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# Module 2 CAD Methods and Systems

Module 2 CAD Methods and Systems. Product Design and CAD CAD Systems hardware G eometric Modeling S olid Modeling Data Exchange Standards Rapid Prototyping. Integrated CAD/CAM.

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## Module 2 CAD Methods and Systems

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1. Module 2 CAD Methods and Systems Product Design and CAD CAD Systems hardware Geometric Modeling Solid Modeling Data Exchange Standards Rapid Prototyping

2. Integrated CAD/CAM • Kernel in figure 2.1 should contain the complete description of the part – in sufficient views and appropriate format – to convey the full intent of the designer • Geometric modeling is very important to CAD/CAM integration – it is the basis for future automated processes e.g. mathematical analyses, CAPP, automated inspection, etc.

3. Part description • A part is fully defined by: • Geometric entities – dimensions, surface finish, definition of surfaces and edges, fit and function • Materials of manufacture and • functionality [Show samples of part drawings and review format]

4. Geometric Modeling • Understanding of geometric modeling concepts is essential to understanding engineering design • Geometric representation of a part (product) is a necessary first step in mechanical and/or discrete part manufacturing

5. Definitions • Geometric Modeling – a technique that uses computational geometry to define geometric objects. It has three components: 1) part design 2) part representation and 3) rendering. • Rendering (realistic image generation) – goal is to generate a lifelike picture i.e. close as possible to picture of object.

6. Definitions • Solid geometric modeling – subset of geometric modeling where only solid objects are defined • Geometric primitives – starting tool set for geometric modelers e.g. lines, points, and surfaces.

7. Geometric Modeling Methods • Multi-view Representation • 2-D drawing – part is described in plan, front, and side views; and elevations • 3-d drawing – is derived by simultaneously examining the three views and an elevation • Wire frame geometry – 3-D vertices are entered as x, y, z triplets and are joined to create the 3-dimensional object. Wire frame geometry contains only points and lines and does not fully describe the part because ….??? • Show wire frame figures

8. Geometric Modeling Methods • Surface Modeling – adds surfaces to wire frame representations. Though an important improvement over wire frames, it does not contain a complete description of part entities to allow for important engineering calculations – like volume and mass properties

9. Geometric Modeling Methods • Solid Modeling – data structure contain all vital data for use in design analyses and manufacturing planning programs: • Its introduction met an important mfg requirement for fully automated and integrated design and mfg planning • Italso overcomes the difficulties of multi-view orthographic, wire frame, and surface modelers

10. Design Process-Figure

11. CAD Procedure • Fig 24.2(b) • Geometric modeling – Create, Manipulate and/or Display aMathematical model (database) of the geometry “graphics” • Engineering analysis - more complicated and thorough analysis - Computer Aided Engineering e.g Finite Element and Tolerance analysis (Communicate with database). • Design review and evaluation • Automatic dimensioning • Error Checking • Animation and Simulations • Rapid prototyping (Stereo-lithography and Virtual) • Automated drafting (500% productivity improvement)

12. Secondary Storage Output Device Graphics Terminal Workstation Input Devices Typical CAD System Computer

13. Workstation Secondary Storage Output Input Graphics Terminal Computer Drum Plotter Electronic Tablet CAD System Hardware

14. Other CAD Configurations • Host and Workstation –Fig 24.6(a) • Host is Mainframe or Minicomputer (Time –sharing) • For large data bases (automotive industry, weather forecast) • Engineering Workstation – Fig 24.6(b) • Stand alone minicomputer • Share data between users and data storage (server) • High performance (3D)/Expensive • A PC-based system – Fig 24.6(c)

16. Output Devices • Plotters Typically, produce paper copies of large format (C-, D- and E-sizes and nonstandard sizes) finished drawings. • Printers Produce a small format (A- or B-size) hardcopy of geometric models, sketches and drawings.

17. Reported Benefits of CAD • Increased the productivity of the designer (CAD improves conceptualization) • Enhanced design quality (variety of design and analysis) • Improved design documentation (legibility, fewer errors, standardization) • Development of manufacturing data base

18. ANSI Y14.xX Standard ISO Standard Datum Geometric Characteristic Dimensional Tolerances Engineering Drawing - Fig 2.2

19. Geometric Modeling Techniques • Representation Techniques • 2D Multiple Views (projections) • 3D Wire Frame Model • 3D Surface Model • 3D Solid Model

20. 2D Multiple Views (example) Convention? Top Front Right Side Orthographic Projection Isometric View More projections maybe needed for more complicated objects

21. 2D Multiple Views (projections) • 2D views of 3D geometry (Fig 2.3) • Objects are represented by points (vertices), lines (edges) and • curves (primitives) • Drafting oriented (limited use in design) • No relations between points and lines (connectivity) in the • different views (not 3D part?) • Used for NC sheet metal

22. 3-D Wire frames (Fig 2.5)

23. 3-D Wire frames (Fig 2.6 & 2.7)

24. 3-D Wire frames • Stick or wire diagrams represent objects (connect dots – no information about surfaces ‘meaningless objects’) • Points and lines (vertices and edges) are the primitives and are defined in 3D • Ambiguous and incomplete representation • Hidden lines can be removed to improve visualization of shape (colors?) • Simple to create and manipulate

25. 3-D Surface Model • Include information about surfaces • Data (vertices & edges) is entered in an ordered manner to define surfaces. • The modeler does not recognize inside or outside of an • object (does not store topology – relationship between • primitives) • The modeler can not determine the physical properties of the object • Adequate for NC machining

26. 3-D Solid Models • Offer complete and unambiguous definition of solids – construct a realizable solid • Six methods are available to construct models, the following are the most used • Pure Primitive Instancing (PPI) • Sweeping (S) • Constructive Solid Geometry (CSG) • Boundary Representation (BREP)

27. Pure Primitive Instancing (PPI) PPI involves recalling the already stored primitive solids (Fig 2.24) . Primitive solids include cubes, spheres, cylinders, and others

28. Sweeping (S) • Sweeping refers to generation of volumes by moving polygon or polyhedron into space (Fig 2.26) Fig 2.26 Sweeping Examples

29. Constructive Solid Geometry (CSG) • CSG uses Boolean operations on solids (PPI and others) Fig 2.27 2-D • Boolean Operations addition (+ or  ) subtraction (-) intersection (* or ) 3-D

30. Boundary Representation (BREP) • BREP enters all bounding edges (in a specific order) for all surfaces to create valid volume (realizable volume) • BREP stores the actual part(vertices, edges, faces, dimensions, topology,etc-)

31. E2 F1 E1 E3 3D Solid Modeler: Storage of Data Base • Two forms of data base storage CSG and BREP (similar in concepts to construction techniques) (Fig 2.30) • CSG stores the instruction for how to make the part (implicit) • BREP stores the actual part data (vertices, edges, and faces); geometry and topology (explicit) • BREP database is Larger than CSG • Efficiency of data structure is measured by ? • Example (Fig 2.31 ) • BREP of cylinder (what about sphere or cone?) Most modern modelers provide several types of construction techniques, but immediately convert each type to an internal B-Rep data structure.

32. Validity Check • A solid modeler must guarantee that the object created is, in fact, a real (valid) solid object. • Euler's equation can be used on B-Rep data (available directly or extracted from CSG models) to validate that a model represents a real polyhedron. • For simple polyhedron V – E + F = 2 • For multiple polyhedra V – E + F – H + 2P – 2S = 0 V = No. of vertices E = No. of edges F = No. of faces H = No. interior loops (connected edges) P= No. of passage ways S = No. exterior shell (connected surfaces)

33. Cube Hole E2 V1 F1 E1 E3 V2 ValidityCheck: Examples • Solid cube • Cylinder with thru hole • a) Apply to the whole object • Rule: V – E + F – H + 2P – 2 S = 0 • Total 10 – 15 + 7 – 2 + 2(1) – 2(1) = 0 b) Apply to individual objects Rule: V – E + F – H + 2P – 2 S = 0 Cube: 8 – 12 + 6 – 0 + 2(0) – 2(1) Hole: 2 – 3 + 1 – 2 + 2(1) – 2(0) Total 10 – 15 + 7 – 2 + 2(1) – 2(1) = 0

34. Validity Check: Revisited • Euler Formula • V – E + F – H + 2P – 2 S = 0 • Can be applied successfully to combined geometries of an object • Caution should be exercised when applied to individual geometries of • an object (it does not add up for objects with protrusions!) • Subface (sub-surface) implicitly indicates an inner loop (H=1) and it • it does not hold significant volume • Study Example in handout (p 22) and validate the geometry (Fig 2.28)

35. Part Feature Recognition • Definitions: • Feature - a general term applied to a physical portion of a part, such as a surface, hole, or slot. • feature-of-size - is one cylindrical or spherical surface or a set of parallel surfaces, each of which is associated with a size dimension.

36. Feature-Based Design • because of non-unique feature construction process between designers, part design and process/manufacturing planning have become two distinct activities with slightly different emphases: • design - fit, form and function • manufacturing planner - feature recognition, process selection and sequence definition.

37. System A System K Standard Format System Z System B CAD Data Transfer Standards • Standard exchange formats (neutral format) permit the sharing of CAD databases across different systems. • Why use a standard exchange format? • To transfer CAD files without loss of information • To ease reuse of data internally (applications) or externally (suppliers) • To archive data for future use despite changes in systems • Minimize transmission and processing costs (encoding)

38. CAD Data Transfer Standards:Proprietary and De-facto Standards • IGES (Initial Graphics Exchange Specification): It is an ISO standard for the majority of 2D and 3D systems. • PDES(Product Definition Exchange Specification) More comprehensive (primitives, material type, and process plan) • DXF (Drawing eXchange File): Originally developed by AutoCAD. Creates ASCII data files. Very common .Many applications

39. Selecting a Solid Modeler • Flexibility - Multiple construction techniques. • Robustness - consistency (minimal errors) in creating realizable objects • Simplicity - Pull down menus • Performance - ? • Cost

40. Object is built up layer by layer Photocurable liquid polymer (Acrylate Resin) Ultraviolet laser beam Rapid Prototyping:Stereolithography with Acrylic Resin • The CAD solid model is converted into a vertical stack of slices as thin as 0.0025”(STL file) for up to 20”x20” objects. • The slices are used to guide a laser beam and solidify the cor-responding layers in the photo-polymer. • The cured acrylic prototypes are not as strong mechanically as the real parts, but have high dimensional accuracy (about 200m inches) suitable for checking space requirements and verifying design concepts.

41. Geometric Transformation • Modify display (modify data structure)

42. c' c T a' b' a b c' b' Rz a' c y a' a q b a x c S c' a' b' a b Transformations: Definitions • Translation a' = Ta • Rotation • a' = Rza • Scaling • a' = Sa

43. y x' y' Replace f with x and y p'(x',y') = y' Rz x' y' x cos (q) - ysin (q) x sin (q) + y cos (q) or = p x y p (x,y) = y x' y' 1 cos q -sin q0 sin q cos q0 0 0 1 x y 1 q p = f x x x' Rz p (x,y) p'(x',y') = Transformations: Rotation x' = p cos (f + q) = p cos (f) cos (q) - p sin (f) sin (q) y' = p sin (f + q) = p cos (f) sin (q) + psin (f) cos (q) but p cos (f) = x and p sin (f) = y The transformation matrix Rz transforms any point having a rotation q about the z-axis at the origin.

44. y x' y' x' = x + Dx y' = y +Dy algebraic form p'(x',y') = y' T ? x' y' x y Dx Dy vector form = + or y x y p (x,y) = x y 1 1 0 Dx 0 1 Dy 0 0 1 x' y' 1 = x x' x homogeneous coordinates T p (x,y) p'(x',y') = Transformations: Translation Dy Matrix Addition to Multiplication (homogeneous coordinates) Dx matrix form The transformation matrix T transforms any point, giving it planar displacements Dx and Dy along the x- and y-axis respectively. Must Equal ‘1’

45. y p (x,y) y sx x sy y x' y' S or = y' p'(x',y') x' y' 1 sx 0 0 0 sy 0 0 0 1 x y 1 = x x x' 10 0 0 10 0 0 1/s S = Transformations: Scaling Scaling operation simply requires multiplying each coordinate with its corresponding scale factor sx or sy. Thus x' = sx x and y' = sy y s = p'/p Non-uniform scaling p p' For uniform scaling, sx = sy = s = scale factor The transformation matrix S transforms any pointbeing scaled by a factor s = sx = sy with respect to the origin. p'(x',y') = Sp(x,y) Negative Scaling?

46. Translation p'(x',y') = Tp(x,y) Rotation x y 1 1 0 Dx 0 1 Dy 0 0 1 x' y' 1 p'(x',y') = Rp(x,y) x' y' 1 sx 0 0 0 sy 0 0 0 1 x y 1 = = x' y' 1 cos q -sin q0 sin q cos q0 0 0 1 x y 1 Scaling = p'(x',y') = Sp(x,y) 2D Transformation Formulas

47. y 6 T ? b' 5 4 (5,3) a' b 3 c' (1,3) 2 (6,1) (4,1) c 1 a x 0 1 0 -3 0 1 2 0 0 1 1 2 3 4 5 6 1 0 Dx 0 1 Dy 0 0 1 = 1 3 1 4 1 1 1 0 -3 0 1 2 0 0 1 = 2 5 1 5 3 1 1 0 -3 0 1 2 0 0 1 6 1 1 1 0 -3 0 1 2 0 0 1 3 3 1 = = Translation Example The corner a of the triangle moved from (4,1) to (1,3), what is the translation transformation matrix T? If points b and c where initially at points (5,3) and (6,1) respectively, determine the new coord- inates c' and b' using T. Solution: the displacements Dx and Dy are Dx = final coord. - initial coord. = x' - x = 1 - 4 = -3 Dy = final coord. - initial coord. = y' - y = 3 - 1 = 2 Thus, T = which is ok. Check point a , a' = Ta = b' = Tb = c' = Tc = and

48. y b' 6 c' 5 4 a' (5,3) b 3 2 (4,1) cos q -sin q0 sin q cos q0 0 0 1 1/2 - Ö3/2 0 Ö3/2 1/2 0 0 0 1 (6,1) 60o c 1 a R = = x 0 1 2 3 4 5 6 1.134 3.964 1 4 1 1 2-Ö3/2 2Ö3 + 1/2 1 1/2 -Ö3/2 0 Ö3/2 1/2 0 0 0 1 = = 1/2 -Ö3/2 0 Ö3/2 1/2 0 0 0 1 1/2 -Ö3/2 0 Ö3/2 1/2 0 0 0 1 5 3 1 6 1 1 - 0.098 5.830 1 2.134 5.696 1 c' = Rc = = = Rotation Example The corner a of the triangle is initially at point (4,1). If the triangle is rotated 60o about the z-axis at the origin, what is the rotation matrix R? What is the new position of point a? If points b and c were initially at points (5,3) and (6,1) respectively, what are the new coordinates of c' and b' using R? R ? Solution: a' = Ra = b' = Rb =

49. y b 3 c 2 b' c' a 1 a' 0 1 2 x -2 3 -1 10 0 0 1 0 0 0 1/0.5 10 0 0 10 0 0 1/s 1 0 0 0 1 0 0 0 2 -1 S = = = -2 The transformed vector must be normalized so that the homogeneous coordinate is 1, thus the division by 2. 1 0 0 0 1 0 0 0 2 3 1 2 1.5 0.5 1 3 1 1 = = 0 2 1 3 3 1 1 0 0 0 1 0 0 0 2 0 2 2 0 1 1 1 0 0 0 1 0 0 0 2 3 3 2 1.5 1.5 1 = = c' = Sc = = = Scaling Example The vertex (corner) a of the polygon is initially positioned at point (3,1). If the polygon is scaled uniformly by 50% (0.50) about the origin, what is the scaling matrix S? What is the new position of vertex a? If points b and c where initially at points (3,3) and (0,2) respectively, determine the new coordinates c' and b' using S. Solution: For a scale factor s= 0.5, the scaling matrix S is a' = Sa = b' = Sb =

50. y 3 T2 2 Rq 1 T1 0 1 2 x -2 3 -1 -1 -2 Combined Transformations • Different transformations can be combined by forming the product of their respective transformation matrices in a proper order. • Rotating an object about a point other than the origin requires the following sequence: • a translation T1 to the origin • followed by a rotation Rq at the origin • a trip T2to bring the object back to its original location. • The combined operations are represented by the matrix M: • M = T2Rq T1 • Note that the right most transformation is always the first one applied and the left most is the transformation applied last. Effective rotation about a point other than the origin. Similar procedure should be followed for scaling

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