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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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**Module 2 CAD Methods and Systems**Product Design and CAD CAD Systems hardware Geometric Modeling Solid Modeling Data Exchange Standards Rapid Prototyping**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.**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]**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**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.**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.**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**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**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**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)**Secondary**Storage Output Device Graphics Terminal Workstation Input Devices Typical CAD System Computer**Workstation**Secondary Storage Output Input Graphics Terminal Computer Drum Plotter Electronic Tablet CAD System Hardware**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)**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.**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**ANSI Y14.xX**Standard ISO Standard Datum Geometric Characteristic Dimensional Tolerances Engineering Drawing - Fig 2.2**Geometric Modeling Techniques**• Representation Techniques • 2D Multiple Views (projections) • 3D Wire Frame Model • 3D Surface Model • 3D Solid Model**2D Multiple Views (example)**Convention? Top Front Right Side Orthographic Projection Isometric View More projections maybe needed for more complicated objects**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**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**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**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)**Pure Primitive Instancing (PPI)**PPI involves recalling the already stored primitive solids (Fig 2.24) . Primitive solids include cubes, spheres, cylinders, and others**Sweeping (S)**• Sweeping refers to generation of volumes by moving polygon or polyhedron into space (Fig 2.26) Fig 2.26 Sweeping Examples**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**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-)**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.**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)**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**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)**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.**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.**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)**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**Selecting a Solid Modeler**• Flexibility - Multiple construction techniques. • Robustness - consistency (minimal errors) in creating realizable objects • Simplicity - Pull down menus • Performance - ? • Cost**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.**Geometric Transformation**• Modify display (modify data structure)**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**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.**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’**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?**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**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**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 =**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 =**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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