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

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

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

CAD Computer Aided Design

CAE Computer Aided Engineering Structural analysis Heat transfer Fluid flow

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

Linear static analysis 선형해석: https://youtu.be/nXu2y2YQKmc Stress σ=F/A  Internal force  External force Strain ε= δL/L  Displacement Linear σ=E ε  F = k δ Force – Displacement relation

Reference MESHFREE http://meshfree.co.kr : http://www.anycastsoftware.com : http://www.afdex.com MAPS-3D : http://wincapa.com

CAPP Computer Aided Process Planning

CAM Computer Aided Manufacturing

Reference NCBrain : www.ncbrain.com I-Master: http://www.cubictek.co.kr CSCam: http://www.cscam.co.kr

CURVE Coordinate Line Curve NURBS

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

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

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

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

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

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

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

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)

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

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

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)

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

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

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

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

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.

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*10 + 0.75*0 + 0.125*0 = 1.25 Y = 0.125*10 + 0.75*10 + 0.125*10 = 10.00 Z = 0.125*0 + 0.75*0 + 0.125*10 = 1.25   C(2.5)=(1.25, 10.00, 1.25)

NURBS

SURFACE Plan Surface NURBS Surface Surface modeling

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

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

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

Surface modeling

Surface modeling

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

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

Boundary Representation Closed surface separate in/out volume

CSG Constructive Solid Geometry Boolean operation of primitives + -

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

Bulk metal part

Plastic part

Sheet metal part

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

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

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

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

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

Scale, Translate

Rotate sin(θ) cos(θ) θ θ -sin(θ) cos(θ)

Rotate

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

Assembly

Assembly

Assembly

Assembly

Assembly: Robot Excavator

Assembly: Robot Excavator

Assembly: Desk

Assembly: Desk

CAD at Youtube https://youtu.be/ZDeLwFwnFKg : 2D CAD Dimension -> Extrude to 3D https://youtu.be/cPB7R8U8x_Q : Solid works 2D CAD Dimension -> Extrude to 3D -> Boolean Operation -> Fillet Chamfer, 3d to 2d Draft, Assmble Interferance (8 min) https://youtu.be/Lm1G5jJ6JC 8 : Mesh vs. NURBS (6 min)