Engineering Graphics Lecture Notes

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Presentation transcript:

Engineering Graphics Lecture Notes UNIT – 1 “PLANE CURVES” I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes PLANE CURVES (or) SPECIAL CURVES ELLIPSE PARABOLA HYBERBOLA CYCLIOD INVOLUTE OF SQUARE INVOLUTE OF CIRCLE I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes PLANE CURVES (or) SPECIAL CURVES I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes CONIC SECTIONS CIRCLE I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes CONIC SECTIONS ELLISPE I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes 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 I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes Construction of Ellipse A. CONCENTRIC CIRCLES METHOD C. INTERSECTING LINES METHOD B. INTERSECTING ARCS METHOD I - SEMESTER 20.09.2012

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX F - FOCUS EF = 50 mm C ● F E ● ● ● D I - SEMESTER 20.09.2012

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

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

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

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

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

Engineering Graphics Lecture Notes 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 ● ● ● ● ● ● ● ● ● ● ● ● ● 1 2 3 4 5 6 7 8 9 ● G ● D I - SEMESTER 20.09.2012 H ●

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

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

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● 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 ●

Engineering Graphics Lecture Notes 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 ● ● ● ● ● ● ● ● ● ● ● ● ● 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 ●

Engineering Graphics Lecture Notes 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 ● ● ● ● ● ● ● ● ● ● ● ● ● 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 ●

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Similarly ,repeat for all the rest of lines C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● 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 ●

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) Make a smooth curve with arc points C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● 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 ●

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) This is your required “ELLIPSE” C ● V1 F V2 E ● ● ● ● ● ● ● ● ● ● ● ● ● 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 ●

Engineering Graphics Lecture Notes CONIC SECTIONS PARABOLA I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes PARABOLA 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 I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes Construction of Parabola A. INTERSECTING LINES METHOD B. INTERSECTING ARCS METHOD I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX F - FOCUS EF = 50 mm C ● F E ● ● ● D I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX F - FOCUS EF = 50 mm Eccentricity (e) = 1 E -V1 = EF/2 C V1 -1 = 5 mm ● 1 - 2 = 10 mm V1 F E ● ● ● ● ● ● ● ● ● ● 1 2 ● D I - SEMESTER 24.09.2012

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

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

Engineering Graphics Lecture Notes 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 ● ● ● ● ● ● ● ● ● ● 1 2 3 4 5 6 7 Using Compass, For “E - 2” as Radius with “F” as centre ● cut the arc in line 2 D I - SEMESTER 24.09.2012

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

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

Engineering Graphics Lecture Notes CONIC SECTIONS HYBERBOLA I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes HYBERBOLA Z ● F X’ X ● ● ● 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 I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes Construction of Hyberbola I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes ECCENTRICITY METHOD (METHOD AS PER SYLLABUS) CD - DIRECTRIX F - FOCUS C ● F E ● ● ● D I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes 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 ● ● ● ● ● ● ● 1 2 3 4 ● G ● D I - SEMESTER 24.09.2012

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

Engineering Graphics Lecture Notes 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 ● ● ● ● ● ● ● 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

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

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

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

Engineering Graphics Lecture Notes CYCLOID DEFINITION:- A curve generated by a point on the circumference of a circle which rolls without slipping along a fixed straight line. I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes 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. I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes 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 Circle Circumference (C) = 2πR i.e; C = 2 x π x 25 = 157 mm The Line AB = 157 mm ● ● A B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Draw a circle with A as centre for the radius of 25mm ● ● A B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Divide the circle into 12 equal parts 6 5 7 4 8 3 ● ● 9 A B 2 10 1 11 12 I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes 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 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 11 12 I - SEMESTER 27.09.2012

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

Engineering Graphics Lecture Notes Construction of Cycloid Draw a horizontal lines through the points 1,2,3 etc…marked on the circumference 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 11 12 I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Using Compass, For “a -a” as Radius cut the arc in point 11 - 1 with ‘a’ as centre 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Using Compass, For “b -b” as Radius cut the arc in point 10 - 2 with ‘b’ as centre 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Using Compass, For “c -c” as Radius cut the arc in point 9 - 3 with ‘c’ as centre 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 24.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Using Compass, For “d -d” as Radius cut the arc in point 8 - 4 with ‘d’ as centre 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Similarly, Repeat for the rest of the radius as “e – e” etc… 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes This is your “CYCLIOD” Make the smooth curve by just touching the arcs in HB Pencil 6 5 7 4 8 3 ● ● ● ● ● ● ● ● ● ● ● ● ● 9 A a b c d e f g h i j k B 2 10 1 ● ● ● ● ● ● ● ● ● ● ● ● 11 12 a b c d e f g h i j k I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes INVOLUTE DEFINITION:- An involute is the locus of a point on a string, as the string unwinds itself from a line or polygon, or a circle, keeping always the string taut. I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Involute Example Problem:- Draw an Involute of a circle, whose diameter is 20 mm I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Solution:- Draw a line AB with the distance equal to the circumference of the circle Circle Diameter (D) = 20 mm Circle Radius (R) = 10 mm Circle Circumference (C) = 2πR i.e; C = 2 x π x 10 = 62.8 mm The Line AB = 62.8 mm ● ● A B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Draw a circle with A as centre for the radius of 10mm ● ● A B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Divide the circle into 12 equal parts 6 7 5 8 4 ● ● 3 A 9 B 10 2 11 1 12 I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Divide the line AB into 12 equal parts 6 7 5 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 9 B 10 2 11 1 12 I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Make tangent lines in the point 1,2,3 ….. upto 11 6 7 5 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B 10 2 11 1 12 I - SEMESTER 27.09.2012

I - SEMESTER 27.09.2012 6 7 5 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 10 11 B 10 2 11 1 12 I - SEMESTER 27.09.2012

Using Compass, For “A - 1” as Radius with “1” as centre 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● Using Compass, 10 2 ● ● ● 11 For “A - 1” as Radius 1 12 with “1” as centre cut the arc in line 1 I - SEMESTER 27.09.2012

Using Compass, For “A - 2” as Radius with “2” as centre 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● Using Compass, 10 2 ● ● ● 11 For “A - 2” as Radius 1 12 with “2” as centre cut the arc in line 2 I - SEMESTER 27.09.2012

Using Compass, For “A - 3” as Radius with “3” as centre 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● Using Compass, 10 2 ● ● ● 11 For “A - 3” as Radius 1 12 with “3” as centre cut the arc in line 3 I - SEMESTER 27.09.2012

Using Compass, For “A - 4” as Radius with “4” as centre 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● Using Compass, 10 2 ● ● ● 11 For “A - 4” as Radius 1 12 with “4” as centre cut the arc in line 4 I - SEMESTER 27.09.2012

Using Compass, For “A - 5” as Radius with “5” as centre 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● Using Compass, 10 2 ● ● ● 11 For “A - 5” as Radius 1 12 with “5” as centre cut the arc in line 5 I - SEMESTER 27.09.2012

cut the arc in all the lines as per their length as radius 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● Using Compass, 10 2 ● ● ● 11 cut the arc in all the lines as per their length as radius 1 12 I - SEMESTER 27.09.2012

Make a smooth curve with arc intersecting points 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● 10 2 ● ● ● 11 1 Make a smooth curve with arc intersecting points 12 I - SEMESTER 27.09.2012

Highlight the curve with HB pencil 6 ● 7 5 ● ● 8 4 ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 A 1 2 3 9 4 5 6 7 8 9 10 11 B ● ● 10 2 ● ● ● 11 1 Highlight the curve with HB pencil 12 This is your “INVOLUTE” I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Involute Example Problem:- Draw an Involute of a square, whose side is 20 mm I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Solution:- Draw a line AB with the distance equal to the circumference of the square Square side (a) = 20 mm Circumference (C) = 4a i.e; C = 4 x 20 = 80 mm The Line AB = 80 mm ● ● A B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Draw a square with A as starting point for the side length of 20 mm ● ● A B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Divide the line AB into 4 equal parts ● ● ● ● ● A 1 2 3 B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Number the corners of the square 3 2 ● ● ● ● ● 1 A 1 2 3 B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Construction of Cycloid Draw tangent line in each points 3 2 ● ● ● ● ● 1 A 1 2 3 B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Using Compass, For “A - 1” as Radius with “1” as centre cut the arc in line 1 3 2 ● ● ● ● ● 1 A 1 2 3 B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Using Compass, For “A - 2” as Radius with “2” as centre cut the arc in line 2 3 2 ● ● ● ● ● 1 A 1 2 3 B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes Using Compass, For “A - 3” as Radius with “3” as centre cut the arc in line 3 3 2 ● ● ● ● ● 1 A 1 2 3 B I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes 3 2 ● ● ● ● ● 1 A 1 2` 3 B Make a smooth curve with arc intersecting points I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes 3 2 ● ● ● ● ● 1 A 1 2` 3 B Highlight the curve with HB pencil This is your “INVOLUTE” C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 27.09.2012

Engineering Graphics Lecture Notes THANK YOU C.R.ENGINEERING COLLEGE Alagarkovil, Madurai - 625301 I - SEMESTER 20.09.2012