Presentation on Engineering Drawing First

Presentation of Engineering Drawing I

1. Engineering Drawing –I

2. Graphics Language 2

3. 1. Try to write a description of this object. 2. Test your written description by having someone attempt to make a sketch from your description. Effectiveness of Graphics Language The word languages are inadequate for describing the size , shape and features completely as well as concisely. You can easily understand that … 3

4. Graphic language in “engineering application” use l ines to represent the surfaces , edges and contours of objects. A drawing can be done using freehand , instruments or computer methods. Composition of Graphic Language The language is known as “ drawing ” or “ drafting ” . 4

5. Freehand drawing The lines are sketched without using instruments other than pencils and erasers. Example 5

6. Instrument drawing Instruments are used to draw straight lines, circles, and curves concisely and accurately. Thus, the drawings are usually made to scale. Example 6

7. Computer drawing The drawings are usually made by commercial software such as AutoCAD, solid works etc. Example 7

8. Engineering Drawing

9. Introduction An engineering drawing is a type of technical drawing, used to fully and clearly define requirements for engineered items, and is usually created in accordance with standardized conventions for layout, nomenclature, interpretation, appearance size, etc. Its purpose is to accurately and unambiguously capture all the geometric features of a product or a component. The end goal of an engineering drawing is to convey all the required information that will allow a manufacturer to produce that component. 9

10. Purpose of an Engineering Drawing An engineering drawing is not an illustration. It is a specification of the size and shape of a part or assembly. The important information on a drawing is the dimension and tolerance of all of its features. 10

11. Elements of Engineering Drawing Engineering drawing are made up of graphics language and word language . Graphics language Describe a shape (mainly). Word language Describe size, location and specification of the object. 11

12. Basic Knowledge for Drafting Graphics language Word language Line types Geometric construction Lettering Projection method 12

13. Traditional Drawing Tools

14. Instruments Drawing board/table. Drawing sheet/paper. Drafting tape. Pencils. Eraser. Sharpener. T-square. Set-squares/triangles. Scales. Compass and divider. 14

15. Drawing table 15

16. Drawing sheet/paper 16

17. Drafting tape 17

18. Pencils Wood pencils: H, 2H, 3H, 4H, 5H, 6H, 7H, 8H, 9H, B, HB, 2B, 3B, 4B, 5B, 6B. Semiautomatic Pencils (lead holder) are more convenient then ordinary wood pencils. 18

19. Eraser 19

20. Erasing Shield 20

21. Sharpener 21

22. T-square 22

23. 23

24. 24

25. 25

26. Set-squares/triangles 26

27. 27

28. Scales 28

29. Compass and divider 29

30. Tissue paper 30

31. Clean paper 31

32. Drawing Standard

33. Introduction Standards are set of rules that govern how technical drawings are represented. Drawing standards are used so that drawings convey the same meaning to everyone who reads them. 33

34. ISO I nternational S tandards O rganization Standard Code ANSI A merican N ational S tandard I nstitute USA JIS J apanese I ndustrial S tandard Japan BS B ritish S tandard UK AS A ustralian S tandard Australia D eutsches I nstitut f ü r N ormung DIN Germany Country Code Full name 34

35. Partial List of Drawing Standards JIS Z 8311 Sizes and Format of Drawings JIS Z 8312 Line Conventions JIS Z 8313 Lettering JIS Z 8314 Scales JIS Z 8315 Projection methods JIS Z 8316 Presentation of Views and Sections JIS Z 8317 Dimensioning Code number Contents 35

36. Drawing Sheet Trimmed paper of a size A0 ~ A4. Standard sheet size ( JIS ) A4 210 x 297 A3 297 x 420 A2 420 x 594 A1 594 x 841 A0 841 x 1189 A4 A3 A2 A1 A0 (Dimensions in millimeters) 36

37. Drawing space Drawing space Title block d d c c c Border lines 1. Type X (A0~A4) 2. Type Y (A4 only) Orientation of drawing sheet Title block Sheet size c (min) d (min) A4 10 25 A3 10 25 A2 10 25 A1 20 25 A0 20 25 37

38. Drawing Scales Scale is the ratio of the linear dimension of an element of an object shown in the drawing to the real linear dimension of the same element of the object. Size in drawing Actual size Length, size : 38

39. Drawing Scales Designation of a scale consists of the word “ SCALE ” followed by the indication of its ratio , as follow SCALE 1:1 for full size SCALE X :1 for enlargement scales (X > 1) SCALE 1: X for reduction scales (X > 1) Dimension numbers shown in the drawing are correspond to “ true size ” of the object and they are independent of the scale used in creating that drawing. 39

40. Basic Line Types Types of Lines Appearance Name according to application Continuous thick line Visible line Continuous thin line Dimension line Extension line Leader line Dash thick line Hidden line Chain thin line Center line NOTE : We will learn other types of line in later chapters. 40

41. Visible lines represent features that can be seen in the current view Meaning of Lines Hidden lines represent features that can not be seen in the current view Center line represents symmetry, path of motion, centers of circles, axis of axisymmetrical parts Dimension and Extension lines indicate the sizes and location of features on a drawing 41

42. Types of Line 42

43. Line Conventions Visible Lines – solid thick lines that represent visible edges or contours Hidden Lines – short evenly spaced dashes that depict hidden features Section Lines – solid thin lines that indicate cut surfaces Center Lines – alternating long and short dashes Dimensioning Dimension Lines - solid thin lines showing dimension extent/direction Extension Lines - solid thin lines showing point or line to which dimension applies Leaders – direct notes, dimensions, symbols, part numbers, etc. to features on drawing Cutting-Plane and Viewing-Plane Lines – indicate location of cutting planes for sectional views and the viewing position for removed partial views Break Lines – indicate only portion of object is drawn. May be random “squiggled” line or thin dashes joined by zigzags. Phantom Lines – long thin dashes separated by pairs of short dashes indicate alternate positions of moving parts, adjacent position of related parts and repeated detail Chain Line – Lines or surfaces with special requirements 43

44. 1 2 3 4 5 6 7 8 9 10 14 13 12 11 Viewing-plane line Extension line Dimension Line Center Line Hidden Line Break Line Cutting-plane Line Visible Line Center Line (of motion) Leader VIEW B-B SECTION A-A Section Line Phantom Line 44

45. ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCD ABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEF Lettering

46. Text on Drawings Text on engineering drawing is used : To communicate nongraphic information. As a substitute for graphic information, in those instance where text can communicate the needed information more clearly and quickly. Uniformity - size - line thickness Legibility - shape - space between letters and words Thus, it must be written with 46

47. Example Placement of the text on drawing Dimension & Notes Notes Title Block 47

48. Lettering Standard ANSI Standard This course Use a Gothic text style, either inclined or vertical. Use all capital letters. Use 3 mm for most text height. Space between lines of text is at least 1/3 of text height. Use only a vertical Gothic text style. Use both capital and lower-case letters. Same. For letters in title block it is recommend to use 6 mm text height N/A. Follows ANSI rule. 48

49. Basic Strokes Straight Slanted Curved Horizontal 1 1 2 3 Examples : Application of basic stroke “ I ” letter “ A ” letter 1 2 3 4 5 6 “ B ” letter 49

50. Suggested Strokes Sequence Straight line letters Curved line letters Curved line letters & Numerals Upper-case letters & Numerals 50

51. The text’ s body height is about 2/3 the height of a capital letter. Suggested Strokes Sequence Lower-case letters 51

52. Stroke Sequence I L T F E H 52

53. V X W Stroke Sequence 53

54. N M K Z Y A Stroke Sequence 4 54

55. O Q C G Stroke Sequence 55

56. D U P B R J Stroke Sequence 1 2 56

57. 5 Stroke Sequence 7 57

58. 6 8 9 Stroke Sequence S 3 58

59. Stroke Sequence l i 59

60. Stroke Sequence v w x k z 60

61. Stroke Sequence j y f r t 61

62. Stroke Sequence c o a b d p q e 62

63. Stroke Sequence g n m h u s 63

64. Word Composition Look at the same word having different spacing between letters. J IRAPONG J I G O R N P A Which one is easier to read ? A) Non-uniform spacing B) Uniform spacing 64

65. Word Composition JIRAPONG \ / \ | )( ) | ( | Space between the letters depends on the contour of the letters at an adjacent side. Spacing Contour | | | | General conclusions are: Good spacing creates approximately equal background area between letters. 65

66. GOOD Not uniform in style. Not uniform in height. Not uniformly vertical or inclined. Not uniform in thickness of stroke. Area between letters not uniform. Area between words not uniform. Example : Good and Poor Lettering 66

67. Leave the space between words equal to the space requires for writing a letter “O”. Example Sentence Composition ALL DIMENSIONS ARE IN MILLIMETERS O O O O UNLESS OTHERWISE SPECIFIED. O 67

68. Dimensioning

69. Dimensioning Guidelines The term “feature” refers to surfaces, faces, holes, slots, corners, bends, arcs and fillets that add up to form an engineering part. Dimensions define the size of a feature or its location relative to other features or a frame of reference, called a datum. The basic rules of dimensioning are: Dimension where the feature contour is shown; Place dimensions between the views; Dimension off the views; Dimension mating features for assembly; Do not dimension to hidden lines; Stagger dimensioning values; Create a logical arrangement of dimensions; Consider fabrication processes and capabilities; Consider inspection processes and capabilities. 69

70. 70

71. Important elements of dimensioning Two types of dimensioning: (1) Size and location dimensions and (2) Detail dimensioning 71

72. Geometrics The science of specifying and tolerancing shapes and locations of features of on objects 72

73. Geometrics It is important that all persons reading a drawing interpret it exactly the same way. Parts are dimensioned based on two criteria: Basic size and locations of the features Details of construction for manufacturing Standards from ANSI (American National Standards Institute) 73

74. Scaling vs. Dimensioning Drawings can be a different scales, but dimensions are ALWAYS at full scale. 74

75. Units of Measure Length English - Inches, unless otherwise stated Up to 72 inches – feet and inches over SI – millimeter, mm Angle degrees, minutes, seconds Angle Dimensions 75

76. Elements of a dimensioned drawing (Be familiar with these terms) 76

77. Arrangement of Dimensions Keep dimension off of the part where possible. Arrange extension lines so the larger dimensions are outside of the smaller dimensions. Stagger the dimension value labels to ensure they are clearly defined. 77

78. Dimensioning Holes Dimension the diameter of a hole. Locate the center-line. Use a notes and designators for repeated hole sizes 78

79. Dimensioning the Radius of an Arc Dimension an arcs by its radius. Locate the center of the radius or two tangents to the arc. 79

80. Drilled Holes, Counter bores and Countersinks Use the depth symbol to define the depth of a drilled hole. Use the depth symbol or a section view to dimension a counter bore. Countersinks do not need a section view. 80

81. Angles, Chamfers and Tapers Dimension the one vertex for an angled face, the other vertex is determined by an intersection. Chamfers are generally 45  with the width of the face specified. 81

82. Rounded Bars and Slots The rounded end of a bar or slot has a radius that is 1/2 its width. Use R to denote this radius, do not dimension it twice. Locate the center of the arc, or the center of the slot. 82

83. Limits of Size All dimensions have minimum and maximum values specified by the tolerance block. Tolerances accumulate in a chain of dimensions. Accumulation can be avoided by using a single baseline. 83

84. Fit Between Parts Clearance Fit Interference Fit Transition Fit Clearance fit: The shaft maximum diameter is smaller than the hole minimum diameter. Interference fit: The shaft minimum diameter is larger than the hole maximum diameter. Transition fit: The shaft maximum diameter and hole minimum have an interference fit, while the shaft minimum diameter and hole maximum diameter have a clearance fit 84

85. Dimensioning standards P. 85

86. Dimension text placement P. 86

87. Unidirectional or aligned dimensioning? 87

88. Dual dimensioning 88

89. Dimensioning Basic Shapes -Assumptions Perpendicularity Assume lines that appear perpendicular to be 90° unless otherwise noted Symmetry If a part appears symmetrical – it is (unless it is dimensioned otherwise) Holes in the center of a cylindrical object are automatically located 89

90. Dimensioning Basic Shapes Rectangular Prism 90

91. Dimensioning Basic Shapes Cylinders Positive Negative 91

92. Dimensioning Basic Shapes Cone Frustum 92

93. Dimensioning Basic Shapes Circle Pattern Center Lines 93

94. Grouping Dimensions Dimensions should always be placed outside the part Yes No 94

95. Dimension guidelines Dimensions should be placed in the view that most clearly describes the feature being dimensioned (contour (shape) dimensioning) 95

96. Dimension guidelines Maintain a minimum spacing between the object and the dimension between multiple dimensions. A visible gap shall be placed between the ends of extension lines and the feature to which they refer. 96

97. Dimension guidelines Avoid dimensioning hidden lines. Leader lines for diameters and radii should be radial lines. 97

98. Where and how should we place dimensions when we have many dimensions? 98

99. Where and how should we place dimensions when we have many dimensions? (cont.) 99

100. Staggering Dimensions Put the lesser dimensions closer to the part. Try to reference dimensions from one surface This will depend on the part and how the tolerances are based. 100

101. Extension Line Practices 101

102. Repetitive Features Use the Symbol ‘x’ to Dimension Repetitive Features 102

103. Symbols for Drilling Operations 103

104. Engineering Curves – I 1. Classification 2. Conic sections - explanation 3. Common Definition 4. Ellipse – ( six methods of construction) 5. Parabola – ( Three methods of construction) 6. Hyperbola – ( Three methods of construction ) 7. Methods of drawing Tangents & Normals ( four cases)

105. Engineering Curves – II 1. Classification 2. Definitions 3. Involutes - (five cases) 4. Cycloid 5. Trochoids – (Superior and Inferior) 6. Epic cycloid and Hypo - cycloid 7. Spiral (Two cases) 8. Helix – on cylinder & on cone 9. Methods of drawing Tangents and Normals (Three cases)

106. ENGINEERING CURVES Part- I {Conic Sections} ELLIPSE 1.Concentric Circle Method 2.Rectangle Method 3.Oblong Method 4.Arcs of Circle Method 5.Rhombus Metho 6.Basic Locus Method (Directrix – focus) HYPERBOLA 1.Rectangular Hyperbola (coordinates given) 2 Rectangular Hyperbola (P-V diagram - Equation given) 3.Basic Locus Method (Directrix – focus) PARABOLA 1.Rectangle Method 2 Method of Tangents ( Triangle Method) 3.Basic Locus Method (Directrix – focus) Methods of Drawing Tangents & Normals To These Curves.

107. CONIC SECTIONS ELLIPSE , PARABOLA AND HYPERBOLA ARE CALLED CONIC SECTIONS BECAUSE THESE CURVES APPEAR ON THE SURFACE OF A CONE WHEN IT IS CUT BY SOME TYPICAL CUTTING PLANES. Section Plane Through Generators Ellipse Section Plane Parallel to end generator. Parabola Section Plane Parallel to Axis. Hyperbola OBSERVE ILLUSTRATIONS GIVEN BELOW..

108. These are the loci of points moving in a plane such that the ratio of it’s distances from a fixed point And a fixed line always remains constant. The Ratio is called ECCENTRICITY. (E) For Ellipse E<1 For Parabola E=1 For Hyperbola E>1 SECOND DEFINATION OF AN ELLIPSE :- It is a locus of a point moving in a plane such that the SUM of it’s distances from TWO fixed points always remains constant. {And this sum equals to the length of major axis .} These TWO fixed points are FOCUS 1 & FOCUS 2 Refer Problem nos. 6. 9 & 12 Refer Problem no.4 Ellipse by Arcs of Circles Method. COMMON DEFINATION OF ELLIPSE, PARABOLA & HYPERBOLA:

109. 1 2 3 4 5 6 7 8 9 10 B A D C 1 2 3 4 5 6 7 8 9 10 Steps: 1. Draw both axes as perpendicular bisectors of each other & name their ends as shown. 2. Taking their intersecting point as a center, draw two concentric circles considering both as respective diameters. 3. Divide both circles in 12 equal parts & name as shown. 4. From all points of outer circle draw vertical lines downwards and upwards respectively. 5.From all points of inner circle draw horizontal lines to intersect those vertical lines. 6. Mark all intersecting points properly as those are the points on ellipse. 7. Join all these points along with the ends of both axes in smooth possible curve. It is required ellipse. Problem 1 :- Draw ellipse by concentric circle method . Take major axis 100 mm and minor axis 70 mm long. ELLIPSE BY CONCENTRIC CIRCLE METHOD

110. 1 2 3 4 1 2 3 4 1 2 3 4 3 2 1 A B C D Problem 2 Draw ellipse by Rectangle method. Take major axis 100 mm and minor axis 70 mm long. Steps: 1 Draw a rectangle taking major and minor axes as sides. 2. In this rectangle draw both axes as perpendicular bisectors of each other.. 3. For construction, select upper left part of rectangle. Divide vertical small side and horizontal long side into same number of equal parts.( here divided in four parts) 4. Name those as shown.. 5. Now join all vertical points 1,2,3,4, to the upper end of minor axis. And all horizontal points i.e.1,2,3,4 to the lower end of minor axis. 6. Then extend C-1 line upto D-1 and mark that point. Similarly extend C-2, C-3, C-4 lines up to D-2, D-3, & D-4 lines. 7. Mark all these points properly and join all along with ends A and D in smooth possible curve. Do similar construction in right side part.along with lower half of the rectangle.Join all points in smooth curve. It is required ellipse. ELLIPSE BY RECTANGLE METHOD

111. C D 1 2 3 4 1 2 3 4 3 2 1 A B 1 2 3 4 Problem 3:- Draw ellipse by Oblong method. Draw a parallelogram of 100 mm and 70 mm long sides with included angle of 75 0. Inscribe Ellipse in it. STEPS ARE SIMILAR TO THE PREVIOUS CASE (RECTANGLE METHOD) ONLY IN PLACE OF RECTANGLE, HERE IS A PARALLELOGRAM. ELLIPSE BY OBLONG METHOD

112. F 1 F 2 1 2 3 4 A B C D p 1 p 2 p 3 p 4 ELLIPSE BY ARCS OF CIRCLE METHOD O PROBLEM 4. MAJOR AXIS AB & MINOR AXIS CD ARE 100 AMD 70MM LONG RESPECTIVELY .DRAW ELLIPSE BY ARCS OF CIRLES METHOD. STEPS: 1.Draw both axes as usual.Name the ends & intersecting point 2.Taking AO distance I.e.half major axis, from C, mark F 1 & F 2 On AB . ( focus 1 and 2.) 3.On line F 1 - O taking any distance, mark points 1,2,3, & 4 4.Taking F 1 center, with distance A-1 draw an arc above AB and taking F 2 center, with B-1 distance cut this arc. Name the point p 1 5.Repeat this step with same centers but taking now A-2 & B-2 distances for drawing arcs. Name the point p 2 6.Similarly get all other P points. With same steps positions of P can be located below AB. 7.Join all points by smooth curve to get an ellipse/ As per the definition Ellipse is locus of point P moving in a plane such that the SUM of it’s distances from two fixed points (F 1 & F 2 ) remains constant and equals to the length of major axis AB.(Note A .1+ B .1=A . 2 + B. 2 = AB)

113. 1 4 2 3 A B D C ELLIPSE BY RHOMBUS METHOD PROBLEM 5. DRAW RHOMBUS OF 100 MM & 70 MM LONG DIAGONALS AND INSCRIBE AN ELLIPSE IN IT. STEPS: 1. Draw rhombus of given dimensions. 2. Mark mid points of all sides & name Those A,B,C,& D 3. Join these points to the ends of smaller diagonals. 4. Mark points 1,2,3,4 as four centers. 5. Taking 1 as center and 1-A radius draw an arc AB. 6. Take 2 as center draw an arc CD. 7. Similarly taking 3 & 4 as centers and 3-D radius draw arcs DA & BC.

114. ELLIPSE DIRECTRIX-FOCUS METHOD PROBLEM 6 :- POINT F IS 50 MM FROM A LINE AB. A POINT P IS MOVING IN A PLANE SUCH THAT THE RATIO OF IT’S DISTANCES FROM F AND LINE AB REMAINS CONSTANT AND EQUALS TO 2/3 DRAW LOCUS OF POINT P. { ECCENTRICITY = 2/3 } F ( focus ) DIRECTRIX V ELLIPSE (vertex) A B STEPS: 1 .Draw a vertical line AB and point F 50 mm from it. 2 .Divide 50 mm distance in 5 parts. 3 .Name 2 nd part from F as V. It is 20mm and 30mm from F and AB line resp. It is first point giving ratio of it’s distances from F and AB 2/3 i.e 20/30 4 Form more points giving same ratio such as 30/45, 40/60, 50/75 etc. 5.Taking 45,60 and 75mm distances from line AB, draw three vertical lines to the right side of it. 6. Now with 30, 40 and 50mm distances in compass cut these lines above and below, with F as center. 7. Join these points through V in smooth curve. This is required locus of P.It is an ELLIPSE. 30mm 45mm

115. 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 5 4 3 2 1 PARABOLA RECTANGLE METHOD PROBLEM 7: A BALL THROWN IN AIR ATTAINS 100 M HIEGHT AND COVERS HORIZONTAL DISTANCE 150 M ON GROUND. Draw the path of the ball (projectile)- STEPS: 1.Draw rectangle of above size and divide it in two equal vertical parts 2.Consider left part for construction. Divide height and length in equal number of parts and name those 1,2,3,4,5& 6 3.Join vertical 1,2,3,4,5 & 6 to the top center of rectangle 4.Similarly draw upward vertical lines from horizontal1,2,3,4,5 And wherever these lines intersect previously drawn inclined lines in sequence Mark those points and further join in smooth possible curve. 5.Repeat the construction on right side rectangle also.Join all in sequence. This locus is Parabola. .

116. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 3 4 5 6 7 8 9 10 11 12 13 14 C A B PARABOLA METHOD OF TANGENTS Problem no.8: Draw an isosceles triangle of 100 mm long base and 110 mm long altitude.Inscribe a parabola in it by method of tangents. Solution Steps : Construct triangle as per the given dimensions. 2. Divide it’s both sides in to same no.of equal parts. 3. Name the parts in ascending and descending manner, as shown. 4. Join 1-1, 2-2,3-3 and so on. 5. Draw the curve as shown i.e.tangent to all these lines. The above all lines being tangents to the curve, it is called method of tangents.

117. A B V PARABOLA ( VERTEX ) F ( focus ) 1 2 3 4 PARABOLA DIRECTRIX-FOCUS METHOD SOLUTION STEPS: 1.Locate center of line, perpendicular to AB from point F. This will be initial point P and also the vertex. 2.Mark 5 mm distance to its right side, name those points 1,2,3,4 and from those draw lines parallel to AB. 3.Mark 5 mm distance to its left of P and name it 1. 4.Take O-1 distance as radius and F as center draw an arc cutting first parallel line to AB. Name upper point P 1 and lower point P 2 . (FP 1 =O1) 5.Similarly repeat this process by taking again 5mm to right and left and locate P 3 P 4 . 6.Join all these points in smooth curve. It will be the locus of P equidistance from line AB and fixed point F. PROBLEM 9: Point F is 50 mm from a vertical straight line AB. Draw locus of point P, moving in a plane such that it always remains equidistant from point F and line AB. O P 1 P 2

118. P O 40 mm 30 mm 1 2 3 1 2 1 2 3 1 2 HYPERBOLA THROUGH A POINT OF KNOWN CO-ORDINATES Solution Steps: 1)       Extend horizontal line from P to right side. 2)       Extend vertical line from P upward. 3)       On horizontal line from P, mark some points taking any distance and name them after P-1, 2,3,4 etc. 4)       Join 1-2-3-4 points to pole O. Let them cut part [P-B] also at 1,2,3,4 points. 5)       From horizontal 1,2,3,4 draw vertical lines downwards and 6)       From vertical 1,2,3,4 points [from P-B] draw horizontal lines. 7)       Line from 1 horizontal and line from 1 vertical will meet at P 1 .Similarly mark P 2 , P 3 , P 4 points. 8)       Repeat the procedure by marking four points on upward vertical line from P and joining all those to pole O. Name this points P 6 , P 7 , P 8 etc. and join them by smooth curve. Problem No.10: Point P is 40 mm and 30 mm from horizontal and vertical axes respectively.Draw Hyperbola through it.

119. VOLUME:( M 3 ) PRESSURE ( Kg/cm 2 ) 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 HYPERBOLA P-V DIAGRAM Problem no.11: A sample of gas is expanded in a cylinder from 10 unit pressure to 1 unit pressure.Expansion follows law PV=Constant.If initial volume being 1 unit, draw the curve of expansion. Also Name the curve. Form a table giving few more values of P & V P V = C + 10 5 4 2.5 2 1 1 2 2.5 4 5 10 10 10 10 10 10 10 + + + + + + = = = = = = Now draw a Graph of Pressure against Volume. It is a PV Diagram and it is Hyperbola. Take pressure on vertical axis and Volume on horizontal axis.

120. F ( focus ) V (vertex) A B 30mm 45mm HYPERBOLA DIRECTRIX FOCUS METHOD PROBLEM 12 :- POINT F IS 50 MM FROM A LINE AB. A POINT P IS MOVING IN A PLANE SUCH THAT THE RATIO OF IT’S DISTANCES FROM F AND LINE AB REMAINS CONSTANT AND EQUALS TO 2/3 DRAW LOCUS OF POINT P. { ECCENTRICITY = 2/3 } STEPS: 1 .Draw a vertical line AB and point F 50 mm from it. 2 .Divide 50 mm distance in 5 parts. 3 .Name 2 nd part from F as V. It is 20mm and 30mm from F and AB line resp. It is first point giving ratio of it’s distances from F and AB 2/3 i.e 20/30 4 Form more points giving same ratio such as 30/45, 40/60, 50/75 etc. 5.Taking 45,60 and 75mm distances from line AB, draw three vertical lines to the right side of it. 6. Now with 30, 40 and 50mm distances in compass cut these lines above and below, with F as center. 7. Join these points through V in smooth curve. This is required locus of P.It is an ELLIPSE.

121. D F 1 F 2 1 2 3 4 A B C p 1 p 2 p 3 p 4 O Q TANGENT NORMAL TO DRAW TANGENT & NORMAL TO THE CURVE FROM A GIVEN POINT ( Q ) JOIN POINT Q TO F 1 & F 2 BISECT ANGLE F 1 Q F 2 THE ANGLE BISECTOR IS NORMAL A PERPENDICULAR LINE DRAWN TO IT IS TANGENT TO THE CURVE. ELLIPSE TANGENT & NORMAL Problem 13 :

122. ELLIPSE TANGENT & NORMAL F ( focus ) DIRECTRIX V ELLIPSE (vertex) A B T T N N Q 90 TO DRAW TANGENT & NORMAL TO THE CURVE FROM A GIVEN POINT ( Q ) 1.JOIN POINT Q TO F. 2.CONSTRUCT 900 ANGLE WITH THIS LINE AT POINT F 3.EXTEND THE LINE TO MEET DIRECTRIX AT T 4. JOIN THIS POINT TO Q AND EXTEND. THIS IS TANGENT TO ELLIPSE FROM Q 5.TO THIS TANGENT DRAW PERPENDICULAR LINE FROM Q. IT IS NORMAL TO CURVE. Problem 14 :

123. A B PARABOLA VERTEX F ( focus ) V Q T N N T 90 TO DRAW TANGENT & NORMAL TO THE CURVE FROM A GIVEN POINT ( Q ) 1.JOIN POINT Q TO F . 2.CONSTRUCT 90 ANGLE WITH THIS LINE AT POINT F 3.EXTEND THE LINE TO MEET DIRECTRIX AT T 4. JOIN THIS POINT TO Q AND EXTEND. THIS IS TANGENT TO THE CURVE FROM Q 5.TO THIS TANGENT DRAW PERPENDICULAR LINE FROM Q. IT IS NORMAL TO CURVE. PARABOLA TANGENT & NORMAL Problem 15 :

124. F ( focus ) V (vertex) A B HYPERBOLA TANGENT & NORMAL Q N N T T 90 TO DRAW TANGENT & NORMAL TO THE CURVE FROM A GIVEN POINT ( Q ) 1.JOIN POINT Q TO F . 2.CONSTRUCT 90 ANGLE WITH THIS LINE AT POINT F 3.EXTEND THE LINE TO MEET DIRECTRIX AT T 4. JOIN THIS POINT TO Q AND EXTEND. THIS IS TANGENT TO CURVE FROM Q 5.TO THIS TANGENT DRAW PERPENDICULAR LINE FROM Q . IT IS NORMAL TO CURVE. Problem 16

125. INVOLUTE CYCLOID SPIRAL HELIX ENGINEERING CURVES Part-II (Point undergoing two types of displacements) 1. Involute of a circle a)String Length = D b)String Length > D c)String Length < D 2. Pole having Composite shape. 3. Rod Rolling over a Semicircular Pole. 1. General Cycloid 2. Trochoid ( superior) 3. Trochoid ( Inferior) 4. Epi-Cycloid 5. Hypo-Cycloid 1. Spiral of One Convolution. 2. Spiral of Two Convolutions. 1. On Cylinder 2. On a Cone Methods of Drawing Tangents & Normals To These Curves. AND

126. CYCLOID: IT IS A LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE WHICH ROLLS ON A STRAIGHT LINE PATH. INVOLUTE: IT IS A LOCUS OF A FREE END OF A STRING WHEN IT IS WOUND ROUND A CIRCULAR POLE SPIRAL: IT IS A CURVE GENERATED BY A POINT WHICH REVOLVES AROUND A FIXED POINT AND AT THE SAME MOVES TOWARDS IT. HELIX: IT IS A CURVE GENERATED BY A POINT WHICH MOVES AROUND THE SURFACE OF A RIGHT CIRCULAR CYLINDER / CONE AND AT THE SAME TIME ADVANCES IN AXIAL DIRECTION AT A SPEED BEARING A CONSTANT RATIO TO THE SPPED OF ROTATION. ( for problems refer topic Development of surfaces) DEFINITIONS SUPERIORTROCHOID: IF THE POINT IN THE DEFINATION OF CYCLOID IS OUTSIDE THE CIRCLE INFERIOR TROCHOID .: IF IT IS INSIDE THE CIRCLE EPI-CYCLOID IF THE CIRCLE IS ROLLING ON ANOTHER CIRCLE FROM OUTSIDE HYPO-CYCLOID . IF THE CIRCLE IS ROLLING FROM INSIDE THE OTHER CIRCLE,

127. INVOLUTE OF A CIRCLE Problem no 17: Draw Involute of a circle. String length is equal to the circumference of circle. 1 2 3 4 5 6 7 8 P P 8 1 2 3 4 5 6 7 8 P 3 3 to p P 4 4 to p P 5 5 to p P 7 7 to p P 6 6 to p P 2 2 to p P 1 1 to p D A Solution Steps: 1) Point or end P of string AP is exactly D distance away from A. Means if this string is wound round the circle, it will completely cover given circle. B will meet A after winding. 2) Divide D (AP) distance into 8 number of equal parts. 3)  Divide circle also into 8 number of equal parts. 4)  Name after A, 1, 2, 3, 4, etc. up to 8 on D line AP as well as on circle (in anticlockwise direction). 5)  To radius C-1, C-2, C-3 up to C-8 draw tangents (from 1,2,3,4,etc to circle). 6)  Take distance 1 to P in compass and mark it on tangent from point 1 on circle (means one division less than distance AP). 7)  Name this point P1 8)  Take 2-B distance in compass and mark it on the tangent from point 2. Name it point P2. 9)  Similarly take 3 to P, 4 to P, 5 to P up to 7 to P distance in compass and mark on respective tangents and locate P3, P4, P5 up to P8 (i.e. A) points and join them in smooth curve it is an INVOLUTE of a given circle.

128. INVOLUTE OF A CIRCLE String length MORE than D 1 2 3 4 5 6 7 8 P 1 2 3 4 5 6 7 8 P 3 3 to p P 4 4 to p P 5 5 to p P 7 7 to p P 6 6 to p P 2 2 to p P 1 1 to p 165 mm ( more than D ) D p 8 Solution Steps: In this case string length is more than  D. But remember ! Whatever may be the length of string, mark  D distance horizontal i.e.along the string and divide it in 8 number of equal parts, and not any other distance. Rest all steps are same as previous INVOLUTE. Draw the curve completely. Problem 18 : Draw Involute of a circle. String length is MORE than the circumference of circle.

129. 1 2 3 4 5 6 7 8 P 1 2 3 4 5 6 7 8 P 3 3 to p P 4 4 to p P 5 5 to p P 7 7 to p P 6 6 to p P 2 2 to p P 1 1 to p 150 mm ( Less than D ) D INVOLUTE OF A CIRCLE String length LESS than D Problem 19: Draw Involute of a circle. String length is LESS than the circumference of circle. Solution Steps: In this case string length is Less than  D. But remember ! Whatever may be the length of string, mark  D distance horizontal i.e.along the string and divide it in 8 number of equal parts, and not any other distance. Rest all steps are same as previous INVOLUTE. Draw the curve completely.

130. 1 2 3 4 5 6 1 2 3 4 5 6 A P D/2 P 1 1 to P P 2 2 to P P 3 3 to P P 4 4 to P P A to P P 5 5 to P P 6 6 to P INVOLUTE OF COMPOSIT SHAPED POLE PROBLEM 20 : A POLE IS OF A SHAPE OF HALF HEXABON AND SEMICIRCLE. ASTRING IS TO BE WOUND HAVING LENGTH EQUAL TO THE POLE PERIMETER DRAW PATH OF FREE END P OF STRING WHEN WOUND COMPLETELY. (Take hex 30 mm sides and semicircle of 60 mm diameter.) SOLUTION STEPS: Draw pole shape as per dimensions. Divide semicircle in 4 parts and name those along with corners of hexagon. Calculate perimeter length. Show it as string AP. On this line mark 30mm from A Mark and name it 1 Mark D/2 distance on it from 1 And dividing it in 4 parts name 2,3,4,5. Mark point 6 on line 30 mm from 5 Now draw tangents from all points of pole and proper lengths as done in all previous involute’s problems and complete the curve.

131. 1 2 3 4 D 1 2 3 4 A B A 1 B 1 A 2 B 2 A 3 B 3 A 4 B 4 PROBLEM 21 : Rod AB 85 mm long rolls over a semicircular pole without slipping from it’s initially vertical position till it becomes up-side-down vertical. Draw locus of both ends A & B. Solution Steps? If you have studied previous problems properly, you can surely solve this also. Simply remember that this being a rod, it will roll over the surface of pole. Means when one end is approaching, other end will move away from poll. OBSERVE ILLUSTRATION CAREFULLY!

132. P C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 1 2 3 4 5 6 7 C D CYCLOID PROBLEM 22: DRAW LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE WHICH ROLLS ON STRAIGHT LINE PATH. Take Circle diameter as 50 mm Solution Steps: 1)      From center C draw a horizontal line equal to D distance. 2)      Divide D distance into 8 number of equal parts and name them C1, C2, C3__ etc. 3)      Divide the circle also into 8 number of equal parts and in clock wise direction, after P name 1, 2, 3 up to 8. 4)      From all these points on circle draw horizontal lines. (parallel to locus of C) 5)      With a fixed distance C-P in compass, C1 as center, mark a point on horizontal line from 1. Name it P. 6)      Repeat this procedure from C2, C3, C4 upto C8 as centers. Mark points P2, P3, P4, P5 up to P8 on the horizontal lines drawn from 2, 3, 4, 5, 6, 7 respectively. 7)      Join all these points by curve. It is Cycloid .

133. C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 1 2 3 4 5 6 7 C D SUPERIOR TROCHOID P PROBLEM 23: DRAW LOCUS OF A POINT , 5 MM AWAY FROM THE PERIPHERY OF A CIRCLE WHICH ROLLS ON STRAIGHT LINE PATH. Take Circle diameter as 50 mm Solution Steps: 1)      Draw circle of given diameter and draw a horizontal line from it’s center C of length  D and divide it in 8 number of equal parts and name them C 1, C2, C3, up to C8. 2)      Draw circle by CP radius, as in this case CP is larger than radius of circle. 3)      Now repeat steps as per the previous problem of cycloid, by dividing this new circle into 8 number of equal parts and drawing lines from all these points parallel to locus of C and taking CP radius wit different positions of C as centers, cut these lines and get different positions of P and join 4)      This curve is called Superior Trochoid.

134. P C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 p 1 p 2 p 3 p 4 p 5 p 6 p 7 p 8 1 2 3 4 5 6 7 C D INFERIOR TROCHOID PROBLEM 24: DRAW LOCUS OF A POINT , 5 MM INSIDE THE PERIPHERY OF A CIRCLE WHICH ROLLS ON STRAIGHT LINE PATH. Take Circle diameter as 50 mm Solution Steps: 1)      Draw circle of given diameter and draw a horizontal line from it’s center C of length  D and divide it in 8 number of equal parts and name them C 1, C2, C3, up to C8. 2)      Draw circle by CP radius, as in this case CP is SHORTER than radius of circle. 3)      Now repeat steps as per the previous problem of cycloid, by dividing this new circle into 8 number of equal parts and drawing lines from all these points parallel to locus of C and taking CP radius with different positions of C as centers, cut these lines and get different positions of P and join those in curvature. 4)      This curve is called Inferior Trochoid .

135. C C 1 C 2 C 3 C 4 C 5 C 8 C 6 C 7 EPI CYCLOID : P O R r = CP + r R 360 = 1 2 3 4 5 6 7 Generating/ Rolling Circle Directing Circle PROBLEM 25: DRAW LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE WHICH ROLLS ON A CURVED PATH. Take diameter of rolling Circle 50 mm And radius of directing circle i.e. curved path, 75 mm. Solution Steps: 1)  When smaller circle will roll on larger circle for one revolution it will cover  D distance on arc and it will be decided by included arc angle  . 2)  Calculate  by formula  = (r/R) x 360 0. 3)  Construct angle  with radius OC and draw an arc by taking O as center OC as radius and form sector of angle  . 4)  Divide this sector into 8 number of equal angular parts. And from C onward name them C1, C2, C3 up to C8. 5)  Divide smaller circle (Generating circle) also in 8 number of equal parts. And next to P in clockwise direction name those 1, 2, 3, up to 8. 6)  With O as center, O-1 as radius draw an arc in the sector. Take O-2, O-3, O-4, O-5 up to O-8 distances with center O, draw all concentric arcs in sector. Take fixed distance C-P in compass, C1 center, cut arc of 1 at P1. Repeat procedure and locate P2, P3, P4, P5 unto P8 (as in cycloid) and join them by smooth curve. This is EPI – CYCLOID.

136. HYPO CYCLOID C P 1 P 2 P 3 P 4 P 5 P 6 P 7 P 8 P 1 2 3 6 5 7 4 C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 O OC = R ( Radius of Directing Circle) CP = r (Radius of Generating Circle) + r R 360 = PROBLEM 26: DRAW LOCUS OF A POINT ON THE PERIPHERY OF A CIRCLE WHICH ROLLS FROM THE INSIDE OF A CURVED PATH. Take diameter of rolling circle 50 mm and radius of directing circle (curved path) 75 mm. Solution Steps: 1)  Smaller circle is rolling here, inside the larger circle. It has to rotate anticlockwise to move ahead. 2)  Same steps should be taken as in case of EPI – CYCLOID. Only change is in numbering direction of 8 number of equal parts on the smaller circle. 3)  From next to P in anticlockwise direction, name 1,2,3,4,5,6,7,8. 4)    Further all steps are that of epi – cycloid. This is called HYPO – CYCLOID .

137. 1 2 3 4 5 6 7 8 P P 1 P P 2 P 3 P 4 P 5 P 6 P 7 P 8 1 2 3 4 5 6 7 HELIX (UPON A CYLINDER ) PROBLEM : Draw a helix of one convolution, upon a cylinder. Given 80 mm pitch and 50 mm diameter of a cylinder. (The axial advance during one complete revolution is called The pitch of the helix) SOLUTION: Draw projections of a cylinder. Divide circle and axis in to same no. of equal parts. ( 8 ) Name those as shown. Mark initial position of point ‘P’ Mark various positions of P as shown in animation. Join all points by smooth possible curve. Make upper half dotted, as it is going behind the solid and hence will not be seen from front side.

138. X Y e’ a’ b’ d’ c’ g’ f’ h’ o’ h a b c d e g f O DEVELOPMENT A B C D E F A G H O 1 2 3 4 6 5 7 1’ 2’ 3’ 4’ 5’ 6’ 7’ 1 2 3 4 5 6 7 HELIX CURVE Problem 9: A particle which is initially on base circle of a cone, standing on Hp, moves upwards and reaches apex in one complete turn around the cone. Draw it’s path on projections of cone as well as on it’s development. Take base circle diameter 50 mm and axis 70 mm long. It’s a construction of curve Helix of one turn on cone : Draw Fv & Tv & dev.as usual On all form generators & name. Construction of curve Helix:: Show 8 generators on both views Divide axis also in same parts. Draw horizontal lines from those points on both end generators. 1’ is a point where first horizontal Line & gen. b’o ’ intersect. 2’ is a point where second horiz . Line & gen. c’o ’ intersect. In this way locate all points on Fv. Project all on Tv.Join in curvature. For Development: Then taking each points true Distance From resp.generator from apex, Mark on development & join.

139. Tangent Normal Q Involute Method of Drawing Tangent & Normal STEPS: DRAW INVOLUTE AS USUAL. MARK POINT Q ON IT AS DIRECTED. JOIN Q TO THE CENTER OF CIRCLE C . CONSIDERING CQ DIAMETER, DRAW A SEMICIRCLE AS SHOWN. MARK POINT OF INTERSECTION OF THIS SEMICIRCLE AND POLE CIRCLE AND JOIN IT TO Q. THIS WILL BE NORMAL TO INVOLUTE. DRAW A LINE AT RIGHT ANGLE TO THIS LINE FROM Q. IT WILL BE TANGENT TO INVOLUTE. 1 2 3 4 5 6 7 8 P P 8 1 2 3 4 5 6 7 8 INVOLUTE OF A CIRCLE D C

140. Q N Normal Tangent CYCLOID Method of Drawing Tangent & Normal STEPS: DRAW CYCLOID AS USUAL. MARK POINT Q ON IT AS DIRECTED. WITH CP DISTANCE, FROM Q. CUT THE POINT ON LOCUS OF C AND JOIN IT TO Q. FROM THIS POINT DROP A PERPENDICULAR ON GROUND LINE AND NAME IT N JOIN N WITH Q.THIS WILL BE NORMAL TO CYCLOID. DRAW A LINE AT RIGHT ANGLE TO THIS LINE FROM Q. IT WILL BE TANGENT TO CYCLOID. P C 1 C 2 C 3 C 4 C 5 C 6 C 7 C 8 D CYCLOID C C P