MRCET CAMPUS MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY (AUTONOMOUS INSTITUTION - UGC, GOVT.OF INDI A) Affiliated to JNTUH; Approved by AICTE, NBA-Tier 1& NAAC with A-GRADE I ISO 9001:2015 Maisammaguda, Dhulapally, Komaplly, Secunderabad - 500100, Telangana State, India

COMPUTER AIDED ENGINEERING GRAPHICS 2022-23 (R22) PREFACE The communication of the ideas through the graphical language is the oldest form of communication among humans; all it requires is some kind of tools to form an image.

Engineering graphics is a study which requires special equipment or tools to form the im ages.

The tools can be simple pencil and draft board or a computer controlled drafting device.

From time to time several attempts were made to make the creation of the objects by graphical means. The Engineering Graphics has evolved from primitive hand dr awing to instrument drawings to present computer 2D find 3D drafting. Today the default industry standard is to use computerized drawings. The computerized drawings have their advantages of storage and retrieval, ease of modification, transmission. Further the most important factor

is the accuracy of creation of overall design and specially curves which no hand drawing can match.

Educational institutions are aware of the present needs of the industry and slowly switching from the drawing boards to computers in their classrooms. With the introduction of computer drawings, the students are able to create better and faster drawings mo re accurately, be it any complicacy in the engineering drawing. Further, there is less likelihood of making mistakes and at the same time avoid the conventional time -consuming procedures in creating

the drawings. Many engineering institutions worldwide have adopted this approach to increase the employability quotient of the students.

This text teaches Engineering Drawing using AutoCAD 2020 as its drawing instrument. Although it follows the general format of many technical drawing texts and presents much of the same material about drawing conventions and practices, the emphasis is on creating accurate, clear drawings. The standards and conventions are presented and their applications are shown by the use of AutoCAD 2020. This integrated teaching concept is

followed throughout the text.

Complied by Faculty of Mechanical Engineering , MRCET.

Acknowledgements This book, Computer Aided Engineering Graphics , is the final outcome of an idea that evolved to replace the conventional Engineering Drawing with AutoCAD based Drawing considering the modernization in Design Industry. During the last seven years we have put in our efforts to produce the revised versio ns of the course notes, with the help and support of

many well -wishers. Thanks are due for all have directly or indirectly contributed to this work.

We thank Prof. Dr. V.S.K.Reddy , Vice Chancellor . Special Thanks to Prof. V. Madhusudan Reddy , Professor and Head, Department of Humanities and Sciences, MRCET, for his continuous motivation in developing this Book.

It is a privilege to express my heartfelt thanks to all our Colleagues and Students for their valuable suggestions and constructive criticism was like a bacon light and became a source of inspiration in compiling and developing this text. Finally, we extend profound and heartfelt thanks to our family members. With out their encouragement, patience and understanding this endeavor would not have been possible.

PROGRAM OUTCOMES A B.Tech –graduate should possess the following program outcomes.

1 Engineering knowledge : Apply the knowledge of mathematics, science, engineering fundamentals and an engineering specialization to the solution of complex engineering problems.

2 Problem analysis : Identify ,formulate, review research literature, and analyze complex engineering problems reaching substantiated conclusions using first principles of mathematics, natural sciences, and engineering sciences.

3 Design/development of solutions : Design soluti ons for complex engineering problems and design system components or processes that meet the specified needs with appropriate consideration for the public health and safety, and the cultural, societal, and environmental considerations.

4 Conduct investigations of complex problems : Use research -based knowledge and research methods including design of experiments, analysi s and interpretation of data, and synthesis of the information to provide valid conclusions.

5 Modern tool usage : Create, select, and apply appropriate techniques, resources, and modern engineering and IT tools including prediction and modeling to complex engineering activities with an understanding of the limitations.

6 The engineer and society : Apply reasoning informed by the contextual knowledge to assess societal ,health, safety, legal and cultural issues and the consequent responsibilities relev ant to the professional engineering practice.

7 Environment and sustainability : Understand the impact of the professional engineering solutions in societal and environmental contexts, and demonstrate the knowledge of, and need for sustainable development.

8 Ethics : Apply ethical principles and commit to professional ethics and responsibilities and norms of the engineering practice.

9 Individual and teamwork : Function effectively as an individual, and as a member or leader in diverse teams ,and in multi disciplinary settings.

10 Communication : Communicate effectively on complex engineering activities with the engineering community and with society at large ,such as, being able to comprehend and write effective reports and design documentation ,make effective presentations ,and give and receive clear instructions.

11 Project management and finance : Demonstrate know ledge and understanding of the engineering and management principles and apply these to one’s own work, as a member and leader in a team, to manage projects and in multi disciplinary environments.

12 Life long learning : Recognize the need for and have the preparation and ability to engage in independent and life -long learning in the broadest context of technological change.

COMPUTER AIDED ENGINEERING GRAPHICS Course Objectives:

1. To learn basic engineering graphics and Au to CAD concepts.

2. To learn the 2D principles of orthographic projections and Multiple views of the same 3. To know the planes and solid Projection 4. To gain the capability of designing 3D objects with isometric principles by using computer aided sketche s 5. To know the conversion of Orthographic Views to isometric Views and isometric to

Orthographic views UNIT -I Introduction to Auto CAD: Introduction to software interface Standard toolbar/menu, Understanding the co -ordinate systems -2D and 3D Visualisation, Setting the Paper sizes and title block importance, printing and plotting. Draw commands: line, arc, circle, rectangle,

polygons, ellipse, polyline, sp lines, text. Modify commands: copy, mirror, offset, arrays, move, extend, break, trim, lengthen, chamfer, fillet.etc., Constraints: horizontal, vertical, parallel, concentric, perpendicular, symmetric, equal, collinear. Dimensioning Commands:

Dimensioning and Dimension Style. Division: Line division, and circle division. Polygons:

Constructing regular polygons - inscribed and circumscribed methods and general method .

UNIT -II:

Projection of Points: Introduction to reference planes, four quadrants, importance of reference lines. Projection of points in all the four quadrants Projection of Lines: Parallel to both the reference planes, Parallel to one plane and perpendicular to oth er plane, Inclined to one plane and parallel to other plane, Inclined to both planes

UNIT -III:

Projections of Planes: Introduction to Regular planes. Parallel/Perpendicular to one reference plane, Inclined to one plane and Inclined to both the reference plane s.

Projections of Solids: Introduction - Prisms, Pyramids, Cone and Cylinder, Axis parallel and perpendicular to one reference plane, Axis inclined to one reference plane.

UNIT -IV Isometric Projection: Introduction, Isometric projection of simple plane figu res, Solids - right regular prisms, pyramids, cylinder, cone – H.P, V.P UNIT -V Conversions: Conversion of Isometric Views to Orthographic Views and Orthographic Views to

Isometric Views TEXT BOOKS:

1. Engineering Drawing – N.D. Bhatt & V.M. Panchal, 48th edition, 2005 Charotar Publishing House, Gujarat.

2. "Computer Aided Engineering Drawing" by Dr. M H Annaiah, Dr C N Chandrappa and Dr B Sudheer Prem Kumar Fifth edition, New Age International Publishers REFERENCE BOOKS:

1. Computer Aided Engineering Draw ing – S. Trymbaka Murthy, - I.K. International Publishing House Pvt. Ltd., New Delhi, 3rd revised edition -2006.

2. Engineering Graphics - K.R. Gopalakrishna, 32nd edition, 2005 - Subash Publishers, Bangalore.

COURSE OUTCOMES:

After the completion of course the student will be capable to 1. To produce geometric construction, dimensioning & Curves and detail drawings.

2. To compile Projections of points, lines, then create virtual drawing by using computer 3. To sketch the Planes and Solid Projections 4. To develop isometric drawings of simple objects reading the orthographic projections of those objects.

5. To understand and visualize the 3 -D view of engineering objects. Elaborate the conversions of 2D -3D and Vice -Versa .

CONTENTS 1 Introduction to Computer Aided Engineering Graphics Engineering Graphics Overview Conventional Engineering Drawing Lettering

Dimensioning About AutoCAD AutoCAD Installation Process AutoCAD user Interface Commands

Drawing Commands Editing Commands Drawings aids Geometrical Constructions 1 - 47 2 Orthogonal Projections

Projection of Points Projection of Lines 48 - 66 3 Projection of Planes Projections of Solids 67 – 107 4 Isometric Projections

Isometric Projections 3D Modeling Commands in AutoCAD 108 – 126 5 Transformations of Projections Orthographic to Isometric Isometric to Orthographic 127 – 142

UNIT 1 INTRODUCTION TO COMPUTER AIDED ENGINEERING GRAPHICS Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 2 | P a g e

Engineering Graphics ngineering Graphics is the principal method of communication in the field of engineering and science . the graphics of engineering design and construction is one among the most important courses of all studies for engineering. It is the language used by the designer, technician and engineer to communicate, design and construct details to others.

The Graphic Language Engineering drawing is the graphic language used by engineers and technologists globally. The graphic language may be defined as the graphic representation of physical objects and their relationships. This language is written in the form of drawings using straight and curved lin es which represent the shape, size and specifications of physical objects. The language is read by

interpreting the drawings so that the physical objects can be constructed exactly as conceived by the designer. An engineer, should have proper understanding of the theory of projection, dimensioning and conventions related to working drawings, in order to become professionally efficient.

Traditional Drafting Engineering drawings are made up of straight and curved lines to represent the surfaces, edges and centres of objects. Symbols, dimensional values and word -notes are added to these lines so that they collectively make the complete description. The traditional drafting is the presentation of these drawings manually, by freehand sketching or with the help o f drawing instruments.

Computer Aided Drafting Computer Aided Drafting is a process of preparing a drawing of an object on the screen of a computer. There are various types of drawings in different fields of engineering and sciences. In the fields of mech anical or aeronautical engineering, the drawings of machine components and the layouts of them are prepared. In the field of civil engineering, plans and layouts of the buildings

are prepared. In the field of electrical engineering, the layouts of power di stribution system are prepared. In all fields of engineering use of computer is made for drawing and drafting.

The use of CAD process provides enhanced graphics capabilities which allows any designer to • Conceptualize his ideas • Modify the design very easil y • Perform animation • Make design calculations

• Use colors, fonts and other aesthetic features.

E Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 3 | P a g e Benefits of CAD The implementation of the CAD system provides variety of benefits to the industries in design and

production as given below:

1. Improved productivity in drafting 2. Shorter preparation time for drawing 3. Reduced man power requirement 4. Customer modifications in drawing are easier 5. More efficient operation in drafting

6. Low wastage in drafting 7. Minimized transcription errors in drawing 8. Improved accur acy of drawing 9. Assistance in preparation of documentation 10. Better designs can be evolved

11. Revisions are possible 12. Colours can be used to customize the product 13. Production of orthographic projections with dimensions and tolerances 14. Hatching of all sections wit h different filling patterns 15. Preparation of assembly or sub assembly drawings

16. Preparation of part list 17. Machining and tolerance symbols at the required surfaces 18. Hydraulic and pneumatic circuit diagrams with symbols 19. Printing can be done to any scale CAD S OFTWARES

The software is an interpreter or translator which allows the user to perform specific type of application or job related to CAD. The following softwares are available for drafting 1. AUTOCAD 2. CREO 3. CATIA

4. SOLID WORKS 5. NX Unigraphics 6. FUSION 360 7. INVENTOR 8. SOLID EDGE

The above software’s are used depending upon their application Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 4 | P a g e Drawing Instruments and aids:

Drawing Instruments are used to prepare drawings easily and accurately. A neat and clean drawing is prepar ed by the help of good quality drawing i nstruments and other aids . The following are the drawing aids commonly used in industries:

• Drawing board • Setsquares • French curves • Templates • Mini drafter

• Instrument box • Protractor • Set of scales • Drawing sheets • Pencils

Drawing Sheet:

Engineering drawings are prepared on standard size drawing sheet. The correct shape and size of the object can be visualized from the understanding of not only its views but also from the various types of lines used, dimensions, no tes, scales etc., The standard drawing sheet sizes are arrived at on the basic Principal of X:Y =1: √2 and XY=1 where x and y are the sides of the sheet. For example, AO, having a surface area of 1Sq.m; X=841mm and Y=1189mm.The successive sizes

are obtaine d by either by halving along the length or doubling the width, the area being in the ratio1:2. Designation of sizes is given in the fig. For class work use of A2 size drawing sheet is preferred.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 5 | P a g e Drawing Sheet Layout It is an important function of engin eering drawing. Also, it is very important to understand the standard for the selection of suitable scale, margin space, title block and part list etc., on the sheet.

The below mentioned details in the drawing sheet is according to IS 46:2003 Title Bloc k Title block is to be placed within the drawing space at the bottom right hand corner of the drawing sheet and it should be visible when prints are folded. It should consist of one or more adjoining rectangles. These rectangles may be divided further into boxes for inserting specific information.

The size of the title block as recommended by the B.I.S. is 185 mm x 65 mm fro all designations of the drawing sheets. All the title blocks should contain at least the particulars mentioned below.

SN Particular s 1 Name of the firm 2 Title of the Drawing 3 Scale 4 Symbol denoting the method of projection

5 Drawing number 6 Initials with dates of persons who have designed, drawn, checked, standards, and approved 7 No. of sheet and total number of sheets of the drawing of the object The Title blocks used in industries and for class work purpose are shown below.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 6 | P a g e Title Block for Industry Title Block for Class Work Types of Lines:

1. Outlines (A): Continuous thick or wide lines drawn to represent the visible edges and surface boundaries of the objects are called Outlines or Principal Lines.

2. Margin Lines (A): They are continuous thick or wide lines along which the prints are trimmed 3. Dimension lines (B): these lines are continuous thin line s that are terminated at the outer ends by pointed arrowheads touching the outlines, extension lines or centre lines.

4. Extension or Projection Lines (B): These are also continuous thin lines that extend by about 3 mm beyond the dimension lines.

5. Construction Lines (B): These continuous thin light lines used for constructing figures.

6. Hatching or Section Lines (B): These are the continuous thin lines generally drawn at an angle of 450 to the main outline of the section and are uniformly spaced about 1mm to 2 mm apart.

These are used to make the section evident.

7. Leader or pointer lines (B): It is a continuous thin line drawn to connect a note with the feature to which it applies.

8. Border Lines (B): Perfectly rectangular working space is determined by d rawing the border lines.

9. Short - break lines (C): These are continuous, thin and wavy lines drawn freehand and are used to show a short break or irregular boundaries.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 7 | P a g e 10. Long -break lines (D): These are thin ruled lines with short zigzags within them and are dr awn to show the long breaks.

11. Hidden or dotted lines (E/F): Interior or hidden edges and surfaces are shown by hidden lines.

They are also called as dotted lines.

12. Centre lines (G): These are thin, long, chain lines composed of alternately long and dot line s drawn to indicate the axes of cylindrical, conical or spherical objects or details and also to show the centres of circles and arcs.

13. Cutting -plane lines (H): The location of cutting plane is shown by this line. It is a long, thin, chain line, thick at e nds only.

Line Type Description General Applications A Continuous thick or Continuous wide Visible outlines, Visible edges, Main representations in diagrams, flow charts etc.,

B Continuous thin (narrow) Imaginary lines of intersection, Dimensions, Extension, Projection, Leader lines, Reference lines, Hatching, Construction lines, Outlines of revolved sections C Continuous thin (narrow) freehand Limits of partial or interrupted views

and sections, if the limit is not a chain thin line D Continuous thin (narrow) with zigzags Long -break line E Dashed thick (wide) Line showing permissible of surface treatment F Dashed thin (narrow) Hidden outlines, hidden edges

G Chain thin Long – dashed dotted Centre lines, lines of symmetry, trajectories, Pitch circle of holes, Axes H Chain thin (narrow) with thick (wide) at the ends and at changing of the position Cutting planes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 8 | P a g e Conventional Representation of Materials Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 9 | P a g e

LETTERING Lettering is defined as writing of titles, sub -titles, dimensions, and other important particulars on a drawing.

To undertake production work of an engineering component as per the drawing, the size and other details are indicated on the drawing. This is done in the form of notes and dimensions. Main features of lettering consume more time. Lettering should be done f reehand with speed. Practice accompanied by continuous efforts would improve the lettering skill and style.

Size of Letters:

• Size of Letters is measured by the height h of the Capital Letters as well as numerals.

• Standard heights for Capital letters and numerals recommended by BIS are given below:

1.8, 2.5, 3.5, 5, 6, 10, 14, 20 mm Note: Size of the letters may be selected based upon the size of the drawing.

Guide lines:

In order to obtain correct and uniform height of letters and numerals, guide lines a re drawn using 2H pencil with light pressure. HB grade conical end pencil is used for lettering.

The following are some of the guidelines for lettering • Drawing numbers, title block and letters denoting cutting planes, sections are written in 10mm size.

• Drawing title is written in 7 mm size.

• Hatching, subtitles, materials, dimensions, notes, etc., are written in 3.5mm size.

• Space between lines = 3/4h • Space between words may be 𝑑= ℎ10 Characteristic Ratio Dimensions (mm)

Lettering height Height of Capitals h h 2.5 3.5 5 7 10 14 20 Height of Lower -case letters c (57) h - 2.5 3.5 5 7 10 14 Spacing between characters a (2

14) h 0.35 0.5 0.7 1 1.4 2 2.8 Minimum spacing of base lines b (107) h 3.5 5 7 10 14 20 2.8 Minimum spacing between words e (37) h 1.05 1.5 2.1 3 4.2 6 8.4

Thickness of lines d (114) h 0.18 0.25 0.35 0.5 0.7 1 1.4 Characteristics of lettering as per BIS Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 10 | P a g e

DIMENSIONING A drawing describes the shape of an object. For complete details of an object, its size description is also required. The information like distance between surfaces and edges with tolerance, location of holes, machining symbols, surface finish, type of mat erial, quantity, etc., is indicated on the drawing by means of lines symbols, and holes. The process of furnishing this information on a

technical drawing as per a code of practice is called dimensioning.

Principles of dimensioning 1. Dimensioning should be done so completely that further calculation or assumption of any dimension or direct measurement from the drawing is not necessary 2. Every dimension must be given, but none should be given more than once.

3. A dimension should be placed on the view where its u se is shown more clearly.

4. Dimensions should be placed outside the views, unless they are clearer and more easily read inside.

5. Mutual crossing of dimension lines and dimensioning between hidden lines should be avoided. Dimension lines should not cross any o ther line of the drawing.

6. An outline or a centre line should never be used as a dimension line. A centre line may extend to serve as an extension line 7. Aligned system of dimensioning is recommended.

Elements of dimensioning 1. Projection or extension Line It is a thin continuous line drawn in extension of an outline. It extends by 3mm beyond the dimension line.

2. Dimension Line It is a thin continuous line terminated by arrowheads touching the outlines, extension lines or centre lines.

3. Leader line A leader line is a thin continuous line connecting a note or a dimension figure with the feature to which it applies. One end of the leader line terminated either in an arrowhead or a dot. The other end of the leader line is terminated in a horizontal line at a bottom level of the first or the last letter of the note. It is always drawn at a convenient angle of not less than 300 to the line

which it touches.

4. Arrow head or Termination of dimension line An arrow head is placed at each end of a dimensional line. Its pointed end touches an outline, an extension line or a centre line. The size of an arrow head should be proportional to the Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 11 | P a g e

thickness of the outlines. The length of the arrowhead should be thre e times its maximum width. Different types of arrowheads can be observed, but closed and filled type of arrowhead is widely used in engineering drawing.

Methods of indicating Dimensions The two methods of indicating dimensions are:

1. Aligned 2. Unidirection al 1. Aligned method In this method, the dimension is placed perpendicular to the dimension line such a way that it may be read from the bottom edge of the right -hand edge of the drawing sheet. The dimensions

must be placed in the middle and above the dimens ion line.

2. Unidirectional method In unidirectional method, all the dimensions are placed in such a Way that they can be read from the bottom edge of the drawing sheet. The dimension lines are broken near the middle for ins erting the dimensions. This is method is generally used on large drawings.

Arrangement of Dimension lines The dimensions of an object can be placed according to either Aligned or Unidirectional methods, but they are arranged in the followings ways and the selection depends on the design and the construction requirements.

1. Chain dimensioning Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 12 | P a g e This type of dimensioning is used only where the possible accumulation of tolerances does not endanger the functional requirements of the part.(fig. )

2. Parallel dimensioning This type of dimensioning is used only where a number of dimensions of a part have common datum feature.

3. Combined dimensioning In this a combination of both chain and parallel dimensioning are a pplied. But, the distance of dimension line from the object boundary or nearby dimensions line should be at least 5mm to 6mm.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 13 | P a g e 4. Superimposed running dimensioning This type of dimensioning is a simple parallel dimensioning and may be used where there ar e space limitations and where no legibility problems will arise. In this, origin is to be indicated

appropriately and the opposite end of each dimension line should be terminated only with arrow head.

5. Dimensioning by coordinates This type of dimensioning follows the principle of coordinate system of identifying the points.

This type of dimensioning follows the principle of coordinate system of identifying the points.

There are three ways of indicating this type of dimensioning.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 14 | P a g e AutoCAD Installation Process 1. Go to the following website: https://www.autodesk.com/education/free -software/all 2. Click AutoCAD

3. Create your login account using the MRCET mail id. xyz@mrcet.ac.in (you can access the software for 3 Years).

4. After you create your account, sign in and choose a. Version: AutoCAD 2020 b. Operating System: 32 or 64 bit (To find the information, Right click on My Computer or My PC and select properties.) c. Language: English (so you can have more effective technical support)

5. Serial number and Product key will be displayed. This information is required at the time of activation after installing the software.

6. Download can be carried in two ways:

a. Download Now (Recommended) b. Browser Download 7. After downloading the file, double click on the installation file, and then click Yes to complete the installation.

8. Now click on Install 9. Check the box I accept the click next 10. For the standalone License type default option, enter the serial key & product k ey details found on the software database for this software version.

11. Click I nstall and the Click Finish to complete the installation.

System Requirements • Operating System : 32 or 64 -bit Microsoft Windows/ XP -professional/vista or more • Processor : Pentiu m 4 or later • RAM : 4GB or more • Graphics Card : 1GB or more/ integrated graphics

• Hard Disk : 20GB free hard disk space available including installation • Pointing devices : Mouse, digitizer with win tab drive, Keyboard • DVD ROM : Any Speed (not mandatory) Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 15 | P a g e

Function Keys The keyboard function keys F1 -F12 control settings that are commonly turned on and off as we work in the product.

Key Feature Description F1 Help Displays Help for the active tooltip, command, Palette or dialog box.

F2 Expanded History Displays an expanded command history in the Command window F3 Object Snap Turns object snap ON and OFF F4 3D Object Snap Turns additional object snaps for 3D ON and OFF F5 Isoplane Cycles through 2D isoplane settings (Top, Right and Left)

F6 Dynamic UCS Turns automatic UCS alignment with planar surfaces ON and OFF F7 Grid display Turns the grid display ON and OFF F8 Ortho Locks cursor movement to horizontal or vertical F9 Grid Snap Restricts cursor movement to specified grid intervals

F10 Polar Tracking Guides cursor movement to specified angles F11 Object Snap Tracking Tracks the cursor horizontally and vertically from object snap locations F12 Dynamic input Displays distances and angles near the cursor and accepts input as we use Tab between fields

Note: F8 and F10 are mutually exclusive -turning one On will turn the other OFF.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 16 | P a g e User Interface Application Menu Menus are available through the application button in the upper left corner of the drawing window.

This menu contains the commands used to create, save, print, and manage your drawing.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 17 | P a g e Command prompt The rectangular horizontal window at lower side of the screen is called the command area. The instructions given to the computer through keyboard is shown in this area. It important to read the

command prompt when working with an unfamiliar command.

To enter a command using the keyboard, type the command name on the command line and press Enter or the Spacebar.

Navigation Bar The navigation bar is a user interface element where you can access both unified and product -specific navigation tools. Unified navigation tools are those that can be found across many Autodesk products. Product -specific navigation tools are unique to a product.

Quick access toolbar The Quick Access toolbar, displayed in the Drafting & Annotation workspace, is located at the very top of the drawing window next to the Application b utton. The Quick Access toolbar may be customized by adding or removing commands. This is done by right clicking on the toolbar and selecting Customize Quick Access toolbar or selecting the arrow at the end of the toolbar.

The Quick Access toolbar cont ains the following commands:

• QNew: Opens a new drawing.

• Open: Opens an existing drawing. (Ctrl+O) • Save: Saves the current drawing. (Ctrl+S) • Save as: Allows you to save the current drawing under a different name. (Ctrl+Shift+S) • Plot: Plots or prints the current drawing. (Ctrl+P) • Undo: Used to undo previous command or actions.

• Redo: Used to redo commands that have been undone.

Drawing area & Cross Hair The rectangular large space between the pull -down menu bar and the command window is the drawing area. The cursor moves moves in this area in the form of a cross hair as mouse is moved by the user. The cross hair position is indicated by coordinate values shown at the left end of the status bar.

View Cube The View Cube is a navigation tool that allows you to switch between viewing directions. While this is very useful in 3D space, it is not very useful in 2D space. It is located in the upper right corner o f the drawing area.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 18 | P a g e Status bar The status bar displays the cursor location, drawing tools, and the tools that affect the drawing environment. It also provides quick access to some of the most commonly used drawing tools,

Coordinates of the cross hair ( Cursor) and we can toggle the settings such ads grid, snap, polar tracking and object snap.

Draw Commands 1. Point:

The Point command will insert a point marker in your drawing at a position which you pick or at any coordinate location which you enter in the Command window. Other ways of defining a point can be accessed through the fly -out menu. The default point style is a simple dot, which Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 19 | P a g e

is often difficult to see but you can change the point style to something more easily visible or elaborate using the point style dialogue box.

Tool Bar : Menu → Draw → Point Command : Point (PO) 2. Line:

Creates a straight line segment . It is used to draw lines continuously. Each segment is a line object that can be edited separately.

Continue : Continues a line from the endpoint of the most recently drawn line.

Close : End the line segment at the beginning of the first line segment, which forms a closed loop of line segment.

Undo : Erases the most recent segment of a line sequence.

Tool Bar : Menu → Draw → Line Command : Line (L) 3. Construction Line (XL):

The construction line (XLINE) command creates a line of infinite length which passes through two picked points. Construction lines are very useful for creating construction frameworks or grids. Construction lines are not normally used as objects in finished dr awings. Therefore, it is usual to draw all your construction lines on a separate layer which will be turned off or frozen prior to printing.

Construction line options • Hor: Creates a horizontal construction line.

• Ver: Creates a vertical construction line.

• Ang: Creates a construction line at a specified angle.

• Bisect: Create a construction line that bisects an angle defined by 3 points.

• Offset: Creates a construction line that is offset from an existing line by a specif ied • distance.

Tool Bar : Menu → Draw → Xline Command : Xline (xl) Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 20 | P a g e 4. Polyline (Pline):

The PLINE command differs from the LINE command in that the segments of the PLINE are connected. When using the LINE command, each segment is its own object. When using PLINE, all line segments are one object.

Tool Bar : Menu → Draw → Polyline Command : Pline (PL) 5. Polygon A polygon of sides ranging from 3 to any number can be drawn using Polygon command. It creates an equilateral closed polyline.

Centre of Polygon: Defines the center of the polygon.

Inscribed in Circle: Specifies the radius of a circle on w hich all vertices of the polygon line.

Circumscribe about circle: Specifies the distance from the centre of the polygon to the midpoints of the edges of the polygons.

Edge: Defines a polygon by specifying the endpoints of the first edge.

Specifying the radius with your pointing device determines the rotation and size of the polygon.

Specifying the radius with a value draws the bottom edge of the polygon at the current snap rotation angle.

Tool Bar : Menu → Draw → Polygon Command : Polygon 6. Arc This command is used to draw an arc accurately. To create an arc, a combination of centre, endpoint, start point, radius, angle, chord length, and direction values can be specified. Arcs are drawn in a counter clockwise direction by default.

Start Point: Draws an arc Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 21 | P a g e Tool Bar : Menu → Draw → Arc Command : Arc 7. Circle

There are many ways to draw a circle, the default being the centre point of circle and radius.

Below are the possible ways of drawing the circle.

i. Centre point and Radius: Defines the radius of the circle.

ii. Centre point and Diameter: Defines the diameter of the circle.

iii. 3P (Three Points): Draws a circle based on thr ee points on circumference.

iv. 2P (Two Points): Draws a circle based on two endpoints of the diameter.

v. Tan, Tan, Tan : Creates a circle tangent to three objects.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 22 | P a g e vi. Tan, Tan, Radius: Creates a circle with a specified radius and tangent to two objects.

Sometimes more than one circle matches the specified criteria. The program draws the circle of the specified radius whose tangent points are closest to the selected points.

Tool Bar : Menu → Draw →Circle Command : Circle (C) Ellipse The Ellipse command gives you a number of different creation options. The default option is to pick the two end points of an axis and then a third point to define the eccentricity of the ellipse.

Tool Bar : Menu → Draw →Ellipse Command : Ellipse (E) 8. Donut The DONUT is a special type of polyline which is made up of arc segments. A DONUT has two properties: it has width, and it is closed. The width of DONUT is set by specifying inside and outside diameters. The inside diameter may be zero thereby making it a fill ed circle.

9. Hatch patterns The HATCH command is used to fill up the area using a suitable pattern. The type of pattern and pattern variables can be chosen from a library of patterns available. The hatching will be carried out inside a closed defined area.

Tool Bar : Menu → Draw →Hatch Command : Hatch (H) Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 23 | P a g e 10. Text Words, messages and numbers can be inserted as required on an engineering drawing. The

alphanumeric keyboard is used extensively for non -graphical input such as text. The text style, height, text angle, aspect ratio, colour, etc. are some of the attributes associated with text. These attributes can be changed as per requirements.

11. Rectangle Creates a rectangular polyline. With this command, the parameters (length, width, rotation) can be specified control the type of corners (fillet, chamfer, square).

Tool Bar: Menu → Draw → Rectangle Command : Rectang (R) Drafting Aids 1. Limits Drawing limits are used to set the boundaries of the drawing. The drawing boundaries are usually set to match the size of a sheet of drawing paper. This means that when the drawing is

plotted and a hard copy is made, it will fit on the drawing paper.

Fig : Page 67 : Engineering Graphics with AutoCAD 2020 Command: Limits Specify lower left corner or [ON/OFF] <0,0>: Specify a point Specify upper right corner or <12,9>: Specify a point Note: Limits has no limit, it can be infinity with respect to paper size

2. Layers A layer is like a clear piece of paper that can be laid directly over the drawing. We can draw on the layer and see through it to the original drawing. Layers can be made invisible, and information can be transferred between layers. Layers are used to control the visibility of objects and to assign properties such as color and linetype. Objects on a layer normally assume

the properties of that layer.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 24 | P a g e 3. Dimensioning Create several types of dimensions and save dimension settings by name.

Linear Dimensions horizontal, vertical, aligned, and radial dimensions can be created with the DIM command. The type of dimension depends on the object that is selected and the direction of dimension line.

Dimension Styles Dimension styles help establish and enforce drafting standards. There are many dimension variables that can be set with the DIMSTYLE command to control virtually every nuance of the appearance and behavior of dimensions. All these settings are stored in each dimension style. The Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 25 | P a g e default dimension style is named either Standard (imperial) or ISO -25 (metric). It is assigned to all dimensions until you set another style as the current dimension style.

The current dimension style name, Hitchhiker in this case, is displayed in the drop -down l ist of the Annotation panel.

4. Object snap Object snap provide a way to specify precise locations on objects whenever you are prompted for a point within a command. With running object snap(Osnap) settings, a snap point at an exact location on an object can be specified. When more than one option is selected, the selected snap modes are applied to return a point closest to the center of the aperture box.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 26 | P a g e Object Snap ON (F3) Turns running object snaps ON and OFF. The object snaps selected under Object Snap Modes are active while the Osnap mode in ON.

Object Snap Tracking On (F11) Turns object snap tracking ON and OFF. With object snap tracking, the cursor can track along alignment paths based on other object snap points when specifying points in a command.

Object Snap Modes:

End Point Snaps to the closest endpoint of an arc, elliptical arc, line, multiline, polyline segment, spline, region or to the closest corner of a trace. Solid or 3D face.

Midpoint Snaps to the midpoint of an arc, ellipse, elliptical arc, line, multiline, polyline segment, region, solid, spline or xline.

Center Snaps to the center of an arc, circle, ellipse, or elliptical arc.

Node Snaps to a point object, dimension definition point, or dimension text origin.

Quadrant Snaps to a quadrant point of an arc, circle, ellipse, or elliptical arc.

Intersection Snaps to the intersection of an arc, circle, ellipse, line, multiline, polyline, spline, or xline and other geometrical objects. Extended intersections are not available as a running object snap.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 27 | P a g e Extension It causes a temporary extension line or arc to be displayed when the cursor is passed over the endpoint of objects, so that points can be specified on the extension.

Insertion Snaps to the insertion point of an attribute, a block, a shape, or text.

Perpendicular Snaps to a point perpendicular to the selected geometric object.

Deferred Perpendicular snap mode is automatically turned on w hen the object you are drawing requires that more than one perpendicular snap can be completed . An object such as a line, arc, circle, polyline, ray, xline, multiline, or 3D solid edge as an object from which to draw a perpendicular line can be used .

Tangent Snaps to the tangent of an arc, circle, ellipse, elliptical arc, polyline arc, or spline. Deferred Tangent snap mode is automatically turned on when the object that is being drawn requires and complete more than one tangent snap. It can be used to draw a line or xline that is tangent to arcs, polyline arcs, or circles. When the cursor passes over a Deferred Tangent snap point,

a marker and an AutoSnap tooltip are displayed.

Apparent Intersection Snaps to the visual intersection of t wo objects that do not intersect in 3D space but may appear to intersect in the current view.

Nearest Snaps to the nearest point on an arc, circle, ellipse, elliptical arc, line, multiline, point, polyline, ray, spline or xline.

Parallel Constraints a line segment, polyline segment, ray or xline to be parallel to another linear object.

The parallel object snap is to be specified, after specifying the first point of a linear object.

Unlike other object snap modes, the cursor must be moved and hover over another linear object until the angle is acquired. Then, move the cursor back toward the object that is to be creat ed.

When the path of the object is parallel to the previous linear object, an alignment path is displayed, which you can use to create the parallel object.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 28 | P a g e Select All Turns on all running object snap modes.

Clear All Turns off all running object snap modes.

5. Zoom The objects viewed in the drawing area can be zoomed in or out, and moved to see different portions of the sheet in deta il by using the following commands:

The zoom flyout of standard tool bars has nine icons to opt.

a) Zoom window : This command enlarges a rectangular area of a drawing based on a defined window using the cross hair b) Zoom all : This command displays the are of the drawing limits or extent whichever are greater.

c) Zoom dynamic : Pans and zooms using a rectangular view box .

d) Zoom scale : Zooms to change the magnification of a view using a scale factor.

e) Zoom center : Zooms to display a view defined by a center point and a magnification value or a height.

f) Zoom Object: Zooms to display one or more selected objects as large as po ssible and in the center of the view.

g) Real Time: Zooms interactively to change the magnification of the view.

h) Zoom extends : Zooms to display the maximum extents of all objects.

i) Zoom Previous: Zooms to display the previous view. You can restore up to 10 pr evious views.

Out of these “Zoom window” and “Zoom all” command are more useful. Similarly, “Zoom real time”, “Pan real time” and “Zoom previous” commands are also frequently applied for drafting.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 29 | P a g e Editing Commands (Modify Commands) 1. Move The Move command works in a similar way to the COPY command except that no copy is

made; the selected object(s) is simply moved from one location to another Tool Bar : Menu → Modify→ Command : explode 2. Rotate The Rotate command allows an object or objects to be rotated about a base point selected and the angle can be typed in the command prompt by the user.

Tool Bar : Menu → Modify→ Command : explode 3. Copy The Copy command can be used to create one or more duplicates of any object(s) which have been previously created.

Tool Bar : Menu → Modify→ Command : explode Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 30 | P a g e 4. Mirror The Mirror command allows you to mirror selected objects in your drawing by picking them

and then defining the position of an imaginary mirror line using two points. To create perfectly horizontal or vertical mirror lines turn the ORTHO command on.

Tool Bar : Menu → Modify→ Command : explode 5. Array The Array command makes multiple copies of a selected objects in a rectangular pattern (columns and rows) or a polar (circular) pattern or a along a path that is defined.

Tool Bar : Menu → Modify→ Command : explode 6. Erase The Erase command is one of the simplest AutoCAD commands and is one of the most used.

The command erases or deletes any selected object(s) from the drawing.

Tool Bar : Menu → Modify→ Command : explode Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 31 | P a g e 7. Break The Break command helps to break (remove a part of) an object by defining two break points.

Tool Bar : Menu → Modify→ Command : explode 8. Fillet The Fillet command is a very useful tool which allows to draw a tangent arc between two objects. The objects are usually intersecting. The objects do not have to intersect, but their separation cannot be more than the fillet radius.

Tool Bar : Menu → Modify→ Command : explode 9. Chamfer The Chamfer command creates an angled corner (Chamfer) between any two non -parallel lines or any two adjacent polyline segments. A chamfer is usually applied to intersecting lines.

Tool Bar : Menu → Modify→ Fillet → Command : explode Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 32 | P a g e 10. Extend

The Extend command is used to extend a line, polyline or arc to meet an already existing object.

Tool Bar : Menu → Modify→ Command : explode 11. Offset The OFFSET command creates a new object parallel to or concentric with a selected object.

The new object is drawn at a user defined distance (the offset) from the original and in a direction chosen. The OFFSET command may only be used on one object or entity at a time.

Tool Bar : Menu → Modify→ Command : explode 12. Stretch The STRETCH command can be used to move one or more vertices of an object while leaving the rest of the object unchanged Tool Bar : Menu → Modify→ Command : explode

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 33 | P a g e 13. Trim The Trim command is used to trim off the part of an object that is not necessary. In order to trim an object, a second object which forms the cutting edge must be drawn. Cutting edges can

be lines, xlines, rays, polylines, circles, arcs or ellipses.

Tool Bar : Menu → Modify→ Command : explode 14. Scale The Scale command can be used to change the size of an object or group of objects. It allows to shrink or enlarge the already existing drawing objects about a base point on specifying the scale factor.

Tool Bar : Menu → Modify→ Command : explode 15. Explode This command is used to break a single compound object into their constituent parts. In other words, s compound object explodes when the components to be modified separately. the command is used to return blocks, polylines, rectangles, etc.,

Tool Bar : Menu → Modify→ Command : explode Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 34 | P a g e Quick access toolbar The Quick Access toolbar, displayed in the Drafting & Annotation workspace, is located at the

very top of the drawing window next to the Application button. The Quick Access toolbar may be customized by adding or removing commands. This is done by right clicking on the toolbar and selecting Customize Quick Access toolbar or selecting the arrow at the end of the toolbar.

The Quick Access toolbar contains the following commands (reading left to right):

• QNew: Opens a new drawing.

• Open…: Opens an existing drawing. (Ctrl+O) • Save: Saves the current drawing. (Ctrl+S) • Save as: Allows you to save the current drawing under a different name. (Ctrl+Shift+S) • Plot…: Plots or prints the current drawing. (Ctrl+P) • Undo: Used to undo previous command or actions.

• Redo: Used to redo commands that have been undone Start ing a new Drawing When starting a new drawing (QNEW), you have a choice of either starting from the Create New Drawing window or the Select Template window. The Create New Drawing window allows you to set up a drawing to your preferences. You may set parameters such as the units (Imperial or

Metric), the size of the drawing, and the degree of precision. The Select Template window allows you to choose from predefined templates. Figure 2.5 -1 shows both startup windows. The STARTUP variable is used to choose what is displayed w hen the application is started, or which window will appear when you start a new drawing. It has 4 values that may be set (i.e., 0, 1, 2, and 3). However, for starting a new drawing, only 0 and 1 are of interest. If STARTUP = 0, then the

Select Template window will appear. If STARTUP = 1, then the Create New Drawing window will appear.

Template drawings store all the settings for a drawing and may also include predefined layers, dimension styles, and views. Template drawings are distinguished from other dra wing files by the .dwt file extension. Several template drawings are included in AutoCAD®. You can make additional template drawings by changing the extensions of drawing file names to .dwt.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 35 | P a g e Starting a new drawing using the Create New Drawing window Command: startup Enter new value for STARTUP <0>: 1

Quick Access toolbar or Application button: File – New… (Ctrl+N ). The Create New Drawing window will appear.

4) Create New Drawing window: Activate the Start from Scratch button, activate either Imperial or Metric toggle, and then select OK 5) Quick Access toolbar:

6) Create New Drawing window:

a. Activate the Use a Wizard button.

b. Select a Wizard field: Select Advanced Setup and then OK.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 36 | P a g e 7) The wizard will take you through a setup which will allow you to choose your drawings nits, angle, angle measure, angle direction and drawing area.

Saving and opening a drawing When saving (or open) a drawing ( Application button - Save or Saveas or Open ), you have the option of saving (or opening) the following file types.

• DWG (DraWinG) is a binary file format used for storing two- and three -dimensional design data and metadata. Most of what you draw will be saved in this format.

• DWT is a template file. These files are used as a starting point when sta rting a new drawing.

They may contain drawing preferences, settings, and title blocks that you do not want to create over and over again for every new drawing.

• DXF (Drawing Interchange Format, or Drawing Exchange Format) is a CAD data file format developed by Autodesk® for enabling data interoperability between AutoCAD® and other programs.

• DWS is a standards file. To set standards, you create a file that defines properties for layers, dimension styles, linetypes, and text styles, and you save it as a standa rds file with the .dws file name extension.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 37 | P a g e Plotting of Drawings To print a drawing, click on the icon ‘Plot’. This opens a dialogue box having two pages, namely ‘Plot device and Plot Settings’.

The plotter configuration or its equivalent has to be sel ected in the Plot Device page. And the following options to be set in the Plot setting page Page Size : A4 (210x297 mm) or A3 or etc., Units : Mm Drawing Orientation : Portrait / Landscape

Plot Area : Limits Plot Scale : 1:1 By clicking on the Full preview button, the area of the figure to printed will be projected. Click OK if it has a suitable orientation to start printing.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 38 | P a g e Geometrical Constructions Introduction:

Engineering drawing consists of a number of geometrical Constructions. A few methods are illustrated here without mathematical proofs .

1. To divide a straight line 65 mm into a given number of equal parts say 5.

Solution 1. Draw a line of 65 mm with Command L 2. Name the Line With Text Command A,B 3. To Di vide line Type Command DIV Enter 4. Select Object To Divide Select Line

5. Enter the Number Of Segment of 5 Enter 6. Select Point Style from utilities to show divisions.

2. To bisect a given angle 900 Solution 1. Draw a line of 50 mm with Command L Name the Lane With Text Command A,B 2. Draw another Line 50 mm From the End of Previous Line with 900 Angle with Command L name the Line With Text Command B,C

3. To Bisect Line Type Command XL press enter 4. Select Bisect Option or Enter B and specify angle vertex point at End Point.

5. Specify Angle Starting Point 6. Specify angle end point enter 7. Mention Angle After Bisection Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 39 | P a g e

Polygons 1. To construct a regular polygon (say a pentagon) given the length of the side 5(EDGE METHOD) Solution 1. To construct any polygon Enter Comman d POL

2. Enter No of Sides 5 3. Specify Center pf Polygon or Edge enter Command E 4. Specify First End Point of Edge & Specify second End Point of Edge by entering specific Distance 5 5. Name the Edges With text Command TEXT

2. Inscribe a hexagon in a given circle of 50 mm Diameter (Inscribe Circle Method) Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 40 | P a g e Solution 1. To construct any polygon Enter Command POL

2. Enter No of Sides 6 3. Specify Center pf Polygon or Edge enter select Center 4. Enter an option with Inscribed in Circle with command I 5. Specify radius Of Circle with 50 6. Name the Edges With text Command TEXT

Practice Exercises 1. Divide an 80 mm long straight line into five equal parts.

2. Divide a 90 mm long straight line into parts that are in proportion to 2:3:5.

3. Draw a perpendicular to a 100 mm l ong line AB, at a point P lying on the line at a distance of 40 mm from the end A.

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.

5. Draw perpendicular to a 100 m m long line AB, from a point P lying at a distance 60 mm from end A and 70 mm from end B.

6. Draw a line AB inclined at 30º to the horizontal. Draw another line CD parallel to and 50 mm away from AB.

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.

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.

9. Two circles of radii 20 mm and 30 mm have their centres 50 mm apart. Draw all the pos sible common tangents to both the circles.

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.

11. Draw a tangent to connect two circles of radii 25 mm and 40 mm. The centres of the circles are 15 mm apart.

12. Draw an arc of 30 mm radius connecting two straight lines inclined at 135º to each other.

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.

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 tang entially.

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.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 41 | P a g e 16. Two circles have their centres 70 mm apart and radii 20 mm and 30 mm, re spectively. Draw a circle of radius 55 which connects tangentially both the circles and (a) include 20 mm circle (b) include 30 mm circle.

17. 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.

18. 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.

19. Inscribe a circle in a triangle of 75 mm, 65 mm and 55 mm long sides.

20. Draw a square of 60 mm long diagonals. Circumscribe another square on the square.

21. Draw regular pentagon, hexagon and a heptagon on a common edge of side 30 mm.

22. Draw a pentagon of 30 mm side with a side vertical. Attach a non-overlapping hexagon of same side length with common vertical edge.

23. 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.

24. Draw an octagon of 25 mm side keepin g one of the sides vertical.

25. Draw five circles in a given circle of 80 mm diameter, each touching the given circle and the other two circles.

26. Draw five circles inside the pentagon of 30 mm side, such that each circle touches one side of the pentagon and t wo other circles.

27. Draw five circles inside the pentagon of 30 mm side, such that each circle touches two side of the pentagon and two other circles.

28. Draw three circles inside a hexagon of 30 mm side, such that each circle touches one side of the hexagon a nd two other circles.

29. Draw five circles outside the pentagon of 20 mm side, such that each circle touches one side of the pentagon and two other circles.

30. Draw six circles outside a given circle of 30 mm diameter, such that each circle touches the given and two other circles.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 42 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 43 | P a g e

Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 44 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 45 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 46 | P a g e Notes

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 47 | P a g e Notes UNIT 2 ORTHOGRAPHIC PROJECTIONS

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 49 | P a g e Projections Projection As per the optical physics, projection is a process of causing an image by rays of light taken in a

particular direction from an object to a picture plane. The imaginary ray of light between the object and the projection plane is called line of sight or pr ojector.

Orthographic Projection In orthographic projection, the projectors are parallel and perpendicular to the plane of projection.

Orthographic projections on mutually perpendicular projection planes will fully describe the object in its shape and size. Hence, all design and manufacturing drawings are made with orthographic projections.

Projectors ⊥ to the Projection plane Vertical Plane and Front Elevation A view looking from the front is projected onto the vertical plane. This view is called front view or front elevation and shows the width and height dimensions. A vertical plane of projection, which is behind the object in relation to the observer, is shown

in figure below.

Horizontal Plane and Top View A view looking from the to p is projected onto the horizontal plane placed below the object. This view is called top view or plan. Top view shows the width and depth dimensions of an object. A horizontal plane with a top view is shown in figure below.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 50 | P a g e Profile Plane and End View A view looking from the side of an object is projected onto the profile plane. The observer and the projection plane are on different sides of the object (i.e.) the object is between the observer

and the projection plane. The viewing can be from the right or the left side of the object. The view drawn looking the object from the right is called right side view or right end elevation. The view looking the object from the left is called left side view or left end elevation. Side view of an object shows the de pth and height dimensions. A profile plane with a left side view is shown in figure below.

First Angle Projection An arrangement of vertical, horizontal, and profile planes and quadrants used to draw first angle projections is shown below. Front view is projected onto the vertical plane, top view onto the horizontal plane, and side view onto the profile plane.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 51 | P a g e Projection in First Angle An object placed in the first quadrant. The vertical plane is behind the object, horizontal plane below the object, and profile plane to right of the object. The views with the corresponding planes

are shown in figure. The top view is seen below the elevation and left side view is seen on the right of front view. This is the arrangement of views in the first ang le projection.

Projection in Third Angle:

An object placed in the third quadrant. The vertical plane is in front of the object, horizontal plane above the object and profile plane to the left of the object. The views with corresponding planes are shown i n figure. Top view is above the front view and left side view is to the left of the front view. This is the arrangement of the views in third angle projection.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 52 | P a g e Multiview Projection It consists of a set of two or more orthographic views of an object taken from different directions, which are mutually perpendicular. These views are arranged relative to each other in a particular

way. Each of these views shows the shape of the object for a particular view direction. Multiple views collectively describe the o bject completely and exactly. Hence, multiview projections are used in engineering to describe the true shape of any object.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 53 | P a g e Projections of Points Point A point usually represented by a dot is a dimensionless geometrical entity that has a position but

no magnitude. Whereas in computer aided engineering drawing the point has dimension but it is not considered or neglected. A point is obtained wherever two straight or curved lines intersect each other.

Projection of Points Projection of points in various quadrants is the basis for projection of lines, projection of planes and projection of solids. In a conventional coordinate system, the position of a point in space is denoted by its three coordinates i.e., x, y and z.

In projections, two principal planes are used to get the projection of an object that is vertical plane and horizontal plane, the vertical plane denoted by (V.P.) and horizontal plane denoted by (H.P.) as shown in Fig. They intersect each other at right angle s and the line of intersection is known as axis of the plane. The vertical plane of projection is always infront of the observer and the projection on this plane is known as front view or elevation. The other plane is the horizontal plane

of projection and the projection on this plane is called the top view or plan.

Pictorial view of Principal Planes The view obtained by viewing object form right side is called right side view or right end view. A plane perpendicular to both H.P. and V.P. is called profile plane (P.P). The right side view is always on the right to the front view. If the object is viewed from left on profile plane then the view is known as left side view or left end view.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 54 | P a g e Position of Points in Various Quadrants 1. When point is in First Quadrant When a Point P is situated in I quadrant i.e., above H.P. and in front of V.P. , Its front view

(p’) will be above XY line and its top view (p) will be below the XY line.

2. When point is in Second Quadrant When a Poi nt P is situated in II quadrant i.e., above H.P. and behind V.P. , Its front view (p’) will be above XY line and its top view (p) will also be above the XY line.

3. When point is in Third Quadrant When a Point P is situated in III quadrant i.e., below H .P. and behind of V.P. , Its front view (p’) will be below XY line and its top view (p) will be above the XY line.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 55 | P a g e 4. When point is in Fourth Quadrant When a Point P is situated in IV quadrant i.e., below H.P. and infornt V.P. , Its front view (p’) will b e below XY line and also its top view (p).

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 56 | P a g e Positions of geometrical entities in various quadrants of the projections When Position Quadrant Front View Top View VP HP Point is Infront Above I Above XY Below XY

Point is Behind Above II Above XY Above XY Point is Behind Below III Below XY Above XY Point is Infront Below IV Below XY Below XY Point is Infront In or on I or IV On XY Below XY Point is In or on Above I or II Above XY On XY

Point is Behind In or on II or III On XY Above XY Point is In or on Below III or IV Below XY On XY Point is In or on In or on I, II, III, or IV On XY On XY System of Notation 1. The actual points in space are denoted by capital letters A, B, C etc.

2. The front view (FV) of the points are denoted by their corresponding lower -case letters with dashes as a', b', c', etc.

3. The top view (TV) of the points are denoted by their corresponding lower -case letters without dashes as a, b, c etc.

4. The side view (SV) of the points are denoted by their cor responding lower -case letters with double dashes as a", b", c" etc.

5. Projectors are always drawn as continuous thin lines and Points with Dot.

In Computer Aided Engineering Graphics for projection of points following commands are used other than evoking software, opening file, saving file and giving print command. Using these minimum nine commands any type of projection of point problem can be solved they are as follows:

1. Select tool Command.

2. Point command.

3. Poly-line command.

4. Two point line command.

5. Parallel line command.

6. Bisector command.

7. Smart dimension command.

8. Line width command.

9. Insert text command.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 57 | P a g e Solved Problem :

1. Draw the projections of the following points on the same ground line, keeping the projectors 25 mm apart.

i. A is in the H.P. and 20 mm behind the V.P.

ii. B is 40 mm above the H.P. and 25 mm in front of the V.P.

iii. C is in the V.P. and 40 mm above the H.P.

iv. D is 25 mm below the H.P. and 25 mm behind the V.P.

v. E is 15 mm above the H.P. and 50 mm behind the V.P.

vi. F is 40 mm below the H.P. a nd 25 mm in front of the V.P.

vii. G is in both the H.P. and the V.P.

Solution 1. Open the Software. Click on the Application Menu and click on New and select “acad “in the open dialog box and click Open.

2. Enter the command “UNITS “in command bar and Select unit s as “Millimeters and click ok.

3. Enter the command “LIMITS “in command bar and enter 0,0 click enter and enter upper right corner as 120,90 and click enter 4. Enter the command “ZOOM “in command bar and enter A and click enter 5. As per the problem ,draw a XY li ne by using Xline command. Mark VP and HP above and below it by using “XTEXT” command in command bar

6. Divide the line into some equal parts depend upon how many points given.

7. Draw the lines representing the Projectors as per the dimensions mentioned in the problem and mark the front and top views of the points using P oint command.

8. Mention the dimensions for all points from the XY line using dimlinear command Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 58 | P a g e Practice Problems 1. Draw the orthographic projections of the following points.

i. Point P is30 mm. above H.Pand40mm.infrontof VP.

ii. Point Q is25 mm. Above H.P and 35mm.behind VP.

iii. Point R is 32 mm. below H.P and 45mm behind VP.

iv. Point S is 35 mm. below H.P and 42mm in front to VP.

v. Point T is in H.P and 30 mm behind VP.

vi. Point U is in V.P and 40 mm. below HP.

vii. Point V is in V.P and 35 mm. above H.P.

viii. Point W is in H.P and 48 mm. in front of VP.

2. Draw the projections of the following points on the same XY line, keeping convenient distance between each projectors. Name the quadrants in which they l ie.

i. Point A is 30 mm above HP and 35 mm in front of VP.

ii. Point B is 35 mm above HP and 40 mm behind VP.

iii. Point C is 40 mm above HP and on VP.

iv. Point D is 35 mm below HP and 30 mm in front of VP.

3. Draw the projections of the following points on the same XY line, keeping convenient distance between each projectors. Name the Quadrants in which they lie.

i. Point E is 30 mm below HP and 25 mm behind VP.

ii. Point F is 35 mm below HP and 30 mm in front of VP.

iii. Point G is on HP and 30 mm in front of VP.

iv. Point H is on HP and 35 mm behind VP.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 59 | P a g e Projection of Straight Lines Introduction A line may be defined as the locus of a point moving along a fixed path. A line consists of a number

of points; its projections are drawn by joining the projection of its extreme (end) points. Hence, the projections of a straight line may be drawn by joini ng the respective projections of its ends, which are points. In a conventional drawing, a line has only length but no thickness . Whereas in computer aided engineering graphics the line has length and thickness.

The position of a straight line may have d ifferent orientations in space. As per first angle projection, it may be parallel, perpendicular or inclined to either or both the Reference planes (horizontal or vertical planes) as mentioned in the below classification.

Classification of Line Positions A line may be placed in infinite number of positions with respect to the reference planes. These positions may be classified according to the inclination of the line to reference planes and the quadrants in which it is placed.

1. Line parallel to both the r eference planes (HP & VP) (a) Line away from both HP and VP.

(b) Line in HP and away from VP.

(c) Line in VP and above HP.

(d) Line on both HP and VP.

2. Line perpendicular to either of reference planes (HP or VP) (a) Line perpendicular to HP and away from V P.

(b) Line perpendicular to HP and on VP.

(c) Line perpendicular to VP and above HP.

(d) Line perpendicular to VP and on HP.

3. Line inclined to HP and parallel to VP (a) Line inclined to HP, parallel to VP and away from VP.

(b) Line inclined to HP, paralle l to VP and in VP.

4. Line inclined to VP and parallel to HP (a) Line inclined to VP, parallel to HP and away from HP.

(b) Line inclined to VP, parallel to HP and in HP.

5. Line inclined to both HP and VP (a) One end of line in HP and the other end away from VP.

(b) One end of line in VP and the other end away from HP.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 60 | P a g e (c) One end above HP and the other end away from VP.

(d) One end away from VP and the other end above HP.

(e) One end in HP and VP and other end away from HP and VP.

(f) Both ends on HP and VP.

System of Notation 1. The actual line in space is denoted by capital letters A and B, or C and D etc.

2. The front view (FV) of a line is denoted by their corresponding lower letters with dashes as a' and b', c' and d' etc.

3. The top view (TV) of a line is denoted by their corresponding lower case letters without dashes as a and b, c and d etc.

4. The side view (SV) of a line are denoted by their corresponding lower case letters with double dashes as a" and b", c" and d" etc.

5. Projectors are always drawn as con tinuous thin lines.

6. Line with specific thickness for a particular type of line.

Solved Problems 1. Draw the projections of a 75 mm long straight line, in the following positions:

i. Parallel to both the H.P. and the V.P. and 25 mm from each.

ii. Perpendicular to the H.P., 20 mm in front of the V.P. and its one end 15 mm above the H.P.

iii. Inclined at 30° to the H.P. and its one end 20 mm above it; parallel to and 30 mm in front of the V.P.

i. Parallel to both the H.P. and the V.P. and 25 mm from each.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 61 | P a g e Solution:

1. Draw XY line Using Xline Command.

2. Mark the annotations X, Y, VP, HP to the line drawn by using INSE RT TEXT command from drafting tool bar. This must be done just by typing and inserting at the required positions using the left click of the mouse.

3. According to question 75 mm line Parallel and 25 mm from HP put the Point 25 mm from above XY line by Usin g Point Command Name the Point with p’ 4. As per the problem, mark points p, q, p’ and q’ according to the dimensions given on boths side of XY line.

5. Draw a line of 75 mm that is parallel and above XY from point p’ to q’ by using Text command.

6. Draw another line of 75 mm parallel line and below XY from point p to q by using Text command 7. Mention the Dimensions by using DIMLINEAR Command.

ii. Perpendicular to the H.P., 20 mm in front of the V.P. and its one end 15 mm above the H.P.

Solution:

1. Draw XY line By Using Line Command L and Name with X,Y at two ends By Using Text Command 2. According to question 75 mm line perpendicular to HP and 15 mm above HP. put the Point 15 mm from above XY line by Using Point Command Name the Point with p’ 3. Line P arallel to and 25 mm in front of VP Put the point 25 mm below the XY line by

using Point Command. Name the Point with p.

4. Draw 75 mm perpendicular line from p’. Name the end point q’ by using Text command 5. When line Perpendicular to HP & Parallel to VP in t op view Line Like Point its two end points on the same point then mention q on the same point 25 below XY line 6. Mention the Dimensions by using DIMSTYLE Command.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 62 | P a g e iii. Inclined at 30° to the H.P. and its one end 20 mm above it; parallel to and 30 mm in front of the V.P.

Solution:

1. Draw XY line By Using Line Command L and Name with X,Y at two ends By Using Text Command 2. According to question 75 mm line30 inclined and 20 mm above the H.P put the Point 20 mm from above XY line by Using Point Command Name the Po int with p’ 3. Line Parallel to and 30 mm in front of VP Put the point 30 mm below the XY line by

using Point Command. Name the Point with p.

4. Draw 75 mm linen from p’ with inclination of 30. Name the end point q’ by using Text command Name it F.V 5. When line Inclined to HP & Parallel to VP in top view Line will be reduced Draw Perpendicular line from q’ to locus of p name the intersection point as q & Name the reduced line as Length of Top View (LTV).

6. Mention the Dimensions by using DIMLINEAR Command.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 63 | P a g e 2. A line AB 80 mm long has its end A 20 mm above the HP and 30 mm in front of VP. It is inclined at 30° to HP and 45° to VP. Draw the projections of the line.

Solution :

1. Draw XY line By Using Line Command L and Name with X,Y at two ends By Using Text Com mand 2. According to question 80 mm line 30θ inclined and 20 mm above the H.P put the Point 20 mm from above XY line by Using Point Command Name the Point with p’ 3. Draw 80 mm line from p’ with inclination of 30 θ. Name the end point q1’ by using Text

comman d 4. According to question 80 mm line 45θ inclined and 30 mm in front of V.P put the Point 30 mm from above XY line by Using Point Command Name the Point with p 5. Draw 80 mm line from p with inclination of 45θ. Name the end point q2 by using Text command

6. Draw perpendicular line from q1’ to locus of p name it As q1. Draw another Perpendicular line from q2 to locus od p1 name the intersection point as q2’ 7. Name p’q2’ Line as LFV and Name pq1 line as LTV.

8. For Final front View take P’ as center p’q2’line as rad ius draw arc which will intersect Locus of P’ at q’ Join p’q’ LINE it as FFV 9. For Final Top View take P as center p’q1’ line as radius draw arc which will intersect Locus of P at q Join p q line it as FTV 10. Mention the Dimensions by using DIMLINEAR Comm and.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 64 | P a g e Practice Problems:

1. The top view of a line AB, 80 mm long measures 65 mm and the length of the front view is 50 mm. The end A is on HP and 15 mm infront of VP. Draw the projections 2. Line AB has its end A 20 mm above the HP and 15 mm infront of the VP. The other end B is 60 mm above the HP and 45 mm in front of VP. The distance between end projectors is 70 mm. Draw its projections. Determine the apparent lengths and true inclinations.

3. A line has its end A 10 mm above HP and 15 mm in front of VP. The end B is 55 mm above HP and l ine is inclined at 30º to HP and 35º to VP. The distance between the end projectors is 50 mm. Draw the projections of the line. Determine the true length of the line and its inclination with VP.

4. A line CD 60mm long has its end ‘C’ in both H.P. and V.P. It is inclined at 300 to H.P. and 450 to V.P. Draw the projections.

5. A point C is 40mm below H.P. and 20mm behind V.P. another points D and E are 60mm above H.P. and in front V.P., 90mm below H.P. and 45mm in front of V.P. respectively. Draw the projections o f all points on same reference line.

6. The end P of a straight line PQ is 20 mm above the H.P. and 30mm in from V.P. The end Q is 15mm below the H.P. and 45mm behind the V.P. If the end Projectors are 50mm apart, Draw the Projection of PQ and determine the true length, traces and inclination with the reference planes.

7. The front view of line inclined at 300 to V.P. is 65mm long. Draw the projections of a line, when it is parallel to and 40mm above H.P. and one end being 20mm in front of V.P.

8. Line PQ has72mm l ength in the front view and 66mm length in the top view. The end P is 48mm below HP and 40mm behind VP, while the end Q is 12mm below HP. Draw the projection of the line, locate the traces and determine the true length and inclinations of the line with the reference planes.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 65 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 66 | P a g e

Notes UNIT 3 PROJECTIONS OF PLANES & SOLIDS Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 68 | P a g e Projection of Planes Introduction A plane is a two -dimensional geometrical entity. It has length and width but no thickness. For practical purposes, a flat face of an object may be treated as a plane. A plane which has limited

extent is termed as a lamina.

A plane can be located by:

(i) Thre e non -collinear points, (ii) A straight line and a point outside it, (iii) Two parallel or intersecting straight lines, or (iv) Traces of the lines.

This chapter deals with the projections of laminas of pre -defined shapes, e.g., triangular plane, square plane, rectangul ar plane, pentagonal plane, hexagonal plane, circular plane, semicircular plane, etc. Sometimes, a given plane is composed of two or more planes mentioned above. Such planes are called composite planes, e.g., plane composed of a half hexagon and a semicirc le, circular plane with hexagonal hole, etc.

Planes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 69 | P a g e Positions of Planes 1. Plane parallel and perpendicular to reference planes (HP & VP)

A. Plane parallel to HP and perpendicular to VP.

B. Plane parallel to VP and perpendicular to HP.

2. Plane perpendicular and inclined to reference planes (HP & VP) A. Plane perpendicular to HP and inclined to VP.

B. Plane perpendicular to VP and inclined to HP.

3. Plane perpendicular to both HP & VP.

4. Plane inclined to both HP & VP A. Inclination to HP and VP is not equal t o 90°.

B. Inclination to HP and VP is equal to 90°.

Terms Used in Projections of Planes The following terms must be understood before we proceed for the step -by-step procedure of obtaining the projections of a plane.

True Shape: The actual shape of a plane i s called its true shape.

Inclination with the RPs: The inclination of a plane with an RP is the acute angle the plane makes with that RP. It is always measured in a plane perpendicular to the given plane and the RP.

Inclination with the HP (θ p) It is the acute angle the plane makes with the HP.

Inclination with the VP ( ϕp) It is the acute angle the plane makes with the VP.

Traces of the Plane: Just like a line, a plane also has traces. The traces of a plane are the lines of intersections of the plane with the RPs. A plane may have a horizontal trace or vertical trace or both.

Horizontal Trace (HT ) The real or imaginary line of intersection of a plane with the HP is called horizontal trace of the plane. HT is always located in the TV.

Vertical Trace (VT) The real or imaginary line of intersection of a plane with the VP is called vertical trace of the plane. VT is always located in the FV.

It shou ld be noted that the plane has no trace on the RP to which it is parallel. For example, a plane parallel to the HP will have no HT. Similarly, a plane parallel to the VP will have no VT. HT and VT of a plane (produced if necessary) meet at a point on the X Y.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 70 | P a g e Perpendicular Planes: The planes perpendicular to one or both the RPs are called perpendicular planes. The first three positions of the planes mentioned in the previous section represent perpendicular planes.

Oblique Planes : The planes inclined to both the RPs are called oblique planes. The fourth position of the planes mentioned in the previous section represents oblique planes.

Line View or Edge View : The view of a plane seen as a line is called line view or edge view of the plane. One view of a perpen dicular plane is always an edge view. The edge view always represents the trace of the plane. For example, if a plane is perpendicular to the VP, then its FV will be an edge view representing VT of the plane. Similarly, TV of a plane perpendicular to the H P Will be an edge view representing HT.

System of Notation 1. The actual plane in space is denoted by capital letters A, B, C and D etc.

2. The front view (FV) of a plane is denoted by their corresponding lower -case letters with dashes as a', b', c' and d' etc.

3. The top view (TV) of a plane is denoted by their corresponding lower -case letters without dashes as a, b, c and d etc.

4. The side view (SV) of a plane are denoted by their corresponding lower -case letters with double dashes as a”, b", c" and d" etc.

5. Projecto rs are always drawn as continuous thin lines.

6. Line with specific thickness for a particular type of line.

In Computer Aided Engineering Graphics for projection of plane following commands are used other than evoking software, opening file, saving file and giving print command. Using these minimum12 commands any type of projection of line problem can be solved they are as follows:

1. Select tool Command.

2. Point command.

3. Poly-Line command.

4. Two Point Line command.

5. Parallel line command.

6. Center Circle command 7. Bisector command.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 71 | P a g e 8. Smart Dimension command.

9. Line Width command.

10. Insert Text command.

11. Move Copy command.

12. Rectangle command.

Plane parallel and perpendicular to reference planes (HP & VP) If the given plane is parallel to an RP, it remains perpendicular to th e other RP. In such a case, the view of the plane on the RP to which it is parallel gives the true shape. Another view is always an edge view parallel to XY.

Plane parallel to HP and perpendicular to VP.

If a plane is parallel to the HP, its TV gives the true shape. Therefore, TV should be drawn first.

FV will be an edge view parallel to XY. SV will be perpendicular to X Y.

Plane parallel to HP and perpendicular to VP.

Plane parallel to VP and perpendicular to HP.

If a plane is parallel to the VP, its FV gives the true shape. Therefore, FV should be drawn first.

TV will be an edge view parallel to XY. SV will be perpendicular to X Y.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 72 | P a g e Plane parallel to VP and perpendicular to HP.

Plane Inclined to one RP and Perpendicular to the other RP If a plane is inclined to one RP and perpendicular to the other RP, none of its views will give the true shape. The view on the RP to which the plane is inclined will be smaller than the actual size of the plane. The view on the RP to which the plane is perpendicular wi ll be a line view. Such problems can be solved in two stages. In the first stage, the given plane is assumed to be parallel

to the RP to which it is finally inclined. The true shape can thus be obtained in one view. In the second stage, another view (which is an edge view parallel to XY) is tilted so as to make desired inclination with the first RP.

Plane Inclined to the HP and Perpendicular to the VP When the surface of the plane is inclined at θ to the H.P. and perpendicular to the V.P., the projections a re obtained in two stages. In the first stage, the plane is assumed to lie on the H.P.

The true shape of the plane is viewed in the top view and a straight line lying on xy in the front view. In the second stage, the plane is tilted at θ to the H.P. The fr ont view is redrawn inclined at θ to the xy. The final top view is obtained by joining the points of intersection of the vertical projectors of the corners from the front view with the horizontal projectors of the corners from the top view of the preceding stage.

Note 1 If the plane has a side on the H.P. (or parallel to the H.P. or on the ground), then keep an edge of the plane perpendicular to xy in the top view of the first stage.

Note 2 If the plane has a corner in the H.P. (or on the ground), then keep the line joining a corner and the centre of the plane parallel to xy.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 73 | P a g e Plane Inclined to the HP and Perpendicular to the VP Plane Inclined to the VP and Perpendicular to the HP When the s urface of the plane is inclined at ϕ to the V.P. and perpendicular to the H.P., the

projections are obtained in two stages. In the first stage, the plane is assumed to lie on the V.P.

The true shape of the plane is viewed in the front view and a straight l ine lying on xy in the top view. In the second stage, the plane is tilted at ϕ to the V.P. The top view is redrawn inclined at ϕ to the xy. The final front view is obtained by joining the points of intersection of the vertical projectors of the corners fro m the top view with the horizontal projectors of the corners from the front view of the preceding stage.

Note 1 If the plane has a side on the V.P. (or parallel to the V.P. or on the ground), then keep an edge of the plane perpendicular to xy in the fron t view of the first stage.

Note 2 If the plane has a corner in the V.P. (or on the ground), then keep the line joining a corner and the centre of the plane parallel to xy in the front view of the first stage.

Plane Inclined to the VP and Perpendicular to the HP Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 74 | P a g e Plane perpendicular to both HP & VP.

If a plane is perpendicular to both the RPs, then its FV and TV both will be seen as edge views perpendicular to XY. Such a plane is parallel to the PP and hence its true shape is seen in SV.

Therefore, for su ch problems, it is advisable to draw SV first.

Plane Perpendicular to both HP & VP Plane inclined to both HP & VP.

A plane inclined to both the RPs is called an oblique plane. None of the views of the oblique plane gives the true shape. It should be note d that the angles made by the oblique plane with the RPs (i.e., θ and ϕ) might not be directly given in the problem. Often, either of the inclinations, θ or ϕ, is given along with some other condition(s) that automatically pose the restriction on the other inclination.

The problems on oblique planes are solved in three stages. In the first stage, the plane is often assumed to be parallel to one of the RPs so that the true shape can be obtained in one view. In the second stage, the given angle between the pl ane and the RP (i.e., either the HP or the VP) or some other condition mentioned in the problem is established. In the third stage, all other remaining conditions are satisfied.

Plane Inclined to both HP & VP Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 75 | P a g e Solved Problems 1. An equilateral triangular la mina of 25 mm side lies with one of its edges on HP such that the

surface of the lamina is inclined to HP at 60º. The edge on which it rests is inclined to VP at 60º. Draw the projections.

Solution 1. Open the Software. Click on the Application Menu and click on New and select “acad “in the open dialog box and click Open.

2. Enter the command “UNITS “in command bar and Select units as “Millimeters and click ok.

3. Enter the command “LIMITS “in command bar and enter 0,0 click enter and enter upper right corner a s 120,90 and click enter 4. Enter the command “ZOOM “in command bar and enter A and click enter 5. Draw a XY line by using line command. Mark VP and HP above and below it by using “XTEXT” command in command bar

6. As per the problem equilateral triangular lamina o f 25mm has to be drawn in HP, hence draw a vertical line of 25 mm using POLYLINE command and in format select VL and enter length as 25 and angle as –90 in mini dialog box. Mark annotations a and b using XTEXT Command as shown below.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 76 | P a g e 7. Draw an arc of rad ius of 25 from a and b to cut each other at c using CENTER CIRCLE command in drafting tool bar and in format select PL. In mode option select arc. Join abc to get triangular lamina of 25 mm using POLYLINE command

8. Draw front view of the triangular lamina u sing POLYLINE command and in format select VL, mark annotations as (a') b' and c' as shown below.

9. Since the lamina is inclined at 60° to HP. By using POLYLINE command and in format select VL enter length equal to length of first stage front view and angl e as 60 in mini dialog box, mark annotations as (a') b' and c' using XTEXT Command 10. Draw vertical projectors downwards from the second front view using POLYLINE command and in format select PL. Draw horizontal projectors from top view to intersect vertica l

projectors at a, b and c which forms the second stage top view as shown below.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 77 | P a g e 11. Since the edge on which it rests is inclined to VP to 60° Draw a line of 60° in HP using POLYLINE command and in format select PL. From edit menu select MOVE COPY command an d then select second stage top view. In selection tree right click on the start point

and click reset to select the start point anywhere on the edge of lamina to shift on to 60° line drawn. Click and drag the lamina on 60° line. Click or drag to rotate and enter angle as 30 in mini dialog box and click on OK 12. Draw the vertical projection upwards from all the corners of triangular lamina from third stage top view using POLYLINE command and in format select PL. Again, draw horizontal

projectors from second st age front view to intersect vertical projectors at a' b' and c'.

13. Join a' b' and c' using POLYLINE Command 14. Using DIMENSION Command in Annotation tool bar or Enter DIM command in command bar dimension the drawing Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 78 | P a g e

2. A square plate of 40 mm side rests on HP such that one of the diagonals is inclined at 30º to HP and 45º to VP. Draw its projections.

Solution 1. Open the Software. Click on the Application Menu and click on New and select “acad “in the open dialog box and click Open.

2. Enter the command “UNITS “in command bar and Select units as “Millimeters and click ok.

3. Enter the command “LIMITS “in command bar and enter 0,0 click enter and enter upper right corner as 100,100 and click enter 4. Enter the command “ZOOM “in command bar and enter A and click enter Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 79 | P a g e

5. Draw a XY line by using line command. Mark VP and HP above and below it by using “XTEXT” command in command bar.

6. As per the problem a square lamina of 40 mm has to be drawn in HP, hence draw a square of 40 mm using RECTANGLE command Now enter X size = 40, Y size = 40 and angle as 45 in mini dialog box. Mark annotations a b c and d using XTEXT Command as shown be low.

7. Draw the vertical projection upwards from all the corners of square lamina in top view until it touches XY line, using POLYLINE command and in format select PL.

8. Draw front view of the triangular lamina using POLYLINE command and in format select VL, mark annotations as a' b' c' and (d') as shown below.

9. Since the diagonal of lamina is inclined at 30° to HP. By using POLYLINE command and in format select VL enter length equal to length of first stage front view and angle as 30 in mini dialo g box, mark annotations as a' b' (d') and c' using XTEXT command 10. Draw vertical projectors downwards from the second front view using POLYLINE command and in format select PL. Draw horizontal projectors from top view to intersect vertical

projectors at a, b c and d which forms the second stage top view as shown below.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 80 | P a g e 11. Since the diagonal of lamina is inclined to VP at 45°. Draw a line of 45° in HP using POLYLINE command and in format select PL. Draw an arc of radius equal to diagonal length of lamina from f irst stage top view to cut on 45° line drawn. Draw a locus from point a1, now

with radius equal to diagonal length of lamina from second stage top view to cut on the locus.

Join ac to get the diagonal of third stage top view. From edit menu select MOVE com mand and then select second stage top view. In selection tree right click on the start point and click reset to select the start point anywhere on the diagonal of lamina to shift on to new diagonal line drawn. Click and drag the lamina on new diagonal line . Click or drag to rotate and enter angle so as to match both diagonals and click on OK. Mark annotations as a b c and d.

12. Draw the vertical projection upwards from all the corners of square lamina from third stage top view using POLYLINE command and in format select PL. Again, draw horizontal projectors from second stage front view to intersect vertical projectors at a' b' c' and d'.

13. Join a' b' c' and d' using LINE Command and in format select VL.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 81 | P a g e 14. Using DIMENSION Command in Annotation tool bar or Ent er DIM command in command bar dimension the drawing Practice Problems

1. A Square plane with a 40 mm side has its surface parallel to and 20mm above the HP. Draw its Projections, when A. A side is parallel to VP B. A side is inclined at 300 to VP and C. All sides are equally inclined to VP.

2. A Hexagonal plane with a 30mm side has its surface parallel to and 20mm infront of the VP.

Draw its Projections, when A. A side is perpendicular to HP B. A side is parallel to the HP C. Side is inclined at 450 to the HP 3. A Pentagona l plane with a 30 mm side has an edge on the HP, the surface of the Plane is

inclined at 450 to the HP. Draw it’s Projections?

4. A Hexagonal plate with a 30mm side and negligible thickness has its surface Perpendicular to the HP and inclined at 450 to the VP . Draw its Projections? When one of its sides of the Plane is Parallel to and 15 mm Infront of the VP Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 82 | P a g e

5. A Circular plane with a 60 mm Diameter is resting on a point it’s circumference on the VP.

The center is 40mm above the HP, and the surface is inclined at 450 to the VP. and perpendicular to the HP Draw Its Projections?

6. Rectangle 30mm and 50mm sides is resting on HP on one of its small side which is 300 inclined to VP, while the surface of the plane makes 450 inclination with HP. Draw it’s projections?

7. A regular pentagon of 30 mm sides is resting on HP, on one of its sides with its surface 450 inclined to HP. Draw it’s projections when the side in HP makes300 angle with VP?

8. A circle of 50mm diameter is resting on HP on end A of its diameter AC which is 300 inclined to HP while it’s TV is 450 inclined to VP. Draw its Projections?

9. A semicircle of 100mm diameter is suspended from a point on its straight edge 30mm from the midpoint of that edge so that the surface makes an angle of 450 with VP. Draw its projectio ns.

10. A pentagon of sides 30mm rests on the ground on one of its corners with the sides containing the corners being equally inclined to the ground. The side opposite to the corner on which it rests is inclined at30degrees to the VP and is parallel to the HP . The surface of the pentagon makes10 degrees with the ground. Draw the top and front views of the pentagon.

11. A regular pentagon of 30mm side is resting on one of its edges on HP which is inclined at 45 degrees to VP. Its surface is inclined at 30degrees to HP. Draw its projections.

12. Draw the projections of a regular hexagon of 25mm side, having one of its sides in the H.P.

and inclined at 60degrees to the V.P and its surface making an angle of 45degreeswithH.P.

13. A thin circular plate of 40mm diameter having i ts plane vertical and inclined at 40 to V.P. Its center is30mm above H.P. and 35mm infront of V.P. Draw the projections.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 83 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 84 | P a g e

Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 85 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 86 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 87 | P a g e Projections of Solids

Introduction Any object having definite length, width and height is called a solid. In engineering drawing, solids are often represented by two or more orthographic views, i.e., FV, TV or SV. The study of the projections of a solid is very important in mechanical -design problems. The knowledge of projections of solids is e ssential in 3D modeling and animation. Projections of solids find wide

applications in the construction industry.

Basic Solids Basic solids are those which have predefined shapes. The basic solids are the constituent parts of any complex solid. Objects in the real world are made up of combinations of basic solids. In 3D modeling, the basic solids are called solid primitives. Solid primitives are combined in logical ways to obtain the desired 3D shape.

System of Notation 7. The actual plane in space is denoted by capital letters A, B, C and D etc.

8. The front view (FV) of a plane is denoted by their corresponding lower -case letters with dashes as a', b', c' and d' etc.

9. The top view (TV) of a plane is denoted by their corresponding lower -case letters without dashes as a, b, c and d etc.

10. The side view (SV) of a plane are denoted by their corresponding lower -case letters with double dashes as a”, b", c" and d" etc.

11. Projectors are always drawn as continuous thin lines.

12. Line with specific thickness for a particular type of line.

In Computer Aided Engineering Graphics for projection of solids following commands are used other than evoking software, opening file, saving file and giving print command. Using these minimum 13 commands any type of project ion of line problem can be solved they are as follows:

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 88 | P a g e 1. Select tool Command.

2. Point command.

3. Poly-Line command.

4. Two Point Line command.

5. Parallel line command.

6. Center Circle command 7. Bisector command.

8. Smart Dimension command.

9. Line Width command.

10. Insert Text command.

11. Move Copy command.

12. Rectangle command.

13. Smart Delete Command Classification of solids Figure 3.1 Classification of Regular Solids Polyhedron A polyhedron is a solid bounded by planes called faces, which meet in straight lines called

edges. A regular polyhedron has all the faces equal and regular as shown in Fig. 3.2.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 89 | P a g e Figure 3.2 Regular Polyhedron Prism A prism is a polyhedron with two n -sided polygonal bases which are parallel and congruent,

and lateral faces are rectangles. All cross -sections parallel to the bases are congruent with the bases. An imaginary line that joins the centre of the bases is called an axis. A right and regular prism has regular polygonal bases, axis perpendicular to the bases and all t he faces are equal rectangles, as shown in Fig. 3.3. Prisms are named according to the shape of their base, so a prism with a triangular base is called a triangular prism; a square base is called a square prism

and so on.

Figure 3.3 Prisms Pyramid A pyr amid is a polyhedron with n -sided polygonal base and lateral faces are triangles meeting at a point called the vertex or apex. An imaginary line that joins the apex with the centre of the base is known as the axis. A right and regular pyramid has a regular polygon base, axis

perpendicular to the base and all the faces are equal isosceles triangles, as shown in Fig. 3.4.

Pyramids are named according to the shape of their base, so a pyramid with a triangular base is called a triangular pyramid; a square base is called a square pyramid and so on. The centre of gravity of pyramids lies on the axis at one -fourth of its height from the base.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 90 | P a g e Figure 3.4 Pyramids Solid of Revolution These solids are obtained by revolving a plane figure like rectangle, triangle or a semi -circle

about a fixed line.

Cylinder : A cylinder is a solid of revolution obtained by revolving a rectangle about one of its fixed side called an axis. It can be imagined as a prism of infinite number of lateral faces. Any line on the sur face of a cylinder is called its generator. Thus, a cylinder has an infinite number of generators. A right cylinder has all the generators and the axis perpendicular to the base, as shown in Fig. 3.5(a).

Cone : A cone is obtained by revolving a triangle abo ut its fixed side called an axis. A cone can be imagined as a pyramid with infinite number of lateral faces. Any line on the surface of a cone is called its generator. Thus, a cone has an infinite number of generators. A right cone has all generators of eq ual length and the axis perpendicular to the base, as shown in Fig. 3.5(b).

Sphere : A sphere is obtained by revolving a semi -circle around its diameter, as shown in Fig Figure 3.5 Solids of Revolution Oblique Solid An oblique solid such as oblique prism, pyramid, cylinder or cone has its axis inclined to its base as shown in Fig. 3.6. The faces of an oblique prism are parallelograms of different sizes.

The faces of an oblique pyramid are triangles of different sizes. The generators in an oblique cylinder have equal lengths whereas those in an oblique cone have unequal lengths.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 91 | P a g e Figure 3.6 Oblique Solids Frustum of Pyramid and Cone When a regular pyramid or a cone is cut by a plane parallel to its base and the portion of the

solid containing apex is removed, the remaining portion of the solid is called the frustum of that pyramid or cone, as shown in Fig. 3.7.

Figure 3.7 Frustums Recommended Method of Labelling It is recommended to label the corners of the solids in a manner as shown in Fig. 3.8.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 92 | P a g e Figure 3.8 Method of Labelling Positions of Solids The position of a solid in space is specified by the inclinations of its axis with the RPs.

Therefore, a solid will have positions with respect to RPs same as that of a line. Depending on the orientation of its axis in space, a solid may have the following positions:

Figure 3.9 Truncated Solids The solid may be in one of the following positions:

1. Axis perpendicular to the H.P.

2. Axis perpendicular to the V.P.

3. Axis parallel to both the H.P. and the V.P. (i.e., perpendicular to the profile plane) 4. Axis inclined to the H.P. and parallel to the V.P.

5. Axis inclined to the V.P. and parallel to the H.P.

6. Axis incli ned to both the H.P. and the V.P.

Axis Perpendicular to H.P.

This is one of the basic positions of the solid. It is evident that if the axis of a right solid is perpendicular to the H.P., its base will be parallel to the H.P. The true shape and size of the base can be viewed in the top view. Therefore, first obtain the top view of the solid and then project it to obtain the front view.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 93 | P a g e Figure 3. 10 Axis Perpendicular to H.P.

Axis Perpendicular to V.P.

This is one of the basic positions of the solid. It is evident that if the axis of a right solid is perpendicular to the V.P., its base will be parallel to the V.P. The true shape and size of the base can be viewed in the front view. Therefore, first obtai n the front view of the solid and then project it to obtain the top view.

Figure 3. 11 Axis Perpendicular to V.P.

Axis Parallel to both H.P. and V.P.

It is evident that if the axis of right solids is parallel to both H.P. and V.P., the base of the solid will be perpendicular to the reference planes and parallel to the profile plane. The true shape Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 94 | P a g e and size of the base can be viewed in the side view. Therefore, first obtain the side view of the

solid and then project it to obtain the front and the top views .

Figure 3. 12 Axis P arallel to both H.P and V .P.

Axis inclined to the R.P. and parallel to the R.P.

If the axis of a solid is inclined to one RP and parallel to the other RP then the problem is solved in two stages. In the first stage, the axis is assumed to be perpendicular to the RP to which it is finally inclined. The view obtained on that RP will give the true shape of the base. The corresponding other view will give the TL of the axis. In the second stage, the other view is redrawn in such a way that the axis will make the required angle with the given RP.

Here, it should be noted that the inclination of the axis with a particular RP might not be given directly. Instead, it may be expressed in terms of other parameters, as mentioned earlier.

Figure 3. 13 Axis inclined to the H.P. and parallel to the V.P.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 95 | P a g e Figure 3. 14 Axis inclined to the V.P. and parallel to the H.P.

Axis inclined to the both R.P ‘S.

If the axis of a solid is inclined to both the RPs then the problem is solved in three stages. As already mentioned, the inclinations of the axes may not be given directly. Instead, it may be indirectly mentioned by means some other parameters. If the inclinations are given directly then, in the first stage, the axis is assumed to be perpendicular to any one RP. The view obtained on that RP will give the true shape of the base. The corresponding other view will give the TL

of the axis. In the second stage, the other view is redrawn so that the axis will make the required angle with the RP to which it was initially perpendicular. The corresponding next view is obtained in the second stage. In the third stage, the next view i s redrawn so as to make the ‘desired inclination’ of the axis with the other RP. Here, the ‘desired inclination’ is the apparent inclination of the axis which is obtained by using the theory of projections of the lines. The

view thus obtained satisfies al l the conditions, i.e., inclinations with both the RPs, and hence represents the final view. This view is then projected to obtain the other corresponding final view.

If the inclinations are not given directly then the first stage must be decided carefull y. Often an inclination of the axis with one RP is given and the inclination with the other RP is given in terms of the inclination of an edge or face of the solid. In such a case, the first stage is to keep the axis perpendicular to that RP with which its inclination is known. In the second stage, the required inclination with that RP is obtained. In the third stage, the other condition, viz.,

inclination of the face or inclination of an edge, is established. It must be remembered that, in the first stage, the solid is always kept in such a way that the true shape of the base and TL of the axis are visible. This helps to satisfy the condition on the axis (mentioned directly or Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 96 | P a g e

indirectly) easily in the second stage. Note that one view in the second stage always gives TL of the axis (since it is simply redrawn from the first stage).

Other possibilities are explained with the help of examples.

Figure 3. 15 Axis inclined to the both R. P.

Solved Problems 1. A square prism 35 mm side of base and 60 mm axi s length rests on HP on one of its edges of the base which is inclined to VP at 30º. Draw the projections of the prism when the axis is inclined to HP at 45º.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 97 | P a g e Solution 1. Open the Software. Click on the Application Menu and click on New and select “ acad “in the open dialog box and click Open.

2. Enter the command “UNITS “in command bar and Select units as “Millimeters and click ok.

3. Enter the command “LIMITS “in command bar and enter 0,0 click enter and enter upper right corner as 100,100 and click enter 4. Enter the command “ZOOM “in command bar and enter A and click enter 5. Draw a XY line by using line command. Mark VP and HP above and below it by using “XTEXT” command in command bar

6. As per the problem draw a square lamina of 35 mm in HP using RECTANGL E command and in format select first corner and click enter and select Area, Now enter X size = 35, Y size = 35 and similarly label the bottom face as a1 b1 c1 d1 center as o1 using XTEXT Command 7. Draw the horizontal line at a distance of 60 mm i.e., equal to height of the square prism

above the XY line using LINE COMMAND and enter 60 in mini dialog box. Draw the vertical projection upwards from top view, until they intersect horizontal line at 60 mm above XY line using POLYLINE command. Mark the intersecti on points as a' b' c' d' and o' for the top face and a1' b1' c1' d1' and o1' for bottom of the square prism.

8. Since the square prism axis is inclined at 45° to HP. By using POLYLINE command and in format select PL enter length equal to length (60) of first stage front view and angle as 45 in mini dialog box draw a line of 45°. Mark the annotations as shown below.

9. Draw vertical projectors downwards from the second stage front view using POLYLINE command and in format select PL. Draw horizontal projectors from top view to intersect vertical projectors to get required second stage top view by joining intersection points by Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 98 | P a g e

using LINE Command and in format select VL as shown below. Note the invisible (hidden) lines are to be dotted. Hence draw invisible line using POLYLINE command and in format select DL.

10. Since the edge on which prism rests is inclined to VP at 30°. Draw a line of 30° in HP using POLYLINE command and in format select PL. Mark annotations as shown below.

11. Draw the vertical projection u pwards from the third stage top view using POLYLINE command and in format select PL. Again, draw horizontal projectors from second stage front view to intersect vertical projectors to get the final front view. Join all the intersection points using LINE Co mmand and in format select VL.

12. Using DIMENSION Command in Annotation tool bar or Enter DIM command in command bar dimension the drawing Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 99 | P a g e 2. A hexagonal prism 25 mm sides of base and 50 mm axis length rests on HP on one of its

corners of the base such that the two base edges containing the corner on which it rests make equal inclinations with HP. Draw the projections of the prism when the axis of the prism is inclined to HP at 40º and to VP at 30º.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 100 | P a g e Solution 1. Open the Software. Click on the Application Menu and click on New and select “acad “in the open dialog box and click Open.

2. Enter the command “UNITS “in command bar and Select units as “Millimeters and click ok.

3. Enter the command “LIMITS “in command bar and enter 0,0 click enter and enter upper right corner as 100,100 and click enter 4. Enter the command “ZOOM “in command bar and enter A and click enter 5. Draw a XY line by using line command. Mark VP and HP above and below it by using “XTEXT” command in command bar

6. As per the problem draw a he xagonal lamina of 25 mm in HP using POLYLINE command and in format select VL and enter edges as 6, radius as 25. Mark the corner points of top face as a b c d e f and center as o. Similarly label the bottom face as a1 b1 c1 d1 e1 f1 center as o1 using XTEX T Command 7. Draw the horizontal line at a distance of 50 mm i.e., equal to height of the hexagonal prism

above the XY line using PARALLEL LINE COMMAND and enter 50 in mini dialog box.

Draw the vertical projection upwards from top view, until they intersect horizontal line at 50 mm above XY line using POLYLINE command. Mark the intersection points as a' b' c' d' e' f' and o' for the top face and a1' b1' c1' d1' e1' f1' and o1' for bottom of the square prism.

8. Since the hexagonal prism axis is inclined at 40 ° to HP. By using POLYLINE command and in format select PL enter length equal to length (50) of first stage front view and angle as 40 in mini dialog box to draw a line of 40°. Mark the annotations as shown below.

9. Draw vertical projectors downwards from the second stage front view using POLYLINE command and in format select PL. Draw horizontal projectors from top view to intersect vertical projectors to get required second stage top view by joining intersection points by using LINE Command and in format s elect VL as shown below. Note the invisible (hidden) Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 101 | P a g e lines are to be dotted. Hence draw invisible line using POLYLINE command and in format select DL.

10. As per the problem draw a line of 30° in HP using P OLYLINE command and in format select PL. Draw an arc of radius equal to axis of prism from first stage front view to cut on 30° line drawn. Draw a locus from point o1, now with radius equal to axis of prism from second stage top view to cut on the locus. Join o o 1 to get the axis of third stage top view.

11. Draw the vertical projection upwards from the third stage top view using POLYLINE command and in format select PL. Again, draw horizontal projectors from second stage front view to intersect vertical projectors t o get the final front view. Join all the intersection points using LINE Command and in format select VL and draw invisible line using POLYLINE command and in format select DL.

12. Using DIMENSION Command in Annotation tool bar or Enter DIM command in comman d bar dimension the drawing Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 102 | P a g e Practice Problems

1. A Square Pyramid, having base with a 40mm side and 60mm axis is resting on its base on the HP. Draw its Projections when (a) A side of the base is parallel to the VP.

(b) A side of the base is inclined at 300 to the VP and (c) All the sides of base are equally inclined to the VP 2. A pentagonal Prism having a base with 30 mm side and 60 mm long Axis, has one of Its bases in the VP. Draw Its projections When (a) Rectangular face is parallel to and 15 mm above the HP

(b) A rectangular face perpendicular to HP and (c) A rectangular face is inclined at 450 to the HP 3. A pentagonal Prism having a base with a 30 mm side and 60 mm long axis, is resting on one of its rectangular faces on the HP. with axis parallel to the VP. Draw its projections?

4. A hexa gonal Prism having a base with a 30 mm side and 75 mm long axis, has an edge its base on the HP, its axis parallel to the VP and inclined at 450 to the HP . Draw its projections?

5. A hexa gonal Prism having a base with a 30 mm side and 65 mm long axis, has an edge its base on the VP, its axis parallel to the HP and inclined at 300 to the VP . Draw its projections?

6. A cube of 50 mm long edges is so placed on HP on one corner that a body diagonal is Parallel to HP and perpendicular to VP. Draw it s projections.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 103 | P a g e 7. A cone 40 mm diameter and 50 mm axis are resting on one of its generators on HP which makes 300 inclinations with VP. Draw its projections.

8. A circular cone, 40 mm base diameter and 60 mm long axis is resting on HP, on one point of base circle such that its axis makes 450 inclination with HP and 400 inclination with VP.

Draw its projections.

9. A cylinder 40 mm base diameter and 50 mm long axis is resting on one point of base circle on V P, while its axis makes 450 inclination with VP and FV of the axis 300 inclination with HP. Draw its projections.

10. A cone of base diameter 50 mm and height 60 mm is rest s on the ground on a point of its base circle such that the axis of the cone inclined at 45° to the H.P. and inclined at 45° to the H.P. Draw i ts front and top views.

11. A hexa gonal Prism having a base with a 40 mm side and 80 mm long axis, has an edge its base on the HP. The end containing that edge is inclined at 300 to the HP and axis parallel to the VP . It is cut a plane perpendicular to the VP and parallel to the HP. The cutting plane bisects the axis. and inclined at 450 to the HP . Draw its front and sectional top views.

12. A square pyramid of base side 30 mm and altitude 50 mm lies on one of its triangular faces on the HP with its axis parallel t o the VP. It is cut by a vertical plane inclined at 300 to the VP and meeting the axis at 40 mm from the vertex measured in the plan. Draw the top view, sectional front view and the true shape of the section.

13. A cone, diameter of base 50 mm and axis 65 mm long .is lying on the H P on one of its generators with the axis parallel to the VP. It is cut by a horizontal Section plane 12 mm above the ground. Draw its front and sectional top views.

14. Draw the projections of a hexagonal pyramid of side of base 30mm and axis 60 mm long resting on one of its base edges in HP with its axis inclined at 300 to HP and the top view of axis is 450 to VP.

15. Draw the projections of a pentagonal prism, base 25 mm side and axis 50 mm long resting on one of its rectangular faces on HP, with the axis inclined at 45 degrees to VP.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 104 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 105 | P a g e

Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 106 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 107 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 108 | P a g e UNIT 4

ISOMETRIC PROJECTIONS Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 109 | P a g e Isometric Projection In engineering drawing, orthographic projection of a solid is best way of projecting the details

of an object when a solid is resting in its simple position . As t he front view or top view taken separately, gives an incomplete idea of the object , a pictorial projection is the best method to show the object in one view only. Basically, pictorial projection represents three dimensional shape of an object and represents real things in one view only, which indicates length, breadth and height of the object. Therefore, the object is easily visualized from a pictorial projection

than from its orthographic projection.

The pictorial projection may be divided as:

1. Oblique projection 2. Perspective projection 3. Axonometric projection.

Axonometric Projection An axonometric projection is a type of single -view parallel projection used to create a pictorial drawing of an object. The object is placed in such a position that the three mutually perpendicular faces are visible from a single dir ection . The word ‘axonometric projection ’ means measuring along axis in which “axon” means axis while metron means measuring.

Axonometric projections are commonly used to draw mechanical parts of an object for the clear picture of an object which are visua lized from the orthographic projection. In this projection the object can be drawn at different angles and having the different length of edges.

Axonometric projections are again classified as:

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 110 | P a g e Trimetric Projection In this type, an object is placed in such a way that no two axes make an equal angle with the plane of projection.

Dimetric Projection In this type of projection, an object is placed in such a way that two of its axes make equal angle with the plane of projection and the third axis makes either a smaller or a greater angle .

Isometric Projection In this type of projection, an object is placed in such a way that all three axes make equal angle with the plane of projection .

The isometric projection is the most common pictorial representation used in industries where visualization of the three dimensions of a solid are not only shown in one view, but their actual sizes can be measured directly from it. As it shows views of three faces of an object equally, it is very he lpful to even a layman to understand the shape of the object. A multiview drawing requires two or more orthographic projections to define the exact shape of a three dimensional

object. Each orthographic view is a two -dimensional drawing showing only two ou t of three dimensions of the object.

Principle of Isometric Projection The isometric projection can be visualized is by considering a view of a cube with one of the solid diagonals perpendicular to the vertical plane and the three axes equally inclined to the vertical plane . The final front view is the isometric projection of the cube. Figure 15.3(a) shows the front view when hidden lines are removed. It gives the realistic view of the cube. The

corners are renamed in capital letters. A keen study of this view reveals the following information.

1. The outer boundary ABFGHDA is a regular hexagon.

2. All the faces of the cube which are actually square in shape appear as rhombus.

3. The three lines CB, CD and CG meeting at C, represent the three mutually perpendicula r edges of the cube.

a. They make equal angles of 120° with each other.

b. They are equal in length but smaller than the true length of the edge of the cube.

c. The line CG is vertical, and the other lines CB and CD make 30° with the horizontal.

4. All other lines representing the edges of the cube are parallel to one or the other of the above three lines, i.e., CB, CD and CG, and are equally foreshortened.

5. The diagonal BD of the top face ABCD is parallel to V.P., and hence shows its true length.

A comparison of the rhombus ABCD of the front view with the square face of the cube is shown in below figure.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 111 | P a g e Isometric Axes, Lines and Planes 1. The three lines CB, CD, CG meeting at a point C and making an angle of 1200 with each other are called Isometric axes.

2. The lines (AB, BF, FG, GH, DH and AD) parallel to the Isometric axis are termed as Isometric lines.

3. The lines (BD, AC, CF, BG, etc.,) which are not parallel to the isometric axes are known as Non-Isometric lines 4. The plane (ABCD, BCGF, CGHD, etc.,) representing any face of the cube as well as other plane parallel to it is called an Isometric Plane.

5. The plane (ABGH, CDEF, AFH, CFH, etc.,) which is not parallel to isometric planes are known as Non-Isometric Planes.

6. The scale which is used to convert the true length into isometric length is known as Isometric Scale .

Isometric Scale Referring to the above Fig., all the edges of the cube are equally foreshortened. Therefore, the square faces are seen as rhombuses in the isometric projection. The foreshortening of the edge can be calculated as follows:

In triangle ABO, 𝐵𝐴𝐵𝑂= 1cos 300= 2√3 In triangle A’BO, 𝐵𝐴′

𝐵𝑂= 1cos 450= √21 Therefore, 𝐼𝑠𝑜𝑚𝑒𝑡𝑟𝑖𝑐 𝑙𝑒𝑛𝑔𝑡 ℎ𝑇𝑟𝑢𝑒 𝑙𝑒𝑛𝑔 ℎ𝑡= 𝐵𝐴

𝐵𝐴′= 2√3 ×1√2= 911 Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 112 | P a g e Conventional Isometric Scale Simplified Isometric Scale This reduction of the true length can be obtained either by multiplying it by a factor 0.816 or by taking the measurement with the help of an isometric scale.

Isometric Projection and View Isometric projection of an object is the front view of the object placed in isometric position.

Isometric projection is the actual projection of the object on V.P. Here as the edges of the transparent cube are inclined 35016’ to V.P., their projection on VP will have a length of about 82% of the true length, when measured in the isometric position.

Isometric projection can be drawn directly, using the true length of the dges of the cube along the isometric axes. As a result, t he projection obtained is larger in size than the actual. This projection is called isometric View or Isometric Drawing.

(a) Multiview projection (b) Isometric projection (c) isometric view Dimensioning The general rules for the dimensioning of multi view projection is applicable for isometric projection, except the following:

1. All the extension lines and dimension lines should be parallel to the isometric axes and they should be on any of the isometric planes.

2. The text should be placed at the middle of the dimension line, after breaking it to a short length.

3. The dimensional values in X direction should be readable from the right side. While the Y direction from left side and Z direction from the right side respectively.

4. The numerals placed alon g the three axes should be aligned with the direction of the axes.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 113 | P a g e System of Notation 1. The actual solid in space is denoted by capital letters A1 , B1, C1 and D1 etc for Base of solid and A, B, C and D etc for top face of the solid and axis as o1 and o.

2. The front view (FV) of a solid is denoted by their corresponding lower case letters with dashes as a1 ', b1', c1' and d1 ' etc for base of solid and a ', b' c' and d ' etc for top face of the solid and for axis as o1 ' and o '.

3. The top view (TV) of a solid is de noted by their corresponding lower case letters with dashes as a1, b1, c1 and d1 etc for bottom of solid and a, b c and d etc for top face of the solid and for axis as o1 and o.

4. Projectors are always drawn as continuous thin lines.

5. Isometric projection ann otations are made with the corresponding letters of the solid.

6. Line with specific thickness for a particular type of line.

Isometric Drawing using AutoCAD In Computer Aided Engineering Graphics for isometric projections following commands are used other than evoking software, opening file, saving file and giving print command. A 2D isometric drawing is a flat representation of a 3D isometric projection. This method of drawing provides a fast way to create an isometric view of a simple design. Dista nces measured along

an isometric axis are correct to scale, but the 3D distances and areas cannot be extracted since the drawing s will be in 2D, display objects from different viewpoints, or remove hidden lines automatically.

By using the ISODRAFT command , several system variables and settings are automatically changed to values that facilitate isometric angles. Isoplane specifies the current isometric plane.

The standard isometric planes, called isoplanes , are as follows:

• Right. : Selects the right -hand plane, defined by the 30- and 90 -degree axes pair • Left: Selects the left -hand plane, defined by the 90- and 150 -degree axes pair.

• Top: Selects the top face, called the top plane, defined by the 30- and 150 -degree ax is pair.

You can use the Isometric Drafting tool on the status bar to select the desired isoplane.

Alternatively, you can press F5 or Ctrl+E to cycles through the isoplanes.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 114 | P a g e Using these following commands and features are the most com monly used ones to maintain precision in isometric drawings:

• Polar tracking and direct distance entry • Object snaps and grid snaps • Object snap tracking • Move and Copy Extrude

The EXTRUDE command creates a solid or surface that extends the shape of a curve. Open curves create surfaces and closed curves create solids or surfaces When you extrude objects, you can specify any of the following options:

Mode. Sets whether the extrude creates a surface or a solid.

Specify a path for extrusion. With the Path option, create a solid or surface by specifying an object to be the path for the profile, or shape, of the extrusion. The extruded object starts from the plane of the profile and ends on a plane perpendicular to the path at the endpoint of the path.

For best results, use object snaps to make sure that the path is on or within the boundary of the object being extruded.

Taper angle. Tapering the extrusion is useful for defining part that require a specific taper angle, such as a mold used to create meta l products in a foundry.

Direction. With the Direction option, you can specify two points to set the length and direction of the extrusion.

Expression. Enter a mathematical expression to constrain the height of the extrusion.

Revolve Open profiles crea te surfaces and closed profiles can create either a solid or a surface. The MOde option controls is a solid of surface is created. When creating a surface, SURFACEMODELINGMODE system variable controls if a procedural or NURBS surface is created.

Revolve path and profile curves can be:

• Open or closed • Planar or non -planar • Solid and surface edges • A single object (to extrude multiple lines, convert them to a single object with the JOIN command)

• A single region (to extrude multiple regions, first conve rt them to a single object with the UNION command) The following are the options for revolving:

Objects to Revolve Specifies the objects to be revolved about an axis.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 115 | P a g e Mode Controls whether the revolve action creates a solid or a surface. Surfaces are ex tended as either NURBS surfaces or procedural surfaces, depending on the SURFACEMODELINGMODE

system variable.

Axis Start Point Specifies the first point of the axis of revolution. The positive axis direction is from the first to the second point.

Axis Endpoint Sets the endpoint for the axis of revolution.

Start Angle Specifies an offset for the revolution from the plane of the object being revolved.

Angle of Revolution Specifies how far the selected object revolves about the axis.

Loft Creates a 3D solid or surface by specifying a series of cross sections. The cross sections define the shape of the resulting solid or surface . Loft cross sections can be open or closed, planar or non-planar, and can also be edge subobjects. Open cross sections create s urfaces and closed cross sections create solids or surfaces, depending on the specified mode.

The following prompts are used under loft:

Cross Sections in Lofting Order Specifies open or closed curves in the order in which the surface or solid will pass through them.

Point Specifies first or last point of the lofting operation. If you start with the Point option, you must next select a closed curve.

Join Multiple Edges Handles multiple, end -to-end edges as one cross section.

Mode Controls whether the l ofted object is a solid or a surface.

Continuity This option only displays if the LOFTNORMALS system variable is set to 1 (smooth fit).

Specifies whether the continuity is G0, G1, or G2 where the surfaces meet.

Bulge Magnitude This option only displays if the LOFTNORMALS system variable is set to 1 (smooth fit).

Specifies a bulge magnitude value for objects that have a continuity of G1 or G2.

Guides Specifies guide curves that control the shape of the lofted solid or surface. Guide curves can b e used to control how points are matched up on corresponding cross sections to prevent undesired results, such as wrinkles in the resulting solid or surface.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 116 | P a g e Problem:

1. Draw the isometric view of a Circle (Isocircle) with a 60mm Diameter on all three Principle Planes Using Co -ordinate methods?

Solution:

1. Do one of the following:

• On the status bar, click Find.

• At the Command prompt, enter ISODRAFT.

2. Choose which isoplane orientation that you want to use: Left, Right, or Top.

• Press F5 or Ctrl+E to c ycle through the different isoplanes • On the status bar, Isodraft button, click the dropdown arrow and choose an option • At the Isodraft prompt in the Command window, enter an option 3. At the Command prompt, enter ELLIPSE.

4. At prompt, enter i (Isocircle).

5. The Isocircle option is available only when an isometric drawing plane is active.

6. Specify the center of the isocircle.

7. Specify the radius or diameter of the isocircle.

2. Draw the isometric view of a square of side 40mm kept in (a) vertical Position and (b) horizontal position Solution:

1. Do one of the following:

• On the status bar, click Find.

• At the Command prompt, enter ISODRAFT.

2. Choose which isoplane orientation that you want to use: Left, Right, or Top.

• Press F5 or Ctrl+E to cycle through the different isoplanes • On the status bar, Isodraft button, click the dropdown arrow and choose an option • At the Isodraft prompt in the Command window, enter an op tion 3. At the Command prompt, enter Line.

4. The Polyline option is available only when an isometric drawing plane is active.

5. Specify the coordinates of the square to draw the square .

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 117 | P a g e 3. Draw the isometric view of a square prism of base side 40 mm and axis 60 m m resting on the H.P. on the (a) base with axis perpendicular to the H.P., (b) rectangular face with axis perpendicular to the V.P., and (c) rectangular face with axis parallel to the V.P.

Solution:

1. At first, you need to change your snap settings to isometric. Type DS on the command line and press enter.

2. Drafting settings window will pop up from this window select snap and grid tab and make sure Isometric snap radio button is checked. Click OK to exit drafting settings window.

3. Now make sure ortho mode is turned on from the status bar, if it is not turned on then press F8 to turn it on.

4. You can now select isometric plane for your drawing by pressing the F5 key. The three Isoplanes available for selection are Isoplane top, right and left.

5. Press F5 ke y to activate Isoplane top and then select line command and click anywhere in the drawing area to start your line. Specify a direction and type 5 on the command line then press enter, repeat this process by changing directions of line to make a closed square 4. A of cone base diameter 30mm and height 40mm rests centrally over a cube of side 50mm.

Draw the isometric projection of combination of solids.

Solution:

1. Open the SOFTWARE. Click on the DRAWING in the open dialog box and say OK.

2. To set up the sheet of required size (Ex: A4) by selecting TOOLS from Main Menu Bar and click on OPTIONS/PROPERTIES. Select document properties in dialog box appeared and then select drawing in selection panel. Select the required size say A4, and click OK.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 118 | P a g e 3. As per the problem draw top and front view of combined solids using suitable commands.

4. Draw the isometric scale, as per the dimensions of the problem using POLYLINE command and in format select PL for construction lines draw two lines of iso length of 50 mm along 30° line a s shown. Draw another two lines, using PARALLEL LINE COMMAND and using TRIM/EXTEND CURVES, so that they are connected systematically .

5. Draw the vertical lines at corners of parallelogram equal to isometric height of square prism of 50 mm using POLYLINE com mand and in format select VL.

6. Join all the top end points using 2 POINT LINE Command and in format select PL to get top face as shown below.

7. Since the axis of solids is collinear (square prism and cone), identify the center of rectangle represent it as o. With o as center construct a box of iso length of side 30 mm similar to base drawn earlier as shown using POLYLINE command and in format select PL.

8. Using 3 POINT CIRCLE command in drafting tool bar. In mode option select arc, and use three center method draw an ellipse to get the bottom of cone.

9. Using POLYLINE command and in format select AL draw vertical line upwards at the center of rectangle, equa l to the height of cone 40 mm (given) to get apex of the cone.

10. Using POLYLINE command and in format select VL draw tangential line from bottom of cone to apex as shown. Trim all the unwanted construction lines by using SMART DELETE COMMAND.

11. Using SMART DIM ENSION Command in drawing tool bar dimension the drawing as shown. To get a Hard Copy of the standard drawing select print from file menu bar.

Print dialog window will appear select page and change width to Entities and select the activated button now subs titute width 1 as 0.15 mm, width 2 as 0.05 mm, width 3 as 0.5 mm, width 4 as 0.35 mm and say OK. Select print to get a hard copy and finally save the file. The required standard drawing is as shown below.

5. A hemisphere diameter 50mm is resting on its curved surface centrally on the top face of frustum of a rectangular pyramid base 80mm x 60mm and top 60mm x 40mm, height 55mm. Draw the isometric projection of combined solids.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 119 | P a g e Solution:

1. Open the SOFTWARE . Click on the DRAWING in the open dialog box and say OK.

2. To set up the sheet of required size (Ex: A4) by selecting TOOLS from Main Menu Bar and click on OPTIONS/PROPERTIES . Select document properties in dialog box appeared and then select drawing in selection panel. Select the required size say A4, and click OK.

3. As per the problem draw top and front view of combined solids using suitable commands.

4. Draw the isometric scale, as per the dimensions of the problem.

5. Using POLYLINE command and in format select VL for visible edges draw two lines of iso length of 80 mm and 60 mm along 30° line as shown. Draw another two lines, using PARALLEL LINE COMMAND and using TRIM/EXTEND CURVES so that, they are connected systematically.

6. Using PO LYLINE command and in format select AL draw vertical line upwards at the center of rectangle, equal to the height of rectangular frustum 55 mm (given).

7. At top end of vertical line drawn, using POLYLINE command and in format select VL for visible edges draw two lines of iso length of 60 mm and 40 mm along 30° line as shown. Draw another two lines, using PARALLEL LINE COMMAND and using TRIM/EXTEND CURVES so that, they are connected systematically.

8. Join all the relevant corners of top to base frustum using 2 P OINT LINE command and in format select VL to get frustum as shown below.

9. Since the axis of solids is collinear (hemisphere and rectangular pyramid), identify the center of rectangle represent it as o. With o as center using POLYLINE command and in format select AL draw vertical line upwards at the center o of height equal to height of hemisphere 25 mm (given). Construct a box of iso length of side 50 mm to fit top face of hemisphere using POLYLINE command and in format select PL.

10. Using 3 POINT CIRCLE comma nd in drafting tool bar. In mode option select arc, and select 3 points on rectangle draw a top face of hemisphere.

11. Using CENTER CIRCLE command in drafting tool bar. In mode option select arc, with center as center of top face of hemisphere and radius as a ctual radius of hemisphere draw an arc, so that it touches the top face of hemisphere and passes through the center of top face of the rectangle frustum.

12. Trim all the unwanted construction lines by using SMART DELETE COMMAND.

Using SMART DIMENSION command in drawing tool bar dimension the drawing as shown. To get a Hard Copy of the standard drawing select print from file menu bar.

Print dialog window will appear select page and change width to Entities and select the activated button now substitute width 1 as 0.15 mm, width 2 as 0.05 mm, width 3 as 0.5 mm, width 4 as 0.35 mm and say OK. Select print to get a hard copy and finally save the file. The required standard drawing is as shown below.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 120 | P a g e Practice Exercises:

Plane Surface 1. Draw the isometric view of a h exagon of side 30 mm whose surface is parallel to the V.P.

and a side perpendicular to the H.P.

2. Draw isometric views of a triangle of sides 80 mm, 60 mm and 50 mm on all the three principal planes.

3. Draw the isometric view of a cube of side 50 mm. Also show in the view, circles of diameter 50 mm marked on all the visible faces of the cube.

4. Draw isometric view of a hexagonal plane of side 40 mm with a central hole of diameter 40 mm when the surface of the plane is parallel to the H.P.

5. Draw isometric view of a composite plane made up of a rectangle of sides 60 mm and 40 mm with a semicircle on its longer side.

Simple Solid 1. Draw the isometric view of a cylinder of base diameter 50 mm and axis 60 mm lying on one of its generator on the H.P 2. A square prism of base edge 40 mm and axis 60 mm has an edge of its base on the H.P. The axis is parallel to the V.P. and inclined at 30° to the H.P. Draw its isometric view

3. Draw an isometric view of a pentagonal prism of base side 30 mm and axis 60 mm resti ng on its base in the H.P. with a face parallel and nearer to the V.P.

4. A pentagonal pyramid of base side 30 mm and axis 60 mm long is resting on a face on the H.P. with axis parallel to the V.P. Draw its isometric view in the stated condition.

Truncated P rism 1. Draw isometric projection of the frustum of a pentagonal pyramid of base side 40 mm, top side 20 mm and height 35 mm resting on its base on the H.P 2. A triangular pyramid having a base 50 mm side and axis 65 mm long is resting on its base in the H.P. wi th a side of the base parallel to the V.P. It is cut by an A.I.P. inclined at 45°

with the H.P. and bisecting the axis. Draw its isometric view 3. A paper weight is in the form of a sphere of diameter 50 mm truncated by a horizontal plane at a distance of 40 mm from the topmost point of the sphere. Draw its isometric projection.

Combined Solids 1. A cone of base diameter 30 mm and axis 50 mm rests centrally over a square prism of base side 50 mm and axis 30 mm. Draw the isometric projection of the arrangement 2. A spherical ball of diameter 60 mm is placed centrally over a square block of side 60 mm and thickness 30 mm. Draw the isometric view of the arrangement

3. A hexagonal prism of base side 30 mm and axis 50 mm has an axially drilled circular hole of diameter 30 m m. Draw its isometric projection.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 121 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 122 | P a g e

Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 123 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 124 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 125 | P a g e Notes

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 126 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 127 | P a g e

UNIT 5 TRANSFORMATION OF PROJECTIONS Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 128 | P a g e Transformation of Projections

Introduction Projection: Projection is defined as an Image or drawing of the object made on a plane. The lines form the object to the Plane are called projectors.

Methods of Projec tions: In Engineering drawing the following four methods of Projection are commonly used they are Orthographic Projection Isometric projection Oblique projection

Perspective Projection In orthographic projection an object is represented by two are three views on the mutual perpendicular projection planes each projection view represents two dimensions of an object.

In iso, oblique and perspective projections represents the object by a pictorial view as eyes see it. In these methods of projects in three dimensional object is represented on a projection plane by one view only.

OrthographicProjection When the Projectors are parallel to each other and also perpendicular to the plane the projection is called orthographic Projection Example: Orthographic projection of a car shown in below figure Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 129 | P a g e Orthographic Projection is a way of drawing an 3D object from different directions.

Usually a front, side and plan view is drawn so that a person looking at the drawing can see all the important sides. Orthographic drawings are useful especially when a design has been developed to a stage where by it is almost ready to manufacture.

Plane of projection : Two planes employed for the purpose of orthographic projections are called reference planes or planes of projection. They are intersecting each other at right angle to each other the vertical plane of projection is usually denoted by the letters VP and the other Plane is horizontal plane of Projection is denoted by HP. The line in which they intersect is termed as the reference line and is denoted by the letters XY.

Problems 1. The front and top views of a casting are shown in Fig . Draw its isometric view.

2. The front and top views of a casting are shown in Fig . Draw its isometric view Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 130 | P a g e 3. The front and top views of an angle plate are shown in Fig. Draw its isometric view.

4. The front and top views of an angle plate are shown in Fig. Draw its isometric view.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 131 | P a g e 5. The front and top views of an angle plate are shown in Fig. Draw its isometric view.

6. The front and side views of an angle plate are shown in Fig. Draw its isometric view.

7. The front and top views of a casting are shown in Fig. Draw its isometric view.

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 132 | P a g e Solved Problems 1. To generate 3D Wireframe model as shown in figure, using 3D Absolute Coordinate Method and 3D Rectangular Coordinate Method.

Solution Command: -VPOINT ( ) • Current view direction: VIEWDIR=0.0000, 0.0000, 1.0000 • Specify a view point or [Rotate] : 1, -1,1 (

) • Regenerating model.

Command: UCS () • Current ucs name: *WORLD* • Enter an option [New/Move/orthoGraphic/Prev/Restore/ .. ./World ] :

() Command: ZOOM () • Specify corner of window, enter a scale factor (nX or nXP), or [All/Center/Dynamic/Extents/Previous/Scale/ ... ] < real time>: ALL (

) Command: LINE ( ) • Specify first point: 0,0,0 ()

• Specify next point or [Undo]: 50,0,0 () • Specify next point or [Undo]: 50,80,0 () • Specify next point or [Close/Undo]: 0,80,0 (

) • Specify next point or [Close/Undo]:

C () Command: LINE () • Specify first point: 50,0,0 ()

• Specify next point or [Undo]: @0,0,40 () • Specify next point or [Undo]: @0,20,0 () • Specify next point or [Close/Undo]: @0,20, -15 (

) • Specify next point or [Close/Undo]: @0,20, 15 () • Specify next point or [Close/Undo]: @0,20,0 ()

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 133 | P a g e • Specify next point or [Close/Undo]: @0,0, -40 () • Specify next point or

[Close/Undo]: ( ) Command: LINE () • Specify first point: 0,0,0 (

) • Specify next point or [Undo]: @0,0,40 () • Specify next point or [Undo]: @0,20,0 ()

• Specify next point or [Close/Undo]: @0,20, -15 () • Specify next point or [Close/Undo]: @0,20, 15 () • Specify next point or [Close/Undo]: @0,20,0 (

) • Specify next point or [Close/Undo]: @0,0, -40 () • Specify next point or [Close/Undo]: ()

Command: _qsave Command: _dimaligned Specify first extension line origin or :

Specify second extension line origin:

Command: _dimlinear Specify first extension line origin or

:

Specify second extension line origin:

Specify dimension line location or [Mtext /Text/Angle/Horizontal/Vertical/Rotated]:

Dimension text = 48.0000 Command: _dimedit Enter type of dimension editing [Home/New/Rotate/Oblique] : _o Select objects: 1 found Enter obliquing angle (press ENTER for none): 30

Command: _qsave Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 134 | P a g e 2. Draw the following figure using ACAD Solution

COMMANDS USED Line, Dimensions, Drafting commands PROCEDURE Command: -VPOINT ( )

• Current view direction: VIEWDIR=0.0000, 0.0000, 1.0000 • Specify a view point or [Rotate] : 1,-1,1 () • Regenerating model.

Command: UCS () • Current ucs name: *WORLD* • Enter an option [New/Move/orthoGraphic/Prev/Restore/ .. ./World] :

() Command: ZOOM () • Specify corner of window, enter a scale factor (nX or nXP), or [All/Center/Dynamic/Extents/Previous/Scale/ ... ] < real time>: ALL (

) Command: LINE ( ) Specify next point or [Undo]: @ 0,0,0

Specify next point or [Undo]: @ 72,0,0 Specify next point or [Undo]: @ 72,104,0 Specify ne xt point or [Undo]: @ 0,104,0 Specify next point or [Close/Undo]: C ()

Command: LINE ( ) Specify next point or [Undo]: @ 0,0,0 Specify next point or [Undo]: @ 0,48,0 Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 135 | P a g e Specify next point or [Undo]: @ 24,0,0 Specify next point or [Undo]: @ 24, -16,0 Specify next point or [Undo]: @ 24,0,0 Specify next point or [Undo]: @ 24, -16,0

Specify next point or [Undo]: @ 24,0,0 Specify next point or [Undo]: @ 24, -16,0 Specify next point or [Close/Undo]: C () Command: LINE (

) Specify next point or [Undo]: @ 0,0,0 Specify next point or [Undo]: @ 72,16,0 Specify next point or [Undo]: @ 80,0,24 Specify next point or [Undo]: @ -80,0,0

Specify next point or [Close/Undo]: C () Command: LINE ( ) Specify next point or [Undo]: @ 72,32,24

Specify next point or [Undo]: @ 80, 0,24 Specify next point or [Undo]: @ -80,0,0 Specify next point or [Close/Undo]: C () Command: LINE (

) Specify next point or [Undo]: @ 0,48,0 Specify next point or [Undo]: @ 104,0, 72 Specify next point or [Undo]: @ -24,0, 72 Specify next point or [Undo]: @ -24,0, 48

Specify next point or [Undo]: @ 24,0, 0 Specify next point or [Close/Undo]: C () Command: _qsave Command: _dimaligned

Specify first extension line origin or :

Specify second extension line origin:

Command: _dimlinear Specify first extension line origin or

:

Specify second extension line origin:

Specify dimension line location or [Mtext/Text/Angle/Horizontal/Vertical/Rotated]:

Dimension text = 48.0000 Command: _dimedit Enter type of dimension editing [Home/New/Rotate/Oblique] : _o Select objects: 1 found Enter obliquing angle (press ENTER for none): 30

Command: _qsave Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 136 | P a g e Convert Isometric to Orthographic 1. Draw the (i) Front view (ii) Top View (iii) Side view of the Following Isometric Dra wings

using AutoCAD Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 137 | P a g e Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 138 | P a g e

Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 139 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR

MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 140 | P a g e Notes Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 141 | P a g e Notes

Computer Aided Engineering Graphics (CAEG) B.TECH – I YEAR MALLA REDDY COLLEGE OF ENGINEERING AND TECHNOLOGY 142 | P a g e References 1. Engineering Drawing by ND Bhatt, Charotar Publishing House Pvt. Ltd.

2. Engineering Graphics for Degree by K.C. John, PHI Learning Private Limited 3. Computer Aided Engineering Graphics by Rajashekar Patil, New Age International Pvt.

Ltd.

4. Engineering Graphics with AutoCAD 2020 by James D. Bethune, Pearson Publications 5. Fundamentals of Engineering Drawing and AutoCAD by Dr. Mohd. Parvez, Galgotia Publications Pvt. Ltd.

6. Engineering Graphics Essentials with AutoCAD 2018 Instruction Text and Video Instruction. by Kirstie Plantenberg, SDC Publications.

7. https://knowledge.autodesk.com/support/autocad -lt/learn -explore