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1. TA 101Think and Analyze AnupamSaxena Associate Professor Mechanical Engineering Compliant and Robotic Systems Lab Indian Institute of Technology Kanpur

2. Axonometric ViewsIsometric views

3. Organization of Lectures and Laboratory Assignments

4. Unit cube Rotation about ‘z’, then about ‘x’ and then projection on the y-z plane  z G = PRxRz = R (0, 0, 1) |OP|= |OQ|=  |OR|= P x |OR| = |OQ| and |OR| = |OP| gives O (1, 0, 0) Q (0, 1, 0) () = 1 () = 1 =  35.26 =  45 () = 2/3 ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION

5. Unit cube Rotation about ‘z’, then about ‘x’ and then projection on the y-z plane  G = PRxRz = z Z R (0, 0, 1) X Y  P x O (1, 0, 0) 30 deg 30 deg Q (0, 1, 0) O =  35.26 =  45 () = 2/3 cos() = foreshortening happens by ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION

6. Unit cube Rotation about ‘z’, then about ‘x’ and then projection on the y-z plane  G = PRxRz = z Z R (0, 0, 1) X Y  P x O (1, 0, 0) 30 deg 30 deg Q (0, 1, 0) O =  35.26 =  45 () = 2/3 cos() = foreshortening happens by ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION

7. 40 10 45 30 20 40 ANUPAM SAXENA TA101 LECTURE VII ISOMETRIC VIEW

8. Not Unique: Choose the orientation NO HIDDEN LINES: ALL LINES ARE SOLID BE CAREFUL WITH VISIBLE/INVISIBLE LINES 40 10 30 45 20 40 ISOMETRIC VIEWS ARE “REALISTIC” WE SHOW WHAT WE SEE ! ANUPAM SAXENA TA101 LECTURE VII ISOMETRIC VIEW: SCALE 1:0.67

9. TA: What happens to the shape of a circle on the x-y plane ? G = PRxRz = z X = a + rcos Y = b + rsin Z = 0 = y R Q P x x + = O AGz + C = 0 A Ellipse on the ‘isometric Xn-Zn’ plane ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION

10. TA: What happens to the shape of a circle on the y-z plane ? G = PRxRz = z X = 0 Y = a + rcos Z = b + rsin  = z R Q P y x + = O AGz + C = 0 A Ellipse on the ‘isometric Xn-Zn’ plane ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION

11. TA: What happens to the shape of a circle on the x-z plane ? G = PRxRz = z X = a + rcos Y = 0 Z = b + rsin  = z R Q P x x + = O AGz + C = 0 A Ellipse on the ‘isometric Xn-Zn’ plane ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION

12. 60 10 30 60 40 40 40 30 ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION: EXAMPLE WITH ELLIPSES

13. Y Z 60 10 30 60 40 Z 40 10 X X 40 30 Y ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION: SCALE 1:1

14. Y Z 60 10 30 60 40 Z 40 10 X TA: TRICK ! X SAVES A LOT OF TIME 40 30 Y ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION: SCALE 1:1

15. keep Thinking and Analyzing Until next time...