A Computer Based Training Package On
ENGINEERING DRAWING
Student’s Guide
Salem – 636005.
First Edition, October 2000
2000 Sonaversity, Salem, All Rights Reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publishers.
CONTENTS CHAPTER I
II
III
IV
TITLE
P.NO
Introduction to Engineering Drawing 1.1 Introduction 1.2 Objectives 1.3 Drawing Instruments 1.4 BIS & ISO Conventions 1.5 Beginning your Drawing 1.6 Exercises Geometric Construction 2.1 Introduction 2.2 Geometrical Terms 2.3 General Construction Orthographic Projection 3.1 Introduction 3.2 Objectives 3.3 What is a projection 3.4 Types of Projection Projections
3 3 3 7 20 21 25 25 31 37 37 37 38
Projections of a Point
4.1 Objectives 4.2 Notation 4.3 Projection of Point in the I-quadrant II-quadrant III-quadrant IV-quadrant 4.4 Exercises Projections of Straight lines 4.5 Introduction 4.6 Objectives 4.7 Projection of Straight line Perpendicular to the HP and parallel to the VP Perpendicular to the VP and parallel to the HP Parallel to the HP and Inclined to the VP Parallel to the VP and Inclined to the HP Inclined to the HP and the VP Parallel to the HP and the VP 4.8 Exercises Projections of Solids 4.9 Introduction 4.10 Objectives 4.11 Classification of Solids
42 42 43 43 44 45 46 47 47 48 49 50 51 52 53 54 56 56 56
V
VI
VII
VIII IX
4.12 Projection of Solids Perpendicular to the HP Parallel to the HP and the VP Parallel to the HP and Inclined to the VP Parallel to the VP and Inclined to the HP Inclined to the VP and the HP 4.13 Exercises Section of Solids 5.1 Introduction 5.2 Objectives 5.3 Sectional view and convention 5.4 Types of section 5.5 Section of Solids when the cutting plane is Perpendicular to the VP and parallel to the HP Perpendicular to the HP and parallel to the VP Perpendicular to the VP and inclined to the HP Perpendicular to the HP and inclined to the VP 5.6 Exercises Pictorial projections 6.1 Introduction Isometric projection 6.2 Objectives 6.3 Terminology 6.4 Isometric views of prism 6.5 Isometric views of Cylinder and Cone 6.6 Isometric views of Compound solids 6.7 Exercises Development of Surfaces 7.1 Introduction 7.2 Parallel line development 7.3 Radial line development 7.4 Exercises Intersection of Surfaces 8.1 Introduction Further development in Engineering Drawing 9.1 Introduction
64 66 68 69 71 73 76 76 76 77 79 81 83 87 91 93 93 94 98 101 105 110 120 120 123 125 127 128
Chapter - I Engineering Drawing Introduction A picture is worth saying a thousand words; hence drawings are used to visually communicate ideas, thoughts, and designs. Drawings drawn by an engineer for engineering purposes is Engineering Drawing. Drawing is the Universal Graphical Language of Engineers, spoken, read and written in its own way. Engineers must have perfect drawing skills and excellent working knowledge of engineering concepts. An inaccurate drawing may misguide the workman and ultimately affect the production. Objectives In this, the first session, you'll be looking at drawing instruments and the typical accessories used in drawing. On completion of the session, you should be able to: •= Identify various types of drawing instruments and their uses. •= Classify drawing sheets and the different grades of drawing pencils. •= Draw the layout and title block on a drawing sheet. •= Use the lettering and dimensioning techniques in common practice. Drawing Instruments The Drawing Board The D2 or D3 drawing boards are usually used in polytechnics and engineering colleges. Drawing boards are made of well-seasoned softwood such as Oak or Pine. The standard sizes of drawing boards as per BIS (1444-1977) are given in the table.
The Drawing Sheet The standard sizes of drawing sheets as per BIS (10711-1983) are given in the table. The ratio of the width of a drawing sheet to its length is 1: √2. The drawing sheet should be tough and strong and its fibers should not disintegrate when an eraser is used on its surface.
Minidrafter: A minidrafter is a device with two scales set at right angles to each other. It combines the functions of a T-square, setsquares, scales and a protractor. It can be easily and quickly moved to any location on the drawing sheet without altering the scales. The T-Square A T-square is mainly used together with setsquares for drawing horizontal lines, angles and perpendicular lines. There are two essential parts of a T-square, namely the stock and the blade. The blade is fitted with ebony or a plastic piece to form the working edge of the T-square. The stock and the blade of a T-square are held together at right angles to each other. T-squares are made of hard quality wood such as teak or mahogany, etc.
Instrument Box The instrument box contains the following instruments and accessories. •=
Compasses-Large compasses and Bow compasses
•=
Dividers-Plain Dividers and Bow Dividers
•=
An Inking pen
•=
A lead case
•=
A Small Screwdriver
The instruments in an instrument box are made of nickel coated steel or brass.
The Compasses A pair of compasses are used to draw circles and arcs. Compasses are used in conjunction with scales (rulers). Large compasses Large compasses are used to draw circles up to 100 mm diameter. For drawing circles of more than 100 mm diameter, a lengthening bar is used. Bow compasses Bow compasses are used for drawing small circles up to 25 mm diameter. The Dividers Dividers are used in conjunction with scales. Plain Dividers Plain dividers are used to divide straight or curved lines into a prescribed number of equal parts, for transferring dimensions and for setting of distances from a scale to drawings. Bow Dividers Bow dividers are used to hold precise distances for dividing or transferring. Inking Pen An inking pen is used to draw straight or curved lines in tracing ink.
Lead Case A lead case is used to store pencil leads. Small screwdriver A screwdriver is used to tune the screws in the instruments. The Setsquares Setsquares are used to draw parallel and perpendicular lines. Setsquares are made of transparent celluloid or acrylic and may also contain French curves.
The Procircle A procircle is circular in shape. Its periphery is divided into 0.5° graduations that are used to mark and measure angles. It also has circular holes of different sizes that may be used to draw circles of specific diameter. The Scales Scales or rulers are devices with precise graduations marked on their straight edges for precise measurements. Scales are made of celluloid or cardboard. Eight types of scales are used (M1, M2,..,M8) as per BIS 10713 - 1983. Scale of a Drawing The drawing of an object is usually produced to a definite proportion with respect to the actual size of the object. This ratio is called the "scale of drawing". Drawing to Full scale: When a drawing is produced to a size equal to that of the object, the drawing is said to be drawn to "full scale". Drawing to a reduced scale: When a drawing is produced to a size smaller than that of the object, the drawing is said to be drawn to a "reduced scale". Drawing to an enlarged scale: When a drawing is produced to a size greater than that of the object, the drawing is said to be drawn to an "enlarged scale".
DrawingPencils Drawing pencils are of different grades. The HB pencil is a soft grade used for drawing thick lines, borderlines, lettering and arrowheads. The H pencil is used to draw finishing lines, visible lines and hidden lines. The 2H pencil is a hard grade pencil used for drawing construction lines, dimension lines, centre lines and section lines. Other grades are used for artistic application. Eraser An eraser is a good quality rubber that is used to erase unwanted lines, arcs etc., from a drawing.
Clips Drawing clips are used to fix the drawing sheet on the drawing board. They are made of nickelcoated steel. Cello tape (Adhesive tape) may also be used in place of clips to fix the drawing sheet on the board.
Sharpener and Emery Paper A pencil sharpener is used to give pencils with good drawing tips. Emery paper (120 grade) is used to obtain a conical or chisel tipped pencil. French curves French curves are used for drawing irregular curves that cannot be drawn by compasses. BIS & ISO Drawing Conventions The International Standards Organization (ISO) Geneva has formulated International standards for Engineering Drawing. The Bureau of Indian Standards (BIS) previously known as Indian Standards Institution (ISI) has adopted the ISO standards. The ISO standards are applicable to the following topics: •= Layout of Drawing sheet •= Line Types •= Lettering in Drawing •= Dimensioning Methods •= Arrows
Layout of Drawing Sheet Engineering students generally use A2 or A3 size drawing sheets. After fixing the drawing sheet on to the drawing board, the "Border lines" and the "Title block" are first drawn. The Borderlines: An ideal working space for drawing is obtained by drawing the borderlines. The following steps are involved in drawing the borderlines: Draw a filing margin of 30 mm width at the left-hand edge of he drawing sheet. Provide margins of a minimum of 10 mm each at the top, bottom and right side of the drawing sheet. Use an HB pencil for drawing the borderlines. 30
Border line BORDER LINE
10
10
10
SHEET LAYOUT
The Title block: A rectangle of 185mm x 65mm, drawn at the bottom right side corner of the drawing sheet, is called the “Title Block” and should give the following details: 1. Name of the institution. 2. Name of student, class, roll. no., etc. 3. Title of the drawing. 4. Date of submission, etc. Use an HB pencil for drawing the title block and the lettering of the details included in it. 185 130 15
65
THIAGARAJAR GROUP OF INSTITUTIONS
10
STANLY RAJ.S
10
ROLL NO:99223
10
I YEAR
BATCH:A
SCALES
DATE:15-12-99
1010
1
1010
SHEET N
TITLE BLOCK
Folding of a Drawing Sheet: After the completion of a drawing, the sheet must be properly folded and neatly filed.
Line Types: In an engineering drawing, every line has a definite meaning. Various types of lines are used to represent different parts or portions of an object.
Lettering in Drawing: Lettering plays a major role in engineering drawing. It indicates details like dimensioning, name of the drawing, etc. The use of instruments for lettering is not advised, as it will consume more time. Free hand lettering should be used instead.
Rules and Features: -
Lettering in drawing must be of standard height. The standard heights of letters used are 3.5mm, 5mm, 7mm and 10mm.
-
Generally, the height to width ratio of letters and numerals are approximately 5:3.
-
The height to width ratio of the letters M and W are approximately 5:4.
-
Different sizes of letters are used for different purposes: Main Title
- 7 or 10mm
Sub-title
- 5 or 7mm
Others
- 3.5 or 5mm.
Features: The essential features of lettering used in engineering drawing are: •=
Legibility
•=
Uniformity
•=
Similarity
Single stroke letters are the simplest form of letters and are generally used in engineering drawing. Vertical Lettering: Vertical lettering is upright, i.e. 90 ( to the horizontal. Both uppercase or large and lowercase or small letters are used.
Inclined Lettering: Inclined lettering has letters inclined at 75° to the horizontal and as for vertical lettering both uppercase and lowercase letters are used.
Dimensioning Methods: Dimensioning is used to describe a drawing in terms of details such as the size, shape and position of the object as per the Dimensioning Code 11669 - 1986. Expressing these details in terms of numerical values, lines and symbols is known as dimensioning.
General Rules of Dimensioning:
1. Dimension lines are to be drawn maintaining a gap of 12 mm from the object line and a gap of 10 mm between adjacent dimension lines.
35
12 m m
12 m m 10 m m 10 m m
10 20 30
2. Dimension lines should not cross extension lines.
15
15
Correct
Incorrect
3. All the information should be written horizontally. 10 ,15 DEEP
10, 15 DEEP
Correct
Incorrect
4. A given dimension should be indicated only once. It should not be repeated at another place. 15
15
10
10 Front view Side view
5.
a. The overall dimensions should be placed outside the smaller dimensions. 30 10
10 30
Correct
Incorrect
5. b. When an overall dimension is given, one of the smaller dimensions should not be given unless it is needed for reference. 30
10
30 10
10
10
10
Incorrect
Correct
6. The larger dimensions should be placed outside the smaller ones such that the extension lines do not cross the dimension lines. 30 10
10
30 10
10
Correct
Incorrect
7. No dimensions other than those that are necessary need be given.
Unnecessary indication of dimension
25
50
25
100
8. Avoid indicating dimensions inside a drawing.
20 20
Correct
10
10
Incorrect
9. Always indicate the diameter of a circle, not its radius. The symbol ( is used before the dimension, except when it is obvious.
15 15
Correct
R 7.5
Incorrect
10. The radius of an arc should always be indicated with the abbreviation R placed before the dimension. R5
5
Correct
Incorrect
11. Extension lines should not cross each other or dimension lines unless this can be done without making the drawing more complicated. 10
10
10
10
10
10
10
10
Correct
Incorrect
12. Avoid dimensioning of hidden lines if possible.
10
10
Correct
Incorrect
13. Always show the angles outside the space representing an object.
0
45
45 0
14. Dimensions should be given from the centre lines, finished surfaces, or datum’s as applicable to a drawing. 10 10 10
10
30 60 90
15. The centre line should never be used as a dimension line. 50 50
Correct
Incorrect
16. In the unidirectional system of dimensioning, all dimensions must be upright and readable
15
when the drawing is viewed in its normal upright position.
20
17. In the aligned system, the dimensions must be readable when the drawing is viewed in its
15
normal upright position or from its right hand side.
20
18. In a drawing of a part with circular ends, the centre-to-centre dimension is given instead of an overall dimension.
R 10 20
19. When a number of dimensions are indicated on one side of a drawing, they should appear on a continuous line.
15 15
20
35
35
20
Correct
Incorrect
20. Intersecting construction lines and projection lines shall extend slightly beyond their point of intersection.
60
0
POINT OF INTERSECTION
Unidirectional Method: In this system, the dimensions are indicated in the vertical / upright position so that they can be read easily when the drawing is viewed in its upright position. The numerical values are placed at
F
F
20
50
the centres of the dimension lines.
26
65
Aligned Dimensioning: In this system, the dimensions are indicated so as to be perpendicular to the dimension lines. In other words, the horizontal dimensions can be read conveniently when the drawing is viewed normally. Similarly, the vertical dimensions can be read easily from the right side of the sheet.
F 50
F 20
26
65
Dimensioning Arrangements Chain Dimensioning: When successive dimensions are arranged in a straight line, the method used is called chain dimensioning.
30
20
5
20
20
30
Parallel Dimensioning: When a number of dimensions are indicated from a common datum, the system is known as parallel dimensioning.
20 45 65 85 105 125 145
Progressive Dimensioning: In this method, a dot and a zero sign indicate the datum line. The dimensions are indicated
40
18
0
40 32
22 62
20 74
85
100
16
progressively from the datum.
Co-ordinate Dimensioning: The method of dimensioning shown in the figure is known as co-ordinate dimensioning. For simplicity, the same dimensions can be shown separately in a tabular form as shown in the figure.
0
200
180
20
140
Sample: 2 0
Sample: 1 X 0
0
20
1
0
25 0
20
0 02
Y
3 20 0
2
3
4
5
0 02
1
15
4
0
5 160
X 20 20 60 60 100 Y 20 160 60 120 90 f 20 20 10 15 25
2
Arrows: Drawing an arrowhead terminates dimension lines. The arrowhead may be open, closed or closed and filled. The length to width ratio of an arrowhead should be limited to 3:1.
O pen arrow C losed arrow C losed and Filled arrow
Your First Drawing Step1: Clean the drawing board and instruments. Step2: Fix the thick cardboard sheet as padding sheet on the drawing board using clips/cello tape. Step3: Fix the drawing sheet over the cardboard using clips/cello tape. Step4: Fix the Minidrafter at the top-left corner of the drawing board. Step5: Draw the borderlines using an HB pencil.
Introduction to Engineering Drawing – Exercises 1. Write freehand in single stroke vertical capital letters of 5mm height the following sentence. i)
“The correct use of energy is at the root of industrial progress and productivity.”
ii)
“Small things make perfection, but perfection is not a small thing”.
iii)
“Engineering Drawing is a graphical language an universal language of all engineers”.
iv)
“The main requirements for lettering on engineering drawings are legibility, uniformity, ease and rapidity in execution”.
2.
Read the dimensioned drawing shown in figure. Redraw the figure to full size and dimension it as per BIS. i.
ii.
iii.
iv.
v.
vi.
Chapter - II Geometric Construction Introduction This chapter deals with some of the important basic construction techniques frequently used in Engineering Drawing. Geometric Terms Triangle A triangle has three sides; the sum of its angles is equal to 180º. Equilateral Triangle An equilateral triangle is a triangle, which has three equal sides. AB = BC = CA
A
∠ABC = ∠BCA = ∠CAB = 60°
60
B
Right-Angled Triangle
o
C
In a right-angled triangle, the included angle between two of its sides is equal to 90º. ∠ABC = 90º
A
90” B
C
Isosceles Triangle: An isosceles triangle is a triangle, which two sides, and two angles are equal. AB=AC and ∠ACB=∠ABC
A
B
C
Quadrilateral A quadrilateral has four sides; the sum of all its angles is equal to 360º. Square When all the sides of a quadrilateral are equal and all its internal angles are right angles, the quadrilateral is called a square.
D
C
A
B
AB = BC = CD = DA
Rectangle
When the opposite sides of a quadrilateral are equal and all its internal angles are right angles, the quadrilateral is called a rectangle. AB = CD and BC = AD
D
C
A
B
Rhomboid When the opposite sides and angles of a quadrilateral are equal and none of its angles are right angles, the quadrilateral is called a rhomboid. AB = CD
D
C
BC = AD ∠=ABC= ∠=CDA and ∠=BCD= ∠=DAB
A
B
Rhombus When all the sides of a quadrilateral are equal and none of its internal angles are right angles, but the opposite angles are equal, the quadrilateral is called a rhombus. AB = BC = CD = DA
D
C
∠=ABC= ∠=CDA and ∠=BCD = ∠=DAC.
A
B
Trapezoid When two opposite sides of a quadrilateral are equal and the other two opposite sides are parallel, the quadrilateral is called a trapezoid. AB = CD
C
AD || BC
D
A
Trapezium
B
When no side of a quadrilateral is parallel or perpendicular to any of its other sides, the quadrilateral is called a trapezium.
C
D
A
B
Parts of a Circle Arc The part of a circle between any two points on its circumference is called an arc. Arc = AB A
B A
Arc
B
Segment The part of a circle bounded by an arc and a chord is called a segment. Segment = ABC
Chord A A C B C B Segm ent
Chord A straight line joining any two points on the circumference of a circle is called a chord. Chord = AB
Chord A
B
Sector The part of circle bounded by two radii and an arc is called a sector. Sector = DEF D Chord
E F D
F
E Sector
Polygons Types of Polygons A plane figure bounded by straight lines is called a polygon. Polygons are classified into two types. They are: 1. Regular Polygon 2. Irregular Polygon
Regular Polygon A polygon in which all the sides and all the angles are equal is called a regular polygon.
Pentagon: A regular pentagon has five equal sides. Its angles are equal. The internal angle of a regular polygon of "n" sides= {(2n-4) 90°}/n. The internal angle of a regular pentagon = 108° AB = BC = CD = DE = EA
D
C
E
o
108
Hexagon:
A
B
A regular hexagon has six equal sides. Its angles are equal. The internal angle of a regular hexagon =120° AB = BC = CD = DE = EF = FA
E
D
F
C o
120 A
B
Heptagon: A regular heptagon has seven equal sides. Its angles are equal. The internal angle of a regular heptagon = 128.57° AB = BC = CD = DE = EF = FG = GA
E D
F
C
G
128.57 A
o
B
Octagon A regular octagon has eight equal sides. Its angles are equal. The internal angle of a regular octagon = 135°
F
E
AB=BC=CD=DE=EF=FG=GH=HA D
G
H
135 A
C
o
B
Nonagon A regular nonagon has nine equal sides. Its angles are equal. The internal angle of a regular nonagon = 140°
F
AB=BC=CD=DE=EF=FG=GH=HI=IA
G
E
H
D
I
140
C
o
B
A
Decagon A regular decagon has ten equal sides. Its angles are equal. The internal angle of a regular decagon = 144°
G
F
AB=BC=CD=DE=EF=FG=GH=HI=IJ=JA H
E
I
D
J
Irregular Polygon
144 A
o
C
B
The sides and angles of an irregular polygon are unequal. Hence irregular polygons are not used in engineering drawing.
Geometric Construction: To Bisect a Line: 1. Draw the given line AB. 2. With A as centre and radius greater than half AB, draw arcs on both sides of AB. 3. Similarly with B as centre and the same radius, draw arcs to intersect the previous arcs at C and D. 4. Join C and D. The line AB is now bisected. C
A
B
o
D
To Bisect an Arc: 1. Draw the given arc AB. 2. With A as centre and a radius greater than half AB, draw an arc on both sides of AB. 3. Similarly with B as centre, and the same radius draw arcs to intersect the previous arcs at C and D. 4. Join C and D. The arc AB is now bisected. C
A
B
D
To find the centre of an arc: 1. Draw the given arc AB. 2. Draw two chords PQ and RS of any length within AB. 3. Bisect the chords. 4. Let the bisectors intersect at O; then O is the centre of the arc.
R
A
P
Q
s O
B
To Bisect an Angle: 1. Draw the given angle ABC 2. With B as centre and any radius, draw an arc cutting AB at D and BC at E 3. With D and E as centres and the same or any other radius, draw arcs within the angle to intersect each other at F 4. Join B and F. The line BF divides the angle ABC equally, or "bisects" it. A
D
F
B
E
C
To construct a regular Pentagon: 1. Draw a line BA equal in length to the given side of the pentagon. 2. At B, draw a line at an angle of 108º (angle of regular polygon of "n" sides= {(2n-4) 90°}/n) to AB. 3. Similarly at A draw a line at angle of 108º to AB. 4. With B as centre and radius equal to AB draw an arc on the first line to cut it at C (AB=BC). 5. Similarly, with A as centre and radius AB draw an arc on the second line to cut it at E (BA=AE). 6. With C and E as centres and radius equal to AB draw arcs to intersect at D. 7. Join CD and ED. ABCDE is the required pentagon.
D
E
C
108
B
108
A
To Construct a regular Hexagon: 1. Draw a line AB equal in length to the given side of the hexagon. 2. Draw perpendiculars at A and B. 3. Draw two lines at 120° to AB, one at the left of A and another one at right of B. 4. With A as centre and the radius equal to AB, draw an arc on the second line to cut it at F. 5. With B as centre and radius equal to AB, draw an arc to cut the first line at C. 6. With C and F as centres and equal to AB cut the perpendiculars at D and E. 7. Join CD, FE and ED. ABCDEF is the required hexagon.
D
E
C
F 120 60
0
0
120
0
A
60 B
0
To construct a regular Octagon: 1. Draw a line BA equal in length to the given side of the octagon. 2. Draw perpendiculars at A and B. 3. Draw two lines at 135° to AB, one at the left of B and the other one at the right of A. 4. With B as centre and radius equal to AB, draw an arc to cut the first line at C. 5. With A as centre and the same radius (=AB), draw an arc on the second line to cut it at H. 6. Through C and H draw lines parallel to the perpendiculars at A and B. 7. Using compasses draw CD and HG equal to AB. 8. With G and D as centres and radius equal to AB cut the perpendiculars (at A and B) at F and E. 9. Join DE, EF and FG. ABCDEFGH is the required octagon. E
F
D
G
C
H
135 135 B
A
GENERAL CONSTRUCTION METHOD OF POLYGON:
D E C O
B
A
M
Chapter – III Orthographic Projection Introduction Engineers are mainly involved in the design and development of machines and structures. To design and communicate every detail of a machine /structure, engineers must prepare a drawing that shows the true size and shape of the entire machine or structure. It is difficult to represent a three dimensional object exactly on a sheet of paper by showing a single view. Hence sets of views from different positions are prepared to define the object completely. Though different methods of projections are available to obtain the views of objects, the orthographic projection is used for most engineering purposes.
Objectives This session will help you to learn •= What a projection is. •= What the horizontal and vertical planes are. •= What are the types of projections normally used. •= How to identify and differentiate between the first angle and third angle projections. What is Projection The views of an object formed on a transparent plane, by viewing it perpendicularly from the front, top or side of the object are called its projections.
The Front View of an Object: The view of an object formed on a transparent plane by viewing it perpendicularly from the front of the object is called its front view. It can also be called as "elevation". Note: In general, the front view of an object (FV) is taken as the view normal (or perpendicular) to the longest side of the object.
The Top view of an Object: The view of an object formed on a transparent plane, by looking at it perpendicularly from the top is called the top view of the object. Note: 1. The top view is usually placed above the front view in the case of third angle projection. 2. The top view is also called "plan" and is placed below the front view in the case of first angle projection. The Side view of an Object: The view of an object formed on a transparent plane, by looking at it perpendicularly from the side is called the side view of the object. The view taken from the right hand side of the object is called its "right side view". Similarly the view from the left hand side is the "left side view". Types of Projection: 1. Pictorial Projection 2. Orthographic Projection Pictorial Projection: 1. Isometric Projection 2. Oblique Projection 3. Perspective Projection 1. Isometric Projection: "Iso" means equal and "metric projection" means projection to a reduced measure. The tilting angle of the view is 30º to the horizontal.
R S P0 120
120
Q
0
120
D
0
B
30
0
A
30
0
2. Oblique Projection: Oblique projection is a slanting projection. The tilting angle is either 30º or 45º. Thus an oblique drawing can be drawn directly without using any of the projection techniques.
45
0
3. Perspective Projection: In perspective drawings, the objects are represented more realistically than other drawings. A photograph of a person or object is a perspective of the person or the object. Very often an architect uses photographic representation. Perspective drawings show three-dimensional objects in a single plane as they appear to our eye.
Orthographic Projection: "Ortho" means right angle and "Ortho-graphic" means right-angled drawing. The projections of an object are perpendicular to the plane on which the projections are` obtained are known as orthographic projections. Imaginary rays of light from an observers eyes viewing an object from an infinite distance will be parallel to each other and perpendicular to the object and the plane on which a projection of the object will be produced.
Vertical and Horizontal Planes: The picture planes that are used for obtaining orthographic projections are customarily called the principal planes of projection or the reference planes. The plane in front of an observer is the vertical plane and is denoted by VP. The other plane, which is perpendicular to the VP, is called the horizontal plane and is denoted by HP.
XY – reference line HP – Horizontal Plane
Vertical and Horizontal Planes: To obtain projections on a drawing sheet: It is conventional to rotate the HP through 90º in a clockwise (CW) direction about the reference line XY, so that it lies in the extension of the VP, as shown in the figure. The front view of an object is obtained in the VP and its top view is obtained in the HP, if the object lies in the I-Quadrant. The Four Quadrants: When the planes of projection are extended beyond their line of intersection, they form four quadrants, as shown in the figure. These four quadrants are named as the I-Quadrant, the II-Quadrant, the III-Quadrant, and the IVQuadrant, moving in the counter clockwise direction. II Quadrant
I Quadrant l tica r e V e 90 o n Pla ine Y
III Quadrant
The First Angle Projection:
H o r P izo la n n ta e l
R
X
eL nc a r efe
IV Quadrant
When an object is situated in the I-Quadrant, the projection obtained is called the first angle projection. In this projection, 1. The object lies between the observer and the plane of projection. 2. The object is situated above the HP and in front of the VP. 3. The front view of the object comes above its top view with respect to the reference line. This is the ISI symbol for first angle projection.
The Third Angle Projection: When the object is situated in the III-Quadrant, the projection obtained is called the third angle projection. In this projection, 1. The planes of projection lie between the object and the observer 2. The object is situated above the ground or below the HP and behind the VP. 3. The top view of the object comes above its front view with respect to the reference line. This is the ISI symbol for third angle projection
Chapter – IV Projections The views of an object formed on a transparent plane by viewing it perpendicularly from the front, top or side of the object are called its projections.
Projections of a Point Objectives At the end of this session, you will be able to •= Draw the projections of a point in the four quadrants. •= Identify the position of the point in different quadrants. Notation To obtain the projections of points in space, standard notations are followed: 1. The actual points in space are denoted by capital letters A, B, C, D, etc., 2. The front views are denoted by the corresponding lowercase letters with dashes like a', b', c', d', etc., and their top views are denoted by the corresponding lowercase letters like a, b, c, d, etc. 3. Projectors are always drawn as continuous thin lines using a 2H pencil. 4. The visible points are drawn with a H pencil. 5. Lettering is always drawn with a HB pencil.
Projection of a Point in the I-Quadrant OK...! Let us imagine that a Point A is 20 mm above the HP and 30 mm in front of the VP 1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line. 2. Draw a line perpendicular to XY. 3. On the perpendicular line mark a point ‘a’ 30 mm below XY. (Top view) 4. On the perpendicular line mark a point ‘a'’ 20 mm above XY. (Front view) 5. Erase the unwanted lines. 6. The points a and a' are the projections of the point A in the I- quadrant. a'
X VP
HP
Y
O
a
Projection of a Point in the II-Quadrant OK...! Let us imagine that a Point B is 25 mm above the HP and 35mm behind the VP. 1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line. 2. Draw a line perpendicular to XY. 3. On the perpendicular line mark a point b 35mm above XY.(Top view) 4. On the perpendicular line mark a point b' 25mm above XY.(Front view) 5. Erase the unwanted lines. 6. The points b' and b are the projections of the point B in the II- quadrant. b b'
X
O
Y
Projection of a Point in the III-Quadrant OK...! Let us imagine a Point C 35 mm below the HP and 25 behind the VP. 1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line. 2. Draw a line perpendicular to XY. 3. On the perpendicular line mark a point ‘c’ 25mm above XY. .(Top view) 4. On the perpendicular line mark a point ‘c'’ 35mm below XY. .(Front view) 5. Erase the unwanted lines. 6. The points c and c' are the projections of the point C in the III- quadrant.
c
X
HP VP
O
c'
Y
Projection of a Point in the IV-Quadrant OK...! Let us imagine a Point D 30mm below the HP and 40 mm in front of the VP. 1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line. 2. Draw a line perpendicular to XY. 3. On the perpendicular line mark a point ‘d’ 40mm below XY.(Top view) 4. On the perpendicular line mark a point ‘d'’ 30mm below XY.(Front view) 5. Erase the unwanted lines. 6. The points d and d' are the projections of the point D in the IV- quadrant.
X
O
d' d
Y
Projection of Points – Exercises 1. Draw the projections of the point A, 35mm below the HP and in the VP. 2. Draw the projections of the point B, 45mm behind the VP and in the HP. 3. Draw the projections of the point C, 25mm below the HP and 25mm in front of the VP. 4. Draw the projections of the point D, 30mm above the HP and 30mm behind the VP. 5. Draw the projections of the point E, 20mm above the HP and 25mm in front of the VP. 6. Draw the projections of the point F, in both the VP and the HP. 7. Draw the projections of the point G, 40mm below the HP and 35mm behind the VP. 8. Draw the projections of the point H, 35mm above the HP and 40mm behind the VP.
X
Y
9. Figure shows the projections of different points. Determine the position of the Points with reference to the projection planes. 10. A Point 30mm below XY is the plan of two points A and B. Point A is the Horizontal plane and point B is 40mm below the Horizontal plane. Draw the projections of A and B.
Projections of a Straight Line Introduction The shortest distance between any two points is called a "straight line". Different surfaces and planes form the configuration or shape of any object. Revolving or moving straight lines in different ways obtains these surfaces and planes. Thus a straight line is the basic conceptual figure using which any object like a machine component or a structural element is represented. Thus projection of a straight line is the foundation of Engineering Drawing. In the previous session, we have studied the projections of given points. Joining the respective projections of two points therefore gives the projection of the straight line joining the two points. As per ISO convention the first angle of projection is used. Objectives At the end of the session, you will be able to •=
Define straight line.
•=
Draw the projections of a straight line located at different positions with respect to the VP and the HP.
Perpendicular to the HP and Parallel to the VP OK...! Let us imagine that a Line AB 25mm is parallel to the VP and perpendicular to the HP! Point A is 35mm above the HP and 20mm in front of the VP! B is 10 mm above the HP..! 1. Draw the line XY. 2. Draw a line perpendicular to XY using a 2H pencil. 3. Mark b' 10mm above XY on the perpendicular line. 4. Mark a' 25mm above b'. 5. a' b' is the front view, join a', b' using a H pencil. 6. Mark a (b) 20mm below XY; a (b) is the top View. 7. Erase the unwanted Lines.
25
a’
10
b’
Y 20
X
VP HP
a(b)
Perpendicular to the VP and Parallel to the HP Ok...! Let us imagine that a Line AB of length 25mm is perpendicular to the VP and Parallel to the HP. The point A is 20mm above the HP and 10mm in front of the VP. 1. Draw the line XY. 2. Draw a line perpendicular to XY using a 2H pencil. 3. Mark "a" 10mm below XY on the perpendicular line. 4. Mark "b" 25mm below "a". 5. Join "a" and "b" using an H pencil to get the top view. 6. Mark a' (b') 20mm above XY line on the perpendicular line 7. Erase the unwanted Lines b'(a')
VP X
Y
HP a
b
Parallel to the HP and Inclined to the VP Ok ...! Let us imagine that a line PQ of length 40mm is parallel to the HP and inclined at an angle of 35° to the VP. The end P is 20mm above the HP and 15mm in front of the VP. 1. Draw the line XY. 2. Draw a line perpendicular to XY using a 2H pencil 3. Mark “p'” and “p” respectively 15 mm above XY and 20mm below XY on the perpendicular line 4. From “p” draw a line at an angle of 35° to XY and mark “q” such that pq = 40mm = true length. 5. pq is the top view of the given line in the I-Quadrant. 6. From “q” draw a projector (perpendicular line) to intersect the horizontal line drawn from “p'” at “q'”. 7. p' q ' is the front view. 8. Erase the unwanted line.
p’
20
q’
VP X HP
15
Y
p
35” 40
q
Parallel to the VP and Inclined to the HP Ok...!
Let us imagine that a line PQ of length 40mm is parallel to the VP and inclined at an
angle of 30° to the HP. The end P is 15mm above the HP and 20mm in front of the VP. 1. Draw the line XY. 2. Draw a perpendicular line to XY using 2H pencil. 3. Mark p' & p 15mm above XY & 20mm below XY on the perpendicular line. 4. From p' draw a line at angle of 30° to XY and mark q'. such that p'q'= 40mm = True length 5. p' q' is the required Front View 6. From q' draw a projector (perpendicular line) to intersect the horizontal line drawn from p at q. 7. pq is the required Top View 8. Erase the unwanted Line
q'
p'
30º
VP Y
X
HP p
q
Inclined to the HP and the VP Ok...! Let us imagine that the line pq is inclined to both the VP and the HP. 1. Draw the line XY. 2. Mark “p” below XY line and draw 45° line and mark q2 at 80mm 3. Mark “p'” above XY line and draw 30° line and mark “q1' ” at 80mm 4. Draw locus of “q1' ” and “q2” 5. Project from “q1' ” and “p” as centre rotate, it cuts locus of “q2” at “q” 6. Joint “p” and “q” to get top view 7. Project from “q2” and “p' ” as centre rotate, it cuts locus of “q1' ” at “q' ” 8. Joint “p’” and “q’” to get front view
p’
q 1’ Locus of q’
q’
80 e e lin Tru 30 0
20
q 2’ VP HP
Y
30
X
q p
1
45 Tr u
80
el
in
e
Locus of q
q q
2
Parallel to the HP and the VP Ok...! Let us imagine that a Line CD 30mm long is parallel to both planes. The line is 40mm above the HP and 25mm in front of the VP. 1. Draw the line XY. 2. Draw a line perpendicular to XY using a 2H pencil. 3. Draw another perpendicular line 30mm from the previous line. 4. Mark “c'” and “d' ” on the Perpendicular lines and join them to get the front view. 5. Mark “c” 25mm below line XY; join “c” and “d” to get the top view. 6. Erase the unwanted Lines. 30 c'
d'
VP X
HP
c
d
Y
Projection of Straight Line - Exercises 1.
A line AB, 55mm long kept parallel to both the HP and VP: 20mm above the HP and 25mm in front of VP. Draw the Projections.
2.
A Line CD, 50mm long kept perpendicular to the VP and 20mm above the HP. The end C, nearer to the VP is 15 mm in front of it.
3.
A Line MN, 85mm long is parallel to the VP and inclined at 450 to the HP. The end M is 25mm above the HP and 20mm in front of the VP. Draw the projections of the line MN.
4.
The end L of line 55mm long is 10mm above the HP and 10mm in front of the VP. The line is parallel to the HP and inclined to the VP. The length of the elevation is 40mm. Draw the projections of the line and find the inclination of the line with the VP.
5.
A line RS, 70mm long lies in the HP and has its end R in both the HP and the VP. It is inclined at 400 to the VP. Draw the projections of the line.
6.
A line EF is parallel to the VP. The end E is 20mm above the HP and 25mm in front of the VP. The end F is 65mm above the HP. The distance between the end projectors is 65mm. Find the true length and inclination of the line with the HP.
7.
One end I of the line IJ is in the VP and 35mm above the HP. The line is parallel to the HP and inclined at 350 to the VP. The length of the elevation is 55mm. Find the true length of the line.
8.
A line EF, 70mm long has its end E, 20mm above the HP and 20mm in front of the VP. The line is inclined at 500 to the HP and 300 to the VP. Draw the projections of the line and find the traces of the line.
9.
The end U of the line UV, 85mm long is in both the HP and the VP. The line is inclined at 350 to the HP and 400 to the VP. Draw its operations.
10.
A line RS, 70mm long is in the first quadrant with the end R in the HP and the end in the VP. The line is inclined in the 300 to the HP and 450 to the VP. Draw the projections of the line RS and indicate the projections of the mid-point M to the line.
11.
The end M of the line MN is 25mm behind the VP and 35mm below the HP. The other end N is 45mm above the HP and 55mm in front of the VP. The distance between the
projectors of M and N is 75mm. Draw the projections of the line MN and find its true length, traces and inclinations with the reference planes. Use rotating line method. 12.
The end L of the line LM is 20mm behind the VP and 30mm below the HP. The other end M is 40mm above the HP and 50mm in front of the VP. The distance between the projectors of L and M is 70mm. Draw the projections of the line LM and find its true length, traces and inclinations with the reference planes. Use rotating trapezoidal plane method.
13.
The projections of E and F of the line EF given in problem 11 are on the same projector. Draw the projections of the line EF. Find its true length, traces and inclinations with the reference planes.
14.
The projectors of two points K and L are 100mm apart. K is 55mm below the HP and 40mm in front of the VP. L is 100mm above the HP and 35mm behind the VP. Draw the projections of the line joining K and L. Determine the true length and inclinations of the line KL with the reference planes.
15.
One end of P of line PQ, 80mm long is 10mm above the HP and 15mm in front of the VP. The line is inclined at 400 to the HP and top view makes 500 with the VP. Draw the projections of the line and find its true inclination with the VP.
16.
One end of I of line IJ, 75mm long is 20mm above the HP and 15m in front of the VP. The line is inclined at 350 to the VP and top view has a length of 45mm. Draw the projections of the line and find its true inclination with the HP.
Projections of Solids Introduction An object having three dimensions, i.e., length, breadth and height is called as solid. In orthographic projection, minimums of two views are necessary to represent a solid. Front view is used to represent length and height and the top view is used to represent length and breadth. Sometimes the above two views are not sufficient to represent the details. So a third view called as side view either from left or from right is necessary. Objectives At the end of this session, you will be able to •= Classify the different types of solids •= Draw the projections of solids in various positions in the given quadrant
Classification of Solids Solids are classified into two groups. They are •= Polyhedra •= Solids of Revolution Polyhedra A solid, which is bounded by plane surfaces or faces, is called a polyhedron. Polyhedra are classified into three sub groups; these are 1. Regular Polyhedra 2. Prisms 3. Pyramids Regular Polyhedra Polyhedra are regular if all their plane surfaces are regular polygons of the same shape and size. The regular plane surfaces are called "Faces" and the lines connecting adjacent faces are called "edges".
Tetrahedran O
Apex
C
B
A
Octahedran O
1
D C
A B
O
2
Hexahedran
D
Top face C
A B 4
Base 3
1 2
Prisms: A prism has two equal and similar end faces called the top face and the bottom face or (base) joined by the other faces, which may be rectangles or parallelograms. Triangular prism
C
Top face
B
Longer edge
A
Axis Face
3
Bottom face
2 1
Square Prism
Top face Longer edge Axis Face
C D
B A
3
Bottom face (Base)
2
4 1 Rectangular Prism C D
Top face
B
A
Longer edge Axis Face Bottom face (Base)
3 4
2 1
Pentagonal Prism
Top face
C
D
B
E A
3
4
Bottom face (Base)
5
2 1
Hexagonal Prism
D
E F
C A
5
Top face
B
4 3
6 1
2
Bottom face (Base)
3. Pyramids: A pyramid has a plane figure as at its base and an equal number of isosceles triangular faces that meet at a common point called the "vertex" or "apex". The line joining the apex and a corner of its base is called the slant edge. Pyramids are named according to the shapes of their bases.
Triangular Pyramid
O
Apex or Vertex Slant Edges
Triangular face
Bottom face (Base)
C
A B
Square Pyramid O
Apex or Vertex Slant Edges Triangular face
D
Bottom face (Base) Base edge
C
A B
Rectangular Pyramid O
Apex or Vertex Slant Edges Triangular face Bottom face (Base)
D
A B
C
Pentagonal Pyramid Apex or Vertex
Bottom face (Base)
Hexagonal Pyramid
Apex or Vertex
Bottom face (Base)
Solids of Revolution: If a plane surface is revolved about one of its edges, the solid generated is called a Solid of Revolution.
Sphere A sphere can be generated by the revolution of a semi-circle about its diameter that remains fixed.
Cone A cone can be generated by the revolution of a right-angled triangle about one of its perpendicular sides, which remains fixed. A cone has a circular base and an apex. The line joining apex and the centre of the base is called the “Axis” of the cone.
Apex
Generators Axis
Base
Cylinder A right circular cylinder is a solid generated by the revolution of a rectangular surface about one of its sides, which remains fixed. It has two circular faces. The line joining the centres of the top and the bottom faces is called “Axis”.
Generators Axis
Base
Projections of Solids Perpendicular to the HP 1. OK...! Let us imagine that a cube of 50mm side is resting with one of its square faces on the HP. 1. Draw the line XY. 2. Draw the top view as a square (Side 50 mm) and name its corners. 3. Draw projectors at each corner of the top view through line XY. 4. Draw the front view as a square (Side 50 mm) and name its corners. 5. Dimension the completed drawing.
(d') a'
X
b' (c')
(4') 1'
2' (3') Y
(4) d
c (3)
(1) a
b (2)
2. Ok...! Let us imagine that a square prism of base 30mm and height 60mm is resting with its base on the HP and one of its vertical faces perpendicular to the VP. 1. Draw the line XY 2. Draw the top view as square and name its corners. 3. Draw projectors from each corner of the top view through XY. 4. Draw the front view as shown and name its corners. 5. Dimension the completed drawing.
b’(c’)
60
(d’) a’
(4’)1’
2’(3’)Y
(4) d
c (3)
30
X
(1) a
b (2)
Parallel to the HP and the VP 1. OK...! Let us imagine that a square prism of base 30mm and axis 60mm long lies on the HP, such that its axis is parallel to both the HP and the VP. 1. Draw the line XY. 2. Draw the projections ( top and front views) of the solid in simple position ( an edge of its base is perpendicular to the VP). 3. Rotate the front view through 90°. 4. Draw projectors from the rotated front view and the initial top view and name the points of intersection. 5. Join the points correspondingly to get the final top view.
a (d)
X
b(c)
(4) 1
a (d)
(4) (4)1
2(3) 2(3)
b(c) Y
d
(3) (2)4
(d) c
(3)1
(a) b
c
(4)
a(1)
b(2)
2. OK...!Let us imagine that a hexagonal prism of base 30mm and axis 60mm long lies on one of its rectangular faces on the HP, such that its axis is parallel to both the HP and the VP. (Side View Method) 1. Draw the lines XY and X1Y1 perpendicular to each other, intersecting at P as shown. 2. Draw the side view of the hexagonal prism and name its corners. 3. Draw projectors from the corners of the side view perpendicular to X1Y1. 4. Draw the front view and name its corners. 5. From P draw a line at 45° to XY and X1Y1. (This line is called the Miter line). 6. From the side view draw projectors to meet the Miter line. 7. From the Miter line draw projectors parallel to XY. 8. From the front view draw projectors parallel to X1Y1 and name the intersection points. 9. Draw the final top view. X
1
60
30 (1’’) a’’
(2") b’’ (3")c’’
X
f’’(6")
e’’(5")
d’’(4") 45
o
(6’)1’
a’(f’)
(5’)2’
b’(e’)
(4’)3’
c’(d’)
P
Y
5 (4)6
f(d)
(3)1
a(c)
2
Y
e
1
b
Parallel to the HP and Inclined to the VP 1. Ok...! Let us imagine that a hexagonal prism of base 30mm and height 60mm lies on one of its rectangular faces lies on the HP, such that its axis is inclined at 45° to the VP. 1. Draw the line XY. 2. Draw the projections of the prism in simple position. 3. Rotate the axis of the top view through 45° with respect to XY. 4. Draw projectors from the rotated top view and the initial front view and name the points of intersection.. 5. Join all the points correspondingly to get the final front view.
30 e' (5')
c' (3')
(6') f '
a' (1')
(2') b'
6
(1) 5
(2) 4
f
(a) e
(b) d
X
51'
d' (4')
(31')
6 1'
1 1' 450 3
c
41 '
2 1'
e1'
d1 '
f1 '
a1'
c1'
b 1'
Y
Parallel to the VP and Inclined to the HP 1. OK...! Let us imagine that a pentagonal prism of base 20mm and axis 40mm long rests on one of the edges of its base on the HP. The edge makes an angle of 30° to the HP and the axis of prism is parallel to the VP. 1. Draw the line XY. 2. Draw the projection of the prism in simple position. 3. Rotate the base of the front view through 300 with respect to XY so that only the edge (3',4') rests on the HP. 4. Draw projectors from the rotated front view and the initial top view and name the points of intersections. 5. Join the points correspondingly to get the final top view.
a'
b' (e')
c' (d')
1'
2' (5')
3' (4')
300
X
Y
51
(5) e
(1) a
11
d1
a1
c (3) b (2)
e1 41
d (4)
c1
31 21
b1
2. OK...!Let us imagine that a pentagonal pyramid of base 25mm and axis 55mm long lies on one of its longer edges on the HP and its axis is parallel to the VP. 1. Draw the line XY. 2. Draw the projection of solid in simple position. 3. Rotate the Front view such that one of the slant edge o'd' will lie on XY Line. 4. Draw projectors from the rotated front view and the initial top view and name it.
5.
Join the points correspondingly to get the final top view.
o’
(b’)
55
a’ e ’ (c ’)
d’ d’
o’
e’ (c’)
(b’) a’
X
c
c
1
b
b
25
o
d
d
1
1
o a
a e
e
Y
1
1
1
Inclined to the VP and the HP 1. OK...! Let us imagine that a square prism of base 20mm and axis 40mm long has its axis inclined at 60° to the HP and an edge of its base is inclined at 45° to the VP. 1. Draw the line XY. 2. Draw the projection of the prism placed in the simple position. 3. Rotate the front view axis through 60°. 4. Draw projectors from the rotated front view and the initial top view and name the points of intersection. 5. Join the points correspondingly to get the top View. 6. Rotate base 2'3' of the rotated top view through 45°. 7. Draw projectors from the rotated top view and the rotated front view and name the point of intersection. 8. Join all the points correspondingly to get the final front view.
a1 '
d1 ' a' (d')
o2'
o2'
b'(c')
c1 '
41 '
b1 '
11 ' o1 '
1' (4')
X
o1 '
2'(3')
31 ' 41
c (3)
(4) d o2 (o1 ) (1) a
11
c1
o2
o1 b (2)
20
d1 (3 1 )
a 1 (2 1)
b1
45
21'
Y
2. OK...! Let us imagine that a cone of base 30mm diameter and axis 60mm long has its axis inclined at 45° to the HP and 30° to the VP. 1. Draw the line XY. 2. Draw the projections of the cone placed in the simple position. 3. Rotate the axis of the front view through 45°. 4. Draw projectors from the rotated front view and the initial top view and name the points of intersection. 5. Join the points correspondingly to get the top view. 6. Rotate the axis of the rotated top view through 30°. 7. Draw projectors from the rotated top view and the rotated front view and name the points of intersection. 8. Join all the points correspondingly to get the final front view.
o’ o’
o 1’
60
a’
a 1’
b’
d 1’p 1’ b 1’
(d ’)
b’ (d’)
c’
c 1’
c’
a’ X
Y
d
d
1
d a
o (p)
c
a
p
1
1
c
1
0
c
1
p
0 30 b
0
1
b
a
1
1
1
b
1
1
1
Projection of Solids – Exercises 1.
A cube of side 55mm resting on the HP on one of its faces with one of its vertical faces inclined at 300 to the VP, draw the top view and front view.
2.
A pentagonal prism side of base 25mm and axis 55mm resting on the HP on its base with one of the rectangular faces inclined at 45° to VP draw the top view and front view.
3.
A hexagonal pyramid side of base 25mm and axis 55mm resting on its base HP, and the base edge is inclined at 45° to VP draw the top view and front view.
4.
A cone of radius 20mm and axis 60mm resting with its base on HP, draw the projections.
5.
Draw the projection of hexagonal prism of base 30mm and axis 65mm rests with its base on HP and the base side is parallel to and 20mm in front of VP.
6.
A tetrahedron of side 50 mm and rests on HP draw the projections when one of its edge is parallel to VP.
7.
Draw the projections of hexagonal prism of base 30mm and axis 55mm resting on one corner of the base on HP and the base containing the edge 45° to HP and axis perpendicular to VP.
8.
A square prism, side of base 35mm and axis 60mm long lies with one of its longer edge on HP. Draw the projection of prism when the axis is perpendicular to VP and one of its rectangular faces is inclined to 35° to HP.
Parallel to Both HP and VP 9. A cylinder of base diameter 30mm and axis 60mm long lies with one of its generators on HP. Draw the projection when the axis is parallel to both planes. 10. A hexagonal prism base 30mm and axis 60mm long lies with one of its longer edge on hp and the axis is parallel to both HP and VP. Draw the projection, use side view method.
Parallel to VP and inclined to HP 11. A square prism, side of base 30mm and axis 60mm, has an edge of its base on HP. Draw the projection, when the axis is inclined at 60° to HP and parallel to VP 12. A cone of base diameter 25mm and axis 50mm resting on HP with a point of its base circle on HP. Draw the projection of cone when the axis is inclined at 30° to HP and parallel to VP. 13. A cylinder of base 30mm and axis 50mm rests with a base circle on HP. Draw the projection when axis making an angle 30° to HP and parallel to VP. 14. A pentagonal prism base 25mm and axis 60mm long rests with base edge on HP. Draw the projection of prism when the axis is inclined at 45° to HP and parallel to VP. 15. A cone base 30mm diameter and axis 60mm long, touches the VP on a point of its base circle. Draw the projection when the axis is inclined at 30° to HP and parallel to VP. 16. Draw the projection of cube 30mm long resting on HP on one of its corner with a solid diagonal parallel to both HP and VP. 17. Draw the projection of square pyramid, base 30mm and axis 55mm rests with its edge of the base on HP such that its base makes an angle of 30° to HP and parallel to VP Parallel to HP and inclined to VP 18. Draw the projection of pentagonal prism base 25mm and axis 60mm long, lies with one of its rectangular edge on HP such that the axis is inclined at 30° to VP. 19. Draw the projection of pentagonal pyramid base 25mm and axis 60mm long lies with one of its triangular edge on HP such that the axis is inclined at 60° to VP. 20. A cylinder of base diameter 25mm and axis 60mm long, lies with one of its generators on HP such that the axis is inclined at 45° to VP. Draw its projection.
Axis inclined to Both HP and VP 21. Draw the projection of a cube of base 40mm rests with its edges on HP and one of the faces containing that edge is inclined to 30° to HP. The edge on which the cube rests is parallel to VP. 22. A hexagonal prism side of base 30mm and axis 60mm, resting with one of the edge of its base on HP. Draw the projection when its axis is inclined at 30° to HP and top view of the axis is 50° to VP. 23. A hexagonal pyramid side of base 30mm and axis 60mm, resting with one of the corner of its base on HP. Draw the projections when its axis is inclined at 30° to HP and 45° to VP.
Chapter - V Section of Solids Introduction The orthographic views of a component may not always give all the information clearly; they give only the component's external information. An object with a lot of inner details, seen in orthographic views will have numerous dotted lines and will be difficult to be understood clearly. To overcome this difficulty, the object is assumed to be cut by one or more planes, so that most of the inner details can be seen and shown in the drawing very clearly. Thus, a study of the sections of solids is of considerable practical importance. The methods of drawing sections of different geometrical solids or "Sections of Solids" are described in this section. Objectives This session will help you to learn •= The need for sectioning. •= How a cutting plane can be described. •= How the true shape of an apparent section can be described. •= How the frustum of a solid can be described. •= How the sectional views of solids may be drawn. Sectional Views and Conventions Cutting plane and sectional view: Sectional View: The projection of the remaining portion of a "sliced" solid is called the sectional view. A sectional view is usually indicated by drawing continuous thin lines inclined at 45° to the axis or to the boundary of the section. Section lines are called hatching lines and they should be equally spaced, depending on the hatching area; the spacing of hatching lines generally varies from 1.5 to 3.5mm.
Cutting plane or sectional Plane: The imaginary plane, which is assumed to cut the object as required, is called a cutting plane or a section plane. Cutting planes are generally shown by long and short dashes, which are thickened at the ends, bends and changes of direction but thin elsewhere. The direction of viewing is indicated by two arrows resting at the ends of the cutting plane and is represented by capital letters (e.g., XX, AA etc.). The points at which sectional plane cut the edges of solids are called sectional points. Sectional points are usually numbered as 1, 2, 3, 4,... etc., in the top view and as 1', 2', 3', 4',...etc., in the front view.
Types of section Sections can be classified into two types. They are: 1. Apparent section 2. True type of section
Apparent section: An apparent section is the projection of the section of a solid cut by a plane that is inclined to horizontal plane or vertical plane.
True type of section: The true shape and size of a section of a solid is obtained by viewing the object normal to the section and projecting the section on a plane parallel to it.
Conic Section: Sections obtained by cutting the cone in different position relative to the axis are called "Conic Section". 1. When cutting plane parallel to base, the sectioned portion is a circle. 2. When cutting plane inclined to axis and cuts all the generators the sectioned portion is an ellipse. 3. When cutting plane parallel to one of its generators the section obtained is a parabola. 4. When the cutting plane is at a very small angle to the axis and cuts the generator on one side of the axis, and the base, the section obtained is a hyperbola. 5. When the cutting plane is parallel to axis, the sectioned obtained is a rectangular hyperbola. Frustum of a solid and Truncated solid: Frustum When a solid is cut by a cutting plane parallel to its base, the portion obtained after removing the top portion is called "Frustum"
Truncated When a solid is cut by a cutting plane inclined to its base, the portion obtained after removing the top portion is called the "truncated" solid.
Sections of Solids Perpendicular to the VP and Parallel to the HP: 1. Ok..! Let us imagine that a pentagonal pyramid of base 25mm and height 55mm rests with its base on the HP such that one of its edges is perpendicular to the VP. A section plane parallel to the HP and perpendicular to the VP cuts the pyramid at 20mm from the apex. 1. Draw the line XY. 2. Draw the top view as a pentagon and name its corners. 3. Draw projectors from each corner of the top view through XY. 4. Draw the front view as shown in the figure and name its corners. 5. Draw the section plane in the front view at 20mm from the apex and name the sectional points. 6. Draw projectors from each sectional point in front view so that they cut the corresponding edges in the top view. 7. Name these points and join them. 8. Draw the hatching lines to get the sectional top view.
20
o’ S
P
55
(4’) 3’(5’)2’ 1’
b’(e’) a’
(d’) c’
Y
X e
25
d
4
5
o 3
1 2
c b
a
2. Ok ..! Let us imagine that a regular pentagonal prism of base edge 25mm and height 60mm rests on the HP on one of the edges of its base and with its axis inclined at 30◦ to the HP. A section plane parallel to the HP and perpendicular to the VP cuts the prism at the highest corner of the prism's base. 1. Draw the line XY. 2. Draw the projections of the prism placed in the simple position (the axis is perpendicular to the HP and parallel to the VP). 3. Rotate the front view so that the axis is inclined at 30° to XY. 4. Draw projectors from the front view through XY and from the initial top view. 5. Draw the rotated top view as shown in the figure and name its corners. 6. Draw the section plane in the rotated front view through the top corner of the base and name the sectional points. 7. Draw projectors from each sectional point of the front view through XY to cut the corresponding edges of the top view. 8. Name the points and join them, as shown. 9. Draw the hatching lines to get the sectional top view. 1
a
1 b (e
1)
1 c (d
a
1)
1 1 b (e
1)
P
S 1
1 2 (5
1 b 1(e
x
a
1
1
b 1(e
e (e
1)
1
1 c 1(d
0
1)
1 c 1(d
e d (d
y
1 1 )
5
1
d
1
c
1
1 a 1
25
c (c b (b
1)
e 4
1)
(a a1)
1)
3 (4
1 1 )
1
1)
1
1 c (d
30 1
1)
1 1
a
60
1
d
a c
1)
3 b
1
2
b
1)
Perpendicular to the HP and Parallel to the VP: 1. Ok ..! Let us imagine that a rectangular prism 40 x 25mm and height 60mm rests with its base on the HP such that one of its rectangular faces is parallel to the VP. A section plane parallel to the VP and perpendicular to the HP bisects the prism. 1. Draw the line XY. 2. Draw the top view as a rectangle (40x25) and name its corners. 3. Draw projectors from each corner of top view up to line XY. 4. Draw the front view as a rectangle (40x60) and name its corners. 5. Draw the section plane in the top view at the center and name the sectional points. 6. Draw projectors from each sectional point in the top view so that they cut the corresponding edges of the front view. 7. Name the points and Join them. 8. Draw the hatching lines (inclined at 45°) to get the sectional front view.
d’ 4’
60
3’c’
25
X
a’ 1’
2’
d
c
S (3)1
Y
(4) 2 P
b
a 40
2. Ok ..! Let us imagine that a cylinder of diameter 55mm and axis 65mm long, rests with its base on the HP such that its axis is parallel to the VP. A section plane parallel to the VP and perpendicular to the HP cuts the cylinder 15mm in front of the axis. 1. Draw the line XY. 2. Draw the top view as a circle and name it as shown. 3. Draw projectors from the top view through XY. 4. Draw the front view as a rectangle and name its corners. 5. Draw the section plane in the top view at 15mm in front of the axis and name the sectional points. 6. Draw projectors from each sectional point in the top view so that they cut the corresponding edges of the front view. 7. Name these points and join them. 8. Draw the hatching lines to get the sectional front view.
a’
b’ (d’) 2’ c’
65
1’
c 1’
a 1’ 4’
X
’ b 1(d d(d
(a a1)
3’ 1’)
Y
1)
1)
15
c (c
S
(4)1
2(3)
b (b
1)
P
55
Perpendicular to the VP and Inclined to the HP: Ok ..! Let us imagine that a square prism of base 35mm and height 60mm rests with its base on the HP such that one of its edges is inclined at 30° to the VP. A section plane inclined at 60° to the HP and perpendicular to the VP cuts the prism through a point on the axis 20mm from the top of the prism. 1. Draw the line XY. 2. Draw the top view as a square such that it is inclined at 30° to XY and name its corners. 3. Draw projectors from each corner of the top view to XY. 4. Draw the front view as shown in the figure and name its corners. 5. Draw the section plane in the front view through a point on the axis 20mm from the top of the prism such that it is inclined at 60° to XY, and name the sectional points. 6. Draw projectors from each sectional point through XY. 7. The projectors cut the corresponding edges of the top view. Name the points and join them. 8. Draw the hatching lines to get the sectional top view To get the True Shape of the section: 9. Draw a line X1Y1 parallel to SP, as shown. 10. Draw projectors from each sectional point in the front view through X1Y1. 11. Transfer the distances, from XY, of the sectional points in the top view to the corresponding projectors through X1Y1, measuring from X1Y1 in each case. 12. Join these points as shown and draw the hatching lines to get the true shape of the section.
P b’ 3’ c’ (4’) 2’
(d’)
20
a’
Y
1
60
(5’) 4
1
3 1’ 60
S
a’ 1 30
(d’ 5
d (d
b’
1)
c’
1
y
1
1)
X
1
4
c (c
1)
1
(a a1)
1
1
0
3
35
x
5
1 2
b (b
1)
1
2
1
2. Ok ..! Let us imagine that a pentagonal pyramid of base 35mm and height 60mm, rests with its base on the HP such that one of its edges is perpendicular to the VP. A section plane inclined at 45° to the HP and perpendicular to the VP cuts the pyramid through its axis at 25mm from the apex. 1. Draw the line XY. 2. Draw the top view as a pentagon such that one of its edges is perpendicular to XY. Name the corners of the pentagon. 3. Draw projectors from the top view to XY. 4. Draw the front view as shown in the figure and name its corners. 5. Draw the section plane in the front view through a point on the axis 25mm below the apex and inclined at 45° to XY and name the sectional points. 6. Draw projectors from the sectional points through XY. 7. The projectors cut the corresponding edges of the top view. Name the points of intersection and join them. 8. Draw the hatching lines to get the sectional top view To get the True Shape of the section: 9. Draw a line X1Y1 parallel to SP, as shown. 10. Draw projectors from each sectional point in the front view through X1Y1. 11. Transfer the distances, from XY, of the sectional points in the top view to the corresponding projectors through X1Y1, measuring from X1Y1 in each case. 12. Join these points as shown and draw the hatching lines to get the true shape of the section.
o’ 25
P
60
2’
3’
(4’)
1’ (5’) S
Y 45
0
a’ (e’)
X
b’(d’) c’
Y
d e
4
35
5 1
3
X
1
4
c
2 5
a b
1
1
1
1
3
1
2
1
1
Perpendicular to the HP and Inclined to the VP 1.Ok ..! Let us imagine that a square prism of base 40mm and height 60mm rests with its base on the HP such that one of its edges is inclined at 30° to the VP. A section plane inclined at 60° the VP and perpendicular to the HP bisects one of the rectangular faces is nearer to the VP. 1. Draw the line XY. 2. Draw the top view as a square such that an edge of its base edge is inclined at 30( to XY and name its corners. 3. Draw projectors from each corner of the top view to XY. 4. Draw the front view as shown in the figure and name its corners. 5. Draw the section plane in the top view such that it is at 60( to XY and bisects an edge of the prism as shown in the figure. Name the sectional points. 6. Draw projectors from each sectional point in the topview through XY to meet the corresponding edges of the front view. Name the points of intersection. 7. Join the sectional points in the front view and draw the hatching lines to get the sectional front view. To get the True Shape of the section: 8. Draw a line X1Y1 Parallel to SP as shown 9. Draw projectors from each sectional point in the top view through X1Y1. 10. Transfer the distances, from XY, of the sectional points in the front view to the corresponding projectors through X1Y1, measuring from X1Y1 in the case. Name these points. 11. Join these points and draw the hatching lines to get the true shape of the section.
1’ (d’)
a’
2’
b’
c’
60
1’’
2’’
4’’ x P
60
1 0
304’ 0(d’
d(d
40
1)3’
b’
1
c’ 1y
1)
c (c
1
3’’ 1)
(4) y
(a a1) (3)
2 S
x
a’
1
b (b
1)
1
2. Ok ..!Let us imagine that a hexagonal pyramid of base 35mm and height 55mm, rests with its base on the HP such that one of its edges is perpendicular to the VP. A section plane inclined at 60° to the VP and perpendicular to the HP cuts the pyramid at 10mm from the axis. 1. Draw the line XY. 2. Draw the top view as a hexagon such that an edge is perpendicular to the VP and name its corners. 3. Draw projectors from the top view through XY. 4. Draw the front view as shown in the figure and name its corners. 5. Draw a circle of radius 10mm at the center of the top view. Draw the section plane in the top view tangential to this circle and inclined at 60° to XY and in front of the axis. Name the sectional points. 6. Draw projectors from each sectional point in the top view so that they cut the corresponding edges of the front view. Name the sectional points in the front view. 7. Join the sectional points and draw the hatching lines to get the sectional front view. To get the True Shape of the section: 8. Draw a line X1Y1 parallel to SP as shown. 9. Draw projectors from each sectional point in the top view through X1Y1. 10. Transfer the distances, from XY, of the sectional points in the front view to the corresponding projectors through X1Y1, measuring from X1Y1 in each case. Name these points. 11. Join these points and draw the hatching lines to get the true shape of the section.
o’
2’
55
3’
2’’ x 11’’
1’
4’ b’ (e’) e
a’(f’)
x
y 4’’
P
2 a
c’(d’)
d
35
S
f 1
3’’
3
c
4
0 20 b
y
1
P
Section of Solids – Exercises Perpendicular to HP and parallel to VP 1. A pentagonal prism, base 30mm and axis 65mm, rests with its base on HP such that on of its rectangular faces is parallel to VP. A section plane parallel to VP and cuts the prism at a distance of 12mm from the axis. Draw the sectional front view and top view. 2. Draw the projection of hexagonal prism side of base 25mm and axis 60mm long, rests with its base on HP such that one of its rectangular faces is inclined at 30° to VP. A sectional plane cuts it perpendicular to HP and parallel to VP at a distance of 10mm from the axis. 3. Draw the sectional view of a square pyramid side of base 40mm and axis 60mm long lies with one of its triangular faces on HP and axis is parallel to VP. Sectional plane is parallel to VP and perpendicular to HP cuts the pyramid at 5mm from the axis. 4. A hexagonal prism side of base 30mm and axis 60mm lies with one of its rectangular faces on HP and axis inclined at 45° to VP. Draw the sectional view is the sectional plane is parallel to VP and passing the front corner of the near hexagonal face. Perpendicular to VP and parallel to HP 5. Draw the sectional top view and front view of a triangular prism, base 30mm and axis 60mmlong, lies with one of the rectangular faces on HP. The axis is perpendicular to VP and parallel to HP. The section plane perpendicular to VP and parallel to HP and at a distance of 10mm from the axis. 6. A hexagonal pyramid base 30mm and axis 55mm long rest with its base on HP and the edges of the base is parallel to VP. Draw the sectional top view and front view, if the sectional plane passes at a distance of 30mm above the base. Perpendicular to VP and Inclined to HP 7. A pentagonal Pyramid base 30mm axis 65mm long, rest with its base on HP and base edge is parallel to VP. Draw the sectional top view if the section plane perpendicular to VP and inclined at 30° to HP at a distance 30mm above the base.
8. A Hexagonal pyramid base 30mm and axis 60mm long, rest on the base of the HP. Draw the sectional top view and true shape of the section when the section plane perpendicular to VP and inclined at 45° to HP and passing through a point on the axis at 15mm below the axis. 9. A cone base diameter 40mm and axis 60mm long, rest with base on HP. Draw the section top view and true shape of section, if the section plane perpendicular to VP and inclined at 45° to HP bisects the axis. Perpendicular to HP and Inclined to VP 10. A cube of 50mm long rest with one of its faces of HP such that its vertical face inclined at 45° to the VP. Draw the section front view and true shape, when the section plane perpendicular to Hp and inclined at 60° to VP and cut into halves. 11. Draw the section front view and true shape of the section of a pentagonal pyramid base 30mm and axis rest its base on the HP such that the edges of its base is parallel to VP. The section plane inclined at 45° to the VP and perpendicular to the HP passing through the pyramid at a distance 10mm from its axis. 12. A cone base 50mm diameter and axis 65mm rest with its base on the HP. Draw the section front view and true shape then it is cut by a section plane perpendicular to the HP and inclined at 45° to the VP at a distance 10mm from its axis.
Chapter-VI Pictorial Projections Introduction: The investor would you to visualize the finished product, as it would appear in a photograph. The customers also want to visualize the house or factory after the construction before being it actually constructed. So a three-dimensional object to be pictorially represented as like as possible in a single view. To give solution to the above, perspective view is the only solution. In the perspective view the object can be visualized more realistically. In engineering, the perspective projection is very often resorted to be architects.
Isometric Projection Objectives At the end of this session, you will be able to:
•=
Show the length, width and height of an object in a single view.
•=
Create a three-dimensional effect of an object by means of an isometric drawing.
Isometric Projection An isometric projection of an object is a single projection on the plane of projection. The three principal axes of an isometric projection are : 1. Length axis 2. Width axis 3. Height axis
Isometric Projection - Terminology Isometric Axes The lines AB, AD and AE meeting at the point A and making an angle of 120° with each other are called the isometric axes. ∠BAD = ∠DAE
= ∠EAB = 120°
AB and AD are referred to as the inclined isometric axis and AE as the vertical axis.
D
B 120 A
120
120
E Isometric Lines Lines parallel to the isometric axes are termed isometric lines. Let us see the figure. Here, DS and BQ are parallel to the isometric axis, AP. RQ and SP are parallel to the isometric axis, AD. SR and PQ are parallel to the isometric axis, AB. Therefore, DS, BQ, RQ, SP, SR and PQ are called isometric lines. R S P0 120
120
Q
0
120
D
0
B
30
0
A
30
0
Non-isometric Lines Lines which are not parallel to any of the isometric axes are termed non-isometric lines. Let us see the figure. Here, Lines BD and BE are not parallel to any of the isometric axes. BD, BE any other lines that are not parallel to the isometric axes. AB, AD and AE are said to be the non-isometric lines.
D
B 120 A
120
120
E
Isometric Planes The planes containing the faces of the cube as well as all other planes parallel to these planes are termed isometric planes. The planes containing the faces PQRS, PQBA and PADS and those parallel to these planes in the figure are the isometric planes.
R S P0 120
120
Q
0
120
D
0
B
30
0
A
30
0
Isometric Scale The isometric length is less than the actual length of an object. Isometric length = 82% of true length. While drawing isometric projection it is necessary to convert true lengths into isometric lengths for measuring and marking edges in the projection. A scale wherein isometric lengths corresponding to true lengths are available is called an isometric scale.
TR U E
LE N G TH
C
3
O R
D
A CT U A L
2 TH
3’ ENG CL RI
1
0
o
1’ 45 o 30 0’
2’ ET M ISO
A
90
0
B
Isometric View and Isometric Projection
Isom etric view ordrawing
Isom etric projection
The picture is drawn to actualscale.
The picture is drawn to isom etric scale.
The lines parallelto the isom etric axes thatrepresent the objectare drawn to theirtrue lengths.
The lines parallelto the isom etric axes thatrepresent the objectare fore shortened to 0.82 tim es the actual lengths.
Points to be remembered while drawing isometric drawings •= At every visible corner of the object three lines must converge. •= Of these three lines, either all the three or any two lines may be visible. •= The hidden lines may not be shown, but it is advisable to check every corner, so that no visible line is left out. •= Two outlines will never cross each other. •= If the axis of the solid is vertical, its end or ends will be horizontal and if the axis of the solid is horizontal, its end or ends will be vertical. Box method The isometric projections of prisms, squares and cylinders are generally drawn by the Box method. Co - ordinate or offset method The isometric projections of pyramids and cones are generally drawn by Co - ordinate or offset method.
Isometric views of Prisms 1.Draw the isometric view of a square prism of side of base 30mm and height 55mm when its axis is vertical. 1. Draw the complete orthographic views of the square prism. 2. Draw a horizontal line nearby and mark a point "a1" on it. 3. Draw the two inclined isometric axes at a1 as shown (the axes are inclined at 30° to the horizontal line and at 120° to each other). 4. With a1 as center and radius equal to 30mm draw two arcs, one each on the two isometric lines, cutting them at b1 and d1 respectively. 5. Draw lines from b1 and d1 parallel to a1d1 and a1b1 respectively. Name the point of intersection of these lines as c1. 6. Draw vertical lines from a1, b1, c1 and d1. Mark a length of 55mm on each of the vertical lines and name the top ends respectively as a, b, c and d. 7. Join ab, bc, cd and da to get the isometric view of the square prism. 8. Darken the visual entities (i.e. the visible edges of the prism in the isometric view).
b (c )
55
a (d )
c
d
b
a
(d ) a
b (c’)
(d ) (d)
c (c )
c
d
b
30
30 a
(a ) a
30
b (b )
2.Draw the isometric view of a hexagonal pyramid of side of base 25 mm and height 60 mm, when it is resting on the HP, such that an edge of the base is parallel to the VP. 1. Draw the orthographic views of the hexagonal pyramid. Enclose the top view in a box pqrs as shown. 2. Draw a horizontal line nearby and mark a point “p” on it. 3. Draw the two inclined isometric axes at “p” as shown ( the axes are inclined at 30° to the horizontal line and at 120° to each other). 4. With “p” as centre and radius equal to pq, draw arcs on both the isometric lines to cut them at “q” and “s” as shown. 5. Draw lines from “s” and “q” parallel to pq and ps respectively to intersect at 'r'. 6. Mark distances equal to pa and qb in the top view, on line pq in the isometric view as shown. 7. Mark a distance equal to pf in the top view, on line pq in the isometric view as shown. 8. Draw lines from “a” and “b” parallel to ps to meet sr at “e” and “d” respectively. 9. Draw a line from “f” parallel to pq to meet qr at “c”. 10. Join ab, bc, cd, de, ef, and fa. 11. Locate a point “o” on fc in the isometric view at a distance "y" from the point “f”. 12. Draw a vertical line from “o” and mark a point “o' “on it 60mm from “o”. 13. Join ao', bo', co', do', eo' and fo' to get the isometric view of the hexagonal pyramid. 14. Darken the visual entities (i.e. the visible edges of the pyramid in the isometric view).
o’
60
o’
r f’ s
d
) ) (c’ b’(d’
a’(e’ )
e
d
c
r
e o
s f
c
o
b f 30
a 30 p
p
ya
b 25
q
q
Isometric views of Cylinder & Cone 1. Draw the isometric view of a cylinder of 40 mm diameter and 60 mm height when it rests with one of its ends on the H.P. 1. Draw the orthographic views of the cylinder. Enclose the front view in a square pqrs as shown. 2. Mark a, b, c, and d as the points at which the square touches the circle. 3. Draw the diagonals sq and pr. They will cut the circle. Name the intersecting points as e,f,g and h. 4. Join ef and hg and extend them to meet ps and qr respectively at 1, 2 and 3, 4. Join bd. 5. Mark the distance y in the top view, as shown. 6. Draw a horizontal line and mark a point “p” on it. 7. Draw the two inclined isometric axes at “p” as shown ( the axes are inclined at 30° to the horizontal line and at 120° to each other). 8. With “p” as center and radius equal to pq taken from the top view, draw arcs on the 30° lines to cut them at “s” and “q” as shown. 9. Draw lines from s and q parallel to pq and ps respectively. Name the point of intersection as “r”. 10. Locate a, b, c and d as the mid points of pq, qr, rs and sp respectively in the isometric view. 11. Mark a point “1”on ps so that “p1” is equal to y taken from the top view. Draw a line from “1” parallel to pq to meet qr at “2”. 12. Mark a point “3” on ps so that “s3” is equal to y taken from the top view. Draw a line from “3” parallel to pq to meet qr at “4”. 13. Mark points e and f on line “12” so that 1e=f2=y. 14. Similarly mark points h and g on line “34” so that 3h=g4=y. 15. With “s” as centre and radius equal to sa, draw arc afb. Similarly, with “p” as center and radius equal to pb, draw arc bgc.
16. Similarly draw the arcs chd and dea. Now the ellipse afbgchde is the isometric view of the base of the given cylinder. 17. Construct an isometric box of height 60mm as shown. 18. Construct a corresponding ellipse on the top of the box as shown.
60
19. Darken the visual entities (i.e. the visible edges of the cylinder in the isometric view).
VP HP
r
Y c
s 3
r 4
g
h
d y1 p
b
e
f 2 q
a y
c
y
s 0 40
X
g
b f
h 3 d 30
e
a 30
1 p
y
4 2 q
2. Draw the isometric view of a cone of base 45 mm diameter and height 65mm when it rests with its base on the HP. 1. Draw the orthographic views of the cone. 2. Draw a box pqrs to enclose the top view. Draw a horizontal line nearby and mark a point “p” on it. 3. Draw the two inclined isometric axes at “p” as shown ( the axes are inclined at 30° to the horizontal line and at 120° to each other). 4. With “p” as centre and radius equal to ps (or pq) taken from the top view, draw arcs on both the lines. Name the points of intersection as “s” and “q” as shown. 5. Draw lines from “s” and “q” respectively parallel to pq and ps, to meet at “r”. 6. Locate a, b, c and d as the midpoints of ps, pq, qr and rs respectively. 7. Join ar, rb, pc and pd. Let ar and pd intersect at “e” and rb and pc at “f”. 8. With “r” as center and radius equal to ra, draw arc ab. Similarly with “f” as centre and radius fb, draw arc bc. 9. With “p” as center and radius equal to pd, draw arc cd. Similarly with “e” as center and radius ed, draw arc da. 10. Draw lines from “b” and “c” respectively parallel to qr and pq, to meet at “o1” as shown. 11. Draw a vertical line at “o1” and mark a point “o” on it such that oo1=65mm. 12. Draw generators from “o” to the ellipse as shown. 13. Darken the visual entities as shown.
o’
65
o
VP HP s
r
Y
o’
d
d
e
s a
c (o )o y
p
b
c
r
y
q
0 45
X
o
f
a
q b
30
30
p
Isometric views of Compound solids 1. A sphere of diameter 45mm is kept on the top face of a square prism of side of base 45mm and height 15mm. The prism is resting on the top face of a cylinder of 60mm diameter and 20mm height. Draw the isometric view of the combination of solids. 1. Draw the orthographic views of the compound solid. Draw a box pqrs to enclose the top view as shown. 2. Draw a horizontal line nearby and mark a point on it as shown. 3. Draw the two inclined isometric axes at the point as shown ( the axes are inclined at 30° to the horizontal line and at 120° to each other). 4. Construct a box pqrs as shown. 5. Mark the mid points on pq, qr, rs and sp and join them as shown. 6. Draw an ellipse using the four-centre method, to represent the isometric view of the circular top view of the cylinder. 7. Similarly construct an ellipse at the bottom face of the box pqrs. Join the two ellipses to get the isometric view of the cylinder. 8. Draw the isometric view of the square prism on the top face of the isometric view of the cylinder, as shown. 9. Mark a point o1 on the top face of the prism as shown. Draw a vertical line from o1 and mark a point o on it so that oo1=22.5mm. 10. With “o” as center and radius equal to oo1 draw a circle. 11. Darken the visual entities to get the isometric view of the compound solid.
20
15
R 25
VP HP s
r
o o1
Y s
q
0 60 p
45
X
r
30
p
q
30
2. A hemisphere of 50mm diameter is nailed to the top face of the frustum of a hexagonal pyramid. The edges of the top and bottom faces of the frustum are 20mm and 35mm each respectively and the height of the frustum is 55mm. The axes of both the solids coincide. Draw the isometric view of the compound solid. 1. Draw the orthographic views of the compound solid. 2. Draw a horizontal line nearby and mark a point "q" on it. 3. Draw the two inclined isometric axes at “q” as shown ( the axes are inclined at 30° to the horizontal line and at 120° to each other). 4. With “q”as center draw arcs to cut the two isometric lines at “p” and “r” such that qp and qr are correspodingly equal to pq and qr of the top view. 5. Draw two isometric lines from “p” and “r” respectively parallel to qr and pq so that they meet at “s”. 6. Mark distances qm and nr taken from the top view on qr as shown. Next mark “i” on rs to correspond to the “i” in the top view. Similarly mark “j” and “k” to correspond to “n” and “m”; finally mark “l” corresponding to “i”. 7. Join ij, kl, lm and ni. 8. Draw the diagonal pr as shown and mark its mid point as o1. 9. Draw a vertical line from o1 and mark a point o2 on it so that o1o2 equals 55mm. 10. Draw two isometric lines bd and ca at o2 parallel to pq and qr, as shown and correspondingly equal to bd and ca of the top view. 11. Construct a hexagon in the plane of bd and ca, as shown, to represent the top face of the frustum. 12. Join the corresponding vertices of the top and bottom hexagons. 13. Mark a point “o3” on the vertical line through “o2”, such that o2o3 equals 25mm. 14. Draw a horizontal line through “o3”. 15. Construct an isometric circle efgh and draw an arc below it to complete the isometric view of the hemisphere, as shown.Darken the visual entities as shown. 16. Darken the visual entities as shown.
o3
o2
R 25 f
e
55
o3 g
j
k
p
r
i e a
f b
i k
n
o1
p d h
c g l
s j
35
s
h
o2 d
c
Y
o1
20
X
VP HP
a
b
l 30
m 30
q m
q
n
r
Perspective projection Examples Note : No need to draw the orthographic projection given in the book, just show the 3D intersection of solid with the intersection curve.
Example 1 : Perspective projection of square prism.
Example 2 : Perspective projection of pentagonal prism.
Isometric Projection – Exercises 1. Draw the isometric view of rectangular prism of base 40x20mm and height 65mm when the axis is (i) Vertical and (ii) Horizontal. 2. Draw the isometric view of cube of a side 50mm. 3. Draw the isometric projection of pentagonal prism of base 30mm and height 65mm when the axis is (i) Horizontal and (ii) Vertical. 4. Draw the isometric view of a triangular pyramid of side 30mm and height 70mm such that are of the edge of the base is parallel to VP. 5. Draw the isometric view of a pentagonal pyramid of base 30mm and height 60mm such that an edge of the base is perpendicular to VP. 6. Draw the isometric view of hexagonal prism with base 30mm and height 55mm, on the top of which a cone is placed of base 50mm diameter and height 30mm. 7. Draw the isometric projection of cylindrical slab 60mm diameter and 25mm thick surmounted by a cube of 30mm edge. On the top of the cube square pyramid of base 30mm and height 30mm.The axes of the solids coincides. 8. Draw the isometric view of a cylinder with base 40mm and axis 60mm long rests on HP with its axis is perpendicular to VP. (Use four-center method and offset method.) 9. Draw the isometric projection of a square pyramid of base 30mm and height 70mm.
Isometric To Orthographic Projection Draw the front, side and top view of the following drawings i.
ii.
iii.
iv
v.
vi.
vii.
viii.
ix.
x.
xi.
2.Draw the isometric projection for the following drawings.
i.
ii.
iii.
iv.
v.
Chapter - VII
Development of Surfaces Introduction: Development of surface of an object means the imaginary representation of the unfolding of all the surfaces of the object such that all of them lie together and flat on one common plane. For example, consider a pyramid; you can imagine that it unfolds to give the development of the pyramid’s surfaces. The principle of development of surfaces is very useful in sheet – metalworking. For instance, from the developed surface of a funnel, we can fold it to the desired shape to make the funnel. Development of Surfaces - Parallel line development. 1. Draw the development of the surfaces of a cube of side 30mm, when one of the edges of its base is parallel to the vertical plane. 1. Draw the orthographic views of the cube. 2. At a convenient distance draw a "Stretch out line" of length 120mm (4 x 30 mm) projecting it from the cube.(In this case, the stretch out line represents the unfolding of the perimeter of the base of the cube) 3. Divide the stretch out line into four equal parts and name the points corresponding to these parts as 1, 2, 3, 4 and 1. 4. Draw a vertical line of length 30mm from “1” and name the top end as "A". 5. Draw the other stretch out line from "A". 6. Divide this stretch out line into four equal parts and name the points corresponding to these parts as B,C,D and A. (This stretch out line represents the unfolding of the perimeter of the top face of the cube.) 7. Join 2B, 3C, 4D and 1A as shown. 1-2-B-A, 2-3-C-B, 3-4-D-C and 4-1-A-D represent the four side faces of the cube. 8. Draw DAB'C' and 12'3'4 to represent the top and bottom faces of the cube to complete the development of the surfaces of the given cube.(This method of drawing the development of surfaces of solids is called the 'PARALLEL LINE DEVELOPMENT' and is mainly used for cubes, prisms and cylinders.)
C’
b’(c’) A
B
C
2
3
D
A
30
a’(d’)
B’
(4’)1’
2’(3’)Y
1
10
X
4
1
c
d
(3)
30
(4)
3’ a(1)
b(2)
2’
2. A hexagonal prism of base edge 30mm and height 50mm stands on one of its ends on the HP such that an edge of its base is parallel to the VP. Draw the lateral development of the prism. 1. Draw the orthographic views of the hexagonal prism. 2. At a convenient distance draw a stretch out line of length 180mm (6 x 30mm) projecting from the base of the prism. 3. Divide the stretch out line into six equal parts and name the points corresponding to these parts as 1, 2, 3, 4, 5, 6 and 1. 4. Draw a vertical line of length 50mm from “1” and name the top end as “A”. 5. Draw the other stretch out line from “A” as shown. 6. Divide this stretch out line into six equal parts and name the points corresponding to these parts as B, C, D, E, F and A. 7. Join B2, C3, D4, E5, F6 and A1 to complete the lateral development of the hexagonal prism, using the parallel line method for drawing the development of surfaces.
c’(d’)
A
B
C
D
E
F
A
1
2
3
4
5
6
1
50
a’(f ’)(e’) b’
X
1’ (6’)
2’(5’) 3’(4’)Y e (5)
f (6) 30
d (4) c (3)
(1) a b (2)
Development of Surfaces - Radial line development 1.Draw the lateral development of a triangular pyramid of base edge 30mm, Lying with its base on the HP. Its apex is vertically 60mm above its base, and one of the edges of the base is parallel to the VP. 1. Draw the orthographic views of the triangular pyramid. 2. Draw a horizontal line from “0” in the top view. 3. With "o" as center and "oc" as radius draw an arc to intersect the horizontal line as shown. 4. Draw a vertical line from the point of intersection to meet the vertical plane(XY) at c''. 5. Join o'c'' to get the true slant length of the edge o'c '. ( The true length of the slant edge of the pramid is required as the radius for the next step.) 6. Locate a point “O” at a convenient distance from the front view. With “O” as center and o'c'' as radius draw an arc as shown. 7. Mark four points A,B,C and A on the arc such that the straight lines AB,BC and CA equal 30mm each in length.
8. Join OA, OB, OC, OA, AB, BC and CA to get the lateral development of the triangular pyramid.
o’
60
O
A A a’
c’ c" c
a o 30
X
b’
b
Y
B
C
2. Draw the lateral development of a hexagonal pyramid of base edge 30mm and height 60mm, resting with its base on the HP such that one of the edges of its base is parallel to the VP. 1. Draw the orthographic views of the hexagonal pyramid. 2. Draw a horizontal line from “o” in the top view as shown. 3. With “o” as center and oa as radius draw an arc to intersect the horizontal line. 4. Draw a vertical line from the point of intersection to meet the vertical plane (XY) at a''. 5. Join o'a'' to get the true slant length of the edge o'a'. 6. Locate a point “O” at a convenient distance from the front view. With “O” as center and o'a'' as radius draw an arc. 7. Mark seven points A, B, C, D, E, F and A on the arc such that the straight lines AB, BC, CD, DE, EF and FA equal 30mm each in length. 8. Join OA, OB, OC, OD, OE, OF, OA, AB, BC, CD, DE, EF and FA. OABCDEFAO is the lateral development of the hexagonal pyramid. O
60
o’
A
A B
a’ X a"
b’ (f ’)
c’ (e’) d’ Y
f
a
e
d
o c
b 30
F C
D
E
Development of Surfaces – Exercises 1. A pentagonal prism, side of base 30mm and axis 55mm rest with the base on HP and an edge of the base is inclined at 60(to the VP. Draw the development of lateral surface of the truncated prism when it is cut by a section plane perpendicular to VP and inclined at 30(to HP at a distance of 35mm to its base. 2. Draw the development of lateral surface of truncated cylinder of diameter 40mm and 60mm long rest with the base of the HP. It is cut by a plane perpendicular to VP and inclined at 45(to HP at a distance 10mm from its top. 3. Draw the development of the given figure. (Page-16.7) 4. Draw the development of the given figure. (Page-16.9) 5. A truncated square pyramid of base 1.2m side, top 0.5m sides and height 1m. Find the shortest distance between one corner of the base and diagonally opposite corner on the top. 6. Develop the lateral surface of the Cone of base 50mm and height 80mm rest with base on HP. A cutting plane perpendicular to VP and parallel to its outermost generator at the distance 20mm from the apex. 7. Develop the lateral surface of the Cone of base 50mm and height 80mm rest with base on HP. 8. A vertical section of the right circular cone through the axis is an isosceles triangle of 40mm base and 50mm height. A fly sits on the extreme left end of the base and walks around the surface of the cone and returns to the starting point. Find the shortest distance that the fly can take. 9. Draw the development of outside case of a matchbox of size 50 x 40.
10. Draw the development of funnel shown in the figure.
11. Draw the development of Sheet metal part shown in the following figure.
Chapter - VIII Intersection of surfaces Introduction When two solids are joining together to form a single object it is called an intersection of solids. Intersection of surfaces Example 1 A cylinder stands vertically on the HP. It is completely penetrated by a horizontal cylinder of equal diameter such that the axes of the two cylinders intersect each other at right angles. The axis of the penetrating cylinder is parallel to the VP. (Refer CD) Example 2 A cone stands vertically on the HP. It is completely penetrated by a horizontal cylinder such that the axes of the cone and the cylinder do not intersect but are at right angles to each other. The axis of the cylinder is parallel to the VP and is some distance in front of the axis of the cone. (Refer CD)
Chapter-IX Further development in Engineering Drawing The advancements in Computer Technology and the tough competition in the field of computers resulting in a drastic fall in their prices have contributed to a sensational breakthrough in the engineering arena as well. As of today, we can use computers for drafting. This application is called Computer Aided Drafting or simply, CAD. Other developments such as Computer Aided Design and Computer Aided Manufacturing or CAD: CAM are also very much in use today. Computer Aided Drafting has both advantages and disadvantages. The main advantage is the ease with which and the speed at which it can be used. Any size of drawing can be done and visualized in three dimensions - or in 3D - on the computer screen itself. Also, with a large drawing, you can have the various entities separately in layers of different colors for quick and easy visualization, storage and retrieval. You can scale it up or down in size without altering the shape of the object. Likewise, you can duplicate the entities easily and translate, rotate or mirror them easily. The disadvantage, if you can call it one, is that the computer can’t think by itself! This means, of course, that you would still have to give computer instructions to create a drawing of exactly what you have in mind.
INDEX A Aligned Dimensioning 20 Apparent section 79,80 Arc 8,10,17,30 Arrows 10,22 B Beginning your drawing Bisect a line 34 Bisect an angle 35 Bisect an arc 34 BIS & ISO Conventions
23
10
C Center of an arc 35 Chord 31, 35 Classification of Solids 59 Clips 10,23 Compound Solids 108 Construct a regular hexagon 37 Construct a regular pentagon 36 Construct a regular octagon 38 Conic Sections 81 Cutting Plane 79, 80, 81, 101 Cylinder and Cone 104 D Decagon 33 Dimensioning Methods 10,14 Drawing Board 6,10,23 Drawing Pencils 10 Drawing Sheet 7 E Emery Paper 10 Equilateral Triangle Eraser 10
28
F Features of lettering 13,14 First Angle Projection 41,44 Four Quadrants 43,45 French curves 10 Front View 40,41,43 Frustum of a solid 79,81
H Heptagon 32 Hexagon 32,37 I Inclined Lettering 14 Instrument Box 7 Intersection of Surfaces 130 Irregular Polygon 31,33 Isometric Projection 41,96 Isometric Projection – Terminology 97 Isosceles Triangle 28,128 Isometric To Orthographic Projection L Layout of drawing sheet Lettering 13 Line Types 10,13
10,11
M Mini Drafter 7,23 Miter Line Projection
70
N Nonagon 33 Notation 45 O Oblique Projection 41,42 Octagon 33,38 Orthographic Projection 40,42 P Parts of a circle 30 Parallel line development 123 Pentagon32,36 Perspective Projection 41,42,112 Pictorial Projection 41,96 Polygons 31 Polyhedra 59 Prism 59,61-64 Procircle 9 Projections 40,43,45 Projections of a point 45 Projections of Solids 59 Projections of a straight line 50 Pyramids 59,62,100 Q Quadrilaterals
29,30
114
R Radial Line Development Rectangle 29,61 Regular Polygon 31 Rhomboid 29 Rhombus29 Right Angle Triangle 28 Rules of Dimensioning 15 Rules of lettering 13
126
S Scales 9 Section plane 80,94 Sectional view 79,94 Sector 31,35 Segment 30 Set Squares 7,8 Sharpener 10 Side View 41 Solids of Revolution 59,64 Square 29 T Third Angle Projection 40,41,44 Top View 41 Trapezium 30 Trapezoid 30,58 Triangle 28 Truncated 81 T-Square 7
Unidirectional Dimensioning 19 V Vertical & Horizontal plane Vertical Lettering 14
43
