1. Conic Section (Ellipse, Parabola & Hyperbola) Orthographic Projection
ENGINEERING GRAPHICS
Unit 1
Conic Section (Ellipse, Parabola & Hyperbola)
Cycloids &Involutes
Orthographic Projection

2. Introduction Engineering Drawing is the language of Engineers.
It is a graphical language used for effective communication among engineers.

3. DRAFTING TOOLS Drawing Board Mini drafter or T- square
Drawing Instrument box
Drawing Pencils
Eraser
Templates
Set squares
Protractor
Scale Set
French curves
Drawing clips
Duster piece of cloth (or) brush
Sand-paper (or) Emery sheet block
Drawing sheet

4. Drawing Board & Minidrafter
Standard Size : 650mm x 470mm

5. Set squares & French curves
Compass & Divider
Set squares & French curves

6. Drawing Pencils with grade

7. Drawing sheet size Designation Dimension, mm Trimmed size A0
841 x 1189 A1
594 x 841
A2 *
420 x 594
A3 **
297 x 420 A4
210 x 297

8. Drawing sheet & Title block

9. Types of Lines & Applications

10. Open type Closed type Closed and filled Oblique stroke
Types of Arrow head
Open type
Closed type
Closed and filled
Oblique stroke

11. Symbols for Shape Indication
R : Radius Square
SR: Spherical Radius  = Diameter

12. Engineering Curves

13. Conic Sections - Circle
When the cutting plane AA is perpendicular to the axis and cuts all the generators, the section obtained is a circle

14. Conic Sections - Ellipse
When the cutting plane BB is inclined to the axis of the cone and cuts all the generators on one side of the apex, the section obtained is an Ellipse

15. Conic sections - Parabola
When the cutting plane CC is inclined to the axis of the cone and parallel to one of the generators, the section obtained is a Parabola

16. Conic Sections - Hyperbola
When the cutting plane DD makes a smaller angle with the axis than that of the angle made by the generator of the cone, the section obtained is a Hyperbola

17. Eccentricity Method- construction of Ellipse, Parabola & Hyperbola
Distance of the moving point from the focus
e =
Distance of the moving point from the directrix
Note
If the e < 1, curve obtained is Ellipse
If the e = 1, curve obtained is Parabola
If the e > 1, curve obtained is Hyperbola

18. Eccentricity Method

19. Exercises – Conic Sections
Draw an ellipse when the distance of focus from the directrix is equal to 35 mm and eccentricity is 3/4. Draw a tangent and normal at a point P located at 30mm above the major axis.
Draw a hyperbola when the distance of focus from the directrix is equal to 40mm and eccentricity is 5/3. Draw a tangent and normal at a point P located at 30mm above the major axis.
A point moves such that its distance from a fixed straight line to its distance from a fixed point is equal. Draw the locus of the curve traced by that point. Add a normal and tangent to the curve at 40mm above the axis

20. Cycloid
It is a curve traced by a point on the circumference of a circle which rolls along a straight line without slipping.
Engineering Applications:
Used in small gears in instruments like dial gauges and watches

21. Exercises – Cycloid
A coin of 40 mm diameter rolls over a horizontal table without slipping. Draw the curve trace by a point on the circumference of the coin for the 3/4th of the revolution.
Draw a cycloid formed by a rolling circle 50 mm in diameter. Use 12 divisions. Draw a tangent and normal at a point on the curve 30 mm above the directing line.

22. Involute
Involute is a single-curved line traced out by an end of a string when unwound itself from straight line or a circle or a polygon, the string being always kept taut.
Engineering Applications: Casings of centrifugal pumps and Cams are of involute shape.

23. Involute of a circle

24. Involute of a Square

25. Involute of a Pentagon

26. Exercises – Involutes
A coir is unwound from a drum of 30 mm diameter. Draw the locus of the free end of the coir for unwinding through an angle of 360o. Draw also the tangent and normal at any point on the curve.
Draw the curve traced out by an end of a thick wire unwound from a square of side 25 mm.
Draw one turn of involute of a hexagon inscribed in a circle of 30mm diameter

27. Orthographic Projection
ORTHO means Right-angle;
GRAPHIC means Drawing;
ORTHO GRAPHIC means Right-angled Drawing

28. Orthographic Projection

29. Orthographic Projection

30. Orthographic Projection

31. Orthographic Projection – Exercise 1

32. Exercise 1 – Answer

33. Orthographic Projection – Exercise 2

34. Exercise 2 – Answer

35. Orthographic Projection – Exercise 3

36. Exercise 3 – Answer

37. Orthographic Projection – Exercise 4

38. Exercise 4 – Answer

39. Orthographic Projection – Exercise 5

40. Exercise 5 – Answer

41. Orthographic Projection – Exercise 6

42. Exercise 6 – Answer

43. Orthographic Projection – Exercise 7

44. Exercise 7 – Answer

45. Orthographic Projection – Exercise 8

46. Exercise 8 – Answer

47. Orthographic Projection – Exercise 9

48. Exercise 9 – Answer

49. Orthographic Projection – Exercise 10

50. Exercise 10 – Answer

51. The End