2D Essentials

Instructor: Laura Gerold, PECatalog #10614113Class # 22784, 24113, 24136, & 24138Class Start: January 18, 2012 Class End: May 16, 2012

Reminders• 50% Project Plans are due next week on April 4th!• Grading handout from last week is also on blackboard in the class

materials / project folder• 3 Views with borders and scales due on April 4th for 30 points

• Optional extra credit is due on April 11th

• Find other countries where 1st and 3rd angle projections are used for 5 extra points

• Details are on blackboard in class materials / extra credit folder

Lingering Questions from Chapter 6 . . .

Runouts• When a rounded corner intersects a curved surface, a runout

is used to show how the edge fades or “tails out.”

Runouts – Group Projects• Break into groups• Look at page 212 in the text, Figure 6.14. • Answer the following questions as a group:• Where are the runouts located on the orthographic sketches?• Where are the corresponding points on the isometric sketches• Be prepared to present one of the examples to the class.

• Does anyone have an example of a runout to show? Can you think of any examples from home, work, in this room?

• Work in groups to sketch example of runouts.

Plotting Curves by Hand• Step 1: Break up the curves

into several points and locate them in the adjacent view

• Step 2: Project the points along the projection lines into the top view from the front view. Transfer the depth from the side view, using the back surface as a reference plane.

• Step 3: Draw the curve through the points.

Plotting Curves by Hand• Break into groups and Plot a curve by hand using example one

on page 207.• Start with the front and right views and use the method to

plot the top view.• How many points do you think you should use for an accurate

curve?

Chapter 3 – Isometric Drawing

Why Isometric Drawing?• Isometric Drawing is used to visualize concepts and to present

results to a client and the public

Some Key Concepts• To Understand Isometric Projection and drawing, we need to

learn a few key concepts first . . .

PICTORIAL SKETCHINGA pictorial sketch represents a 3D object on a 2D sheet of paperby orienting the object so you can see its width, height, and depth in a single view.

Projection Methods

The four principal types of projections:

a Multiview b Axonometric c Oblique d Perspective

Perspective• A perspective sketch is the most realistic view as it is trying to

approximate a 3-D image as seen by the eye on a 2-D piece of paper

• Two most important characteristics of Perspective are:• Portions of the object that are farther from the viewer appear

smaller • Lines recede into the distance

• Perspectives

Perspective Example

Image from: http://www.draw23.com/perspective

Perspective Example

Image from: http://www.khulsey.com/perspective-drawing-basics.html

Oblique• An Oblique sketch shows the front of a surface straight on• Angles and foreshortening are arbitrary• Least realistic as the depth appears to be out of proportion• Crudest 3-D method, but easiest to learn to draw

Oblique Example

Source: Wikipedia

Oblique Example

Source: http://finearts.fontbonne.edu/tech/design/oth_per.html

Isometric• Drawn so that the lines do not recede into the distance, but

remain parallel• Easy to sketch, but doesn’t always appear realistic• Coordinate axes appear equally foreshortened with the angles

between any two equal to 120 degrees.• Comparison

Isometric Example

http://www.birkey.com/technical-illustration/tugboat-isometric-cutaway/attachment/tugboat-isometric/

Isometric Example

http://www.khulsey.com/isometric-drawing-orthographic-projection.html

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

Source: http://wikihelp.autodesk.com/Inventor/enu/2011/Help/What's_New/Drawing_Annotations

ISOMETRIC

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

PERSPECTIVE

Source: http://tlc.howstuffworks.com/family/how-to-draw-in-perspective.htm

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

OBLIQUE

Source: http://draftingmanuals.tpub.com/14276/css/14276_308.htm

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

PERSPECTIVE

Source: http://xenthralx.deviantart.com/art/two-point-perspective-drawing-99599007

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

ISOMETRIC

Source: http://toolboxes.flexiblelearning.net.au/demosites/series12/12_05/toolbox12_05/fpicot3204a_sketches_and_drawings/3204a_30_producing_drawings/3204a_35_drawing_in_3d.htm

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

OBLIQUE

Source: http://chestofbooks.com/crafts/machinery/Shop-Practice-V2/Oblique-Projection.html

Pop Quiz – What Type of Sketch?

Pop Quiz – What Type of Sketch?

ISOMETRIC

Source: http://www.brynmawr.edu/cities/Cities/imgb/071/071m.html

Axonometric Drawings• Axonometric projection is a type of parallel

projection, more specifically a type of orthographic projection, used to create a pictorial drawing of an object, where the object is rotated along one or more of its axes relative to the plane of projection.

• There are three main types of axonometric projection: isometric, dimetric, and trimetric projection.

• "Axonometric" means "to measure along axes".

• With axonometric projections the scale of distant features is the same as for near features, such pictures will look distorted, as it is not how our eyes or photography work.

• Isometric is the most common form of axonometric projection used.

AXONOMETRICDRAWINGS

Various types of pictorial drawings are used extensively in catalogs,sales literature, and technical work. They are often used in patent drawings; in piping diagrams; in machine, structural, architectural design, and in furniture design; and for ideation sketching.

Axonometric

(Courtesy of Douglas Wintin.)

Isometric Projection• To create an isometric projection, an object must be oriented

so that its principal edges (axes) make equal angles with the plane of projection and are foreshortened equally

• On the figure below, when a cube is oriented this way, it has equal angles of 120 degrees

• Isometric projection is the most common kind of projection used by engineers

• Isometric Drawing Video

Isometric Lines• The projections of the edges of a cube make angles of 120

degrees to each other (isometric axes)• Any line parallel to one of these lines is called an isometric

line• The angles in the isometric projection are either 60 degrees or

120 degrees and are projections of a 90 degree angle• Isometric Lines are foreshortened equally

Non-Isometric Lines• Non-Isometric Lines are lines that are not parallel to the

isometric axes • They are drawn other angles and are not equally

foreshortened• The lengths of non-isometric lines cannot be measured

directly with a scale

Isometric Scales• In order to draw correct isometric projections, an isometric

scale must be used• The isometric scale distance is (2/3)^0.5 x true size, which is

approximately 80% of the true size.• More commonly, a standard scale is used • Using a standard scale produces an isometric sketch or

drawing, but not an isometric projection

Positions of the Isometric Axes• 1st step of isometric drawing is to decide which axis to show

the height, width, and depth• Pick a corner of the object to be in front that best describes

the shape of the object• If the object is long, show the axis horizontally• Which position of the block below would you use?

Example• I will draw a beautiful isometric cube• Tip for estimating angles:• When using graph paper, an angle of 30 degrees is roughly equal

to a rise of 1 block to a run of 2 blocks.

Group Project • Draw an isometric cube• Label the angles

Isometric Box Construction• Imagine the object you are drawing has a rectangular box that

encloses it whose sides coincide with the main faces of the object

• Draw the overall dimensions of the object as a box• Draw the irregular features relative to the side of the box• Darken the final lines

Isometric Sketching from an Object

• 1. Hold object in your hand and tilt it towards you

• 2. Sketch the enclosing box lightly making AB vertical and AD and AC approximately 30 degrees from the horizontal (isometric axes)

• 3. Block in the recess the projecting block

• 4. Darken the final lines

ISOMETRIC DRAWINGS steps…

ISOMETRIC DRAWINGS steps…

• 3. Lightly block in any remaining major portions to be removed through the whole block.

• 4. Lightly block in features to be removed from the remaining shape along isometric axes.

• 5. Darken final lines

Offset Location Measurements• 1. Draw main enclosing block• 2. Draw offset lines (CA & BA) full size to locate corner A• 3. Offset measurements are parallel to the edges of the main

block in multiview drawings and will also be in isometric drawings

Group Project – Box Construction

• Create a complex rectangular shape out of your blocks and use the box method to draw an isometric sketch

• Be prepared to present your resulting sketch

Isometric Drawings of Inclined Surfaces• Inclined surfaces are located using

offset or coordinate measurements along the isometric lines

• How to Draw Nonisometric lines• Inclined lines BA and CA are shown

true length in the top view• They are not true length in an

isometric view• To create these lines on an isometric

drawing, use a construction box and offset measurements

• Step 1: Directly measure the dimensions along the isometric lines

Isometric Drawings of Inclined Surfaces• 54mm is not along an isometric axis• Start sketching out the isometric lines: 44 mm, 18mm,

and 22mm

Isometric Drawings of Inclined Surfaces• Step 2: Use trigonometry or draw a line parallel to the

isometric axis to determine the distance to point A• Because this dimension is parallel to an isometric axis, it can

be transferred to the isometric

Isometric Drawings of Inclined Surfaces• Step 3: The dimensions 24 mm and 9 mm are parallel to the

isometric lines and can be measured directly

Group Project - Isometric Drawings of Inclined Surfaces• Draw an isometric drawing of an object with an inclined

surface. Use an object that you brought to class or one of mine.

• In your drawing, identify the isometric and non-isometric lines• Present your results

Oblique Surfaces in Isometric• Step 1: Find the intersections of the oblique surfaces with the

isometric planes. • Note that for this example, the oblique plane contains point A,

B, and C

Oblique Surfaces in Isometric• Step 2: To draw the plane, extend line AB to X and Y, in the

same isometric plane as C• Use lines XC and YC to locate points E and F

Oblique Surfaces in Isometric• Step 3: Finally draw AD and ED using the rule that parallel

lines appear parallel in every orthographic or isometric view

Group Project - Oblique Surfaces in Isometric

• Create a simple isometric sketch of an oblique surface. Use items in the room, or go on a quick scavenger hunt around the 2nd floor

• Label the isometric and non-isometric lines• Shade in the oblique planes• Present your drawing as a group to the class

Inclined Surfaces Example• (a) Orthographic Sketch of an item with inclined and oblique

surfaces to be drawn• (b) Inclined surfaces are located using offset or coordinate

measurements along isometric lines• (c) Final product with inclined surface M and oblique surface N

Visualization Exercise• http://

www.wisc-online.com/objects/ViewObject.aspx?ID=ENG20004

Hidden Lines and Centerlines• Hidden lines are omitted from pictorial drawings unless they

are needed to make the drawing clear• Draw centerlines locating the center of a hole only if they are

needed to indicate symmetry or for dimensioning• Use centerlines sparingly in isometric drawings - “If in doubt,

leave them out”

Group Project - Hidden Lines and Centerlines

• As a group, look through the isometric sketches on pages 228 and 229 of the text.

• When were hidden lines and centerlines used?• When were they not used?• Do you agree with the representation?

Look through your sketches from today. Did you use hidden lines and centerlines.Where they used appropriately?

Angles in Isometric• Angles project true size only when the plane containing the

angle is parallel to the plane of projection• An angle may project to appear larger or smaller than the true

angle depending on its position

Drawing Angles in Isometric• The multi-view below shows three 60 degree angles. None of

the three angles will be 60 degrees in the isometric drawing.

Drawing Angles in Isometric• Step 1. Lightly draw an enclosing box

using the given dimensions, except for dimension X, which is not given.

• Step 2. To find X, draw triangle BDA from the top view full size as shown.

• Step 3. Transfer dimension X to the isometric drawing to complete the enclosing box Find dimension Y by a similar method and then transfer it to the isometric.

• Step 4. Use dimension K to locate point E. A protractor can’t be used to measure angles in a isometric drawing . Convert angular measurements to linear measurements along isometric axes.

Group Project - Angles in Isometric

• Draw a multi-view (orthographic) sketch of a triangle with three angles, 30, 60, and 90 on the front view, with a depth and width of your choice.

• Create an isometric drawing using your orthographic sketch• Present

What’s Next?• Finish Chapter 3 – Orthographic Sketching• Start Chapter 7 – Section Views• Project 50% Plans Due Next Week!!

Questions?• On one of your sketches, answer the following two questions:• What was the most useful thing that you learned today?• What do you still have questions about?

Homework

Read Chapter 7Chapter 3 Exercises: 3.1 (a, g, c, d – isometric sketch only)Chapter 5 Exercises: 5.6 (1, 8 – isometric sketch only)