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Department of Civil Engineering, HSTU, Dinajpur

E-mail : mrz.civil@hstu.ac.bd

Hajee Mohammad Danesh Science and Technology University

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Preface

Engineering Drawing is one of the basic courses to study for all engineering disciplines. The primary

problem faced in learning and teaching of engineering drawing is the limited availability of text books

that focus on the basic rules and specifications in relation to the drawing methods practiced in

Bangladesh. This handbook is prepared with the primary aim to elaborate necessary basic rules and

regulations of engineering drawing that is necessary for students of every engineering discipline. This

book is for beginners to introduce them with different elements of engineering drawing. Several

worked-out examples are provided along with every chapter and also every chapter includes some

exercise and assignments to be practiced by the learners. The course Engineering Drawing is

extremely important as it is the language of engineers, technicians, designers and sanitarians. This

handbook is devoted to provide general aspects of engineering drawing like lettering, geometric

constructions, dimensioning, scaling, orthographic and isometric projections and sectioning. The

handbook is prepared taking aid from a number of textbooks and articles mentioned in bibliography

section. Most of the figures are drawn using AutoCAD, a few of them are collected from Google

image search and some are taken from the textbooks. For further reading, students are encouraged to

refer books which are listed in the bibliography section.

Acknowledgement

The author is delighted to express his thanks and gratitude to Prof. Md. Ruhul Amin, the honorable

Vice-chancellor and chairman of the Department of Civil Engineering, HSTU, without his initiative

and inspiration this material would not come into reality. Author is also grateful to his colleagues of

the Department of Civil Engineering and of the Department of Agricultural and Industrial Engineering

for inspiring him in completing this handbook. And obviously it is the mercy of the Almighty Allah

that the material has finally come into a complete form.

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CHAPTER 1 INTRODUCTION

1.2.2 Engineering Drawing

1.3 Purpose of Engineering drawing

1.4 Applications of Engineering Drawing

1.5 Types of Engineering Drawing

1.5.2 Mechanical Engineering Drawing

1.5.3 Civil Engineering Drawing

1.5.4 Electrical Engineering Drawing

1.6 Specific Purposes of Studying Civil

1.7 Types of Civil Engineering drawing

1.8 Elements of Engineering Drawing

CHAPTER 2 LINES AND SYMBOLS

2.2.1 Common Geometric Symbols U

Drawing…………………………………………………...

12

sed in Civil Engineering Drawing

sed in Electrical Engineerin

Drawing…………………………………………………...

15

CHAPTER 3 LETTERING AND NUMBERING

3.2 Classification of Letters

3.2.1 Extended and Condensed Letters

3.2.2 Light Face and Bold Face Letters

3.3 Technique of Lettering

3.4.1 Guidelines for Capital Letters

3.4.2 Guidelines for Lower

iii

CHAPTER 4 GEOMETRIC CONSTRUCTION

4.2 Geometric Nomenclature

4.3 Techniques of Geometric C

4.3.1 How to Bisect a Line or an Arc

4.3.2 How to Divide a Line into a Number of Equal Parts

4.3.4 How to Draw an Arc or Circle (Radius) through Three

Given Points……………………………………………

29

4.3.5 How to Transfer an Odd Shape (Triangular)

4.3.6 How to Transfer Complex Shapes

4.3.8 How to Draw a Hexagon (6 Sides)

4.3.9 How to Draw an Octagon (8 Sides)

4.3.10 How to Draw any Sided Regular Polygon

4.3.11 How to Locate the Center of

4.3.12 How to Draw Arc Tangent to a Straight Line and a

Curve…………………………………………………

34

4.3.13 How to Draw Arc Tangent to Two Arcs of Different

Radius………………………………………………...

34

4.3.14 How To Draw an Ogee

4.3.15 How to Draw Straight Tangent to Two Arcs of

Different Radius………………………………………

36

4.3.16 How to Draw an Ellipse (Four

Method)……………………………………………….

36

CHAPTER 5 DIMENSIONING

5.5 Direction of Dimensions

5.6 Technique of Dimensioning

5.7 Dimensioning in Limited Space

Dimensioning of Chord length, Arc length and Angle

Dimensioning of Round Holes

Dimensioning of Blind Holes

iv

out Examples of Dimensioning

CHAPTER 6 SCALES

6.4 Classification of Scales

6.5 Necessity of Construction of Scale on Drawing

6.6 Information Necessary for Construction of a Scale

Representative Fraction (R.F.)…………………….

6.6.1.1 Worked out Examples of R.F. calculation

6.6.2 Units of Measurement

Construction of Plain Scale

out Examples of Plain Scale Construction

6.8 Principle of Diagonal Scales

6.9 Construction of Diagonal Scales

CHAPTER 7 PROJECTION

7.1.2 Picture Plane/Plane of Projection

7.2.1 Orthographic Projection

7.2.2 Pictorial Projection

7.2.2.1 Axonometric Projection

7.2.2.2 Oblique Projection

7.2.3 Perspective Projection

7.3 Details of Orthographic Projection

7.3.1 The Glass Box method

7.3.2 The Six Principal Views

lass Box Concept for 1st Angle P

Orthographic Projections of Parallel, Inclined and

Oblique Surfaces………………………………………..

81

Orthographic Projections of Hidden Surfaces

Orthographic Projections of Curved Surfaces and Holes

Method of Obtaining Views

Methods of projecting views

v

Steps for Projecting Views by Diagonal Line Method

out Examples of Orthographic Views

Limitation of Multi View P

7.4 Details of Isometric Projection

7.4.1 Principle of Isometric Projection

7.4.3 Lines in Isometric Projection

7.4.5 Method of Constructing Isometric Drawing

7.4.6 Isometric Drawing of

Isometric Drawing of Rectangular Plane

Isometric Drawing of Pentagonal Plane

Isometric Drawing of a Circular Plane

Isometric Drawing of Solids

emembered for Isometric drawing

7.4.8 Steps for drawing Isometric View

out Examples of Isometric Drawing

CHAPTER 8 SECTIONING

Special Consideration for

ection of Ribs, Spokes and

Lugs…………………………………………………………..

118

8.5 Parts that Should Not Be S

out Examples of Sectioning

Bibliography ………………………………………

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 1

CHAPTER 1

INTRODUCTION

1.1 Drawing

The graphical representation of any object or idea can be termed as drawing. A drawing can be prepared either

using free hand or using engineering instruments or using computer program.

1.2 Types of Drawing

1. Artistic Drawing

2. Engineering Drawing

1.2.1 Artistic Drawing

The drawing representing any object or idea which is sketched in free hand using imagination of artist and in

which proper scaling and dimensioning is not maintained is called an artistic drawing. Example: Painting, Posters,

arts etc.

1.2.2 Engineering Drawing

Engineering drawing can be defined as a graphical language used by engineers and other technical personnel

associated with the engineering profession which fully and clearly defines the requirements for engineered items.

It is a two dimensional representation of a three dimensional object.

In other words, The art of representing a real or imaginary object precisely using some graphics, symbols, letters

and numbers with the help of engineering drawing instruments is called engineering drawing.

The art of representing engineering objects such as buildings, roads, machines, circuits etc. on a paper is called

engineering drawing.

It is used by engineers and technologists. An engineering drawing provides all information about size, shape,

surface type, materials etc. of the object. Example: Building drawing for civil engineers, Machine drawing for

mechanical engineers, Circuit diagrams for electrical and electronics engineers, computer graphics for one and all

etc.

Table 1.1 Difference Between Artistic and Engineering Drawing

drawing is to convey emotion or

artistic sensitivity in some way.

of engineering drawing is to convey

information about engineering object or idea.

Can be understood by all.

Need some specific knowledge or training to

understand.

maintaining is not necessary

Scale maintaining is necessary

No special requirement of engineering instruments.

Engineering drawing instruments is used to make

the drawing precise.

An artistic drawing may not be numerically specific

and informative.

gineering drawing must be numerically

specific and informative.

Standard drawing code need not to be followed.

Standard drawing code (like ISO, ANSI, JIS, BS

etc,) must be maintained.

1.3 Purpose of Engineering drawing

It is very difficult and complex to explain some certain engineering requirements in word. In such cases well

dimensioned and properly scaled graphics can make it easy to understand that for technical personnel. Engineering

drawing serves this purpose. Any product that is to be manufactured, fabricated, assembled, constructed, built, or

subjected to any other types of conversion process must first be designed. To make the outcome from the design

understandable to any third party engineering drawing is the best way.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 2

1.4 Applications of Engineering Drawing

Engineering drawing is an essential part of almost all engineering projects. Some important uses of engineering

drawing are mentioned below:

1. It is used in ships for navigation.

2. For manufacturing of machines, automobiles etc.

3. For construction of buildings, roads, bridges, dams, electrical and telecommunication structures etc.

4. For manufacturing of electric appliances like TV, phone, computers etc.

1.5 Types of Engineering Drawing

Engineering drawing can be grouped into following 4 major categories:

1. Geometrical Drawing

a. Plane geometrical drawing

b. Solid geometrical drawing

2. Mechanical Engineering Drawing

3. Civil Engineering Drawing

4. Electrical & Electronics Engineering drawing etc.

1.5.1 Geometric Drawing

The art of representing geometric objects such as rectangles, squares, cubes, cones, cylinders, spheres etc. on a

paper is called geometric drawing. If the object has only 2 dimensions i.e. length and breadth (as rectangles,

squares, triangles etc.), it is called Plane geometrical drawing and if it has 3 dimensions i.e. length, breadth and

thickness/depth (as cube, prism, sphere, cylinder etc.), it is called Solid geometrical drawing.

1.5.2 Mechanical Engineering Drawing

The art of representing mechanical engineering objects such as machines, machine parts etc. on a paper are

called mechanical engineering drawing or machine drawing. It is used by mechanical engineers to express

mechanical engineering works and projects for actual execution.

1.5.3 Civil Engineering Drawing

The art of representing civil engineering objects such as buildings, roads, bridges, dams etc. on a paper are

called civil engineering drawing. It is used by civil engineers to express civil engineering works and projects for

actual execution.

1.5.4 Electrical Engineering Drawing

The art of representing electrical engineering objects such as motors, generators, transformers, wiring diagrams

etc. on a paper are called electrical engineering drawing. It is used by electrical engineers to express electrical

engineering works and projects for actual execution.

The art of representing electronic circuits of TV, Phones, computers etc. on a paper are called electronic

engineering drawing or electronic drawing. It is used by electronic engineers to express electronic engineering

works and projects for actual execution.

1.6 Specific Purposes of Studying Civ il Engineering Drawing

One needs to study civil engineering drawing for the following purposes:

1. To develop the ability to produce simple civil engineering drawing and sketches based on current practice.

2. To develop the skills to read and understand the drawings used in civil engineering projects.

3. To develop a working knowledge of the layout of buildings, bridges, highways etc. and other civil

engineering structures.

4. To develop skills in abstracting information from calculation sheets and schematic diagrams to produce

working drawings for masons, construction managers and field workers who execute civil engineering

projects.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 3

1.7 Types of Civil Engineering drawing

Civil engineering drawing of a civil work project can be classified in two broad categories:

1. Architectural Drawing

a. Plan:

It shows the position of different objects and elements of the structure in a two dimensional

view. Only length and width of objects are shown here.

b. Elevation and Section:

It shows a view along the height of structure. Elevation can be presented in 2D or 3D. In 2D

elevation view either height and length or height and width is showed.

2. Structural Drawing

It shows the detail requirement of reinforcement and their arrangement in structure. It also shows the

specification and properties of construction materials like concrete, steel, timber etc.

1.8 Elements of Engineering Drawing

1.9 Drawing Standards

An engineering drawing should be well specified and universally acceptable. That's why there are some

specified rules for engineering drawing. These rules may vary slightly for different regions. There are some

drawing standards or drawing codes that accumulates the rules of engineering drawing for a certain region. Well-

known drawing codes and their application region is expressed below:

Table 1.2 Drawing Standards

International Organization for Standardization

American National Standards Institute

Japanese Industrial Standards

In Bangladesh in most of the cases, it is usual practice to follow ISO code for engineering drawing. However, in

some instances ANSI and BS standards are also followed.

1.10 Drawing Instruments

The most common instruments used for engineering drawing are:

1. Drawing Board 4. Rubber/Eraser 7. Instrument box 10. Scales

2. Drawing paper 5. T- square 8. Protractor 11. Pins and clips

3. Pencil 6. Set-square 9. Compass 12. Adhesive tapes

13. French curves etc

Drawing Board

 It is a board or platform rectangular in shape.

 Size of drawing board need to be larger than that of drawing paper.

 It is made of wood.

 Top surface should be smooth.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 4

Drawing Paper

Drawing paper is the paper, on which drawing is to be made. All engineering drawings are made on sheets of

paper of strictly defined sizes, which are set forth in the respective standards. The use of standard size saves paper

and ensures convenient storage of drawings.

Desirable properties a good drawing paper:

 It should be smooth and uniform in thickness.

 It should be thick, strong and tough.

 Fibers of drawing paper should not be disintegrated when a good eraser is used on it.

Paper Types:

1. Detail Paper (used for pencil work).

2. White drawing paper (used for finished drawing)

3. Tracing paper (used for both pencil and ink work and useful for replicating a master copy)

Paper Size:

Table 1.3 ISO Paper Sizes (plus rounded inch values)

Format

A series B series C series

Size mm × mm in × in mm × mm in × in mm × mm in × in

The tolerances specified in the standard are

 ±1.5 mm (0.06 in) for dimensions up to 150 mm (5.9 in),

 ±2 mm (0.08 in) for lengths in the range 150 to 600 mm (5.9 to 23.6 in) and

 ±3 mm (0.12 in) for any dimension above 600 mm (23.6 in).

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 5

D

Standard Sizes of Drawing P

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 6

Paper Layout:

The ISO standard (ISO 5457) require a 20mm border to the left hand edge (for filing) and a 10mm border round

the other three sides of the drawing sheet. However, the margin of paper can be increased according to

requirements and settings of printer/plotter.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 7

For Class Work:

Pencil:

Pencils are used to draw different lines, shapes, symbols and to write texts in engineering drawing. Based on the

hardness of lead pencils are classified in three major grades as hard, medium and soft. They are further sub-

divided and numbered as mentioned in table below:

Table 1.4 Pencils of Different Grades

Selection of proper grade pencil or lead is important for quality drawing. One has to be careful in selecting a lead

because very hard lead might penetrate the drawing, on the other hand, soft lead may smear. Quality and type of

drawing paper is an important factor in selecting lead. One other importance consideration is the importance of

line to be drawn. Inferior lines (like border lines, guide lines, construction lines and any other auxiliary lines

needed to be erased later) are drawn using harder pencil. Comparatively softer grade pencil is used for drawing

superior items (like object line, texts, symbols etc.).

Common uses of different grade pencil are tabulated below:

Table 1.5 Pencil Usage Guideline for Different Line Types

For convenience we will use 2H and HB pencils for our assignments and class drawings.

Grade Items arranged ordering harder to softer

Hard 9H> 8H> 7H>6H>5H>4H

Medium 3H> 2H>H>F>HB >B

Soft 2B>3B>4B>5B>6B>7B

Layout for Class Assignments

Hajee Mohammad Danesh Science and Technology University

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T-square:

1. Used to draw horizontal straight line.

2. Used to guide the triangles when drawing

vertical and inclined lines.

Set-square:

1. Used to construct the most common angles (i.e. 30

0

, 45

0

and 60

0

) in technical drawings.

2. Used to draw parallel and perpendicular lines quickly and conveniently.

Protractor:

It is used for laying out and measuring angle.

Scale (ruler):

A number of kinds of scales are available for varied types of engineering design. Scales with beveled edges

graduated in mm are usually used.

Hajee Mohammad Danesh Science and Technology University

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Compass

It is used to draw circles and arcs both in pencil and ink. It consists of two legs pivoted at the top. One leg is

equipped with a steel needle attached with a screw, and other shorter leg is, provided with a socket for detachable

inserts.

Div iders:

Used chiefly for transferring distances and occasionally for dividing spaces into equal parts. i.e. for dividing

curved and straight lines into any number of equal parts, and for transferring measurements.

French curve :

It is used to draw irregular curves that are not circle arcs. The shape varies according to the shape of irregular

curve.

Review Questions

1. Define drawing and classify it.

2. What are the differences between engineering drawing and artistic drawing?

3. Why Engineering drawing is called the language of engineers?

4. What are specific applications of engineering drawing for your discipline?

5. Classify engineering drawing and give example of each branch.

6. Classify civil engineering drawing.

7. What is difference between plan, elevation and section?

8. Name some codes/standards of engineering drawing. Which one is used in Bangladesh/USA/UK?

9. Name some common drawing instruments and their uses.

10. What is the standard size of a drawing board?

11. What is the standard proportion of drawing paper's length and width?

12. What is the measurement of an A0/A1/A2/A3/A4 paper?

13. What is the difference between white drawing paper and tracing paper?

14. How pencils are classified?

15. On what considerations you will choose pencil for a drawing?

16. Which pencil should be used for drawing object boundary/guideline/dimension line/border line/texts.

17. How paper quality affects choice of pencil?

18. Which angles can be drawn directly with set-squares?

Fig. 1.9 Compass and Divider

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 10

CHAPTER 2

LINES AND SYMBOLS

Objectives

Objective of studying this chapter are:

 To learn to explain the different line types

 To learn to mention the application of each line type in technical drawings

 To learn to mention the application of different symbols.

2.1 Conventional Lines

Each line on a technical drawing has a definite meaning and is drawn in certain ways. There are certain

conventional lines recommended by drawing codes. Usually two types of widths are used for the lines; they are

thick and thin. Thick lines are in between 0.5 mm to 0.8 mm wide while the thin lines are between 0.3 mm to 0.5

mm wide. However, the exact thickness may vary according to the size and type of drawing. If the size of drawing

is larger, the width of the line becomes higher. There should also be a distinct contrast in the thickness of different

kinds of lines, particularly between the thick lines and thin lines. Visible, cutting plane and short break lines are

thick lines, on the other hand hidden, center, extension, dimension, leader, section, phantom and long break lines

are thin.

Table 2.1 Conventional Lines and Their Usage

Cont.

No.

type

Object line

outlines/boundary of an

object. It shows the shape of

an object

Dashed line

To represent hidden edge of

an object. They should end

on both sides by touching

the visible lines and should

touch themselves at

intersection (if any).

through center of hole, pitch

line etc.

Dimension line

and leaders

object

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 11

Table 2.1 Conventional Lines and Their Usage (Contd.)

No.

type

To indicate cut portion of an

object

line

To show imaginary cutting

of an object.

planeline

To show break of an object

in order to shorten the view

of a long part.

Repeat line

To show alternate position

of an object or the position

of an adjacent part.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 12

2.2 Conventional Symbols

A variety of symbols are used in engineering drawing to represent different elements, properties, material types

etc. Some geometric symbols are commonly used in almost every types of drawing while there are some special

symbols used in specific types (civil, mechanical, electrical etc.) of drawing.

2.2.1 Common Geometric Symbols used in Engineering Drawing

Table 2.2 Conventional Geometric Symbols

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 13

2.2.2 Common Symbols used in Civil Engineering Drawing

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 14

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 15

2.2.3 Common Symbols used in Electrical Engineering Drawing

Electrical Symbols Used in Building Drawing

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Exercise and Assignments

1. Make a table showing the conventional lines most commonly used in engineering drawing mentioning

their specific applications.

2. Make a table showing the conventional symbols (geometric/civil/electrical/materials) most commonly

used in engineering drawing with their meanings.

Review Questions

1. Why have you studied lines and symbols?

2. Draw a standard hidden/ center/ cutting plane/ section/ break line and show an example of its use.

3. What is the standard proportion of solid segments and gaps in a hidden/center line.

4. Why there is no specified proportion for dimension and extension line?

5. What is difference between applicability of a section line and a break line?

6. Which conventional lined are to be drawn with 2H pencils?

7. Which conventional lined are to be drawn with HB pencils?

8. What is the standard symbol to show diameter/ radius/ slope/ datum?

9. What is the standard symbol for single /double opening in/out doors?

10. What is the standard symbol for showing sectioning through earth/ concrete/ brick/ metal/ wood.

11. What is the standard symbol to show inductor/ resistor/ gates?

12. Draw some electrical symbol for household weiring.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 17

CHAPTER 3

LETTERING AND NUMBERING

Objectives

Objectives of studying this chapter are:

 To know different style of lettering.

 To learn to write letters and numbers according to the standard

3.1 Letter Styles

 Gothic

 Roman

 Italic

 Text

They were all made with speedball pens, and are therefore largely single-stroke letters. If the letters are drawn in

outline and filled in, they are referred to as "filled- in" letters. The plainest and most legible style is the gothic

from which our single-stroke engineering letters are derived. The term roman refers to any letter having wide

down ward strokes and thin connecting strokes. Roman letters include old romans and modern ro man, and may be

vertical or inclined. Inclined letters are also referred to as italic, regardless of the letter style; text letters are often

referred to as old English.

3.2 Classification of Letters

3.2.1 Extended and Condensed Letters

To meet design or space requirements, letters may be narrower and spaced closer together, in which case they

are called "Compressed" or "Condensed" letters. If the letters are wider than normal, they are referred to as

"Extended" letters.

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3.2.2 Light Face and Bold Face Letters

Letters also vary as to the thickness of the stems or strokes. Letters having very thin stems are called Light Face

Letters, while those having heavy stems are called Bold Face Letters.

3.3 Technique of Lettering

"Any normal person can learn to letter if he is persistent and intelligent in his efforts." While it is true that

"Practice makes perfect," it must be understood that practice alone is not enough; it must be accompanied by

continuous effort to improve.

There are three necessary steps in learning to letter:

 Knowledge of the proportions and forms of the letters and the order of the strokes.

 Knowledge of composition- the spacing of the letters and words.

 Persistent practice, with continuous effort to improve.

3.4 Guide Lines

Extremely light horizontal guidelines are necessary to regulate the height of letters. In addition, light vertical or

inclined guidelines are needed to keep the letters uniformly vertical or inclined. Guidelines are absolutely essential

for good lettering and should be regarded as a welcome aid, not as an unnecessary requirement.

Make guidelines light, so that they can be erased after the lettering has been completed. Use a relatively hard

pencil such as a 4H to 6H, with a long, sharp, conical point.

3.4.1 Guidelines for Capital Letters

On working drawings, capital letters are commonly made 3mm high, with the space between lines of lettering

from ¾ th to the full height of the letters. The vertical guidelines are not used to space the letters (as this should

always be done by eye while lettering), but only to keep the letters uniformly vertical, and they should accordingly

be drawn at random.

A guideline for inclined capital letters is somewhat different. The spacing of horizontal guidelines is the same as

for vertical capital lettering. The American Standard recommends slope of approximately 68.2

0

with the horizontal

and may be established by drawing a "sloped triangle", and drawing the guidelines at random with T-square and

triangles.

3.4.2 Guidelines for Lower-Case Letters

Lower-case letters have four horizontal guidelines, called the cap line, waistline, and base line and drop line.

Strokes of letters that extend up to the cap line are called ascenders, and those that extend down to the drop line,

descenders. Since there are only five letters (p, q.g, j, y) that have descenders, the drop lines are little needed and

are usually omitted. In spacing guidelines, space "a" may vary from 3/5to 2/3 of space "b". 27The term single

stoke or one stoke does not mean that the entire letter is made without lifting the pencil. But the width of the

stroke is the width of the stem of the letter.

3.5 Single Stroke Lettering

The salient features of this type of lettering are:

 Greatest amount of lettering on drawings is done in a rapid single stroke letter i.e. either vertical,

or inclined.

 The ability to letter and perfectly can be acquired only by continued and careful practice

 it is not a matter of artistic talent or event of dexterity in hand writing

3.6 Order of Strokes

They are necessary to have legible and accurate letter styles. In the following description an alphabet of slightly

extended vertical capitals has-been arranged in-group. Study the slope of each letter with the order and direction

of the storks forming it. The proportion of height and width of various letters must be known carefully to letter

them perfectly.

The I-H-T Group

The letter I is The Foundation Stroke. The top of T is drawn first to the full width of the square and the stem is

started accurately at its midpoint.

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Md. Roknuzzaman, Department of Civil Engineering Page 19

The L-E-F Group

The L is made in two strokes. The first two strokes of the E are the same for the L, the third or the upper stoke is

lightly shorter than the lower and the last stroke is the third as long as the lower. F has the same proportion as E

The V-A-K Group

V is the same width as A, the A bridge is one third up from the bottom. The second stroke of K strikes stem one

third up from the bottom and the third stroke branches from it.

The M-W Group

M may be made in consecutive strokes of the two verticals as of N. W is made with two V's.

The O-Q-C-G Group

The O families are made as full circles and made in two strokes with the left side a longer arc than the right. A

large size C and G can be made more accurately with an extra stroke at the top.29

The D- U-J Group

The top and bottom stokes of D must be horizontal, fail line to observe this is a common fault with beginners. U

is formed by two parallel strokes to which the bottom stroke be added. J has the same construction as U, with the

first stroke omitted.

The P-R-B Group

The number of stokes depends up on the size of the letter. The middle line of P and R are on centerline of the

vertical line.

Order of Strokes for Single Stroke Gothic Letters

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Proportion of Width and Height for Single Stroke

Gothic Letters (Uppercase) & Numbers

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Order of Strokes for Single Stroke Gothic Letters (Lowercase)

Order of Strokes for Single Stroke Gothic

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3.7 Spacing of Letters

Uniformity in spacing of letters is a matter of equalizing spaces by eye. The background area between letters,

not the distance between them, should be approximately equal. Some combinations, such as LT and VA, may

even have to be slightly overlapped to secure good spacing. In some cases the width of a letter may be decreased.

For example, the lower stroke of the L may be shortened when followed by A.

Words are spaced well apart, but letters with in words should be spaced closely. Make each word a compact unit

well separated from the adjacent words. For either upper case or lower-case lettering, make the spaces between

words approximately equal to a capital O. Avoid spacing letters too far apart and words too close together.

3.8 Lettering in Maps

Letters are generally used on maps as follows:

 Vertical capital: name of states, countries, towns, capitals, titles of the map etc.

 Vertical lower case: name of small towns, villages, post offices etc.

 Inclined capital: name of oceans, bays, gulfs, large lakes, rivers etc.

 Inclined lower case: name of rivers, creeks, small lakes, ponds, marshes and springs

3.9 Summary of ISO rules for Lettering

1. Most of the lettering is done in single stroke either in vertical or in inclined manner.

2. Only one style of lettering should be used throughout the drawing.

3. Lettering can be done either in free hand or using templates.

4. Proportion of Height & width

a. For A,M,O,Q,T,V,X and Y, Height = Width.

b. For W, height<Width..

c. For Other latters, Height>Width.

d. For all numbers Height>Width

5. Line thickness of lower & upper case letters are made same as well as uniform.

6. Distance between adjacent lines or space between letters or numbers ≥ 2 × ℎ

7. If thickness of 2 adjacent line is different, spacing = 2 × ℎℎ

8. Standard height of letters and numbers are 2.5,3.5,5.0,7.0,10.0,14.0 and 20.0 mm

9. Height of letter or number ≥ 2.5

10. When both capital and lower-case letters are to be combined, if c=2.5mm then h will be 3.5mm.

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ISO 3098-2:2000 specification for relative dimensions of characters and spacing is illustrated here:

Table 3.1 Lettering A (d=h/14):

(without step or tail)

Spacing between characters, a

Minimum spacing of base line, b

Minimum spacing between words, e

Table 3.2 Lettering B (d=h/14):

(without step or tail)

Spacing between characters, a

Minimum spacing of base line, b

Minimum spacing between words, e

Dimensions of Letters and Numbers

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Exercise and Assignments

1. Following ISO guidelines complete lettering of all the uppercase letters and numbers in "Single Stroke

Gothic-Vertical" style.

2. Following ISO guidelines complete lettering of all the uppercase letters and numbers in "Single Stroke

Gothic-Italic" style.

3. Following ISO guidelines complete lettering of all the lowercase letters in "Single Stroke Gothic-

Vertical/Italic" style.

Review Questions:

1. Why have you studied lettering?

2. What is the difference between Gothic and Roman letters?

3. Write the letter "A"/ "a"/"T" in Gothic, Roman, Italic and Text style.

4. Which style of lettering is most commonly used in engineering drawing and why?

5. What do you mean by guidelines? Why is it used?

6. How guidelines are drawn for uppercase/lowercase letters?

7. What are the ISO rules for lettering?

8. How do you maintain the spaces between letters, words and lines?

9. Which letters have equal height and width?

10. Which letters have height>width and which one have width>height?

11. What are the standard heights of letters in engineering drawing?

12. Write a word/your name/Course code in single stroke gothic letters.

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CHAPTER 4

GEOMETRIC CONSTRUCTION

Objectives

Objectives of studying geometric figures are:

 To learn to define geometric nomenclatures like angles, lines etc.

 To improve expertise in using drawing instruments.

 To learn the steps to construct different geometric figures like lines, arcs, polygon, ellipse etc. in

convenient way.

4.1 Introduction

To be truly proficient in the layout of both simple and complex drawings, the drafter must know and fully

understand the many geometric construction methods used. These methods are illustrated in this chapter, and are

basically simple principles of pure geometry. These simple principles are used to actually develop a drawing with

complete accuracy, and in the fastest time possible, without wasted motion or any guesswork. Applying these

geometric construction principles give drawings a finished, professional appearance. Strict interpretation of

geometric construction allows use of only the compass and an instrument for drawing straight lines but in

technical drawing, the principles of geometry are employed constantly, but instruments are not limited to the basic

two as T-squares, triangles, scales, curves etc. are used to make constructions with speed and accuracy. Since

there is continual application of geometric principles, the methods given in this chapter should be mastered

thoroughly. It is assumed that students using this book understand the elements of plane geometry and will be able

to apply their knowledge.

4.2 Geometric Nomenclature

4.2.1 Points in Space

A point is an exact location in space or on a drawing surface. It is actually represented on the drawing by a

crisscross at its exact location.

4.2.2 Lines

Lines are straight elements that have no width, but are infinite in length (magnitude), and they can be located by

two points which are not on the same spot but fall along the line. Lines may be straight lines or curved lines. A

straight line is the shortest distance between two points.

4.2.3 Angle

An angle is formed by the intersection of two lines. There are three major kinds of angles: right angels, acute

angles and obtuse angles.

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4.2.4 Triangles

A triangle is a closed plane figure with three straight sides and their interior angles sum up exactly 180

0

. The

various kinds of triangles: a right triangle, an equilateral triangle, an isosceles triangle, and an obtuse angled

triangle.

4.2.5 Quadrilateral

It is a plane figure bounded by four straight sides. When opposite sides are parallel, the quadrilateral is also

considered to be a parallelogram.

4.2.6 Polygon

A polygon is a closed plane figure with three or more straight sides. The most important of these polygons as

they relate to drafting are probably the triangle with three sides, square with four sides, the hexagon with six sides,

and the octagon with eight sides. A polygon is said to be "Regular Polygon" when all of its sides are equal in

length and each of the internal angles formed at corners are equal in magnitude. Some helpful relations to be

remembered for regular polygons are:

1.  =

(



)





; ℎ , =  . .

2.  ,  =









; ℎ ,  = ℎℎ =  .  .

3.  .  =



(



)



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4.2.7 Circle

A circle is a closed curve with all points on the circle at the same distance from the center point. The major

components of a circle are the diameter, the radius and circumference.

4.2.8 Solids

They are geometric figures bounded by plane surfaces. The surfaces are called faces, and if these are equal

regular polygons, the solids are regular polyhedral.

4.3 Techniques of Geometric constructions

To construct the above mentioned geometric figures, we have to know some principles and procedures of

geometric construction. Thus, the remaining of this chapter is devoted to illustrate step-by-step geometric

construction procedures used by drafters and technicians to develop various geometric forms. First of all we have

to be well-expertise in using set squares particularly for drawing parallel and perpendicular lines. Fig. 4.7

illustrates it.

Fig. 4.6 Solids

Square for Making Parallel and Perpendicular Lines

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4.3.1 How to Bisect a Line or an Arc

To bisect a line means to divide it in half or to find its center point. In the given process, a line will also be

constructed at the exact center point at exactly 90

0

.

Given: Line A-B

 Step 1: Set the compass approximately two-thirds of the length of line A-B and swing an arc from point

A.

 Step 2: Using the exact same compass setting, swing an arc from point B.

 Step 3: At the two intersections of these arcs, locate points D and E

 Step 4: Draw a straight-line connecting point D with point E. Where this line intersects line A-B, it

bisects line A-B. Line D-E is also perpendicular to line A-B at the exact center point.

4.3.2 How to Divide a Line into a Number of Equal Parts

Given: Line A-B

 Step 1: Draw a construction line AC that starts at end A of given line AB. This new line is longer than the

given line and makes an angle preferably of not more than 30

0

with it.

 Step 2: Find a scale that will approximately divide the line AB in to the number of parts needed (5 in the

example below), and mark these divisions on the line AC. There are now 'n' equal divisions from A to D

that lie on the line AC (5 in this example).

 Step 3: Set the adjustable triangle to draw a construction line from point D to point B. Then draw

construction lines through each of the remaining 'n-1' divisions parallel to the first line BD by sliding the

triangle along the straight edge. The original line AB will now be accurately divided.

C

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4.3.3 How to Bisect an Angle

To bisect an angle means to divide it in half or to cut it in to two equal angles.

Given: Angle BAC

 Step 1: Set the compass at any convenient radius and swing an arc from point A

 Step 2: Locate points E and F on the legs of the angle, and swing two arcs of the same identical length

from points E and F, respectively.

 Step 3: Where these arcs intersect, locate point D. Draw a straight line from A to D.This line will bisect

angle BAC and establish two equal angles: CAD and BAD.

4.3.4 How to Draw an Arc or Circle (Radius) through Three Given Points

Given: Three points in space at random: A, B and C.

 Step 1: With straight line, lightly connect points A to B, and B to C,

 Step 2: Using the method outlined for bisecting a line, bisect lines A-B and B-C

 Step 3: Locate point X where the two extended bisectors meet. Point X is the exact center of the arc or

circle.

 Step 4: Place the point of the compass on point X and adjust the lead to any of the points A, B, or C (they

are the same distance), and swing the circle. If all work is done correctly, the arc or circle should pass

through each point.

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4.3.5 How to Transfer an Odd Shape (Triangular)

Given: Triangle ABC.

 Step 1: Letter or number the various corners and point locations of the odd shape in counterclockwise

order around its perimeter. In this example, place the compass point at point A of the original shape and

extend the lead to point B. Swing a light arc at the new desired location. Letter the center point as A' and

add letter B' at any convenient location on the arc. It is a good habit to lightly letter each point as you

proceed.

 Step 2. Place the compass point at letter B of the original shape and extend the compass lead to letter C of

the original shape.

 Step 3. Transfer this distance, B-C, to the layout.

 Steps 4 and 5. Going back to the original object, place the compass point at letter A and extend the

compass lead to letter C. Transfer the distance A-C as illustrated in Figure. Locate and letter each point.

 Step 6. Connect points A', B', and C' with light, straight lines. This completes the transfer of the object.

Recheck all work and, if correct, darken lines to the correct line weight.

4.3.6 How to Transfer Complex Shapes

A complex shape can be transferred in exactly the same way by reducing the shape into simple triangles and

transferring each triangle using the foregoing method.

Given: An odd shape, A, B, C, D, E, F, G.

 Step 1: Letter or number the various corners and point locations of the odd shape in clockwise order

around the perimeter. Use the longest line or any convenient line as a starting point. Line A-B is chosen

here as the example. Lightly divide the shape into triangle divisions, using the baseline if possible.

Transfer each triangle in the manner described in previous procedure. Suggested triangles to be used in

example are ABC, ABD, ABE, ABF and ABG.

 Step 2: This completes the transfer. Check all work and, if correct, darken in lines to correct line

thickness.

Transferring a Triangle to

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4.3.7 How to Draw A Pentagon (5 Sides)

Given: The locations of the pentagon center and the diameter of circle that will circumscribe the pentagon.

 Step 1 : Draw the circle with given diameter taking given location as center (C). Letter a diameter as HB.

 Step 2 : Draw a perpendicular CD that meets the circumference at D.

 Step 3: Bisect radius CB at A.

 Step 4: With A as center, and CD as radius, strike arc DE that meets the radius CH at E.

 Step 5: With D as center, and DE as radius, strike arc EF that meets the nearest circumference at F.

 Step 6: Draw line DF, this is the length of one side. Now set off distances DE around the circumference

of the circle, and draw the sides through these points.

4.3.8 How to Draw a Hexagon (6 Sides)

Given: The locations of the hexagon center and the diameter of circle that will circumscribe the hexagon.

 Step 1 : Draw the circle with given diameter taking given location as center.

 Step 2 : Extend the compass upto a length equal to the radius of the ciecle.

 Step 3: Starting from any point, say A

1

, on the circumference, cut 6 equal segments and mark the points

as A

1

, A

2

, A

3

, A

4

, A

5

and A

6

.

 Step 4: Join each 2 consecutive points to obtain the hexagon A

1

A

2

A

3

A

4

A

5

A

6

.

4.3.9 How to Draw an Octagon (8 Sides)

Given: The locations of the octagon center and the diameter of circle that will be inscribed by the octagon.

 Step 1 : Draw the circle with given diameter taking given location as center.

 Step 2 : Draw any two mutually perpendicular diameters.

 Step 3 : Draw tangents to the circle at the ends of diameters to obtain a square.

 Step 4 : Draw diagonals of the square. Diagonals will intersect the circle at 4 points.

 Step 5: Draw tangent to the circle at the 4 intersection points obtained in step 4. These tangents will meet

the sides of square drawn in step 3. Now darken the obtained octagon.

ransferring a Complex Shape to Another L

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4.3.10 How to Draw any Sided Regular Polygon

i. Given: Number of sides and the diameter of circle that will circumscribe the polygon.

 Step 1: Draw the circle with given diameter taking given location as center. Mark a diameter. As example

let us draw a 7 sided polygon. Mark the diameter as 0-7.

 Step 2 : Divide the diameter in "n" equal segments using parallel line method. Here n=7 for our case.

 Step 3 : Construct an equilateral triangle (0-7-8) with the diameter (0-7) as one of its sides.

 Step 4: Draw a line from the apex (point 8) through the second point on the line (point 2) and extend line

8-2 until it intersects the circle at point 9.

 Step 5: Now 0-9 is the length of each side of the polygon. Taking 0-9 as radius of compass, cut the

circumference in 7 equal segments to obtain the corners of the seven sided polygon and connect the

points.

ii. Given: Length of one side and number of sides (i.e. 5 for pentagon, 6 for hexagon, 8 for octagon etc.)

 Step 1: Calculate one internal angle of the polygon using formula

()



;

 Step 2: Draw a line of length equal to the given side.

 Step 3: Draw the obtained internal angle at one end of the line and set off distances equal to the given

side.

 Step 4: Continue r epeating the step 3 until you reach another end of 1

st

line. Thus the polygon will be

drawn.

iii. Given: Number of sides and diameter of out scribing circle.

 Step 1: Draw the circle. Using protractor, Draw an angle equal to

°



at the center of circle where n =

number of sides.

 Step 2: The lines drawn for the angle cuts the circle at A and B. Then AB is the length of one side. Now

set off distances AB around the circumference of the circle, and draw the sides through these points.

iv . Given: Number of sides and diameter of inscribing circle.

 Step 1: Draw the circle. Using protractor, Divide the central 360

0

angle into "n" number of equal part by

drawing "n" number of angles each equal to

°



at the center of circle where n = number of sides.

 Step 2: The lines drawn for the angles cuts the circle at A, B, C, D…. etc. At each point of intersection

draw a tangent to the circle. The tangents will meet each other at 1, 2, 3, 4…… etc. Then 1-2-3-4-….. is

the required polygon.

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4.3.11 How to Locate the Center of a Given Circle

Given: A circle without a center point.

 Step 1: Using the T-square, draw a horizontal line across the circle approximately halfway between the

estimated center of the given circle and the uppermost point on the circumference. Label the end points of

the chord thus formed as A and B.

 Step 2: Draw perpendicular lines (90°) downward from points A and B. Locate points C and D where

these two lines pass through the circle.

 Step 3: Carefully draw a straight line from point A to point D and from point C to point B. Where these

lines cross is the exact center of the given circle. Place a compass point on the center point; adjust the lead

to the edge of the circle and swing an arc to check that the center is accurate.

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4.3.12 How to Draw Arc Tangent to a Straight Line and a Curve

Given: Straight line AB, an arc with a center point O or radius r, and a required radius (R) of arc tangent.

 Step 1: Take a radius equal to  +  , place the needle of compass at the center of given curve and draw

an arc EF.

 Step 2: Draw a line CD parallel to AB at a distance  so that the line CD and arc EF intersects at point G.

 Step 3: Taking G as center and R as radius draw an arc. This arc will touch the line AB and the given arc.

4.3.13 How to Draw Arc Tangent to Two Arcs of Different Radius

Given: Two arcs AB, CD with their center point O

1

and O

2

or radius r

1

and r

2

, and a required radius (R) of arc

tangent.

 Step 1: If radius of arcs are not given but their center location is known, say O

1

and O

2

; Take any point P

on the 1

st

arc and taking it as center draw an arc EF with radius R. Join O

1

P and extend it until it meets the

curve EF at Q. Take O

1

as center and O

1

Q as radius draw another arc QS. If the radius of arcs are given

then simply take O

1

as center and draw the arc QS by taking radius equal to r

1

+R.

 Step 2: Following similar method as in step 1, draw another arc TS taking O

2

(Center of 2

nd

arc) as center

such that TS intersects QS at S.

 Step 3: Take S as center and R as radius, draw an arc that will touch the given 2 arcs.

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4.3.14 How to Draw an Ogee Curve

An ogee curve is used to join two parallel lines. It forms a gentle curve that reverses itself in a neat symmetrical

geometric form.

Given: Parallel lines A-B and C-D.

 Step 1 : Draw a straight line connecting the space between the parallel lines. In this example, from point B

to point C.

 Step 2: Make a perpendicular bisector to line B-C to establish point X.

 Step 3 : Make perpendicular bisectors to the lines B-X and X-C.

 Step 4 : Draw a perpendicular from line A-B at point B to intersect the perpendicular bisector of B-X,

which locates the first required swing center. Draw a perpendicular from line C-D at point C to intersect

the perpendicular bisector of C-X which locates the second required swing center.

 Step 5 : Place the compass point on the first swing point and adjust the compass lead to point B, and swing

an arc from B to X. Place the compass point on the second swing point and swing an arc from X to C.

This completes the ogee curve.

Note: point X is the tangent point between arcs. Check and. if correct, darken in all work.

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4.3.15 How to Draw Straight Tangent to Two Arcs of Different Radius

Given: Two arcs of different radius and their center location A and B or radius r

1

, r

2

and center distance AB.

 Step 1: Consider the two given circles with centers A and B respectively. If r

1

, r

2

and AB are given draw

them accordingly.

 Step 2: Draw any radius of the curve having larger diameter, BC, in example. Cut BD=radius of curve

with smaller diameter. Taking center as B and radius as CD draw an arc EF. If value of r

1

, r

2

are given

simply draw the arc EF taking radius as r

2

- r

1

and center as B.

 Step 3: Using set square draw a tangent AF to the arc EF from point A.

 Step 4: Join BF and extend it until it meets the given curve at P.

 Step 5: Complete the rectangle AFPQ. Then PQ will be the required tangent.

4.3.16 How to Draw an Ellipse (Four-centered Approximate Method)

Given: Major and Minor axis length (say, a and b respectively).

 Step 1 : Draw a line PQ=a and find out its mid-point O. At O draw a perpendiculars OR=OS=b/2.

 Step 2 : Taking center O and radius OP, draw an arc PA that intersects the extended minor axis (RS) at A.

 Step 3 : Join PR. Taking R as center and RA as radius draw an arc that intersects PR at B.

 Step 4 : Bisect PB at C and draw a perpendicular at C that intersects the extended minor axis (RS) at D.

The line CD also intersects PO at E.

 Step 5 : Draw OE' equal to OE and OD' equal to OD. Join DE', D'E and D'E' and extend them.

 Step 6 : Taking D and D' as centers and DR or D'S as radius draw 2 arcs MRN and KSL respectively.

 Step 7: Taking E and E' as centers and PE or QE' as radius draw another 2 arcs KPM and NQL

respectively. Thus the ellipse will be completed.

Common Tangent to 2 Curves

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Exercise and Assignments

1. Divide a line of length 40mm into 7 equal parts.

2. Draw a circle touching three points A, B and C with coordinates A(0,0), B(0,20) and C(15,0).

3. Draw a regular pentagon inscribing a circle of diameter 80mm. Avoid use of protractor.

4. Draw a regular pentagon out scribing a circle of diameter 100mm.

5. Draw a regular pentagon having length of side as 45mm.

6. Draw a regular hexagon inscribing a circle of diameter 80mm. Avoid use of protractor.

7. Draw a regular hexagon out scribing a circle of diameter 100mm.

8. Draw a regular hexagon having length of side as 45mm.

9. Draw a regular octagon inscribing a circle of diameter 80mm. Avoid use of protractor.

10. Draw a regular octagon out scribing a circle of diameter 100mm. Avoid use of protractor.

11. Draw a regular octagon having length of side as 45mm.

12. Draw a 9 sided regular polygon inscribing a circle of radius 50mm.

13. A 80mm long horizontal straight line is located outside a circle of radius 30mm, such that a 50mm line

drawn from center of the circle meets the mid-point of the straight line at right angle. Draw two arc

tangents, each having a radius of 40mm touching the circle and one of the ends of the straight line.

14. Draw a common arc tangent of radius 70mm to the two circles having their centers 80mm apart and

having diameters of 50mm and 30mm respectively.

15. Draw an ogee curve to connect two parallel lines each of length 20mm and their mid-points spaced 30mm

vertically and 70mm horizontally.

16. Two wheels with diameters 3.5m and 2m are required to be provided with a belt. Draw the line diagram of

the arrangement. Use a reduced scale.

17. Draw an ellipse having major and minor axis length as 90mm and 60mm.

Review Questions

1. Why have you studied geometric drawings?

2. Name the geometric nomenclatures and draw a qualitative shape of them.

3. Name and draw the different types of lines.

4. What do you mean by isosceles, equilateral and scalene triangle?

5. What are different types of quadrilaterals? Draw them.

6. What is the difference between parallelogram, trapezoid, rectangle, square and rhombus?

7. What is name of a 5/6/7/8/9/10/11/12 sided polygon?

8. What do you mean by regular polygon?

9. How can you calculate summation of all internal angles of a polygon?

10. Calculate one internal angle of a 5/7/9/11 sided regular polygon.

11. How can you calculate the length of one side of a regular polygon from the radius/diameter of the circle

that circumscribes it?

12. A circle has a diameter of 100cm. What will be the length of side of a 5/7/9/11 sided regular polygon

drawn inscribing the circle?

13. How many diagonals are possible for a 5/7/9/11 sided polygon?

14. Draw a circle showing chord, diameter, radius, arc, segment and sector.

15. Name some solid geometric form.

16. What is the solid form of a square/circle/triangle?

17. Draw a parallel or perpendicular line to a given line at any point using set-square.

18. Divide a given line into 3/5/9 parts.

19. Find the half, 1/4

th

, 1/8

th

of a given angle without protractor.

20. Transfer a given polygon to other specified point.

21. Locate the center of a given circle.

22. Draw a tangent to the two given circle.

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CHAPTER 5

DIMENSIONING

Objectives

Objectives of studying dimensioning are:

 To know the purposes of dimensioning

 To understand the differences between dimension line, extension line, leaders etc.

 To know the guidelines of dimension system.

 To learn to draw the dimension of technical drawings as per the standard

5.1 Purpose of Dimensioning

The purpose of dimensioning is to provide a clear and complete description of an object. A complete set of

dimensions will permit only one interpretation needed to construct the part. In some cases, engineering drawing

becomes meaningless without dimensioning. Maintaining scale only does not make a drawing sufficient for

manufacturer. By direct measurement from drawing according to the scale is very laborious, time-consuming and

such a part cannot be manufactured accurately. In general dimensioning system provides following information

 Sizes and locations of features

 Material's type

 Number required

 Kind of surface finish

 Manufacturing process

 Size and geometric tolerance

5.2 General Conditions for Dimensioning

 Accuracy: correct values must be given.

 Clearness: dimensions must be placed in appropriate positions.

 Completeness : nothing must be left out, and nothing duplicated.

 Readability: the appropriate line quality must be used for legibility.

5.3 Elements of Dimension System

 Extension lines

 Dimension lines

 Arrowheads

 Leaders

 Texts, numbers and symbols.

5.4 Rules for Dimensioning

5.4.1 General Rules for Dimensioning

 Dimensioning should be given within the extent of the view in general.

 Dimensioning should not be duplicated in other view.

 No subtraction or addition should be required to define or locate a feature.

 Dimensioning should be inserted on relatively larger available view to make it clear.

 One system of dimensions either unidirectional or aligned has to be used throughout the drawing.

 Dimensioning to the hidden lines should be avoided, in general.

 Dimensioning should be made on the view, which represents the shape of the part best.

 A zero must be placed before decimal point.

Fig. 5.1 Dimensioning Elements

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5.4.2 Rules of Extension Lines

Extension lines are the lines that indicate the point or line or space on the drawing to which dimension is being

applied. Following conditions should be maintained while inserting an extension line:

 A gap of 1mm has to be kept between extension line and visible line.

 An extension line should be extended about 3mm from the outmost dimension line.

 Extension lines may cross each other without break.

 Center lines can be used as extension lines.

 Extension lines are drawn usually perpendicular to dimension lines. But for overcrowded drawing

they can be drawn at an oblique angle as well.

5.4.3 Rules of Dimension Lines

Dimension lines are the lines that show the dimensions of a specific portion indicated by extension lines.

Following conditions should be maintained while inserting a dimension line:

 Dimension line should be approximately 10mm away from visible line.

 Spacing between consecutive parallel dimension lines may also be kept as 10mm.

 Dimension lines are broken near the middle to allow space for dimensions.

 As far as possible dimension lines should be placed outside the view.

 Dimension lines should not cross each other.

 Center lines should never be used as dimension lines.

 If space between extension lines is very short for inserting arrows, the arrows may be provided

outside the extension lines.

5.4.4 Rules of Arrowhead

Arrowheads are used at both ends of dimension lines and at the ends of leaders. They are usually drawn

freehand. Following conditions should be maintained while inserting an arrowhead:

 As far as possible all arrowheads should be identical in shape and size throughout the drawing.

 An approximate ratio of the length to width of arrowhead as 3:1 should be maintained.

 Arrowheads must touch the line. It must not be either away from the line or cross the line.

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5.4.5 Rules of Leaders

Leaders are used in engineering drawing for dimensioning of arcs, circles etc. They are also used to present note,

symbols, item number or part number etc. Following conditions should be maintained while inserting a leader:

 A leader should always be inclined at an angle of 60

0

preferably and 45

0

occasionally.

 The length of horizontal bar should be 3mm.

 A leader should be terminated by either an arrowhead or a small dot of about 1.5mm diameter.

 Leaders should not be drawn bent unless necessary.

 Leaders should not cross each other, however, they may be drawn parallel to each other with a

common horizontal bar.

 To direct a circle or an arc the leader should be so drawn, if it is imagined to extend it must pass

through the center of the circle or the arc.

 All notes, symbols and dimensions in a leader need to be provided in horizontal direction.

5.5 Direction of Dimensions

Direction of dimensions is chosen in either of the two systems:

A. Unidirectional system: All the dimensions are oriented to be read from the bottom of drawing. It is

also known as horizontal system. This system is preferred to aligned system.

B. Aligned system: All the dimensions are oriented to be read from the bottom or right side of the

drawing.

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5.6 Technique of Dimensioning

There are two basic steps in dimensioning objects, regardless of the type of object.

 Step 1: Apply the size dimensions. These are dimensions which indicate the overall size of the object

and the various features which make up the object.

 Step 2: Apply the locational dimensions. Locational dimensions are dimensions which locate various

features of an object from some specified datum or surface. Figure 9-29 gives examples of size and

location dimensions .

5.7 Dimensioning in Limited Space

If space between the extension lines is too small to insert the dimension digits, they may be provided al left or

right side of extension lines. Sometimes the space may be even too small to insert arrows, in such case dimensions

as well as arrows can be provided on outside of the extension lines as shown in Fig. 5.9.

If the space is very limited for inserting dimension lines, the portion to be dimensioned are enlarged for clear

dimensioning. Sometimes smaller circular dots are used in place of arrowhead for space limitation. Fig. 5.10

shows such example.

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5.8 Dimensioning of Angles

Angles are normally written in degrees, minutes, and seconds. The symbols used to depict degrees, minutes, and

seconds are also shown in this figure. Angular measurements may also be stated in decimal form. This is

particularly advantageous when they must be entered into an electronic digital calculator. The key to converting

angular measurements to decimal form is in knowing that each degree contains 60 minutes, and each minute

contains 60 seconds.

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5.9 Dimensioning of Arcs

The dimension figure and the arrowhead should be inside the arc, where there is sufficient space. If space is

limited then leaders can be used comfortably.

5.10 Dimensioning of Chord Length, Arc Length and Angle

Chords, arcs, and angles are dimensioned in a similar manner. The difference is:

 When dimensioning a chord length, the dimension line should be perpendicular and the extension

lines parallel to the chord.

 When dimensioning an arc length, the dimension line runs concurrent with the arc curve, but the

extension lines are either vertical or horizontal. An arc symbol is placed above the dimension.

 When dimensioning an angle, the extension lines extend from the sides forming the angle, and the

dimension line forms an arc.

among the Dimensioning Of Chord Length, Arc Length and Angle

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5.11 Dimensioning of Round Holes

 Round holes are dimensioned in the view in which they appear as circles.

 Smaller holes may be dimensioned using a leader which points toward the center of the hole in which

the note gives the diameter, or extension lines may be drawn from the circle with a dimension that

also indicates the diameter.

 Larger circles are dimensioned with a dimension line drawn across the circle through its center at an

angle with the diameter dimension shown.

 It is important when dimensioning holes to call off the diameter, not the radius.

5.12 Dimensioning of Blind Holes

It is usual practice to use leader line and local note to specify diameter and hole's depth in the circular view.

5.13 Dimensioning of Chamfer

It is usual practice to use leader line and note to indicate linear distance and angle of the chamfer.

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5.14 Common Mistakes in Dimensioning

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Fig. 5.17 Common Mistakes in D

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5.15 Worked-out Examples of Dimensioning

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Exercise and Assignments:

Complete Dimensioning of the figures below:

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Review Questions

1. Why have you studied dimensioning?

2. Which information are provided in dimensioning system?

3. What are the conditions for a good dimension system?

4. Name the elements of dimensioning system.

5. What are the rules that must be followed while dimensioning?

6. What is the purpose of extension line and what are the rules to be followed for extension line?

7. What is the purpose of dimension line and what are the rules to be followed for dimension line?

8. What is the purpose of leaders and what are the rules to be followed for leaders?

9. What are the uses of arrowheads in dimensioning and what are the rules to be followed for arrowheads?

10. What is the proportion of width and length of an arrowhead?

11. Draw a square out scribing a circle and complete dimensioning.

12. What is the difference between aligned and unidirectional dimensioning? Give examples.

13. What will you do when the space between extension lines is too small to accommodate the dimension line

with text at its middle?

14. What will you do when the space between extension lines is too small to accommodate the dimension line

with arrows?

15. What will you do when the feature is too small to make the dimension visible?

16. What are the different ways to show dimension of an arc/circle?

17. What is the difference of dimensioning of chord, arc and angle? Give example.

18. Draw a circular hole of 2cm deep and give dimensions to it.

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CHAPTER 6

SCALES

Objectives

Objectives of studying this chapter are:

 To learn to construct different types of scale.

 To learn to produce an enlarged or reduced drawing.

 To learn to make measurements using scales drawn in maps or drawings.

6.1 Scale

The proportion by which we either reduce or increase the actual size of the object on a drawing is known as

scale.

It is not possible always to make drawings of an object to its actual size as the extent of drawing paper is limited

and also sometimes the objects are too small to make it clearly understandable by drawing its actual size in

drawing paper. Scale is the technique by which one can represent an object comfortably as well as precisely

within the extent of drawing paper.

In other words, a scale is a measuring stick, graduated with different divisions to represent the corresponding

actual distance according to some proportion. Numerically scales indicate the relation between the dimensions on

drawing and actual dimensions of the objects.

6.2 Uses of scale

 To prepare reduced or enlarged size drawings.

 To set off dimensions.

 To measure distances directly.

6.3 Sizes of Scales

 Full size scale

 Reducing scale

 Enlarging scale

Full Size Scale

The scale in which the actual measurements of the object are drawn to the same size on the drawing is known as

full size scale. It is represented as 1:1 scale. If possible, drawing should be done in full scale.

Reducing Scale

The scale in which the actual measurements of the object are reduced to some proportion is known as reducing

scale. The standard formats of reducing proportions are:

1:2 - drawing made to one-half of the actual size

1:5 - drawing made to one-fifth of the actual size

1:10 - drawing made to one-tenth of the actual size

1:50 - drawing made to one-fiftieth of the actual size

1:100 - drawing made to one-hundredth of the actual size

Enlarging Scale

The scale in which the actual measurements of the object are increased to some proportion is known as reducing

scale. The standard formats of enlarging proportions are:

2:1 - drawing made to twice the actual size

5:1 - drawing made to five times the actual size

10: - drawing made to ten times the actual size

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6.4 Classification of Scales

 Plain Scales

 Diagonal Scales

 Comparative Scales

 Vernier Scales

 Chord Scales

The first two type (plain and diagonal) of scales are usually used in engineering drawings.

6.4.1 Plain Scale

The scale that can measure one main unit and one sub-unit of the main unit or up to a fraction of 1

st

decimal

point of the main unit is known to be a plain scale. It is simply a line divided into a number of equal parts and the

1

st

part is further sub-divided into small parts.

Kilometers and Hectometers, Meters and Decimeters, Meters and 1/10

th

of Meters etc. can be measured using

plain scales.

6.4.2 Diagonal Scale

The scale that can measure one main unit and two sub-units of the main unit or up to a fraction of 2

nd

decimal

point of the main unit is known to be a diagonal scale. It is so named because the 2

nd

sub-unit or 2

nd

decimal of

main unit is obtained by the principle of diagonal division.

Kilometers-Hectometers-Decameters, Decameters-Meters-Decimeters, Meters-1/10

th

of Meters- 1/100

th

of

Meters etc. can be measured using diagonal scales.

Table 6.1 Difference between Plain Scale and Diagonal Scale

6.4.3 Comparative Scale

When the given scale of a plan reads a certain measure and it is required to construct a new scale for the same plan

to read in some other measures, the new scale is called comparative scale or corresponding scale.

For example let us consider a plan drawn in inch units and scale provided with drawing can measure in feet and

inch. If we draw another scale taking same R.F. that can measure in feet, inch and 1/8

th

of inch it will be a

comparative scale. Also if we draw another scale that can measure in cm and mm with same R.F. it will also be a

comparative scale.

6.4.4 Vernier Scale

It is device for measuring fractional parts of the smallest division of the main scale. It consists of a fixed main

scale and a movable vernier scale. The vernier part is graduated in "n" number of divisions in such a way that it

coincides with "n-1" number of smallest divisions of main scale.

6.4.5 Chord Scale

The scale which is used to make or to measure angles of any magnitude is known as chord scale. This scale is

usually marked on a rectangular protractor.

6.5 Necessity of Construction of Scale on Drawing

In most of the cases the distances in a drawing is found to be different than the corresponding actual distance.

Therefore, to get the actual measurements, it is a must to know the proportion using which the drawing is

prepared. Sometimes the drawing may need to be prepared to an odd proportion (like 1:2.7 or 13.2:1) for which a

physical scale is not available. In such case individual scale construction is required for that specific drawing. It is

often found helpful and convenient to construct and draw the corresponding scale on the drawing than mentioning

the proportion in language. On the other hand if a drawing is to be used after decades, the paper may shrink or

It can measure one main unit and one sub

main unit

It can measure one main unit and two sub

main unit

It can measure up to a fraction of 1

the main unit.

It can measure up to a fraction of 2

the main unit.

Scale is constructed by simply dividing the line

longitudinally.

Scale is constructed by dividing the line

longitudinally as well as vertically and diagonally.

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expand by absorbing or leaving moisture due to temperature effect. Taking measurements from such a drawing

using the proportion mentioned will give some inaccurate result. But if a scale is constructed an drawn during the

preparation of 1

st

time, the drawn scale will also shrink or expand in the same proportion to the drawing. Thus if

one take measurements with the help of the drawn scale, accurate measurements will be obtained.

6.6 Information Necessary for Construction of a Scale

Following are the necessary information required for construction of a scale:

 The representative fraction (R.F.) of the scale.

 The unit or units to be presented.

 The maximum length to be measured.

6.6.1 The Representative Fraction (R.F.) or Scale Factor (S.F.)

The ratio of the distance on drawing paper of an object to the corresponding actual distance of the object is

known as the representative fraction (R.F.) or the scale factor (S.F.). It is to be remembered that for finding RF the

distances used for calculation must be in same unit. And being a ratio of same units, R.F. itself has no unit.

Mathematically,

. . =







[



]

6.6.1.1 Worked out Examples of R.F. Calculation

Example 6.1: In a certain map, 2.5 centimeters of measured length represents 5 hectometers of actual distance.

Calculate R.F. for the scale of this map.

Solution:

Representative Fraction of the scale for this map,

.  . =

 . 

 × × ××

=





1: 20000

Example 6.2: To draw a microscopic element of a machine part, it is to be enlarged in drawing such a manner

that one-fifth of one millimeter is to be represented by 1.5 meters. Find out RF of the scale for this drawing.

Solution:

Representative Fraction of the scale,

.  . =

 .  × × ×





= 7500  7500: 1

Example 6.3: A scale is to be constructed for a drawing of a plot such that 100 square feet of area is to be

represented by 1 square inch. What will be the R.F. of this scale?

Solution:

Here 1 sq. inch represents 100 sq.ft. or we can write 1ℎ



≈ 100



Taking under root on both sides, we get



1ℎ



≈



100 



∴ 1ℎ ≈ 10

, .  . =

1

10 × 12

=

1

120

 1: 120

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6.6.2 Units of Measurement

It is modern practice to use metric system of units in engineering drawing. However, sometimes British system

is also used. It is important to have clear understanding about unit conversion in both system. Table 6.2 to Table

6.7 presents the units of measurements, their symbols and conversions.

Table 6.2 Metric Units for Linear Measurement

Table 6.4 Metric Units for Area Measurement

Table 6.6 Metric Units for Volumetric Measurement

1000 cubic millimeters (mm

1000 cubic centimeters (cm

6.7 Construction of Plain Scale

Following are the steps for constructing a plain scale

 Find out the R.F., if not given directly.

 Find out the length of scale

 = .  . × ℎℎ

[Note: If length of object or maximum length to be measured is not mentioned in problem, for

convenience, take the length of scale about 15 cm or 6 inches]

 Draw a straight line, preferably horizontal, of required length as found in previous step.

 Divide the line into a number of divisions relating to the length of object and maximum length to be

measured such that one segment represents one major unit. Avoid fractions, consider the next integer

value. For instance, if maximum length to be measured is 6.2 km, then number of divisions will be 7.

 Place mark 0 at the end of 1

st

main division (Remember, not at the starting point of 1

st

division) and

mark the other divisions sequentially toward right as 1,2,3….. etc.

 Divide the 1

st

main division into a number of divisions such that each of these smallest division

represents one sub-unit. For instance if the scale need to measure in feet and inches, number of minor

divisions will be 12. On the other hand if the scale is to measure in centimeters and millimeters or in

meters and 1/10

th

of meter number of divisions will be 10.

 Mark the sub-unit sequentially toward left as 1, 2, 3…… etc. or 0.1, 0.2, 0.3……. etc. If space is

limited they can be marked after every 2 division like 0, 2,4,….. etc.

 Mention the R.F. of the scale below the figure.

 Mention the name of main unit and sub-unit either at below or at the respective ends of the scale.

Linear Measurement

Measurement

Volumetric Measurement

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6.7.1 Worked-out Examples of Plain Scale Construction

Example 6.4: Construct a plain scale to show kilometers and hectometers when 2.5 centimeters are equal to 1

kilometer and long enough to measure upto 5.7 kilometers. Find R.F. of the scale and indicate distances

(i) 4 kilometers and 5 hectometers and (ii) 5.4 kilometers on the scale.

Solution:

 .  . =

2.5

1 × 10 × 10 × 10 × 10 × 10

=

1

40000

 1: 40000

ℎ = .  . × ℎ

= 





 × 6 =





 × 6 × 1000 × 100 = 15

[ To avoid fraction, maximum distance is take 6 km instead of 5.7 km ]

Now a horizontal line 15 cm long is drawn and is divided into 6 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, 2, 3, 4 and 5. The 1

st

division is further

divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2

division as 2, 4, 6, 8 and 10 toward left. R.F. and unit names are mentioned accordingly. Thus the scale

is constructed and the required distances are indicated.

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Example 6.5: A rectangular plot of land of area 64 square mile is represented on a certain map by area of 1 square

inch. Draw a plain scale to show units of 10 miles and single miles. Find R.F. and mark a distance of 63 mile on

this scale.

Solution: Given,

1ℎ



≈ 16





1ℎ



≈



64 



∴ 1ℎ ≈ 8

, .  . =

1

8 × 1760 × 3 × 12

=

1

506880

1: 506880

Here maximum distance to be measured is not given, but we need to ensure the measuring a distance of

63 mile. Thus we have to construct the scale for 70 miles of maximum distance.

ℎ =  .  . × ℎ

= 





 × 70 =





 × 70 × 1760 × 3 × 12ℎ = 8.75ℎ

Now a horizontal line 8.75 inch long is drawn and is divided into 7 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 10, 20, 30, 40, 50 and 60. The 1

st

division

is further divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked

after every 2 division as 2, 4, 6, 8 and 10 toward left. R.F. and unit names are mentioned accordingly.

Thus the scale is constructed and the required distances are indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 60

Example 6.6: A car is moving at a speed of 60 kmph. On a scale one centimeter represents one third of a

kilometer. Construct the scale and show the distance travelled by the car in 3 minutes and 30 seconds. What is the

R.F. of the scale?

Solution:

 .  . =

1

1

3

× 1000 × 100

=

1

33333

1: 33333

ℎ = 60ℎ = 60



ℎ

=

60

60





=

1

1

ℎ, , 1 ≈ 1 − − − − − − − −(1)

 ,  , 

1

3

 ≈ 1

∴ 1 ≈ 3 − − − − − − − −(2)



(

1

)



(

2

)

, ℎ , 1 = 3

 , ℎℎ15, 

15

3

= 5 

ℎℎ 3 30 sec ℎℎ

Now a horizontal line 15 cm long is drawn and is divided into 5 equal parts so that each major division

shows one minute. From left staring 0 at 2

nd

division major units are marked sequentially toward right as

0, 1, 2, 3 and 4. The 1

st

division is further divided into 6 divisions so that each minor division shows 10

seconds and starting at 0 mark placed earlier the sub-divisions are marked as 10, 20, 30, 40, 50 and 60

toward left. R.F. and unit names are mentioned accordingly. Thus the scale is constructed and the

required time is indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 61

6.8 Principle of Diagonal Scales

The principle of diagonal scale is to obtain any fractional part of a short line by following the diagonal division

method. In this method we get fractional part of a line, say 1/9

th

of length, 1/15

th

of length etc.

Let the given short line AB which is required to be divided into 12 equal parts.

 Erect a perpendicular BC of any suitable length and divide it into 12 equal parts.

 Join AC and draw lines 1-1', 2-2', 3-3'… etc. parallel to AB at each division point. Thus dividing is

complete indirectly.

 If you need 1/12

th

of AB, 1-1' will be your required length. If you need 2/12

th

of AB, 2-2' is your required

length. Similarly 3-3' represents 3/12

th

of AB, 4-4' represents 4/12

th

of AB and so on.

Proof:

From figure it is obvious that triangle ABC and triangle 4-4'-C are similar triangles.

So,







=







=









=





∴  4 − 4



=

4

12



Fig. 6.1 Diagonal division

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 62

6.9 Construction of Diagonal Scales

Following are the steps for constructing a plain scale

 Find out the R.F., if not given directly.

 Find out the length of scale

 = .  . × ℎℎ

[Note: If data is not available take the length of scale about 15 cm or 6 inches]

 Draw a straight line, preferably horizontal, of required length as found in previous step.

 Divide the line into a number of divisions relating to the length of object and maximum length to be

measured such that one segment represents one major unit.

 Place mark 0 at the end of 1

st

main division and mark the other divisions sequentially toward right as

1,2,3….. etc.

 Divide the 1

st

main division into a number of divisions such that each of these sub-divisions represents

one 1

st

sub-unit. For instance if the scale need to measure in yards, feet and inches, number of

horizontal sub-divisions will be 3. On the other hand if the scale is to measure in decimeter,

centimeters and millimeters or in meters, 1/10

th

of meter and 1/100

th

of meter number of horizontal

sub-divisions will be 10.

 Mark the sub-unit sequentially toward left as 1, 2, 3…… etc. or 0.1, 0.2, 0.3……. etc. If space is

limited they can be marked after every 2 division like 0, 2,4,….. etc.

 Draw a perpendicular of suitable length at the left end and complete the rectangle considering the two

mutually perpendiculars lines as length of two sides.

 Divide the vertical line at left end into a number of divisions such that each of one sub-division

represents one 2

nd

sub-unit. For instance if the scale need to measure in yards, feet and inches, number

of vertical sub-divisions will be 12. On the other hand if the scale is to measure in decimeter,

centimeters and millimeters or in meters, 1/10

th

of meter and 1/100

th

of meter number of vertical sub-

divisions will be 10.

 At each vertical sub-division point draw a line parallel to the baseline.

 Draw a diagonal line by joining left-top corner point and the horizontal sub-division point

immediately before the left-bottom corner. At every horizontal sub-division point draw a parallel line

to this diagonal line.

 Mention the R.F. of the scale below the figure.

 Mention the name of main unit and sub-units either at below or at the respective ends of the scale.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 63

6.9.1 Worked-out Examples of Diagonal Scale Construction

Example 6.7: Construct a diagonal scale to show kilometers, hectometers and decameters when 2.5 centimeters

are equal to 1 kilometer and long enough to measure upto 5.7 kilometers. Find R.F. of the scale and indicate

distances

(i) 4 kilometers 5 hectometers 4 decameters and (ii) 5.86 kilometers on the scale.

Solution:

 .  . =

2.5

1 × 10 × 10 × 10 × 10 × 10

=

1

40000

 1: 40000

ℎ = .  . × ℎ

= 





 × 6 =





 × 6 × 1000 × 100 = 15

[ To avoid fraction, maximum distance is take 6 km instead of 5.7 km ]

Now a horizontal line 15cm long is drawn and is divided into 6 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, 2, 3, 4 and 5. The 1

st

division is further

divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2

division as 2, 4, 6, 8 and 10 toward left. At left end a perpendicular of length equal to one major division

is drawn and a rectangle is completed considering the mutually perpendicular lines as two sides. The

vertical line at left end is divided into 10 equal parts and at each division point a line parallel and equal

length of the base line is drawn. Top left corner and the point corresponding to 9hm is connected with a

diagonal line. At the remaining 9 horizontal sub-division points parallel lines are drawn to the 1

st

diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2 division as

2, 4, 6, 8 and 10. At all the horizontal major division points vertical lines are drawn. R.F. and unit names

are mentioned accordingly. Thus the scale is constructed and the required distances are indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 64

Example 6.8:

Construct a diagonal scale that measures 1 inch for an equivalent actual length of 1 yard, can show yards, feet and

inches and can measure length up to 6 yds. Also show 2 yds. 2 ft 5 inch on it.

Solution:

. . =

1

1 × 3 × 12

=

1

36

1: 36

ℎ =  .  .  × ℎ

= 

1

36

 × 6 =

1

36

 × 6 × 3 × 12ℎ = 6ℎ

Now a horizontal line 6 inch long is drawn and is divided into 6 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, 2, 3, 4 and 5. The 1

st

division is further

divided into 3 divisions and starting at 0 mark placed earlier the sub-divisions are marked as 1, 2 and 3

toward left. At left end a perpendicular of length equal to one major division is drawn and a rectangle is

completed considering the mutually perpendicular lines as two sides. The vertical line at left end is

divided into 12 equal parts and at each division point a line parallel and equal length of the base line is

drawn. Top left corner and the point corresponding to 2ft is connected with a diagonal line. At the

remaining two horizontal sub-division points parallel lines are drawn to the 1

st

diagonal line. Vertical

divisions are marked sequentially from bottom toward top at every 2 division as 2, 4, 6, 8, 10 and 12. At

all the horizontal major division points vertical lines are drawn. R.F. and unit names are mentioned

accordingly. Thus the scale is constructed and the required distances are indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 65

Example 6.9:

In a certain engineering drawing 1m length is represented by 20mm. Construct a scale for this drawing showing

meters, decimeters and centimeters and measure 2 meters, 5 decimeters and 8 centimeters on it.

Solution:

 .  . =

20

1 × 1000

=

1

50

 1: 50

Maximum measuring length is not given here. Assume the drawing scale length is 15 cm (standard

value).



ℎ =

ℎ

 .  .

 = 

15

1/50

 = 750 =  7.5 

As the maximum length is a fractional number , so number of major division may either be 7 (for which

maximum measuring length will be 7 m) or 8 (for which maximum measuring length will be 8 m). Both

are acceptable as we have to show a distance only 2m 5dm 8cm on this scale. Let us take 7.

Now a horizontal line 15cm long is drawn and is divided into 7 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, 2, 3, 4, 5 and 6. The 1

st

division is

further divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked after

every 2 division as 2, 4, 6, 8 and 10 toward left. At left end a perpendicular of length equal to one major

division is drawn and a rectangle is completed considering the mutually perpendicular lines as two sides.

The vertical line at left end is divided into 10 equal parts and at each division point a line parallel and

equal length of the base line is drawn. Top left corner and the point corresponding to 9dm is connected

with a diagonal line. At the remaining 9 horizontal sub-division points parallel lines are drawn to the 1

st

diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2 division as

2, 4, 6, 8 and 10. At all the horizontal major division points vertical lines are drawn. R.F. and unit names

are mentioned accordingly. Thus the scale is constructed and the required distances are indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 66

Example 6.10: Construct a scale to read 1m to 300m.

Maximum measuring length is given here i.e. 300 m. Considering a drawing scale length as 15 cm.





ℎ =  .  .



ℎ



.  . = 

ℎ

ℎ

=

15

300 × 100

=

1

2000

1: 2000

Here, we have to measure single meter as well as 300 meter. So our major unit should be 100

th

of meters, 1

st

sub-unit should be 10

th

of meter and 2

nd

sub-unit or diagonal sub-unit should be single meters.

Now a horizontal line 15cm long is drawn and is divided into 3 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, and 2. The 1

st

division is further

divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2

division as 20, 40, 60, 80 and 100 toward left. At left end a perpendicular of length equal to one major

division is drawn and a rectangle is completed considering the mutually perpendicular lines as two sides.

The vertical line at left end is divided into 10 equal parts and at each division point a line parallel and

equal length of the base line is drawn. Top left corner and the point corresponding to 90m is connected

with a diagonal line. At the remaining 9 horizontal sub-division points parallel lines are drawn to the 1

st

diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2 division as

2, 4, 6, 8 and 10. At all the horizontal major division points vertical lines are drawn. R.F. and unit names

are mentioned accordingly. Thus the scale is constructed and the required distances are indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 67

Example 6.11: On a map 1 inch represents 1 mile. Construct a scale to read miles, furlongs and minimum 20

yards distance and mark 4 miles 6 furlongs and 120 yards on it.

Solution:

Here given, 1 inch = 1 mile

63360

1

12317601

1

1

1

.. 





mile

inch

FR

Here maximum measuring length is not given. Let us assume the drawing scale length is 6 inch.

 Maximum measuring length = Drawing scale length  R.F.

633606

63360

1

6  = 380160 inch = 6 miles

Now a horizontal line 6 inch long is drawn and is divided into 6 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, 2, 3, 4 and 5. The 1

st

division is further

divided into 8 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2

division as 2, 4, 6 and 80 toward left. At left end a perpendicular of length equal to one major division is

drawn and a rectangle is completed considering the mutually perpendicular lines as two sides. The

vertical line at left end is divided into 11 equal parts and at each division point a line parallel and equal

length of the base line is drawn. Top left corner and the point corresponding to 7 furlongs is connected

with a diagonal line. At the remaining 7 horizontal sub-division points parallel lines are drawn to the 1

st

diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2 division as

20, 60, 100, 140, 180 and 220. At all the horizontal major division points vertical lines are drawn. R.F.

and unit names are mentioned accordingly. Thus the scale is constructed and the required distances are

indicated.

 : 

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 68

Example 6.12:

An engineering drawing is prepared for microscopic parts of a machine. It is required to construct a scale for this

drawing that can measure in millimeters, 1/10

th

of single millimeter and 1/100

th

of single millimeters. The scale

should be such that 4mm length is represented by 10cm and it should be able to measure upto 5mm. Construct the

scale and measure 3.33mm and 1.09mm on this scale.

Solution:

.  . =

10 × 10

4

= 2525: 1

ℎ = .  . × ℎ

 =  25 × 5 = 125 = 12.5

Now a horizontal line 12.5cm long is drawn and is divided into 5 equal parts. From left staring 0 at 2

nd

division major units are marked sequentially toward right as 0, 1, 2, 3 and 4. The 1

st

division is further

divided into 10 divisions and starting at 0 mark placed earlier the sub-divisions are marked after every 2

division as 0.2, 0.4, 0.6 and 0.8 toward left. At left end a perpendicular of length equal to one major

division is drawn and a rectangle is completed considering the mutually perpendicular lines as two sides.

The vertical line at left end is divided into 10 equal parts and at each division point a line parallel and

equal length of the base line is drawn. Top left corner and the point corresponding to 0.9mm is

connected with a diagonal line. At the remaining 9 horizontal sub-division points parallel lines are drawn

to the 1

st

diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2

division as 0.02, 0.04, 0.06 and 0.08. At all the horizontal major division points vertical lines are drawn.

R.F. and unit names are mentioned accordingly. Thus the scale is constructed and the required distances

are indicated.

Hajee Mohammad Danesh Science and Technology University

Md. Roknuzzaman, Department of Civil Engineering Page 69

Example 6.13:

An aeroplane is flying at a speed of 360 kmph. Draw a scale to represent 6 km by 1 cm and to show distance upto

60 km. Find R.F. of the scale and on the scale show distances covered by the aeroplane in

1. 3 minutes 22 seconds

2. 5 minutes 36 seconds

Solution:

 .  . =

1

6

=

1

6 × 1000 × 100

=

1

600000

1: 600000

ℎ =  .  . × ℎ

= 

1

600000

 × 60 =

1

600000

 × 60 × 1000 × 100  = 10



 = 360ℎ =

360 

1ℎ

=

360

60 

=

1 

1

6



∴ 1 ≈

1

6

 … … … … … … … … … … … (1)

From R.F.,

6 ≈ 1 ∴ 1 ≈





 … … … … … … … … … … … (2)

From equations (1) and (2), 





 ≈





 ∴ 1 ≈ 1

Now a horizontal line 10cm long is drawn and is divided into 10 equal parts so that each division

represents 1 minute. From left staring 0 at 2

nd

division major units are marked sequentially toward right

as 0, 1, 2, 3…… and 9. The 1

st

division is further divided into 6 divisions so that each sub-division

represents 10 seconds and starting at 0 mark placed earlier the sub-divisions are marked after every 2

division as 20, 40 and 60 toward left. At left end a perpendicular of length equal to one major division is

drawn and a rectangle is completed considering the mutually perpendicular lines as two sides. The

vertical line at left end is divided into 10 equal parts and at each division point a line parallel and equal

length of the base line is drawn. Top left corner and the point corresponding to 50 seconds is connected

with a diagonal line. At the remaining 5 horizontal sub-division points parallel lines are drawn to the 1

st

diagonal line. Vertical divisions are marked sequentially from bottom toward top at every 2 division as

2, 4, 6, 8 and 10. At all the horizontal major division points vertical lines are drawn. R.F. and unit names

are mentioned accordingly. Thus the scale is constructed and the required distances are indicated.

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Exercise and Assignments:

1. Construct a plain scale to show meters and decimeters, when 3 centimeters are equal to 2 meters and long

enough to measure upto 5 meters. Show a distance of 2 meters 7 decimeter and 4.8 meters on the scale.

2. Construct a plain scale that can measure 1m to 50m. Show a distance 38m on the scale.

3. Construct a scale to show miles and furlongs, when 2.5ft on the scale represents 30 mile and long enough

to measure upto 6 miles.

4. In a certain map 1 acre represents 2500 square kilometers of land area. Construct a scale for a portion of

that map which can measure in kilometers and its 1

st

decimal point. The scale should be long enough to

measure upto 9.7 km.

5. On a map a land of 5 sq. cm represents 45 sq. km. Construct a plain scale to measure a maximum distance

of 55 km and show the measurement of 42 km on it.

6. The volume of a room is 640 cubic metre. It is represented by a volume of 80 cubic cm. By measuring

R.F. construct a plain scale to measure upto 30 metre. Also show the measurement of 12 metre on it.

7. The distance between Dinajpur and Joypurhat railway station is 144 km and it is covered by the Drutajan

Express in 4 hours. Draw a plain scale to measure the time upto single minute. Take R.F. of the scale as





. Calculate and show the distance covered by the train in 45 minutes on the scale.

8. Construct a diagonal scale to read meters, decimeters and centimeters and long enough to measure upto 5

meters when 1 meter is represented by 3 centimeters. Indicate on the scale a distance of

a. 4 meters 7 decimets 6 centimeters.

b. 3.33 meters.

9. Construct a diagonal scale of R.F. = 1/25 showing millimetre, centimetre and metre and show the

measurement of 3 metre 50 cm and 60 mm on it.

10. A plan of a house 12 cm represents 240 m. Construct a diagonal scale to read 250 metres to one metre and

show the measurement 137 metres on it.

11. The distance between two station is 480 km. On a map it is represented by a 12 cm length line. Construct

a diagonal scale to show kilometers and to measure a distance of 275 km.

12. On a map 15 cm × 8 cm represents an area of 1920 square metres. Find the R.F. and draw the scale of the

map to read upto metre and decimeter. Also mark a distance 46 metres and 5 decimetres on it.

13. Ina drawing of machine parts, the original shapes are magnified 50 times. Construct a scale to measure

upto 2

nd

decimal point of a single millimeter and long enough to measure upto 4mm. Show a length of

2.22mm and 1.11mm on the scale.

14. A person is running at a speed of 6 kmph. Draw a scale to represent 6 km by 1 cm and to show distance

upto 60 km. Find R.F. of the scale and on the scale show distances covered by the person in

1. 3 hours 22 minutes

2. 5 hours 36 minutes

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Review Questions

1. Why have you studied scale?

2. Define scale. When scale becomes necessary?

3. Why have you learned to draw scale? In which situation scale is to be drawn along with the drawing?

4. Classify scales according to scale size. Define each type and give practical examples.

5. Classify scale according to measurement capacity. Define each type.

6. Which scales are usually used by engineers?

7. Differentiate between plain and diagonal scale.

8. Which information you think necessary to construct a scale?

9. Define R.F.

10. What is the unit of R.F.? Give logic to your answer.

11. What do you understand when an R.F. is found to be more/less than unity?

12. Is it possible to get a negative/zero value of R.F.? Give logic to your answer.

13. It is mentioned in a drawing that R.F. = 1:5. What is its meaning?

14. It is mentioned in a drawing that R.F. = 2:1. What is its meaning?

15. On a map of Bangladesh you measured the distance from Dinajpur to Dhaka as 6 inch. Actually the

distance is 500 miles. What is the R.F. of this map?

16. What should be the possible R.F. for drawing a microscopic element of length 1 nanometer?

17. A 15 cm scale measures a maximum length of 10 km. What is its R.F.?

18. If 9 hectares of area is represented by 1mm

2

in a map, what is the value of R.F.?

19. During the construction of scale why the zero notation placed at 2

nd

division?

20. How can you divide a 1mm line in 7 equal parts?

21. Draw a qualitative diagram of a plain/diagonal scale and show a distance.

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CHAPTER 7

PROJECTION

Objectives

Objectives of studying this chapter are:

 To learn to explain the purpose and theory of multi view projections

 To understand "Glass Box Method" of orthographic projection

 To learn to mention the principal views and combination of views

 To learn to convert pictorial drawings into orthographic or multi view projection

 To learn to represent circular surfaces, hidden surfaces in orthographic projection

 To know the precedence of lines in multi view projection

 To know the necessity of pictorial projection

 To learn the procedure to construct box for isometric and oblique drawings

 To learn to convert orthographic projection into isometric projection

7.1 Introduction

All forms of engineering and technical work require that a two dimensional surface (paper) be used to

communicate ideas and the physical description of a variety of shapes. To provide necessary information about an

object to the manufacturer or to any other concerned party, it is usual practice to provide projection(s) of that

object.

7.1.1 Projection

Projection is the process in which the rays of sight are taken in a particular direction from an object to form an

image on a plane. If straight lines (rays) are drawn from various points on the contour of the object to meet a

transparent plane, thus the object is said to be projected on that plane. The figure or view formed by joining, in

correct sequence, the points at which these lines meet the plane is called the projection of the object.

7.1.2 Picture Plane/Plane of Projection

The plane or surface on which the rays of sight are projected and combined to form a view is called picture plane.

7.1.3 View

The image formed on a picture

plane by projecting rays of sight is

called a view.

7.1.4 Projector

The lines or rays drawn from the

object to the plane are called

projectors.

Fig. 7.1 Projection and I

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7.2 Types of Projection

1. Orthographic/ multi view Projection

2. Pictorial Projection

3. Perspective Projection

7.2.1 Orthographic Projection

'ORTHO' means right angle and orthographic means right angled drawing. When the projectors are perpendicular

to the plane on which the projection is obtained, it is known as orthographic projection. Following six views are

possible in orthographic projection of a solid object.

a. Top View

b. Front view

c. Left View

d. Right View

e. Rear view

f. Bottom view

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7.2.2 Pictorial Projection

The Projections in which the description of the object is completely understood in one view is known as pictorial

projection. They have the advantage of conveying an immediate impression of the general shape and details of the

object, but not its true dimensions or sizes. Pictorial projections may be of two types as

a. Axonometric

b. Oblique

7.2.2.1 Axonometric Projection

It is a type of parallel pictorial projection in which an object appears to be rotated to show its all three dimensions.

Axonometric projections are classified according to how the principle axes are oriented relative to the projected

surface. There may be three types as:

i. Isometric

ii. Dimetric

iii. Trimetric

7.2.2.2 Oblique Projection

It is a type of parallel pictorial projection in which projectors are parallel to each other but they are not

perpendicular to the picture plane. The angle is usually kept 15

0

-45

0

. This may be of two types:

i. Cavalier Projection: In this case,

the dimensions along all the axes

are plotted in full scale.

ii. Cabinet Projection: In this case,

the dimensions along the diagonal

axis are plotted by reducing it to

half of the actual value. Dimensions

along other axes are plotted in full

scale.

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7.2.3 Perspective Projection

It is a type of pictorial projection in which projectors are not parallel to each other and they occur at an angle to

the picture plane in such a way that they converge to a point as if an observer sees the view on the picture plane

from that point. In case of perspective projection observer is considered to be at finite distance where in case of

any other type of projection observer is considered to be at infinity.

7.3 Details of Orthographic Projection

Basically, Orthographic projection is any single projection made by dropping perpendiculars to a plane. In short,

orthographic projection is the method of representing the exact shape of an object by dropping perpendiculars

from two or more sides of the object to planes, generally at right angles to each other; collectively, the views on

these planes describe the object completely. Descriptive geometry is basically the use of orthographic projection

in order to solve for advanced technical data involving the spatial relationship of points, lines, planes, and solid

shapes. The most common means of understanding these types of orthographic projection is - The Glass Box

method.

7.3.1 The Glass Box Method

The Glass Box method was used primarily for descriptive geometry problems. It can be suitably used for

understanding the generation of orthographic views. Key points of "the glass box method" are:

 The user imagines that the object is enclosed in a transparent "box" said to be "the glass box".

 Each view of the object is established on its corresponding glass box surface.

 To obtain a view, perpendicular projectors are drawn originating at each point of the object and

extending to the related box surface.

 The box is imagined as hinged so that it can be unfolded on to one flat plane (the paper). The box is

unfolded to obtain the arrangement of views.

In figure 7.6, the vertical lines of sight (A) and horizontal lines of sight (B) are assumed to meet at infinity. The

line of sight is always perpendicular to the plane of projection, represented by the surfaces of the glass box (top,

front, and right side). Projection lines(C) connect the same point on the plane of projection from view to view,

always at right angle. A point is projected up on the plane of projection where its projector cuts that image plane.

In the figure 7.6, point 1, which represents a corner of the given object, has been projected on to the three primary

image planes. When it intersects the horizontal plane (top plane of projection), it is identified as 1H, when it

intersects the frontal plane (front plane of projection), it is identified as 1F, and where it intersects the profile

plane (right side plane of projection), it is labeled 1P.

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7.3.2 The Six Principal Views

Let us surround the object entirely by asset of six planes, each at right angles to each other. On these planes, views

of the object can be obtained as is seen from the top, front, right side, left side, bottom and rear. Consider the

object and its projection in fig. 7.2; think now of the six sides, or the plane of the paper; the front is already in the

plane of the paper, and the other sides are, as it were, hinged and rotated in position as shown in figure 7.5.

 The projection on the frontal plane is called the front view or vertical projection or front elevation.

 The projection on the horizontal plane is called the top view or horizontal projection or plan.

 The projections on the left/right sides are called left/right profile views or left/right side view or left/right

profile projection or left/right side elevation.

 By reversing the direction of sight a bottom view is obtained instead of a top view or a rear view instead

of a front view.

In actual work, there is rarely an occasion when all six principal views are needed on one drawing. All these views

are principal views. Each of the six views shows two of the three dimensions of height, width and depth.

In general, when the glass box is opened, its six sides are revolved outward so that they lie in the plane of the

paper. And each image plane is perpendicular to its adjacent image plane and parallel to the image plane across

from it. Before it is revolved around its hinged fold line (reference line).A fold line is the line of intersection

between any hinged (adjacent) image planes.

The left side, front, right side, and back are all elevation views. Each is vertical. The top and bottom planes are in

the horizontal plane. But in most cases the top, front, and right sides are required.

Six Principal Views by Glass Box Method (3

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7.3.3 Arrangement of Views

As discussed earlier, the most usual combination selected from the six possible views consists of the top, front and

right side views. Sometimes the left- side view helps to describe an object more clearly than the light side view.

Orthographic views are arranged in two techniques as

a. 1

st

angle projection (Used in European countries; ISO standard) also known as British system

b. 3

rd

angle projection (Used in Bangladesh, Canada, USA, Japan, Thailand) also known as American

system.

Relative Position of Object in First and Third Angle Projection System

Standard Symbol to Indicate First and Third Angle Projection in Drawing

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7.3.3.1 Glass Box Concept for 1

st

Angle Projection

Glass Box Presentation of 1

Angle Projection and Arrangements of Views

Generation

of Views

Unfolding

the paper

Final

arrangement of

views on paper

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7.3.3.2 Glass Box Concept for 3

rd

Angle Projection

Glass Box Presentation of 3

Angle Projection and Arrangements of Views

Generation

of Views

Unfolding

the paper

Final

arrangement of

views on paper

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7.3.4 Orthographic Projections of Parallel, Inclined and Oblique Surfaces

 An edge appears in true length when it is parallel to the plane of projection, as a point when it is

perpendicular to the plane and shorter than true length when it is inclined to the plane.

 Similarly, a surface appears in true shape when it is parallel to the planes of projection, as line when

it is perpendicular to the plane and fore-shortened when it inclined to the plane.

 A line that is not parallel to any plane of projection is called an oblique skew line and it does not

show in true shape in any of the views, but each of the bounding edges shows interval length in one

view and is fore shortened in the other two views.

When an inclined or oblique line is to be projected it is helpful to identify and draw the end points and then

joining them to obtain the projection.

Orthographic Projection of objects with inclined surface.

Orthographic Projection of Parallel, Inclined and Oblique Surfaces (3

Inclined

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7.3.5 Orthographic Projections of Hidden Surfaces

To describe an object with complex internal features completely, a drawing should contain lines representing all

the edges, intersections, and surface limits of the objects. In any view there will be some parts of the object that

cannot be seen from the position of the observer, as they will be covered by portion of the object closer to the

observer's eye. The edges, intersections, and surface limits of these hidden parts are indicated by a discontinuous

line called a dashed line or hidden line. Particular attention should be paid to the execution of these dashed lines.

If carelessly drawn, they ruin the appearance of a drawing.

7.3.6 Orthographic Projections of Curved Surfaces and Holes

To represent curved surfaces in orthographic projections, center lines are commonly utilized. All the center lines

are the axes of symmetry.

 Every part with an axis, such as a cylinder will have the axis drawn as center line before the part is drawn.

 Every circle will have its center at the intersection of two mutually perpendicular center lines.

7.3.7 Precedence of Lines

In any view there is likely to be a coincidence of lines. Hidden portions of the object may project to coincide with

visible portions. Center lines may occur where there is a visible or hidden out line of some part of the object.

Since the physical features of the object must be represented full and dashed lines take precedence over all other

lines since visible out line is more prominent by space position, full lines take precedence over dashed lines. A full

line could cover a dashed line, but a dashed line could not cover a full line. When any two lines coincide, the one

that is more important to the readability of the drawing takes precedent over the other. The following line gives

the order of precedence of lines.

1. Full line

2. Dashed line

3. Careful line or cutting – plane line

4. Break lines

5. Dimension and extension lines.

6. Crosshatch lines.

Orthographic Projection of Objects with Hole and Curved Surface (3

Orthographic Projection of Pbjects with Hidden Surfaces (3

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7.3.8 Method of Obtaining Views

To obtain the front view of an object let the observer take a position in front of the object at an infinite distance.

 Let the object is being looked from an infinite distance, therefore all the rays of sight originated from

object will be parallel to each other.

 In case of 3rd angle projection, place an imaginary vertical plane in between the object and the observer

such that all the rays of sight cut the plane.

 In case of 1

st

angle projection the vertical plane should be placed behind the object such that all the rays of

sights, if extended backward, cut the plane.

 According to be shape of objects, join the points of intersection of the vertical plane and rays of sight. The

points which are connected by lines in original object should be connected in the vertical plane.

 Thus a front view of the object will be obtained on the vertical plane.

All other 5 views can be obtained in similar way. The plane of projection (vertical, in case of front view) should

be parallel to the face for which views are being drawn. For example, in case of top view the plane will be

horizontal.

15 Method of Obtaining Views

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7.3.9 Methods of Projecting Views

There are several methods of projecting views in orthographic projection which are shown in Figure 7.18. In the

projection there is a relationship of different views. It is usual practice to draw the front view first, then top and

side views are drawn with the help of the vertical and horizontal projection lines. This can be done using T-square,

set-squares and compasses. Here only the figure (C) requires the use of compass in addition to T-squares and set-

squares.

The method shown in fig. 7.18 (A) and 7.18 (B) are mostly used. This method is sometimes said to be "the

diagonal line method".

7.3.10 Spacing Between the Views

In case of figure 7.18 (A) the spacing between views are kept equal where in case of fig. 7.18 (B) the spacing

between the front and right side view is wider than that in front and top view. The spacing between views has to

be determined or decided beforehand and if equal spacing is needed then fig. (A) can be followed and if a

different spacing is needed then fig. (B) can be followed. However, spacing to provide between views depends on

 Space required for dimensioning.

 Space required for naming the views.

 Space required for writing essential notes.

Sufficient space should be provided in order to give dimensions avoiding any crowding and also excessive space

should be avoided. If not mentioned or required otherwise 30mm-40mm spacing can be provided between two

successive views.

16 Different Methods of Projecting Views

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7.3.11 Steps for Projecting Views by Diagonal Line Method

Fig. 7.19 describes the steps of projecting views (3

rd

angle) by diagonal line method. The steps are:

 Step 1: Following method described in section 7.3.10 draw the front view on the drawing paper.

 Step 2: Project vertically upward lines from every point of the front view where there is a change in

shape.

 Step 3: Draw the top view according to the shape of object within its extent enclosed by the vertical

projected lines.

 Step 4: Project horizontal lines from every point of the front view where there is a change in shape.

 Step 5: Draw a diagonal line (a line at an angle 45

0

with horizontal) using set-square. Position of this line

depends on the spacing requirement between side view and front view. If equal spacing is required then

the line should originate at the corner of the front view.

 Step 6: Project horizontal lines toward the diagonal line from every point of the top view where there is a

change in shape. These lines will cut the diagonal line.

 Step 7: From every point of intersection draw perpendicular lines toward the horizontal projection lines

drawn from the front view.

 Step 8: Now, the area for side view (left/right) will be enclosed. Draw the shapes of left/right view.

 Step 9: Erase unnecessary lines and darken the views.

It is to be noted that for 1

st

angle projection the lines should be projected according to position of views. For

example to draw top view, vertically downward lines need to be projected from front view so that the top view is

generated below the front views; for getting right side view horizontal lines from front view are to be projected

toward left and so on.

17 Diagonal Line Method for Projecting Views (3

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Diagonal Line Method for Projecting Views (3

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7.3.12 Worked-out Examples of Orthographic Views

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7.3.13 Limitation of Multi View Projection

Multi view orthographic projections generally show length along two principle axis in any particular view. The

length along the third axis cannot be shown in same view. This makes it difficult to understand them and only

technically trained persons can understand the meaning of these orthographic views. A layman cannot imagine the

shape of the object from orthographic projections.

To make the shape of an object easy to understand for both technical persons and non-technical laymen pictorial

projections are used. Most commonly used pictorial drawing is Isometric drawing.

7.4 Details of Isometric Projection

Isometric means "equal measure ". Isometric projection is that type of pictorial or single view projection of object

where all three principal edges (along height, width and depth) or axes are projected with equal 120° angles.

When a drawing is prepared with an isometric scale or otherwise if the object is actually projected on a plane of

projection, it is an isometric projection.

7.4.1 Principle of Isometric Projection

An isometric projection is an orthographic projection, but it is obtained in such a way that all the principle axes

are projected in the same view with reduction of their lengths in the same proportion. For this purpose the object is

so placed that its principle axes are equally inclined to the plane of projection. In other words, the front view of a

cube, resting on one of its corners is the isometric projection of the cube as shown in fig. 7.21. In comparison to

orthographic projection, an object is rotated by 45

0

with respect to its front face and then tilted forward or

backward by 35

0

16' and then its view is drawn and that is its isometric view. But as the object is tilted all the

lengths projected on the plane appears to be shortened and thus they are drawn shortened in isometric projection.

Fig. 7.18 Object Placement in Isometric Projection

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Fig. 7.19 Isometric Projection of a Cube

7.4.2 Isometric Scale

As discussed, in case of isometric projection,

due to the tilting effect a line does not project to

its true length on the picture plane. In the

isometric projection of a cube shown in Fig.

7.21, when the cube is tilted backward, the top

face ABCD is sloping away from the observer

and hence the edges of the top face will appear

fore-shortened. The true shape of the triangle

DAB is represented by the triangle DPB. The

extent of reduction of an isometric line can be

easily found by construction of a diagram called

isometric scale. For this, reproduce the triangle

DPA as shown in Fig. 7.22. Mark the divisions

of true length on DP. Through these divisions

draw vertical lines to get the corresponding

points on DA. The divisions of the line DA give

dimensions to isometric scale. From the triangle

ADO and PDO in Fig. 7.21, the ratio of the

isometric length to the true length,





=

 °

 °

= 0.816

In words, the isometric axes are reduced in the ratio

1: 0.816 or 82% approximately.

Fig. 7.20 Isometric Scale

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7.4.3 Lines in Isometric Projection

The following are the rules for presenting the lines in isometric projection:

1. The lines that are parallel on the object are parallel in the isometric projection.

2. Vertical lines on the object appear vertical in the isometric projection.

3. Horizontal lines on the object are drawn at an angle of 30° with the horizontal in the isometric projection.

4. A line parallel to an isometric axis is called an isometric line and it is foreshortened to 82%.

5. A line which is not parallel to any isometric axis is called non-isometric line and the extent of fore-

shortening of non-isometric lines is different if their inclinations with the vertical planes are different.

7.4.4 Isometric Drawing

When an isometric projection is prepared

with an ordinary scale, it is called an

isometric drawing. Drawing of objects is

seldom drawn in true isometric

projections, as the use of an isometric

scale is inconvenient. Instead, a

convenient method in which the

foreshortening of lengths is ignored and

actual or true lengths are used to obtain

the projections, is applied which is called

isometric drawing or isometric view.

This is advantageous because the

measurement may be made directly from

a drawing.

The isometric drawing is 22.5% larger

than the isometric projection, but the

pictorial value is obviously the same in

both. An isometric drawing is so much

easier to execute and, for all practical

purposes, is just as satisfactory as the

isometric projection.

Fig. 7.22 Isometric Drawing

Fig. 7.22 Isometric Scale

Fig. 7.21 Lines and Axes in Isometric Projection

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7.4.5 Methods of Constructing Isometric Drawing

The methods used are:

1. Box method.

2. Off-set method.

In both the methods it must be always kept in mind that in isometric projection, vertical lines are drawn vertical

and the horizontal lines are drawn inclined 30° to the base line.

7.4.5.1 Box Method

When an object contains a number of non-isometric lines, the isometric drawing may be conveniently constructed

by using the box method. In this method, the object is imagined to be enclosed in a rectangular box and both

isometric and non-isometric lines are located by their respective points of contact with the surfaces and edges of

the box. It is always helpful to draw or imagine the orthographic views first and then proceed for isometric

drawing. Fig. 7.24 illustrates an example isometric drawing by box method.

7.4.5.2 Off-set Method

Off-set method of making an isometric drawing is preferred when the object contains irregular curved surfaces. In

the off-set method, the curved feature may be obtained by plotting the points on the curve, located by the

measurements along isometric lines. Fig. 7.25 illustrates the application of this method.

Fig. 7.23 Isometric Drawing by Box Method

Fig. 7.24 Isometric Drawing by Off

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7.4.6 Isometric Drawing of planes

Isometric drawing of planes can be obtained simply by keeping in mind that vertical lines will be vertical in

projection and horizontal lines will be at 30

0

inclined in projection. If there are some inclined lines in the plane it

will be helpful to enclose the plane with a rectangle and then obtain the projection with reference to the sides of

that rectangle.

7.4.6.1 Isometric Drawing of Rectangular Plane

Let us draw the isometric drawing of a rectangle of 100mm and 70mm sides if its plane is Vertical and Horizontal.

When the plane is vertical

 Step 1: Draw the given rectangle ABCD as shown in Fig. 7.26 (a)

 Step 2: Draw the side A D inclined at 30° to the base line as shown in Fig. 7.26 (b) and mark A D =

70mm.

 Step 3: Draw the verticals at A and D and mark off A B = D C = 100mm on these verticals.

 Step 4 : Join BC which is parallel to AD. ABCD is the required isometric projection. This can also be

drawn as shown in Fig. 7.26(c). Arrows show the direction of viewing.

When the plane is horizontal

 Draw the sides AD and DC inclined at 30° to be base line and complete the isometric projection ABCD as

shown in Fig.9.IOd. Arrow at the top shows the direction of viewing.

7.4.6.2 Isometric Drawing of Pentagonal Plane

Let us draw the isometric drawing of a regular pentagon of 25mm sides if its plane is Vertical and Horizontal.

 Step 1: Draw the given pentagon abcde and enclose it by a rectangle 1234 as shown in Fig. 7.27 (a).

 Step 2: Make the isometric drawing of the rectangle 1234 as described in fig. 7.26.

 Step 3: On the isometric drawing of rectangle locate the points A and B such that 1A = 1a and 1B = 1b.

 Step 4: Similarly locate points C, D and E such that 2C = 2c, 3D = 3d and 4E = 4e.

 Step 4 : Join A, B, C, D, E sequentially; Now ABCDE is the required isometric view in vertical plane as

shown in fig. 7.27 (b). Similarly the fig. 7.27 (c) can be obtained for horizontal plane.

Fig. 7.25 Isometric Drawing of Rectangular Plane

Fig. 7.26 Isometric Drawing of Pentagonal Plane

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7.4.6.3 Isometric Drawing of a Circular Plane

Let us draw the isometric drawing of a circle of 60mm radius if its surface is vertical and horizontal.

 Step 1: Draw the given circle and enclose it by a square 1234 as shown in Fig. 7.28 (a).

 Step 2: Make the isometric drawing of the square 1234 that will form a rhombus.

 Step 3: Mark the mid-points A, B, C and D of each sides of the rhombus as shown in fig 7.28 (b).

 Step 4: Draw longest diagonal 2-4 and join point 3 and A. The line 3-A will intersect the line 2-4 at point

M. Similarly obtain the intersecting point N.

 Step 5: With center M and radius MA draw an arc AB. With center N and radius NC draw and arc CD.

 Step 6: With center 1 and radius 1-C draw an arc BC. With center 3 and radius 3-D draw an arc AD.

 Step 7: The ellipse ABCD is the required isometric drawing of the circle on horizontal plane. Similarly

the isometric views can be obtained on vertical planes as shown in fig. 7.28 (c)

7.4.7 Isometric Drawing of Solids

Before drawing of an isometric view of a solid object it is always convenient to draw the orthographic views first.

Then the isometric box is constructed and the orthographic views are reproduced on the respective faces of the

box. Finally by joining the points relating to the object and erasing unnecessary lines the isometric view is

obtained.

7.4.7.1 Points to be Remembered for Isometric drawing

 Three isometric axes will be at 120

0

angle with each other.

 Height will be along vertical isometric axis.

 Length and width will be along isometric axes each being 30

0

inclined with horizontal.

 Isometric lines will be in their true length.

 Non-isometric lines will be either in enlarged or reduced length.

 No hidden line will be shown in isometric drawing unless necessary.

7.4.8 Steps for Drawing Isometric View

Let us draw isometric view of a solid object as shown in fig. 7.30 (a)

 Step -1: Draw the orthographic views. In a specific isometric drawing three maximum faces can be

shown. Usually front view, top view and either left or right side view are selected.

 Step -2: Draw three isometric axes. Use set square to make 30

0

angles.

 Step -3: Cut corresponding distances equal to major (maximum) length, width and height of object from

each isometric axis. Remember to cut height along vertical isometric axis. Choose length and width

according to given/chosen views. If right side view is given/chosen, then length of front view should be

chosen along the left side axis of vertical axis so as to allow drawing of right side view along right side

axis.

 Step -4: Draw an isometric box. To do this, draw 2 parallel lines of each isometric axis at the end points

of other two axes.

 Step -5: Draw given views (front, top and left/right) on the corresponding face of the isometric box.

Fig. 7.27 Isometric Drawing of Circular Plane

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 Step -6: Look through the individual views and identify non-existing lines and surfaces. Erase the non-

existing lines. While erasing a line, take the question in mind "why I have drawn this earlier?" If you

erase a line from isometric box, there must be a visible line parallel to that line.

 Step -7: Finally, darken the visible lines. Compare the orthographic views with your obtained Isometric

views. Check if any logical line/surface is missing. If not, you are done.

(b)

Step-1

Step-2

Step-3

(c) (d)

Step-4

(e)

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Step-5

Step-6

(f)

(g)

(h)

Step-7

Fig. 7.28 Steps for Isometric Drawing of Solid Object (Contd.)

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7.4.9 Worked-out Examples of Isometric Drawing

1. Draw isometric view from the orthographic views given in figures below:

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Solution:

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See section 7.3.12 for more examples.

2. Draw isometric view of a hexagonal prism 30mm sides and 60mm height.

Solution:

Draw the orthographic

views first. Following

section 7.4.7.2, complete

the projection. For

projecting the hexagonal

top view on the top face

of isometric box follow

section 7.4.6.2.

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3. Draw isometric view of a cone with base diameter 30mm and axis 50 mm long.

Solution:

Draw the orthographic views first. Following section 7.4.7.2, complete the projection. For projecting the circular

top view on the top face of isometric box follow section 7.4.6.3.

Exercise and Assignments:

1. Draw orthographic views of the following objects (wooden objects available):

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2. Draw orthographic views for the following pictorial views (Assume arbitrary dimension):

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3. Draw necessary orthographic views to represent

i. A reading table

ii. Sitting chair

iii. Twin seats of university bus.

iv. Laptop computer

v. Wall clock.

vi. Refrigerator.

vii. D-box of HSTU.

viii. A pentagonal pyramid.

ix. A Cylindrical pen holder.

x. An oval shaped paper-weight.

4. Draw isometric view of a rectangular plane having length of sides as 10 cm and 15 cm when its plane is

(a) horizontal and (b) vertical.

5. Draw isometric view of a square prism with a side of base 5cm and axis 15 cm long when the axis is (a)

vertical and (b) horizontal.

6. Draw isometric view of a cylinder with base diameter 10cm and axis 15 cm long.

7. A pentagonal pyramid of side of base 30mm and height 70mm is resting with its base on horizontal plane.

Draw the isometric drawing of the pyramid.

8. Draw isometric views of

i. A reading table

ii. Sitting chair

iii. Twin seats of university bus.

iv. Laptop computer

v. Wall clock.

vi. Refrigerator.

vii. D-box of HSTU.

viii. A pentagonal pyramid.

ix. A Cylindrical pen holder.

x. An oval shaped paper-weight.

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9. Prepare isometric drawing from the given orthographic views. (Use assumed value for missing

dimensions)

1

2

3

4

5

6

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7

8

10

9

11

12

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Review Questions

1. Why have you studied projection?

2. Define projection. Why it is necessary?

3. What do you mean by projection plane, projector and view? Show in a sketch.

4. Classify projection and define the types.

5. What are the possible orthographic views of an object?

6. Are all the orthographic views necessary to describe an object? If not, how will you choose the necessary

views?

7. Describe the glass box method.

8. What do you mean by 1

st

angle and 3

rd

angle projection? Which one is British and which one is American

System? Which one is easier and why?

9. Differentiate between 1

st

angle and 3

rd

angle projection.

10. Show the arrangement of views in 1

st

and 3

rd

angle projection system.

11. What is the standard symbol of 1

st

angle/ 3

rd

angle projection system?

12. Which lines are projected to their actual length?

13. Which lines are not projected to their actual length? How will you obtain projection of such lines?

14. How do you represent a hidden edge in a particular view? Give example.

15. How do you represent a circular/curved edge in a particular view? Give example.

16. How do you represent a hole in orthographic view? Give example.

17. What is the order of precedence of line in orthographic projection?

18. What will you do, if a solid line and a hidden line occur at the same location?

19. What will you do, if a center line and a hidden line occur at the same location?

20. How do you obtain views by diagonal line method?

21. How do you select/ decide spacing between views?

22. What is the standard spacing to be maintained between views?

23. How to control space between views in diagonal line method?

24. What are the advantages of orthographic projection?

25. What are the limitation/disadvantages of orthographic projection?

26. What do you mean by pictorial projection? Classify it.

27. What is the difference between axonometric and oblique projection?

28. What are the different types of axonometric projection? Why they are so named?

29. What is the difference between isometric, diametric and trimetric projection?

30. What is the difference between cabinet and cavalier projection?

31. What do you mean by perspective projection? How does it differ with pictorial projection?

32. Why the object appears to be shortened in perspective projection?

33. Why isometric projection is the most commonly used pictorial projection in engineering drawing?

34. What are the advantages of isometric projection over other types of pictorial projection?

35. In which position of object its front view becomes its isometric view?

36. How the object is rotated to obtain its isometric view?

37. Why are the objects appeared to be shortened in case of isometric projection? What is the percentage of

shortening?

38. What is isometric scale? How it is constructed?

39. What is the difference between isometric projection and isometric drawing/view? Which one is

advantageous and why?

40. What do you mean by isometric and non-isometric lines? Give examples.

41. How isometric drawing are constructed by box method.

42. Why is it helpful to draw orthographic views before drawing the isometric view of the object?

43. What is the isometric form of a rectangle/ square/ triangle/ circle?

44. In the box method, how will you decide the isometric axis for plotting width, length and height?

45. Draw isometric view of a pen/box/cube/paper weight.

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CHAPTER 8

SECTIONING

Objectives

Objectives of studying this chapter are:

 Describe the purpose of sectioning in technical drawings

 Define cutting plane lines, direction of sight, section lining etc.

 Mention and explain the different kinds of sectioning

8.1 Introduction

The conventional method used to draw an object using the multi view or orthographic method of representation is

discussed in Chapter 7. This system is excellent to illustrate various external features. In this method, complicated

interior features are illustrated with hidden lines. These interior features can be shown more clearly by the use of

sectional views.

8.2 Terminology

8.2.1 Sectioning

It is defined as an imaginary cut made through an object to expose the interior or to reveal the shape of a portion.

8.2.2 Sectional View

A sectional view is a view of an imaginary surface, exposed by an imaginary slicing-open of an object, allowing

interior details to become visible. A sectional view is sometimes referred to as a cross section or simply section. It

is a view in which all or a substantial portion of the view is sectioned.

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8.2.3 Cutting Plane

Cutting plane is a plane that imaginarily cuts the object to reveal the internal features.

8.2.4 Cutting Plane Line

Cutting plane line is an edge view of the cutting plane. The cutting-plane line indicates the path that an imaginary

cutting plane follows to slice through an object. Think of the cutting-plane line as a saw blade that is used to cut

through the object. The cutting-plane line is represented by a thick black dashed line. Standard format of cutting

plane line is already discussed in chapter 2.

Standard Cutting Plane Line

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8.2.5 Section Lining

Section lining shows the locations where the object is sliced or cut by the cutting plane or the location where the

surface or surfaces are cut by the cutting plane. Symbol for section lining is different for different materials, but in

practice the symbol of cast iron i.e. the cross-hatch lines are used for sectioning of any materials. They are

represented by thin, black lines drawn at 45

0

to the horizontal, unless there is some specific reason for using a

different angle. Section lining is spaced by eye from 1/16" (1.5mm) to 1/4"(6 mm) apart, depending upon the

overall size of the object. The average spacing used for most drawings is .13"(3 mm). However, all the section

lines in a drawing must be of uniform thickness and they should be evenly spaced.

If a cutting plane passes through two parts, each part has section lines using a 45° angle or other principal angle.

These section lines should not be aligned in the same direction. If the cutting plane passes through more than two

parts, the section lining of each individual part must be drawn at different angles. When an angle other than 45° is

used, the angle should be 30° or 60°. Section lining should not be parallel with the sides of the object to be section

lined.

8.3 Types of Section

The different kinds of sections used today are:

i. Full section

ii. Offset section

iii. Half section

iv. Broken-out section

v. Revolved section

vi. Removed section.

vii. Auxiliary section etc.

In this part, we only discuss the most commonly used types of sections.

Section Lining of Different Materials

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8.3.1 Full Section

A full section is simply a section of one of the regular multi views that is sliced or cut completely in two. When

the cutting plane passes through the entire object a full sectional view is obtained. Hidden lines are omitted from

sectional view.

8.3.2 Offset Section

Many times, important features do not fall in a straight line as they do in a full section. These important features

can be illustrated in an offset section by bending or offsetting the cutting-plane line. An offset section is very

similar to a full section, except that the cutting-plane line is not straight.

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8.3.3 Half Section

The sectional view obtained by passing the cutting plane halfway through an object is called a half sectional view.

In this case a quarter portion of the object is imagined to be removed. A cutting plane is added to the front view,

with only one arrowhead to indicate the viewing direction. Half sections are best used when the object is

symmetrical, that is, the exact same shape and size on both sides of the cutting-plane line. A half-section view is

capable of illustrating both the inside and the outside of an object in the same view.

A center line is used to separate the sectioned half from the unsectioned half of the view. As usual, hidden lines

are omitted from sectional view.

8.3.4 Broken-out Section

Sometimes, only a small area needs to be sectioned in order to make a particular feature or features easier to

understand. In this case, a broken-out section is used. It is the sectional view of a fractional part of object. Broken-

out sections are helpful when some interior details are to be shown but a full or half section is not feasible because

that would remove some essential feature of the object. In such case a broken-out section is made directly of the

exterior view. In fig. 8.9 the top section is somewhat confusing and could create a question. To clarify this area, a

portion is removed. The view is made by passing the cutting plane normal to the viewing direction and removing

the portion of an object in front of it. A break line is used to separate the sectioned portion from the unsectioned

portion of the view. There is no cutting plane line.

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8.3.5 Revolved Section

A revolved section, sometimes referred to as a rotated section, is used to illustrate the cross section of ribs, webs,

bars, arms, spokes or other similar features of an object. Revolved sections show cross-sectional features of a part.

One great advantage of revolved section is that there is no need for additional orthographic views. This section is

especially helpful when a cross-section varies. An imaginary cutting plane is assumed to pass across the feature to

be sectioned and then the obtained section is rotated by 90

0

. The rotated section is then either superimposed on the

orthographic view of positioned with break lines.

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Following is the steps of constructing a revolved section

 Step 1: Assign position of cutting plane on the top view or plan.

 Step 2: Draw axis of rotation in front view.

 Step 3: Transfer the depth dimension to the front view.

 Step 4: Draw the revolved section on the front view enclosed by the lines indicating depth dimension.

Steps for Construction of R

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8.3.6 Removed Section

Revolved sections tend to be confusing, and often create problems for the people who must interpret the drawings.

Today, it is recommended to use a removed section instead of a revolved or rotated section. A removed section is

very similar to a rotated section except that, as the name implies, it is drawn removed or away from the regular

views. The removed section is also used to illustrate the cross section of ribs, webs, bars, arms, spokes or other

similar features of an object. Note that a removed section must identify the cutting-plane line from which it was

taken. In the sectional view, do not draw features other than the actual section. the removed section should be

drawn on the same page as the regular views.

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Object with odd number of ribs

8.4 Special Consideration for section of Ribs, Spokes and lugs

Even Number of Ribs

Sectioning of Object with Odd

Number of Ribs

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8.5 Parts that Should Not Be Sectioned

Shaft, bolts, nuts, rivets, balls, pin and keys are not

sectioned even when they are in the line of cutting

plane. They are always left in full view to avoid

confusion.

Plan with cutting plane line

Plan with cutting plane line

Sectioning of Object with Odd

Number of Spokes

Fig. 8.16 Sectioning of Object with Lug

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8.6 Worked-out Examples of Sectioning

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Exercise and Assignments

1. Draw plan and section along the centroidal axis of the plan.

2. Draw top view and a suitable section for the slider block shown below.

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3. Draw top view and a suitable section for the bearing shown below.

4. Draw top view and a suitable section for the bearing container shown below.

5. Draw plan and sectional view of a single storied building.

6. Draw plan, elevation and cross section of a rectangular water tank having walls made of brick and floor

made of concrete.

7. Draw plan, elevation and section of the objects shown in chapter 7, exercise 1.

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Review Questions

1. Why have you studied sectioning?

2. Define section, section line, cutting plane and cutting plane line. How are they represented in drawing?

3. Draw section lining to represent cast iron, steel, concrete and wood.

4. What is common section lining used for any type of materials? How it is aligned?

5. How will you draw section lines if the cutting plane passes two separate element of an object?

6. How will you draw section line if the object is aligned?

7. How will you chose spacing between section lines?

8. What are the different types of section?

9. When and how a full section is obtained?

10. What is the similarity/difference between a full section and an offset section?

11. When does offset section become necessary?

12. When and how a half section is obtained?

13. What are the advantages of a half section over a full section?

14. What is broken-out section? When is it used?

15. When and how a revolved section is obtained?

16. What are the different methods of placing the revolved section? Give example.

17. What is the similarity/difference of removed section and revolved section?

18. Why is a removed section being preferred to a revolved section?

19. What is the special consideration for sectioning a rib, spoke and lug?

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Bibliography

1. D.N. Ghose, Civil Engineering Drawing and Design, 1987, 1

st

ed., Delhi – CBS publishers and

Distributors .

2. Dr. Amalesh Chandra Mandal, Dr. Md. Quamrul Islam, Mechanical Engineering Drawing, 2007, 1

st

ed.,

Dhaka – Associate Printing Press.

3. Wuttet Taffesse, Laikemariam Kassa, Lecture Notes on Engineering Drawing, 2005, 1

st

ed., Ethiopia

Public Health Training Initiative – Ethiopia Ministry of Education.

4. David L. Goetsch, John A. Nelson, William S. Chalk, Technical Drawing Fundamentals Cad Design,

1986, 2

nd

ed., New York – Delmar Publishers Inc.

5. R.K. Dhawan, A Textbook of Machine Drawing, 2001, 2

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Publishers Distributors.

9. Wikipedia

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• David L Goetsch
• John A Nelson
• William S Chalk

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A Textbook of Machine Drawing

• R K Dhawan

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• Subhash C Sharma

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• C Subhash
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Source: https://www.researchgate.net/publication/283622413_Engineering_Drawing_for_beginners

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