Text: Engineering Graphics a problem solving approach, 3rd Edition

Text: Engineering Graphics a problem solving approach, 3rd Edition
D. McAdam, R. Winn Addison Wesley, 2006

Preliminaries Lecture Times Tuesday, Wednesday 2:00 PM EN 2043
Thursday 10:00 AM EN 2043 Office Hours: Tuesday 1:00-2:00 pm EN-2077e Thursday 9:00-10:00 am Midterm Exam: 8:30 am November 2nd, 2006

Course Outline Introduction to Engineering Graphics and Principles of projection (Ch. 1) Sketching (Ch. 2) Sectioning (Ch. 3) Dimensioning (Ch. 4) Visualization (Ch.6) Intersection (Ch. 7) Presenting Technical Information (Ch. 8) Special Topics

Grading Scheme The grading system for this course is comprised of AutoCad Labs, graphics assignments, a midterm examination, and a final examination. Assignments % AutoCad % Midterm test % Final Examination % Total %

Grading Policy & Guidelines
All assignments will be due at the date and time specified on the assignment. All in-class assignments are due at the end of class. Assignments not submitted on time or submitted during the incorrect period will be given a grade of zero. All assignments will be graded for neatness and clarity. Submissions should be professional and follow the graphics principles taught during the course. All assignments must include the student name, student number, and lecture day Discussion and consultation between students is encouraged, but every submission must be unique and individual. Failure to submit all assignment (including AutoCad) will result in an incomplete grade for the course – DO THE ASSIGNMENTS

Today’s Objectives Introduction to Engineering graphics
Principles of projection Take home assignment

Introduction to Engineering Graphics
What this course is intended to do Improve visualization in 2 and 3D Improve sketching ability Improve your engineering communication skills What this course is not intended to do Teach drafting (go to CONA)

What is Engineering Graphics?
Engineering graphics is the area of engineering responsible for translating ideas and designs onto paper – in a standard format Engineering drawings describe the shape and size of an object, and all other necessary information for fabrication

What you should learn Graphics Theory – geometry and projection techniques Visualization – the ability to mentally control visual information Standards – sets of rules that govern how technical drawings are presented Conventions – commonly accepted methods Tools – some of the devices used in engineering graphics

Engineering Drawings Freehand sketching Drawing with instruments CAD

Required Materials Pencil and eraser Instrument set Scales Scap paper

Your new Geometry set – bring it each class
Dividers Triangles Compass Protractor Eraser pencil

Changeup 5 minute class exercise

How Would You Describe This?
In teams of two, describe using only words How effective is this approach? Instructor: This is an in-class interactive exercise(active learning). Allow students about 5 minutes to discuss with partner and then ask random students to put in words their description. Then ask the class the question shown on the slide.

Introduction to Projections
Present 3-D objects with 2-D media Two Basic Categories Orthographic Pictorial Definitions: Projection: the process or technique of reproducing a spatial (3-D) object upon a plane or curved (2-D) surface Orthographic sketches present the object in a series of projections, each one showing only two of the object’s three dimensions. Pictorial sketches present the object in a single view with all three dimensions represented Discuss the trade-offs in using any type of projection; some are more realistic, some are easier to draw, and some are easier to interpret by non-technical people

Principles of Projection
Before drawing an object three things must be defined Location of the eye The object The picture plane Orthographic projection is the arrangement of these elements such that the viewpoint is perpendicular to the picture plane

Recall: orthogonal means ‘at right angles’ So if observer moves backwards to infinity, the projection lines become parallel The shape formed on picture plane same shape and size as object

We generally need more than one view to describe an object There are six principle picture planes Think of a glass box surrounding an object. Each face is a picture plane

Glass Box Approach The object, whose orthographic projection needs to be drawn, is enclosed in a glass-box

Glass Box Approach Project points on the front view of the glass-box

Glass Box Approach Project points on the the top view of the glass-box, just as done for front

Glass Box Approach Project points on the right view of the glass-box, just as done for front and top

Glass Box Approach Unfold the glass box, see how the views align

Defining the Six Principal Views or Orthographic Views
Although any face could be chosen to be the front, once front and two other face are selected all are determined. There are really SIX PRINICPAL VIEWS as defined in the diagram. Generally do not need all six to fully describe the object. A conventional Engineering Drawing will normally have 2 to 3 views unless it required more views to describe the geometry/ profile. We know which ones they are on the drawing, because we always present them in the same relationship to each other. I.e. Top above front, right to right of front, etc. This convention is called as the Third angle method.. The other method in which the views can be placed is the First angle method in which the Top view is below front view, Right side view is on left side of front view. For this class we will be following the Third angle convention. These are often called orthographic projections – because the line of sight is perpendicular to the principal view

Usually only three planes are required to define an object Front Top Right side

Creating the Orthographic Projection Sketch
Front View Right Side View Top View From Bertoline: Figure 2.45/ Pg 47 The next few slides show how to create a three view sketch. A detailed explanation of this procedure is given in the book. Please urge the students to go through this explanation. Things to emphasize The glass box approach. How the object projects itself on the front, top and right side face of the glass box. The animation shows the glass box approach on a different object. We also define front-view by width and height, not depth and height

Orthographic Projection
By definition for each element of a orthographic projection drawing you only present 2 of the three dimensions. Think of it as an observer look at one face, what do they see. Any orthographic projection drawing normally has three views… Front view, Top view and side view (Right or left side view)

Which Views to Present? General Guidelines
Pick a Front View that is most descriptive of object, and shows how it is normally used (if known) Normally the longest dimension is chosen as the width (or depth) Most common combination of views is to use: Front, Top, and Side View Objects should be oriented to minimise hidden lines Views other than the Principal Views are called Auxiliary Views Pick the views which will help in describing the object with highest clarity. Explain what is an auxiliary view. Explain that they are drawn to show specific features that are not clear in the Principal views.

The Idea is to have them take an object from the table.
Declare front. FRONT View is the MOST DESCRIPTIVE VIEW OF THE OBJECT. The view that gives MORE INFORMATION ABOUT THE OBJECT. Rotate 90 degrees “up” to get top view. Rotate Back. Rotate 90 degrees clockwise to get right side. This give three principal views commonly used.

Conventional Orthographic Views
Height Depth Width Front View Top View Right Side View Note that the views are placed and aligned in the manner shown in the diagram. Remind the students that they have to follow the above convention for all their home work problems and exam problems. It is very important to maintain the alignment and correct placement relative to each other. Means line for top (and bottom) is straight across for both front view and right side view for example. Same thing between front and top for sides. Note : The following can be seen from the slide: Top View and front view have the same width Front View and Right / Left side view have the same height. The depth of Top view is same as the width of right/ left side view.

Hidden and Center Lines in Orthographic Projections
Hidden Lines – represent features that cannot be seen in the current view Centerlines – represent symmetry and mark the center of circles, the axes of cylinders, and the axes of symmetrical parts, such as bolts Note the graphical convention for hidden and centerlines.

For Example: 1. Visible 2. Hidden 3. Center
From Bertoline: Figure 2.38 / Pg 42 In engineering and technical drawing, it is important that hidden features be represented, so that the reader of the drawing can clearly understand the object. Thus we need hidden lines to emphasize that those features exist and are hidden in that particular view. We also need center lines to understand how the features defined in the 2D views translate into 3D. NOTE: It must be emphasized that hidden lines and center lines are used only on Orthographic projection drawings, never on isometric drawings Q: Do we need a convention for what line to show if two lines fall on top of each other? A: Yes! Otherwise features which are more important (eg: visible lines) would be overridden by less important features (eg: hidden lines) and the resulting drawing would be interpreted inaccurately. The next slide shows the convention followed. 2. Hidden 3. Center

Line Precedence Often a line will appear over another line (eg. a hidden line behind a visible) Line precedence states: Visible and hidden lines take precedence over all others Visible lines take precedence over hidden A visible line may cover a hidden line, but not vice-versa If possible, try to locate other lines so that they do not coincide with other lines

Points and Lines A line will project as a point on any plane to which it is perpendicular A line will project true shape on any plane to which it is parallel In all other cases a line will appear foreshortened and not true length

Projection of Surfaces
A surface (or plane) will always project as either a line or an area Surface appears True size if surface is parallel to a plane of projection As a line if surface is perpendicular to plane of projection Foreshortened – if positioned at an angle

Projection Between Views
Given two views of any point, the same point in any other orthographic view can be found A 45º mitre line is used to locate points and transfer depth dimensions between top and side views

Align View Bounding Boxes
WIDTH DEPTH TOP WIDTH DEPTH Miter line at 45° HEIGHT HEIGHT FRONT RIGHT

Sketch Features – View Projection
TOP Miter line at 45° Note: see figure 1.29 in text FRONT RIGHT

Assignment #1 Due at beginning of next class
Read Chapter 1 in textbook Using worksheets that accompany textbook: Complete the lettering practise exercises Complete questions 50-55 Notes: there are very few take-home assignments in this course, so make sure to bring your instruments for next class. If you are looking for more problems, try any of # 1-50 in your text.

Engineering Graphics 1504 Lecture 2 – Orthographic Sketches
Objectives Recap of Orthographic Projections Lettering and title blocks In-class assignment

Recap: Lines Strong contrast between drawing lines and construction lines Visible lines indicate all visible edges. Hidden lines show surface, edge, or corner hidden from view Centerlines show holes and symmetric features Cutting plane used to designate where cutting plane takes place Extension & dimension lines used when dimensioning Break lines used to shorten view of a long part Section lines used to indicate the surface in a section view

Visible Line Functions
“LIMITS” The only lines drawn in a pictorial represent either (1) an abrupt change of direction in a surface or (2) a contour boundary (even if there is no abrupt change). “EDGES”

Hidden Line Conventions
evenly spaced dashes spaces  1/2 of dash length dashes commonly  1/8” long

Centerline Conventions
to show circle/arc center or axis of symmetry long lines separated by dash and two gaps dashes commonly  1/8” long

Tangent Surfaces When a curved surface is tangent to a plane NO LINE IS SHOWN

Producing a Multiview Sketch
Select Front View Align View Bounding Boxes Sketch Features True Shapes Remain Project Between Views Label Vertices if Needed

Select Front View Universally Used -- Clock Face
Shows Most Characteristic Shape -- the “U” shape of a horse shoe. Generates Fewest Number of Hidden Lines for Entire Drawing

Glass Box Approach Unfold the glass box, see how the views align

Creating the Orthographic Projection Sketch
Front View Right Side View Top View From Bertoline: Figure 2.45/ Pg 47 The next few slides show how to create a three view sketch. A detailed explanation of this procedure is given in the book. Please urge the students to go through this explanation. Things to emphasize The glass box approach. How the object projects itself on the front, top and right side face of the glass box. The animation shows the glass box approach on a different object. We also define front-view by width and height, not depth and height

Align View Bounding Boxes
WIDTH DEPTH TOP WIDTH DEPTH Miter line at 45° HEIGHT HEIGHT FRONT RIGHT

Sketch Features – View Projection
TOP Miter line at 45° Note: see figure 1.29 in text FRONT RIGHT

Standard Letters (ASME Y14.2M-1992)
Vertical Gothic Style – All Capitals A Lettering Template Choose either vertical or slant Gothic lettering . Do not mix them on a sketch. Use 1/8 inch letters -- common fractions are a total of 1/4” tall The space between words is equal to the space used by a capital letter “O” These suggested lettering strokes may be helpful.

Lettering Guidelines Letter size should be at least 3mm high for clarity and reproducibility Draw a construction line to help you judge lettering height. Decimal points must be clearly visible, solid, and in-line with bottom of text To be aligned with the bottom of the page (preferred) or with the right side of the page.

Spacing & Fractions Don’t use equal spacing between letters
Instead, try to balance the area between letters. The space between words should be equal to letter height. The space between lines of text should be at least half the height of a letter and at most equal to the letter height.

Lettering Example Extremely light horizontal lines regulate letter height Guidelines are not removed Vertical lines may be used to keep letters vertical (not used to space the letters)

Lettering Cont. Note: strict adherence to these guidelines is not necessary, but … Make sure that all letters are in upper case, and construction lines are visible

Title Block Vary in layout In this course must include Name
Title or description Scale and units Drawn by: Date: Session identifier (eg. Wed.)

Class Assignment Using your workbook, complete questions 9,11,13,15
Include a title block on the first page

Engineering Graphics 1504 Lecture 2 – General Sketching
Objectives Lines Arcs Pictorial Types

Sketching Straight Lines
Lightly mark endpoints of line. Lightly sketch from one endpoint to the other. Use 1 to 2 inch strokes, keeping eye on the second endpoint. DON’T USE A STRAIGHT EDGE! Always complete a sketch with construction lines and then darken the visible edges and boundaries to form the final sketched object.

Sketching Circles and Arcs
Diameter 2/3 of center distance Diameter The “2/3” method PLUS SIGN MARKS CENTER SKETCH SQUARE SKETCH AND MARK DIAGONALS Normally the circle only needs to be proportional to the other surfaces of a sketched object. Care should be taken to place the center of the circle as accurately as possible and the lengths representing the diameters should be shown as equal. SKETCH ARCS FOR CIRCLE DARKEN CIRCLE

Pictorial Representation
Illusion of three dimensions Shows more information Easier to visualize Often used to explore ideas, aid explanation, present information

Three Types of Pictorial Sketches
Notice that all three give a 3D appearance to the object but their orientations in 2D space are different. The choice of axes used by the three type of pictorials are what make them appear different. perspective isometric oblique

Perspective Drawings Represents what the eye sees
Railway tracks come together Vanishing points Do not show true size or lengths. Used to show “artist’s conception”

Isometric Drawings Want to show more sides of the object in one view
Rotate 45º about vertical axis through centre Two views sides shown in front view

Isometrics Tip forward about the corner ‘x’
Top view now shows front, top, and side of cube Isometric if cube is ‘tipped’ so that sides are of equal length and make angle of 30º to the horizontal

Isometrics Isometric – equality of measure
All sides in an isometric drawing are drawn to actual size (close to truth)

Isometrics Any line parallel to an isometric axis is measured as true length Any line not parallel to an axis is not true length Diagonals on a real cube are of equal length – not the case here

Oblique Projection Sometimes an isometric drawing may have features that are difficult or time consuming to represent (e.g. circle). If lines of sight through picture plane are at an angle other than 90º, get oblique projection Front view drawn to normal size, other views are drawn at some angle (typically 30º, 45º, 60º)

Oblique Projection Two common types of oblique projections are cavalier and cabinet Front view is full size in both types but scale on receding axis is different

Break Time Take 5 minute break

Making an Isometric Drawing
Construct isometric axes Block out space occupied by the shape

Making an Isometric Drawing
Draw lines parallel to axes at key points No hidden lines are shown in a pictorial!

Sketching Circles in Isometric Drawings
A circle appears as an ellipse in isometric Locate centre by joining the corners and drawing diagonals Use same procedure as outlined for orthographic sketching

Class Assignment #3 Sketch an isometric of example 2.6 in text (freehand) Sketch an isometric of question #80 in Chapter 2 of the text (use instruments and scale to larger size)

Engi 1504 – Graphics Lecture 4: More on visualization
Review of isometrics Adjacent and similar areas Projection studies and assignment 4

Isometric Example

Isometric Sketching: Steps
Visualize object by breaking into known shapes (circles, prisms, etc) Define overall size defining width, height and depth Sketch known shapes Connect ‘loose ends’ Darken

Adjacent Areas Adjacent areas are surfaces that reside next to each other The boundary between surfaces is represented by a line indicating a change in plane

Many possible solutions
Adjacent areas represent surfaces that are: At different levels Inclined or oblique Cylindrical A combination of the above Use all views necessary to represent the object clearly

Similar Areas A surface always appears as either a line or as an area
When a surface appears as an area it may be true size or distorted. Only angles and lengths of sides are changed, the number of sides and their sequence are unaffected

Similar Areas cont. Rule of configuration:
Every plane surface, regardless of shape, always appears either as an edge or as a figure of similar configuration

Similar Areas cont. If a surface shows similar configuration in two views and appears as an edge in the third view: Inclined surface An inclined surface is perpendicular to one of the principal planes of projection and inclined to the others. If a surface shows similar configuration in all views: Oblique surface

Inclined and Oblique Surfaces
(vertical) Inclined Inclined Oblique

Inclined and Oblique Surfaces
Based on what we’ve learned, where is the error? Remove corners The corners should be removed since the top surface must have the same shape as the front view (and the actual object).

Projection Studies

Finding Missing Information
Today’s assignment is to complete the views of an object that are missing some information. Let’s looks at Example 2.8 in the text.

Given that the front view is incomplete and the side view is complete, draw the top view, complete the front view, and sketch the isometric

Front view: there is no line corresponding to the bottom of the slot

Top view: project the width, depth and slot points

Darken lines and complete the sketch

Class Assignment 4 Sketch the missing view (or missing lines) and an isometric for Questions 104 and 106 in workbook. Notes: the missing views must be completed using your drawing instruments the isometric must be done freehand

Engi 1504 – Graphics Lecture 5: Sectioning and Dimensioning
Sectioning an object Sectioning symbols Locating sections conventions Dimensioning Class assignment 5

Intro to Sectioning We know what the outside looks like, but what’s going on inside? Internal details are shown by ‘removing’ a section

Intro to Sectioning cont.
To show that the front has been removed section lines are added Only show surface on cut line, not hole

In orthographic view show internal details by drawing view on cutting plane Arrows indicate direction of eye

Draw view on section A-A Section lines show cut surface and only show surface formed by cutting plane, not hole

Note: still have to show all visible lines. Hidden lines are omitted, but must show all visible lines (i.e. back of hole)

Sectioning Symbols Symbols are standardized (ANSI) to show different materials Placed at 45º unless section lines appear parallel to any portion of an outline

Locating Sections Locate section to show the required internal details
Sections can be taken anywhere and need not be taken through middle of object. Examples include: Full section Half section Offset section Revolved section Removed section

Full Section Cutting plane cuts all the way through the object in a straight line.

Offset Section If internal details of a hole are required, section should pass through centre of hole.

Offset Section All sections shown as if the holes were in line.

Half Section Cutting plane is optional So far both full and offset sections have cut all the way through the object. If there is an axis of symmetry only one side needs to be drawn.

Revolved Section Revolved sections are the same as full sections, but drawn at a different location. A revolved section is drawn directly on the view, rather than in a different view.

Removed Section A section located somewhere other than in a “normal” position. Note: Can also be included on a separate piece of paper for large objects (like buildings).

Conventions to make life easier
Some features are simplified to make them easier to draw and not shown as they would actually appear. Important to know these conventions in order to understand a drawing.

Breaks If a part is long (say a shaft), only need to show the ends and a part of the centre with a conventional break Length is specified, but full length is not drawn.

Imagine them in rotated position! Rotations If side view were drawn using principles of projection it would be confusing, and time consuming. Section is drawn as if the holes were rotated to where they would show a true cross section and diameter can be seen. Rotate holes in section view

Rotations (webs) Same problem, so rotate the webs so that they appear full size in front view. To avoid confusion, Webs are not crosshatched!

Rotations (summary) Holes, ribs, and lugs must be aligned in a section view.

Intro to Dimensioning Before you can build something need to know:
How big it will be Size and location of any features The material it is to be made of How many to make Dimensioning Notes on drawing

Intro to Dimensioning cont.
Various organizations publish standard methods for dimensioning and tolerancing engineering documents Canadian Standards Association (CSA) B78.2 American Society of Mechanical Engineers Standard Dimensioning and Tolerancing (ASME) Y14.5M

Intro to Dimensioning cont.
Units SI units. Common linear unit is mm (e.g. 5 mm) Imperial units. Customary linear unit is the decimal inch (0.25 in) If all dimensions are in either millimetres or inches, the symbol after each dimension can be omitted. Put a note on the drawing: ALL DIMENSIONS IN MILLIMETRES

Dimensioning Terms

Dimensioning terms Extension lines Dimension lines Notes Leaders
Indicate length to which dimension applies Do not touch the object (gap) Should not cross other lines Dimension lines Show extent of the dimension Notes Give information about object Always in uppercase letters Leaders Point to a feature, terminate with arrowhead Point to a surface, terminate with dot

Linear Dimensions Linear dimensions apply to straight lines or distances. Chain (starting point for one dimension is the end of previous dimension) Coordinate dimensions (referenced from one point)

Tolerances Tolerance is the maximum amount by which a length can vary and still be acceptable. In general, the smaller the tolerance, the more it will cost to manufacture But parts still must fit together!

Tolerances Consider a shaft passing through a hole
Max shaft diameter = 30.5 mm Minimum hole diameter = 29.5 Interference

Tolerances Solution? Unilateral tolerance (can vary in only one direction).

Tolerances Also tolerances on dimensions
Tolerances can add up, and parts may be too tight (or loose). Edge A could be 1.5mm too big Edge B could be 2mm too short

Tolerances Solution? Use coordinate dimensioning to reduce effect of tolerance addition

Rules for Dimensioning
Dimensions must be complete with no information missing. User must not be required to make assumptions or measure anything directly on drawing.

Do not add extra dimensions here Not here

Show dimensions on true profile and refer to visible outlines, not hidden lines Incorrect Correct

Show where shape shows best

Dimensions should be arranged for maximum readability

Group dimensions around features

Should be no redundant dimensions, but sometimes can add reference dimensions for more information (e.g. overall size).

Place Dimensions OFF View
* and don’t use visible boundary lines for extension lines*

Place Dimensions BETWEEN Views

Other Guidelines … Place the largest dimension farthest from the part boundary Avoid: long extension lines; dimensioning to hidden lines; crossing dimension lines with extension lines

Dimensioning Features
Angular Dimensions specify angle between two points

Circular Dimensions are defined by specifying the location of the centre and either the radius or diameter Diameter a solid cylinder is dimensioned where both length and diameter are in same view with visible outlines A hole (a negative cylinder) is dimensioned where the circular shape is seen

Large diameter holes are dimensioned specifying the diameter

Radius Incomplete circular features are specified by the location of the centre, the starting point, the end point, and the radius The location may not be specified by the drawing, other information such as tangent points must be given to locate its centre

Assignment #5 In your workbook, complete question 32 in Chapter 3.
Note: the question is fairly simple, so make sure it is neat and complete.

Engi 1504 – Graphics Lecture 6: Descriptive Geometry
Properties of lines Properties of planes Auxiliary planes Midterm hints Class assignment 6

Points and Lines The point is the basic building block for an object.

Points and Lines Standard notation
AF is the view of point A on the frontal plane The height, width, and depth are specified with reference to the reference (folding lines)

Points and Lines Note: The distance behind a plane (say the front plane) is seen in all other adjacent views. If the distance to point A from the folding line is known in one adjacent view, point A can be located in another adjacent view

Lines A line is made up of two points 3 views of line AB are shown

Lines Vertical line – shows as a point in top view, parallel to front and right side planes Horizontal – infinite positions, but all points must have equal elevation

Lines Inclined line – parallel to front or right plane. Always parallel to one plane and inclined to the others Oblique line – inclined to all principal planes

Auxiliary Planes The length of a line can only be measured if it is seen in true length Recall: A line can be seen true length if projected onto a plane parallel to it So to find the true length of a line we draw an auxiliary folding line parallel to it.

Auxiliary Planes Consider the front and top view of oblique line ab
We can draw an auxiliary plane parallel to either line aFbF or aHbH

Auxiliary Planes Auxiliary plane parallel to line aHbH
TL Auxiliary plane parallel to line aHbH The line is perpendicular to horizontal (top) view H2 H1 H2

Point View of a line Recall: A line can be seen as a point if projected onto a plane perpendicular to it So an auxiliary plane perpendicular to a line that shows true length will show as a point. Note: to show line as a point, need a view that shows true length first.

Point View of a line D3 D3 aobo
Recall: A line can be seen as a point if projected onto a plane perpendicular to it So an auxiliary plane perpendicular to a line that shows true length will show as a point. Note: to show line as a point, need a view that shows true length first. D3 D3 aobo A O

Slope of a line The slope (or grade) of a line is the inclination of the line with the horizontal Slope can be measured in a view that shows vertical height and the line in true length So we draw a folding line in the horizontal (top) view.

Slope of a line So we need an auxiliary view (folded from the top view), that shows the line as true length Slope is the angle between the true length line and a line parallel to the folding line

Direction of a line Bearing Azimuth
The direction of a line (given as a compass reading) is seen only in the top view. Think of holding a compass. A bearing is measured from either north or south, with north usually at top of page Azimuth is measured from north and specified as an angle from 0-360º Azimuth

Summary Find true length of a line: Find point view of a line:
Place an auxiliary view parallel to the line and project two points on the line onto the auxiliary view Find point view of a line: Need a true length line first Locate an auxiliary view perpendicular to the true length line and project endpoints Find slope of a line Need a true length line and an edge view of the horizontal Find an auxiliary view (folded off the top view) that will show true length

Summary Continued … Things to remember about lines:
If a line is parallel to a folding line, it will appear true length in the adjacent view Bearing and azimuth are seen only in the plan (top) view If two lines intersect, the intersection point will correspond in all views The shortest distance between two lines is seen where one of the lines appears as a point Perpendicular lines appear perpendicular in any view in which one or both of the lines appear in true length A line will appear true length in any view folded off a point view of the line.

Midterm Hints and Topics
Midterm exam is November 2nd Lectures 1-5 are covered (Chapters 1-4 in text) Review your assignments Review visualization exercises Practice as many problems as you can Contact me if you are stuck. My office hours are 1-2 pm on Tuesdays and 9-10am on Thursdays Student Questions?

Class Assignment #6 Point A is 15 m behind the frontal plane and 30 m below the horizontal plane. Point B is 33 m behind the frontal plane and 12 m below the horizontal plane. The line AB bears N 65º E. Using an appropriate scale draw a point view of line AB.

Engi 1504 – Graphics Lecture 6: Descriptive Geometry II
Properties of planes Midterm issues Class assignment # 7

Properties of Planes Two limiting cases of a plane:
True shape Edge view Can be used to solve any problem involving planes

Properties of Planes At least three lines are required to define a plane Edge view must be found before a true shape can be found

Finding the Edge view of a Plane
A plane will be seen as an edge if any line in it is seen as a point. It is often easier to add a line (where we want it) than to use an existing line Recall: a line must show true length before it can be seen as a point

We can find the true length of any line (AB, BC, or CA) using an auxiliary plane parallel to it. Then we can find the line as a point, which will show the plane as an edge. This requires two auxiliary planes – there is an easier way! We will create a True length line in the plane.

Note: none of the given lines are parallel to a folding line, and hence not true length. So we construct a true length line in the plane and then show it as a point. This requires only one auxiliary view

True Length Draw a line in the plane parallel to a folding line (say in the front view). Project the endpoints into the top view. This line is true length Now we have a true length line, so all we have to do is show it as a point. X2 x1

Edge View of a Plane cont.
To find the point view of AX, we construct a folding line perpendicular to AX and project onto auxiliary plane 3 3 a3x3 2 D Point view D

Edge View of a Plane cont.
Project B and C onto plane 3 and join the points to show plane ABC as an edge

True Shape of a Plane If we place an auxiliary plane parallel to the edge view, then the plane can be seen as true shape. Recall: An edge view must be found first So we place an auxiliary plane parallel to the edge view and project the plane onto it

True Shape of a Plane Draw the plane in edge view.
Place a folding line parallel to the edge view. Project all points onto the auxiliary plane (plane 4 in this case) and join them. Recall: the distance from the folding line is found from the view adjacent to the edge view (plane 2 here)

a4 Plane shows true shape b4 c4

The Slope of a Plane The slope of a plane is the angle it make with the horizontal. Slope is seen only in the front or profile view (the elevation views) Recall: slope can only be determined from a true length line. So, the TL line used to find the edge view of the plane must be in the top view so that the edge of the plane appears in the horizontal view

The Slope of a Plane Create a TL line in the horizontal view
Find the edge view of the plane Measure the angle it makes with the horizontal 54o slope

The Strike of a Plane N The strike of a plane is the angle that a true length line in the plane makes with the North (top view) So strike is the bearing of the horizontal line AX strike 54o slope

Summary Find edge view of a plane: Find true shape of a plane:
Draw a line parallel to a folding line and project the line into the adjacent view, where it will be true length Find a point view of this line and project other points in the plane. The plane will appear as an edge Find true shape of a plane: Find edge view of a plane and create an auxiliary view parallel to the edge view Project the points defining the plane onto this auxiliary view. The plane will be true shape

Engi 1504 – Graphics Lecture 8: Special Topic 1
Presenting technical information

Presenting Technical Information
Engineers: Solve problems Communicate the solution to others Your writing should be: Possible to understand Impossible to misunderstand

The 5 C’s Clear – make sure it is understood Concise – not too wordy
Correct – spelling, grammar, names, etc Concrete – specific statements Courteous – polite (e.g. )

The Writing Process Careful planning Multiple revisions
Don’t start the night before Multiple revisions Remember – your name is on it

Tips for Everyone Identify your objective Prepare an outline
Identify your audience Prepare a 1st draft Edit Review

Tips for Everyone cont. Identify your objective
Write a clear, precise statement of your reasons for writing Read it from time to time to stay focused Keep in mind: “What must the reader know?”

Tips for Everyone cont. Identify your audience
Reports are meant to be read Identify the background of your reader

Tips for Everyone cont. Prepare a 1st draft
Get your ideas on paper (don’t worry about the finished work) Use outline, write short, concise paragraphs Use grammar and spell checker (carefully) to clean it up Print a copy, put it aside until the next day

Tips for Everyone cont. Edit Next day read 1st draft
Helps to read aloud Edit your work for flow, extra words, slang, idioms, gender specific language, spelling and grammar

Edit cont. Flow Extra words Edit it so one idea flows into the next
Each paragraph expresses one idea Extra words Remove redundant words Can shorten 1st draft Make every word count. If you can say it in five, don’t use ten. Don’t waste the time of the reader

Edit cont. Slang and idioms Gender inclusive language
Slang: “It took a lot of guts to ask his boss for a raise ” Idiom: “keep an eye on the ball” Engineers work in a global environment so avoid colloquialisms Gender inclusive language He, she, etc. Use they, engineers, etc.

Edit cont. Spelling and grammar
Poor spelling distracts the reader from your message Implies poor quality work Don’t rely on spelling and grammar checker (Wood ewe due this?)

General Proofreading Tips
Spelling Check for spelling errors, repeated words, names of people and places Grammar Avoid switching between present and past tense Check for complete sentences

Page layout Check all figures Check column and paragraph spacing All pages should have same format Consistency Check that headings of the same level use same format Check headers and footers No pages missing!

Graphics Reference all graphics in the body of the text Check captions

Engineering Formal Report
Main Sections Cover Title page Abstract or summary Table of contents Table of figures Table of Tables

Engineering Formal Report cont.
Nomenclature Introduction Discussion Conclusions Recommendations Appendices References

Abstract or Summary A report in miniature An accurate summary of topic, important results, and conclusions Brief and concise. Reader must understand key elements Write it last

Introduction Provide the reader with all the background necessary to properly read the report Introduce the subject, state why the report is being written, along with any limitations

Introduction has three main components Background Purpose (what the report hopes to achieve), who authorized it, etc) Scope (limitations imposed on the report and who imposed them, cost, time, extent of study, factors omitted)

Discussion (body of report) All information presented in an organised, logical manner Not called discussion! Should have a relevant name Conclusions Based only on material in report Each conclusion in a separate paragraph

Recommendations Follow logically from conclusions Appendices Referenced in report Supplementary material such as calculations, physical properties, etc.

Technical Presentations
The Presentation Formula The 4 P’s Slide Rules of Thumb MS PowerPoint Commands

The Presentation Formula
Tell them what you’re going to tell them. Tell them. Tell them what you told them

The 4 P’s Plan Prepare Practice Present

Plan Know your audience Define the purpose of your presentation
Inform? Persuade? Motivate? Teach? Plan the content of your presentation around: your purpose audience's level of understanding (and interest). Use words and phrases common to your audience, and focus on your purpose.

Prepare Center on a message with key points that you can back up with evidence Prepare an attention-getting opening (5 to 10 % of presentation) An audience can only remember 4 to 6 different points (85% of presentation) Close by summarizing or restating the message

Practice Is your message clear?
Does your evidence support your key points? Are your graphics and illustrations clear, appealing, and relevant to the topic? Is your close memorable?

Practice Did you achieve your intended results?
Rehearse multiple times Choose the techniques that you are most comfortable with Rehearse the timing of your presentation

Present Make a positive first impression.
Establish eye contact with your audience. Be yourself and relax. Slow down and emphasize important points

Slide Rules of Thumb Keep titles short One message per slide
Six lines or less Not too busy – colors, visuals, effects

Text Guidelines Don’t mix fonts Sans serif – better than serif
Large enough for easy viewing Color contrast with background

Charts, Graphs, Figures Used to reduce textual information
Visible to whole audience Choose colors for contrast Communicate!

Class Assignment In a group of 3-4 people, prepare and present a short 5 minute presentation on anything. Each group member must present! Time limits will be strictly enforced, so be prepared Can be on any topic you wish, provided it is not offensive to anyone Have a bit of fun

Engi 1504 – Graphics Lecture 9:
Special Topic 2 – Introduction to Solids Modelling Take home assignment

Solids Modelling There are three ways to represent 3-D shapes
Wireframe Surface True solid

Solids Modelling Wireframe Model
Shows only the edges and no surfaces shown No distinction between front and back The inside is ‘empty’ Fast and simplified

Solids Modelling Surface Model Shows only the surface and edges
The inside is still ‘empty’ No hidden lines, so no confusion

Solids Modelling Solids Model Shows the surfaces and edges
Includes interior details Includes information about the material

How Simple Solids are Made
Extrusion Sweeping Revolving

How Simple Solids are Made cont.
Extrusion – specify a cross-sectional area and a path

Sweeping – refers to extrusion along a curved path

Render the ramp

Revolving – revolve an area around an axis

Dave, will we ever use this crap?
Simulation of Waterjet propulsion using CFD and Windtunnel tests

Rapid Prototyping

Class Assignment Read chapter 9 in the text
Choose a simple household object and model it as a solid Submit a rendered picture of the object next class For each class, the student with the best submission (in my opinion) will receive an extra 2 marks towards their final mark Note: can download rhino3d for 20 saves at:

Engi 1504 – Graphics Lecture 10: Exam tips Plane example

Final Exam (Dec 11th, 2006) Tips
Exam will be similar to midterm in terms of difficulty You are responsible for everything Some key areas not covered on midterm: Dimensioning Sectioning Descriptive Geometry (planes, lines, etc) Presenting technical information Solids modelling

Exam tips Review all of your assignments
Keep up with the practice problems Chapters in text: Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 6 Chapter 9 Chapter 10

Exam tips Work on your speed Get to know your triangles
Dedicate some time to the course

Plane Example Plane ABC is shown along with a line AD. Line AD bears N 70º E and is in the plane of ABC. B is 100 m east and 150 m north of A C is 300 m east and 70 m south of A D is 300 m east of A The elevations of these points are A=545 m, B=430 m, C = 670 m

Plane Example What is the slope of plane ABC?
What is the elevation of D?

bA bH dH aA Slope = 43º aH cA cH cF 670 545 aF bF 430

dA 78 cH aH bH dH cF aF bF 670 430 545 bA cA aA

Text: Engineering Graphics a problem solving approach, 3rd Edition

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Text: Engineering Graphics a problem solving approach, 3rd Edition

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