1. Computer Aided Design; CAD
Professor Su-Jin Kim
School of Mechanical and Aerospace Engineering
Gyeongsang National University

2. Computer Aided ? C A Design C A Engineering C A Process Planning
C A Manufacturing

3. Product Cycle Analysis CAE Design Customer’s Requirements Design CAD
Quality control, Packaging, Shipping
Production
CAM
Process Planning
CAPP
Manufacturing

4. CAD
Computer Aided Design

5. CAE Computer Aided Engineering Structural analysis Heat transfer
Fluid flow

6. Computer Aided Engineering
(Linear) Stiffness analysis
(Non-linear) Strength analysis
Vibration mode analysis
Heat transfer
Fluid analysis
Optimal design

7. Linear static analysis
선형해석: Stress σ=F/A  Internal force  External force Strain ε= δL/L  Displacement Linear σ=E ε  F = k δ Force – Displacement relation

8. Reference
MESHFREE : : MAPS-3D :

9. CAPP
Computer Aided Process Planning

10. CAM
Computer Aided Manufacturing

11. Reference NCBrain : www.ncbrain.com
I-Master:
CSCam:

12. CURVE
Coordinate
Line
Curve
NURBS

13. Coordinate Spherical : Rad, W-E, S-N; GPS
Cylindrical : Rad, Angle, Height; Missile
Orthogonal : X Y Z

14. Line Explicit equation y = ax + b Parametric equation x(u) = a0 + a1u
y(u) = b0 + b1u
z(u) = c0 + c1u
c(u) = p0 + (p1-p0)u p1 b1 p0
(a0, b0, c0) a1

15. Line Explicit equation y = ax + b Parametric equation x(u) = x1 + axu
y(u) = y1 + ayu
z(u) = z1 + azu p
(x, y, z) p2 ay p1
(x1, y1, z1) ax

16. Q1
Parametric equations of line that starts at P0(1, 1, 2) and ends at P1(4, 2, 3).
c(u) = p0 + (p1-p0)u
x(u) = 1+ 3u
y(u) = 1+ u
z(u) = 2+ u p1 p0

17. Circle Explicit equation (x-a)2+ (y-b)2 = r2 Parametric equation
x(u) = r cos(u) +a
y(u) = r sin(u) +b
x,y r u
a, b

18. Q Parametric equation r2 = (17-6) 2+(34-16) 2, r=21.1
x(u) = 21.1 cos(u) +6
y(u) = 21.1 sin(u) +16
17,34 r u
6, 16

19. Curve 3rd degree Polynomial Parametric equation
x(u) = a0 + a1u + a2u2 + a3u3
y(u) = b0 + b1u + b2u2 + b3u3
z(u) = c0 + c1u + c2u2 + c3u3 p1 p0

20. Curve Boundary conditions 1) Start point u=0, P0 x(0) = a0 =1
y(0) = b0 =1
z(0) = c0 =2
2) End point u=1, P1
x(1) = a0 + a1 + a2 + a3 =9
y(1) = b0 + b1 + b2 + b3 =8
z(1) = c0 + c1 + c2 + c3 =7 p1
(9,8,7) p0
(1,1,2)

21. Curve Tangent vector (gradient) x’(u) = a1 + 2a2u + 3a3u2
y'(u) = b1 + 2b2u + 3b3u2
z'(u) = c1 + 2c2u + 3c3u2 p1 p0

22. Curve Boundary conditions: Tangent vector
3) Start tangent vector u=0, t0
x’(0) = a1=3
y'(0) = b1=4
z'(0) = c1=5
4) End tangent vector u=1, t1
x’(1) = a1 + 2a2 + 3a3=9
y'(1) = b1 + 2b2 + 3b3=6
z'(1) = c1 + 2c2 + 3c3=7 t1
(9, 6, 7) t0
(3, 4, 5) p1 p0

23. Q. Curve 3rd degree Polynomial Parametric equation
x(u) = 1 + 3u + 9u2 - 4u3
y(u) = 1 + 4u + 7u2 - 4u3
z(u) = 2 + 5u - 2u2 + 2u3
(9, 6, 7) t1
(3, 4, 5) t0 p1
(9,8,7) p0
(1,1,2)

24. NURBS Non-uniform Rational B-spline Control points (제어점) Pi Pn C(u) P0
Ri,p(u)
Rational Basis function
p-th degree

25. Basis Function Basis Function (기저함수) for B-Spline 0-th degree, point uu C0
1-th degree, line C1
p-th degree, spline C2 ui
ui+1
ui+2
ui+3
ui+4
Knots(마디)

26. B-spline Curves p-th degree B-spline curve
where p-th degree Basis function is

27. B-spline Curves 3rd degree B-spline curve 3rd degree Basis function
C(u)=N0,3P0 + N1,3P1 + … + N6,3P6 P0 P1 P2 P3 P4 P5 P6
3rd degree Basis function
u0,1,2,3 u4 u5 u6
u7,8,9,10
N3,3
N2,3
N1,3
N0,3

28. Q2 B-spline Curves If, Knot is u={u0=0, u1=0, 0, 1, 2, 3, 4, 4, u8=4}
Control Points are P0(0,0,0), P1(10,0,0), P2(10,10,0), P3(0,10,0), P4(0,10,10), P5(-10,10,10)
and Degree p=2 ,
Compute the point C(2.5) on NUBS curve when parameter u=2.5.

29. Q2 B-spline Curves Basis Function (기저함수) 값
N4,0(2.5)=1 (u4≤2.5<u5) (other Ni,0=0 )
N3,1(2.5)=0.5 N4,1(2.5)=0.5 (other Ni,1=0 )
N2,2(2.5)=0.125 N3,2(2.5)=0.75 N4,2(2.5)=0.125 (other Ni,2=0 )
NUBS 곡선위의 점
C(2.5) = N2,2(2.5)P2 + N3,2(2.5)P3 + N4,2(2.5)P4
X = 0.125* * *0 = 1.25
Y = 0.125* * *10 = 10.00
Z = 0.125* * *10 = 1.25
C(2.5)=(1.25, 10.00, 1.25)

30. NURBS

31. SURFACE
Plan
Surface
NURBS Surface
Surface modeling

32. Plan x(u,v) = a00 + a10u + a01v y(u,v) = b00 + b10u + b01v
z(u,v) = c00 + c10u + c01v
p01 v
p00
(a0 , b0, c0) u
p10

33. Polynomial Surface x(u,v) = a00 + a10u + a01v + a11uv +
a20u2 + a02v2 + a21u2v + a12uv2 +
a30u3 + a03v3 + a31u3v + a13uv3
Y(u,v) = ..
Z(u,v) = .. u v
p00
p10
p01
p11

34. NURBS Surface
Plan, Spline, Arc, Sphere, Conic ..

35. Surface modeling

36. Surface modeling

37. SOLID Wireframe Surface vs. Solid Boundary Representation
Constructive Solid Goemetry
© Su-Jin Kim, GNU

38. Wireframe Surface vs. Solid
Wireframe: ambiguity
Surface: visual
Solid: volume, mass

39. Boundary Representation
Closed surface separate in/out volume

40. CSG
Constructive Solid Geometry
Boolean operation of primitives + -

41. Data Exchange Format
A neutral data format allows the digital data exchange among different CAD systems.
IGES (Initial Graphics Exchange Specification, 1980 US NIST)
STEP (Standard for the Exchange of Product model data, 1984 ISO)
DXF (Drawing Interchange Format, Autodesk)
IGES
STEP

42. Bulk metal part

43. Plastic part

44. Sheet metal part

45. ASSEMBLY Degree of freedom Joints / Constraints
Geometry Transformation
Homogeneous Transformation Matrix
© Su-Jin Kim, GNU

46. Degree of freedom Translation: X Y Z axis Rotation: A B C angle C B Z

47. Joints / Constraints Revolute Prismatic Cylindrical Spherical
Coincident
Contact
Fixed
© Su-Jin Kim, GNU

48. Geometry Transformation
Translation
Rotation
Scaling
C maxis rotation
B axis rotation
Y Z Translation
X Translation

49. Homogeneous Representation
The representation is introduced to express all geometric transformations in the from of matrix multiplication for the convenience of manipulation.
Dummy 4th coordinate

50. Scale, Translate

51. Rotate
sin(θ)
cos(θ) θ θ
-sin(θ)
cos(θ)

52. Rotate

53. Kinematics
Joint space (θ, d) Kinematics Cartesian space (X, Y, Z, A, B, C) Y0 X0 d1 θ1 d2 θ2 θ6 d6 Y6 X6 Z6

54. Assembly

55. Assembly

56. Assembly

57. Assembly

58. Assembly: Robot Excavator

59. Assembly: Robot Excavator

60. Assembly: Desk

61. Assembly: Desk

62. CAD at Youtube
: 2D CAD Dimension -> Extrude to 3D : Solid works 2D CAD Dimension -> Extrude to 3D -> Boolean Operation -> Fillet Chamfer, 3d to 2d Draft, Assmble Interferance (8 min) 8 : Mesh vs. NURBS (6 min)