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Engineering drawing

Basant Agrawal, C. M. Agrawal

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ENGINEERING DRAWING Second Edition  ABOUT THE AUTHORS Basant Agrawal obtained his BE and MTech. from Maulana Azad National Institute of Technology Bhopal, and PhD from Indian Institute of Technology Delhi. He is awarded the Gold Medal in MTech. by Rajiv Gandhi Technical University Bhopal and the 'Promising Research Award 2010' from BAG Energy Research Society Varanasi. Presently, he is Assistant Professor in the Department of Mechanical Engineering at Shri Govindram Seksaria Institute of Technology and Science, Indore. He has over 12 years of teaching experience at undergraduate and postgraduate level. His broad areas of interest include thermal engineering, heat transfer, solar energy and passive building design. He has published over 35 research papers in various international/national journals and conferences. He is a life member of Indian Society for Technical Education, Institution of Engineers (India) and International Association of Engineers (IAENG). C M Agrawal obtained his BE from BIT Sindri, MTech. and PhD from Indian Institute of Technology Kharagpur. He received the 'Best Application Oriented Research Paper Award' at AIMTDR Jadavpur University, in 1988. Presently, he is Dean, Students Welfare and Senior Professor in the Department of Mechanical Engineering at Maulana Azad National Institute of Technology Bhopal. He has over 43 years of teaching experience at undergraduate and postgraduate level and guiding research scholars. His broad areas of interest include engineering drawing, industrial and production engineering. He has published over 50 research papers in various international/national journals and conferences. He is honoured to chair the technical session at the IMECS 2012 held in Hong Kong. He is a life member of Institution of Engineers (India) and International Association of Engineers (IAENG). Both the authors have also written the textbook, Engineering Graphics, published by McGraw Hill Education (India).  ENGINEERING DRAWING Second Edition  Basant Agrawal Assistant Professor Dep; artment of Mechanical Engineering Shri Govindram Seksaria Institute of Technology and Science Indore  C M Agrawal Professor and Dean Department of Mechanical Engineering Maulana Azad National Institute of Technology Bhopal  McGraw Hill Education (India) Private Limited NEW DELHI McGraw Hill Education Offices New Delhi New York St Louis San Francisco Auckland Bogotá Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal San Juan Santiago Singapore Sydney Tokyo Toronto  McGraw Hill Education (India) Private Limited Published by McGraw Hill Education (India) Private Limited P-24, Green Park Extension, New Delhi 110 016 Engineering Drawing 2e Copyright © 2014, 2008 by McGraw Hill Education (India) Private Limited. No part of this publication may be reproduced or distributed in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise or stored in a database or retrieval system without the prior written permission of the publishers. The program listings (if any) may be entered, stored and executed in a computer system, but they may not be reproduced for publication. This edition can be exported from India only by the publishers, McGraw Hill Education (India) Private Limited ISBN-13: 978-1-25-906288-9 ISBN-10: 1-25-906288-0 Vice President and Managing Director: Ajay Shukla Head—Higher Education Publishing and Marketing: Vibha Mahajan Publishing Manager—SEM & Tech Ed.: Shalini Jha Sr. Editorial Researcher: Harsha Singh Manager—Production Systems: Satinder S. Baveja Copy Editor: Preyoshi Kundu Production Executive: Anuj K Sriwastava Asst. General Manager—Higher Education Marketing: Vijay Sarathi Product Specialist: Sachin Tripathi Sr. Graphic Designer—Cover: Meenu Raghav General Manager—Production: Rajender P. Ghansela Production Manager: Reji Kumar Information contained in this work has been obtained by McGraw Hill Education (India), from sources believed to be reliable. However, neither McGraw Hill Education (India) nor its authors guarantee the accuracy or completeness of any information published herein, and neither McGraw Hill Education (India) nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw Hill Education (India) and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought. Typeset at The Composers, 260, C.A. Apt., Paschim Vihar, New Delhi 110 063 and printed at ** Cover Printer: ** R**  CONTENTS  Preface  xv  Abbreviations, Notations and Symbols  xxi  1.  Drawing Instruments and Sheet Layout 1.1 Introduction 1.1 1.2 International and National Codes 1.1 1.3 Drawing Instruments 1.2 1.4 Drawing Board 1.2 1.5 Mini Drafter 1.3 1.6 Drawing Sheet 1.4 1.7 Drawing Pencil 1.6 1.8 Compass 1.7 1.9 Divider 1.8 1.10 Protractor 1.9 1.11 Ruler (Scale) 1.10 1.12 French Curves 1.11 1.13 Set Squares 1.12 1.14 Eraser 1.12 1.15 Sheet Fasteners 1.13 1.16 Templates 1.13 1.17 Pencil Cutters 1.14 1.18 Sand Paper Pad 1.14 1.19 Brush or Towel 1.14 1.20 General Preparation for Drawing 1.14 1.21 Planning and Layout of Sheet 1.15 1.22 Frames and Borders 1.15 1.23 Title Block 1.17 1.24 Space for Text 1.19 1.25 Item References on Drawing and Item Lists 1.26 Folding of Drawing Sheets 1.21 1.27 Conclusion 1.23 Exercise 1A 1.23 Viva-Voce Questions 1.25 Multiple-Choice Questions 1.25  1.1–1.26  1.20  vi  Contents  2.  Lines, Lettering and Dimensioning 2.1 Introduction 2.1 2.2 Lines 2.1 2.3 Lettering 2.5 2.4 Dimensioning 2.7 2.5 Placement of Dimensions 2.9 2.6 Arrangement of Dimensions 2.10 2.7 Symbols and Notes for Dimensioning 2.12 2.8 Rules of Dimensioning 2.19 Exercise 2A 2.24 Viva-Voce Questions 2.25 Multiple-Choice Questions 2.25  2.1–2.26  3.  Geometrical Constructions 3.1 Introduction 3.1 3.2 Bisect a Line and an Arc 3.1 3.3 Perpendicular to a Line 3.2 3.4 Parallel Lines 3.4 3.5 Divide a Line 3.4 3.6 Angle Bisector 3.6 3.7 Centre of an Arc or Circle 3.6 3.8 Circle through Three Points 3.7 3.9 Divide a Circle 3.7 3.10 Tangent to a Circle 3.7 3.11 Tangent to Two Circles 3.9 3.12 Arc to Connect Lines and Circles Tangentially 3.10 3.13 Arc to Connect Line and Point 3.12 3.14 Circle to Connect Another Circle and a Point 3.13 3.15 Polygons 3.13 3.16 Construction of a Triangle 3.15 3.17 Rectangle and Square 3.17 3.18 Construction of a Regular Pentagon 3.18 3.19 Construction of a Regular Hexagon 3.19 3.20 Inscribe Polygon in a Circle 3.19 3.21 Inscribe an Octagon in a Square 3.22 3.22 Circumscribe Polygon to a Circle 3.22 3.23 Inscribe a Circle in a Polygon 3.22 3.24 Engineering Applications 3.27 Exercise 3A 3.28 Viva-Voce Questions 3.31 Multiple-Choice Questions 3.31  3.1–3.31  4.  Scales 4.1 Introduction 4.1 4.2 Representation of Scale 4.1 4.3 Units of Measurements 4.2  4.1–4.36  Contents  vii  4.4 Types of Scales 4.2 4.5 Representative Fraction (RF) 4.2 4.6 Requirements of a Scale 4.4 4.7 Plain Scale 4.4 4.8 Diagonal Scale 4.10 4.9 Comparative Scale 4.19 4.10 Vernier Scale 4.24 4.11 Scale of Chords 4.31 Exercise 4A 4.34 Viva-Voce Questions 4.36 Multiple-Choice Questions 4.36 5.  Conic Sections 5.1 Introduction 5.1 5.2 Cone 5.1 5.3 Conic Sections 5.1 5.4 Construction of Ellipse 5.6 5.5 Locate Centre, Major Axis and Minor Axis 5.12 5.6 Tangents and Normal to the Ellipse 5.13 5.7 Construction of Parabola 5.14 5.8 Locate Axis, Focus and Directrix 5.18 5.9 Tangent and Normal to the Parabola 5.19 5.10 Construction of Hyperbola 5.20 5.11 Locate Asymptotes and Directrix 5.26 5.12 Tangent and Normal to the Hyperbola 5.27 5.13 Miscellaneous Problems 5.28 Exercise 5A 5.36 Viva-Voce Questions 5.38 Multiple-Choice Questions 5.39  5.1–5.39  6.  Engineering Curves and Loci of Points 6.1 Introduction 6.1 6.2 Roulettes 6.1 6.3 Cycloidal Curves 6.1 6.4 Trochoid, Epitrochoid and Hypotrochoid 6.6 6.5 Involute 6.12 6.6 Spiral 6.14 6.7 Helix 6.19 6.8 Miscellaneous Problems 6.20 Exercise 6A 6.28 6.9 Loci of Points 6.30 Exercise 6B 6.36 Viva-Voce Questions 6.37 Multiple-Choice Questions 6.38  6.1–6.38  7.  Orthographic Projections 7.1 Projection 7.1  7.1–7.50  viii  Contents  7.2 Pictorial View and Multi-View 7.1 7.3 Orthographic Projection 7.2 7.4 Multi-View Drawing 7.3 7.5 Terminology 7.4 7.6 First Angle Projection 7.4 7.7 Features of First Angle Projection 7.6 7.8 Third Angle Projection 7.6 7.9 Features of Third Angle Projection 7.8 7.10 Second and Fourth Angle Projections 7.8 7.11 Symbols 7.9 7.12 Reference Arrows Method 7.9 7.13 Assumptions 7.10 7.14 General Preparation for Multi-View Drawings 7.11 7.15 Conversion of Pictorial View into Orthographic Views 7.16 Miscellaneous Problems 7.22 Exercise 7A 7.23 7.17 Sectional Views 7.29 7.18 Representation of a Cutting Plane 7.30 7.19 Section Lines or Hatching 7.30 7.20 Features Left Uncut 7.31 7.21 Simplified Representation of Intersections 7.32 7.22 Section Line Conventions 7.33 7.23 Types of Sectional Views 7.33 7.24 Conventional Breaks 7.38 7.25 Problems on Sectional Views 7.38 Exercises 7B 7.40 7.26 Auxiliary Views 7.42 7.27 Full and Partial Auxiliary Views 7.43 7.28 Primary Auxiliary Views 7.43 7.29 Secondary Auxiliary Views 7.45 Exercise 7C 7.46 Viva-Voice Questions 7.48 Multiple-Choice Questions 7.48 8.  Projections of Points 8.1 Introduction 8.1 8.2 Location of a Point 8.1 8.3 Conventional Representation 8.1 8.4 Point above the H.P. and in Front of the V.P. 8.2 8.5 Point above the H.P. and behind the V.P. 8.3 8.6 Point below the H.P. and behind the V.P. 8.3 8.7 Point below the H.P. and in Front of the V.P. 8.4 8.8 Point on the H.P. and in Front of the V.P. 8.5 8.9 Point above the H.P. and on the V.P. 8.6 8.10 Point on the H.P. and behind the V.P. 8.6 8.11 Point below the H.P. and on V.P. 8.7  7.11  8.1–8.11  Contents  ix  8.12 Point on both H.P. and V.P. 8.8 8.13 Summary 8.8 8.14 Miscellaneous Problems 8.8 Exercise 8A 8.10 Viva-Voce Questions 8.10 Multiple-Choice Questions 8.11 9.  10.  Projections of Straight Lines 9.1 Introduction 9.1 9.2 Orientation of a Straight Line 9.1 9.3 Trace of a Straight Line 9.1 9.4 Line Parallel to Both H.P. and V.P. 9.2 9.5 Line Perpendicular to H.P. 9.3 9.6 Line Perpendicular to V.P. 9.4 9.7 Line Inclined to H.P. and Parallel to V.P. 9.4 9.8 Line Inclined to V.P. and Parallel to H.P. 9.5 9.9 Line Situated on H.P. 9.6 9.10 Line Situated in the V.P. 9.7 9.11 Line Situated Both in H.P. and V.P. 9.8 9.12 Summary 9.9 9.13 Miscellaneous Problems 9.10 Exercise 9A 9.12 9.14 Line in First Angle and Inclined to Both the Reference Planes 9.15 Miscellaneous Problems 9.23 Exercise 9B 9.44 9.16 Projections of a Line in Different Angles 9.46 9.17 Miscellaneous Problems 9.48 Exercise 9C 9.57 Viva-Voice Questions 9.58 Multiple-Choice Questions 9.59 Projections of Planes 10.1 Introduction 10.1 10.2 Orientation of Planes 10.1 10.3 Plane Parallel to H.P. 10.2 10.4 Plane Parallel to V.P. 10.3 10.5 Plane Parallel to Profile Plane 10.4 10.6 Plane Inclined to H.P. and Perpendicular to V.P. 10.4 10.7 Plane Inclined to V.P. and Perpendicular to H.P. 10.10 10.8 Trace of a Plane 10.14 10.9 Summary 10.17 Exercise 10A 10.18 10.10 Plane Inclined to Both the Reference Planes 10.20 Exercise 10B 10.36 10.11 Auxiliary Plane Method 10.38 10.12 Alternative Auxiliary Plane Method 10.41  9.1–9.60  9.14  10.1–10.56  x  Contents  10.13 True Shape of Plane 10.46 10.14 Distance of a Point from the Plane 10.49 10.15 Locate a Point 10.50 10.16 Angle between Two Intersecting Planes 10.52 Exercise 10C 10.53 Viva-Voce Questions 10.55 Multiple-Choice Questions 10.55 11.  Projections of Solids 11.1 Introduction 11.1 11.2 Classification of Solids 11.1 11.3 Recommended Method of Labelling 11.4 11.4 Orientation of Solid 11.5 11.5 Axis Perpendicular to H.P. 11.5 11.6 Axis Perpendicular to V.P. 11.7 11.7 Axis Parallel to Both H.P. and V.P. 11.8 11.8 Miscellaneous Problems 11.9 Exercise 11A 11.11 11.9 Initial Position of the Solid 11.13 11.10 Identify Visible and Hidden Lines 11.13 11.11 Axis Inclined to H.P. and Parallel to V.P. 11.14 11.12 Axis Inclined to V.P. and Parallel to H.P. 11.21 11.13 Miscellaneous Problems 11.25 Exercise 11B 11.27 11.14 Axis Inclined to Both H.P. and V.P. 11.28 Exercise 11C 11.51 11.15 Auxiliary Plane Method 11.53 11.16 Projections of Spheres 11.61 Exercise 11D 11.66 Viva-Voce Questions 11.67 Multiple-Choice Questions 11.67  11.1–11.68  12.  Sections of Solids 12.1 Introduction 12.1 12.2 Terminology 12.1 12.3 Type of Section Planes 12.2 12.4 Section by a Plane Perpendicular to V.P. 12.5 12.5 Section by a Plane Perpendicular to H.P. 12.21 12.6 Section by a Plane Perpendicular to Both H.P. and V.P. 12.7 Miscellaneous Problems 12.32 Exercise 12A 12.38 12.8 Anti-Section 12.40 Exercise 12B 12.57 Viva-Voce Questions 12.59 Multiple-Choice Questions 12.59  12.1–12.60  12.31  Contents  xi  13.  Development of Surfaces 13.1 Introduction 13.1 13.2 Classification of Surfaces 13.1 13.3 Methods of Development 13.1 13.4 Development of Prisms 13.2 13.5 Development of Cylinders 13.7 13.6 Development of Cones 13.12 13.7 Development of Pyramids 13.18 13.8 Development of Spheres 13.24 13.9 Development of Transition Pieces 13.26 13.10 Development of Tray 13.29 13.11 Development of Oblique Objects 13.31 13.12 Applications 13.34 Exercise 13A 13.37 13.13 Anti-Development 13.40 Exercise 13B 13.51 Viva-Voce Questions 13.52 Multiple-Choice Questions 13.52  13.1–13.52  14.  Intersection of Surfaces 14.1 Introduction 14.1 14.2 Engineering Applications 14.1 14.3 Methods of Determining the Curves of Intersection 14.1 14.4 Types of Interpenetrating Solids 14.2 14.5 Intersection of Prism by Another Solid 14.2 14.6 Intersection of Cylinder by Another Solid 14.8 14.7 Intersection of Pyramid by Another Solid 14.14 14.8 Intersection of Cone by Another Solid 14.18 14.9 When Axes Intersect at an Angle other than Right Angle 14.24 14.10 Intersection of Sphere by Another Solid 14.26 14.11 Miscellaneous Problems 14.27 Exercises 14.30 Viva-Voce Questions 14.33 Multiple-Choice Questions 14.33  14.1–14.34  15.  Isometric Projections 15.1 Introduction 15.1 15.2 Axonometric Projection 15.1 15.3 Principle of Isometric Projection 15.2 15.4 Terminology 15.3 15.5 Construction of an Isometric Scale 15.4 15.6 Characteristics of Principal Lines in Isometric Projection 15.5 15.7 Isometric Projection and Isometric View 15.5 15.8 Dimensioning on Isometric Projection 15.6 15.9 Isometric View of Planes 15.6 15.10 Four Centre Method to Draw Ellipse and Elliptical Arcs 15.9  15.1–15.52  xii  Contents  15.11 Isometric View of Right Solids 15.11 15.12 Isometric View of Solid Containing Non-Isometric Lines 15.12 15.13 Isometric View of Truncated Solid 15.17 15.14 Isometric View of Composite Solids 15.20 Exercise 15A 15.27 15.15 Conversion of Orthographic Views into Isometric Views 15.28 15.16 Miscellaneous Problems 15.37 Exercise 15B 15.46 15.17 Free Hand Sketching of Isometric Views 15.48 15.18 Missing Views 15.49 Exercise 15C 15.50 Viva-Voce Questions 15.50 Multiple-Choice Questions 15.50 16.  Oblique Projections 16.1 Introduction 16.1 16.2 Terminology 16.1 16.3 Direction of Projectors 16.2 16.4 Rules for The Choice of Position of an Object 16.3 16.5 Dimensioning Oblique Drawings 16.3 16.6 Advantages of Oblique Drawing 16.4 16.7 Oblique Projections 16.4 Exercise 16 16.14 Viva-Voce Questions 16.15 Multiple-Choice Questions 16.15  16.1–16.16  17.  Perspective Projections 17.1 Introduction 17.1 17.2 Applications of Perspective 17.1 17.3 Types of Perspective 17.1 17.4 Characteristic Features of Perspective Projections 17.3 17.5 Terminology 17.3 17.6 The Myth of Perspectives 17.4 17.7 Methods of Drawing Perspective Views 17.4 17.8 Miscellaneous Problems 17.16 Exercise 17 17.24 Viva-Voce Questions 17.25 Multiple-Choice Questions 17.25  17.1–17.26  18.  Computer Aided Design (CAD) 18.1 Introduction 18.1 18.2 CAD Application 18.1 18.3 Software Providers 18.1 18.4 Hardware and Operating System Technologies 18.2 18.5 Basic Components of a Computer 18.2 18.6 Introduction to Autocad 18.4 18.7 Starting with AutoCAD 2013 18.5  18.1–18.67  Contents  xiii  18.8 Application Windows 18.5 18.9 Ribbon Tabs, Panel and Tools 18.7 18.10 Display Menu Bar and Toolbars 18.9 18.11 Status Bar 18.10 18.12 Setting up a Drawing Space 18.12 18.13 Specifying Coordinates 18.15 18.14 Draw Panel 18.16 18.15 Modify Panel 18.29 18.16 Construction Panel 18.37 18.17 Adding Text 18.38 18.18 Adding Dimensions 18.40 18.19 Adding Different Types of Line 18.43 18.20 Applications of Autocad in Elementary Drawing 18.44 18.21 Applications of Autocad in Engineering Drawing 18.48 Exercise 18A 18.63 Viva-Voce Questions 18.65 Multiple-Choice Questions 18.66 Index  I.1–I.7  PREFACE  Engineering Drawing is a core subject taught at the first-year level in all disciplines of engineering, both at the degree as well as the diploma level. It is also a pre-requisite to all engineering professionals since it acts as an 'international language of engineers'. It is a viable method of communicating technical ideas in a recorded form. When exact visual understanding is necessary, engineering graphics is the accurate technique that can be used. It develops the ability to visualise any object with all the physical and dimensional configurations.  Making of the Book Engineering Drawing book is mainly intended to meet the requirements of the first year BE/B.Tech. students of all the technical universities and institutes and other basic courses of professional technical bodies. As it is essentially intended to be a classroom textbook, it contains a large number of solved problems covering every phase of the subject in a simple and understandable form. Problems have been classified from simple to typical ones and step-by-step procedures are given for solving them. The presentation of the subject matter and illustrations is simplified so as to enable the readers understand the basic concepts of the subject easily. It can also be used as a reference book for engineers working in the design office as well as on the shop floor. This book has been written considering the newly revised syllabus of various universities, the new pattern of university examinations, previous exam question papers and will fulfill the requirement of engineering drawing for the future learning of drawing-oriented subjects like machine drawing, building drawing, etc. One of the first things that attracts everyone's attention is the excellent presentation in a clear, logical and concise manner. The work is an extract of the knowledge gained by the experience of successful classroom teaching of this subject with utmost devotion. Anyone who goes through the book cannot miss the enormous work that has gone into preparing the text in the present form. This book is designed to be a comprehensive guide to cover the basic principles and also includes every significant feature of graphics software to make use of computers as drawing instruments. The miscellaneous problems on almost every topic will develop professional-level drawing skills. Although the basics are fully covered, many advanced features are also included. Therefore, the beginners should not feel concerned if some of the material seems too advanced. It will be useful in their professional career.  Salient Features of the Book The drawings have been prepared to the scale with the help of advanced software packages, maintaining the required recommendations of ISO and the latest BIS standards. Simple language, systematic introduction  xvi  Preface  of concepts, variety of solved and exercise questions and easy-to-grasp formatting are some of the major features of the text. The salient features include the following: Emphasis on basic concepts with simplified presentation of the subject matter and illustrations Use of latest BIS and ISO standards Classification of problems from simple to typical ones Large number of solved problems from university question papers provided with step-by-step procedures An exclusive chapter on application of CAD software Questions for viva-voce and Multiple-choice questions on each chapter Excellent illustrations (2D and 3D) for effective visualization of the objects Enhanced pedagogy includes ■ 625 Solved problems ■ 810 Practice questions ■ 212 Questions for viva-voce ■ 264 Multiple-choice questions  Chapter Organisation This book is divided into 18 chapters. The overall organization of the book goes from simple to complex, and each chapter has exhaustive pedagogy to support the text. Chapter 1 provides the list of essential drawing equipments and instruments required in engineering graphics and their uses. Chapter 2 highlights the latest recommendations of The Bureau of Indian Standards in its bulletin 'SP 46: 2003 Engineering Drawing Practice for Schools and Colleges'. Chapter 3 reviews the elementary geometrical constructions. Chapter 4 describes the different types of engineering scales and their typical applications. Chapters 5 and 6 deal with the construction of curves used in engineering practice. Chapter 7 begins with the fundamentals of orthographic projections. Chapters 8 through 12 present the orthographic projections of points, straight lines, planes, solids and sections of solids. Chapter 13 describes the development of surfaces as applied to sheet metal work. Chapter 14 deals with the curves of intersection of interpenetrating solids. It is recommended that beginners read chapters 8 through 14 in the same chronological order as given in this book. Chapter 15 through Chapter 17 describe the principal methods of construction of pictorial views. Finally, Chapter 18 deals with the use of computer graphics with the help of the latest version of the popular graphics software AutoCAD 2013 developed by Autodesk Inc. An attempt is made to present some of its basic commands in a simple way. The readers are, however, advised to refer to the manuals prepared by Autodesk for its detailed features and applications.  Web Supplements The Web supplements for this book can be accessed at http://www.mhhe.com/agrawal/ed2 and they contain the following material:  For Students Answers to selected practice questions  For Instructors Solution manual PPTs of figures  Preface  xvii  Acknowledgements The authors are indebted to the following reviewers for sparing time and giving their valuable suggestions: Pushpendra Kumar Jain  TIT Excellence, Bhopal, Madhya Pradesh  Nitin Shrivastava  University Institute of Technology, Rajiv Gandhi Proudyogiki Vishwavidyalaya, Bhopal, Madhya Pradesh IIT Kharagpur, West Bengal MM Engineering College, Ambala, Haryana NIT Durgapur, West Bengal Jadavpur University, West Bengal ISM Dhanbad, Jharkhand SVNIT Surat, Gujarat SVNIT Surat, Gujarat Shivaji Rao S Jodhale College of Engineering, Thane, Maharashtra Datta Meghe College of Engineering, Navi Mumbai, Maharashtra Mepco Schlenk Engineering College, Sivakasi, Tamil Nadu Institute of Aeronautical Engineering, Hyderabad, Andhra Pradesh Mahakal Institute of Technology & Science, Ujjain, Madhya Pradesh Corporate Institute of Science & Technology, Bhopal, Madhya Pradesh  Sankha Deb D K Chhabra Niloptal Banerjee Gautam Pohit Shibayan Sarkar Sandeep Soni Chetan R Patel A D Dhale O G Sonare K R Srinivasan B Yesu Manish Soni Pavan Srivastava  We would also like to thank the editorial and production staff at McGraw-Hill Education (India) for their assistance and cooperation. Our acknowledgements would be incomplete if we forget to mention the love, care and patience rendered by our family members. We thank all of them wholeheartedly. Any further suggestion or criticism from the readers for improvement of the text will be highly appreciated and shall be incorporated in the next edition. For any assistance or clarification, readers may contact the authors at bas_agr@yahoo.co.in and/or cma2004@rediffmail.com. Basant Agrawal C M Agrawal  Publisher's Note We look forward to receiving valuable views, comments and suggestions for improvements from teachers and students, all of which can be sent to tmh.corefeedback@gmail.com, mentioning the title and author's name on the subject line. Report of any piracy related problems/issues will be highly appreciated.  VISUAL WALKTHROUGH Chapter  DRAWING INSTRUMENTS AND SHEET LAYOUT  1  1.1 INTRODUCTION using any of a wide variety of tools and techniques. It generally involves making marks by moving graphite pencils, ink pen, wax colour pencils, crayons, charcoals, pastels, or markers on a plane surface such as paper, canvas, etc. Engineering drawing is a graphical way to convey an unambiguous and accurate description necessary for engineered items. It is made in accordance with the standard conventions for layout, nomenclature, interpretation, appearance, size, etc. The purpose of engineering drawing is to provide exact geometrical configuration for the construction or analysis of machines, structures, or systems. Today, the mechanics of the drawing task has been largely automated and greatly accelerated through a number of computer softwares. This chapter deals with an introduction and use of drawing instruments and accessories commonly required in preparing engineering drawings.  Introduction provides a quick look into the concepts that the reader is going to learn.  1.2 INTERNATIONAL AND NATIONAL CODES Engineering drawing follows certain codes of practice. International Organisation for Standardisation (ISO) recommended international standards for engineering drawing in 1982. At present, these are adopted by 164 countries out of 205 total countries in the world. The standards published by ISO are designated as ISO XXXX:YEAR, where XXXX represents a unique number allocated to the standard and the YEAR represents the year of publication. If a standard has been published before and is updated, the number remains the same as the previous number but the YEAR changes to the new year of publication. Each country has its own standard organisation. For example, in the United Kingdom (UK), it is the British Standards Institution (BSI), in the United States of America (USA), it is the American National Standards Institute (ANSI) and in Germany, it is the Deutsches Institut fur Normung (DIN). In India, the Bureau of Indian Standards (BIS) is engaged in the preparation and implementation of standards, operation of certification schemes both for products and systems, organisation and management of testing laboratories, creating consumer awareness and maintaining close liaison with international standards bodies. The standards published by BIS, irrespective of developed or adopted from ISO, are designated as IS YYYY:YEAR, where YYYY represents another unique number allocated to the standard and the YEAR represents the year of publication. In addition to this, the BIS also publishes some special bulletin which contains a copy of Indian Standards defining special area of interest.  10.10  Orthographic Projections  (a)  Diagrams have been prepared with the help of advanced software packages maintaining the recommendations of latest BIS code.  7.32  (b)  Fig. 7.9  Projections when object is kept in (a) second angle (b) fourth angle  7.11  SYMBOLS  The front and the top views do not overlap and give the clear picture when an object is placed in either the first angle or the third angle. Thus, internationally, only two methods of projections are adopted for multiview drawings namely; the first angle projection and the third angle projection. The angle of projection is indicated in the title block of the drawing sheet with the help of multi-views drawn for the frustum of a cone shown in Fig. 7.10(a). The diameters of the frustum of the cone are in the ratio of 1:2 and the length is equal to the diameter at the bigger end. Figures 7.10(b) and (c) show the multiviews of the cone in the first angle projection and the third angle projection respectively. These views are considered as symbols and should be drawn in the space provided for the purpose in the title block of the drawing sheet.  Fig. 7.10  7.12  (a) F  one (b) Symbol for first angle projection (c)  In addition to the conventional layout of the first and the third angle projections, IS 15021 (part 2): 2001 allows a simplified layout of orthographic views using reference arrows. the views freely. Each view is identified by a letter in accordance with Table 7.1 except the front view. In the front view, the direction of observation and a lower-case letter indicates the other views. These lower-case letters are identified by the corresponding upper-case letters placed at the upper-left corner of the view. The identified views are placed in any convenient position irrespective of the front view. The upper-case letters identifying the views are positioned to be read from the normal direction of viewing the drawing (See Figs. 7.11 and 7.12). No symbol is needed on the drawing to identify this method.  (b)  Fig. 7.42 (a) and (b) Webs left unsectioned  Fig. 7.43 Spokes left unsectioned  Fig. 7.44  Gear teeth left unsectioned  7.21 SIMPLIFIED REPRESENTATION OF INTERSECTIONS When a section is drawn through a small intersection in which the exact figure or curve of intersection is small or of no consequence, the curve of intersection may be simplified as shown in Figs. 7.45(a) and (b). However, when the intersecting features are larger, they are drawn as their true representation as shown in Fig. 7.45(c).  (a)  (b)  (c)  Fig. 7.45 Simplified representation of intersections (a) Small extrusion (b) Small hole (c) Large hole  ojection  REFERENCE ARROWS METHOD  Engineering Drawing  (a)  7.9  3D Illustrations Assist in visualisation of the object in lucid manner.  10.10  Projections of Straight Lines  9.53  Problem 9.54 A 120 mm long line PQ has the end projectors 50 mm apart. Ends P and Q are 10 mm and 60 mm below the H.P., respectively. The mid-point of PQ lies in the V.P. Draw the projections of the line and find its true inclinations with both reference planes. Assume that the end P lies in the fourth quadrant. Given Data  Interpretation  Line PQ is 120 mm long, M is the mid-point  p1¢m¢ = m¢q1¢ = p2m = mq2 = 60 mm  End projectors are 50 mm apart  p¢p and q¢q are 50 mm apart along xy  End P is 10 mm below the H.P.  Point p¢ is 10 mm below xy  End Q is 60 mm below the H.P.  Point q¢ is 60 mm below xy  Mid-point M lies in the V.P.  Point m is on xy  Construction Refer to Fig. 9.54. 1. Draw a reference line xy. Mark points o and o1 on it such that oo1 = 50 mm. 2. On the projector though point o, mark q q2 point p¢ 10 mm below xy. On the projector though point o1 mark point q¢ 60 mm below xy. Join p¢q¢ to represent the front view. 3. Mark m¢ as the mid-point of p¢q¢. Project point m¢ to meet xy at point m. Points m¢ q1 p1 m x y and m represents the front and top view p' of the mid-point M. p1' 4. Draw an arc with centre m and radius 60 mm to meet the horizontal lines from p2' q2' points p¢ and q¢ at points p1¢ and q1¢, rem' spectively. Join 120 mm long line p1¢q1¢ 120 p2 p and measure its inclinations with xy as q1' q' true inclination of line PQ with the H.P. 50 Here q = 25°. Fig. 9.54 5. Project p1¢ and q1¢ to meet horizontal line through m (i.e., on xy) at points p1 and q1, respectively. Draw an arc with centre m and radii mp1 and mq1 to meet the projectors from points p¢ and q¢ at points p and q respectively. Join pmq to represent the top view. 6. Draw an arc with centre m¢ and radii m¢p¢ and mq¢ to meet the horizontal line from point m¢ at points p2¢ and q2¢, respectively. Project p2¢ and q2¢ to meet the horizontal lines from points p and q at points p2 and q2, respectively. Join p2q2 and ensure that it equal to 120 mm. Measure inclination p2q2 with xy as the true inclination of line PQ with the V.P. Here f = 54°. 12  0  Problems are simplified to enable the readers understand the basic concepts in a clear, logical and concise manner easily.  54  25°  60  10  °  Projections of Solids 11.33  Problem 11.31 A hexagonal pyramid of base side 30 mm and axis 60 mm has one of its slant edges on the H.P. and inclined at 45° to the V.P. Draw its projections when the base is visible. o'  a'  a'  Result  f'  Inclination with the H.P., q = 25°. Inclination with the V.P., f = 54°.  b'  60  b',f'  e'  c',e' x  a'  c',e'  f  e  d' d'  o' e  o' o  d' 45°  b',f'  c'  f  y  f d  a  a  d  o  o  e  a d  b  HEX30  First stage  c  c  b Second stage  b c  Third stage (Final projections)  Fig. 11.39  Refer to Fig. 11.39. Draw a hexagon abcdef keeping ad parallel to xy. Join the corners of the hexagon with the centroid o. This represents the top view. Project the corners and obtain a¢d¢o¢ as the front view. 2. Second stage Reproduce the front view of the first stage keeping d¢o¢ on xy. Obtain a, b, c, d, e, f and o in the top view as the intersecting points of the projectors from the front view of the second stage with the corresponding locus lines from the top view of the first stage. Join the points and obtain bcdefo as the top view. (Join the outlines using continuous lines. The corner a¢ is towards observer, therefore join a¢o¢, a¢b¢ and a¢f¢ using continuous lines.) 3. Third stage Reproduce the top view of the second stage keeping oad inclined at 45° to xy. The base abcdef should be farther to the xy than the apex o, so that the base is visible. Obtain a¢, b¢, c¢, d¢, e¢, f¢ and o¢ in the front view as the intersecting points of the projectors from the top view of the third stage with the corresponding locus lines from the front view of the second stage. Join the points and obtain b¢a¢f¢e¢d¢o¢ as the required front view. (Join the outlines and the edges of the base using continuous lines. The corner c is towards observer, therefore join c'o¢ using continuous lines.)  Construction  Step-by-step Construction procedure is given to understand the solved problems.  Problem 11.32 A hexagonal pyramid of base side 30 mm and axis 60 mm rests on an edge of base on the H.P. with the triangular face containing that edge perpendicular to the H.P. and parallel to the V.P. Draw its projections so that the base is visible. Construction Refer to Fig. 11.40. 1. First stage Draw a hexagon abcdef keeping de perpendicular to xy. Join the corners of the hexagon with the centroid o. This represents the top view. Project the corners and obtain b¢d¢o¢ as the front view.  Isometric Projections 15.37  15.16  MISCELLANEOUS PROBLEMS The front and top views of a casting are shown in Fig. 15.51(a). Draw its isometric  Ø  50  30  35  25  30  Problem 15.45 view.  25  15 60  (a)  (b)  Fig. 15.51  Figure 15.51(b) shows the required isometric view. Construction lines are left intact for guidance. Problem 15.46 The front and left-hand side views of a casting are shown in Fig. 15.52(a). Draw its isometric view.  15  40  15  Miscellaneous Problems with Solutions of some typical problems are given to develop professional level drawing skills.  25  30  55  (a)  (b)  Fig. 15.52  Figure 15.52(b) shows the required isometric view. Construction lines are left intact for guidance.  3.28  Engineering Drawing  EXERCISE 3A Divide an 80 mm long straight line into five equal parts. 3.2 Divide a 90 mm long straight line into parts that are in proportion to 2:3:5. 3.3 Draw a perpendicular to a 100 mm long line AB, at a point P lying on the line at a distance of 40 mm from the end A. 3.4 Draw a 120 mm long line AB inclined at 60° to the horizontal. Erect a perpendicular to AB from point P, lying at a distance 30 mm from end A. 3.5 Draw perpendicular to a 100 mm long line AB, from a point P lying at a distance 60 mm from end A and 70 mm from end B. 3.6 Draw a line AB inclined at 30º to the horizontal. Draw another line CD parallel to and 50 mm away from AB. 3.7 Draw tangent to a circle of 40 mm diameter from any point P which is at a distance of 65 mm from the centre of the circle. 3.8 Two circles of radii 20 mm and 30 mm have their centres 65 mm apart. How many common tangents to both the circles are possible? Draw an internal and an external common tangent to these circles. 3.9 Two circles of radii 20 mm and 30 mm have their centres 50 mm apart. Draw all the possible common tangents to both the circles. 3.10 Two circles of radii 20 mm and 30 mm have their centres 40 mm apart. Draw a pair of common tangents to both the circles. 3.11 Draw a tangent to connect two circles of radii 25 mm and 40 mm. The centres of the circles are 15 mm apart. 3.12 Draw an arc of 30 mm radius connecting two straight lines inclined at 135º to each other. 3.13 Draw arc of 20 mm radius to connect a straight line AB and a circle of 30 mm radius, tangentially. The centre of the circle is at a distance 25 mm from AB. Consider the centres of the arc lies (a) within the circle (b) outside the circle. 3.14 Two circles have their centres 70 mm apart and radii 20 mm and 30 mm, respectively. Draw a circle of radius 25 lying internal to and connect both the circles tangentially. 3.15 Two circles have their centres 70 mm apart and radii 20 mm and 30 mm, respectively. Draw a circle of radius 65 lying external to and connect both the circles tangentially.  3.16  3.17  3.18  3.19 3.20 3.21 3.22  3.23  3.24 3.25  3.26  3.27  3.28  3.29  3.30  radii 20 mm and 30 mm, respectively. Draw a circle of radius 55 which connects tangentially both the circles and (a) include 20 mm circle (b) include 30 mm circle. A point P is 40 mm from a line AB. Another point Q is in the AB and is 50 mm from the point P. Draw a circle passing through point P and tangential to the line AB at point Q. Draw two possible circles to connect a given circle of 50 mm diameter AB and a point P, lying at a distance 70 mm and 25 mm from the ends of the diameter AB. Inscribe a circle in a triangle of 75 mm, 65 mm and 55 mm long sides. Draw a square of 60 mm long diagonals. Circumscribe another square on the square. Draw regular pentagon, hexagon and a heptagon on a common edge of side 30 mm. Draw a pentagon of 30 mm side with a side vertical. Attach a non-overlapping hexagon of same side length with common vertical edge. Construct a heptagon of edge length 30 mm. Construct a pentagon of same edge length inside the heptagon with one edge of the polygons being common. Draw an octagon of 25 mm side keeping one of the sides vertical. Draw five circles in a given circle of 80 mm diameter, each touching the given circle and the other two circles. Draw five circles inside the pentagon of 30 mm side, such that each circle touches one side of the pentagon and two other circles. Draw five circles inside the pentagon of 30 mm side, such that each circle touches two side of the pentagon and two other circles. Draw three circles inside a hexagon of 30 mm side, such that each circle touches one side of the hexagon and two other circles. Draw five circles outside the pentagon of 20 mm side, such that each circle touches one side of the pentagon and two other circles. Draw six circles outside a given circle of 30 mm diameter, such that each circle touches the given and two other circles.  Exercise covers a large number of unsolved problems for practice.  5.38  Engineering Drawing  5.31 A fixed point is 90 mm from a fixed straight line. Draw the locus of a point P moving in such a way that its distance from the fixed point is twice its distance from the fixed straight line. Name the curve. 5.32 Construct two branches of a hyperbola when its transverse axis is 50 mm long and foci are 70 mm apart. Locate its directrix and determine the eccentricity. 5.33 Two points are fixed at 100 mm apart. Draw the locus of a point moving in such a manner that the difference of its distance from the points is 75 mm. Name the curve. 5.34 Draw two branches of a hyperbola when the distance between its foci is 90 mm and the vertices are 15 mm from the foci. Locate the asymptotes and measure the angle between them. 5.35 Draw two branches of a rectangular hyperbola having its vertices 60 mm apart and determine its directrices and foci graphically. 5.36 Draw a rectangular hyperbola whose directrices are 40 mm apart and locate its foci and vertices. 5.37 The asymptotes of a hyperbola are inclined at an angle of 75°. Its foci are 60 mm apart. Locate its foci graphically and construct two branches of the hyperbola. Also draw a tangent and a normal to the curve at a point 20 mm from one of the foci. 5.38 The asymptotes of a hyperbola are inclined at an angle of 120° and its transverse axis is 80 mm. Construct two branches of the hyperbola and  determine its foci. Take at least eight points for constructing each branches of the hyperbola. 5.39 Half the transverse axis, double ordinate and abscissa of a hyperbola are 30 mm, 100 mm and 40 mm respectively. Construct two branches of the hyperbola. 5.40 The transverse axis of a hyperbola is 80 mm long. Its double ordinate is 90 mm long and the corresponding abscissa is 50 mm. Construct the hyperbola. 5.41 The asymptotes of a hyperbola are inclined at 105° to each other. A point P on the curve is 40 mm and 50 mm from the asymptotes respectively. Construct two branches of the hyperbola, and determine (a) distance between its vertices, (b) distance between its directrices, (c) distance between its foci and (d) eccentricity. 5.42 Draw a rectangular hyperbola when the position of a point P on the curve is 30 mm from the horizontal asymptote and 50 mm from the vertical asymptote. Show at least four points on either side of point P. 5.43 The asymptotes of a hyperbola are inclines at 75° to each other. A point P on the curve is 25 mm and 40 mm from its asymptotes. Draw the curve showing within 10 mm distance from each asymptotes. Also determine the directrix and focus of the hyperbola. 5.44 The asymptotes of a hyperbola are at right angle to each other and a point on the curve is at a distance of 30 mm from each of the asymptotes. Draw two branches of the hyperbola. Also draw a tangent and a normal at a point 45 mm from one of the asymptotes.  VIVA-VOCE QUESTIONS 5.1  Viva-voce Questions are added at the end of each chapter to prepare students for viva-voce held during practical examinations.  Conic Sections  5.39  MULTIPLE-CHOICE QUESTIONS 5.7  5.2  5.3  5.4  5.5  5.6  sum of its distances from two fixed points is constant the curve so traced is called (a) ellipse (b) parabola (c) hyperbola (d) None of these Name the curve traced out by a point moving in a plane such that the difference between its distances from two fixed points is constant (a) ellipse (b) parabola (c) hyperbola (d) Any of these When a bullet is shot in air the path traversed by the bullet is called (a) cycloid (b) semicircle (c) parabola (d) hyperbola A right circular cone when cut by a plane parallel to its generator, the curve obtained is a (a) ellipse (b) parabola (c) hyperbola (d) circle When a right circular cone is cut by a plane passing through its apex, the curve obtained is (a) ellipse (b) parabola (c) hyperbola (d) triangle When a right circular cone is cut which meets its axis at an angle greater than the semi-apex angle, the curve obtained is (a) ellipse (b) parabola (c) hyperbola (d) triangle  axis at an angle less than the semi-apex angle, the curve obtained is (a) ellipse (b) parabola (c) hyperbola (d) triangle 5.8 The angle between the asymptotes of a rectangular hyperbola is (a) 30° (b) 45° (c) 60° (d) 90° 5.9 Name the curve which has zero eccentricity (a) ellipse (b) parabola (c) hyperbola (d) circle 5.10 Which of the following curves obeys the Boyle's law? (a) Ellipse (b) Parabola (c) Hyperbola (d) Circle 5.11 Which of the following applications hyperbolic curve is used? (a) Solar collector (b) Cooling tower (c) Lamp reflectors (d) Monuments 5.12 The major and minor axes of an ellipse are 100 mm and 60 mm respectively. What will be the distance of its foci from the end of the minor axis? (a) 30 mm (b) 40 mm (c) 50 mm (d) 60 mm  sections. 5.2 What is the inclination of the cutting plane in order to obtain following sections from a cone. (a) parabola, (b) ellipse, (c) hyperbola, (d) rectangular hyperbola. 5.3 Give two practical applications of (a) parabola (b) ellipse (c) hyperbola. 5.4 Define eccentricity. 5.5 Enlist any four methods of drawing (a) parabola (b) ellipse (c) hyperbola.  by intersecting arcs method? 5.7 How a tangent is drawn from a point on the ellipse? 5.8 What do you understand by conjugate diameters? 5.9 Which principle is used in construction of parabola by offset method? 5.10 How is a tangent drawn from a point on the parabola. 5.11 Define ordinate, double ordinate, abscissa and latus rectum. 5.12 Which principle is used in construction of hyperbola by intersecting arcs method.  Multiple-Choice Questions are added at the end of each chapter for the purpose of competitive examinations. Chapter  18  COMPUTER AIDED DESIGN (CAD)  Answers to multiple-choice questions 5.1 (a), 5.2 (c), 5.3 (c), 5.4 (b), 5.5 (d), 5.6 (a), 5.7 (c), 5.8 (d), 5.9 (d), 5.10 (d), 5.11 (b), 5.12 (c)  18.1  INTRODUCTION  The drafting work can be automated and accelerated through the use of Computer Aided Design (CAD) systems. It may be applied for a wide variety of products in the field of automotive, electronics, aerospace, naval, architecture, civil and other disciplines of engineering. The CAD systems were originally used for automated drafting only, but now they also include three-dimensional modeling and computer-simulated operations of the models. Sometimes CAD is translated as 'computer-assisted drafting', 'computer-aided drafting', or a similar phrase. Related acronyms are CADD, which stands for "computer-aided design and drafting"; CAID, for Computer-aided Industrial Design; and CAAD, for "computer-aided architectural design". All these terms are essentially synonymous, but there are some subtle differences in meaning and application.  An exclusive chapter on application of CAD software is made to present some of the basic commands of the latest version of the popular graphics software "AutoCAD 2013" in a simple way.  18.2  CAD APPLICATION  CAD is used to design, develop and optimize products, which can be goods used by end consumers or intermediate goods used in other products. CAD is also extensively used in the design of tools and equipment required in the manufacturing process, and in the drafting and design of all types of buildings ranging from small residential houses to the largest commercial or industrial complexes. CAD enables designers to layout and to develop their work on a computer screen, print and save it for future editing, thus saving a lot of time on their drawings. CAD is mainly used for detailed engineering of 3D models and/or 2D drawings of physical components, but it is also used throughout the engineering process from conceptual design and layout of products to definition of manufacturing methods of components. Rather than building prototypes and changing components to determine the effects of tolerance ranges, engineers can use CAD systems to simulate operation to determine loads and stresses. The major benefits of such systems include lower product development costs and a greatly shortened design cycle. The CAD systems running on workstations and mainframe computers are increasingly integrated with computer aided manufacturing systems.  18.3  SOFTWARE PROVIDERS  There are many CAD software products currently on the market. They can be classified into three types: 2D drafting systems (e.g., AutoCAD, General CADD Pro, VectorWorks, MicroStation); mid-range 3D solid feature modelers (e.g., Inventor, TopSolid, IronCAD, SolidWorks, SolidEdge, Alibre Design, VariCAD, ArchiCAD); and high-end 3D hybrid systems (e.g., CATIA, NX (Unigraphics), Pro/ENGINEER). However, these classifications cannot be applied too strictly as many 2D systems have 3D modules, the mid-range  ABBREVIATIONS, NOTATIONS AND SYMBOLS  2D Two-dimensional 3D Three-dimensional A.G.P. Auxiliary Ground Plane A.I.P. Auxiliary Inclined Plane ALU Arithmetic Logic Unit AV Axis of Vision A.V.P. Auxiliary Vertical Plane BIOS Basic input/output system B.I.S. Bureau of Indian Standards CAAD Computer Aided Architectural Design CAD Computer Aided Drafting CADD Computer Aided Drafting and Design CAID Computer Aided Industrial Design CL Centre Line CP Central Plane CPU Central Processing Unit CU Control Unit F.V. Front View GL Ground Line GP Ground Plane HL Horizon Line H.P. Horizontal Plane HP Horizon Plane H.T. Horizontal Trace IS Indian Standards ISO International Standards Organization LC Least Count LS Length of Scale M.S.D. Main Scale Division P.P. Profile Plane PP Picture Plane RAM Random-Access Memory ROM Read-Only Memory  R.F. Representative Fraction SP Station point S.V. Side View T.S. True Shape TL True Length T.V. Top View UCS User Coordinate System V.P. Vertical Plane V.S.D. Vernier Scale Division V.T. Vertical Trace WCS World Coordinate System Abbreviations and Symbols used in dimensioning f Diameter of circle R Radius of circle Sf Diameter of sphere SR Radius of sphere Side of square HEX Side of regular hexagon Abbreviations for units of length km kilometre Hm hectometre Dm or dam decametre m metre dm decimetre cm centimetre mm millimetre mi mile fur furlong ch chain yd yard ft foot in inch  xxii  Abbreviations, Notations and Symbols  Symbols a Apparent inclination of line or element with the H.P. b Apparent inclination of line or element with the V.P. q True inclination of line or element of plane/solid with the H.P. f True inclination of line or element of plane/solid with the V.P. e Eccentricity of conic sections  Notations a, b, c Top views of points A, B, C a9, b9, c9 Front views of points A, B, C a0, b0, c0 Side views of points A, B, C h Horizontal trace h9 Front view of horizontal trace o Origin or centre point v Top view of vertical trace v9 Vertical trace xy, x1y1, x2y2 Reference lines  Chapter  1 1.1  DRAWING INSTRUMENTS AND SHEET LAYOUT  INTRODUCTION  Drawing is an art of representing objects or forms on a flat surface or a canvas chiefly by means of lines, using any of a wide variety of tools and techniques. It generally involves making marks by moving graphite pencils, ink pen, wax colour pencils, crayons, charcoals, pastels, or markers on a plane surface such as paper, canvas, etc. Engineering drawing is a graphical way to convey an unambiguous and accurate description necessary for engineered items. It is made in accordance with the standard conventions for layout, nomenclature, interpretation, appearance, size, etc. The purpose of engineering drawing is to provide exact geometrical configuration for the construction or analysis of machines, structures, or systems. Today, the mechanics of the drawing task has been largely automated and greatly accelerated through a number of computer softwares. This chapter deals with an introduction and use of drawing instruments and accessories commonly required in preparing engineering drawings.  1.2  INTERNATIONAL AND NATIONAL CODES  Engineering drawing follows certain codes of practice. International Organisation for Standardisation (ISO) recommended international standards for engineering drawing in 1982. At present, these are adopted by 164 countries out of 205 total countries in the world. The standards published by ISO are designated as ISO XXXX:YEAR, where XXXX represents a unique number allocated to the standard and the YEAR represents the year of publication. If a standard has been published before and is updated, the number remains the same as the previous number but the YEAR changes to the new year of publication. Each country has its own standard organisation. For example, in the United Kingdom (UK), it is the British Standards Institution (BSI), in the United States of America (USA), it is the American National Standards Institute (ANSI) and in Germany, it is the Deutsches Institut fur Normung (DIN). In India, the Bureau of Indian Standards (BIS) is engaged in the preparation and implementation of standards, operation of certification schemes both for products and systems, organisation and management of testing laboratories, creating consumer awareness and maintaining close liaison with international standards bodies. The standards published by BIS, irrespective of developed or adopted from ISO, are designated as IS YYYY:YEAR, where YYYY represents another unique number allocated to the standard and the YEAR represents the year of publication. In addition to this, the BIS also publishes some special bulletin which contains a copy of Indian Standards defining special area of interest.  1.2  Engineering Drawing  SP 46:2003 Engineering Drawing Practices for School and Colleges is such a special bulletin of Bureau of Indian Standards, which provides standard codes to be used for engineering drawing practice by all the students and practicing engineers.  1.3  DRAWING INSTRUMENTS  To be proficient in engineering drawing, it is essential to be familiar with the drawing instruments and the techniques of using them. Great care must be taken for the proper choice of drawing instruments to get the desired accuracy with ease. Following is a list of common drawing instruments and accessories: 1. Drawing board 9. French curves 2. Mini drafter 10. Set squares 3. Drawing sheet 11. Eraser or rubber 4. Drawing Pencil 12. Sheet fasteners 5. Compass (pivot joint type and spring bow type) 13. Template 6. Divider (pivot joint type and spring bow type) 14. Pencil cutter 7. Protractor 15. Sand paper pad 8. Ruler (scale) 16. Brush or towel cloth  1.4  DRAWING BOARD  Figure 1.1(a) shows a conventional drawing board. It is made of softwood which provides a flat surface. Engineers and draftsmen use the drawing board for making and modifying drawings on paper with pencil or ink. The working surface must be smooth and free from cracks, bumps and holes so that pencils can easily draw lines. Usually, the surface is covered with a thin vinyl sheet to prevent damage while using the compasses and the dividers. The standard sizes of drawing boards prepared according to recommendations of Bureau of Indian Standards are given in Table 1.1. Drawing boards designated by D00 and D0 are used for drawing offices whereas D1 and D2 are used by engineering students.  (a)  (b)  Fig. 1.1 Drawing board (a) Conventional (b) Modern Table 1.1 Designation and size of Drawing Board (All dimensions in are millimetres) Designation  Length × Width  D00 D0 D1 D2 D3  1525 × 1220 1270 × 920 920 × 650 650 × 470 500 × 350  Tolerance on Length/Width ±5 ±5 ±5 ±5 ±5  Thickness 22 22 22 22 22  Tolerance on Thickness ±1 ±1 ±1 ±1 ±1  Recommended for use with sheet sizes A0 A0, A1 A1, A2 A2, A3 A3, A4  Drawing Instruments and Sheet Layout  1.3  Ancient drawing boards were provided with ebony strips on their left edge to guide the T-squares. As the T-squares are outdated, the modern boards do not require such strips. Presently drawing boards are supported on steel frame as shown in Fig. 1.1(b). The steel frame provides mechanical linkages which help in controlling the height and the inclination of the drawing board to suit comfortable working in standing position. A tall drawing stool prepared according to IS 4209:1989 is generally used for sitting purpose.  1.5  MINI DRAFTER  A mini drafter is used to draw horizontal, vertical or inclined parallel lines of desired lengths anywhere on the drawing sheet with considerable ease. It is basically an arm-type drafting machine which combines the functions of a T-square, set-square, protractor and scale. The size of the mini drafter is specified by the length of arms, usually 43 cm long. Figure 1.2(a) shows a mini drafter used by the students of school and colleges. It consists of linear and circular scales, an adjusting knob, steel bars, a bar plate and a clamping knob. The linear scale is in the form of a pair of blades fixed at right angles and graduated in millimetres. In normal position, one of the blades of the scale is horizontal and the other is vertical. This can be set and clamped at any angle with the help of the circular scale and the adjusting knob. The bigger version of the mini drafter is called a drafting machine. It is permanently fixed on a large drawing board and is used in industries.  1.5.1  Clamping the Mini Drafter  The following procedure should be adopted for clamping the mini-drafter on a drawing board: 1. Set the circular scale of the drafter at zero degree and tighten the adjusting knob. 2. Take the clamping knob towards the top edge of the board and align the linear scales with the vertical and the horizontal boundary lines (or edges in case boundary lines are not drawn) of the drawing sheet. 3. Firmly grip the scales and tighten the clamping knob of the mini drafter, as shown in Fig. 1.2(b). The mini-drafter mechanism will keep the scale always parallel to the original position wherever it may slide over the board.  Clamping knob  Steel bars Adjusting knob  Bar plate  Linear scale  Circular scale (a)  Fig. 1.2 (a) Mini-drafter (b) Clamping mini-drafter  (b)  1.4  1.5.2  Engineering Drawing  Rolling Ruler  Figure 1.3 shows a rolling ruler. It consists of a rolling cylinder which enables it to roll over the drawing sheet. This facilitates to draw parallel straight lines. Sometimes a small protractor is also attached in the middle portion of Fig. 1.3 Rolling ruler it. The rolling ruler must be handled and rolled carefully otherwise it may lead to error. However, a mini drafter should be preferred as it serves the desired purpose with ease and accuracy.  1.5.3  T-Square  Figure 1.4 shows a T-square. Its name comes from the general shape of the instrument where the head is supported on the edge of the drawing board and the long transparent Fig. 1.4 T-square plastic scale slides on the drawing sheet. This scale is used to draw parallel horizontal lines. The T-square serves as a guide for the set-squares for drawing parallel lines at commonly used angles 30º, 45º and 60º. Some T-squares are designed with adjustable heads to allow angular adjustments of the blade. A mini-drafter is used as an alternative of a T-square.  1.6  DRAWING SHEET  A drawing sheet comprises a thick paper onto which the drawing is made. It is available in standard thickness and size. The thickness is specified by weight in grams per square metre (gsm). A sheet with 150 to 250 gsm is suitable for drawing. Size of the sheet depends upon the size of drawing. The Bureau of Indian Standards in its bulletin is 10711:2001 recommends "ISO-A series" of paper size for the drawing sheet as given in Table 1.2. This series of paper always has a length-to-width ratio  Table 1.2  Paper sizes for ISO-A series Series  Paper size (mm × mm)  A0  841 × 1189  A1  594 × 841  A2  420 × 594  A3  297 × 420  A4  210 × 297  A5  148 × 210  A6 105 × 148 A0 has an area of 1 square metre. Successive sizes in the series are designated as A1, A2, A3, etc., which are A7 74 × 105 obtained by halving the preceding size. Figure 1.5 shows A8 52 × 74 the relationship among various sizes. In addition to the ISO-A series, there is a less common special elongated size and exceptional elongated size of drawing sheets. These sizes are obtained by extending the shorter sides of the ISO-A series to lengths that are multiple of the shorter side of the chosen basic format. Such elongated size sheets are used when greater length is required. Coloured sheet with thickness equivalent to drawing sheet is commonly called card sheet. It is spread on the drawing board before fixing the drawing sheet. The card sheet helps to prevent the drawing sheet from getting impressions of the flaws, holes or knots that may be present on the surface of the drawing board.  Drawing Instruments and Sheet Layout  74  148  297  1.5  594  420  841  210  105  52  1189  Fig. 1.5 Drawing sheet sizes of ISO-A series (in mm)  1.6.1  Selection of Sheets  The drawing sheet should be white enough to produce better impression of the drawing than any dull white or light yellowish type. The card sheet of black colour is preferred as it gives less strain on eyes while working. Students generally use A1 size card sheet and A2 size drawing sheet.  1.6.2  Fixing the Sheets  First, spread the card sheet on the drawing board and fix all its four corners with the help of drawing clips. The edges of the card sheet should be parallel to the edges of the drawing board. Now spread the drawing sheet over the card sheet aligning the edges and fix with adhesive tape. It is suggested to place the drawing sheet slightly towards the lower right corner of the card sheet to enable the drafter easily move over the whole working area of the drawing sheet.  1.6.3  Keeping the Drawing Sheet  Valuable drawings need satisfactory handling and storage facilities in order to preserve them in good condition. Figure 1.6 shows a sheet holder which can be used to store sheets (both card and drawing sheets) and carry during travel. It is a cylinder shaped box made up of plastic. The inner diameter is 8 cm and the length can be varied from 70 cm to 130 cm.  Fig. 1.6  Sheet holder  1.6  1.7  Engineering Drawing  DRAWING PENCIL (a)  In engineering drawing, a pencil is used to create marks on the drawing sheet via physical abrasion. It contains a graphite lead with either wooden or mechanical type pro(b) tective casing. A good quality pencil draws line of uniform shade and thickness. A wooden pencil with hexagonal Fig. 1.7 Pencil (a) Wooden (b) Mechanical cross-sectional shape is shown in Fig. 1.7(a). A mechanical pencil shown in Fig. 1.7(b) is basically a lead holder that requires a piece of lead to be manually inserted. It contains a mechanical system, either propeller or clutch type, to push lead through a hole at the end. Such a pencil is easier to use and always guarantees a sharp point.  1.7.1  Grading of Pencils  Pencils are graded according to the proportion of graphite to clay mixture in the pencil lead. A set of pencils ranges from hardest to softest as follows: 9H  8H  7H  6H  5H  4H  3H  2H  H  F HB Medium  B  2B  3B  4B  5B  6B  7B  A pencil that is considered the medium grade is designated by the letter HB. The grade becomes harder shown by the value of the figure preceding the letter H, viz. 2H, 3H, 4H, etc. Similarly, the grade becomes softer shown by the figure preceding the letter B, viz. 2B, 3B, 4B, etc. A hard pencil produces thin, grey line while a soft pencil produces thick line.  1.7.2 Selection of Pencil Engineers prefer harder pencils which allow for a greater control in the shape of the lead and line intensity. Usually, three line qualities are needed in engineering drawing. Thick black lines are used to represent visible and outlines, thin grey lines are used for construction work and medium thick lines are used for dimensioning. Pencil manufacturers have not established uniformity in grades. A pencil with grade H may vary in hardness from one brand to other brand. Moreover, amount of pressure exerted on the pencil also varies with user. Hence, with experience and preference one should select the trade name and grade of pencil that suits the needs. Humidity affects the graphite core of lead pencils. On dry days, the pencil leaves more dust or residue than on days of high humidity. On damp days, pencil lines appear more black or dense. When continuing the drawing on a day of high humidity, use a pencil with one grade harder to produce drawing quality similar to that on a dry day. Different line qualities may also be obtained by varying the amount of pressure exerted on the pencil, but this should not be attempted without experience.  1.7.3 Working End of Pencil The working end of a pencil may have a number of different shapes, namely; conical, chiselled or bevelled as shown in Fig. 1.8. These ends are carefully prepared by blade-type pencil cutters and sand papers. Conical point is used for  Fig. 1.8 Working ends of pencil (a) Conical (b) Chiseled (c) Beveled  Drawing Instruments and Sheet Layout  1.7  general purpose including writing, dimensioning and making arrowheads. Chisel edge is suitable for drawing straight lines while bevelled is preferred for drawing circles and arcs. Always maintain uniform sharpness of the pencil lead to produce a uniform thick line. A pencil with too sharp point breaks easily and a too dull point produces fuzzy lines. Hold the pencil comfortably and naturally. Keep the pencil aligned with the drafting instrument and tilt at an angle of approximately 45° in the direction of pulling. Lines may increase or decrease in thickness when direction of the stroke is changed. Maintain even pressure to produce the line of uniform thickness.  1.8  A compass is used to draw circles, arcs and curves. In engineering drawing, use of a pivot joint compass and a spring bow compass are recommended.  1.8.1  Hold the compas here during use  COMPASS  Pivot Joint Compass  Self-centreing device Set screw  Knee joints Needle  (b) A pivot joint compass shown in Fig. 1.9(a) is used to draw circles, arcs and Extension arm circular curves of diameter greater than 20 mm. It consists of two legs pivoted together at its upper end which provides enough friction to hold the legs of the compass in a set position. One of the legs is equipped with pointed (a) (c) needle at the lower end while the other Fig. 1.9 (a) Pivot joint compass (b) Legs bended at knee joints leg is equipped with a setscrew for (c)Extension arm inserted to draw large circles mounting either a pen or a pencil attachment on the compass. Both legs of the compass are provided with a knee joint so that when bigger circles are drawn, the needle point and the pencil lead point may be kept perpendicular to the drawing sheet (see Fig. 1.9(b)). An extension bar can be inserted in the leg equipped with marking leg to increase the radius of the circle (see Fig. 1.9(c)).  1.8.2  Spring Bow Compass  A spring bow compass shown in Fig. 1.10 is used to draw circles, arcs and circular curves of diameter less than 50 mm. They are usually of the centre adjustment type in which a knurled nut is placed at the centre to adjust the distance between the legs. Side adjustment type bow-compasses are also available in which a knurled nut is placed at the side to adjust the distance between the legs. Both legs of the compass are provided with a knee joint to keep the needle point and the pencil lead point perpendicular to the drawing sheet.  1.8.3  Working with Compass  To draw a circle with a compass, adjust the opening of the legs of the compass to the required radius. Hold the compass and place the needle point lightly on the centre. Slightly press the needle point into the drawing sheet and rotate the  Fig. 1.10  Spring bow compass  1.8  Engineering Drawing  Sandpaper pad  (a)  (b)  Fig. 1.11 (a) Setting length of needle point (b) Preparing pencil lead  marking leg around it. Always rotate the compass clockwise. While drawing circles and arcs with compass, consider the following: 1. As the needle is required to be inserted slightly inside the paper, it is kept slightly longer than the lead point (see Fig. 1.11(a)). 2. The lead of the compass should be sharpened with a single elliptical face (see Fig. 1.11(b)). 3. An even pressure should be applied during rotating the compass to have uniform thickness of the line. 4. It is important that the circles and arcs produced with the compass are of the same quality as corresponding pencil lines. Since much pressure on the compass cannot be exerted as with pencils, a lead of the compass that is one grade softer than the lead of the pencil should be used for corresponding line work. 5. When many circles are drawn using the same centre, the needle of the compass may tend to bore an oversized hole in the drawing sheet. To prevent these holes, a device called a horn centre or centre disk may be is placed over the centre point.  1.9  DIVIDER  Fig. 1.12  Pivot joint divider  Fig. 1.13  Spring bow divider  A divider is used to divide lines or curves into a number of equal parts (using trail method), to transfer measurement from one part of the drawing to another part and to step-off a series of equal distances on the drawing. In engineering drawing, use of a pivot joint divider and a spring bow divider are recommended.  1.9.1  Pivot Joint Divider  A pivot joint divider shown in Fig. 1.12 consists of two legs pivoted together at its upper end which provides enough friction to hold the legs of the divider in a set position. At the lower end both legs are equipped with pointed needle, but it does not have knee joint. In most of the instrument boxes, a needle attachment is provided which has to be mounted on the setscrew of the compass for converting it into the divider.  1.9.2  Spring Bow Divider  A spring bow divider shown in Fig. 1.13 is used for marking minute divisions and large number of short distances. They are usually of centre adjustment type in which a knurled nut is placed at the centre to adjust the distance between the legs.  Drawing Instruments and Sheet Layout  1.9.3  1.9  Working with Divider  To divide either a line or a curve into a given number of equal parts by trial, open the dividers to a rough approximation of the first division and step-off the distance lightly, holding the dividers by the handle and pivoting the instrument on alternate sides of the line at each step. If the dividers fall short of the end of the line, hold the back leg in place and advance the forward leg, by guess, one division of the remaining distance. Repeat the procedure until the last step falls at the end of the line. During this process, do not punch holes in the paper, but just barely mark the surface for future reference. To transfer measurements from one part of the drawing to another part, set the dividers to the correct distance then transfer the measurements to the drawing by pricking the drawing surface very lightly with the points of the dividers. To measure off a series of equal distances on the line, set the dividers to the given distance. Then step-off this distance as many times as desired by swinging the dividers from one leg to the other along the line, first swinging clockwise 180 degrees, then anticlockwise 180 degrees, and so on.  1.9.4  Equal Space Divider  An equal space divider shown in Fig. 1.14 has usually 11 legs. They use multiple metal strips to form ten equal spaces that may be expanded or compressed to set at desired lengths. They can also be used to divide a line into equal number of parts with ease. However, their use in engineering drawing is limited as it may lead to slight error in the division.  1.10  PROTRACTOR  Fig. 1.14  Equal space  divider A protractor is used to draw and measure angles, and to divide circles or sectors into desired number of equal parts. They are available in semi-circular and circular shapes. A semi-circular protractor used by engineers, as shown in Fig. 1.15(a), is generally labelled from 0º to 180º in both directions and graduated in increments of 1/2º. The line joining 0º-180º is called the baseline of the protractor and centre of the baseline is called origin of the protractor. Circular protractors as shown in Fig. 1.15(b) may be labelled from 0º to 360º (both clockwise and counter clockwise), or they may be labelled from 0º to 90º in four quadrants.  (a)  (a)  Fig. 1.15 Protractor (a) Semi-circular (b) Circular  (b)  (b)  1.10  Engineering Drawing  1.10.1 Use of the Protractor To measure the given angle, first align the origin of the protractor over the vertex of the angle to be measured. Then align one of the edges of the angle along the baseline of the protractor. The other edge of the angle is read from one of the two scales of the protractor, whichever is more convenient. Similarly to draw an angle, first align the origin of the protractor over the origin of the given line and align the line along the baseline of the protractor. Mark the point at required angle and join it with the origin of the line.  1.11  RULER (SCALE)  A ruler is used to measure distances and to draw straight lines in centimetres and millimetres. A flat ruler with bevel edges is shown in Fig. 1.16(a). It is available in 15 cm or 30 cm length. One edge is calibrated in millimetres while the other is in half millimetres. Another variant of metric ruler has triangular cross section as shown in Fig. 1.16(b). It has three sides providing six scales, with each side showing two scales. They are easy to pick up. A clip is attached to identify the scale in use. 10  11  12  13  14  7  9  15  16  6  8  17  18  19  5  8  7  20  21  22  4  6  23  24  25  3  5  26  27  2  9  10  4  28  1  3  29  30  0 INCHES  0 1 2 CENTIMETRE 11  12  (a)  Clip  12 0  11 2  4  2 46  48  50  1 52  54  0  80  56  58  10  60  (b)  Fig. 1.16 Ruler (a) Flat with bevel edge (b) Triangular  1.11.1  Working with a Ruler  Keep the edge of the ruler on the line on which the measurement is to be marked, looking from exactly above the required division. Mark the desired dimension with a fine pencil point.  1.11.2  Engineer's Scale  The word 'scale' usually employs for an instrument used for drawing or measuring the length of a straight line. It is also used to represent the proportion in which the drawing is made with respect to the object. It is used to make full size, reduced size or enlarged size drawing conveniently depending upon the size of the object and that of the drawing sheet. Usually, the engineers scale is made up of cardboard and as recommended by Bureau of Indian Standards are available in a set of eight scales. These are designated from M1 to M8 as shown in Table 1.3.  Drawing Instruments and Sheet Layout  1.11  Table 1.3 Designation and description of Engineer's scale Designation  Description  Scales  Designation  Description  Scales  M1  Full size 50 cm to a metre  1:1 1:2  M5  5 mm to a metre 2 mm to a metre  1:200 1:500  M2  40 cm to a metre 20 cm to a metre  1:2.5 1:5  M6  3.3 mm to a metre 1.66 mm to a metre  1:300 1:600  M3  10 cm to a metre 5 cm to a metre  1:10 1:20  M7  2.5 mm to a metre 1.25 mm to a metre  1:400 1:800  M4  2 cm to a metre 1 cm to a metre  1:50 1:100  M8  1 mm to a metre 0.5 mm to a metre  1:1000 1:2000  1.12 FRENCH CURVES French curves are used to draw smooth curves of almost any desired curvature in mechanical drawings. They are made of transparent plastic having an edge composed of several different curves. They are available in a variety of shapes and sizes. A typical set of three French curves available in Indian market are illustrated in Fig. 1.17.  1.12.1  Fig. 1.17  French curves  Use of the French Curves  French curves are used to draw a perfectly smooth curve through predetermined points in short steps. First plot the points by a light pencil to connect the points freehand resulting into a smooth flowing curve. Select a suitable French curve and match a part of its edge with the freehand curve already drawn. Move the dark pencil along the part of the curve matching with the French curve edge. Now move the French curve forward to match the next segment of the freehand curve and darken it in the same manner. This will result into a series of plotted points. Figure 1.18 shows how a smooth line is drawn through a series of plotted points. The French curve in view A matches points 1, 2, 3, and 4. Draw a line from 1 to 3 only (not to 4). At B, the curve matches points 3 to beyond 6. Draw a line from 3 to 6. At C, it matches a point short of 6 to beyond 7. Draw a line from 6 to 7. At D, it matches a point short of 7 to beyond 9. Draw a line from 7 to 9. At E, it matches a point short of 9 to beyond 11. Draw a line from 9 to 11. While plotting the desired curve, consider the following:  Fig. 1.18 Use of French curve in drawing predetermined curve  1.12  Engineering Drawing  1. French curve should be so placed that it intersects at least two points of the curve. If the curve is sharp enough, you may consider some more points on the curve. 2. Avoid abrupt changes in curvature by placing the short radius of the French curve toward the short radius portion of the curve. 3. Avoid working on the underside of the French curve. You may need to change your position around the drawing board, when necessary, so that you can work on the side of the French curve that is away from you.  1.12.2 Flexible Cord Recently a flexible cord shown in Fig. 1.19 is also used in place of French curves for drawing smooth curves with relatively great ease. It consists of a lead bar embedded in rubber covering. The flexibility of the material allows it to bend to any contour.  Flexible cord  SET SQUARES 21 20 19 18 17 16  16  15  15  13  14  14  12 11 10 9 8 7 6 5  °  45°  60 6  5  4  3  2  13 11 10 9 8 7 6 5 4  4  7  3  3  8  1  16  15  14  13  12  11  2  2  9  10  9  8  7  6  1  10  5  4  3  2  1 1  11  ERASER  12  12  45°  (a)  1.14  30°  13  A pair of right angled triangle is called set squares. A set square has either 45º-45º angle or 30º–60º angle. The 45º set square shown in Fig. 1.20(a) is a right-angled triangle in which acute angles measure 45º. The 30º–60º set-square shown in Fig. 1.20(b) is a right-angled triangle in which acute angles measure 30º and 60º. Set squares are usually made of transparent plastic to see the work underneath. They are used to draw lines inclined at 30º, 45º and 60º with the horizontal. By using two set squares, lines inclined at 15º and 75º can also be drawn.  22  23  1.13  Fig. 1.19  Fig. 1.20  (b)  Seta square (a) 45° (b) 30°–60°  An eraser, also known as a rubber, is used for removing pencil markings. An eraser that is popular is the art gum eraser, made of soft pliable gum. It is especially suited to removing large areas, and does not damage the paper. It leaves much residue which should be whisked away with a draftsman's brush or cloth. A kneaded eraser is usually made of a grey or light blue material that resembles putty or gum. It erases by absorbing graphite particles and can be used for precision erasing. Generally, it leaves no residue. If this eraser becomes overly warm, the substance may break down leaving a stain on the drawing surface. A soft vinyl eraser has a plastic-like texture and is commonly white in colour. When large areas or dark marks are erased, the eraser causes smearing. Therefore, it is generally used to erase light marks and for precision erasing. Engineers favour this type of eraser for work on technical drawings due to their gentleness on paper. A harder eraser is designed for erasing lines in ink. Figure 1.21 shows an electric eraser with refill box. It has a knob in a short thin rod attached to a motor. The eraser knob turns at a uniform speed achieving a smooth erasure with a minimum of paper trauma. Electric erasers work quickly and completely. Holding the electric eraser steady in one spot Fig. 1.21 Electric eraser with refill may easily wear a hole or damage the surface of the material being erased.  Drawing Instruments and Sheet Layout  1.13  When there are many lines close together and only one of them is to be removed or changed, the desired lines may be protected by an erasing shield shown in Fig. 1.22.  1.15  SHEET FASTENERS  Sheet fasteners are used to fix the card sheet and the drawing sheets on the drawing board. Figures 1.23(a-c) show drawing pins, drawing clips and adhesive tapes that can be used as sheet fasteners. 1. Drawing pins or thumb tacks They are easy to use and Fig. 1.22 Eraser shield remove. They offer a firm grip on the drawing sheet. Their use should be avoided as it damages the drawing board surface. Moreover the heads of the pin may obstruct the free movement of the mini-drafter. 2. Drawing clips They are made of steel or plastics and have a spring action. They can be used for fixing the card sheet and drawing sheets at all the four corners when their sizes are compatible with the drawing board. In case the drawing sheet is much smaller than the drawing board, it is not possible to use such clips. 3. Adhesive tape Generally, adhesive tapes having width of 10 mm to 15 mm are used to fix the drawing sheet on the card sheet. A length of around 40 mm is cut and fixed across the corners of the drawing sheet. Lighter coating of adhesive helps in removing the tape without tearing or marring the drawing sheet.  (a)  (b)  (c)  Fig. 1.23 Sheet fasteners (a) Drawing pins (b) Drawing clip (c) Adhesive tape  1.16  TEMPLATES  Drawing templates or stencils are time saving devices that are used for drawing various shapes and standard symbols. They are especially useful when shapes and symbols repeatedly appear on the drawing. They are available in a wide variety of shapes including lettering, circles, ellipses, isometric circles, polygons and arrowheads. Figures 1.24(a) and (b) show a few of them that can be used to draw circles, polygons, arrowheads, isometric circles and lettering. A template should be hold firmly while using to keep it from slipping out of position. They should be used only when accuracy can be sacrificed for speed.  (a)  Fig. 1.24 Drawing templates (a) General purpose (b) Lettering  (b)  1.14  1.17  Engineering Drawing  PENCIL CUTTERS  A pencil cutter or sharpener is used to prepare the working end of a pencil. A pencil with softer lead requires sharpening more often than with hard lead. Figure 1.25(a) shows a conventional sharpener which can produce only short length conical point. Figures 1.25(b) and (c) show blade-type cutters and mechanical sharpener. They are suitable for removing the wood from pencil. Thereafter, the desired working end can be prepared by rubbing over the sandpaper pad.  (a)  (a)  (b)  Fig. 1.26  (a) Sandpaper Pad (b) Conical point is produced  (b) (c)  Fig. 1.25  1.18  Sharpeners (a) Conventional (b) Blade cutter (c) Mechanical  Fig. 1.27  Brush  SAND PAPER PAD  A sand paper pad or block is used to sharpen the pencil lead. It should be kept within reach of the user as it is frequently required to prepare the pencil edge. Figure 1.26(a) shows a sand paper pad. Figure 1.26(b) shows a conical or needlepoint being produced by rubbing pencil lead on the sandpaper pad.  1.19  BRUSH OR TOWEL  Figure 1.27 shows a brush. The brush, duster or towel cloth is used to keep the drawing surface clean by removing crump (formed after the use of eraser), graphite particles or accumulated dirt before they spread over the drawing sheet. Crump and graphite particles should not be brushed off with hands as they may spoil the drawing instead of cleaning it.  1.20 GENERAL PREPARATION FOR DRAWING Arrange the drawing board and stool so that work could be done comfortably without fatigue or eye strain. The working area should be well lighted. Natural light is the best, if available and ample. The drawing  Drawing Instruments and Sheet Layout  1.15  board should be arranged such that the light may come from the front-left (from the front right in case of a left-handed person). This minimises shadows cast by drawing instruments and hands. Every possible care must be taken to eliminate eye strain. Clean all the drawing instruments and accessories so that their surface may not spoil the sheet. Arrange them in a systematic manner, which is essential for saving time. Place the drawing instruments and reference publications on a small worktable adjacent to the drawing board. Clamp the mini-drafter on the drawing board and fasten the drawing sheet such that the mini-drafter can slide over the entire working area of the sheet. Switch to a harder pencil lead to draw fine or precise details.  1.21  PLANNING AND LAYOUT OF SHEET  A proper planning and layout of drawing sheet facilitates the easy reading of drawings and interchange of information. A standard arrangement should ensure that all necessary information for understanding the content of drawing is included and sufficient extra margin is left to facilitate easy filing and binding wherever necessary. The Bureau of Indian Standards in its bulletin IS 10711:2001 specifies the size and layout of the standard drawing sheets. It is recommended that standard formats should be followed to improve readability, handling, filing and reproduction. Individual companies may use a slightly different layout for the sake of their own convenience but all necessary information is located at approximately the same place on most engineering drawings. Companies generally use pre-printed title block, borders and frames on drawing sheet to reduce drafting time and cost.  1.22  FRAMES AND BORDERS  The drawing sheets of sizes greater than that of the ISO-A series sizes are called untrimmed sheet. The sheet cut from the untrimmed sheet are called trimmed sheet. The frame limits the drawing space. It is recommended that the frame must be provided on the drawing sheets of all sizes and should be executed with continuous lines of 0.7 mm width. Table 1.4 provide the sizes of the untrimmed sheet, trimmed sheet and drawing space. Figure 1.28 shows relation between untrimmed sheet and trimmed sheet of A3 size along with other information. Table 1.4  Preferred sizes of untrimmed sheet, trimmed sheets and drawing space  Designation  Untrimmed sheet (in mm)  Trimmed sheet (in mm)  Drawing space (in mm)  Number of grid reference fields  A0  880 3 1230  841 3 1189  821 3 1159  16 3 24  A1  625 3 880  594 3 841  574 3 811  12 3 16  A2  450 3 625  420 3 594  400 3 564  8 3 12  A3  330 3 450  297 3 420  277 3 390  638  A4  240 3 330  210 3 297  180 3 277  436  The space between the edges of the trimmed sheet and the frame is called a border. The width of the border is 20 mm on the left edge and 10 mm on the other edges. The larger border on the left edge helps in filing without damaging the drawing space. The border contains the following items: 1. Trimming marks Trimming marks are used as an aid to trimming the untrimmed sheet. The marks are provided in the borders at the four corners of the sheet. The marks are either in the form of two overlapping  1.16  Engineering Drawing untrimmed trimmed drawing space 10  5 1  2  3  4  5  6  7  8  50 A  A  Trimming Mark  Grid Reference Number 3.5 mm high Grid Reference Letter 3.5 mm high  Centring Mark  untrimmed trimmed drawing space  Metric Reference Graduation (0.35 mm wide continuous line)  Grid Reference Border (0.35 mm wide continuous line)  C  C  Drawing Space  D  Centring Mark (0.7 mm wide continuous line)  Grid Reference Field Line (0.35 mm wide continuous line)  D  5  170  Drawing Frame (0.7 mm wide continuous line)  F  Orientation Mark 5  1  10  E  2  Title Block  65  E  F  10 3  4  5  6  7  8  Frames and borders  Frame  Frame  Trimmed  Trimmed  Trimming mark  Fig. 1.29  B  Orientation Mark  5 20  Fig. 1.28  50  Grid Reference Fields  B  Trimming mark  Trimming marks  filled rectangles having 10 mm × 5 mm size or right angled isosceles triangles having 10 mm long sides as shown in Fig. 1.29. The sheets are trimmed to the outer edges of these marks and therefore remain on the sheet after it has been trimmed. 2. Grid references A grid reference system, also called alpha-numeric referencing, provides an easy reference method to locate a specific area on the drawing for additions, modifications, revisions, etc. For execution, a grid reference border is drawn all around the outside of the frame at a distance of 5 mm. Starting from the centre of each sides, short lines are drawn at every 50 mm to form a reference field of size 5 mm × 50 mm. The corner reference fields may be longer or shorter than 50 mm to account for the remainders resulting from the divisions. Table 1.4 provides the number of reference fields on short × long sides of the standard size drawing sheets.  Drawing Instruments and Sheet Layout  1.17  The letters and numerals of nearly 3.5 mm height are written in vertical characters within the grid reference field. Usually, letters are placed in chronological order from the top to the downwards on both left and right side reference fields (except for the A4 size sheet where they are placed in the right side area only). Letters I and O are not used. The numbers are placed in chronological order from the left to the right side on both top and bottom reference fields (except for the A4 size sheet where they are placed in the top side area only). Figures 1.30(a) and (b) illustrates the grid reference system for A1 and A2 size drawing sheets. 1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  1 A  A  B  B  C  C  D  D  E  E  F  F  G  G  H  H  J  J  K  K  L  L  2  3  4  5  6  7  8  9  10  11  12  A  A  B  B  C  C  D  D  E  E  F  F  G  G  Title Block H  Title Block M  H  M  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  1  2  3  (a)  4  5  6  7  8  9  10  11  12  (b)  Fig. 1.30 Planning and layout of drawing sheet for (a) A1 size (b) A2 size  3. Centring mark Four centring marks are provided to facilitate positioning of the drawing sheet for photocopying, scanning, etc. The marks are placed at the centre of each of the four sides. The centring marks are 10 mm long starting from the grid reference border enters in the area of drawing space as shown in Fig. 1.28. The marks should be executed with a continuous line of 0.7 mm width. 4. Orientation mark Two orientation marks are provided to indicate the orientation of the drawing sheet on the drawing board. The marks are in the form of arrows as shown in Fig. 1.28. The marks are placed across the frame, one at a shorter side and one at a longer side, coinciding with the centring marks on those sides. One of the orientation marks always points to the draftsman. 5. Metric reference graduation A metric reference graduation shows usefulness in knowing the scale factor of the drawing which has been scanned or photocopied in a scale different than that of the original. The metric reference graduation starts from the left side frame and extends into the border for nearly 3 mm width. The graduation is 100 mm long, divided into 10 mm intervals and disposed symmetrically about a centring mark as shown in Fig. 1.28.  1.23 TITLE BLOCK A title block provides information for identification, administration and interpretation of the whole drawing. It is placed in the bottom right-hand corner of the drawing frame, where it is readily seen when the prints are folded in the prescribed manner. The size of the title block recommended is 170 mm × 65 mm for all sizes of drawing sheets. Figures 1.31 and 1.32 show the sample title block used by draftsmen in industries and engineering students in colleges respectively. A title block should contain the following information: 1. Name of the legal owner of the drawing (company, firm, organisation or enterprises) 2. Title of the drawing  1.18  Engineering Drawing  Fig. 1.31 Title block used by draughtsmen in industries  Fig. 1.32 Title block used by students in engineering colleges  3. 4. 5. 6.  Drawing sheet number The scale Symbol indicating the angle of projection used The signature or initials of the staff designing, drawing, checking, approving officer and issuing officer, along with dates. 7. Other information, as required Titles of drawings should be as concise as possible, consistent with adequate description. Multiple sheet drawings with the same identification number should be indicated as 'N of P', where N is the sheet number and P is the total number of sheet. The scale is the ratio of the linear dimension of an element of an object as represented in the drawing to the real linear dimension of the same element of the object itself. All drawings should be drawn to the scale for which, the selected scale should be large enough to permit easy and clear interpretation of the information depicted. The scale should be noted in the title block. When more than one scale is used, they should be shown close to the views to which they refer, and the title block should read 'scales as shown'. If a drawing uses predominantly one scale, it should be noted in the title block together with the wording 'or as shown'. All orthographic drawings are made either according to first angle or third angle projection. These are depicted in the title block by their corresponding symbols. Title block should also contain statement "All dimensions are in millimetres unless otherwise specified". This means that all the features or dimension on drawing have a relationship or specifications given in the title block unless a specific note or dimensional tolerances is provided at a particular location in the drawing.  Drawing Instruments and Sheet Layout  1.24  1.19  SPACE FOR TEXT  The space for text on a drawing sheet should provide all information necessary for the understanding the contents of the drawing. The space for text should be provided at the right-hand frame of the drawing space as shown in Fig. 1.33(a). The width of the space shall be equal to that of the title block, i.e., maximum 170 mm or at least 100 mm. If a figure takes up the whole width of the drawing sheet then the space for the text shall be provided at the bottom edge of the drawing sheet as shown in Fig. 1.33(b). The height of the space for text shall be chosen as required. 1  2  3  4  5  6  7  A  SPACE FOR TEXT  Explanation  B  C  2  4  3  5  6  7  8  A  A  A  B  B  B  C  C  C  D  D  D  E  E  Instruction References Location figures Revision table Item references  D  1  8  Minimum 100 mm  Explanation  Maximum 170 mm E  Instruction  References  Item references E  SPACE FOR TEXT 65  TITLE BLOCK  TITLE BLOCK  F  F  1  2  3  4  5  6  7  F  8  (a)  F  Revision table 1  2  3  4  5  6  7  8  (b)  Fig. 1.33 Space for text (a) Right-hand edge (b) Bottom edge  The space for text should provide the following information: 1. Explanations Here the explanation of special symbols, designation, abbreviations and units of dimensions should be given which are needed to read the drawing. 2. Instructions Here the instruction related to material, realisation, surface treatment, assembly placing, number of units and combined dimensions should be given. 3. References Here the reference should be made to supplementary drawings and other documents. 4. Location figures Location figures are used in architectural and building drawings. A location figure may comprise the following: (a) Schematic site plan with area, arrow indicating the north, building, part of building, etc. (b) Schematic plan of building with area, part, etc. (c) Schematic section through building with floor plan direction of view, etc. 5. Revision table Revision tables are used to record all document modifications, alterations or revisions which are made time to time to the drawing. In addition, any other factor which might influence the validity of the drawing shall be located in the revision table. The method of recording may vary in detail, but commonly the necessary information is entered in a table made of thin or thick continuous lines. The word 'ditto' or its equivalent abbreviations should not be used. To facilitate extension of revision panel, entries for revision should begin from bottom upwards if the revision panel is a part of the title block as shown in Fig. 1.34 and from top downwards when revision panel is at the top right hand corner on drawing. It may contain the following information:  Engineering Drawing 5 mm  1.20  DESIGNATION  Fig. 1.34  DETAILS OF REVISION  DATE  SIGNATURE  Revision table  (a) Designation The identification of a change on a drawing may be a symbol, number or letter enclosed within a circle, square or triangle. The designation column should show the reference to this identification mark or appropriate grid reference. (b) Detail of revision The detail of revision column should show brief record of the changes in the drawing. (c) Date The date column should show dated initials of the person who carried out the revision. (d) Signature The signature column should show dated initials of the approving authority. (e) Other applicable information To accompany other information necessary for clarity regarding revision in the drawing, more columns can be added.  1.25  ITEM REFERENCES ON DRAWING AND ITEM LISTS  If the drawing contains a number of items, or if it is an assembly drawing, a tabulated list of items is attached to the bottom right of the drawing frame, just above the title block. The list may be in conjunction with the title block. The item list included in the drawing should have its sequence from bottom to top, with headings of the column immediately underneath as shown in Fig. 1.35. It should be such as to be read in the viewing direction of the drawing. It is recommended that the item list be arranged in columns to allow information to be entered under the following headings: 1 2  3 4 Fig. 1.35  5 mm.  2  4.  1  HEXAGONAL NUT  3.  1  WASHER  2.  1  SQUARE HEADED BOLT  1.  2  S. NO.  QUANTITY  PLATES DESCRIPTION  M.S. REFERENCE  MATERIAL  Item list (bill of materials)  1. Quantity The quantity column should show the total number of that particular item necessary for one complete assembly. 2. Description The description column should show the designation of the item. If the item concerns a standard part such as bolt, nut, stud, etc., its standard designation may be used. 3. Item reference The reference column should show the reference to the relevant item reference number. It is generally composed of Arabic numerals. To distinguish them from other indications the numerals used have either (a) height twice as used for dimensioning and similar indications, and/or (b) encircling. The item reference must assign in a sequential order to each component part shown in assembly and each detailed item on the drawing. The identical parts in an assembly should have the same item reference. 4. Material The material column should show the type and quality of the material to be used. If this is a standard material, its standard designation should be mentioned.  Drawing Instruments and Sheet Layout  1.21  5. Other applicable information To accompany other information necessary for finish products such as stock number, unit mass, state of delivery, etc., more columns can be added.  1.26  FOLDING OF DRAWING SHEETS  The drawing sheet after completion of the drawing should be folded properly according to IS 11664:1986 recommended by Bureau of Indian Standards. Figure 1.36(a) shows the method of folding the drawing sheet  Fig. 1.36(a) Folding of drawing sheets for filing or binding, all dimensions are in millimetres  1.22  Engineering Drawing  intended for filing or binding while Fig. 1.36(b) shows the method of folding the drawing sheet intended to keep individually in filing cabinet. It can be seen that the title block of all the folded prints appears in topmost position. Depending upon the folding method adopted, suitable folding marks are to be introduced in the tracing sheets as a guide.  Fig. 1.36(b) Folding of drawing sheets for storing in filing cabinet, all dimensions are in millimetres  Drawing Instruments and Sheet Layout  1.27  1.23  CONCLUSION  One should practice handling and using drawing instruments before working with complex drawing problems. Developing correct drawing habits will enable to make continuous improvement in the quality of drawings. Each drawing will offer an opportunity for practice. Later on, good form in the use of instruments will become a natural habit.  EXERCISE 1A 1.1 Use a mini-drafter to draw Figs. E1.1 to E1.3 in a square of 100 mm side. Take the distance between consecutive parallel lines as 10 mm.  Fig. E1.1  Fig. E1.2  Fig. E1.3  1.2 Use a mini-drafter to draw Figs. E1.4 to E1.6 in a square of 90 mm side. Take the distance between consecutive parallel lines as 10 mm.  Fig. E1.4  Fig. E1.5  Fig. E1.6  1.3 Use a mini-drafter to draw Fig. E1.7 to E1.9 in a square of 100 mm side. In Figs. E1.7 and Fig. E1.8, take the distance between consecutive parallel lines as 10 mm.  Fig. E1.7  Fig. E1.8  Fig. E1.9  1.24  Engineering Drawing  1.4 Use necessary drawing instruments to draw Figs. E1.10 to E1.12 in a square of 100 mm.  R10  10  Fig. E1.10  Fig. E1.11  Fig. E1.12  1.5 Use necessary drawing instruments to draw Figs. E1.13 to E1.15 in a square of 100 mm.  15°  15 °  15° °  15  15°  Fig. E1.13  Fig. E1.14  Fig. E1.15  1.6 Use necessary drawing instruments to draw Figs. E1.16 to E1.18 in a circle of diameter 100 mm.  Fig. E1.16  Fig. E1.17  Fig. E1.18  1.7 Use necessary drawing instruments to draw Figs. E1.19 to E1.21 in a circle of diameter 100 mm.  Fig. E1.19  Fig. E1.20  Fig. E1.21  Drawing Instruments and Sheet Layout  1.25  VIVA-VOCE QUESTIONS 1.1 What do you mean by the International Organisation for Standardisation and Bureau of Indian Standards? 1.2 What is the standard designation of the drawing boards recommended by Bureau of Indian Standards? Which drawing board is recommended for the A2 size drawing sheet? 1.3 How pencils are graded? Which grade of pencil is suitable for lettering, drawing outlines and visible edges, and construction lines? 1.4 What is the use of Engineer's scales? List the types of engineer's scale as recommended by Bureau of Indian Standards. 1.5 What is the use of French curves? Explain its working in brief. 1.6 What is the use of a pair of set-squares? How parallel lines are drawn with the help of a set-square? 1.7 How a pair of set-squares can be used to draw an angle of 15° and 75°?  1.8 Name different types of fasteners that can be used to fix a drawing sheet on the drawing boards. Give their relative merits and demerits. 1.9 What do you mean by drawing frames and borders? Enlist different items contained by them. 1.10 Explain the purpose of the items contained by frames and borders. 1.11 What information should be contained in the title block of a drawing sheet? 1.12 Write short notes on (a) grid reference and (b) metric reference graduation. 1.13 What information may be included in the space for text? 1.14 What is a revision table? What information should be contained by it? 1.15 When an item references is required? How is the item list prepared?  MULTIPLE-CHOICE QUESTIONS 1.1 Which of the following is bulletin is the recent publication of Bureau of Indian Standards, contains codes for practice in engineering drawing? (a) IS 696 (b) SP 46 (c) BS 8888 (d) ASME Y14.100 1.2 A device which combines the functions of a Tsquare, set square, protractor and sca

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