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TA 101 T hink and A nalyze Anupam Saxena Associate Professor Mechanical Engineering Compliant and Robotic Systems Lab Indian Institute of Technology Kanpur

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Organization of Lectures and Laboratory Assignments TopicWeek (No. of Lectures)Lab Intro and Basic ConstructionsWeek 1 (2) Orthographic ProjectionsWeek 2 (2)Lab 1 Orthographic ProjectionsWeek 3 (2)Lab 2 Isometric ProjectionsWeek 4 (2)Lab 3 Missing ViewsWeek 5 (2)Lab 4 Sectional and AssemblyWeek 6 (2)Lab 5 Oblique ProjectionsWeek 7 (2)Lab 6 Perspective ProjectionsWeek 8 (2)Lab 7 Lines and PlanesWeek 9 (2)Lab 8 Lines and PlanesWeek 10 (2)Lab 9 Auxiliary ProjectionsWeek 11 (2)Lab 10 Intersection of lines/planes/solids Week 12 (2)Lab 11 Intersection and DevelopmentWeek 13 (2)Lab 12 TOTAL2612

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Basic Construction and Conics

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ANUPAM SAXENA TA101 LECTURE II POLYGONS: HEXAGONS d Vertex-to-vertex distance Distance between flats d 60 Circumscribing circle Inscribing circle

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ANUPAM SAXENA TA101 LECTURE II POLYGONS: PENTAGON d A B C D E F r R

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ANUPAM SAXENA TA101 LECTURE II POLYGONS: OCTAGON

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ANUPAM SAXENA TA101 LECTUREII POLYGONS: SEPTAGON OR ANY REGULAR POLYGON Given a side 2 3 4 5 6 7 A B

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES (x, y) P (bcos, bsin ) P Q Q (acos, asin ) x = acos y = bsin Exact Ellipse

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES P Tangent-Normal at P M F G |FM| + |MG| = 2a

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: CONCENTRIC CIRCLES P Tangent-Normal at P M F G n TA: Why is n the normal?

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS 2a2a 2b2b |FT| + |TG| = 2a F G M Q P Q P T

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS 2a2a 2b2b F G M Q P Q P T TA: What is the maximum radius of the arc possible from F? ?

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: INTERSECTING ARCS 2l2l 2b2b |FT| + |TG| = 2l F G M Q P T d1d1 d2d2 (x, y) (a, 0) Ellipse if C 2a

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: STRING APPROACH Source: wiki

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes 2a2a 2b2b Q P m n

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Trammel of Archimedes Q P m n y x fl 1 R Precise Ellipse!

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Parallelogram Method 1 2 3 4 5 6 7 0 8 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 TA: An exact or approximate Ellipse? TA: Can you identify the Conjugate Diameters?

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: Conjugate Diameter Method A B C D Q AB, CD: Conjugate Diameters O: Center of Ellipse O OQ: Perpendicular to AB TA: Exact Ellipse?

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: FOUR CENTER METHOD

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF ELLIPSE: FOUR CENTER METHOD C1 C2 C3 C4 TA: An exact or approximate Ellipse? Clue: The longest diagonal first TA: Only with Rhombus?

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ANUPAM SAXENA TA101 LECTURE II CONSTRUCTION OF A PARABOLA 1 2 3 4 5 6 7 7 6 5 4 3 2 1

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Keep T hinking and A nalyzing Until next time...

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