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## TA 101 T hink and A nalyze

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**TA 101Think and Analyze**AnupamSaxena Associate Professor Mechanical Engineering Compliant and Robotic Systems Lab Indian Institute of Technology Kanpur**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**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**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**40**10 45 30 20 40 ANUPAM SAXENA TA101 LECTURE VII ISOMETRIC VIEW**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**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**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**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**60**10 30 60 40 40 40 30 ANUPAM SAXENA TA101 LECTURE VIII ISOMETRIC PROJECTION: EXAMPLE WITH ELLIPSES**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**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**keep Thinking and Analyzing**Until next time...