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UNIT-III Solid modeling contains geometrical information necessary to unambiguously describe a 3D object: It is a well advanced geometric modeling technique. 3.1. GEOMETRIC MODELING • The geometric modeling is the computer compatible mathematical description of the geometry of the object. • The mathematical description allows the image of the object to be displayed and manipulated on the computer screen and also it can be stored in the memory and retrieved back and displayed on the computer screen whenever required. The geometric modeling can be classified into 1. Wire frame modeling. 2. Surface modeling 3. Solid modeling. 3.2. WIRE FRAME MODELING • Wire frame modeling is the simplest method of modeling the object. • Wire frame models can be considered as networks of inter connected lines to represent the edges of the physical objects being modeled. • A typical wire frame may consist of points, lines, arcs, circles, conies and curves. • There are two types of wire frame modeling – 21/2 and 3D modeling. • Projecting the 2D plane profile along its normal or rotating the 2D plane profile about an axes is known as 21/2 D projection. A simplest 2’ /2 D model is shown in fig 3.1

Fig 3.1. Simple model of 2! D projection Similarly, a simple 3D wire frame model is shown in fig 3.2

(a). Without hidden line removal Fig 3.2. A 3D wireframe model

(b). With hidden line removal

Advantages: 1. Wire frame models are simple and easy to create, with little computer time and memory. 2. Wire frame model form the basis for surface model. 3. CPU time required to retrieve, edit or update a wire frame model is usually small compared with surface or solid models. • •

Wire frame modeling can be considered as extension of computer aided drafting. Wire frame models provide accurate information about the location of surface discontinuity on the part. • It can be used as a basis for automatic generation of cutter paths to drive NC machine tool to manufacture component. Disadvantages: 1. There is always some ambiguity in visualizing the 3D model.

Fig 3.3 Interpretation of 3D wireframe model The wire frame model shown in fig 3.3 (a) may be interpreted as a model shown in fig 3.3 (b) or 3.3 (c) i.e. 3D wire frame model can be interpreted in more number of ways. 2. Without hidden line removal object become clumsy and difficult to understand the object. 3. Calculation of section properties and mass properties are impossible. 4. It has limited use in manufacturing and analysis. 5. Presentation of circular holes and curved surfaces are poor. 6. Interference checking will be difficult. 3.3. SURFACE MODELING • The ambiguities of wire frame modeling are overcome with surface models. • The surface modeling takes the modeling of an object one step beyond wire frame model by providing information on surfaces connecting the object edges. i.e., A surface model can be built by defining the surface on the wire frame. This is analogous to stretching a thin sheet of material over a frame work. The surfaces generated by the surface modeling are classified into (a) Flat surface - most basic feature of surface model. (b) Sculptured surfaces - based on flat face mostly used in FE analysis. (c) Sculptured surfaces based on patches. (d) Analytical surfaces (very rarely used). (e) Combination of the above types.

• • •

Simple and basic form of surface is flat surface. The most general and complex surface representations are generally known as sculptured surface. Sculptured surface means the surface produced from combining two families of curves that intersects one another in a cross-cross manner, creating network of inter connected patches.

Fig 3.4. Scultured surface Common entities used in a surface modeling software’ s are a. Plane surface. b. Ruled (lofted) surface. c. Surface of revolution. d. Tabulated surface. e. Bezier surface f. B-spline surface g. coons patch h. Fillet surface. i. Offset surface. (a) Plane surface: This is the simplest surface. It requires 3 non-coincident points on an infinite plane.

Fig 3.7 Surface of revolution (b) Ruled (lofted) surface: This is a linear surface. It interpolates linearly between two boundary curves as shown in fig.

Fig 3.6. Ruled surface

(c) Surface of revolution:

This is an axis symmetric surface that can model axisymmetric objects. It is generated by rotating a planer curve in a space about the axis of symmetry for certain angle of rotation. (d) Tabulated surface: This is a surface generated by translating a planner curve along a specified direction as shown in fig 3.8.

Fig 3.8 Tabulated surface (e) Bezier surface: The Bezier surface is generated from the basis of Bezier curve. The simple fonn of the Bezier curve is shown in fig 3.9.

The curve is represented by general equation that

Polygon P is known as control polygon. The points Po. P1, P2 and P3 are known as control points. Since there are four control points, the curve which represents a cubic curve (order of curve is (n —1) control points). The curve passes through only first and last point P and P Using the same concept, the simple bezier surface can be generated as shown in fig 3.10.

Fig 3.10. Bezier surface Similar to the Bezier curve, it does not pass through all given data points. It is a general surface that pennits, twist and kinks. The Bezier surface allows only global control of the surface. (1) B-spline surface: The B-spline surface is generated from the basis of B-spline curve. The simple form of the B splineis shown in fig 3.11.

Fig 3.11. B-spline curve The general equation of the B-spline curve is in the fonn of

Fig 3.14. Filleted surface

(i) Offset surface: • Existing surfaces can be offset to create new ones identical in shape but have different dimension. • The new surface will be created at a faster rate. For example, to create a holding cylinder, first inner or outer cylinder can be created using a cylinder command. • Based on this surface, other cylindrical surface can be created by using offset command. This is shown in fig 3.15

Fig 3.15. Offset surface Application: • Surface modeling can be used generally to model exterior shell objects like sheet metal works and thin moulded plastic parts. • Other areas of applications of surface modeling are: 1. Body panels of passenger cars, structural components of aircraft and marine structures. 2. Plastic containers, telephones, impellers of pump and turbine, development of surface for cutting shoe leather, glass marking etc. Advantages: 1. Unambiguitiveness in the interpretation of object is less than wire frame models by using the provision of hidden line removal. 2. Surface modeling can be used to perform interference checking (i.e. penetration of one part with other). 3. Surface modeling can be used to check the aesthetic look of the product (By using coloring and shade facilities).

• •

In Bezier curves, the degree of the polynomials is determined by number of track points or control points where as in B-spline curve degree may be specified independent of number of control points, as shown in fig 3.11. The B-spline curve will have local control.

Fig 3.12. B-spline surface

•

B-spline surface that can approximate or interpolate given data points as shown in fig 3.12. • It is a general surface like the Bezier surface but with the advantage of pennitting local control of the surface. (g) Coons patch: The coons patch is used to create a surface using curves that forms closed boundaries.

(h) Fillet surface: This is a B-spline surface that blends two surfaces together as shown in fig 3.14. Fig 3.13. Coons patch 4. As the surface models precisely define the part geometry such as surface and boundaries, they can help to produce NC machine instructions automatically. 5. Complex surface features like shoes, car panels, doors etc can be created very easily. Disadvantages: 1. Interpretation of surface model is still ambiguous. 2. Surface models require more computational time when compared to wire frame models. 3. More skill is required for surface modeling. 4. Mass properties such as weight, volume and moment of inertia cannot be derived from surface models. 5. Surface models cannot be used as a basis for finite element analysis for stress strain prediction. 6. Neither hidden lines can be easily removed nor internal sections can be easily displayed. 3.4. SOLID MODELING • Solid modeling is the most powerful 3D modeling technique. • There are more number of methods available to generate solid models. • Out of which two basic approaches are important from our subject point of view. They are (1) Constructive solid geometry (CSG). (2) Boundary representation (B-rep.)

3.4.1. Constructive solid geometry: A solid modeler has a library of set of basic element shapes known as primitives like, cuboid, cylinder, sphere, cone, wedge, torus etc (as shown in fig 3.16).

Fig 3.17 Types of Boolean operation • • • •

In this approach, the physical objects are modeled by combining these primitives by a set of Boolean operations. The type of Boolean operations is used in CSG are Union (U), difference and intersection (n). These Boolean operations are explained in fig 3.17. Here, directed graph (Binary tree) scheme is used to store the model in the data structure. The general form of the tree-type data structure used in CSG approach is shown in fig 3.18.

Fig 3.18 General tree type data structure • Any node may have one parent node and two-child node. The root node (R) has no parent and leaf node (L) has no children. • For example to create a model as shown in fig 3.19, four primitives — two rectangular blocks and two cylinders are required. • To create the final object following Boolean operation has to be carried out.

Fig 3.19 Tree structure of model Advantages: 1. Since, the data to be stored are less, memory required will be less. 2. Create fully valid geometrical solid model. 3. Complex shapes may be developed relatively quicker with the available set of primitives. 4. Less skill is enough. Disadvantages: 1. More computational effort and time are required whenever the model is to be displayed in the screen. 2. Getting fillet, chamfer and taperness in the model is very difficult. 3.4.2. Boundary representation (B - rep.) This approach is widely used in most of solid modelers. The solid model created by using B- rep technique may be stored in graph based on data structure system. This is illustrated with an simple example of tetrahedron shown in fig 3.20.

Fig 3.20. Illustration of B-rep data structure of tetrahedron

• • •

The tetrahedron is composed of four vertices namely A, B, C and D. The co-ordinate of these vertices is stored in the database. The fig. (b) shows how the vertices are connected to form edges (a, b, c, d, e and f) and how these edges are connected together to form the face (ABC, BCD, ACD, ABD) which makes the complete solid of tetrahedron. These connectivities to form the solid are popularly known as “topology”. • In B-rep modeler, in addition to store the topology of solid, topological consistency of the models is also carried out in order to create geometrically valid solid models. • For topological consistency, certain rules have to be followed. • They are (a) Faces should be bound by a simple loop of edges and should be not intersected by itself (b) Each edge should exactly adjoin two faces and each edge should have a vertex at each end. (c) At least three edges should meet at each vertex.

Fig 3.21. Elements of topology (a) For bodies without holes should satisfy Euler’ s rule.

• • • • • •

Even if the topological consistency is achieved, in some cases like solids having concave faces will not give geometrically valid solid. The B-rep scheme is more widely used because In CSG the number of basic primitives available are limited. The performance of B-rep scheme is very much superior to that of CSG scheme for complex engineering models. Conversion of CSG to B-rep is possible, but conversion from B-rep to CSG is not possible. Combining the wire frame and surface model is possible only through B-rep solid representation.

Advantages: 1. Computational effort and time required to display the model are less compared with CSG. 2. Combining wire frame and surface model are possible. 3. Complex engineering objects can be modeled very easily compared with CSG. 4. Since the topology and geometry are treated separately, incorporating new geometries in the existing model is easy. 5. It is particularly suitable for modeling part having internal symmetry. Disadvantages: 1. The data to be stored is more and hence it requires more memory. 2. Some times geometrically valid solids are not possible.

3.5. FUNCTIONS OF SOLID MODELING

Fig 3.22. Functions of solid modeling.

Fig 3.26 Structural parameterization In the above example shown in fig 3.26, it can be seen that both topology (no. of holes) and size of flange are varied. Steps followed: 1. Input numerical value for parametric variables. 2. Calculate the other dimensions of the components/parts for either geometrical or structural parameterization. Automatic generation of history of commands (for geometrical entities, Boolean operation etc) to create the geometric modeling of the object.

Advantages: The design modifications can be done easily. The effort of the designer can be reduced. It can be used where repeated tedious design works involved. Error in the design can be reduced. Time for modeling the design change can be reduced. 3.8.2. Feature based modeling:

Fig 3.27. Types features •

First of all, we should know what is the meaning of features. Feature has two meaning (1) Geometrical meaning (2) Engineering meaning. • Shapes such as drilled holes, ribs, bosses in castings, grooves in the shaft etc are considered as features from geometrical meaning. And, from the engineering meaning, feature means related machining operations or attributes of components or data of the components like material properties. • More widely used definition of feature is that it is a prototypical shape with some engineering significance or meaning. (1) Techniques of feature based modeling: • Features can be considered as higher-level primitives which can be used to model the object. • There are two techniques available to model the object by using feature facilities. • The first one is known as “Destructive solid geometry”. Here, features typically represent the machining operations (Ex. Driller/mill), which subtracts material from the raw material or blank piece from which object is produced. • Example: the fig 3.28, explain the steps involved in making such feature on the work piece.

Fig 3.28 Example of material subtraction by destructive solid modeling • •

These operations can be considered as machining with computers. This technique helps to generate automated process plan. The second technique of constructing the model by adding features with the base model is known as “Constructional design by features”. In the fig 3.29, shows the design of plastic moudling by feature.

Fig 3.29. Design of a plastic moulding by features Most of the features are developed by solid modeling approaches B-rep, CSG and combination of both and these features are stored in the library of a solid modeler. 2. ClassWcation: Library or user defined feature may be classified into 1. Elementary - Simple features 2. Composite — Two or more elementary features added together. The composite feature further classified as 1. Patterns-Repeated usage of simple feature. Example: Bolt holes set of gear teeth etc. 2. Compound-Which is built from simple features. Example: Counter sink- bored holes.

The features are also classified into 1. Implicit/unevaluated feature: - In this, the full detail of the feature will not be given but only essential details will be given. Other data are calculated from essential details. Example: For gears —only module and number of teeth are given. 2. Explicit/Evaluated feature: All the details of the feature will be given. Advantages: a. Rapid designing of the components using standard features are possible. b. Assisting the integration of CAD/CAM. Example: Feature based on models are very much useful in computer aided process planning works where the sequence of operations required to manufacture the component will be generated automatically. This is possible only when the computers are able to recognize these from CAD model popularly known as feature recognition. 3.8.3. Other general features of modeling softwares: 1. Sketching 2. Part creation 3. Assembling 4. Documentation 1. Sketching: Many of 3D engineering solids are created from 2D sketch of cross-section of the solid. This is explained with simple examples in fig 3.30.

Fig 3.30.

2. Part creation: Creates each individual components of assembly using the features, Bookan operators available with modeling software. 3. Assembling: Each individual developed component is assembled together. Interference checking and animation facilities can be utilized for checking the design. 4. Documentation: Finally, hardcopy of individual components and assembly may be taken out. Most of the modelers have semi-automatic tolerance facility. 3.9. INTERFACING IN CAD-CAM ENVIRONMENT Interfacing means compatible ways of transferring the data from one system to another system and vice versa. There are 3 types of interfacing in CAD-CAM environment. They are 1. Hardware-Hardware interface. 2. Hardware-Software interface. 3. Software-Software interface. 1. Hardware-Hardware interface: • It can be classified into two types (1) Internal interface. (2) External interface. • The computer CPU is connected with Input/Output units and memory by hardware link. This is known as internal interface. • The computers are connected to variety of machines and processes as well as to computers of different makes are known as external interface. This is once again a category into serial and parallel interfacing. a) Serial interface: • In serial interface, the communication is at the rate of one bit at a time. RS 232C connection which is a standard of Electronic Industries Association (ETA) is used for serial interfacing. • The advantage of this technique is only fewer components are required for interfacing and also it is easy to install. • The disadvantage is lower speed of communication. Example moderns and Terminals are connected by serial interfacing technique. b) Parallel interfacing: The data is communicated as one packet (one or several bytes properly packed). Simultaneously, it results in higher data transmission rate. The disadvantage is that it requires more data lines. Example: Data acquisition and some printers require parallel interfacing technique. 2. Hardware-Software interface: Softwares are used to link the hardware of computer with software program. Example: The operating system is used to interface the hardware and application program. 3. Software-Software interface: It is necessary to export the model data from a CAD package to other packages like analysis, NC programming or other packages. One of the ways to achieve this is done by writing a neutral file formats shown in fig3.31.

1. IGES —Initial Graphics Exchange Specification. 2. DXF —Data Exchange Format. 3. STEP —Standard for Exchange of Product data. 4. PDES —Product Data Exchange Specification

Fig 3.31. Exchange of data file format For online CAD data transfer between two computers, the following five steps are involved as shown in fig 3.32. 1. Choose a data exchange format common to both systems. 2. Select a common data transfer mode. 3. Convert source data into common data exchange format. 4. Transfer the converted data into the receiver format

• •

Fig 3.32. Method of CAD model data transfer There is always some loss while transferring data between systems. To reduce the data loss, CAD softwares have their own data exchange system for example Ansys /AutoCAD, Ansys/Pro-E, NISA1AutoCAD, NISAIPro-E, etc.

3.10. DESIGN ANALYSIS • The computer can be used to aid the analysis work such as stress-strain analysis, heat transfer analysis, etc. • The analysis can be done either by using specific program generated for it or by using general purpose software commercially available in the market. • The geometric models generated can be used for the analysis by properly interfacing the modeling software with the analysis software. Two types of important engineering analysis are 1. Analysis for mass properties. 2. Finite element analysis (FEA). • By using mass properties analysis, properties of solid object can be determined, such as surface area, weight volume, C.G. and Ml. Similarly, for plane surfaces perimeter, Area and ML can be determined. • Finite element analysis is the most powerful feature of a CAD system. Here, the object is divided into a large number of finite elements. • The entire object can be analysed for stress-analysis, heat transfer analysis etc. For solving the FEA problems, computers with larger memory and computational capabilities are required.

The graphical output of FEA is displayed in the computer terminal for better understanding of results through visualization. Designer can modify/redesign the model, and using FEA software analysis can be done easily.

First 72 columns are data columns. 73 to 80 columns are for the sequence number (utilized as pointer) with identification for data. An IGES file consists of the following file sections. They are. (i). Start section - for initializing IGES file. (ii). Global section — they are necessary to translate the file from any graphic software to other. (iii). Directory section:- Reference the entities and necessary data required for entities which are given in the next section. (iv). Parameter data section: - Constraint details, co-ordinate value, text and so on. (v) Termination section: - Marks the end of file. (d) PDES-Product Data Exchange Specification: To overcome limitations in application of IGES as standard for CAD data exchange, new standard were developed by IGES organization in 1984 called PDES-Product Data Exchange Specification. (e) CAD * I —Computer Aided Design Interface: It is also a CAD data exchange format developed by European country Research project group. (f) STEP- Standard for Exchange of Product Model Data: New CAD data standard is developed through worldwide effort known as STEP in year 1997. The STEP overcomes many of the limitations ol’ IGES. (g) CGM-Computer Graphics Metafile: It establishes a format for device independent definition, to capture. store and transfer any Graphic image. Here picture is described as collection of graphic entities such as lines, polv lines, arc, ellipse, filled areas, texts, etc and attributes such as colour, line wide, text style etc. (i,) Bitmaps: Each pixel of image will be assigned with number equal to colour on that pixel. Now a days. 3 2bits are used to represent the colour of the pixel. Some of standard formats are (i) BMP-Windows Bitmap format. (ii) JPEG-Joint Photographic Expert Group. (iii) GIF- Graphic Interchange Format (iv) TIFF-Tagged Image File Format

TWO MARKS QUESTIONS 1. Define geometric modeling. 2. What is meant by lofted surface? 3. Local surface variation on the model can be done on __________ B - spline surface. 4. Car doors and panels can be done with _________ modeling. 5. Name the two basic approaches followed in solid modeling. 6. List the basic entities available in CSG approach of solid modeling. 7. Name the data structure used in CSG. 8. What are the Boolean operations available in CSG? 9. Out of CSG and B-rep approaches of solid modeling which approach requires more memory. 10. Out of CSG and B-rep approaches of solid modeling which approach requires more computational time? 11. Name the data structure used in B-rep. 12. Out of CSG and B-rep approaches of solid modeling which approach will be used for creating complex geometries? 13. What is the use of topological consistency checking in B-rep? 14. State Euler rule for topological checking. 15. State Euler-Poincare formula for topological checking. 16. In which solid modeling approach, the integration of wire frame and surface modeling can be done. 17. List some of the solid modeling software? 18. Define parametric modeling. 19. What are the types of parametric modeling? 20. What is meant by feature? Feature has two meaning 21. Name the two types of feature based modeling technique. 22. What is meant Implicit/unevaluated feature? 23. List the genera/features of a solid modeler. 24. Define computer interfacing. 25. List the types of interfacing in CADCAM environment. 26. Classify hardware-hardware interfacing. 27. List some of neutral file format to achieve software interfacing? 28. What is PDES? 29. What is STEP? 30. Briefly explain the term constructive solid geometry (CSG). 31. How a model is defined in B-rep? 32. What is DXF? 33. What is IGES? 34. Classify wire frame modeling.

REVIEW QUESTIONS 1. Define and classify geometrical modeling? 2. Explain wire frame modeling and discuss its advantages and disadvantages? 3. Define surface modeling? List its applications, benefits and drawbacks. 4. V/hat are the common entities available in a typical surface modeler? Discuss the use of each entity with examples. 5. Reason out why local control of surface is not possible with Bezier surface, where as it is possible in B-spline surface. 6. What are the two important basic approaches followed in solid modeling? Discuss each of them in detail? 7. B-rep solid modeling approaches is better than CAG solid modeling approach why? 8. Discuss the data structure used in CSG and B-rep solid modeling techniques? 9. What is meant by topological consistency? Discuss the rules to be followed to get geometrical valid solid models? 10. Enumerate advantages of solid modeling/geometric modeling? Technique. 11. Explain the salient features available in typical solid modeler. 12. Define parametric modeling. Explain two types of parameterization and steps followed in parametric modeling. Also discuss its benefits. 13. What is meant by feature? Classify the features? 14. Explain two techniques followed in feature based modeling with an example to each. 15. What are the types of design analysis that can be carried out using a solid model? 16. Define computer interfacing. Classify and explain each type of interfacing with an example. 17. Classify the graphic standards? Name some important standards used in plotting and CAD data exchange. 18. What are the various schemes for representing solid object? Discuss boundary representations (B-rep) technique. 19. What is a DXF file? Explain the general DXF file structure? 20. What are different types of geometric modeling? Compare 2D and 3D wire frame models. 21. What is geometric modeling? Explain the geometric models, bringing out their limitations and applications. 22. What are the differences between surface modeling and solid modeling? 23. Explain the technique of CSG for solid modeling. 24. With suitable examples explain how solid model are generated using Boolean operation.

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Fig 3.1. Simple model of 2! D projection Similarly, a simple 3D wire frame model is shown in fig 3.2

(a). Without hidden line removal Fig 3.2. A 3D wireframe model

(b). With hidden line removal

Advantages: 1. Wire frame models are simple and easy to create, with little computer time and memory. 2. Wire frame model form the basis for surface model. 3. CPU time required to retrieve, edit or update a wire frame model is usually small compared with surface or solid models. • •

Wire frame modeling can be considered as extension of computer aided drafting. Wire frame models provide accurate information about the location of surface discontinuity on the part. • It can be used as a basis for automatic generation of cutter paths to drive NC machine tool to manufacture component. Disadvantages: 1. There is always some ambiguity in visualizing the 3D model.

Fig 3.3 Interpretation of 3D wireframe model The wire frame model shown in fig 3.3 (a) may be interpreted as a model shown in fig 3.3 (b) or 3.3 (c) i.e. 3D wire frame model can be interpreted in more number of ways. 2. Without hidden line removal object become clumsy and difficult to understand the object. 3. Calculation of section properties and mass properties are impossible. 4. It has limited use in manufacturing and analysis. 5. Presentation of circular holes and curved surfaces are poor. 6. Interference checking will be difficult. 3.3. SURFACE MODELING • The ambiguities of wire frame modeling are overcome with surface models. • The surface modeling takes the modeling of an object one step beyond wire frame model by providing information on surfaces connecting the object edges. i.e., A surface model can be built by defining the surface on the wire frame. This is analogous to stretching a thin sheet of material over a frame work. The surfaces generated by the surface modeling are classified into (a) Flat surface - most basic feature of surface model. (b) Sculptured surfaces - based on flat face mostly used in FE analysis. (c) Sculptured surfaces based on patches. (d) Analytical surfaces (very rarely used). (e) Combination of the above types.

• • •

Simple and basic form of surface is flat surface. The most general and complex surface representations are generally known as sculptured surface. Sculptured surface means the surface produced from combining two families of curves that intersects one another in a cross-cross manner, creating network of inter connected patches.

Fig 3.4. Scultured surface Common entities used in a surface modeling software’ s are a. Plane surface. b. Ruled (lofted) surface. c. Surface of revolution. d. Tabulated surface. e. Bezier surface f. B-spline surface g. coons patch h. Fillet surface. i. Offset surface. (a) Plane surface: This is the simplest surface. It requires 3 non-coincident points on an infinite plane.

Fig 3.7 Surface of revolution (b) Ruled (lofted) surface: This is a linear surface. It interpolates linearly between two boundary curves as shown in fig.

Fig 3.6. Ruled surface

(c) Surface of revolution:

This is an axis symmetric surface that can model axisymmetric objects. It is generated by rotating a planer curve in a space about the axis of symmetry for certain angle of rotation. (d) Tabulated surface: This is a surface generated by translating a planner curve along a specified direction as shown in fig 3.8.

Fig 3.8 Tabulated surface (e) Bezier surface: The Bezier surface is generated from the basis of Bezier curve. The simple fonn of the Bezier curve is shown in fig 3.9.

The curve is represented by general equation that

Polygon P is known as control polygon. The points Po. P1, P2 and P3 are known as control points. Since there are four control points, the curve which represents a cubic curve (order of curve is (n —1) control points). The curve passes through only first and last point P and P Using the same concept, the simple bezier surface can be generated as shown in fig 3.10.

Fig 3.10. Bezier surface Similar to the Bezier curve, it does not pass through all given data points. It is a general surface that pennits, twist and kinks. The Bezier surface allows only global control of the surface. (1) B-spline surface: The B-spline surface is generated from the basis of B-spline curve. The simple form of the B splineis shown in fig 3.11.

Fig 3.11. B-spline curve The general equation of the B-spline curve is in the fonn of

Fig 3.14. Filleted surface

(i) Offset surface: • Existing surfaces can be offset to create new ones identical in shape but have different dimension. • The new surface will be created at a faster rate. For example, to create a holding cylinder, first inner or outer cylinder can be created using a cylinder command. • Based on this surface, other cylindrical surface can be created by using offset command. This is shown in fig 3.15

Fig 3.15. Offset surface Application: • Surface modeling can be used generally to model exterior shell objects like sheet metal works and thin moulded plastic parts. • Other areas of applications of surface modeling are: 1. Body panels of passenger cars, structural components of aircraft and marine structures. 2. Plastic containers, telephones, impellers of pump and turbine, development of surface for cutting shoe leather, glass marking etc. Advantages: 1. Unambiguitiveness in the interpretation of object is less than wire frame models by using the provision of hidden line removal. 2. Surface modeling can be used to perform interference checking (i.e. penetration of one part with other). 3. Surface modeling can be used to check the aesthetic look of the product (By using coloring and shade facilities).

• •

In Bezier curves, the degree of the polynomials is determined by number of track points or control points where as in B-spline curve degree may be specified independent of number of control points, as shown in fig 3.11. The B-spline curve will have local control.

Fig 3.12. B-spline surface

•

B-spline surface that can approximate or interpolate given data points as shown in fig 3.12. • It is a general surface like the Bezier surface but with the advantage of pennitting local control of the surface. (g) Coons patch: The coons patch is used to create a surface using curves that forms closed boundaries.

(h) Fillet surface: This is a B-spline surface that blends two surfaces together as shown in fig 3.14. Fig 3.13. Coons patch 4. As the surface models precisely define the part geometry such as surface and boundaries, they can help to produce NC machine instructions automatically. 5. Complex surface features like shoes, car panels, doors etc can be created very easily. Disadvantages: 1. Interpretation of surface model is still ambiguous. 2. Surface models require more computational time when compared to wire frame models. 3. More skill is required for surface modeling. 4. Mass properties such as weight, volume and moment of inertia cannot be derived from surface models. 5. Surface models cannot be used as a basis for finite element analysis for stress strain prediction. 6. Neither hidden lines can be easily removed nor internal sections can be easily displayed. 3.4. SOLID MODELING • Solid modeling is the most powerful 3D modeling technique. • There are more number of methods available to generate solid models. • Out of which two basic approaches are important from our subject point of view. They are (1) Constructive solid geometry (CSG). (2) Boundary representation (B-rep.)

3.4.1. Constructive solid geometry: A solid modeler has a library of set of basic element shapes known as primitives like, cuboid, cylinder, sphere, cone, wedge, torus etc (as shown in fig 3.16).

Fig 3.17 Types of Boolean operation • • • •

In this approach, the physical objects are modeled by combining these primitives by a set of Boolean operations. The type of Boolean operations is used in CSG are Union (U), difference and intersection (n). These Boolean operations are explained in fig 3.17. Here, directed graph (Binary tree) scheme is used to store the model in the data structure. The general form of the tree-type data structure used in CSG approach is shown in fig 3.18.

Fig 3.18 General tree type data structure • Any node may have one parent node and two-child node. The root node (R) has no parent and leaf node (L) has no children. • For example to create a model as shown in fig 3.19, four primitives — two rectangular blocks and two cylinders are required. • To create the final object following Boolean operation has to be carried out.

Fig 3.19 Tree structure of model Advantages: 1. Since, the data to be stored are less, memory required will be less. 2. Create fully valid geometrical solid model. 3. Complex shapes may be developed relatively quicker with the available set of primitives. 4. Less skill is enough. Disadvantages: 1. More computational effort and time are required whenever the model is to be displayed in the screen. 2. Getting fillet, chamfer and taperness in the model is very difficult. 3.4.2. Boundary representation (B - rep.) This approach is widely used in most of solid modelers. The solid model created by using B- rep technique may be stored in graph based on data structure system. This is illustrated with an simple example of tetrahedron shown in fig 3.20.

Fig 3.20. Illustration of B-rep data structure of tetrahedron

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The tetrahedron is composed of four vertices namely A, B, C and D. The co-ordinate of these vertices is stored in the database. The fig. (b) shows how the vertices are connected to form edges (a, b, c, d, e and f) and how these edges are connected together to form the face (ABC, BCD, ACD, ABD) which makes the complete solid of tetrahedron. These connectivities to form the solid are popularly known as “topology”. • In B-rep modeler, in addition to store the topology of solid, topological consistency of the models is also carried out in order to create geometrically valid solid models. • For topological consistency, certain rules have to be followed. • They are (a) Faces should be bound by a simple loop of edges and should be not intersected by itself (b) Each edge should exactly adjoin two faces and each edge should have a vertex at each end. (c) At least three edges should meet at each vertex.

Fig 3.21. Elements of topology (a) For bodies without holes should satisfy Euler’ s rule.

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Even if the topological consistency is achieved, in some cases like solids having concave faces will not give geometrically valid solid. The B-rep scheme is more widely used because In CSG the number of basic primitives available are limited. The performance of B-rep scheme is very much superior to that of CSG scheme for complex engineering models. Conversion of CSG to B-rep is possible, but conversion from B-rep to CSG is not possible. Combining the wire frame and surface model is possible only through B-rep solid representation.

Advantages: 1. Computational effort and time required to display the model are less compared with CSG. 2. Combining wire frame and surface model are possible. 3. Complex engineering objects can be modeled very easily compared with CSG. 4. Since the topology and geometry are treated separately, incorporating new geometries in the existing model is easy. 5. It is particularly suitable for modeling part having internal symmetry. Disadvantages: 1. The data to be stored is more and hence it requires more memory. 2. Some times geometrically valid solids are not possible.

3.5. FUNCTIONS OF SOLID MODELING

Fig 3.22. Functions of solid modeling.

Fig 3.26 Structural parameterization In the above example shown in fig 3.26, it can be seen that both topology (no. of holes) and size of flange are varied. Steps followed: 1. Input numerical value for parametric variables. 2. Calculate the other dimensions of the components/parts for either geometrical or structural parameterization. Automatic generation of history of commands (for geometrical entities, Boolean operation etc) to create the geometric modeling of the object.

Advantages: The design modifications can be done easily. The effort of the designer can be reduced. It can be used where repeated tedious design works involved. Error in the design can be reduced. Time for modeling the design change can be reduced. 3.8.2. Feature based modeling:

Fig 3.27. Types features •

First of all, we should know what is the meaning of features. Feature has two meaning (1) Geometrical meaning (2) Engineering meaning. • Shapes such as drilled holes, ribs, bosses in castings, grooves in the shaft etc are considered as features from geometrical meaning. And, from the engineering meaning, feature means related machining operations or attributes of components or data of the components like material properties. • More widely used definition of feature is that it is a prototypical shape with some engineering significance or meaning. (1) Techniques of feature based modeling: • Features can be considered as higher-level primitives which can be used to model the object. • There are two techniques available to model the object by using feature facilities. • The first one is known as “Destructive solid geometry”. Here, features typically represent the machining operations (Ex. Driller/mill), which subtracts material from the raw material or blank piece from which object is produced. • Example: the fig 3.28, explain the steps involved in making such feature on the work piece.

Fig 3.28 Example of material subtraction by destructive solid modeling • •

These operations can be considered as machining with computers. This technique helps to generate automated process plan. The second technique of constructing the model by adding features with the base model is known as “Constructional design by features”. In the fig 3.29, shows the design of plastic moudling by feature.

Fig 3.29. Design of a plastic moulding by features Most of the features are developed by solid modeling approaches B-rep, CSG and combination of both and these features are stored in the library of a solid modeler. 2. ClassWcation: Library or user defined feature may be classified into 1. Elementary - Simple features 2. Composite — Two or more elementary features added together. The composite feature further classified as 1. Patterns-Repeated usage of simple feature. Example: Bolt holes set of gear teeth etc. 2. Compound-Which is built from simple features. Example: Counter sink- bored holes.

The features are also classified into 1. Implicit/unevaluated feature: - In this, the full detail of the feature will not be given but only essential details will be given. Other data are calculated from essential details. Example: For gears —only module and number of teeth are given. 2. Explicit/Evaluated feature: All the details of the feature will be given. Advantages: a. Rapid designing of the components using standard features are possible. b. Assisting the integration of CAD/CAM. Example: Feature based on models are very much useful in computer aided process planning works where the sequence of operations required to manufacture the component will be generated automatically. This is possible only when the computers are able to recognize these from CAD model popularly known as feature recognition. 3.8.3. Other general features of modeling softwares: 1. Sketching 2. Part creation 3. Assembling 4. Documentation 1. Sketching: Many of 3D engineering solids are created from 2D sketch of cross-section of the solid. This is explained with simple examples in fig 3.30.

Fig 3.30.

2. Part creation: Creates each individual components of assembly using the features, Bookan operators available with modeling software. 3. Assembling: Each individual developed component is assembled together. Interference checking and animation facilities can be utilized for checking the design. 4. Documentation: Finally, hardcopy of individual components and assembly may be taken out. Most of the modelers have semi-automatic tolerance facility. 3.9. INTERFACING IN CAD-CAM ENVIRONMENT Interfacing means compatible ways of transferring the data from one system to another system and vice versa. There are 3 types of interfacing in CAD-CAM environment. They are 1. Hardware-Hardware interface. 2. Hardware-Software interface. 3. Software-Software interface. 1. Hardware-Hardware interface: • It can be classified into two types (1) Internal interface. (2) External interface. • The computer CPU is connected with Input/Output units and memory by hardware link. This is known as internal interface. • The computers are connected to variety of machines and processes as well as to computers of different makes are known as external interface. This is once again a category into serial and parallel interfacing. a) Serial interface: • In serial interface, the communication is at the rate of one bit at a time. RS 232C connection which is a standard of Electronic Industries Association (ETA) is used for serial interfacing. • The advantage of this technique is only fewer components are required for interfacing and also it is easy to install. • The disadvantage is lower speed of communication. Example moderns and Terminals are connected by serial interfacing technique. b) Parallel interfacing: The data is communicated as one packet (one or several bytes properly packed). Simultaneously, it results in higher data transmission rate. The disadvantage is that it requires more data lines. Example: Data acquisition and some printers require parallel interfacing technique. 2. Hardware-Software interface: Softwares are used to link the hardware of computer with software program. Example: The operating system is used to interface the hardware and application program. 3. Software-Software interface: It is necessary to export the model data from a CAD package to other packages like analysis, NC programming or other packages. One of the ways to achieve this is done by writing a neutral file formats shown in fig3.31.

1. IGES —Initial Graphics Exchange Specification. 2. DXF —Data Exchange Format. 3. STEP —Standard for Exchange of Product data. 4. PDES —Product Data Exchange Specification

Fig 3.31. Exchange of data file format For online CAD data transfer between two computers, the following five steps are involved as shown in fig 3.32. 1. Choose a data exchange format common to both systems. 2. Select a common data transfer mode. 3. Convert source data into common data exchange format. 4. Transfer the converted data into the receiver format

• •

Fig 3.32. Method of CAD model data transfer There is always some loss while transferring data between systems. To reduce the data loss, CAD softwares have their own data exchange system for example Ansys /AutoCAD, Ansys/Pro-E, NISA1AutoCAD, NISAIPro-E, etc.

3.10. DESIGN ANALYSIS • The computer can be used to aid the analysis work such as stress-strain analysis, heat transfer analysis, etc. • The analysis can be done either by using specific program generated for it or by using general purpose software commercially available in the market. • The geometric models generated can be used for the analysis by properly interfacing the modeling software with the analysis software. Two types of important engineering analysis are 1. Analysis for mass properties. 2. Finite element analysis (FEA). • By using mass properties analysis, properties of solid object can be determined, such as surface area, weight volume, C.G. and Ml. Similarly, for plane surfaces perimeter, Area and ML can be determined. • Finite element analysis is the most powerful feature of a CAD system. Here, the object is divided into a large number of finite elements. • The entire object can be analysed for stress-analysis, heat transfer analysis etc. For solving the FEA problems, computers with larger memory and computational capabilities are required.

The graphical output of FEA is displayed in the computer terminal for better understanding of results through visualization. Designer can modify/redesign the model, and using FEA software analysis can be done easily.

First 72 columns are data columns. 73 to 80 columns are for the sequence number (utilized as pointer) with identification for data. An IGES file consists of the following file sections. They are. (i). Start section - for initializing IGES file. (ii). Global section — they are necessary to translate the file from any graphic software to other. (iii). Directory section:- Reference the entities and necessary data required for entities which are given in the next section. (iv). Parameter data section: - Constraint details, co-ordinate value, text and so on. (v) Termination section: - Marks the end of file. (d) PDES-Product Data Exchange Specification: To overcome limitations in application of IGES as standard for CAD data exchange, new standard were developed by IGES organization in 1984 called PDES-Product Data Exchange Specification. (e) CAD * I —Computer Aided Design Interface: It is also a CAD data exchange format developed by European country Research project group. (f) STEP- Standard for Exchange of Product Model Data: New CAD data standard is developed through worldwide effort known as STEP in year 1997. The STEP overcomes many of the limitations ol’ IGES. (g) CGM-Computer Graphics Metafile: It establishes a format for device independent definition, to capture. store and transfer any Graphic image. Here picture is described as collection of graphic entities such as lines, polv lines, arc, ellipse, filled areas, texts, etc and attributes such as colour, line wide, text style etc. (i,) Bitmaps: Each pixel of image will be assigned with number equal to colour on that pixel. Now a days. 3 2bits are used to represent the colour of the pixel. Some of standard formats are (i) BMP-Windows Bitmap format. (ii) JPEG-Joint Photographic Expert Group. (iii) GIF- Graphic Interchange Format (iv) TIFF-Tagged Image File Format

TWO MARKS QUESTIONS 1. Define geometric modeling. 2. What is meant by lofted surface? 3. Local surface variation on the model can be done on __________ B - spline surface. 4. Car doors and panels can be done with _________ modeling. 5. Name the two basic approaches followed in solid modeling. 6. List the basic entities available in CSG approach of solid modeling. 7. Name the data structure used in CSG. 8. What are the Boolean operations available in CSG? 9. Out of CSG and B-rep approaches of solid modeling which approach requires more memory. 10. Out of CSG and B-rep approaches of solid modeling which approach requires more computational time? 11. Name the data structure used in B-rep. 12. Out of CSG and B-rep approaches of solid modeling which approach will be used for creating complex geometries? 13. What is the use of topological consistency checking in B-rep? 14. State Euler rule for topological checking. 15. State Euler-Poincare formula for topological checking. 16. In which solid modeling approach, the integration of wire frame and surface modeling can be done. 17. List some of the solid modeling software? 18. Define parametric modeling. 19. What are the types of parametric modeling? 20. What is meant by feature? Feature has two meaning 21. Name the two types of feature based modeling technique. 22. What is meant Implicit/unevaluated feature? 23. List the genera/features of a solid modeler. 24. Define computer interfacing. 25. List the types of interfacing in CADCAM environment. 26. Classify hardware-hardware interfacing. 27. List some of neutral file format to achieve software interfacing? 28. What is PDES? 29. What is STEP? 30. Briefly explain the term constructive solid geometry (CSG). 31. How a model is defined in B-rep? 32. What is DXF? 33. What is IGES? 34. Classify wire frame modeling.

REVIEW QUESTIONS 1. Define and classify geometrical modeling? 2. Explain wire frame modeling and discuss its advantages and disadvantages? 3. Define surface modeling? List its applications, benefits and drawbacks. 4. V/hat are the common entities available in a typical surface modeler? Discuss the use of each entity with examples. 5. Reason out why local control of surface is not possible with Bezier surface, where as it is possible in B-spline surface. 6. What are the two important basic approaches followed in solid modeling? Discuss each of them in detail? 7. B-rep solid modeling approaches is better than CAG solid modeling approach why? 8. Discuss the data structure used in CSG and B-rep solid modeling techniques? 9. What is meant by topological consistency? Discuss the rules to be followed to get geometrical valid solid models? 10. Enumerate advantages of solid modeling/geometric modeling? Technique. 11. Explain the salient features available in typical solid modeler. 12. Define parametric modeling. Explain two types of parameterization and steps followed in parametric modeling. Also discuss its benefits. 13. What is meant by feature? Classify the features? 14. Explain two techniques followed in feature based modeling with an example to each. 15. What are the types of design analysis that can be carried out using a solid model? 16. Define computer interfacing. Classify and explain each type of interfacing with an example. 17. Classify the graphic standards? Name some important standards used in plotting and CAD data exchange. 18. What are the various schemes for representing solid object? Discuss boundary representations (B-rep) technique. 19. What is a DXF file? Explain the general DXF file structure? 20. What are different types of geometric modeling? Compare 2D and 3D wire frame models. 21. What is geometric modeling? Explain the geometric models, bringing out their limitations and applications. 22. What are the differences between surface modeling and solid modeling? 23. Explain the technique of CSG for solid modeling. 24. With suitable examples explain how solid model are generated using Boolean operation.

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