1. W ELCOME Engineering Graphics - Lect 2 1

2. O VERVIEW OF P LANE C URVES Conic Section Involute Cycloid 2

3. Conic section Ellipse Parabola Hyperbola O VERVIEW 3

4. M ETHODS TO D RAW C ONIC S ECTION Directrix Focus Method Ellipse Parabola Hyperbola Ellipse Concentric Circles Method Rectangle or oblong Method Arc of circle method Parabola Rectangle or oblong method Tangent Method Hyperbola Directrix Focus Method 4

5. C ONIC S ECTION When a right circular cone is cut by section plane in different positions with respect to the axis of the cone, the sections obtained are called as conics. 5

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9. C ONIC S ECTION When the section plane is inclined to the axis and cuts all the generators on one side of the vertex we get an ellipse as section. When the section plane is inclined to the axis and is parallel to the one of the generators we get parabola as section. Hyperbola is obtained, When the section plane is inclined to the axis and cuts the cone on one side. 9

10. D EFINITION It is a path generated by a point in one plane in such way that ratio of its distance from fixed point (Focus) to its distance from fixed line (Directrix) remains constant. This ratio is called as Eccentricity (e) If Ratio (e) < 1 it is Ellipse IF Ratio (e) =1 it is Parabola If Ratio (e) >1 it is Hyperbola The line at right angle to the directrix and passing through a focus is called axis. The point at which the conic curve cuts its axis is called as the vertex. 10

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15. D IRECTX F OCUS METHOD To construct an ellipse when the distance of the focus from directrix is equal to 60mm and eccentricity = 2/3 by using directrix focus method. 15

16. Draw a vertical line which represents directrix, At any point O, a right angle draw an axis OO 2 and mark focus F on the axis so that OF=60mm 16

17. Now divide OF into five equal parts Mark vertex V on the 3rd part of from O so that VF/VO=2/3=e (VF=60x2/5=24mm,VO=60x3/5=36mm) 17

18. Through V, draw a perpendicular VV´ to the axis, which is equal to the V 1 F. 18

19. Draw a line joining O and V’, and extend it. 19

20. Mark points 1,2,3…on the axis, and draw perpendicular lines to meet OA when produced at 1´ 20

21. With F as a centre and radius equal to 11´, Draw arcs to cut the perpendicular through 1 on the both sides of the axis. 21

22. Repeat the same procedure for other points, e.g. for point 2, take radius equal to 22’ and F as a centre, draw arks to cut the perpendicular through 2 on the both sides of the axis. 22

23. Finally, draw a smooth curve through all these points. Then this curve is required ellipse. 23