16.810 (16.682) Engineering Design and Rapid Prototyping Instructor(s) Lecture 3 Computer Aided Design (CAD) January 9, 2004 Prof. Olivier de Weck Dr. Il Yong Kim 16.810 (16.682) 2 Plan for Today ? CAD Lecture (ca. 50 min) ? CAD History, Background ? Some theory of geometrical representation ? SolidWorks Introduction (ca. 40 min) ? Follow along step-by-step ? Create CAD model of your part (ca. 90 min) ? Work in teams of two ? Use hand sketch as starting point 16.810 (16.682) 3 Course Concept today 16.810 (16.682) 4 Course Flow Diagram CAD/CAM/CAE Intro FEM/Solid Mechanics Overview Manufacturing Training Structural Test “Training” Design Optimization Hand sketching CAD design FEM analysis Produce Part 1 Test Produce Part 2 Optimization Problem statement Final Review Test Learning/Review Deliverables Design Sketch v1 Analysis output v1 Part v1 Experiment data v1 Design/Analysis output v2 Part v2 Experiment data v2 Drawing v1 due today today Monday Design Intro 16.810 (16.682) 5 What is CAD? ? Computer Aided Design (CAD) ? A set of methods and tools to assist product designers in ? Creating a geometrical representation of the artifacts they are designing ? Dimensioning, Tolerancing ? Configuration Management (Changes) ? Archiving ? Exchanging part and assembly information between teams, organizations ? Feeding subsequent design steps ? Analysis (CAE) ? Manufacturing (CAM) ? …by means of a computer system. 16.810 (16.682) 7 Brief History of CAD ? 1957 PRONTO (Dr. Hanratty) – first commercial numerical- control programming system ? 1960 SKETCHPAD (MIT Lincoln Labs) ? Early 1960’s industrial developments ? General Motors – DAC (Design Automated by Computer) ? McDonnell Douglas – CADD ? Early technological developments ? Vector-display technology ? Light-pens for input ? Patterns of lines rendering (first 2D only) ? 1967 Dr. Jason R Lemon founds SDRC in Cincinnati ? 1979 Boeing, General Electric and NIST develop IGES (Initial Graphic Exchange Standards), e.g. for transfer of NURBS curves ? Since 1981: numerous commercial programs ? Source: http://mbinfo.mbdesign.net/CAD-History.htm 16.810 (16.682) 8 Major Benefits of CAD ? Productivity (=Speed) Increase ? Automation of repeated tasks ? Doesn’t necessarily increase creativity! ? Insert standard parts (e.g. fasteners) from database ? Supports Changeability ? Don’t have to redo entire drawing with each change ? EO – “Engineering Orders” ? Keep track of previous design iterations ? Communication ? With other teams/engineers, e.g. manufacturing, suppliers ? With other applications (CAE/FEM, CAM) ? Marketing, realistic product rendering ? Accurate, high quality drawings ? Caution: CAD Systems produce errors with hidden lines etc… ? Some limited Analysis ? Mass Properties (Mass, Inertia) ? Collisions between parts, clearances 16.810 (16.682) 9 Generic CAD Process Start Settings Engineering Sketch Units, Grid (snap), … Construct Basic Solids dim 3D 2D Boolean Operations (add, subtract, …) Annotations Dimensioning Verification Create lines, radii, part contours, chamfers - Add cutouts & holes extrude, rotate = CAD file Output Drawing (dxf) x.x IGES file 16.810 (16.682) 10 Example CAD A/C Assembly ? Boeing (sample) parts ? A/C structural assembly ? 2 decks ? 3 frames ? Keel ? Loft included to show interface/stayout zone to A/C ? All Boeing parts in Catia file format ? Files imported into SolidWorks by converting to IGES format 16.810 (16.682) 12 Vector versus Raster Graphics Raster Graphics .bmp -raw data format ? Grid of pixels ? No relationships between pixels ? Resolution, e.g. 72 dpi (dots per inch) ? Each pixel has color, e.g. 8-bit image has 256 colors 16.810 (16.682) 13 Vector Graphics .emf format CAD Systems use vector graphics Most common interface file: IGES ? Object Oriented ? relationship between pixels captured ? describes both (anchor/control) points and lines between them ? Easier scaling & editing 16.810 (16.682) 14 Major CAD Software Products ? AutoCAD (Autodesk) ? mainly for PC ? Pro Engineer (PTC) ? SolidWorks (Dassault Systems) ? CATIA (IBM/Dassault Systems) ? Unigraphics (UGS) ? I-DEAS (SDRC) 16.810 (16.682) 15 Some CAD-Theory Geometrical representation (1) Parametric Curve Equation vs. Nonparametric Curve Equation (2) Various curves (some mathematics !) -HermiteCurve -Bezier Curve - B-Spline Curve - NURBS (Nonuniform Rational B-Spline) Curves Applications: CAD, FEM, Design Optimization 16.810 (16.682) 16 Curve Equations Two types of equations for curve representation (1) Parametric equation x, y, z coordinates are related by a parametric variable (2) Nonparametric equation x, y, z coordinates are related by a function ( or )u T Parametric equation cos , sin (0 2 )xR yRTTTS dd Example: Circle (2-D) Nonparametric equation 22 2 0xyR 22 yRx r  (Implicit nonparametric form) (Explicit nonparametric form) 16.810 (16.682) 17 Curve Equations Two types of curve equations (1) Parametric equation Point on 2-D curve: [() ()]xu y u p Point on 3-D surface: [() () ()]xu y uzu p : parametric variable and independent variableu ():2-D, (, ):3-Dyfx zfxy (2) Nonparametric equation Which is better for CAD/CAE? : Parametric equation cos , sin (0 2 )xR yRTTTS dd 22 2 0xyR 22 yRx r  T' It also is good for calculating the points at a certain interval along a curve 16.810 (16.682) 18 Parametric Equations – Advantages over nonparametric forms 1. Parametric equations usually offer more degrees of freedom for controlling the shape of curves and surfaces than do nonparametric forms. e.g. Cubic curve 32 Nonparametric curve: yax bx cxd  32 32 Parametric curve: xau bu cud yeu fu gxh   / / dy dy du dx dx du ? 2. Parametric forms readily handle infinite slopes / 0 indicates /dx du dy dx f 3. Transformation can be performed directly on parametric equations e.g. Translation in x-dir. 32 000 Nonparametric curve: ( ) ( ) ( )yaxx bxx cxx d  32 0 32 Parametric curve: xau bu cudx yeu fu gxh   16.810 (16.682) 19 Hermite Curves * Most of the equations for curves used in CAD software are of degree 3, because two curves of degree 3 guarantees 2nd derivative continuity at the connection point ? The two curves appear to one. * Use of a higher degree causes small oscillations in curve and requires heavy computation. 23 01 2 3 () [() () ()] (0 1) uxuyuzu uu u u    dd P aa a a * Simplest parametric equation of degree 3 0123 ,,, :aaaa Algebraic vector coefficients The curve’s shape change cannot be intuitively anticipated from changes in these values u (0)u START (1)u END 16.810 (16.682) 20 Hermite Curves 23 01 2 3 () (0 1)uuuuu    ddPaaaa Instead of algebraic coefficients, let’s use the position vectors and the tangent vectors at the two end points! 0 P 1 P (0)u START (1)u END 0 c P 1 c P u 00 10123 01 112 Position vector at starting point: (0) Position vector at end point: (1) Tangent vector at starting point: (0) Tangent vector at end point: (1) 2 3  c c c c  PP a PP aaaa PP a PP a a 3 a No algebraic coefficients 00 11 ,,,: cc PP PP Geometric coefficients The curve’s shape change can be intuitively anticipated from changes in these values 0 1 2 3 2 3 23 23 0 1 () [1 3 2 3 2 2 ]u u u u uuuu uu ao ?? ??        ?? c ?? ?? c ?? P P P P P Blending functions : Hermit curve 16.810 (16.682) 21 Effect of tangent vectors on the curve’s shape u (1, 1) (0)u START (5,1) (1)u END 0 1 0 1 (0) (1) : Geometric coefficient matrix (0) (1) ao ao ?? ?? ?? ?? ?? ?? c c ?? ?? ?? ?? c c ?? ?? P P P P P P P P ao ?? ?? ?? ?? ?? 11 51 11 1-1 ao ?? ?? ?? ?? ?? 11 51 55 5-5 ao ?? ?? ?? 11 51 13 13 13 -13 Is this what you really wanted? ao ?? ? ? ?? ?? ?? 11 51 22 2-2 Geometric coefficient matrix controls the shape of the curve ao ?? ?? ?? ?? ?? 11 51 40 40 /0 0 /4 dy dy du dx dx du 16.810 (16.682) 22 Bezier Curve * In case of Hermite curve, it is not easy to predict curve shape according to changes in magnitude of the tangent vectors, 01 and cc PP 0 ! () (1 ) , where !( )! n ini i i nn n uuu iiini  §· §·  ¨? ¨?  ?1 ?1 | PP : i P Position vector of the i th vertex (control vertices) * Bezier Curve can control curve shape more easily using several control points (Bezier 1960) Control vertices Control polygon n=3 0 P 1 P 2 P 3 P * Order of the curve: n * Number of vertices: n+1 (No of control points) * Number of segments: n * The order of Bezier curve is determined by the number of control points. n control points Order of Bezier curve: n-1 16.810 (16.682) 23 Bezier Curve Properties - The curve passes through the first and last vertex of the polygon. -The tangent vector at the starting point of the curve has the same direction as the first segment of the polygon. - The nth derivative of the curve at the starting or ending point is determined by the first or last (n+1) vertices. 16.810 (16.682) 24 Two Drawbacks of Bezier curve (1) For complicated shape representation, higher degree Bezier curves are needed. ? Oscillation in curve occurs, and computational burden increases. (2) Any one control point of the curve affects the shape of the entire curve. ? Modifying the shape of a curve locally is difficult. (Global modification property) Desirable properties : 1. Ability to represent complicated shape with low order of the curve 2. Ability to modify a curve’s shape locally B-spline curve! 16.810 (16.682) 25 B-Spline Curve * Developed by Cox and Boor (1972) , 0 ,1 1,1 , 11 1 ,1 () () where : Position vector of the th control point ( ) () ( ) () () 1 () 0otherwise n ik i i i iik ik ik ik ik i ik i ii i uNu i utN u t uN u Nu tt tt tut Nu         dd - ? ˉ | PP P 00 1 2 i ik tik kin nk nink d - °  dd ? °  d ˉ (Nonperiodic knots) k: order of the B-spline curve The order of curve is independent of the number of control points! n+1: number of control points 16.810 (16.682) 26 B-Spline Curve Example Order (k) = 3 (first derivatives are continuous) No of control points (n+1) = 6 (1) The order of the curve is independent of the number of control points (contrary to Bezier curves) - User can select the curve’s order and number of control points separately. - It can represent very complicated shape with low order (2) Modifying the shape of a curve locally is easy. (contrary to Bezier curve) - Each curve segment is affected by k (order) control points. (local modification property) Advantages 16.810 (16.682) 27 NURBS (Nonuniform Rational B-Spline) Curve , 0 , 0 () () () n ii ik i n iik i hN u u hN u | | P P , 0 B-spline : ( ) ( ) n iik i uNu §· ¨? ?1 | PP : Position vector of the th control point : Homogeneous coordinate i i i h P * If all the homogeneous coordinates (h i ) are 1, the denominator becomes 1 , 0 If 0 , then ( ) 1. n iiik i hi hNu  | * B-spline curve is a special case of NURBS. * Bezier curve is a special case of B-spline curve. 16.810 (16.682) 28 Advantages of NURBS Curve over B-Spline Curve (1) More versatile modification capacity - Homogeneous coordinate h i , which B-spline does not have, can change. - Increasing h i of a control point ? Drawing the curve toward the control point. (2) NURBS can exactly represent the conic curves - circles, ellipses, parabolas, and hyperbolas (B-spline can only approximate these curves) (3) Curves, such as conic curves, Bezier curves, and B-spline curves can be converted to their corresponding NURBS representations. 16.810 (16.682) 29 Summary (1) Parametric Equation vs. Nonparametric Equation (2) Various curves -HermiteCurve -Bezier Curve - B-Spline Curve - NURBS (Nonuniform Rational B-Spline) Curve (3) Surfaces - Bilinear surface - Bicubic surface - Bezier surface - B-Spline surface - NURBS surface 16.810 (16.682) 30 Flat surface 1 G 2 G 1 F 2 F 3 F Not separate parts (the surface at the position must be flat) 16.810 (16.682) 31 Design Freedom 4.000 3.500 0.500 3.0004.750 0.500 0.500 0.500 45° I4× 0.406 Design freedom: r 0.800 Design freedom: r 0.100 Both the flat surface and holes move together along the design freedom line 16.810 (16.682) 32 Displacement Horizontal displacement or rotation is fine! 1 G 2 G 1 F 2 F 3 F 16.810 (16.682) 33 Linear vs. Nonlinear deformation Order of applying loads - For linear deformation, it does not matter. - For nonlinear deformation (eg. buckling), it is important. 1 G 2 G 1 F 2 F 3 F 16.810 (16.682) 34 IAP 2004 Schedule Week Monday Wednesday Friday Lecture L1 – Introduction (de Weck) L2 – Hand Sketching (Wallace) L3 – CAD modeling ( Kim, de Weck) 1 Hands-on activities Tour - Design studio - Machine shop - Testing area Sketch Initial design Make a 2-D CAD model (Solidworks) Nadir Lecture L4 – Introduction to CAE (Kim) L5 – Introduction to CAM (Kim) L6 – Guest Lecture 1 (Bowkett) Rapid Prototyping 2 Hands-on activities FEM Analysis (Cosmos) Water Jet Intro machine shop Omax (Weiner, Nadir) Make part version 1 Lecture Martin Luther King Jr. Holiday – no class L7 – Structural Testing (Kim, de Weck) L8 – Design optimization (Kim) 3 Hands-on activities Test part ver. 1 (Kane) Introduction to Structural Optimization Programs Lecture L9 – Guest Lecture 2 (Sobieski) Multidisciplinary Optimization 4 Hands-on activities Carry out design optimization Manufacture part ver. 2 Test part ver. 2 Final Review (de Weck, Kim) 16.810 (16.682) 35 SolidWorks Introduction ? SolidWorks ? Most popular CAD system in education ? Will be used for this project ? 40 Minute Introduction ? http://www.solidworks.com (Student Section)