Chapter 1 of 8
NCERT Solutions
Lines, Angles, Letters, Dimensioning and Rectilinear Figures
CBSE · Class 11 · Engineering Graphics
NCERT Solutions for Lines, Angles, Letters, Dimensioning and Rectilinear Figures — CBSE Class 11 Engineering Graphics.
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ASSIGNMENT (Lines and Types)
1Draw and write which type of line you will use for drawing the following:
(a) Axis of a Cone
(b) Boundary line
(c) Projection line
(d) Line for short Break
(e) Line for long break
(f) Dimension lineShow solution
Given: Various features of an engineering drawing and the requirement to identify the correct line type for each.
(a) Axis of a Cone: A Chain thin line (long-dash dot, thin) is used for the axis (centre line) of a cone.
(b) Boundary line: A Continuous thick line (visible outlines/boundary lines) is used for the boundary/outline of an object.
(c) Projection line (Extension line): A Continuous thin line is used for projection/extension lines.
(d) Line for Short Break: A Continuous thin line with zigzags (irregular freehand) is used for short break lines.
(e) Line for Long Break: A Thin straight line with zigzags (ruled line with short zigzag) is used for long break lines.
(f) Dimension line: A Continuous thin line (with arrowheads at both ends) is used for dimension lines.
(a) Axis of a Cone: A Chain thin line (long-dash dot, thin) is used for the axis (centre line) of a cone.
(b) Boundary line: A Continuous thick line (visible outlines/boundary lines) is used for the boundary/outline of an object.
(c) Projection line (Extension line): A Continuous thin line is used for projection/extension lines.
(d) Line for Short Break: A Continuous thin line with zigzags (irregular freehand) is used for short break lines.
(e) Line for Long Break: A Thin straight line with zigzags (ruled line with short zigzag) is used for long break lines.
(f) Dimension line: A Continuous thin line (with arrowheads at both ends) is used for dimension lines.
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2What do you understand by the 'order of priority of coinciding lines'?Show solution
Given: The concept of 'order of priority of coinciding lines' in Engineering Graphics.
Explanation:
In engineering drawings, it is common for two or more different types of lines to coincide (fall on the same position). In such cases, a definite order of priority is followed to decide which line should be drawn/shown. The order of priority is:
1. Visible outlines and edges (Continuous thick lines) — highest priority
2. Hidden outlines and edges (Dashed thin lines)
3. Cutting plane lines (Chain thin, thick at ends)
4. Centre lines / Axis lines (Chain thin lines)
5. Lines of symmetry (Chain thin lines)
6. Projection/Extension lines (Continuous thin lines) — lowest priority
This means that if a visible outline coincides with a centre line, the visible outline is drawn and the centre line is omitted at that location.
Explanation:
In engineering drawings, it is common for two or more different types of lines to coincide (fall on the same position). In such cases, a definite order of priority is followed to decide which line should be drawn/shown. The order of priority is:
1. Visible outlines and edges (Continuous thick lines) — highest priority
2. Hidden outlines and edges (Dashed thin lines)
3. Cutting plane lines (Chain thin, thick at ends)
4. Centre lines / Axis lines (Chain thin lines)
5. Lines of symmetry (Chain thin lines)
6. Projection/Extension lines (Continuous thin lines) — lowest priority
This means that if a visible outline coincides with a centre line, the visible outline is drawn and the centre line is omitted at that location.
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3Write full form of 'CAD'. Explain the term 'CAD' in brief.Show solution
Full form of CAD: Computer Aided Design (or Computer Aided Drafting)
Explanation:
CAD stands for Computer Aided Design. It refers to the use of computer software and systems to assist in the creation, modification, analysis, and optimisation of engineering drawings and designs.
- In CAD, a designer uses a computer with specialised software (such as AutoCAD, SolidWorks, CATIA, etc.) to create 2D drawings or 3D models of objects.
- CAD replaces traditional manual drafting on drawing boards.
- It allows precise and accurate drawings to be made quickly.
- Drawings can be stored, retrieved, modified, and reproduced easily.
- CAD is widely used in Mechanical, Civil, Electrical, Electronics, and Architectural engineering.
Explanation:
CAD stands for Computer Aided Design. It refers to the use of computer software and systems to assist in the creation, modification, analysis, and optimisation of engineering drawings and designs.
- In CAD, a designer uses a computer with specialised software (such as AutoCAD, SolidWorks, CATIA, etc.) to create 2D drawings or 3D models of objects.
- CAD replaces traditional manual drafting on drawing boards.
- It allows precise and accurate drawings to be made quickly.
- Drawings can be stored, retrieved, modified, and reproduced easily.
- CAD is widely used in Mechanical, Civil, Electrical, Electronics, and Architectural engineering.
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4How 'CAD' can save time, labour and natural resources?Show solution
Given: The advantages of CAD in saving time, labour, and natural resources.
CAD saves Time:
- Drawings can be created much faster on a computer than by hand.
- Standard components and symbols can be inserted from libraries instantly.
- Modifications and corrections can be made quickly without redrawing.
- Multiple copies of a drawing can be printed in seconds.
CAD saves Labour:
- One CAD operator can do the work that previously required several draughtsmen.
- Repetitive tasks (like copying, mirroring, arraying) are automated.
- Less physical effort is required compared to manual drafting.
CAD saves Natural Resources:
- Paper consumption is greatly reduced as drawings are stored digitally.
- Less use of pencils, erasers, drawing sheets, and other stationery.
- Digital transmission of drawings eliminates the need for physical blueprints, saving paper and printing materials.
- Energy-efficient designs can be analysed and optimised on computer before manufacturing, reducing material waste.
CAD saves Time:
- Drawings can be created much faster on a computer than by hand.
- Standard components and symbols can be inserted from libraries instantly.
- Modifications and corrections can be made quickly without redrawing.
- Multiple copies of a drawing can be printed in seconds.
CAD saves Labour:
- One CAD operator can do the work that previously required several draughtsmen.
- Repetitive tasks (like copying, mirroring, arraying) are automated.
- Less physical effort is required compared to manual drafting.
CAD saves Natural Resources:
- Paper consumption is greatly reduced as drawings are stored digitally.
- Less use of pencils, erasers, drawing sheets, and other stationery.
- Digital transmission of drawings eliminates the need for physical blueprints, saving paper and printing materials.
- Energy-efficient designs can be analysed and optimised on computer before manufacturing, reducing material waste.
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5In which language the Engineers converse with each other and what is their script?Show solution
Answer:
Engineers all over the world converse with each other in the universal language known as 'Engineering Graphics' (also called Engineering Drawing).
Their script consists of:
- Lines of various types (thick, thin, dashed, chain, etc.)
- Symbols and conventions (standard symbols for materials, welds, surface finish, etc.)
- Dimensions and numerals (to specify size and location)
- Letters and notes (written in single-stroke Gothic lettering)
Just as different countries have different spoken languages, Engineering Graphics is understood by all technically trained persons regardless of their nationality, making it a truly universal language.
Engineers all over the world converse with each other in the universal language known as 'Engineering Graphics' (also called Engineering Drawing).
Their script consists of:
- Lines of various types (thick, thin, dashed, chain, etc.)
- Symbols and conventions (standard symbols for materials, welds, surface finish, etc.)
- Dimensions and numerals (to specify size and location)
- Letters and notes (written in single-stroke Gothic lettering)
Just as different countries have different spoken languages, Engineering Graphics is understood by all technically trained persons regardless of their nationality, making it a truly universal language.
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6Fill in the blanks by choosing the correct term. (curved thin line, thin, thin straight line with zigzags, thin continuous thin lines at 45°, thick)
(a) Axis line is drawn as a ... line.
(b) Visible outline is shown graphically as ...
(c) Short break line is shown as ...
(d) Long break line is shown as a ...
(e) Hatching line is shown as ...Show solution
(a) Axis line is drawn as a thin (chain thin / long-dash dot thin) line.
(b) Visible outline is shown graphically as thick (continuous thick line).
(c) Short break line is shown as curved thin line (continuous thin freehand/irregular line).
(d) Long break line is shown as a thin straight line with zigzags.
(e) Hatching line is shown as thin continuous thin lines at 45°.
(b) Visible outline is shown graphically as thick (continuous thick line).
(c) Short break line is shown as curved thin line (continuous thin freehand/irregular line).
(d) Long break line is shown as a thin straight line with zigzags.
(e) Hatching line is shown as thin continuous thin lines at 45°.
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TEST YOURSELF / ASSIGNMENT (Lettering)
1How many types of letters are there?Show solution
Answer:
In Engineering Graphics, letters are broadly classified into two types:
1. Gothic Letters (Single Stroke Gothic):
- (a) Vertical (Upright) Gothic Letters — strokes are vertical
- (b) Inclined (Italic) Gothic Letters — strokes are inclined at 75° to the horizontal
2. Roman Letters:
- (a) Upper case (Capital) Roman Letters
- (b) Lower case (Small) Roman Letters
For Engineering Graphics (as per BIS/ISO standards), Single Stroke Gothic Letters (both vertical and inclined) are recommended because they are simple, clear, and can be drawn quickly.
In Engineering Graphics, letters are broadly classified into two types:
1. Gothic Letters (Single Stroke Gothic):
- (a) Vertical (Upright) Gothic Letters — strokes are vertical
- (b) Inclined (Italic) Gothic Letters — strokes are inclined at 75° to the horizontal
2. Roman Letters:
- (a) Upper case (Capital) Roman Letters
- (b) Lower case (Small) Roman Letters
For Engineering Graphics (as per BIS/ISO standards), Single Stroke Gothic Letters (both vertical and inclined) are recommended because they are simple, clear, and can be drawn quickly.
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2What do you understand by 'letter printing'?Show solution
Answer:
'Letter printing' (also called Lettering) in Engineering Graphics refers to the art of writing letters, numerals, and other characters on engineering drawings in a clear, legible, and uniform manner.
Key points:
- Letters are written using a single stroke of the pencil (no sketching or outlining first).
- The letters must be uniform in shape, size, shade, and spacing.
- Guide lines are drawn lightly (with 4H pencil) to maintain uniform height.
- The purpose is to write notes, dimensions, titles, and other information on the drawing so that it is easily readable by any engineer.
- Good lettering is an essential skill in Engineering Graphics.
'Letter printing' (also called Lettering) in Engineering Graphics refers to the art of writing letters, numerals, and other characters on engineering drawings in a clear, legible, and uniform manner.
Key points:
- Letters are written using a single stroke of the pencil (no sketching or outlining first).
- The letters must be uniform in shape, size, shade, and spacing.
- Guide lines are drawn lightly (with 4H pencil) to maintain uniform height.
- The purpose is to write notes, dimensions, titles, and other information on the drawing so that it is easily readable by any engineer.
- Good lettering is an essential skill in Engineering Graphics.
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3Write the following sentence into Capital and small letters:
"Engineering Graphics is the language of Engineers".Show solution
In Capital Letters:
ENGINEERING GRAPHICS IS THE LANGUAGE OF ENGINEERS
In Small (Lowercase) Letters:
engineering graphics is the language of engineers
*(Note: In practice, these are written using single-stroke Gothic lettering with proper guide lines. Capital letters use two guide lines; small letters use four guide lines — cap line, waist line, base line, and drop line.)*
ENGINEERING GRAPHICS IS THE LANGUAGE OF ENGINEERS
In Small (Lowercase) Letters:
engineering graphics is the language of engineers
*(Note: In practice, these are written using single-stroke Gothic lettering with proper guide lines. Capital letters use two guide lines; small letters use four guide lines — cap line, waist line, base line, and drop line.)*
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4Write the following letters and numerals in the single stroke gothic letters:
"The height of main title may be taken as 6 mm, subtitles as 4 mm and any other title or dimension in 2 mm".Show solution
In Capital (Uppercase) Single Stroke Gothic Letters:
THE HEIGHT OF MAIN TITLE MAY BE TAKEN AS 6 MM, SUBTITLES AS 4 MM AND ANY OTHER TITLE OR DIMENSION IN 2 MM
In Small (Lowercase) Single Stroke Gothic Letters:
the height of main title may be taken as 6 mm, subtitles as 4 mm and any other title or dimension in 2 mm
*(Note: In actual drawing practice, these are drawn carefully between guide lines using a conical blunt pencil with uniform stroke thickness. The numerals 6, 4, 2 are also written in single-stroke Gothic style.)*
THE HEIGHT OF MAIN TITLE MAY BE TAKEN AS 6 MM, SUBTITLES AS 4 MM AND ANY OTHER TITLE OR DIMENSION IN 2 MM
In Small (Lowercase) Single Stroke Gothic Letters:
the height of main title may be taken as 6 mm, subtitles as 4 mm and any other title or dimension in 2 mm
*(Note: In actual drawing practice, these are drawn carefully between guide lines using a conical blunt pencil with uniform stroke thickness. The numerals 6, 4, 2 are also written in single-stroke Gothic style.)*
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5Write the name of guide lines as used for capital letters and for small letters.Show solution
Guide lines for Capital Letters:
Two guide lines are used:
1. Base line — the lower line on which letters rest
2. Cap line — the upper line indicating the top of capital letters
The distance between these two lines equals the height of the capital letter (e.g., 6 mm for main title).
Guide lines for Small (Lowercase) Letters:
Four guide lines are used:
1. Base line — the lower line on which letters rest
2. Waist line — the top of the body of small letters (e.g., a, c, e, m, n, etc.)
3. Cap line (Ascender line) — the top of tall letters (e.g., b, d, f, h, k, l, t)
4. Drop line (Descender line) — the bottom line for letters with descenders (e.g., g, j, p, q, y)
Guide lines are drawn lightly with a 4H pencil and erased after lettering if required.
Two guide lines are used:
1. Base line — the lower line on which letters rest
2. Cap line — the upper line indicating the top of capital letters
The distance between these two lines equals the height of the capital letter (e.g., 6 mm for main title).
Guide lines for Small (Lowercase) Letters:
Four guide lines are used:
1. Base line — the lower line on which letters rest
2. Waist line — the top of the body of small letters (e.g., a, c, e, m, n, etc.)
3. Cap line (Ascender line) — the top of tall letters (e.g., b, d, f, h, k, l, t)
4. Drop line (Descender line) — the bottom line for letters with descenders (e.g., g, j, p, q, y)
Guide lines are drawn lightly with a 4H pencil and erased after lettering if required.
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6What points should be kept in mind while writing single stroke gothic letters?Show solution
Points to be kept in mind while writing Single Stroke Gothic Letters:
1. Letters should be written by a single stroke of pencil; no prior sketching is done.
2. All letters should be uniform in shape, size, stroke, shade, and spacing.
3. The shine and boldness of letters and numerals should be the same throughout.
4. Letters should be legible and uniform in height and width, except for 'I', 'J', 'M', and 'W'.
5. Letters can be written in expanded or compressed form according to available space.
6. The space between two letters must be kept uniform; a gap equal to twice the thickness of the letter stroke is maintained (except for combinations like LT, AV, PA, LY, AT, TV where the gap is reduced).
7. The space between two words should be equal to the width of one letter.
8. The line thickness for small and capital alphabets shall be the same.
9. Guide lines should be drawn with a 4H pencil (thin lines) and unnecessary lines erased after completion.
1. Letters should be written by a single stroke of pencil; no prior sketching is done.
2. All letters should be uniform in shape, size, stroke, shade, and spacing.
3. The shine and boldness of letters and numerals should be the same throughout.
4. Letters should be legible and uniform in height and width, except for 'I', 'J', 'M', and 'W'.
5. Letters can be written in expanded or compressed form according to available space.
6. The space between two letters must be kept uniform; a gap equal to twice the thickness of the letter stroke is maintained (except for combinations like LT, AV, PA, LY, AT, TV where the gap is reduced).
7. The space between two words should be equal to the width of one letter.
8. The line thickness for small and capital alphabets shall be the same.
9. Guide lines should be drawn with a 4H pencil (thin lines) and unnecessary lines erased after completion.
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7How we can write beautiful and legible letters?Show solution
To write beautiful and legible letters, the following practices should be followed:
1. Acquire thorough knowledge of all types of letters — their general shape, proportion, design, and direction of strokes.
2. Learn to compose letters in words with proper and uniform spacing.
3. Practice consistently and conscientiously — regular practice is the key to good lettering.
4. Use guide lines for titles and subtitles; draw them lightly with a 4H pencil.
5. Use a conical blunt pencil (H or HB grade) for lettering to get uniform stroke thickness.
6. Maintain uniform height, width, and spacing of all letters.
7. Write letters with single strokes — do not sketch or outline first.
8. Keep the shine and boldness of all letters the same.
9. Ensure letters are legible — not too compressed or too expanded.
1. Acquire thorough knowledge of all types of letters — their general shape, proportion, design, and direction of strokes.
2. Learn to compose letters in words with proper and uniform spacing.
3. Practice consistently and conscientiously — regular practice is the key to good lettering.
4. Use guide lines for titles and subtitles; draw them lightly with a 4H pencil.
5. Use a conical blunt pencil (H or HB grade) for lettering to get uniform stroke thickness.
6. Maintain uniform height, width, and spacing of all letters.
7. Write letters with single strokes — do not sketch or outline first.
8. Keep the shine and boldness of all letters the same.
9. Ensure letters are legible — not too compressed or too expanded.
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8What is the ratio of height and width in capital letters?Show solution
Answer:
For Capital (Uppercase) Single Stroke Gothic Letters, the standard ratio of height to width is:
This means if the height of a capital letter is 6 units, its width is approximately 5 units.
Exceptions:
- Letter 'I' — has only width equal to the stroke thickness (very narrow)
- Letter 'J' — slightly narrower
- Letter 'M' — width is approximately equal to height (6:6)
- Letter 'W' — width is greater than height (6:8 approximately)
In general, most capital letters have a height-to-width ratio of approximately 6:5.
For Capital (Uppercase) Single Stroke Gothic Letters, the standard ratio of height to width is:
This means if the height of a capital letter is 6 units, its width is approximately 5 units.
Exceptions:
- Letter 'I' — has only width equal to the stroke thickness (very narrow)
- Letter 'J' — slightly narrower
- Letter 'M' — width is approximately equal to height (6:6)
- Letter 'W' — width is greater than height (6:8 approximately)
In general, most capital letters have a height-to-width ratio of approximately 6:5.
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9What is the ratio between height and width of small letters? How we should divide the height for small letters?Show solution
Ratio of Height to Width for Small (Lowercase) Letters:
For small letters, the ratio of total height to width of the body is approximately:
Division of Height for Small Letters:
The total height of small letters is divided into three equal parts using four guide lines:
- **Bottom — for descenders (lower portion, for letters like g, j, p, q, y)
- Middle — the body height (for letters like a, c, e, m, n, o, r, s, u, v, w, x, z)
- Top ** — for ascenders (upper portion, for letters like b, d, f, h, k, l, t)
Thus, four guide lines are needed: drop line, base line, waist line, and cap/ascender line.
For small letters, the ratio of total height to width of the body is approximately:
Division of Height for Small Letters:
The total height of small letters is divided into three equal parts using four guide lines:
- **Bottom — for descenders (lower portion, for letters like g, j, p, q, y)
- Middle — the body height (for letters like a, c, e, m, n, o, r, s, u, v, w, x, z)
- Top ** — for ascenders (upper portion, for letters like b, d, f, h, k, l, t)
Thus, four guide lines are needed: drop line, base line, waist line, and cap/ascender line.
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10How much gap between two letters and two words may be given?Show solution
Gap between two Letters:
The space between two adjacent letters must be kept uniform. A gap equal to twice the thickness of the letter stroke is maintained between two letters.
Special cases:
- For letter combinations like LT, AV, PA, LY, AT, TV — the gap is reduced (less than normal) because these letters have slanting strokes that naturally create visual space.
- For combinations like AWA, ATA, PAT, AVA, AYA — no gap is given between the letters.
Gap between two Words:
The space between two words should be equal to the width of one letter (approximately equal to the height of the letter for capital letters).
The space between two adjacent letters must be kept uniform. A gap equal to twice the thickness of the letter stroke is maintained between two letters.
Special cases:
- For letter combinations like LT, AV, PA, LY, AT, TV — the gap is reduced (less than normal) because these letters have slanting strokes that naturally create visual space.
- For combinations like AWA, ATA, PAT, AVA, AYA — no gap is given between the letters.
Gap between two Words:
The space between two words should be equal to the width of one letter (approximately equal to the height of the letter for capital letters).
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11Explain the rule of spacing between the letters.Show solution
Rules of Spacing between Letters:
1. The space between two letters must be uniform throughout the word.
2. A gap equal to twice the thickness of the letter stroke is normally maintained between two letters.
3. For certain letter combinations — LT, AV, PA, LY, AT, TV — the gap is reduced because the slanting strokes of these letters create an optical illusion of more space. Reducing the gap makes the word look visually uniform.
4. For combinations like AWA, ATA, PAT, AVA, AYA — no gap is given between the letters, as the overlapping slanting strokes fill the visual space.
5. The spacing rule is based on optical uniformity — the letters should appear equally spaced to the eye, even if the actual measured distances differ slightly.
6. The space between two words is equal to the width of one letter.
Purpose: Proper spacing makes the lettering legible, neat, and professional.
1. The space between two letters must be uniform throughout the word.
2. A gap equal to twice the thickness of the letter stroke is normally maintained between two letters.
3. For certain letter combinations — LT, AV, PA, LY, AT, TV — the gap is reduced because the slanting strokes of these letters create an optical illusion of more space. Reducing the gap makes the word look visually uniform.
4. For combinations like AWA, ATA, PAT, AVA, AYA — no gap is given between the letters, as the overlapping slanting strokes fill the visual space.
5. The spacing rule is based on optical uniformity — the letters should appear equally spaced to the eye, even if the actual measured distances differ slightly.
6. The space between two words is equal to the width of one letter.
Purpose: Proper spacing makes the lettering legible, neat, and professional.
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12Write in capital and small letters the following lines:
"The letters and numerals are written with a conical blunt pencil, these consist of horizontal, vertical, inclined and curved strokes to give the required letters."Show solution
In Capital (Uppercase) Letters:
THE LETTERS AND NUMERALS ARE WRITTEN WITH A CONICAL BLUNT PENCIL, THESE CONSIST OF HORIZONTAL, VERTICAL, INCLINED AND CURVED STROKES TO GIVE THE REQUIRED LETTERS.
In Small (Lowercase) Letters:
the letters and numerals are written with a conical blunt pencil, these consist of horizontal, vertical, inclined and curved strokes to give the required letters.
*(Note: In actual drawing practice, these sentences are written carefully between guide lines using single-stroke Gothic lettering with a conical blunt pencil of appropriate grade.)*
THE LETTERS AND NUMERALS ARE WRITTEN WITH A CONICAL BLUNT PENCIL, THESE CONSIST OF HORIZONTAL, VERTICAL, INCLINED AND CURVED STROKES TO GIVE THE REQUIRED LETTERS.
In Small (Lowercase) Letters:
the letters and numerals are written with a conical blunt pencil, these consist of horizontal, vertical, inclined and curved strokes to give the required letters.
*(Note: In actual drawing practice, these sentences are written carefully between guide lines using single-stroke Gothic lettering with a conical blunt pencil of appropriate grade.)*
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TEST YOURSELF (Drawing Instruments)
1Why drawing instruments are needed for drawing?Show solution
Answer:
Drawing instruments are needed for drawing because:
1. They help in making accurate and precise drawings with correct dimensions.
2. They ensure uniformity in line thickness, length, and angles.
3. They save time and effort compared to freehand drawing.
4. They help in drawing standard lines (thick, thin, dashed, chain, etc.) as required by engineering standards.
5. They allow reproducibility — the same drawing can be made again with the same accuracy.
6. Instruments like compasses and dividers help in drawing circles, arcs, and equal divisions accurately.
7. They help maintain cleanliness and neatness of the drawing.
Without proper drawing instruments, it is impossible to make engineering drawings that meet the required standards of accuracy and clarity.
Drawing instruments are needed for drawing because:
1. They help in making accurate and precise drawings with correct dimensions.
2. They ensure uniformity in line thickness, length, and angles.
3. They save time and effort compared to freehand drawing.
4. They help in drawing standard lines (thick, thin, dashed, chain, etc.) as required by engineering standards.
5. They allow reproducibility — the same drawing can be made again with the same accuracy.
6. Instruments like compasses and dividers help in drawing circles, arcs, and equal divisions accurately.
7. They help maintain cleanliness and neatness of the drawing.
Without proper drawing instruments, it is impossible to make engineering drawings that meet the required standards of accuracy and clarity.
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2What is a mini drafter?Show solution
Answer:
A Mini Drafter (also called a Drafting Machine) is a compact drawing instrument that is clamped to the drawing board. It consists of:
- A clamp that fixes it to the top edge of the drawing board.
- A protractor head that can be rotated and locked at any desired angle.
- Two scales (blades) fixed at right angles to each other (one horizontal, one vertical), which can be rotated together to any angle.
Uses of Mini Drafter:
1. It can draw horizontal, vertical, parallel, and inclined lines at any angle.
2. It replaces the need for a Tee-square, set squares, and protractor.
3. It saves time and increases accuracy.
4. Lines can be drawn at any angle by rotating the protractor head.
5. It is especially useful for drawing parallel lines at any inclination quickly.
A Mini Drafter (also called a Drafting Machine) is a compact drawing instrument that is clamped to the drawing board. It consists of:
- A clamp that fixes it to the top edge of the drawing board.
- A protractor head that can be rotated and locked at any desired angle.
- Two scales (blades) fixed at right angles to each other (one horizontal, one vertical), which can be rotated together to any angle.
Uses of Mini Drafter:
1. It can draw horizontal, vertical, parallel, and inclined lines at any angle.
2. It replaces the need for a Tee-square, set squares, and protractor.
3. It saves time and increases accuracy.
4. Lines can be drawn at any angle by rotating the protractor head.
5. It is especially useful for drawing parallel lines at any inclination quickly.
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3Write the important drawing instruments and their uses in drawing.Show solution
Important Drawing Instruments and Their Uses:
| Instrument | Use |
|---|---|
| Drawing Board | Provides a flat, smooth surface to fix the drawing sheet |
| Tee-square | Used to draw horizontal lines; also used as a base for set squares |
| Set Squares (45° and 30°–60°) | Used to draw vertical, inclined lines and angles that are multiples of 15° |
| Compass | Used to draw circles and arcs of required radius |
| Divider | Used to transfer distances, divide lines into equal parts |
| Protractor | Used to measure and draw angles |
| Scale (Ruler) | Used to measure and draw lines of required length |
| Mini Drafter | Used to draw horizontal, vertical, parallel, and inclined lines at any angle |
| French Curves | Used to draw irregular curves |
| Pencils (H, HB, B grades) | Used for drawing lines and lettering |
| Eraser (Rubber) | Used to remove unwanted lines |
| Drawing Pins / Clips | Used to fix drawing sheet to the drawing board |
| Instrument | Use |
|---|---|
| Drawing Board | Provides a flat, smooth surface to fix the drawing sheet |
| Tee-square | Used to draw horizontal lines; also used as a base for set squares |
| Set Squares (45° and 30°–60°) | Used to draw vertical, inclined lines and angles that are multiples of 15° |
| Compass | Used to draw circles and arcs of required radius |
| Divider | Used to transfer distances, divide lines into equal parts |
| Protractor | Used to measure and draw angles |
| Scale (Ruler) | Used to measure and draw lines of required length |
| Mini Drafter | Used to draw horizontal, vertical, parallel, and inclined lines at any angle |
| French Curves | Used to draw irregular curves |
| Pencils (H, HB, B grades) | Used for drawing lines and lettering |
| Eraser (Rubber) | Used to remove unwanted lines |
| Drawing Pins / Clips | Used to fix drawing sheet to the drawing board |
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4What precautions may be taken for drawing a clean and neat drawing?Show solution
Precautions for a Clean and Neat Drawing:
1. Always clean hands and instruments before fixing the drawing sheet.
2. Wipe hands frequently with a clean handkerchief during drawing work.
3. Move set squares lightly with fingernails while using.
4. Clean pencil smudge with a clean cloth.
5. Remove rubbed pencil powder away from the drawing sheet to prevent smudging.
6. Use a soft rubber for erasing only when absolutely necessary.
7. Remove rubber dust with a clean piece of cloth, never with hands.
8. Use a clean piece of cloth or paper as a hand rest while lettering.
9. Do not keep any articles or utensils on the drawing sheet.
10. When not in use, cover the drawing sheet with a cotton cloth or wide paper.
11. Avoid unnecessary rubbing of lines.
12. Do not touch the drawing sheet with direct hands.
1. Always clean hands and instruments before fixing the drawing sheet.
2. Wipe hands frequently with a clean handkerchief during drawing work.
3. Move set squares lightly with fingernails while using.
4. Clean pencil smudge with a clean cloth.
5. Remove rubbed pencil powder away from the drawing sheet to prevent smudging.
6. Use a soft rubber for erasing only when absolutely necessary.
7. Remove rubber dust with a clean piece of cloth, never with hands.
8. Use a clean piece of cloth or paper as a hand rest while lettering.
9. Do not keep any articles or utensils on the drawing sheet.
10. When not in use, cover the drawing sheet with a cotton cloth or wide paper.
11. Avoid unnecessary rubbing of lines.
12. Do not touch the drawing sheet with direct hands.
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5What are the common grades of pencil available in the market? What do the letters on them indicate?Show solution
Common Grades of Pencil:
Pencils are graded based on the hardness or softness of their lead (graphite core). The common grades available are:
Hard pencils: 9H, 8H, 7H, 6H, 5H, 4H, 3H, 2H, H
Medium pencil: HB, F
Soft pencils: B, 2B, 3B, 4B, 5B, 6B, 7B
What the letters indicate:
- H stands for Hard — the higher the H number, the harder the lead and the lighter/thinner the line drawn.
- B stands for Black (Soft) — the higher the B number, the softer the lead and the darker/thicker the line drawn.
- HB stands for Hard Black — a medium grade pencil, neither too hard nor too soft.
- F stands for Fine point — slightly harder than HB.
Use in Engineering Drawing:
- 4H or 6H — for guide lines (very light lines)
- H or 2H — for construction lines and dimension lines
- HB or H — for visible outlines and lettering
Pencils are graded based on the hardness or softness of their lead (graphite core). The common grades available are:
Hard pencils: 9H, 8H, 7H, 6H, 5H, 4H, 3H, 2H, H
Medium pencil: HB, F
Soft pencils: B, 2B, 3B, 4B, 5B, 6B, 7B
What the letters indicate:
- H stands for Hard — the higher the H number, the harder the lead and the lighter/thinner the line drawn.
- B stands for Black (Soft) — the higher the B number, the softer the lead and the darker/thicker the line drawn.
- HB stands for Hard Black — a medium grade pencil, neither too hard nor too soft.
- F stands for Fine point — slightly harder than HB.
Use in Engineering Drawing:
- 4H or 6H — for guide lines (very light lines)
- H or 2H — for construction lines and dimension lines
- HB or H — for visible outlines and lettering
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6What we mean by 'H', 'HB' or 'B' pencil?Show solution
H Pencil:
- 'H' stands for Hard.
- The lead is hard, produces thin, light grey lines.
- Used for construction lines, dimension lines, and guide lines in engineering drawing.
- Higher H numbers (2H, 4H, 6H) are progressively harder.
HB Pencil:
- 'HB' stands for Hard Black.
- It is a medium grade pencil — neither too hard nor too soft.
- Produces medium dark lines.
- Used for outlines, lettering, and general drawing work.
- It is the most commonly used pencil for everyday writing.
B Pencil:
- 'B' stands for Black (Soft).
- The lead is soft, produces thick, dark, bold lines.
- Used for visible outlines and bold lettering in engineering drawing.
- Higher B numbers (2B, 4B, 6B) are progressively softer and darker.
- Not preferred for fine engineering drawing as lines tend to smudge.
- 'H' stands for Hard.
- The lead is hard, produces thin, light grey lines.
- Used for construction lines, dimension lines, and guide lines in engineering drawing.
- Higher H numbers (2H, 4H, 6H) are progressively harder.
HB Pencil:
- 'HB' stands for Hard Black.
- It is a medium grade pencil — neither too hard nor too soft.
- Produces medium dark lines.
- Used for outlines, lettering, and general drawing work.
- It is the most commonly used pencil for everyday writing.
B Pencil:
- 'B' stands for Black (Soft).
- The lead is soft, produces thick, dark, bold lines.
- Used for visible outlines and bold lettering in engineering drawing.
- Higher B numbers (2B, 4B, 6B) are progressively softer and darker.
- Not preferred for fine engineering drawing as lines tend to smudge.
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7What angles can be drawn with a pair of set-squares?Show solution
Angles that can be drawn with a pair of set squares:
A pair of set squares consists of:
- 45°–45°–90° set square
- 30°–60°–90° set square
By using these individually or in combination with each other and the Tee-square, the following angles (multiples of 15°) can be drawn:
How:
- 30° — using 30°–60° set square alone
- 45° — using 45° set square alone
- 60° — using 30°–60° set square alone
- 75° — combining 45° + 30° set squares
- 90° — using either set square against Tee-square
- 105° — combining 60° + 45°
- 120° — using 60° set square
- 135° — using 45° set square
- 150° — using 30° set square
- 15° — combining 45° − 30° set squares
A pair of set squares consists of:
- 45°–45°–90° set square
- 30°–60°–90° set square
By using these individually or in combination with each other and the Tee-square, the following angles (multiples of 15°) can be drawn:
How:
- 30° — using 30°–60° set square alone
- 45° — using 45° set square alone
- 60° — using 30°–60° set square alone
- 75° — combining 45° + 30° set squares
- 90° — using either set square against Tee-square
- 105° — combining 60° + 45°
- 120° — using 60° set square
- 135° — using 45° set square
- 150° — using 30° set square
- 15° — combining 45° − 30° set squares
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8What grade of pencil may be used in compass for a particular grade used for drawing straight line to get the same shine and brightness?Show solution
Answer:
When drawing with a compass, the pencil lead in the compass should be one grade softer than the pencil used for drawing straight lines.
Reason: When drawing with a compass, the lead is held at an angle and the pressure applied is less uniform compared to drawing straight lines. A softer lead compensates for this and produces lines of the same darkness and brightness.
Examples:
- If H pencil is used for straight lines → use HB pencil in compass
- If 2H pencil is used for straight lines → use H pencil in compass
- If HB pencil is used for straight lines → use B pencil in compass
This ensures that the circles and arcs drawn with the compass have the same shade and brightness as the straight lines drawn with the pencil.
When drawing with a compass, the pencil lead in the compass should be one grade softer than the pencil used for drawing straight lines.
Reason: When drawing with a compass, the lead is held at an angle and the pressure applied is less uniform compared to drawing straight lines. A softer lead compensates for this and produces lines of the same darkness and brightness.
Examples:
- If H pencil is used for straight lines → use HB pencil in compass
- If 2H pencil is used for straight lines → use H pencil in compass
- If HB pencil is used for straight lines → use B pencil in compass
This ensures that the circles and arcs drawn with the compass have the same shade and brightness as the straight lines drawn with the pencil.
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9How parallel lines can be drawn with a pair of set squares? Draw parallel lines at a distance of 25 mm.Show solution
Method to draw parallel lines with a pair of set squares:
Given: A line AB, and requirement to draw a line parallel to it at a distance of 25 mm.
Procedure:
1. Place one set square (say the 30°–60° set square) with its hypotenuse along the given line AB.
2. Place the second set square (45° set square) against the vertical side of the first set square, so that it acts as a base/support.
3. Hold the second set square firmly in position.
4. Slide the first set square along the second set square to the required distance (25 mm, measured with a scale).
5. Draw a line along the hypotenuse of the first set square — this line is parallel to AB at a distance of 25 mm.
Result: The new line CD is parallel to AB and at a distance of 25 mm from it.
*(Note: In actual drawing, mark 25 mm distance on a perpendicular from line AB and draw the parallel line through that point using the set square method.)*
Given: A line AB, and requirement to draw a line parallel to it at a distance of 25 mm.
Procedure:
1. Place one set square (say the 30°–60° set square) with its hypotenuse along the given line AB.
2. Place the second set square (45° set square) against the vertical side of the first set square, so that it acts as a base/support.
3. Hold the second set square firmly in position.
4. Slide the first set square along the second set square to the required distance (25 mm, measured with a scale).
5. Draw a line along the hypotenuse of the first set square — this line is parallel to AB at a distance of 25 mm.
Result: The new line CD is parallel to AB and at a distance of 25 mm from it.
*(Note: In actual drawing, mark 25 mm distance on a perpendicular from line AB and draw the parallel line through that point using the set square method.)*
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10Where a divider is used?Show solution
Uses of a Divider:
1. Transferring distances: A divider is used to transfer a distance from one part of the drawing to another without measuring with a scale.
2. Dividing a line into equal parts: A line can be divided into any number of equal parts by trial and adjustment with a divider.
3. Marking equal distances: Equal distances can be stepped off along a line repeatedly.
4. Comparing distances: Two distances can be compared by setting the divider to one distance and checking against the other.
5. Enlarging or reducing distances: Distances can be proportionally enlarged or reduced.
Difference from Compass: A divider has two pointed legs (no pencil), while a compass has one pointed leg and one pencil leg.
1. Transferring distances: A divider is used to transfer a distance from one part of the drawing to another without measuring with a scale.
2. Dividing a line into equal parts: A line can be divided into any number of equal parts by trial and adjustment with a divider.
3. Marking equal distances: Equal distances can be stepped off along a line repeatedly.
4. Comparing distances: Two distances can be compared by setting the divider to one distance and checking against the other.
5. Enlarging or reducing distances: Distances can be proportionally enlarged or reduced.
Difference from Compass: A divider has two pointed legs (no pencil), while a compass has one pointed leg and one pencil leg.
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11Fill in the blanks with appropriate words:
(a) To remove unnecessary lines we use ...
(b) To make an accurate drawing we use ...
(c) To measure angle/angles on a drawing we use ...
(d) We use Tee-square for drawing ... lines
(e) The mini drafter can be used for drawing ...
(f) We use a pair of set squares to draw...
(g) We use ... for drawing circles and arcs.
(h) We use ... for transferring distances, marking a line into equal distances.
(i) A mini-drafter obviates the use of ...Show solution
(a) To remove unnecessary lines we use eraser.
(b) To make an accurate drawing we use instruments.
(c) To measure angle/angles on a drawing we use protractor.
(d) We use Tee-square for drawing horizontal lines.
(e) The mini drafter can be used for drawing vertical, horizontal and inclined lines.
(f) We use a pair of set squares to draw vertical, parallel and inclined lines.
(g) We use Compass for drawing circles and arcs.
(h) We use Divider for transferring distances, marking a line into equal distances.
(i) A mini-drafter obviates the use of Tee-square, Protractor and a scale.
(b) To make an accurate drawing we use instruments.
(c) To measure angle/angles on a drawing we use protractor.
(d) We use Tee-square for drawing horizontal lines.
(e) The mini drafter can be used for drawing vertical, horizontal and inclined lines.
(f) We use a pair of set squares to draw vertical, parallel and inclined lines.
(g) We use Compass for drawing circles and arcs.
(h) We use Divider for transferring distances, marking a line into equal distances.
(i) A mini-drafter obviates the use of Tee-square, Protractor and a scale.
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12Match the following from the list 'A' with 'B'.
Table A:
(a) Straight lines can be drawn with its help
(b) The two parts of the Tee-square are
(c) The distance are measured in millimeters by
(d) Lines of different thickness are drawn by using
(e) Equal distances can be drawn on the drawing sheet by
(f) For measuring any angle we use
(g) We can draw angles in multiple of 15° with this
Table B:
(a) Using a scale
(b) Using a divider
(c) Butt and blade
(d) Set squares
(e) Pencils
(f) Protractor
(g) Tee-squareShow solution
Matched Answers:
| Table A | Table B |
|---|---|
| (a) Straight lines can be drawn with its help | (g) Tee-square |
| (b) The two parts of the Tee-square are | (c) Butt and blade |
| (c) The distances are measured in millimeters by | (a) Using a scale |
| (d) Lines of different thickness are drawn by using | (e) Pencils |
| (e) Equal distances can be drawn on the drawing sheet by | (b) Using a divider |
| (f) For measuring any angle we use | (f) Protractor |
| (g) We can draw angles in multiple of 15° with this | (d) Set squares |
| Table A | Table B |
|---|---|
| (a) Straight lines can be drawn with its help | (g) Tee-square |
| (b) The two parts of the Tee-square are | (c) Butt and blade |
| (c) The distances are measured in millimeters by | (a) Using a scale |
| (d) Lines of different thickness are drawn by using | (e) Pencils |
| (e) Equal distances can be drawn on the drawing sheet by | (b) Using a divider |
| (f) For measuring any angle we use | (f) Protractor |
| (g) We can draw angles in multiple of 15° with this | (d) Set squares |
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ASSIGNMENT (Dimensioning)
1What is a leader line?Show solution
Answer:
A leader line is a thin continuous line used in engineering drawing to connect a note, dimension, or specification to the feature it refers to on the drawing.
Characteristics of a Leader Line:
1. It is a thin continuous line (same thickness as dimension lines).
2. It is drawn at an angle (usually 30°, 45°, or 60° to the horizontal) — never horizontal or vertical.
3. One end terminates with:
- An arrowhead — when it ends on the outline/boundary of the object
- A dot — when it ends inside the object (on a surface)
- No arrowhead — when it ends on a dimension line
4. The other end connects to a horizontal shoulder on which the note or dimension is written.
5. Leader lines should not cross each other and should not be drawn parallel to adjacent dimension lines.
A leader line is a thin continuous line used in engineering drawing to connect a note, dimension, or specification to the feature it refers to on the drawing.
Characteristics of a Leader Line:
1. It is a thin continuous line (same thickness as dimension lines).
2. It is drawn at an angle (usually 30°, 45°, or 60° to the horizontal) — never horizontal or vertical.
3. One end terminates with:
- An arrowhead — when it ends on the outline/boundary of the object
- A dot — when it ends inside the object (on a surface)
- No arrowhead — when it ends on a dimension line
4. The other end connects to a horizontal shoulder on which the note or dimension is written.
5. Leader lines should not cross each other and should not be drawn parallel to adjacent dimension lines.
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2Draw first angle projection symbol.Show solution
First Angle Projection Symbol:
The first angle projection symbol (as per BIS/ISO standards) consists of a truncated cone drawn in two views:
- The front view shows the full circular end of the cone (a circle).
- The side view (placed to the LEFT of the front view in first angle projection) shows the tapered/truncated side of the cone.
Description for drawing:
1. Draw a circle of diameter 'd' (representing the front view — circular end of cone).
2. To the left of this circle, draw the side view of the truncated cone — it appears as a trapezium (wider at left, narrower at right, with the narrow end pointing toward the circle).
3. Both views are enclosed within a rectangle (the title block symbol box).
Note: In first angle projection, the object is placed between the observer and the projection plane. The symbol indicates that the side view is placed on the opposite side from where the observer is looking.
*(In actual drawing practice, this symbol is drawn in the title block of the drawing sheet to indicate the projection method used.)*
The first angle projection symbol (as per BIS/ISO standards) consists of a truncated cone drawn in two views:
- The front view shows the full circular end of the cone (a circle).
- The side view (placed to the LEFT of the front view in first angle projection) shows the tapered/truncated side of the cone.
Description for drawing:
1. Draw a circle of diameter 'd' (representing the front view — circular end of cone).
2. To the left of this circle, draw the side view of the truncated cone — it appears as a trapezium (wider at left, narrower at right, with the narrow end pointing toward the circle).
3. Both views are enclosed within a rectangle (the title block symbol box).
Note: In first angle projection, the object is placed between the observer and the projection plane. The symbol indicates that the side view is placed on the opposite side from where the observer is looking.
*(In actual drawing practice, this symbol is drawn in the title block of the drawing sheet to indicate the projection method used.)*
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3Dimension a circle, concentric circle and an arc of 50 mm radius.Show solution
Dimensioning a Circle:
- The diameter of a circle is dimensioned using the symbol 'Ø' (phi) before the numerical value.
- A dimension line passes through the centre of the circle with arrowheads touching the circle.
- Example: Ø100 (for a circle of 100 mm diameter)
- Alternatively, a leader line with an arrowhead pointing to the circle boundary can be used with the note Ø100.
Dimensioning Concentric Circles:
- Each circle is dimensioned separately.
- Dimension lines are drawn from the centre, and the diameter values are written with the Ø symbol.
- To avoid crowding, leader lines pointing to each circle can be used.
- Example: Inner circle Ø40, Outer circle Ø80.
Dimensioning an Arc of 50 mm radius:
- The radius of an arc is dimensioned using the symbol 'R' before the numerical value.
- A dimension line (leader) is drawn from the centre of the arc to the arc, with an arrowhead at the arc end.
- The dimension is written as R50.
- The dimension line for radius always starts from the centre of the arc (or points toward the centre if the centre is outside the drawing area).
- The diameter of a circle is dimensioned using the symbol 'Ø' (phi) before the numerical value.
- A dimension line passes through the centre of the circle with arrowheads touching the circle.
- Example: Ø100 (for a circle of 100 mm diameter)
- Alternatively, a leader line with an arrowhead pointing to the circle boundary can be used with the note Ø100.
Dimensioning Concentric Circles:
- Each circle is dimensioned separately.
- Dimension lines are drawn from the centre, and the diameter values are written with the Ø symbol.
- To avoid crowding, leader lines pointing to each circle can be used.
- Example: Inner circle Ø40, Outer circle Ø80.
Dimensioning an Arc of 50 mm radius:
- The radius of an arc is dimensioned using the symbol 'R' before the numerical value.
- A dimension line (leader) is drawn from the centre of the arc to the arc, with an arrowhead at the arc end.
- The dimension is written as R50.
- The dimension line for radius always starts from the centre of the arc (or points toward the centre if the centre is outside the drawing area).
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4Dimension an acute, obtuse and a right angled triangle.Show solution
Dimensioning Triangles:
Acute Triangle:
- Dimension the base with a dimension line below the base (with extension lines and arrowheads).
- Dimension the other two sides with dimension lines parallel to each respective side.
- Dimension the angles using arc symbols at the vertices with the angle value written alongside.
- Alternatively, dimension the altitude with a dimension line perpendicular to the base.
Obtuse Triangle:
- Dimension the base with a dimension line below the base.
- Dimension the sides with dimension lines parallel to each side.
- The obtuse angle is dimensioned with an arc at the obtuse vertex.
- Extension lines are drawn perpendicular to the dimension lines.
Right Angled Triangle:
- Dimension the base (MN) with a dimension line below the base.
- Dimension the altitude (MO) with a dimension line to the left/right of the altitude.
- Dimension the hypotenuse (ON) with a dimension line parallel to the hypotenuse.
- The right angle (90°) is indicated by a small square symbol at the right angle vertex — it need not be dimensioned numerically.
*(Note: All dimension lines are thin continuous lines with arrowheads; extension lines do not touch the object outline but leave a small gap of about 1 mm.)*
Acute Triangle:
- Dimension the base with a dimension line below the base (with extension lines and arrowheads).
- Dimension the other two sides with dimension lines parallel to each respective side.
- Dimension the angles using arc symbols at the vertices with the angle value written alongside.
- Alternatively, dimension the altitude with a dimension line perpendicular to the base.
Obtuse Triangle:
- Dimension the base with a dimension line below the base.
- Dimension the sides with dimension lines parallel to each side.
- The obtuse angle is dimensioned with an arc at the obtuse vertex.
- Extension lines are drawn perpendicular to the dimension lines.
Right Angled Triangle:
- Dimension the base (MN) with a dimension line below the base.
- Dimension the altitude (MO) with a dimension line to the left/right of the altitude.
- Dimension the hypotenuse (ON) with a dimension line parallel to the hypotenuse.
- The right angle (90°) is indicated by a small square symbol at the right angle vertex — it need not be dimensioned numerically.
*(Note: All dimension lines are thin continuous lines with arrowheads; extension lines do not touch the object outline but leave a small gap of about 1 mm.)*
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5Explain the necessity of dimensioning.Show solution
Necessity of Dimensioning:
Dimensioning is an essential part of engineering drawing because:
1. Specifies Size: Dimensions tell the manufacturer the exact size (length, width, height, diameter, radius, angle) of each feature of the object. 2. Specifies Location: Dimensions specify the exact position/location of features (holes, slots, bosses) relative to each other or to a reference. 3. Enables Manufacturing: Without dimensions, a craftsman or machinist cannot manufacture the part to the correct size. 4. Ensures Interchangeability: Proper dimensioning with tolerances ensures that parts made at different places can be assembled together (interchangeability). 5. Avoids Ambiguity: Dimensions remove any doubt about the size and shape of the object. 6. Facilitates Inspection: Quality control inspectors use dimensions to check whether the manufactured part meets the design requirements. 7. Universal Communication: Dimensions make the drawing universally understandable regardless of the scale of the drawing.
Dimensioning is an essential part of engineering drawing because:
1. Specifies Size: Dimensions tell the manufacturer the exact size (length, width, height, diameter, radius, angle) of each feature of the object. 2. Specifies Location: Dimensions specify the exact position/location of features (holes, slots, bosses) relative to each other or to a reference. 3. Enables Manufacturing: Without dimensions, a craftsman or machinist cannot manufacture the part to the correct size. 4. Ensures Interchangeability: Proper dimensioning with tolerances ensures that parts made at different places can be assembled together (interchangeability). 5. Avoids Ambiguity: Dimensions remove any doubt about the size and shape of the object. 6. Facilitates Inspection: Quality control inspectors use dimensions to check whether the manufactured part meets the design requirements. 7. Universal Communication: Dimensions make the drawing universally understandable regardless of the scale of the drawing.
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6What is the difference between 'Aligned' and 'Uni-directional' system?Show solution
Aligned System:
1. In the aligned system, dimensions are placed parallel to the dimension line.
2. The dimension figures are written so that they can be read from the bottom or from the right side of the drawing sheet.
3. Horizontal dimensions are read from the bottom; vertical dimensions are read from the right side.
4. Dimensions on inclined dimension lines are written parallel to the inclined line.
5. This system is preferred for large drawings where the drawing sheet may be rotated for reading.
Uni-directional System:
1. In the uni-directional system, all dimensions are written in one direction only — horizontally, so that they can be read from the bottom of the drawing sheet.
2. Dimension lines are broken near the middle to accommodate the dimension figure.
3. All dimensions — horizontal, vertical, and inclined — are written horizontally.
4. This system is preferred for small drawings and is easier to read without rotating the drawing sheet.
5. It is the recommended system as per BIS standards for modern engineering drawings.
Key Difference: In the aligned system, the reader may need to rotate the drawing to read some dimensions; in the uni-directional system, all dimensions are read from one direction (bottom) without rotating.
1. In the aligned system, dimensions are placed parallel to the dimension line.
2. The dimension figures are written so that they can be read from the bottom or from the right side of the drawing sheet.
3. Horizontal dimensions are read from the bottom; vertical dimensions are read from the right side.
4. Dimensions on inclined dimension lines are written parallel to the inclined line.
5. This system is preferred for large drawings where the drawing sheet may be rotated for reading.
Uni-directional System:
1. In the uni-directional system, all dimensions are written in one direction only — horizontally, so that they can be read from the bottom of the drawing sheet.
2. Dimension lines are broken near the middle to accommodate the dimension figure.
3. All dimensions — horizontal, vertical, and inclined — are written horizontally.
4. This system is preferred for small drawings and is easier to read without rotating the drawing sheet.
5. It is the recommended system as per BIS standards for modern engineering drawings.
Key Difference: In the aligned system, the reader may need to rotate the drawing to read some dimensions; in the uni-directional system, all dimensions are read from one direction (bottom) without rotating.
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7What are two systems of dimensioning?Show solution
The two systems of dimensioning are:
1. Aligned System:
- Dimensions are written parallel to the dimension line.
- Horizontal dimensions are read from the bottom; vertical dimensions from the right side.
- The dimension is placed above the dimension line, in the middle.
2. Uni-directional System:
- All dimensions are written horizontally (in one direction).
- All dimensions are read from the bottom of the drawing sheet.
- The dimension line is broken near the middle to insert the dimension figure.
- This is the preferred/recommended system as per BIS/ISO standards.
1. Aligned System:
- Dimensions are written parallel to the dimension line.
- Horizontal dimensions are read from the bottom; vertical dimensions from the right side.
- The dimension is placed above the dimension line, in the middle.
2. Uni-directional System:
- All dimensions are written horizontally (in one direction).
- All dimensions are read from the bottom of the drawing sheet.
- The dimension line is broken near the middle to insert the dimension figure.
- This is the preferred/recommended system as per BIS/ISO standards.
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8What system is adopted to dimension a drawing of large size such as a ship drawing?Show solution
Answer:
For dimensioning a drawing of large size such as a ship drawing, the Aligned System of dimensioning is adopted.
Reason:
- In large drawings, the drawing sheet may be too large to read all dimensions from one direction.
- The aligned system allows dimensions to be read by rotating the drawing sheet, which is practical for large drawings.
- Dimensions are placed parallel to the dimension line, so they can be read from the bottom or from the right side, making it convenient for large-format drawings.
- The uni-directional system is more suitable for small to medium-sized drawings where all dimensions can be conveniently read from the bottom.
For dimensioning a drawing of large size such as a ship drawing, the Aligned System of dimensioning is adopted.
Reason:
- In large drawings, the drawing sheet may be too large to read all dimensions from one direction.
- The aligned system allows dimensions to be read by rotating the drawing sheet, which is practical for large drawings.
- Dimensions are placed parallel to the dimension line, so they can be read from the bottom or from the right side, making it convenient for large-format drawings.
- The uni-directional system is more suitable for small to medium-sized drawings where all dimensions can be conveniently read from the bottom.
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9How a narrow space is dimensioned?Show solution
Dimensioning a Narrow Space:
When the space between extension lines is too narrow to accommodate the dimension figure and arrowheads, the following methods are used:
1. Arrowheads outside, dimension inside: The arrowheads are placed outside the extension lines (pointing inward), and the dimension figure is written between the extension lines.
2. Arrowheads and dimension outside: Both the arrowheads and the dimension figure are placed outside the extension lines. A small dot or tick mark may be used instead of arrowheads.
3. Leader line method: A leader line is drawn from the narrow space to a clear area where the dimension is written.
4. Staggered dimensions: When several narrow dimensions are adjacent, they are staggered (placed alternately above and below) to avoid crowding.
5. Oblique arrowheads: Very small oblique strokes (ticks) may be used instead of arrowheads when space is very limited.
When the space between extension lines is too narrow to accommodate the dimension figure and arrowheads, the following methods are used:
1. Arrowheads outside, dimension inside: The arrowheads are placed outside the extension lines (pointing inward), and the dimension figure is written between the extension lines.
2. Arrowheads and dimension outside: Both the arrowheads and the dimension figure are placed outside the extension lines. A small dot or tick mark may be used instead of arrowheads.
3. Leader line method: A leader line is drawn from the narrow space to a clear area where the dimension is written.
4. Staggered dimensions: When several narrow dimensions are adjacent, they are staggered (placed alternately above and below) to avoid crowding.
5. Oblique arrowheads: Very small oblique strokes (ticks) may be used instead of arrowheads when space is very limited.
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10How dimension is written for an oblique line?Show solution
Dimensioning an Oblique (Inclined) Line:
In Aligned System:
- The dimension line is drawn parallel to the oblique line.
- Extension lines are drawn perpendicular to the dimension line (i.e., perpendicular to the oblique line).
- The dimension figure is written parallel to the dimension line (i.e., at the same inclination as the oblique line).
In Uni-directional System:
- The dimension line is drawn parallel to the oblique line.
- Extension lines are drawn perpendicular to the dimension line.
- The dimension line is broken near the middle, and the dimension figure is written horizontally (readable from the bottom of the sheet).
Note: The true length of the oblique line is dimensioned, not its horizontal or vertical projection.
In Aligned System:
- The dimension line is drawn parallel to the oblique line.
- Extension lines are drawn perpendicular to the dimension line (i.e., perpendicular to the oblique line).
- The dimension figure is written parallel to the dimension line (i.e., at the same inclination as the oblique line).
In Uni-directional System:
- The dimension line is drawn parallel to the oblique line.
- Extension lines are drawn perpendicular to the dimension line.
- The dimension line is broken near the middle, and the dimension figure is written horizontally (readable from the bottom of the sheet).
Note: The true length of the oblique line is dimensioned, not its horizontal or vertical projection.
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11What type of extension and dimension line is? Show them on an equilateral triangle.Show solution
Extension Line:
- An extension line is a thin continuous line drawn from the feature being dimensioned, extending beyond the dimension line.
- It is drawn perpendicular to the dimension line.
- It does not touch the outline of the object — a small gap of about 1 mm is left between the object outline and the start of the extension line.
- Extension lines extend about 2–3 mm beyond the dimension line.
Dimension Line:
- A dimension line is a thin continuous line drawn parallel to the feature being dimensioned.
- It has arrowheads at both ends, touching the extension lines.
- The dimension figure is written above the dimension line (aligned system) or the line is broken and the figure written in the gap (uni-directional system).
- Dimension lines should be at least 8 mm away from the object outline and from each other.
On an Equilateral Triangle (e.g., side = 60 mm):
- For the base: extension lines are drawn vertically downward from both ends of the base; a horizontal dimension line is drawn below with arrowheads; '60' is written above the dimension line.
- For the left side: extension lines are drawn perpendicular to the left side; a dimension line parallel to the left side is drawn with arrowheads; '60' is written.
- For the right side: similarly dimensioned.
- All three sides show the dimension '60' with proper extension and dimension lines.
- An extension line is a thin continuous line drawn from the feature being dimensioned, extending beyond the dimension line.
- It is drawn perpendicular to the dimension line.
- It does not touch the outline of the object — a small gap of about 1 mm is left between the object outline and the start of the extension line.
- Extension lines extend about 2–3 mm beyond the dimension line.
Dimension Line:
- A dimension line is a thin continuous line drawn parallel to the feature being dimensioned.
- It has arrowheads at both ends, touching the extension lines.
- The dimension figure is written above the dimension line (aligned system) or the line is broken and the figure written in the gap (uni-directional system).
- Dimension lines should be at least 8 mm away from the object outline and from each other.
On an Equilateral Triangle (e.g., side = 60 mm):
- For the base: extension lines are drawn vertically downward from both ends of the base; a horizontal dimension line is drawn below with arrowheads; '60' is written above the dimension line.
- For the left side: extension lines are drawn perpendicular to the left side; a dimension line parallel to the left side is drawn with arrowheads; '60' is written.
- For the right side: similarly dimensioned.
- All three sides show the dimension '60' with proper extension and dimension lines.
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12Dimension a rectangle according to aligned system.Show solution
Dimensioning a Rectangle — Aligned System:
Given: Rectangle MNOP with length = 80 mm and width = 50 mm (example values).
Procedure:
1. Draw the rectangle MNOP.
2. For the length (horizontal dimension):
- Draw extension lines vertically downward from M and N (leaving a 1 mm gap from the outline).
- Draw a horizontal dimension line below the rectangle (at least 8 mm from the outline) between the two extension lines, with arrowheads touching the extension lines.
- Write the dimension '80' above the dimension line, parallel to it (readable from the bottom).
3. For the width (vertical dimension):
- Draw extension lines horizontally to the right from N and O (leaving a 1 mm gap).
- Draw a vertical dimension line to the right of the rectangle (at least 8 mm from the outline) between the two extension lines, with arrowheads.
- Write the dimension '50' above the dimension line, parallel to it (readable from the right side).
Result: The rectangle is fully dimensioned in the aligned system with length and width clearly indicated.
Given: Rectangle MNOP with length = 80 mm and width = 50 mm (example values).
Procedure:
1. Draw the rectangle MNOP.
2. For the length (horizontal dimension):
- Draw extension lines vertically downward from M and N (leaving a 1 mm gap from the outline).
- Draw a horizontal dimension line below the rectangle (at least 8 mm from the outline) between the two extension lines, with arrowheads touching the extension lines.
- Write the dimension '80' above the dimension line, parallel to it (readable from the bottom).
3. For the width (vertical dimension):
- Draw extension lines horizontally to the right from N and O (leaving a 1 mm gap).
- Draw a vertical dimension line to the right of the rectangle (at least 8 mm from the outline) between the two extension lines, with arrowheads.
- Write the dimension '50' above the dimension line, parallel to it (readable from the right side).
Result: The rectangle is fully dimensioned in the aligned system with length and width clearly indicated.
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13Dimension a rectangle according to the uni-directional system.Show solution
Dimensioning a Rectangle — Uni-directional System:
Given: Rectangle MNOP with length = 80 mm and width = 50 mm (example values).
Procedure:
1. Draw the rectangle MNOP.
2. For the length (horizontal dimension):
- Draw extension lines vertically downward from M and N.
- Draw a horizontal dimension line below the rectangle with arrowheads.
- Break the dimension line near the middle and write '80' horizontally in the gap (readable from the bottom).
3. For the width (vertical dimension):
- Draw extension lines horizontally to the right from N and O.
- Draw a vertical dimension line to the right of the rectangle with arrowheads.
- Break the dimension line near the middle and write '50' horizontally in the gap (readable from the bottom — NOT rotated).
Key difference from Aligned System: In the uni-directional system, the dimension '50' for the vertical side is written horizontally (not vertically), so all dimensions are read from the bottom of the sheet without rotating it.
Given: Rectangle MNOP with length = 80 mm and width = 50 mm (example values).
Procedure:
1. Draw the rectangle MNOP.
2. For the length (horizontal dimension):
- Draw extension lines vertically downward from M and N.
- Draw a horizontal dimension line below the rectangle with arrowheads.
- Break the dimension line near the middle and write '80' horizontally in the gap (readable from the bottom).
3. For the width (vertical dimension):
- Draw extension lines horizontally to the right from N and O.
- Draw a vertical dimension line to the right of the rectangle with arrowheads.
- Break the dimension line near the middle and write '50' horizontally in the gap (readable from the bottom — NOT rotated).
Key difference from Aligned System: In the uni-directional system, the dimension '50' for the vertical side is written horizontally (not vertically), so all dimensions are read from the bottom of the sheet without rotating it.
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14(a)Fill in the blank: Two recommended systems of placing a dimension on the drawing are ... and ...Show solution
Two recommended systems of placing a dimension on the drawing are Aligned and Uni-directional.
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14(b)Fill in the blank: Dimension lines should be drawn at least 8 mm away from the ... and from ...Show solution
Dimension lines should be drawn at least 8 mm away from the Outline and from each other.
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14(c)Fill in the blank: The two main types of dimensions used on a drawing are ...Show solution
The two main types of dimensions used on a drawing are location and size (dimensions).
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14(d)Fill in the blank: Projection line, dimension line, leader line and dimension itself on a drawing are called ... of ...Show solution
Projection line, dimension line, leader line and dimension itself on a drawing are called Elements of dimensioning.
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14(e)Fill in the blank: The hatching lines are continuous ... Lines, and are drawn at an ... of ... an outline of the section.Show solution
The hatching lines are continuous thin lines, and are drawn at an angle of 45° to an outline of the section.
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14(f)Fill in the blank: A dimension is a numerical value expressed in appropriate units of measurement and indicated graphically on a technical drawing with ..., ... and ...Show solution
A dimension is a numerical value expressed in appropriate units of measurement and indicated graphically on a technical drawing with Line, symbol, and note.
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14(g)Fill in the blank: All dimensions on the single drawing should be expressed in the ... units.Show solution
All dimensions on the single drawing should be expressed in the same units.
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14(h)Fill in the blank: All dimensions are shown from a common base line in ... dimensioning.Show solution
All dimensions are shown from a common base line in Progressive or parallel dimensioning.
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14(i)Fill in the blank: No dimension should be written twice on a drawing until unless it is ...Show solution
No dimension should be written twice on a drawing until unless it is unavoidable.
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14(j)Fill in the blank: A dimension given for information only is written as a ...Show solution
A dimension given for information only is written as a note.
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14(k)Fill in the blank: Two principal requirements of engineering graphics are to specify ... and ...Show solution
Two principal requirements of engineering graphics are to specify Shape and size.
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14(l)Fill in the blank: Dimension of cylinder should never be given as a ...Show solution
Dimension of cylinder should never be given as a R (radius). It should always be given as diameter (Ø).
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14(m)Fill in the blank: Generally we prefer a single unit of measurement is in ...Show solution
Generally we prefer a single unit of measurement is in Millimeter (mm).
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14(n)Fill in the blank: A leader line end on a dimension line without a ...Show solution
A leader line end on a dimension line without a Arrowhead.
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14(o)Fill in the blank: A leader line end on a surface of an object in an ...Show solution
A leader line end on a surface of an object in an Arrowhead.
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14(p)Fill in the blank: A leader line end inside an object in a ...Show solution
A leader line end inside an object in a Dot.
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14(q)Fill in the blank: An ... or ... should never be used as a dimension line.Show solution
An Outline or axis should never be used as a dimension line.
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14(r)Fill in the blank: When a number of parallel dimensions are to be shown near each other, the dimensions should be ...
ASSIGNMENT ON LINES AND ANGLES
1To divide a straight line AB = 78 mm into two equal parts.
2To divide a straight line AB = 78 mm into four equal parts with compasses.
3On a line MN = 80 mm draw angles of (a) 72° (b) 36° and (c) 18° (without using protractor)
4Draw a line 'MN' parallel to a given line 'OP' at a distance of 57 mm, with the help of (a) compasses (b) set squares.
5To divide a straight line MN = 86 mm into six equal parts.
6With the help of compasses draw the following angles:
(a) 60° (b) 30° (c) 15° (d) 90° (e) 45° (f) 75°, 120° (g) 135° (h) 150°
(a) 60° (b) 30° (c) 15° (d) 90° (e) 45° (f) 75°, 120° (g) 135° (h) 150°
7Geometrically draw an angle equal to the difference of two given angles of 74° and 35°.
8Geometrically draw an angle equal to the sum of two given angles of 74° and 35°.
9To divide an angle of 70° into two equal parts with the help of compasses.
10Two converging lines 'MN' and 'OP', converging at an angle of 67°. Draw an angle bisector of these converging lines without producing them to meet.
11Two points O, P are given outside a line MN. Find a point 'C' on the line MN such that OC = PC.
12A point 'O' is given outside the line 'MN'. Draw a perpendicular line from it without producing the line 'MN'.
ASSIGNMENT ON TRIANGLES
1To construct an isosceles triangle MNO such that its base angle is twice the vertical angle (a) with protractor (b) with compass (c) by dividing a semicircle.
2To construct a right angle triangle MNO, having its altitude MO = 45 mm and the vertical angle ∠MON = 30°.
3To construct a right angle triangle MNO, having its base MN = 50 mm and its altitude MO = 55 mm.
4To construct a right angle triangle MNO, having its altitude MO = 40 mm and its hypotenuse ON = 60 mm.
5A median of triangle MNO is 50 mm and it makes an angle of 50° with its base, 55° with the side of the triangle.
6Construct a right angle Δ MNO, having its base edge = 55 mm and the base angle ∠MNO = 30°.
7Construct a right angle Δ MNO, having its hypotenuse ON = 60 mm, and the distance of the hypotenuse from the right angle = 25 mm.
8Construct a right angle Δ MNO, having its hypotenuse ON = 65 mm and the median from the angular point O, making the angle ∠ODN with the hypotenuse = 40°.
9Construct a right angle Δ MNO, having its hypotenuse ON = 70 mm and the difference of its hypotenuse and one side = 30 mm.
10Construct an isosceles triangle MNO having its base MN = 40 mm and each of its sides = 60 mm.
11Construct a right angle Δ MNO, having its hypotenuse ON = 70 mm and the difference of the sides = 22 mm.
12Construct a right angle Δ MNO, having its altitude ON = 47 mm and the sum of the hypotenuse and its base = 70 mm.
13Construct an isosceles Δ MNO, having each of its sides = 60 mm and each of its base angle = 50°.
14Construct a right angle triangle MNO, having hypotenuse ON = 60 mm and the sum of its base and its altitude = 55 mm.
15Construct an isosceles Δ MNO, having its altitude OD = 45 mm and each of its base angle = 50°.
16Construct an isosceles Δ MNO, having its base MN = 40 mm and its altitude AD = 50 mm.
17Construct an isosceles Δ MNO, having its vertical angle = 40° and the base MN = 50 mm.
18Construct an isosceles Δ MNO, having its altitude OD = 45 mm, and its vertical angle = 45°.
19Construct an isosceles Δ MNO, having its side = 60 mm and its vertical angle = 1/3 of base angle.
20Construct an isosceles Δ MNO, having its perimeter = 70 mm and its altitude OD = 30 mm.
21Construct an isosceles right angle Δ MNO, having its perimeter = 70 mm.
22Construct an isosceles Δ MNO, having its base MN = 40 mm and each of its base angle twice of the vertical angle.
23Construct an isosceles right angle Δ MNO, having the sum of its hypotenuse and one side = 60 mm.
24Construct an isosceles Δ MNO, having its base MN = 50 mm and the sum of its altitude and one side = 60 mm.
25Construct a triangle MNO, having given its base MN = 70 mm, altitude OM = 40 mm and side OD = 55 mm.
26Construct a triangle MNO, having its base MN = 55 mm, side ON = 45 mm and side NM = 55 mm.
27Construct a triangle MNO, having its altitude OD = 40 mm, side ON = 50 mm and side OM = 45 mm.
28Construct a Δ MNO, having its altitude OD = 40 mm, side ON = 50 mm and side OM = 45 mm.
29Construct a triangle MNO, having its base MN = 70 mm, the side ON = 45 mm and included angle = 60°.
30Construct a Δ MNO, having its base MN = 55 mm and its angles are in the ratio of 4 : 6 : 8.
31Construct a Δ MNO, having its perimeter = 100 mm and its sides in the ratio of 3 : 5 : 4.
32Construct a Δ MNO, having its base MN = 50 mm, the difference of the other two sides = 15 mm and the base angle = 60°.
33Construct a Δ MNO having its perimeter = 70 mm and its angles in the ratio of 5 : 6 : 7.
TRY THESE (Quadrilaterals)
1Construct a square with side = 65 mm.
2Construct a rhombus whose diagonals are 55 mm and 70 mm.
3Construct a quadrilateral MORE with MO = 60 mm, OR = 45 mm, ∠M = 60°, ∠O = 105° and ∠R = 105°.
4Construct a parallelogram ABCD with AB = 50 mm, BC = 60 mm and ∠D = 85°.
ASSIGNMENT ON QUADRILATERALS
1Construct a rectangle MNOP, having its base MN = 60 mm and its sides NO = 40 mm.
2Construct a rectangle MNOP, having its diagonal MO = 70 mm and the difference of its sides = 25 mm.
3Construct a parallelogram MNOP having its diagonal MO = 50 mm, and the diagonal NP = 40 mm and the included angle OQN = 60°.
4Construct a rectangle MNOP having each of its diagonals = 70 mm and the included angle between them = 45°.
5Construct a rhombus MNOP having its one side = 50 mm and the included angle ∠PMN = 60°.
6Construct a trapezium MNOP having MO, the difference of its diagonal = 30 mm.
7Construct a trapezium MNOP, having its sides MP = 40 mm and side PO = 30 mm and side ON = 40 mm and the difference of the parallel side = 25 mm.
ASSIGNMENT (Regular Polygons)
1Construct a regular pentagon of side 25 mm.
2Construct a regular hexagon of side 30 mm.
3Construct a regular Octagon of side 25 mm.
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