are in an assembly model. Visual analysis is also used to make aesthetic decisions concerning the “look” of the model. Industrial designers and marketing professionals depend heavily on visual analysis to judge aesthetic appearance. Kinematics is an analysis technique used to evaluate the design of a mechanism; that is, an assembly of multiple parts, some which move with respect to other parts. Linking parts together into a kinematic model allows the designer to evaluate the paths of motion of various parts. This movement requires the addition of a fourth dimension, time, to the computer model. The time dimension specifies the orientation or location of a given part at a given time. One way to represent this movement over time is to use sweeping tools in the 3-D modeler to represent the path of a part. Kinematics is also used to evaluate whether any parts, movable or otherwise, clash; that is, whether the volumes representing two different parts intersect each other. Boolean intersections taken at different time intervals will show the exact topology and geometry of any overlap during movement of the mechanism. Mass properties analysis gives information such as its volume and inertial properties. When mass properties analysis is combined with kinematic information, a more sophisticated technique called a dynamic analysis can be performed on the model. An initial kinematic analysis could indicate that there are no clashes between the parts of an assembly. However, once force is applied, a dynamic analysis could show distortion in one or more parts, a distortion that causes a clash between the distorted parts and those around them. A process called discretization divides more complex geometries into simpler forms, so that how a solid responds to forces can be estimated. The process of creating a model of primitive geometries is called finite element modeling (FEM), and the analysis done on the resulting model is finite element analysis (FEA). Ergonomics examines the interaction between technology and humans. Virtual models of humans and the systems being designed can be constructed to evaluate how they interact. In addition, reach envelopes, indicating the maximum extent of arm and leg movements, and a cone of vision, indicating the field of view, can be used to help evaluate the modelled space. |
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COMPUTER-AIDED MANUFACTURING (CAM) |
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| 7.14 Three-dimensional modeling techniques can be combined with computer-aided manufacturing (CAM) capabilities to ensure that a product design satisfies the desired manufacturability requirements as closely as possible. This coordination has become increasingly important, given the limited timeframe in which most manufacturers now have to develop their products. The first step in the manufacturing of a product is process planning in which the most efficient approach for producing the product is determined. Virtual 3-D models provide information used to determine how much time, materials, and labor would be required to manufacture the product as modeled. If special types of tooling (e.g., cutters, jigs, etc.) are required, 3-D models can also be made for them. These programs control the machine tools through a process called numeric control (NC). Improvements in technology have led to the full-scale integration of computers with machine tools, and the development of computer numeric control (CNC). In the current generation of CNC technology, simulations of the tool cutting action are created and tested on virtual models before actual materials and equipment are used. The parametric equations describing a sculpted surface in a surface modeler can be used directly to create NC code. |
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DATA ASSOCIATIVITY |
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| 7.15 Often, the 3-D modeling system is the primary generator of engineering data for the product being designed. Data associativity creates a dynamic linkage of information between the 3-D model database and the supporting applications. Whenever the model is altered, the associated data in the supporting application is also automatically updated, giving all design team members the most current information to work with. Links made between the 3-D model and supporting applications can either be unidirectional or bidirectional. With unidirectional associativity, the supporting application's data can be altered by changing the 3-D model, but not vice-versa. With bidirectional associativity, changes in either the 3-D model or data in the supporting application will affect the other. |
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DOCUMENTATION |
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| 7.16 When 2-D documentation of a product is needed, it is relatively easy to generate. Traditional multiview projections of an object can typically be captured directly from the projection of the 3-D model in the viewport. Some software uses a special port to document geometry extracted from the 3-D model. |
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DATA EXCHANGE STANDARDS |
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| 7.17 Data exchange standards have been developed for the purpose of allowing databases to be shared by CAD and CAM systems and from one CAD/CAM system to another. Modern CAD/CAM systems allow information on every phase of the design and manufacturing process to be stored in a database. In direct data exchange data is exchanged either directly or indirectly. While indirect data exchange avoids many of the problems of direct exchange by requiring a vendor to develop only a single two-way translator for its system. Different data exchange standards are designed to support differing amounts of information pertaining to the design and manufacture of a product. |
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SUMMARY |
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Three-dimensional modeling is becoming the standard method in engineering for developing product designs for many industries. The advantages of using 3-D modeling versus 2-D drafting are numerous. New engineering design methods require the use of intelligent graphics; that is, graphics, such as surface and solid models, that contain important information beyond the basic geometric shapes. The more information contained in the model, the more useful the model is for designing manufacturing, marketing, and servicing a product or structure. |