TECHNICAL DRAWING COURSE CODE: MEC 112

UNESCO-NIGERIA TECHNICAL & VOCATIONAL EDUCATION REVITALISATION PROJECT-PHASE II NATIONAL DIPLOMA IN MECHANICAL ENGINEERING TECHNOLOGY TECHNICAL DRAW...
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UNESCO-NIGERIA TECHNICAL & VOCATIONAL EDUCATION REVITALISATION PROJECT-PHASE II

NATIONAL DIPLOMA IN MECHANICAL ENGINEERING TECHNOLOGY

TECHNICAL DRAWING COURSE CODE: MEC 112 YEAR I- SE MESTER I THEORY/PRACTICAL Version 1: December 2008

MECHANICAL ENGINEERING TECHNOLOGY TECHNICAL DRAWING (MEC 112) TABLE OF CONTENTS WEEK 1

1.0 :

INTRODUCTION

1.1:

INTRODUCTION TO DRAWING EQUIPMENTS

1.1.1:

T-SQUARE

1.1.2:

SET SQUARE

1.1.3:

COMPASS

1.1.4:

DRAWING TABLE

1.1.5:

IRREGULAR CURVES (FRENCH CURVES)

1.1.6:

PROTRACTOR

1.1.7:

DRAWING PENCIL:

1.1.8:

ERASER:

1.2:

LINES

1.2.1:

LINES AND LINE STYLES

1.2.2:

LINE THICKNESS

1.2.3:

LINE STYLES

1.2.4:

BREAK LINES

1.2.5:

LEADERS

1.2.6:

DATUM LINES

1.2.7:

PHANTOM LINES

1.2.8:

STITCH LINES

1.2.9:

CENTER LINES

1.2.10:

EXTENSION LINES

1.2.11:

OUTLINES OR VISIBLE LINES

1.2.12:

CUTTING-PLANE/VIEWING-PLANE LINES

1.2.13:

HIDDEN LINES

1.2.14:

SECTIONING LINES

1.2.15:

DIMENSION LINES

1.3:

DIMENSIONING - AN OVERVIEW

1.3.1:

PARALLEL DIMENSIONING

1.3.2:

SUPERIMPOSED RUNNING DIMENSIONS

1.3.3:

CHAIN DIMENSIONING

1.3.4:

COMBINED DIMENSIONS

1.3.5:

DIMENSIONING BY CO-ORDINATES

1.3.6:

SIMPLIFIED DIMENSIONING BY CO-ORDINATES

1.3.7:

DIMENSIONING SMALL FEATURES

1.3.8:

DIMENSIONING CIRCLES

1.3.9:

DIMENSIONING HOLES

1.3.10:

DIMENSIONING RADII

1.3.11:

SPHERICAL DIMENSIONS

1.3.12:

TOLERANCE

1.4 :

LINE STYLES

1.5 :

TASK SHEET 1

2.1:

PLANNING YOUR ENGINEERING DRAWING

2.2:

LAYOUT OF DRAWING PAPER

2.3:

COMMON INFORMATION RECORDED ON THE TITLE BLOCK

2.4.

TITLE BLOCK SAMPLE

2.5:

DRAWING SHEETS/PAPERS

2.6 :

DRAWING SCALES

2.7:

LETTERING METHOD

2.8:

TASK SHEET 2

3.1:

GEOMETRICAL DRAWINGS

3.2:

STRAIGHT LINES AND ANGLES

3.3:

TRIANGLE

3.4:

TASK SHEET 3

WEEK 2

WEEK 3

WEEK 4

3.5:

QUADRILATERALS

3.5.1.

SQUARE

3.5.2.

RECTANGLE

3.5.3.

PARALLELOGRAM

3.5.4.

RHOMBUS

3.5.5

TRAPEZIUM

3.5.6.

TRAPEZOID

3.6:

CONSTRUCTION OF QUADRILATERALS

3.7:

CIRCLES

3.7.1:

TYPES OF CIRCLES

3.7.2:

PROPERTIES OF A CIRCLE

3.7.3:

CONSTRUCTION INVOLVING CIRCLES

3.8:

TASK SHEET 4

3.7.3:

CONSTRUCTIONS INVOLVING CIRCLES

4.0:

TANGENCY

4.1:

CONSTRUCTION OF TANGENT

5.0:

POLYGONS

5.1:

CONSTRUCTION OF POLYGONS

5.2:

TASK SHEET 5

6.0

ELLIPSE:

6.1

PROPERTIES OF AN ELLIPSE

WEEK 5

WEEK 6

6.2

CONSTRUCTION OF ELLIPSE USING CONCENTRIC CIRCLES METHOD

6.3

CONSTRUCTION

OF

ELLIPSE

USING

RECTANGULAR

METHOD 6.4

CONSTRUCTION OF ELLIPSE USING TRAMMEL METHOD

6.5

CONSTRUCTION OF NORMAL AND THE TANGENT TO AN ELLIPSE, AND TO FIND THE FOCI.

6.7

TASK SHEET 6

7.0

ISOMETRIC PROJECTION:

7.1

HOW TO DRAW IN ISOMETRIC PROJECTION:

7.2

TASK SHEET 7

8.0

ORTHOGRAPHIC PROJECTION

8.1

THREE VIEW OF AN OBJECT IN FIRST AND THIRD ANGLE

WEEK 7

WEEK 8

PROJECTIONS 8.2

THE MAIN FEATURES OF THE SIX VIEW OF AN OBJECT

8.3

ONE POINT PERSPECTIVE

8.4

TWO POINT PERSPECTIVE

8.5

THREE POINT PERSPECTIVE

8.6

TASK SHEET 8.1

8.7

MULTI-VIEWS DRAWING USING 1ST & 3RD ANGLE OF

WEEK 9

PROJECTION 8.7.1

MULTI VIEWS PROJECTION

8.8

THE

DIFFERENCES

BETWEEN

1ST

&

3RD

ANGLE

OF

PROJECTION 8.8.1

FIRST-ANGLE PROJECTION

8.8.2

THIRD-ANGLE PROJECTION

8.9

TASK SHEET 8.2

WEEK 10

9.0

ABBREVIATIONS AND SYMBOLS USED ON MECHANICAL AND ELECTRICAL DRAWINGS.

9.1

INTRODUCTION

9.2

TECHNICAL DRAWING SYMBOLS

9.3

MECHANICAL CONVENTIONS

9.4

ELECTRICAL CONVENTIONS

9.5

LINES AND BLOCK DIAGRAMS

9.5.1

BLOCK DIAGRAM METHOD

9.5.2

LINE DIAGRAM METHOD

9.6

PNEUMATIC SYSTEM

9.7

HYDRAULIC SYSTEM

9.8

PNEUMATIC SYMBOLS

9.9

TASK 10

10.0

MISSING VIEW IN ORTHOGRAPHIC

10.1

FIRST ANGLE OF PROJECTION:

10.2

THIRD ANGLE OF PROJECTION

10.3

TASK SHEET 11

11.0

FREE HAND SKETCH

11.1

INTRODUCTION:

WEEK 11

WEEK 12

11.2

GENERAL NOTES BEFORE SKETCHING:

11.3

TASK SHEET 12

12.0

SKETCHING THE VIEWS FROM AN ACTUAL OBJECT

12.1

OBLIQUE SKETCHING

12.2

TASK SHEET 13

13.0

INTERSECTION AND DEVELOPMENT

13.1

CONSTRUCTION OF SOLID WITH INTERPENETRATION

13.2

TWO DISSIMILAR SQUARE PRISMS MEETING AT RIGHT

WEEK 13

WEEK 14

ANGLES. 13.3

TWO DISSIMILAR SQUARE PRISMS MEETING AT AN ANGLE.

13.4

TWO DISSIMILAR HEXAGONAL PRISMS MEETING AT AN ANGLE.

13.5

TWO DISSIMILAR CYLINDERS MEETING AT RIGHT ANGLES.

13.6

TWO DISSIMILAR CYLINDERS MEETING AT AN ANGLE.

13.7

TASK SHEET 14

14.0

DEVELOPMENT

14.1

TASK SHEET 15

WEEK 15

WEEK1: 1.0

INTRODUCTION

Technical drawing is concerned mainly with using lines, circles, arcs etc., to illustrate general configuration of an object, however, it is very important that the drawing produced to be accurate and clear. The ability to read and understand drawings is a skill that is very crucial for technical education students; this text aims at helping students to gain this skill in a simple and realistic way, and gradually progressed through drawing and interpreting different level of engineering drawings. Some basic equipments are necessary in order to learn drawing, here are the main ones. 1.1 INTRODUCTION TO DRAWING EQUIPMENTS

1.1.1:T-SQUARE A T-square is a technical drawing instrument primarily guides for drawing horizontal lines on a drafting table, it also used to guide the triangle that is used to draw vertical lines. The name “Tsquare” comes from the general shape of the instrument where the horizontal member of the T slides on the side of the drafting table. (Fig.1.1)

(Fig.1.1)

1.1.2: SET SQUARE A set square or triangle is a tool used to draw straight vertical lines at a particular planar angle to a baseline. The most common form of Set Square is a triangular piece of transparent plastic with the centre removed. The outer edges are typically beveled. These set squares come in two forms, both right triangles: one with 90-45-45 degree angles, and the other with 90-60-30 degree angles. (Fig.1.2)

(Fig.1.2)

1.1.3: COMPASS Compasses are usually made of metal, and consist of two parts connected by a hinge which can be adjusted. Typically one part has a spike at its end, and the other part a pencil. Circles can be made by pressing one leg of the compasses into the paper with the spike, putting the pencil on the paper, and moving the pencil around while keeping the hinge on the same angle. The radius of the circle can be adjusted by changing the angle of the hinge. (Fig.1.3) (Fig.1.3)

1.1.4: DRAWING TABLE It is a multi-angle desk which can be used in different angle according to the user requisite. The size suites most paper sizes, and are used for making and modifying drawings on paper with ink or pencil. Different drawing instruments such as set of squares, protractor, etc. are used on it to draw parallel, perpendicular or oblique lines. (Fig.1.4)

(Fig.1.4)

1.1.5: IRREGULAR CURVES (FRENCH CURVES) French curves are used to draw oblique curves other than circles or circular arc; they are irregular set of templates. Many different forms and sizes of curve are available. (Fig.1.5)

(Fig.1.5)

1.1.6: PROTRACTOR Protractor is a circular or semi-circular tool for measuring angles. The units of measurement used are degrees. Some protractors are simple half-discs. More advanced protractors usually have one or two swinging arms, which can be used to help measuring angles. (Fig.1.6)

(Fig.1.6)

1.1.7: DRAWING PENCIL Is a hand-held instrument containing an interior strip of solid material that produces marks used to write and draw, usually on paper. The marking material is most commonly graphite, typically contained inside a wooden sheath. Mechanical pencils are nowadays more commonly used, especially 0.5mm thick (Fig.1.7a/ Fig.1.7b)

(Fig.1.7a)

Fig 7.1b

1.1.8: ERASER Erasers are article of stationery that is used for removing pencil writings. Erasers have made of rubbery material, and they are often white. Typical erasers are made of rubber, but more expensive or specialized erasers can also contain vinyl, plastic, or gum-like materials. (Fig.1.8) (Fig.1.8)

1.2: LINES 1.2.1: LINES AND LINE STYLES 1.2.2: LINE THICKNESS For most engineering drawings you will require two thicknesses, a thick and thin line. The general recommendations are that thick lines are twice as thick as thin lines. A thick continuous line is used for visible edges and outlines. A thin line is used for hatching, leader lines, short centre lines, dimensions and projections.

1.2.3: LINE STYLES Other line styles used to clarify important features on drawings are:

1.2.4: BREAK LINES Short breaks shall be indicated by solid freehand lines. For long breaks, full ruled lines with freehand zigzags shall be used. Shafts, rods, tubes, etc.,

1.2.5: LEADERS Leaders shall be used to indicate a part or portion to which a number, note, or other reference applies and shall be an unbroken line terminating in an arrowhead, dot, or wavy line. Arrowheads should always terminate at a line; dots should be within the outline of an object.

1.2.6: DATUM LINES Datum lines shall be used to indicate the position of a datum plane and shall consist of one long dash and two short dashes, evenly spaced.

1.2.7: PHANTOM LINES Phantom lines shall be used to indicate the alternate position of parts of the item delineated, repeated detail, or the relative position of an absent part and shall be composed of alternating one long and two short dashes, evenly spaced, with a long dash at each end.

1.2.8: STITCH LINES Stitch lines shall be used to indicate the stitching or sewing lines on an article and shall consist of a series of very short dashes, approximately half the length of dash or hidden lines, evenly spaced. Long lines of stitching may be indicated by a series of stitch lines connected by phantom lines.

1.2.9: CENTER LINES Center lines shall be composed of long and short dashes, alternately and evenly spaced, with a long dash at each end. Center lines shall cross without voids. See Figure below, Very short center lines may be unbroken if there is no confusion with other lines. Center lines shall also be used to indicate the travel of a center.

1.2.10: EXTENSION LINES Extension lines are used to indicate the extension of a surface or to point to a location outside the part outline. They start with a short, visible gap from the outline of the part and are usually perpendicular to their associated dimension lines.

1.2.11: OUTLINES OR VISIBLE LINES The outline or visible line shall be used for all lines on the drawing representing visible lines on the object;

1.2.12:CUTTING-PLANE/VIEWING-PLANE LINES The cutting-plane lines shall be used to indicate a plane or planes in which a section is taken. The viewing-plane lines shall be used to indicate the plane or planes from which a surface or surfaces are viewed. On simple views, the cutting planes shall be indicated as shown below

1.2.13: HIDDEN LINES Hidden lines shall consist of short dashes, evenly spaced. These lines are used to show the hidden features of a part. They shall always begin with a dash in contact with the line from which they begin, except when such a dash would form a continuation of a full line. Dashes shall touch at corners, and arcs shall begin with dashes on the tangent points.

1.2.14: SECTIONING LINES Sectioning lines shall be used to indicate the exposed surfaces of an object in a sectional view. They are generally thin full lines, but may vary with the kind of material shown in section.

1.2.15: DIMENSION LINES

Dimension lines shall terminate in arrowheads at each end. They shall be unbroken except where space is required for the dimension. The proper method of showing dimensions and tolerances is explained in Section 1.7 of ANSI Y14.5M-1982.

1.3: DIMENSIONING - AN OVERVIEW A dimensioned drawing should provide all the information necessary for a finished product or part to be manufactured. An example dimension is shown below.

Dimensions are always drawn using continuous thin lines. Two projection lines indicate where the dimension starts and finishes. Projection lines do not touch the object and are drawn perpendicular to the element you are dimensioning. In general units can be omitted from dimensions if a statement of the units is included on your drawing. The general convention is to dimension in mm's. All dimensions less than 1 should have a leading zero. i.e. .35 should be written as 0.35

1.3.1: PARALLEL DIMENSIONING Parallel dimensioning consists of several dimensions originating from one projection line.

1.3.2: SUPERIMPOSED RUNNING DIMENSIONS Superimposed running dimensioning simplifies parallel dimensions in order to reduce the space used on a drawing. The common origin for the dimension lines is indicated by a small circle at the intersection of the first dimension and the projection line. In general all other dimension lines are broken. The dimension note can appear above the dimension line or in-line with the projection line.

1.3.3: CHAIN DIMENSIONING Chains of dimension should only be used if the function of the object won't be affected by the accumulation of the tolerances. (A tolerance is an indication of

the accuracy the product has to be made to. Tolerance will be covered later in this chapter).

1.3.4: COMBINED DIMENSIONS A combined dimension uses both chain and parallel dimensioning.

1.3.5: DIMENSIONING BY CO-ORDINATES Two sets of superimposed running dimensions running at right angles can be used with any features which need their centre points defined, such as holes.

1.3.6: SIMPLIFIED DIMENSIONING BY CO-ORDINATES It is also possible to simplify co-ordinate dimensions by using a table to identify features and positions.

1.3.7: DIMENSIONING SMALL FEATURES

When dimensioning small features, placing the dimension arrow between projection lines may create a drawing which is difficult to read. In order to clarify dimensions on small features any of the above methods can be used.

1.3.8: DIMENSIONING CIRCLES

All dimensions of circles are proceeded by this symbol; . There are several conventions used for dimensioning circles: (a) Shows two common methods of dimensioning a circle. One method dimensions the circle between two lines projected from two diametrically opposite points. The second method dimensions the circle internally. (b) Is used when the circle is too small for the dimension to be easily read if it was placed inside the circle. A leader line is used to display the dimension. (c) The final method is to dimension the circle from outside the circle using an arrow which points directly towards the centre of the circle. The first method using projection lines is the least used method. But the choice is up to you as to which you use.

1.3.9: DIMENSIONING HOLES

When dimensioning holes the method of manufacture is not specified unless they necessary for the function of the product. The word hole doesn't have to be added unless it is considered necessary. The depth of the hole is usually indicated if it isn't indicated on another view. The depth of the hole refers to the depth of the

1.3.10: DIMENSIONING RADII Cylindrical portion of the hole and not the bit of the hole caused by the tip of the drip. All radial dimensions are proceeded by the capital R. All dimension arrows and lines should be drawn perpendicular to the radius so that the line passes through the centre of the arc. All dimensions should only have one arrowhead which should point to the line being dimensioned. There are two methods for dimensioning radii. (a) Shows a radius dimensioned with the centre of the radius located on the drawing. (b) Shows how to dimension radii which do not need their centres locating.

1.3.11: SPHERICAL DIMENSIONS The radius of a spherical surface (i.e. the top of a drawing pin) when dimensioned should have an SR before the size to indicate the type of surface.

1.3.12: TOLERANCE It is not possible in practice to manufacture products to the exact figures displayed on an engineering drawing. The accuracy depends largely on the manufacturing process used and the care taken to manufacture a product. A tolerance value shows the manufacturing department the maximum permissible variation from the dimension. Each dimension on a drawing must include a tolerance value. This can appear either as:  

A general tolerance value applicable to several dimensions. i.e. a note specifying that the General Tolerance +/- 0.5 mm. or a tolerance specific to that dimension

The method of expressing a tolerance on a dimension as recommended by the British standards is shown below:

Note the larger size limit is placed above the lower limit.

All tolerances should be expressed to the appropriate number to the decimal points for the degree of accuracy intended from manufacturing, even if the value is limit is a zero for example.

1.4: LINE STYLES Line styles are used to clarify important features on drawings, and they are as shown below. (Fig.1.9)

FIGURE 1.9 – Line styles and types Line styles are used to graphically represent physical objects, and each has its own meaning, these include the following:     

Visible lines - are continuous lines used to draw edges directly visible from a particular angle. Hidden lines- are short-dashed lines that may be used to represent edges that are not directly visible. Centerlines - are alternately long- and short-dashed lines that may be used to represent the axis of circular features. Cutting plane - are thin, medium-dashed lines, or thick alternately longand double short-dashed that may be used to define sections for section views. Section lines - are thin lines in a parallel pattern used to indicate surfaces in section views resulting from "cutting." Section lines are commonly referred to as "cross-hatching."

FIGURE 1.10 Here is an example of an engineering drawing (Fig.1.10). The different line types are colored for clarity. Black = object line and hatching. Red = hidden lines Blue = center lines Magenta = phantom line or cutting plane Fig.1.10 – Illustrating types of Lines used in an engineering Drawing.

1.5: TASK (1) Using the right drawing tools copy the drawings shown in Fig. 1.11 to 1.14:

Fig.1.11

Fig.1.12

Fig. 1.13

Fig. 1.14

WEEK 2: 2.0

PLANNING YOUR ENGINEERING DRAWING

2.1: PLANNING YOUR ENGINEERING DRAWING Before starting your engineering drawing you should plan how you are going to make best use of the space. It is important to think about the number of views your drawing will have and how much space you will use of the paper.    

Try to make maximum use of the available space. If a view has lots of detail, try and make that view as large as possible. If necessary, draw that view on a separate sheet. If you intend to add dimensions to the drawing, remember to leave enough space around the drawing for them to be added later. If you are working with inks on film, plan the order in which you are drawing the lines. For example you don't want to have to place your ruler on wet ink

2.2: LAYOUT OF DRAWING PAPER It is important that you follow some simple rules when producing an engineering drawing which although may not be useful now, will be useful when working in industry. All engineering drawings should feature an information box (title block).

BOADER LINE (MARGINS)

TITLE BLOCK

2.3: COMMON INFORMATION RECORDED ON THE TITLE BLOCK 2.3.1. TITLE:The title of the drawing.

2.3.2. NAME:The name of the person who produced the drawing. This is important for quality control so that problems with the drawing can be traced back to their origin.

2.3.3. CHECKED In many engineering firms, drawings are checked by a second person before they are sent to manufacture, so that any potential problems can be identified early.

2.3.4. VERSION Many drawings will get amended over the period of the parts life. Giving each drawing a version number helps people identify if they are using the most recent version of the drawing.

2.3.5. DATE The date the drawing was created or amended on.

2.3.6. SCALE The scale of the drawing. Large parts won't fit on paper so the scale provides a quick guide to the final size of the product.

2.3.7. PROJECTION SYSTEM The projection system used to create the drawing should be identified to help people read the drawing. (Projection systems will be covered later).

2.3.8. COMPANY NAME / INSTITUTION NAME Many CAD drawings may be distributed outside the company so the company name is usually added to identify the source.

2.3.9. MATRIC NO (Reg. no) / LEVEL / DEPARTMENT This part is for student’s identification for exams records

2.4. TITLE BLOCK SAMPLE

KADUNA POLYTECHNIC MECHANICAL ENGINEERING DEPARTMENT DRAWING NO

5

SCALE

1:150

DATE

MATRIC NO

KPT/COE/ 07/0056

I. A. HARUNA

02/05/08

LEVEL

100

T. I. GARBA / A.A. GIRBO

03/05/08

CLASS

ORTHOGRAPHIC PROJECTION NAME

SIGN

DRAWN BY CHECHED BY

ND I A

2.5: DRAWING SHEETS/PAPERS The standard sizes of drawing papers used for normal purposes should be as follows: Designation size in millimeters A0 841 x 1189 A1 594 x 841 A2 420 x 594 A3 297 x 420 A4 210 x 297 A5 148 x 210 A6 105 x 148 A0

A2

A1 A4 A3

A6 A5

A6

2.6: DRAWINGS SCALES Generally, it is easier to produce and understand a drawing if it represent the true size of the object drawn. This is of course not always possible due to the size of the object to be drawn, that is why it is often necessary to draw enlargements of very small objects and reduce the drawing of very large ones, this is called “SCALE”. However, it is important when enlarging or reducing a drawing that all parts of the object are enlarged or reduced in the same ratio, so the general configuration of the object is saved. Thus, scales are multiplying or dividing of dimensions of the object. The scale is the ratio between the size represented on the drawing and the true size of the object.

Scale= Dimension to carry on the drawing ÷ True Dimension of the object. Examples: 1. Dimension carried on the drawing = 4mm. True dimension= 40mm Scale = 4 ÷ 40 = 1:10 2. Calculating drawing dimension of a line having a true dimension of 543 mm to a scale of 1/10.   

If a true dimension of 10mm is represented as 1mm, a true dimension of 543mm is represented as X Then 10 mm ---------------- 1 mm 543 mm---------------- X mm We have 1/10= x ÷ 543 or X= 54.3mm.

Therefore, a true dimension of 543mm is represented to a scale of 1/10 by a length of 54.3mm.

2.6.1: AN EXAMPLE OF SCALING A DRAWING

2.7: LETTERING METHODS Lettering is more as freehand drawing and rather of being writing. Therefore the six fundamental strokes and their direction for freehand drawing are basic procedures for lettering.

There are a number of necessary steps in learning lettering, and they include the following:  Knowledge of proposition and form of letters and the orders of the stroke.  Knowledge of the composition the spacing of letters and words.  Persistent practices. Capital letters are preferred to lower case letters since they are easier to read on reduced size drawing prints although lower case letters are used where they from of a symbol or an abbreviation. Attention is drawn the standard to the letters and characters. Table (2.1) below give the recommendation for minimum size on particular drawing sheets:

Application

Drawing Sheets Size

Drawing numbers, etc. Dimension and notes

Minimum character height

A0, A1, A2 and A3 A4 A0 A1, A2, A3 and A4

5 mm 3 mm 3.5 mm 2.5 mm

Table (2.1) Recommendations for minimum size of lettering on drawing sheets

The spaces between lines of lettering should be consistent and preferably not less than half of the character height. There are two fundamental methods of writing the graphic languages freehand and with instruments. The direction of pencil movements are shown in Fig. 2.1 and Fig.2.2.

Fig. (2.1)Vertical Capital Letters & Numerals

Fig.(2.2) – Vertical lower case letter.

2.8

TASK (2):

On a drawing sheet copy the following text in Fig (2.3) using the correct lettering methods:

Fig (2.3)

WEEK 33.1: GEOMETRICAL DRAWINGS 3.1.1. Point: It is a non-dimensional geometrical element. It is occurred by Interception of various lines. 3.1.2. Line: It is a 1D geometrical element occurred by moving of a point in various direction. The picture below illustrates lines, drawn in various directions, and other geometrical elements occurred by these lines. 3.1.3. Plane: A plane is occurred by at least three points or connection of one point and one line. A plane is always 2D. When the number of element forming a plane increases, shape and name of the plane will change.

3.2: STRAIGHT LINES AND ANGLES

3.1

Fig. 3.4

Fig. 3.5 Fig. 3.2

Fig. 3.3

Fig. 3.6

Fig 3.7

Fig 3.9

Fig 3.8

Fig 3.10

Fig 3.11

Fig 3.12

Fig 3.13

3.3: TRIANGLE The triangle is a plane figure bounded by three straight sides, the connection of three points at certain conditions form triangle. A

Triangle 3 Point

B

C

There different type of triangles such as: 1. Scalene triangle: is a triangle with three unequal sides 2. Isosceles triangle: is a triangle with two sides and hence two angles equal. 3. Equilateral triangle: is a triangle with all the sides and hence all the three angles equal. 4. Right-angled triangle: is a triangle containing one right angle. The side opposite the right-angle is called the hypotenuse.

Scalene triangle

Isosceles triangle

Right-angled triangle

Equilateral triangle

3.3.1: CONSTRUCTION OF TRIANGLES

Fig. 3.14

Fig. 3.15

Fig. 3.16 Fig. 3.16

3.4

TASK (3)

1. 2. 3.

Construct the following using a pairs of compasses:- 900, 600, 300, 450, 67.50, and 150 Line AB is 120mm long divide this line into Ratio 5:3:7. Construct a perpendicular line to line AB 60mm long from a point P 30mm above the line and 35mm from B. Construct an equilateral triangle with sides 60 mm long. Construct an isosceles triangle that has a perimeter of 135 mm and an altitude of 55 mm. Construct a triangle with base angles 60° and 45° and an altitude of 76 mm. Construct a triangle with a base of 55 mm, an altitude of 62 mm and a vertical angle of 371/2°. Construct a triangle with a perimeter measuring 160 mm and sides in the ratio 3:5:6. Construct a triangle with a perimeter of 170 mm-and sides in the ratio 7:3:5. Construct a triangle given that the perimeter is 115 mm, the altitude is 40 mm and the vertical angle is 45°.

4. 5 6 7. 8. 9. 10.

WEEK 4 3.5: QUADRILATERALS QUADRILATERALS: A

quadrilateral is a plane figure bounded by four straight sides, the connection of four points at certain conditions form quadrilaterals. A

D

Square 4 Point

Fig 4.1 B

C

Below are some examples of quadrilaterals: 3.5.1. square is a quadrilateral with all four sides of equal length and all its angles are right angles. 3.5.2. rectangle is a quadrilateral with its opposite sides of equal length and all its angles a right angle. 3.5.3. parallelogram is a quadrilateral with opposite sides equal and therefore parallel. 3.5.4. rhombus is a quadrilateral with all four sides equal. 3.5.5trapezium is a quadrilateral with one pair of opposite sides parallel. 3.5.6. trapezoid is a quadrilateral with all four sides and angles unequal. SQUARE

RECTANGLE

a

b

PARALELLOGRA M

c Fig 4.2

. RHOMBUS

TRAPEZIUM

d

e

TRAPEZOID f

3.6: Construction of quadrilaterals 3.6.1 Construction of a Parallelogram given two sides and an angle. 1. 2. 3. 4. 5.

Draw AD equal to the length of one of the sides. From A construct the known angle. Mark off AB equal in length to the other known side With compass point at B draw an arc equal in radius to AD. With compass point at D draw an arc equal in radius to AB. ABCD is the required parallelogram

Fig 4.3

Fig. 4.4 Fig. 4.5

Fig. 4.6

3.7: CIRCLES A circle is a locus of a point which moves so that its always a fixed distance from another stationary point. The connection of infinite points at certain conditions form circle.

Circle Infinite point

A Concentric circles

3.7.1: PROPERTIES OF A CIRCLE

Eccentric circles

Types of circles

NOMAL

3.7.2: Construction involving circles

To draw a tangent to a circle from any point on the circumference. 1. Draw the radius of the circle. 2. at any point on the circumference of the circle, the tangent and then radius are perpendicular to each other. Thus the tangent is found by constructing an angle of 900 from the point where the radius crosses the circumference.

TASK 4 1. 2. 3.

4 5

Construct a square of side 50 mm. Find the mid-point of each side by construction and join up the points with straight lines to produce a second square. Construct a square whose diagonal is 68 mm. 12. Construct a square whose diagonal is 85 mm. Construct a parallelogram given two sides 42 mm and 90 mm long, and the angle between them 67°. 14. Construct a rectangle which has a diagonal 55 mm long and one side 35 mm long. Construct a rhombus if the diagonal is 75 mm long and one side is 44 mm long. Construct a trapezium given that the parallel sides are 50 mm and 80 mm long and are 45 mm apart.

WEEK 5 3.7.3: CONSTRUCTIONS INVOLVING CIRCLES 5.1.1. To construct the circumference of a circle, given the diameter. 1.

2. 3. 4. 5.

Draw a semi circle of the given diameter AB, center O. From B mark off three times the diameter, BC. From O draw a line at 300 to OA to meet the semi circle in D. From D draw a line perpendicular to OA to meet OA in E. Join EC, EC is the required circumference.

FIG. 5.1

5

FIG. 5.2

FIG. 5.3

4.0: TANGENCY 4.1: CONSTRUCTION OF TANGENT

To construct a tangent from a point P to a circle, center O 1. 2.

Joint OP. Erect a semi-circle on to cut the circle in A. PA produced is the required tangent.

FIG. 5.4

5.0: POLYGONS A polygon is a plane figure bounded by more than four straight sides. There are two classes of polygons, regular and irregular polygons. A regular polygon is one that has all its sides equal and therefore all its exterior angles equal and its interior angles equal. An irregular polygon is the one that has unequal sides and also unequal angles (both interior and exterior). Polygons are frequently referred to have particular names. Some of these are listed below. A pentagon is a plane figure bounded by five sides. A hexagon is a plane figure bounded by six sides. A heptagon is a plane figure bounded by seven sides. An octagon is plane figure bounded by eight sides. A nonagon is a plane figure bounded by nine sides. A decagon is a plane figure bounded by ten sides. Etc.

pentagon

octagon

hexagon

CONSTRUCTION OF POLYGONS:

Fig. 5.8 Fig. 5.7

Fig 5.9 Fig. 5.10

Method 3: 1. 2. 3. 4. 5.

6. 7. 8.

Draw a line GA equal in length to one of the side Bisect GA. From A construct an angle of 450 to intersect the bisector at point 4. From G construct an angle of 600 to intersect the bisector at point 6. Bisect between points 4 and 6 to give point 5. Point 4 is the centre of a circle containing a square: point 5 is a the centre of a circle containing a pentagon. Point 6 is the centre of a circle containing a hexagon. By marking off points at similar distances the centers of circles containing any regular polygon can be obtained. Mark off point 7 so that 6 to 7 = 5 to 6 etc. With centre at point 7 draw a circle, radius 7 to A (=7 to G). Step off the sides of the figure from A to B, B to C, etc. ABCDEFG is the required heptagon. Fig. 5.11

Fig. 5.12

5.2: TASK SHEET 5 1. 2.

3.

4 5

Construct a regular hexagon, 45 mm side. Construct a regular hexagon if the diameter is 75 mm. 19. Construct a regular hexagon within an 80 mm diameter circle. The corners of the hexagon must all lie on the circumference of the circle. Construct a square, side 100 mm. Within the square, construct a regular octagon. Four alternate sides of the octagon must lie on the sides of the square. 21. Construct the following regular polygons: a pentagon, side 65 mm, a heptagon, side 55 mm, a nonagon, side 45 mm, a decagon, side 35 mm. Construct a regular pentagon, diameter 82 mm. Construct a regular heptagon within a circle, radius 60 mm. The corners of the heptagon must lie on the circumference of the circle.

WEEK 6 6.0: ELLIPSE: An ellipse is the locus of a point which moves so that its distance from a fixed point (called the focus) bears a constant ratio, always less than 1, to its perpendicular distance from a straight line (called directrix).

6.1

PROPERTIES OF AN ELLIPSE:

An ellipse has two foci, major axis, minor axis and two directrices. Fig. 6.1

6.2

CONSTRUCTIONS OF ELLIPSE: A.

To construct an ellipse using concentric circles method. 1. Draw two concentric circles, radii = half (1/2) major and half (1/2) minor axes. 2. divide the circle into a number of sectors. (12 0r 8). 3. where the sector lines cross the smaller circle, draw the horizontal lines cross the larger circle, draw the vertical line to meet the horizontal lines. 4. draw a neat curve through the intersections.

B.

Fig. 6.2

To construct an ellipse using rectangular method. 1. Draw a rectangle, length and breadth equal to the major and minor axes 2. Divide the two shorter sides of the rectangle in the same even numbers of equal parts. Fig. 6.3 Divide the major axis into the same number of equal parts. 3. from the points where the minor axis crosses the edge of the rectangle, draw the intersecting lines as shown in figure 6.3 4. Draw a neat curve through the intersections.

C.

To construct an ellipse using trammel method. A trammel is a piece of stiff paper or card with a straight edge. 1. Mark the trammel with a pencil so that half the major and minor axes are marked from the point P Fig. 6.4

2. keep B on the minor axis ,A on the major axis and slide the trammel. 3. mark at frequent intervals the position of P. Figure 6.4 shows the trammel in position for plotting the top half of the ellipse; to plot the bottom half , A stays on the major axis and B goes above the major axis, still on the minor axis.

Fig. 6.5

D.

To construct the normal and the tangent of an ellipse, and to find the foci. 1. 2.

3.

Normal: Normal at any point P. Draw two lines from P, one to each focus and bisect the angle thus formed. This bisector is a normal to the ellipse. Tangent: Tangent at any point P. since the tangent and normal are perpendicular to each other by definition, construct the normal and erect a perpendicular to it from P. this perpendicular is the tangent. Foci: Foci with compasses set at a radius of half (1/2) major axis, center at the point where the minor axis crosses the top (or the bottom) of the ellipse, strike an arc to cut the major axis twice, these are the foci.

TANGENT

TANGE NT Fig. 6.6

FOCI FO CI

TASK SHEET 6 1.

Fig. T6.1 shows an elliptical fish-pond for a small garden. The ellipse is 1440 mm long and 720 mm wide. Using a scale of 1/12 draw a true elliptical shape of the pond. (Do not draw the surrounding stones.) All construction must be shown.

FIG. T6.1

2

Fig. T6.2 shows a section, based on an ellipse, for a handrail which requires cutting to form a bend so that the horizontal overall distance is increased from 112 mm to 125 mm. Construct the given figures and show the tangent construction at P and P1. Show the true shape of the cut when the horizontal distance is increased from 112 mm to 125 mm.

FIG T6.2

WEEK 7: 7.0: ISOMETRIC PROJECTION Isometric is a mathematical method of constructing a three dimensional (3D) object without using perspective. Isometric was an attempt to make drawings more and more realistic. The mathematics involved mean that all lengths when drawn at 30 degrees can be drawn using their true length. An isometric drawing shows two sides of the object and the top or bottom of the object (FIG. 7.1). All vertical lines are drawn vertically, but all horizontal lines are drawn at 30 degrees to the horizontal. Isometric is an easy method of constructing a reasonable 3D images.

(Fig. 7.1) 7.1

HOW TO DRAW IN ISOMETRIC PROJECTION:

To draw in isometric you will need a 30/60 degree set square (FIG. 7.2). Follow the steps below to draw a box in isometric. (Fig. 7.2)

1. Draw the Front vertical edge of the cube

2. The sides of the box are drawn at 30 degrees to the horizontal to the required length.

3. Draw in the back verticals

4. Drawn in top view with all lines drawn 30 degrees to the horizontal

Note: All lengths are drawn as actual lengths in standard isometric. Figures 7.3 to 7.6 illustrate four (4) isometric pictorial drawing of components, study the drawing and by using scale 1:1 re-draw them. Note: All dimensions are in mm

Fig. 7.3

Fig. 7.5

Fig. 7.4

Fig. 7.6

TASK SHEET (7) Figures T7.1 to T7.4 shows four (4) isometric pictorial drawing of components, study the drawing and by using proper drawing tools and scale 1:1 re-draw the isometric pictorial drawings. Note: All dimensions are in mm

Fig. T7.1

Fig.T7.2

Fig. T7.3

Fig. T7.4

WEEK 8 8.0: ORHTOGRAPHIC PROJECTION Orthographic projection is a mean of representing a three-dimensional object (Fig.8.1) in two dimensions (2D). It uses multiple views of the object, from points of view rotated about the object's center through increments of 90°. The views are positioned relative to each other according to either of two schemes: first-Angle or third-Angle projection. In each, the appearances of views may be thought of as being projected onto planes that form a transparent "box" around the object. Figure (8.2) demonstrate the views of an object using 1St. Angle and 3rd. Angle projections.

(Fig. 8.1)- Orthographic projection

Fig. (8.2)- Illustrating the difference between 1st. and 3rd. Angles projection

8.1

THREE VIEW OF AN OBJECT IN FIRST AND THRID

ANGLE OF PROJECTIONS Figures (8.3 to 8.6) shows isometric pictorial drawing of a number of components, study the drawing and using 1st and 3rd angle of projection and a scale of 1:1 draw the following: 

A front view in direction "A".



Side view in direction "B".



Top view in direction "C".

Note: All dimensions are in mm

Fig. (8.3)

Fig. (8.5)

Fig. (8.4)

Fig. (8.6)

8.2

THE MAIN FEATURES OF THE SIX VIEW OF AN OBJECT

8.2.1 INTRODUCTION Any object can be viewed from six mutually perpendicular directions, as shown in Figure (8.7) below. Thus, six views may be drawn if necessary. These six views are always arranged as shown below, which the American National Standard arrangement of views. The top, front, and bottom views line up vertically, while the rear, left-side, front, and right-side views line up horizontally.

Fig. (8.7)

Fig. (8.8) If the front view is imagined to be the object itself, the right-side view is obtained by looking toward the right side of the front view, as shown by the arrow RS. Likewise, if the right-side view is imagined to be the object, the front view is obtained by looking toward the left side of the right-side view, as shown by the arrow F. The same relation exists between any two adjacent views. Obviously, the six views may be obtained either by shifting the object with respect to the observer, as we have seen, or by shifting the observer with respect to the object Fig. (8.8).

8.3

ONE POINT PERSPECTIVE:

Using one point perspective (Fig.8.9), parallel lines converge to one point somewhere in the distance. This point is called the vanishing point (VP). This gives objects an impression of depth.

(Fig.8.9) The sides of an object diminish towards the vanishing point. All vertical and horizontal lines though are drawn with no perspective. I.e. face on. One point perspective though is of limited use, the main problem being that the perspective is too pronounced for small products making them looking bigger than they actually are. (Fig 8.10) (Fig 8.10)

Although it is possible to sketch products in one point perspective, the perspective is too aggressive on the eye making products look bigger than they actually are.(Fig 8.11).

(Fig 8.11)

8.4

TWO POINT PERSPECTIVE

Two Points Perspective is a much more useful drawing system than the simpler One Point Perspective. Objects drawn in two point perspective have a more natural look (Fig 8.12). In two point perspective the sides of the object vanish to one of two vanishing points on the horizon. Vertical lines in the object have no perspective applied to them. By altering the proximity of the vanishing points to the object, you can make the object look big or small (Fig. 8.13).

(Fig. 8.12 )

(Fig 8.13) Fig (8.13) – Shows affect of different locations of Vanishing Points

8.5

THREE POINT PERSPECTIVE

Three points perspective is a development of two points perspective. Like two point it has two vanishing points somewhere on the horizon. But three points perspective also has a vanishing point somewhere above or below the horizon which the vertical vanish to. The nearer the vanishing point is to the object, the bigger the object looks. Look at these buildings (FIG.8.14), all the vanishing points are too close. This has caused an excessive amount of vertical perspective. Learning how to apply vertical perspective is the key to making your drawings realistic.

(Fig 8.14)

In general most designers create drawings with a vanishing point far below the horizon so that the depth added to the verticals is only slight. In many cases the vanishing point is not even on the paper (FIG. 8.15). Learning how to apply vertical perspective will make your drawings more and more realistic.

(FIG.8.15)

8.6

TASK SHEET (8.1)

Figures (T13a to T13d) shown are isometric pictorial drawings for a number of components, study the drawing and using 1st and 3rd angle of projection with scale of 1:1 draw the following: 

A front view in direction "A".



Side view in direction "B".



Top view in direction "C". Note: All dimensions are in mm

Fig. (T8.1a)

Fig. (T8.1b)

Fig. (T8.3c)

Fig. (T8.4d)

WEEK (9): 8.7

MULTI-VIEWS DRAWING USING 1ST & 3RD ANGLE OF PROJECTION

8.7.1 Multi views projection: Multi views projection is a mean of producing the true shape and dimension of all details of three-dimensional object or two-dimensional plane surface such as tile drawing paper. For this reason, this method of projection is universally used for the production of working drawing, which is intended for manufacturing purposes.

Fig. 9.1- Multi-views projection In multi-views projection, the observer looks directly at each face of the object and draws what can be seen directly (90 Degree rays). Consecutively, other sides are also seen and drawn in the same way (Fig. 9.1).

Hence, there are two system of multi-views projection that is acceptable as British standard (Fig. 9.2), these are known as: 1. First Angle (1st Angle) or European projection. 2. Third Angle (3rd Angle) or American projection.

Fig.9.2- Different Angles of projections

8.8

THE DIFFERENCES BETWEEN 1st & 3rd ANGLE OF PROJECTION

8.8.1 FIRST-ANGLE PROJECTION

In first-angle projection, each view of the object is projected in the direction (sense) of sight of the object, onto the interior walls of the box Fig.9.3.

Fig.9.3

A two-dimensional representation of the object is then created by "unfolding" the box, to view all of the interior walls Fig.9.4.

Fig.9.4

Fig.9.5

8.8.2 THIRD-ANGLE PROJECTION

In third-angle projection, each view of the object is projected opposite to the direction (sense) of sight, onto the (transparent) exterior walls of the box Fig.9.6

Fig.9.6

A two-dimensional representation of the object is then created by unfolding the box, to view all of the exterior walls Fig.9.7.

Fig.9.7

Fig.9.8

8.9 1.

TASK (8.2) Figures T8.2a and T8.2b show two (2) isometric pictorial drawing of components, study the drawing and by using scale 1:1 draw the following: Fig. (T8.2a) use 1st angle of projection draw,1- Front view 2 -Side view 3Top view.

Fig. T8.2a 

Fig (T8.2b) use 3st angle of projection draw,1- Front view 2-Side view view

Fig. T8.2b

3 - Top

2.

Fig T8.2c and T8.2d show two (2) isometric pictorial drawing of components, study the drawing and by using scale 1:1 and third angle of projection draw the following:- Front view- Side view - Top view

Fig T8.2c

Fig T8.2d

WEEK -10 9.0: ABBREVIATIONS AND SYMBOLS USED ON MECHANICAL AND ELECTRICAL DRAWINGS. 9.1: INTRODUCTION There is a number of common engineering terms and expression, which are frequently replaced by abbreviation or symbols on drawing, to save space and drafting time. This will include the electrical, electronic, pneumatic and hydraulic symbols (Table – 10.1).

9.2: TECHNICAL DRAWING SYMBOLS

Table (10.1)

9.3: MECHANICAL CONVENTION There are many common engineering features which are difficult to draw in full. In order to save drafting time and spaces on drawing, these features are represented in simple conventional form as show in Table 10.2 below.

Table (10.2)

9.4: ELECTRICAL CONVENTION

Table (10.3)

9.5: LINE AND BLOCK DIAGRAMS Engineering Diagrams usually indicate the only relative positions of inter-connected components or systems represented their relevant diagrams.

9.5.1: BLOCK DIAGRAM METHOD Block diagram indicates simple form as to functional system where a number of blocks represent the elements of that system- Fig. 10.1.

Fig. (10.1)

9.5.2: LINE DIAGRAM METHOD

Fig. (10.2) The diagram indicates the standard symbols representing the functional components and connection disregarding their physical size or position Fig. (10.2).

9.6: PNEUMATIC SYSTEM The pneumatic system is a mechanical system that uses pressurized gas (usually air) to perform various kinds of control processes. The pneumatic system consist of pressure generator set, pressure actuated component like (cylinder & vales).Fig.10.3. The use of pneumatic system has been come very popular especially in the food industry for in easy maintenance and running cost. Fig. (10.3)- Air pump

9.7: HYDRAULIC SYSTEM The hydraulic system is a mechanical system that uses pressurized liquid (usually oil) to perform various kinds of control processes Fig. (10.4). The pressurized liquid in a hydraulic system circulates I close loop.

Fig.(10.4)- Hydraulic Jack

9.8: PNEUMATIC SYMBOLS - (FIG.10.5)

9.9

TASK (10)

1) The drawing in Figure (10.6) illustrates assembled mechanical parts, study the drawing then list the items below accordingly.

Fig. (10.6) 2) The drawing in Figure (10.7) illustrates a pneumatic/Hydraulic diagram, study the drawing then list the items in a tabular form below accordingly.

Figure (10.7)

3) The drawing in Figure (10.8) illustrates an electrical circuit, study the drawing and then list the items below accordingly.

Figure (87) Figure (10.8)

WEEK11: 10.0 MISSING VIEW In orthographic projection, the object has principle dimensions, width, height, and depth which are fixed terms used for dimensions of the three views. Note that the front view shows only the height and width of the object, the top view shows the depth and width only. In fact, any one view of three-dimensional object can show only two dimensions, the third dimension will be found in an adjacent view Fig. (11.1).

Fig. (11.1). Note that:    

The top view is the same width as front view. The top view is placed directly above or below the front view depending on the angle of projection (1st or 3rd). The same relation exists between front and side view, same height. The side view is placed directly right or left to the front view, (right side view or left side view).

10.1

FIRST ANGLE OF PROJECTION:

The Fig. (11.2) is a pictorial drawing of given object, three-views of which are required using first angle of projection. Each corner of the object is given a number as shown. At I the top view and the front view are shown, with each corner properly numbered in both views. Each number appears twice, once in the top view and again front view.

Fig. (11.2) At I point 1 is visible in both views, therefore placed outside the corner in both views. however point 2 is visible in the top view and number is placed outside, while in the front view it is invisible and placed inside.

10.2

THIRD ANGLE OF PROJECTION:

Fig. (11.3)

Fig. (11.4)

Fig (11.5)

Fig (11.6)

10.3 TASK SHEET (11) Complete the drawing shown in Fig (T11) to produce the third missing view

Fig. T11

WEEK (12): 11.0 FREEHAND SKETCHING 11.1 INTRODUCTION: Free-hand sketching is used extensively during the early design phases as an important tool for conveying ideas, guiding the thought process, and serving as documentation. Unfortunately there is little computer support for sketching. The first step in building a sketch understanding system is generating more meaningful descriptions of free-hand. One of the advantages of freehand sketching is it require only few simple items such as 1. Pencil (soft pencil i.e. HB). 2. Paper (A3 & A4). 3. Eraser. When sketches are made on the field, where an accurate record is required, a sketching pad with clipboard are frequently used (Fig.12.1). Often clipboard is employed to hold the paper.

(Fig. 12.1)

11.2 General notes before sketching: 1. The pencil should be held naturally, about 40mm from general direction of the line down. 2. Place the paper rotated position so the horizontal edge is perpendicular to the natural position of your forearm. 3. When ruled paper is being used for sketching try to locate the sketched line on ruling line (Fig.12.2). 4. Use your imagination and common sense when choosing the most suitable angle of view.

(Fig. 12.2)

1) Demonstration of sketching technique of horizontal and vertical lines (Fig. 12.3)

2) Demonstration the sketching technique of circles (Fig. 12.4)

3) Demonstration the sketching technique of an arc (Fig. 12.5)

4) Demonstration the sketching technique of an ellipse (Fig. 12.6):

5) Demonstration the sketching technique of an arc (Fig. 12.7):

11.3 Task sheet (12) 1) Use A4 sheet with a pencil and try to draw the lines as shown in Fig. T12.1 below.

Fig. T12.1 2) Use A4 sheet with a pencil and try to draw the component shown in Fig. T12.2 below.

Fig. T12.2

WEEK13: 12.0 SKETCHING THE VIEWS FROM AN ACTUAL OBJECT In industry a complete and clear description of the shape and size of an object is necessary to be able to make it. In order to provide all dimensions and information clearly and accurately a number of views are used. To sketch these views from an actual object the following steps should be followed:

1. Look at the object carefully and choose the right position that shows the best three main views (Fig. 13.1).

(Fig. 13.1)

2. Estimate the proportions carefully, sketch lightly the rectangles of views and set them according to the projection method (1st or 3rd angle) chosen. 3. Hold the object, keeping the front view toward you (Fig. 13.2), and then start sketching the front view.

(Fig. 13.2)

4. To get the top view, revolve the object so as to bring the top toward you, then sketch the top view (Fig. 13.3)

(Fig. 13.3)

5. To get the right side view, revolve the object so as to bring the side view in position relative to the front view, and then sketch the side view (Fig. 13.4)

(Fig. 13.4) 6. make sure the relationships between all views are carried out correctly (Fig. 13.5)

(Fig. 13.5)

12.1 OBLIQUE SKETCHING: Another method for pictorial is sketching the oblique sketching. To made an oblique sketch from an actual object follow these steps: 1. hold the object vertically, making sure most circular features in front of you (Fig. 13.6)

(Fig. 13.6) 2. Sketch the front face of the object in suitable proportional dimensions (Fig. 13.7)

(Fig. 13.7) 3. Sketch the receding lines parallel to each other or a convenient angle between (30°45°) with horizontal, these lines may in full length to sketch a caviller oblique or may be one half sizes to sketch cabinet oblique.

(Fig. 13.8) 4. Complete the required sketch as explained for isometric sketch previously.

(Fig. 13.9)

12.2 TASK SHEET 13 Fig. T13 shows an isometric pictorial drawing of a component; study the drawing and then using scale 1:1 draw the following:  An isometric pictorial drawing (freehand).  The following views (freehand).  A front view.  Side view.  Top view. Note: All dimensions are in mm



Fig. T13

WEEK 14

13.0 INTERSECTION AND DEVELOPMENT: When two solid interpenetrate, a line of intersection is formed. Many object are formed by a collection of geometrical shapes such as cubes, cones, spheres, cylinders, prisms, pyramids, etc, and where any two of these shapes meet, some sort of curves of intersections or interpenetrations are formed. It is necessary to be able to draw these curves to complete drawings in orthographic projection or to draw patterns and developments.

Construction: Interpenetration: 13.1

CONSTRUCTION OF SOLID WITH INTERPENETRATION

13.2

Two dissimilar square prisms meeting at right angles. Fig. 14.1

The end elevation shows where corners 1 and 3 meet the larger prism and these are projected across to the front elevation the plan shows where corners 2 and 4 meet the larger prism and this is projected up to the front elevation.

Fig 14.1

13.3 Two dissimilar square prisms meeting at an angle. Fig 14.2 The front elevation shows where corners one 1 and 3 meet the larger prism. The plan shows where corners 2 and 4 meet the larger prism and this is projected down to the front elevation.

3RD ANGLE PROJECTION

Fig 14.2

13.4 Two dissimilar hexagonal prisms meeting at an angle. Fig. 14.3 The front elevation shows corners 3 and 6 meet the larger prism. The plan shows corners 1,2,4, and 5 meet the larger prism and these are projected up to the front elevation.

Fig 14.3

13.5 Two dissimilar cylinders meeting at right angles. Fig.14.4 The smaller cylinder is divided in to 12 equal sector on the front elevation and on plan, the plan shows where these sectors meet the larger cylinder and these intersections are projected down to the front elevation to meet there corresponding sector at 1’,2’,3’,etc

Fig 14.4

3.6

Two dissimilar cylinders meeting at an angle. Fig 14.5 The method is identical with above principle. The smaller cylinder is divided in to 12 equal sector on the front elevation and on plan, the plan shows where these sectors meet the larger cylinder and these intersections are projected down to the front elevation to meet there corresponding sector at 1’,2’,3’,etc Fig 14.5

13.7 TASK SHEET (14)

WEEK 15 14.0 DEVELOPMENT Many articles such as cans, pipes, elbows, boxes, etc are manufactured from thin sheet materials. Generally a template is produced from an orthographic drawing when small quantities are required. The figures below illustrate some of the more commonly used development in pattern marking. An example of an elbow joint is shown developed in fig. 15.1. The length of the circumference has been calculated and divided into twelve equal parts. A part plan, divided into six parts, has the division lines projected up to the joint, then across to the appropriate point on the pattern. It is normal practice on a development drawing to leave the joint along the shortest edge; however, on part B the pattern can be cut more economically if the joint on this half is turned through 180°.

Fig 15.1

A typical interpenetration curve is given in fig. 15.2. The development of part of the cylindrical portion is shown viewed from the inside. The chordal distances on the inverted plan have been plotted on either side of the centre line of the hole, and the corresponding heights have been projected from the front elevation. The method of drawing pattern for the branch is identical to that shown for the two piece elbow in fig. 15.1 An example of radial-line development is given in fig. 15.3. The dimensions required to make the development are the circumference of the base and the slant height of the cone. The chordal distances from the plan view have been used to mark the length of arc required for the pattern; alternatively, for a higher degree of accuracy, the angle can be calculated and then subdivided. In the front elevation, lines 0 1 and 07 are true lengths, and distances OG and OA have been plotted directly onto the pattern. The lines 02 to 06 inclusive are not true lengths, and, where these lines cross the sloping face on the top of the conical frustum, horizontal lines have been projected to the side of the cone and been marked B, C, D, E, and F. True lengths OF, OE, OD, OC, and OB are then marked on the pattern. This procedure is repeated for the other half of the cone. The view

Fig 15.2

on the sloping face will be an ellipse, Part of a square pyramid is illustrated in Fig 15.3 fig. 15.4. The pattern is formed by drawing an arc of radius OA and stepping off around the curve the lengths of the base, joining the points obtained to the apex O. Distances OF The development of part of a hexagonal pyramid is shown in fig. 15.5. The method is very similar to that given in the previous example, but note that lines OB, OC, OD, OE, and OF are true lengths obtained by projection from the elevation. Fig. 15.6 shows an oblique cone which is developed by triangulation, where the surface is assumed to be formed from a series of triangular shapes. The base of the cone is divided into a convenient number of parts (12 in this case) numbered 0-6 and projected to the front elevation with lines drawn up to the apex A. Lines OA and 6A are true-length lines, but the other five shown all slope at an angle to the plane of the paper. The true lengths of lines IA, 2A, 3A, 4A, and 5A are all equal to the hypotenuse of right-angled triangles where the height is the projection of the cone height and the base is obtained from the part plan view by projecting distances 131, B2, B3, B4, and B5 as indicated. Assuming that the join will be made along the shortest edge, the pattern is formed as follows. Start by drawing line 6A, then from A draw an arc on either side of the line equal in length to the true length 5A. From point 6 on the pattern, draw an arc equal to the chordal distance between successive points on the plan view. This curve will intersect the first arc twice at the points marked 5. Repeat by taking the true length of line 4A and swinging another arc from point A to intersect with chordal arcs from points 5. This process is continued as shown on the solution. Fig. 15.7 shows the development of part of an oblique cone where the procedure described above is followed. The points of intersection of the top of the cone with lines 1A, 2A, 3A, 4A, and 5A are transferred to the appropriate true-length constructions, and true-length distances from the apex A are marked on the pattern drawing. A plan and front elevation is given in fig. 15.8 of a transition piece which is formed from two halves of oblique cylinders and two connecting triangles. Fig 15.4 The plan view of the base is divided

into 12 equal divisions, the sides at the top into 6 parts each. Each division at the bottom of the front elevation is linked with a line to the similar division at the top. These lines, P l, Q2, etc., are all the same length. Commence the pattern construction by drawing line S4 parallel to the component. Project lines from points 3 and R, and let these lines intersect with arcs equal to the chordal distances C, from the plan view, taken from points 4 and S. Repeat the process and note the effect that curvature has on the distances between the lines projected from points P, Q, R, and S. After completing the pattern to line Pl, the triangle is added by swinging an are equal to the length B from point P, which intersects with the arc shown, radius A. This construction for part of the pattern is continued as indicated.

Fig. 15.5

Fig 15.7 Fig 15.6

RAD C

14.1 TASK SHEET (15) 1.

Fig T15.1 shows three pipes, each of 50 mm diameter and of negligible thickness, with their axes in the same plane and forming a bend through 90°. Draw: (a) the given view, and (b) the development of pipe K, using TT as the joint line.

Fig T15.1

2.

Fig. T15.2 shows the plan and elevation of a tin-plate dish. Draw the given views and construct a development of the dish showing each side joined to a square base. The plan of the base should be part of the development.

Fig T15.2