Engineering Drawing

A Computer Based Training Package

On

ENGINEERING DRAWING

ENGINEERING DRAWING

ENGINEERING DRAWING

ENGINEERING DRAWING

Student’s Guide

Salem – 636005.

First Edition, October 2000

2000

Sonaversity, Salem, All Rights Reserved. No part of this book may be

reproduced in any form, by mimeograph or any other means, without permission in

writing from the publishers.

CONTENTS

CHAPTER TITLE

P.NO

I Introduction to Engineering Drawing

1.1 Introduction

1.2 Objectives

1.3 Drawing Instruments 1.4 BIS & ISO Conventions 1.5 Beginning your Drawing 1.6 Exercises 3 3 3 7 20 21 II Geometric Construction 2.1 Introduction 2.2 Geometrical Terms 2.3 General Construction 25 25 31

III Orthographic Projection

3.1 Introduction 3.2 Objectives 3.3 What is a projection 3.4 Types of Projection 37 37 37 38 IV Projections Projections of a Point 4.1 Objectives 4.2 Notation

4.3 Projection of Point in the I-quadrant II-quadrant III-quadrant IV-quadrant 4.4 Exercises Projections of Straight lines

4.5 Introduction 4.6 Objectives

4.7 Projection of Straight line

Perpendicular to the HP and parallel to the VP Perpendicular to the VP and parallel to the HP Parallel to the HP and Inclined to the VP Parallel to the VP and Inclined to the HP Inclined to the HP and the VP

Parallel to the HP and the VP 4.8 Exercises Projections of Solids 4.9 Introduction 4.10 Objectives 4.11 Classification of Solids 42 42 43 43 44 45 46 47 47 48 49 50 51 52 53 54 56 56 56

4.12 Projection of Solids Perpendicular to the HP Parallel to the HP and the VP

Parallel to the HP and Inclined to the VP Parallel to the VP and Inclined to the HP Inclined to the VP and the HP

4.13 Exercises 64 66 68 69 71 73 V Section of Solids 5.1 Introduction 5.2 Objectives

5.3 Sectional view and convention 5.4 Types of section

5.5 Section of Solids when the cutting plane is Perpendicular to the VP and parallel to the HP Perpendicular to the HP and parallel to the VP Perpendicular to the VP and inclined to the HP Perpendicular to the HP and inclined to the VP 5.6 Exercises 76 76 76 77 79 81 83 87 91 VI Pictorial projections 6.1 Introduction Isometric projection 6.2 Objectives 6.3 Terminology

6.4 Isometric views of prism

6.5 Isometric views of Cylinder and Cone 6.6 Isometric views of Compound solids 6.7 Exercises 93 93 94 98 101 105 110

VII Development of Surfaces

7.1 Introduction 7.2 Parallel line development 7.3 Radial line development 7.4 Exercises

120 120 123 125

VIII Intersection of Surfaces

8.1 Introduction 127

IX Further development in Engineering Drawing

Chapter - I

Engineering Drawing

Introduction

A picture is worth saying a thousand words; hence drawings are used to visually communicate ideas, thoughts, and designs. Drawings drawn by an engineer for engineering purposes is Engineering Drawing.

Drawing is the Universal Graphical Language of Engineers, spoken, read and written in its own way. Engineers must have perfect drawing skills and excellent working knowledge of engineering concepts. An inaccurate drawing may misguide the workman and ultimately affect the production.

Objectives

In this, the first session, you'll be looking at drawing instruments and the typical accessories used in drawing. On completion of the session, you should be able to:

•= Identify various types of drawing instruments and their uses.

•= Classify drawing sheets and the different grades of drawing pencils.

•= Draw the layout and title block on a drawing sheet.

•= Use the lettering and dimensioning techniques in common practice.

Drawing Instruments

The Drawing Board

The D2 or D3 drawing boards are usually used in polytechnics and engineering colleges. Drawing boards are made of well-seasoned softwood such as Oak or Pine. The standard sizes of drawing boards as perBIS(1444-1977) are given in the table.

The Drawing Sheet

The standard sizes of drawing sheets as per BIS (10711-1983) are given in the table. The ratio of the width of a drawing sheet to its length is 1: √2.

The drawing sheet should be tough and strong and its fibers should not disintegrate when an eraser is used on its surface.

Minidrafter:

A minidrafter is a device with two scales set at right angles to each other. It combines the functions of a T-square, setsquares, scales and a protractor. It can be easily and quickly moved to any location on the drawing sheet without altering the scales.

The T-Square

A T-square is mainly used together with setsquares for drawing horizontal lines, angles and perpendicular lines. There are two essential parts of a T-square, namely the stock and the blade. The blade is fitted with ebony or a plastic piece to form the working edge of the T-square. The stock and the blade of a T-square are held together at right angles to each other. T-squares are made of hard quality wood such as teak or mahogany, etc.

Instrument Box

The instrument box contains the following instruments and accessories.

•= Compasses-Large compasses and Bow compasses

•= Dividers-Plain Dividers and Bow Dividers

•= An Inking pen

•= A lead case

•= A Small Screwdriver

The Compasses

A pair of compasses are used to draw circles and arcs. Compasses are used in conjunction with scales (rulers).

Large compasses

Large compasses are used to draw circles up to 100 mm diameter. For drawing circles of more than 100 mm diameter, a lengthening bar is used.

Bow compasses

Bow compasses are used for drawing small circles up to 25 mm diameter.

The Dividers

Dividers are used in conjunction with scales.

Plain Dividers

Plain dividers are used to divide straight or curved lines into a prescribed number of equal parts, for transferring dimensions and for setting of distances from a scale to drawings.

Bow Dividers

Bow dividers are used to hold precise distances for dividing or transferring.

Inking Pen

An inking pen is used to draw straight or curved lines in tracing ink.

Lead Case

A lead case is used to store pencil leads.

Small screwdriver

A screwdriver is used to tune the screws in the instruments.

The Setsquares

Setsquares are used to draw parallel and perpendicular lines. Setsquares are made of transparent celluloid or acrylic and may also contain French curves.

The Procircle

A procircle is circular in shape. Its periphery is divided into 0.5° graduations that are used to mark and measure angles. It also has circular holes of different sizes that may be used to draw circles of specific diameter.

The Scales

Scales or rulers are devices with precise graduations marked on their straight edges for precise measurements.

Scales are made of celluloid or cardboard. Eight types of scales are used (M1, M2,..,M8) as per

BIS 10713 - 1983.

Scale of a Drawing

The drawing of an object is usually produced to a definite proportion with respect to the actual size of the object. This ratio is called the "scale of drawing".

Drawing to Full scale: When a drawing is produced to a size equal to that of the object, the

drawing is said to be drawn to "full scale".

Drawing to a reduced scale: When a drawing is produced to a size smaller than that of the

object, the drawing is said to be drawn to a "reduced scale".

Drawing to an enlarged scale: When a drawing is produced to a size greater than that of the

DrawingPencils

Drawing pencils are of different grades.

The HB pencil is a soft grade used for drawing thick lines, borderlines, lettering and arrowheads. The H pencil is used to draw finishing lines, visible lines and hidden lines.

The 2H pencil is a hard grade pencil used for drawing construction lines, dimension lines, centre lines and section lines.

Other grades are used for artistic application.

Eraser

An eraser is a good quality rubber that is used to erase unwanted lines, arcs etc., from a drawing.

Clips

Drawing clips are used to fix the drawing sheet on the drawing board. They are made of nickel-coated steel.

Cello tape (Adhesive tape) may also be used in place of clips to fix the drawing sheet on the board.

Sharpener and Emery Paper

A pencil sharpener is used to give pencils with good drawing tips. Emery paper (120 grade) is used to obtain a conical or chisel tipped pencil.

French curves

French curves are used for drawing irregular curves that cannot be drawn by compasses.

BIS & ISO Drawing Conventions

The International Standards Organization (ISO) Geneva has formulated International standards for Engineering Drawing. The Bureau of Indian Standards (BIS) previously known as Indian Standards Institution (ISI) has adopted the ISO standards. The ISO standards are applicable to the following topics:

•= Layout of Drawing sheet

•= Line Types

•= Lettering in Drawing

•= Dimensioning Methods

Layout of Drawing Sheet

Engineering students generally use A2 or A3 size drawing sheets. After fixing the drawing sheet on to the drawing board, the "Border lines" and the "Title block" are first drawn.

The Borderlines:

An ideal working space for drawing is obtained by drawing the borderlines. The following steps are involved in drawing the borderlines:

Draw a filing margin of 30 mm width at the left-hand edge of he drawing sheet.

Provide margins of a minimum of 10 mm each at the top, bottom and right side of the drawing sheet. Use an HB pencil for drawing the borderlines.

30 30 30 30 10101010 10 1010 10 10 1010 10 BORDER LINE BORDER LINEBORDER LINE BORDER LINE

SHEET LAYOUT SHEET LAYOUTSHEET LAYOUT SHEET LAYOUT

The Title block:

A rectangle of 185mm x 65mm, drawn at the bottom right side corner of the drawing sheet, is called the “Title Block” and should give the following details:

1. Name of the institution.

2. Name of student, class, roll. no., etc. 3. Title of the drawing.

4. Date of submission, etc.

Use an HB pencil for drawing the title block and the lettering of the details included in it.

Folding of a Drawing Sheet:

After the completion of a drawing, the sheet must be properly folded and neatly filed.

TITLE BLOCK TITLE BLOCK TITLE BLOCK TITLE BLOCK

THIAGARAJAR GROUP OF INSTITUTIONS

SCALES

ROLL NO:99223 YEAR BATCH:A DATE:15-12-99 SHEET N STANLY RAJ.S 185 185 185 185 130 130130 130 15 15 15 15 10 10 10 10 10 10 10 10 10 10 10 10 65 6565 65 10 10 10 10 10 10 10 10 1 I I I I 10 10

Line Types:

In an engineering drawing, every line has a definite meaning. Various types of lines are used to represent different parts or portions of an object.

Lettering in Drawing:

Lettering plays a major role in engineering drawing. It indicates details like dimensioning, name of the drawing, etc. The use of instruments for lettering is not advised, as it will consume more time. Free hand lettering should be used instead.

Rules and Features:

- Lettering in drawing must be of standard height. The standard heights of letters used are 3.5mm, 5mm, 7mm and 10mm.

- Generally, the height to width ratio of letters and numerals are approximately 5:3. - The height to width ratio of the letters M and W are approximately 5:4.

- Different sizes of letters are used for different purposes: Main Title - 7 or 10mm

Sub-title - 5 or 7mm Others - 3.5 or 5mm.

Features:

The essential features of lettering used in engineering drawing are:

•= Legibility

•= Uniformity

•= Similarity

Single stroke letters are the simplest form of letters and are generally used in engineering drawing.

Vertical Lettering:

Vertical lettering is upright, i.e. 90 ( to the horizontal.

Both uppercase or large and lowercase or small letters are used.

Inclined Lettering:

Inclined lettering has letters inclined at 75° to the horizontal and as for vertical lettering both uppercase and lowercase letters are used.

Dimensioning Methods:

Dimensioning is used to describe a drawing in terms of details such as the size, shape and position of the object as per the Dimensioning Code 11669 - 1986. Expressing these details in terms of numerical values, lines and symbols is known as dimensioning.

12 m m 10 m m 10 m m 10 20 30 35 12 m m

1. Dimension lines are to be drawn maintaining a gap of 12 mm from the object line and a gap of 10 mm between adjacent dimension lines.

2. Dimension lines should not cross extension lines.

3. All the information should be written horizontally.

4. A given dimension should be indicated only once. It should not be repeated at another place.

5. a. The overall dimensions should be placed outside the smaller dimensions.

15 Correct 15 Incorrect 10, 15 DEEP 15 DEEP 10 , Correct Incorrect 15 10 15 10 Front view Side view

30

10

10

30

5. b. When an overall dimension is given, one of the smaller dimensions should not be given unless it is needed for reference.

6. The larger dimensions should be placed outside the smaller ones such that the extension lines do not cross the dimension lines.

7. No dimensions other than those that are necessary need be given.

8. Avoid indicating dimensions inside a drawing.

9. Always indicate the diameter of a circle, not its radius. The symbol ( is used before the dimension, except when it is obvious.

30 10 10 Correct Incorrect 30 10 10 10 30 10 10 Correct Incorrect 30 10 10 25 50 25 Unnecessary indication of dimension 100 20 10 Correct Incorrect 20 10 15

Correct

Incorrect

15 R 7.5

10. The radius of an arc should always be indicated with the abbreviation R placed before the dimension.

11. Extension lines should not cross each other or dimension lines unless this can be done without making the drawing more complicated.

12. Avoid dimensioning of hidden lines if possible.

13. Always show the angles outside the space representing an object.

45 0 45 0 10 10 10 10 10 10 10 10 Correct Incorrect R 5 Correct Incorrect 5 10 Incorrect 10 Correct

15

20

14. Dimensions should be given from the centre lines, finished surfaces, or datum’s as applicable to a drawing.

15. The centre line should never be used as a dimension line.

16. In the unidirectional system of dimensioning, all dimensions must be upright and readable when the drawing is viewed in its normal upright position.

17. In the aligned system, the dimensions must be readable when the drawing is viewed in its normal upright position or from its right hand side.

15 20 50 Correct Incorrect 50 10 10 10 30 60 90 10

18. In a drawing of a part with circular ends, the centre-to-centre dimension is given instead of an overall dimension.

19. When a number of dimensions are indicated on one side of a drawing, they should appear on a continuous line.

20. Intersecting construction lines and projection lines shall extend slightly beyond their point of intersection.

Unidirectional Method:

In this system, the dimensions are indicated in the vertical / upright position so that they can be read easily when the drawing is viewed in its upright position. The numerical values are placed at the centres of the dimension lines.

50 65 26 20 F F 60 0 POINT OF INTERSECTION 35 15 20 Correct Incorrect 35 15 20 R 10 20

30 20 5 20 20 30 Aligned Dimensioning:

In this system, the dimensions are indicated so as to be perpendicular to the dimension lines. In other words, the horizontal dimensions can be read conveniently when the drawing is viewed normally. Similarly, the vertical dimensions can be read easily from the right side of the sheet.

Dimensioning Arrangements

Chain Dimensioning:

When successive dimensions are arranged in a straight line, the method used is called chain dimensioning. 50 65 26 20 F F

20 45 65 85 105 125 145 100 85 74 62 32 0 18 40 16 20 22 40 Parallel Dimensioning:

When a number of dimensions are indicated from a common datum, the system is known as parallel dimensioning.

Progressive Dimensioning:

In this method, a dot and a zero sign indicate the datum line. The dimensions are indicated progressively from the datum.

Co-ordinate Dimensioning:

The method of dimensioning shown in the figure is known as co-ordinate dimensioning. For simplicity, the same dimensions can be shown separately in a tabular form as shown in the figure.

Sample: 1 Sample: 2

Arrows:

Drawing an arrowhead terminates dimension lines. The arrowhead may be open, closed or closed and filled. The length to width ratio of an arrowhead should be limited to 3:1.

f 20 20 20 20 20 60 60 60 160 100 10 120 90 15 25 1 2 3 4 5 X Y 1 2 3 4 5 X Y 0 0 0 20 0 15 0 20 0 25 0 20 0 20 0 20 140 180 200 160 0 20

O pen arrow

C losed arrow

C losed and Filled

arrow

Your First Drawing

Step1: Clean the drawing board and instruments.

Step2: Fix the thick cardboard sheet as padding sheet on the drawing board

using clips/cello tape.

Step3: Fix the drawing sheet over the cardboard using clips/cello tape. Step4: Fix the Minidrafter at the top-left corner of the drawing board. Step5: Draw the borderlines using an HB pencil.

Introduction to Engineering Drawing – Exercises

1. Write freehand in single stroke vertical capital letters of 5mm height the following sentence.

i) “The correct use of energy is at the root of industrial progress and productivity.”

ii) “Small things make perfection, but perfection is not a small thing”.

iii) “Engineering Drawing is a graphical language an universal language of all engineers”.

iv) “The main requirements for lettering on engineering drawings are legibility, uniformity, ease and rapidity in execution”.

2. Read the dimensioned drawing shown in figure. Redraw the figure to full size and dimension it as per BIS.

ii.

iv.

Chapter - II

Geometric Construction

Introduction

This chapter deals with some of the important basic construction techniques frequently used in Engineering Drawing.

Geometric Terms

Triangle

A triangle has three sides; the sum of its angles is equal to 180º.

Equilateral Triangle

An equilateral triangle is a triangle, which has three equal sides. AB = BC = CA

∠ABC = ∠BCA = ∠CAB = 60°

Right-Angled Triangle

In a right-angled triangle, the included angle between two of its sides is equal to 90º.

∠ABC = 90º

Isosceles Triangle:

An isosceles triangle is a triangle, which two sides, and two angles are equal. AB=AC and ∠ACB=∠ABC

A B C 60o A B C 90” A B C

A _B C D A _B C D Quadrilateral

A quadrilateral has four sides; the sum of all its angles is equal to 360º.

Square

When all the sides of a quadrilateral are equal and all its internal angles are right angles, the quadrilateral is called a square.

AB = BC = CD = DA

Rectangle

When the opposite sides of a quadrilateral are equal and all its internal angles are right angles, the quadrilateral is called a rectangle.

AB = CD and BC = AD

Rhomboid

When the opposite sides and angles of a quadrilateral are equal and none of its angles are right angles, the quadrilateral is called a rhomboid.

AB = CD BC = AD

∠=ABC= ∠=CDA and ∠=BCD= ∠=DAB

Rhombus

When all the sides of a quadrilateral are equal and none of its internal angles are right angles, but the opposite angles are equal, the quadrilateral is called a rhombus.

AB = BC = CD = DA

∠=ABC= ∠=CDA and ∠=BCD = ∠=DAC.

A B C D A B C D

Trapezoid

When two opposite sides of a quadrilateral are equal and the other two opposite sides are parallel, the quadrilateral is called a trapezoid.

AB = CD AD || BC

Trapezium

When no side of a quadrilateral is parallel or perpendicular to any of its other sides, the quadrilateral is called a trapezium.

Parts of a Circle Arc

The part of a circle between any two points on its circumference is called an arc. Arc = AB

Segment

The part of a circle bounded by an arc and a chord is called a segment. Segment = ABC A B C D A B C D A B A rc A B Segm ent Chord C A B C A B

Chord

A straight line joining any two points on the circumference of a circle is called a chord. Chord = AB

Sector

The part of circle bounded by two radii and an arc is called a sector. Sector = DEF

Polygons

Types of Polygons

A plane figure bounded by straight lines is called a polygon. Polygons are classified into two types. They are:

1. Regular Polygon 2. Irregular Polygon

Regular Polygon

A polygon in which all the sides and all the angles are equal is called a regular polygon.

Chord Sector F D E F D E Chord A B

Pentagon:

A regular pentagon has five equal sides. Its angles are equal. The internal angle of a regular polygon of "n" sides= {(2n-4) 90°}/n. The internal angle of a regular pentagon = 108°

AB = BC = CD = DE = EA

Hexagon:

A regular hexagon has six equal sides. Its angles are equal. The internal angle of a regular hexagon =120°

AB = BC = CD = DE = EF = FA

Heptagon:

A regular heptagon has seven equal sides. Its angles are equal. The internal angle of a regular heptagon = 128.57° AB = BC = CD = DE = EF = FG = GA A B C D E 108o A B C D E F G 128.57o A B C D E F 120o

Octagon

A regular octagon has eight equal sides. Its angles are equal. The internal angle of a regular octagon = 135°

AB=BC=CD=DE=EF=FG=GH=HA

Nonagon

A regular nonagon has nine equal sides. Its angles are equal. The internal angle of a regular nonagon = 140°

AB=BC=CD=DE=EF=FG=GH=HI=IA

Decagon

A regular decagon has ten equal sides. Its angles are equal. The internal angle of a regular decagon = 144°

AB=BC=CD=DE=EF=FG=GH=HI=IJ=JA

Irregular Polygon

The sides and angles of an irregular polygon are unequal. Hence irregular polygons are not used in engineering drawing. A B C E F G D H 135o A B C J I D E F G H 144o A B C D E F G H I 140o

Geometric Construction:

To Bisect a Line:

1. Draw the given line AB.

2. With A as centre and radius greater than half AB, draw arcs on both sides of AB.

3. Similarly with B as centre and the same radius, draw arcs to intersect the previous arcs at C and D.

4. Join C and D. The line AB is now bisected.

To Bisect an Arc:

1. Draw the given arc AB.

2. With A as centre and a radius greater than half AB, draw an arc on both sides of AB. 3. Similarly with B as centre, and the same radius draw arcs to intersect the previous arcs at C

and D.

4. Join C and D. The arc AB is now bisected. D o C D C D B A C D A B

To find the centre of an arc:

1. Draw the given arc AB.

2. Draw two chords PQ and RS of any length within AB. 3. Bisect the chords.

4. Let the bisectors intersect at O; then O is the centre of the arc.

To Bisect an Angle:

1. Draw the given angle ABC

2. With B as centre and any radius, draw an arc cutting AB at D and BC at E

3. With D and E as centres and the same or any other radius, draw arcs within the angle to intersect each other at F

4. Join B and F. The line BF divides the angle ABC equally, or "bisects" it.

A B P _Q R s O D E F A B C

To construct a regular Pentagon:

1. Draw a line BA equal in length to the given side of the pentagon.

2. At B, draw a line at an angle of 108º (angle of regular polygon of "n" sides= {(2n-4) 90°}/n) to AB.

3. Similarly at A draw a line at angle of 108º to AB.

4. With B as centre and radius equal to AB draw an arc on the first line to cut it at C (AB=BC). 5. Similarly, with A as centre and radius AB draw an arc on the second line to cut it at E

(BA=AE).

6. With C and E as centres and radius equal to AB draw arcs to intersect at D. 7. Join CD and ED. ABCDE is the required pentagon.

108 108

A

B

C

E

A B 120 0 120 0 F C D E 60 0 ₆₀ 0

To Construct a regular Hexagon:

1. Draw a line AB equal in length to the given side of the hexagon. 2. Draw perpendiculars at A and B.

3. Draw two lines at 120° to AB, one at the left of A and another one at right of B.

4. With A as centre and the radius equal to AB, draw an arc on the second line to cut it at F. 5. With B as centre and radius equal to AB, draw an arc to cut the first line at C.

6. With C and F as centres and equal to AB cut the perpendiculars at D and E. 7. Join CD, FE and ED. ABCDEF is the required hexagon.

To construct a regular Octagon:

1. Draw a line BA equal in length to the given side of the octagon. 2. Draw perpendiculars at A and B.

3. Draw two lines at 135° to AB, one at the left of B and the other one at the right of A. 4. With B as centre and radius equal to AB, draw an arc to cut the first line at C.

5. With A as centre and the same radius (=AB), draw an arc on the second line to cut it at H. 6. Through C and H draw lines parallel to the perpendiculars at A and B.

7. Using compasses draw CD and HG equal to AB.

8. With G and D as centres and radius equal to AB cut the perpendiculars (at A and B) at F and

E.

9. Join DE, EF and FG. ABCDEFGH is the required octagon.

135 135

A B C D H G F E

GENERAL CONSTRUCTION METHOD OF POLYGON:

C

D

E

O

E

A

B

M

Chapter – III

Orthographic Projection

Introduction

Engineers are mainly involved in the design and development of machines and structures. To design and communicate every detail of a machine /structure, engineers must prepare a drawing that shows the true size and shape of the entire machine or structure. It is difficult to represent a three dimensional object exactly on a sheet of paper by showing a single view.

Hence sets of views from different positions are prepared to define the object completely. Though different methods of projections are available to obtain the views of objects, the orthographic projection is used for most engineering purposes.

Objectives

This session will help you to learn

•= What a projection is.

•= What the horizontal and vertical planes are.

•= What are the types of projections normally used.

•= How to identify and differentiate between the first angle and third angle projections.

What is Projection

The views of an object formed on a transparent plane, by viewing it perpendicularly from the front, top or side of the object are called its projections.

The Front View of an Object:

The view of an object formed on a transparent plane by viewing it perpendicularly from the front of the object is called its front view. It can also be called as "elevation".

Note:

In general, the front view of an object (FV) is taken as the view normal (or perpendicular) to the longest side of the object.

The Top view of an Object:

The view of an object formed on a transparent plane, by looking at it perpendicularly from the top is called the top view of the object.

Note:

1. The top view is usually placed above the front view in the case of third angle projection. 2. The top view is also called "plan" and is placed below the front view in the case of first

angle projection.

The Side view of an Object:

The view of an object formed on a transparent plane, by looking at it perpendicularly from the side is called the side view of the object. The view taken from the right hand side of the object is called its "right side view". Similarly the view from the left hand side is the "left side view".

Types of Projection: 1. Pictorial Projection 2. Orthographic Projection Pictorial Projection: 1. Isometric Projection 2. Oblique Projection 3. Perspective Projection 1. Isometric Projection:

"Iso" means equal and "metric projection" means projection to a reduced measure. The tilting angle of the view is 30º to the horizontal.

30

0

30

0 120 0 120 0 120 0 A B D P Q R S

2. Oblique Projection:

Oblique projection is a slanting projection. The tilting angle is either 30º or 45º. Thus an oblique drawing can be drawn directly without using any of the projection techniques.

3. Perspective Projection:

In perspective drawings, the objects are represented more realistically than other drawings. A photograph of a person or object is a perspective of the person or the object. Very often an architect uses photographic representation. Perspective drawings show three-dimensional objects in a single plane as they appear to our eye.

Orthographic Projection:

"Ortho" means right angle and "Ortho-graphic" means right-angled drawing. The projections of an object are perpendicular to the plane on which the projections are` obtained are known as orthographic projections. Imaginary rays of light from an observers eyes viewing an object from an infinite distance will be parallel to each other and perpendicular to the object and the plane on which a projection of the object will be produced.

Vertical and Horizontal Planes:

The picture planes that are used for obtaining orthographic projections are customarily called the principal planes of projection or the reference planes.

The plane in front of an observer is the vertical plane and is denoted by VP.

The other plane, which is perpendicular to the VP, is called the horizontal plane and is denoted by HP.

Vertical and Horizontal Planes:

To obtain projections on a drawing sheet:

It is conventional to rotate the HP through 90º in a clockwise (CW) direction about the reference line XY, so that it lies in the extension of the VP, as shown in the figure.

The front view of an object is obtained in the VP and its top view is obtained in the HP, if the object lies in the I-Quadrant.

The Four Quadrants:

When the planes of projection are extended beyond their line of intersection, they form four quadrants, as shown in the figure.

These four quadrants are named as the I-Quadrant, the II-Quadrant, the III-Quadrant, and the IV-Quadrant, moving in the counter clockwise direction.

The First Angle Projection:

I Quadrant IV Quadrant III Quadrant II Quadrant X Y Vertical Plane Horizontal _Plane R efer ance Line 90 o XY – reference line HP – Horizontal Plane

When an object is situated in the I-Quadrant, the projection obtained is called the first angle projection. In this projection,

1. The object lies between the observer and the plane of projection. 2. The object is situated above the HP and in front of the VP.

3. The front view of the object comes above its top view with respect to the reference line.

This is the ISI symbol for first angle projection.

The Third Angle Projection:

When the object is situated in the III-Quadrant, the projection obtained is called the third angle projection. In this projection,

1. The planes of projection lie between the object and the observer

2. The object is situated above the ground or below the HP and behind the VP. 3. The top view of the object comes above its front view with respect to the reference

line.

Chapter – IV

Projections

The views of an object formed on a transparent plane by viewing it perpendicularly from the front, top or side of the object are called its projections.

Projections of a Point

Objectives

At the end of this session, you will be able to

•= Draw the projections of a point in the four quadrants.

•= Identify the position of the point in different quadrants.

Notation

To obtain the projections of points in space, standard notations are followed:

1. The actual points in space are denoted by capital letters A, B, C, D, etc.,

2. The front views are denoted by the corresponding lowercase letters with dashes like a', b', c', d', etc., and their top views are denoted by the corresponding lowercase letters like a, b, c, d, etc.

3. Projectors are always drawn as continuous thin lines using a 2H pencil. 4. The visible points are drawn with a H pencil.

O X Y HP VP a' a O X Y b b' Projection of a Point in the I-Quadrant

OK...! Let us imagine that a Point A is 20 mm above the HP and 30 mm in front of the VP

1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line.

2. Draw a line perpendicular to XY.

3. On the perpendicular line mark a point ‘a’ 30 mm below XY. (Top view) 4. On the perpendicular line mark a point ‘a'’ 20 mm above XY. (Front view) 5. Erase the unwanted lines.

6. The points a and a' are the projections of the point A in the I- quadrant.

Projection of a Point in the II-Quadrant

OK...! Let us imagine that a Point B is 25 mm above the HP and 35mm behind the VP.

1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line.

2. Draw a line perpendicular to XY.

3. On the perpendicular line mark a point b 35mm above XY.(Top view) 4. On the perpendicular line mark a point b' 25mm above XY.(Front view) 5. Erase the unwanted lines.

O HP VP X Y

c

c'

Projection of a Point in the III-Quadrant

OK...! Let us imagine a Point C 35 mm below the HP and 25 behind the VP.

1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line.

2. Draw a line perpendicular to XY.

3. On the perpendicular line mark a point ‘c’ 25mm above XY. .(Top view) 4. On the perpendicular line mark a point ‘c'’ 35mm below XY. .(Front view) 5. Erase the unwanted lines.

O

X Y

d d' Projection of a Point in the IV-Quadrant

OK...! Let us imagine a Point D 30mm below the HP and 40 mm in front of the VP.

1. Draw the reference line XY and name it as VP and HP respectively above and below the XY line.

2. Draw a line perpendicular to XY.

3. On the perpendicular line mark a point ‘d’ 40mm below XY.(Top view) 4. On the perpendicular line mark a point ‘d'’ 30mm below XY.(Front view) 5. Erase the unwanted lines.

Projection of Points – Exercises

1. Draw the projections of the point A, 35mm below the HP and in the VP. 2. Draw the projections of the point B, 45mm behind the VP and in the HP.

3. Draw the projections of the point C, 25mm below the HP and 25mm in front of the VP. 4. Draw the projections of the point D, 30mm above the HP and 30mm behind the VP. 5. Draw the projections of the point E, 20mm above the HP and 25mm in front of the VP. 6. Draw the projections of the point F, in both the VP and the HP.

7. Draw the projections of the point G, 40mm below the HP and 35mm behind the VP. 8. Draw the projections of the point H, 35mm above the HP and 40mm behind the VP.

9. Figure shows the projections of different points. Determine the position of the Points with reference to the projection planes.

10. A Point 30mm below XY is the plan of two points A and B. Point A is the Horizontal plane and point B is 40mm below the Horizontal plane. Draw the projections of A and B.

Projections of a Straight Line

Introduction

The shortest distance between any two points is called a "straight line". Different surfaces and planes form the configuration or shape of any object. Revolving or moving straight lines in different ways obtains these surfaces and planes. Thus a straight line is the basic conceptual figure using which any object like a machine component or a structural element is represented. Thus projection of a straight line is the foundation of Engineering Drawing.

In the previous session, we have studied the projections of given points. Joining the respective projections of two points therefore gives the projection of the straight line joining the two points. As per ISO convention the first angle of projection is used.

Objectives

At the end of the session, you will be able to •= Define straight line.

•= Draw the projections of a straight line located at different positions with respect to the VP and the HP.

X Y a(b) a’ b’ 25 20 10 VP HP

Perpendicular to the HP and Parallel to the VP

OK...! Let us imagine that a Line AB 25mm is parallel to the VP and perpendicular to the HP! Point A is 35mm above the HP and 20mm in front of the VP! B is 10 mm above the HP..!

1. Draw the line XY.

2. Draw a line perpendicular to XY using a 2H pencil. 3. Mark b' 10mm above XY on the perpendicular line. 4. Mark a' 25mm above b'.

5. a' b' is the front view, join a', b' using a H pencil. 6. Mark a (b) 20mm below XY; a (b) is the top View. 7. Erase the unwanted Lines.

Perpendicular to the VP and Parallel to the HP

Ok...! Let us imagine that a Line AB of length 25mm is perpendicular to the VP and Parallel to

the HP. The point A is 20mm above the HP and 10mm in front of the VP. 1. Draw the line XY.

2. Draw a line perpendicular to XY using a 2H pencil. 3. Mark "a" 10mm below XY on the perpendicular line. 4. Mark "b" 25mm below "a".

5. Join "a" and "b" using an H pencil to get the top view. 6. Mark a' (b') 20mm above XY line on the perpendicular line 7. Erase the unwanted Lines

X Y b'(a') a b VP HP

Parallel to the HP and Inclined to the VP

Ok ...! Let us imagine that a line PQ of length 40mm is parallel to the HP and inclined at an

angle of 35° to the VP. The end P is 20mm above the HP and 15mm in front of the VP. 1. Draw the line XY.

2. Draw a line perpendicular to XY using a 2H pencil

3. Mark “p'” and “p” respectively 15 mm above XY and 20mm below XY on the perpendicular line

4. From “p” draw a line at an angle of 35° to XY and mark “q” such that pq = 40mm = true length.

5. pq is the top view of the given line in the I-Quadrant.

6. From “q” draw a projector (perpendicular line) to intersect the horizontal line drawn from “p'” at “q'”.

7. p' q ' is the front view. 8. Erase the unwanted line.

X Y q q’ p 20 p’ 15 35” 40 VP HP

Parallel to the VP and Inclined to the HP

Ok...! Let us imagine that a line PQ of length 40mm is parallel to the VP and inclined at an

angle of 30° to the HP. The end P is 15mm above the HP and 20mm in front of the VP. 1. Draw the line XY.

2. Draw a perpendicular line to XY using 2H pencil.

3. Mark p' & p 15mm above XY & 20mm below XY on the perpendicular line. 4. From p' draw a line at angle of 30° to XY and mark q'. such that

p'q'= 40mm = True length 5. p' q' is the required Front View

6. From q' draw a projector (perpendicular line) to intersect the horizontal line drawn from p at q.

7. pq is the required Top View 8. Erase the unwanted Line

X Y p p' q q' 30º VP HP

Inclined to the HP and the VP

Ok...! Let us imagine that the line pq is inclined to both the VP and the HP.

1. Draw the line XY.

2. Mark “p” below XY line and draw 45° line and mark q2 at 80mm 3. Mark “p'” above XY line and draw 30° line and mark “q1' ” at 80mm 4. Draw locus of “q1' ” and “q2”

5. Project from “q1' ” and “p” as centre rotate, it cuts locus of “q2” at “q” 6. Joint “p” and “q” to get top view

7. Project from “q2” and “p' ” as centre rotate, it cuts locus of “q1' ” at “q' ” 8. Joint “p’”and “q’” to get front view

X Y VP HP 30

p

₄₅

q

2 80 Tr_{ue line} 20

p’

80 True line 30 0

q

1

’

Locus of q’ Locus of q

q

1

q

q

2

’

q’

Parallel to the HP and the VP

Ok...! Let us imagine that a Line CD 30mm long is parallel to both planes. The line is 40mm

above the HP and 25mm in front of the VP. 1. Draw the line XY.

2. Draw a line perpendicular to XY using a 2H pencil.

3. Draw another perpendicular line 30mm from the previous line.

4. Mark “c'” and “d' ” on the Perpendicular lines and join them to get the front view. 5. Mark “c” 25mm below line XY; join “c” and “d” to get the top view.

6. Erase the unwanted Lines.

X Y c dd d' c' 30 VP HP

Projection of Straight Line - Exercises

1. A line AB, 55mm long kept parallel to both the HP and VP: 20mm above the HP and 25mm in front of VP. Draw the Projections.

2. A Line CD, 50mm long kept perpendicular to the VP and 20mm above the HP. The end C, nearer to the VP is 15 mm in front of it.

3. A Line MN, 85mm long is parallel to the VP and inclined at 450 to the HP. The end M is 25mm above the HP and 20mm in front of the VP. Draw the projections of the line MN. 4. The end L of line 55mm long is 10mm above the HP and 10mm in front of the VP. The

line is parallel to the HP and inclined to the VP. The length of the elevation is 40mm. Draw the projections of the line and find the inclination of the line with the VP.

5. A line RS, 70mm long lies in the HP and has its end R in both the HP and the VP. It is inclined at 400 to the VP. Draw the projections of the line.

6. A line EF is parallel to the VP. The end E is 20mm above the HP and 25mm in front of the VP. The end F is 65mm above the HP. The distance between the end projectors is 65mm. Find the true length and inclination of the line with the HP.

7. One end I of the line IJ is in the VP and 35mm above the HP. The line is parallel to the HP and inclined at 350 to the VP. The length of the elevation is 55mm. Find the true length of the line.

8. A line EF, 70mm long has its end E, 20mm above the HP and 20mm in front of the VP. The line is inclined at 500 to the HP and 300 to the VP. Draw the projections of the line and find the traces of the line.

9. The end U of the line UV, 85mm long is in both the HP and the VP. The line is inclined at 350 to the HP and 400 to the VP. Draw its operations.

10. A line RS, 70mm long is in the first quadrant with the end R in the HP and the end in the VP. The line is inclined in the 300 to the HP and 450 to the VP. Draw the projections of the line RS and indicate the projections of the mid-point M to the line.

11. The end M of the line MN is 25mm behind the VP and 35mm below the HP. The other end N is 45mm above the HP and 55mm in front of the VP. The distance between the

projectors of M and N is 75mm. Draw the projections of the line MN and find its true length, traces and inclinations with the reference planes. Use rotating line method.

12. The end L of the line LM is 20mm behind the VP and 30mm below the HP. The other end M is 40mm above the HP and 50mm in front of the VP. The distance between the projectors of L and M is 70mm. Draw the projections of the line LM and find its true length, traces and inclinations with the reference planes. Use rotating trapezoidal plane method.

13. The projections of E and F of the line EF given in problem 11 are on the same projector. Draw the projections of the line EF. Find its true length, traces and inclinations with the reference planes.

14. The projectors of two points K and L are 100mm apart. K is 55mm below the HP and 40mm in front of the VP. L is 100mm above the HP and 35mm behind the VP. Draw the projections of the line joining K and L. Determine the true length and inclinations of the line KL with the reference planes.

15. One end of P of line PQ, 80mm long is 10mm above the HP and 15mm in front of the VP. The line is inclined at 400 to the HP and top view makes 500 with the VP. Draw the projections of the line and find its true inclination with the VP.

16. One end of I of line IJ, 75mm long is 20mm above the HP and 15m in front of the VP. The line is inclined at 350 to the VP and top view has a length of 45mm. Draw the projections of the line and find its true inclination with the HP.

Projections of Solids

Introduction

An object having three dimensions, i.e., length, breadth and height is called as solid. In

orthographic projection, minimums of two views are necessary to represent a solid. Front view is used to represent length and height and the top view is used to represent length and breadth. Sometimes the above two views are not sufficient to represent the details. So a third view called as side view either from left or from right is necessary.

Objectives

At the end of this session, you will be able to

•= Classify the different types of solids

•= Draw the projections of solids in various positions in the given quadrant

Classification of Solids

Solids are classified into two groups. They are •= Polyhedra

•= Solids of Revolution

Polyhedra

A solid, which is bounded by plane surfaces or faces, is called a polyhedron. Polyhedra are classified into three sub groups; these are

1. Regular Polyhedra 2. Prisms

3. Pyramids

Regular Polyhedra

Polyhedra are regular if all their plane surfaces are regular polygons of the same shape and size. The regular plane surfaces are called "Faces" and the lines connecting adjacent faces are called "edges".

Tetrahedran Octahedran Hexahedran O B A C Apex O 1 D B C A O 2 D C 3 2 1 A 4 B Top face Base

Top face

Longer edge

Axis

Face

Bottom face

B

A

C

2

1

3

Prisms:

A prism has two equal and similar end faces called the top face and the bottom face or (base) joined by the other faces, which may be rectangles or parallelograms.

Triangular prism Square Prism Rectangular Prism C B D A 2 3 1 4

Top face

Longer edge

Axis

Face

Bottom face

(Base)

C B D A 2 3 4 Top face Longer edge Axis Face Bottom face (Base) 1

Pentagonal Prism

Hexagonal Prism

3. Pyramids:

A pyramid has a plane figure as at its base and an equal number of isosceles triangular faces that meet at a common point called the "vertex" or "apex". The line joining the apex and a corner of its base is called the slant edge. Pyramids are named according to the shapes of their bases.

C B D A 2 3 1 4 5 E

Top face

Bottom face

(Base)

C B D A 2 3 1 4 5 E

Top face

Bottom face

(Base)

F 6

Triangular Pyramid Square Pyramid Rectangular Pyramid C B O A Triangular face Bottom face (Base) Apex or Vertex Slant Edges B A C D O

Triangular face

Bottom face

(Base)

Apex or Vertex

Slant Edges

Base edge

B A C D O Triangular face Bottom face (Base) Apex or Vertex Slant Edges

Pentagonal Pyramid

Hexagonal Pyramid

Solids of Revolution:

If a plane surface is revolved about one of its edges, the solid generated is called a Solid of Revolution. Bottom face (Base) Apex or Vertex Bottom face (Base) Apex or Vertex

Sphere

A sphere can be generated by the revolution of a semi-circle about its diameter that remains fixed.

Cone

A cone can be generated by the revolution of a right-angled triangle about one of its perpendicular sides, which remains fixed. A cone has a circular base and an apex. The line joining apex and the centre of the base is called the “Axis” of the cone.

Base Generators

Axis Apex

Cylinder

A right circular cylinder is a solid generated by the revolution of a rectangular surface about one of its sides, which remains fixed. It has two circular faces. The line joining the centres of the top and the bottom faces is called “Axis”.

Base Generators

Y b a c d (2) (4) (1) (3) X (d') (4')_{1' 2'} (c') a' b' (3')

Projections of Solids

Perpendicular to the HP

1. OK...! Let us imagine that a cube of 50mm side is resting with one of its square faces on the HP.

1. Draw the line XY.

2. Draw the top view as a square (Side 50 mm) and name its corners. 3. Draw projectors at each corner of the top view through line XY. 4. Draw the front view as a square (Side 50 mm) and name its corners. 5. Dimension the completed drawing.

2. Ok...! Let us imagine that a square prism of base 30mm and height 60mm is resting with its base on the HP and one of its vertical faces perpendicular to the VP.

1. Draw the line XY

2. Draw the top view as square and name its corners.

3. Draw projectors from each corner of the top view through XY. 4. Draw the front view as shown and name its corners.

5. Dimension the completed drawing.

Y X b a c d (1) ₍₂₎ (4) (3) a’ (d’) 2’(3’) b’(c’) 1’ (4’) 30 60

Y X b a c d (1) (2) (3) (4) 1 (4)1 (4)1 (4) 2(3) b(c) a(d) (3) 2(3) 1 (4) b(c) a(d) 4 (2) (d)c 1 (3) (a)b

Parallel to the HP and the VP

1. OK...! Let us imagine that a square prism of base 30mm and axis 60mm long lies on the HP, such that its axis is parallel to both the HP and the VP.

1. Draw the line XY.

2. Draw the projections ( top and front views) of the solid in simple position ( an edge of its base is perpendicular to the VP).

3. Rotate the front view through 90°.

4. Draw projectors from the rotated front view and the initial top view and name the points of intersection.

2.OK...!Let us imagine that a hexagonal prism of base 30mm and axis 60mm long lies on one of

its rectangular faces on the HP, such that its axis is parallel to both the HP and the VP. (Side View Method)

1. Draw the lines XY and X1Y1 perpendicular to each other, intersecting at P as shown.

2. Draw the side view of the hexagonal prism and name its corners.

3. Draw projectors from the corners of the side view perpendicular to X1Y1. 4. Draw the front view and name its corners.

5. From P draw a line at 45° to XY and X1Y1. (This line is called the Miter line). 6. From the side view draw projectors to meet the Miter line.

7. From the Miter line draw projectors parallel to XY.

8. From the front view draw projectors parallel to X1Y1 and name the intersection points.

9. Draw the final top view.

Y X 1 Y 1 P a’’ b’’ c’’ d’’ e’’(5") f’’ (1’’) (2") (3") (4") (6") 30 60 (6’)1’ (5’)2’ (4’)3’ a’(f’) b’(e’) c’(d’) P 45 o 5 (4)6 (3)1 2 e f(d) a(c) b X

X a' b' Y c' d' e' f ' (1') (2') (3') (4') (5') (6') (1)5 (2)4 3 6 (a)e (b)d c f 30 450 11' 41' 21' 51' a1' d1' b1' e1' f1' c1' 61' (31')

Parallel to the HP and Inclined to the VP

1. Ok...! Let us imagine that a hexagonal prism of base 30mm and height 60mm lies on one of its rectangular faces lies on the HP, such that its axis is inclined at 45° to the VP.

1. Draw the line XY.

2. Draw the projections of the prism in simple position.

3. Rotate the axis of the top view through 45° with respect to XY.

4. Draw projectors from the rotated top view and the initial front view and name the points of intersection..

X Y a b c d e (1) (2) (3) (4) (5) 1' 2'(5') 3' (4') a' b'(e') c'c' (d') 300 11 21 51 31 41 a1 e1 b1 c1 d1

Parallel to the VP and Inclined to the HP

1. OK...! Let us imagine that a pentagonal prism of base 20mm and axis 40mm long rests on one of the edges of its base on the HP. The edge makes an angle of 30° to the HP and the axis of prism is parallel to the VP.

1. Draw the line XY.

2. Draw the projection of the prism in simple position.

3. Rotate the base of the front view through 300 with respect to XY so that only the edge (3',4') rests on the HP.

4. Draw projectors from the rotated front view and the initial top view and name the points of intersections.

2.OK...!Let us imagine that a pentagonal pyramid of base 25mm and axis 55mm long lies on one

of its longer edges on the HP and its axis is parallel to the VP. 1. Draw the line XY.

2. Draw the projection of solid in simple position.

3. Rotate the Front view such that one of the slant edge o'd' will lie on XY Line. 4. Draw projectors from the rotated front view and the initial top view and name it.

5.

Join the points correspondingly to get the final top view

.

X

Y

a b c d e o a’ (b’) e’(c’) d’ o’ 55 2525 o’ a’ (c’ ) d’ e’ (b’ ) a 1 b 1 c 1 e 1 d 1 _o 1

X Y a b c d (1) (2) (3) (4) o2(o1) 1'(4') 2'(3') o1' a'(d') o2' b'(c') 20 (21) a1 b1 11 (31) 41 d1 c1 o1 o2 45 a1' d1' b1' c1' o2' 11' 41' 21' 31' o1' Inclined to the VP and the HP

1. OK...! Let us imagine that a square prism of base 20mm and axis 40mm long has its axis inclined at 60° to the HP and an edge of its base is inclined at 45° to the VP.

1. Draw the line XY.

2. Draw the projection of the prism placed in the simple position. 3. Rotate the front view axis through 60°.

4. Draw projectors from the rotated front view and the initial top view and name the points of intersection.

5. Join the points correspondingly to get the top View. 6. Rotate base 2'3' of the rotated top view through 45°.

7. Draw projectors from the rotated top view and the rotated front view and name the point of intersection.

2.OK...! Let us imagine that a cone of base 30mm diameter and axis 60mm long has its axis inclined at 45° to the HP and 30° to the VP.

1. Draw the line XY.

2. Draw the projections of the cone placed in the simple position. 3. Rotate the axis of the front view through 45°.

4. Draw projectors from the rotated front view and the initial top view and name the points of intersection.

5. Join the points correspondingly to get the top view. 6. Rotate the axis of the rotated top view through 30°.

7. Draw projectors from the rotated top view and the rotated front view and name the points of intersection.

8. Join all the points correspondingly to get the final front view.

X Y a b c d o(p) a’ b’(d’) c’ o’ 60 0 30 a’ b’ c’ (d’ ) o’ a 1 d 1 b 1 c 1 p 1 0 1 a 1 d 1 b 1 c 1 p 1 0 1 a1’ d1’ b 1’ c1’ o1’ p1’

Projection of Solids – Exercises

1. A cube of side 55mm resting on the HP on one of its faces with one of its vertical faces inclined at 300 to the VP, draw the top view and front view.

2. A pentagonal prism side of base 25mm and axis 55mm resting on the HP on its base with one of the rectangular faces inclined at 45° to VP draw the top view and front view.

3. A hexagonal pyramid side of base 25mm and axis 55mm resting on its base HP, and the base edge is inclined at 45° to VP draw the top view and front view.

4. A cone of radius 20mm and axis 60mm resting with its base on HP, draw the projections. 5. Draw the projection of hexagonal prism of base 30mm and axis 65mm rests with its base

on HP and the base side is parallel to and 20mm in front of VP.

6. A tetrahedron of side 50 mm and rests on HP draw the projections when one of its edge is parallel to VP.

7. Draw the projections of hexagonal prism of base 30mm and axis 55mm resting on one corner of the base on HP and the base containing the edge 45° to HP and axis perpendicular to VP.

8. A square prism, side of base 35mm and axis 60mm long lies with one of its longer edge on HP. Draw the projection of prism when the axis is perpendicular to VP and one of its rectangular faces is inclined to 35° to HP.

Parallel to Both HP and VP

9. A cylinder of base diameter 30mm and axis 60mm long lies with one of its generators on HP. Draw the projection when the axis is parallel to both planes.

10. A hexagonal prism base 30mm and axis 60mm long lies with one of its longer edge on hp and the axis is parallel to both HP and VP. Draw the projection, use side view method.

Parallel to VP and inclined to HP

11. A square prism, side of base 30mm and axis 60mm, has an edge of its base on HP. Draw the projection, when the axis is inclined at 60° to HP and parallel to VP

12. A cone of base diameter 25mm and axis 50mm resting on HP with a point of its base circle on HP. Draw the projection of cone when the axis is inclined at 30° to HP and parallel to VP. 13. A cylinder of base 30mm and axis 50mm rests with a base circle on HP. Draw the projection

when axis making an angle 30° to HP and parallel to VP.

14. A pentagonal prism base 25mm and axis 60mm long rests with base edge on HP. Draw the projection of prism when the axis is inclined at 45° to HP and parallel to VP.

15. A cone base 30mm diameter and axis 60mm long, touches the VP on a point of its base circle. Draw the projection when the axis is inclined at 30° to HP and parallel to VP.

16. Draw the projection of cube 30mm long resting on HP on one of its corner with a solid diagonal parallel to both HP and VP.

17. Draw the projection of square pyramid, base 30mm and axis 55mm rests with its edge of the base on HP such that its base makes an angle of 30° to HP and parallel to VP

Parallel to HP and inclined to VP

18. Draw the projection of pentagonal prism base 25mm and axis 60mm long, lies with one of its rectangular edge on HP such that the axis is inclined at 30° to VP.

19. Draw the projection of pentagonal pyramid base 25mm and axis 60mm long lies with one of its triangular edge on HP such that the axis is inclined at 60° to VP.

20. A cylinder of base diameter 25mm and axis 60mm long, lies with one of its generators on HP such that the axis is inclined at 45° to VP. Draw its projection.

Axis inclined to Both HP and VP

21. Draw the projection of a cube of base 40mm rests with its edges on HP and one of the faces containing that edge is inclined to 30° to HP. The edge on which the cube rests is parallel to VP.

22. A hexagonal prism side of base 30mm and axis 60mm, resting with one of the edge of its base on HP. Draw the projection when its axis is inclined at 30° to HP and top view of the axis is 50° to VP.

23. A hexagonal pyramid side of base 30mm and axis 60mm, resting with one of the corner of its base on HP. Draw the projections when its axis is inclined at 30° to HP and 45° to VP.

Chapter - V

Section of Solids

Introduction

The orthographic views of a component may not always give all the information clearly; they give only the component's external information. An object with a lot of inner details, seen in orthographic views will have numerous dotted lines and will be difficult to be understood clearly. To overcome this difficulty, the object is assumed to be cut by one or more planes, so that most of the inner details can be seen and shown in the drawing very clearly. Thus, a study of the sections of solids is of considerable practical importance. The methods of drawing sections of different geometrical solids or "Sections of Solids" are described in this section.

Objectives

This session will help you to learn

•= The need for sectioning.

•= How a cutting plane can be described.

•= How the true shape of an apparent section can be described.

•= How the frustum of a solid can be described.

•= How the sectional views of solids may be drawn.

Sectional Views and Conventions

Cutting plane and sectional view: Sectional View:

The projection of the remaining portion of a "sliced" solid is called the sectional view. A

sectional view is usually indicated by drawing continuous thin lines inclined at 45° to the axis or to the boundary of the section. Section lines are called hatching lines and they should be equally spaced, depending on the hatching area; the spacing of hatching lines generally varies from 1.5 to 3.5mm.

Cutting plane or sectional Plane:

The imaginary plane, which is assumed to cut the object as required, is called a cutting plane or a section plane.

Cutting planes are generally shown by long and short dashes, which are thickened at the ends, bends and changes of direction but thin elsewhere. The direction of viewing is indicated by two arrows resting at the ends of the cutting plane and is represented by capital letters (e.g., XX, AA etc.).

The points at which sectional plane cut the edges of solids are called sectional points.

Sectional points are usually numbered as 1, 2, 3, 4,... etc., in the top view and as 1', 2', 3', 4',...etc., in the front view.

Types of section

Sections can be classified into two types. They are: 1. Apparent section

2. True type of section

Apparent section:

An apparent section is the projection of the section of a solid cut by a plane that is inclined to horizontal plane or vertical plane.

True type of section:

The true shape and size of a section of a solid is obtained by viewing the object normal to the section and projecting the section on a plane parallel to it.

Conic Section:

Sections obtained by cutting the cone in different position relative to the axis are called "Conic Section".

1. When cutting plane parallel to base, the sectioned portion is a circle.

2. When cutting plane inclined to axis and cuts all the generators the sectioned portion is an ellipse.

3. When cutting plane parallel to one of its generators the section obtained is a parabola.

4. When the cutting plane is at a very small angle to the axis and cuts the generator on one side of the axis, and the base, the section obtained is a hyperbola.

5. When the cutting plane is parallel to axis, the sectioned obtained is a rectangular hyperbola.

Frustum of a solid and Truncated solid: Frustum

When a solid is cut by a cutting plane parallel to its base, the portion obtained after removing the top portion is called "Frustum"

Truncated

When a solid is cut by a cutting plane inclined to its base, the portion obtained after removing the top portion is called the "truncated" solid.

Sections of Solids

Perpendicular to the VP and Parallel to the HP:

1. Ok..! Let us imagine that a pentagonal pyramid of base 25mm and height 55mm rests with its

base on the HP such that one of its edges is perpendicular to the VP. A section plane parallel to the HP and perpendicular to the VP cuts the pyramid at 20mm from the apex.

1. Draw the line XY.

2. Draw the top view as a pentagon and name its corners.

3. Draw projectors from each corner of the top view through XY. 4. Draw the front view as shown in the figure and name its corners.

5. Draw the section plane in the front view at 20mm from the apex and name the sectional points.

6. Draw projectors from each sectional point in front view so that they cut the corresponding edges in the top view.

7. Name these points and join them.

8. Draw the hatching lines to get the sectional top view.

X

Y

e

d

c

b

a

o

25

o’

b’

a’

c’

(d’)

(e’)

20

55

P S _{(4’) (5’)3’ 2’ 1’} 1 5 2 4 3