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ENGINEERING GRAPHICS By R.Nathan Assistant Professor Department of Mechanical Engineering

ENGINEERING GRAPHICS By R.Nathan Assistant Professor Department of Mechanical Engineering. C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301. I - SEMESTER 20.09.2012. UNIT – 1 “PLANE CURVES”. Engineering Graphics Lecture Notes.

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ENGINEERING GRAPHICS By R.Nathan Assistant Professor Department of Mechanical Engineering

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  1. ENGINEERING GRAPHICSBy R.NathanAssistant ProfessorDepartment of Mechanical Engineering C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  2. UNIT – 1“PLANE CURVES” Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  3. PLANE CURVES (or) SPECIAL CURVES ELLIPSE PARABOLA HYBERBOLA CYCLIOD INVOLUTE OF SQUARE INVOLUTE OF CIRCLE Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  4. PLANE CURVES (or) SPECIAL CURVES Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  5. CONIC SECTIONS CIRCLE Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  6. CONIC SECTIONS ELLISPE Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  7. ELLIPSE TERMINOLOGY OF ELLIPSE:- The point C Is the centre of the ellipse Length A-A’ is the Major Axis of the ellipse Length B-B’ is the Minor Axis of the ellipse Length CA = CA’ and is called Semi Major Axis of the ellipse Length CB = CB’ and is called Semi Minor Axis of the ellipse The point F and F’ is known as Focus of the ellipse Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  8. Construction of Ellipse A. CONCENTRIC CIRCLES METHOD C. INTERSECTING LINES METHOD B. INTERSECTING ARCS METHOD Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  9. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX EF = 50 mm F - FOCUS C ● F E ● ● Engineering Graphics Lecture Notes ● D C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012

  10. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX EF = 50 mm Eccentricity (e) = 3 / 4 F - FOCUS EV1 = 40 mm VG = 30 mm C ● V1 F V2 E ● ● ● ● Engineering Graphics Lecture Notes 45° ● G ● D I - SEMESTER 20.09.2012 H ●

  11. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) C ● V1 & V2 are the vertices of your upcoming ellipse V1 F V2 E ● ● ● ● Engineering Graphics Lecture Notes ● G ● D I - SEMESTER 20.09.2012 H ●

  12. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) MEASURE THE DISTANCE C ● V1 F V2 E ● ● ● ● Engineering Graphics Lecture Notes ● G ● D I - SEMESTER 20.09.2012 H ●

  13. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) FOR EXAMPLE C 110 mm ● V1 F V2 E ● ● ● ● Engineering Graphics Lecture Notes ● G ● D I - SEMESTER 20.09.2012 H ●

  14. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) DIVIDE IT BY 10 EQUAL PARTS ie; 110 / 10 = 11 mm C ● V1 F V2 E ● ● ● ● Engineering Graphics Lecture Notes ● G ● D I - SEMESTER 20.09.2012 H ●

  15. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) C Distance between V1 & 1 = 11 mm ● Distance between 1 & 2 = 11 mm Similarly for 3,4,5…. Upto 9 give 11 mm gap V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● G ● D I - SEMESTER 20.09.2012 H ●

  16. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) C ● Make Parallel lines in 1,2,3,4,5,…to 9 V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● G ● D I - SEMESTER 20.09.2012 H ●

  17. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● G ● D I - SEMESTER 20.09.2012 H ●

  18. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● ● G a ● ● a a ● a ● ● a ● D a ● a ● I - SEMESTER 20.09.2012 a ● H a ●

  19. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Using Compass, For “1 - a” as Radius C ● with “F” as centre cut the arc in line 1 V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● ● G a ● ● a a ● a ● ● a ● D a ● a ● I - SEMESTER 20.09.2012 a ● H a ●

  20. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Using Compass, For “1 - a” as Radius C ● with “F” as centre cut the arc in line 1 V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 Using Compass, ● For “2 - a” as Radius ● G a ● ● a with “F” as centre a ● a ● ● a cut the arc in line 2 ● D a ● a ● I - SEMESTER 20.09.2012 a ● H a ●

  21. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Similarly ,repeat for all the rest of lines C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● ● G a ● ● a a ● a ● ● a ● D a ● a ● I - SEMESTER 20.09.2012 a ● H a ●

  22. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Make a smooth curve with arc points C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● ● G a ● ● a a ● a ● ● a ● D a ● a ● I - SEMESTER 20.09.2012 a ● H a ●

  23. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) This is your required “ELLIPSE” C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 5 6 7 8 9 ● ● G a ● ● a a ● a ● ● a ● D a ● a ● I - SEMESTER 20.09.2012 a ● H a ●

  24. CONIC SECTIONS PARABOLA Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  25. PARABOLA Engineering Graphics Lecture Notes TERMINOLOGY OF PARABOLA:- The line x-x’ is called Axis of the Parabola The point F in the axis x-x’ is known as Focus of the Parabola The line z-z’ is called Directrix of the Parabola The line L-R through the point F is called Latus Rectum C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  26. Construction of Parabola A. INTERSECTING LINES METHOD B. INTERSECTING ARCS METHOD Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  27. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX EF = 50 mm F - FOCUS C ● F E ● ● Engineering Graphics Lecture Notes ● D C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  28. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX EF = 50 mm Eccentricity (e) = 1 F - FOCUS E -V1 = EF/2 V1 -1 = 5 mm C ● 1 - 2 = 10 mm V1 F E ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 2 1 ● D C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  29. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX EF = 50 mm Eccentricity (e) = 1 F - FOCUS E -V1 = EF/2 V1 -1 = 5 mm C ● 1 - 2 = 10 mm Similarly for the rest give 10 mm gap V1 F E ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 2 3 4 5 6 7 1 ● D C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  30. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Make a parallel lines in the points C ● V1 F E ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 2 3 4 5 6 7 1 ● D I - SEMESTER 24.09.2012

  31. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Using Compass, For “E - 1” as Radius C ● with “F” as centre cut the arc in line 1 V1 F E ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 2 3 4 5 6 7 1 Using Compass, For “E - 2” as Radius with “F” as centre ● cut the arc in line 2 D I - SEMESTER 24.09.2012

  32. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Similarly ,repeat for all the rest of lines C ● V1 F E ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 2 3 4 5 6 7 1 ● D I - SEMESTER 24.09.2012

  33. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Make a smooth curve with arc points C ● V1 F E ● ● ● ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 2 3 4 5 6 7 1 This is your required “PARABOLA” ● D I - SEMESTER 24.09.2012

  34. CONIC SECTIONS HYBERBOLA Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  35. HYBERBOLA Z ● F X’ X ● ● ● Engineering Graphics Lecture Notes Z’ TERMINOLOGY OF HYBERBOLA:- The line x-x’ is called Axis of the Hyberbola The point F in the axis x-x’ is known as Focus of the Hyberbola The line z-z’ is called Directrix of the Hyberbola C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  36. Construction of Hyberbola Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  37. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX F - FOCUS C ● F E ● ● Engineering Graphics Lecture Notes ● D C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 24.09.2012

  38. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) EF = 55 mm Eccentricity (e) = 1.5 1.5 = 3 / 2 3 / 2 x 11 / 11 = 33 / 22 C ● E -V1 = 22 mm V1 -1 = 5 mm 1 - 2 = 10 mm V1 - G = 33 mm For the rest of points give 10 mm gap V1 F E ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 ● G ● D I - SEMESTER 24.09.2012

  39. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Make a parallel lines in the points C ● V1 F E ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 ● G ● a ● a ● a ● D ● a I - SEMESTER 24.09.2012

  40. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Using Compass, For “1 - a” as Radius C ● with “F” as centre cut the arc in line 1 V1 F E ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 Using Compass, ● G ● a For “2 - a” as Radius ● a with “F” as centre ● a ● cut the arc in line 2 D ● a I - SEMESTER 24.09.2012

  41. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Similarly ,repeat for all the rest of lines C ● V1 F E ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 ● G ● a ● a ● a ● D ● a I - SEMESTER 24.09.2012

  42. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Make a smooth curve with arc points C ● V1 F E ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 ● G ● a ● a ● a ● D ● a I - SEMESTER 24.09.2012

  43. ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Final curve with HB Pencil C ● V1 F E ● ● ● ● ● ● ● Engineering Graphics Lecture Notes 1 2 3 4 ● G ● a This is your required “HYBERBOLA” ● a ● a ● D ● a I - SEMESTER 24.09.2012

  44. CYCLOID Engineering Graphics Lecture Notes DEFINITION:- A curve generated by a point on the circumference of a circle which rolls without slipping along a fixed straight line. C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

  45. Construction of Cycloid Example Problem:- construct a cycliod having a generating circle of 50 mm diameter. Also draw tangent and normal at any point on the curve. Engineering Graphics Lecture Notes C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

  46. Construction of Cycloid Solution:- Draw a line AB with the distance equal to the circumference of the circle Circle Diameter (D) = 50 mm Circle Radius (R) = 25 mm i.e; C = 2 x π x 25 = 157 mm Circle Circumference (C) = 2πR The Line AB = 157 mm Engineering Graphics Lecture Notes ● ● A B C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

  47. Construction of Cycloid Draw a circle with A as centre for the radius of 25mm Engineering Graphics Lecture Notes ● ● A B C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

  48. Construction of Cycloid Divide the circle into 12 equal parts 6 5 7 4 8 Engineering Graphics Lecture Notes 3 ● ● 9 A B 2 10 1 11 12 C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

  49. Construction of Cycloid Divide the line AB into 12 equal parts i.e; 157 / 12 = 13 mm 6 5 7 i.e; a – b = 13 mm, b –c = 13 mm etc… 4 8 Engineering Graphics Lecture Notes 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 11 12 C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

  50. Construction of Cycloid Draw the parallel lines in the points a,b,c,d, etc…. 6 5 7 4 8 Engineering Graphics Lecture Notes 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 11 12 C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

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