1. 2D Essentials
Instructor: Laura Gerold, PE
Catalog #10614113
Class # 22784, 24113, 24136, & 24138
Class Start: January 18, 2012
Class End: May 16, 2012

2. 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

3. Lingering Questions
from Chapter 6 . . .

4. Runouts
• When a rounded corner intersects a curved surface, a runout
is used to show how the edge fades or “tails out.”

5. 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.

6. 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.

7. 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?

8. Chapter 3 – Isometric
Drawing

9. Why Isometric Drawing?
• Isometric Drawing is used to visualize concepts and to present
results to a client and the public

10. Some Key Concepts
• To Understand Isometric Projection and drawing, we need to
learn a few key concepts first . . .

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

12. Projection Methods
The four
principal
types of
projections:
a Multiview
b Axonometric
c Oblique
d Perspective

13. 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

14. Perspective Example
Image from: http://www.draw23.com/perspective

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

16. 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

17. Oblique Example
Source: Wikipedia

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

19. 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

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

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

22. Pop Quiz – What Type of
Sketch?

23. Pop Quiz – What Type of
Sketch?
ISOMETRIC
Source:
http://wikihelp.autodesk.com/Inventor/enu/2011/Help/What's_New/Drawing_Annotations

24. Pop Quiz – What Type of
Sketch?

25. Pop Quiz – What Type of
Sketch?
PERSPECTIVE
Source: http://tlc.howstuffworks.com/family/how-to-draw-in-perspective.htm

26. Pop Quiz – What Type of
Sketch?

27. Pop Quiz – What Type of
Sketch?
OBLIQUE
Source: http://draftingmanuals.tpub.com/14276/css/14276_308.htm

28. Pop Quiz – What Type of
Sketch?

29. Pop Quiz – What Type of
Sketch?
PERSPECTIVE
Source: http://xenthralx.deviantart.com/art/two-point-perspective-drawing-99599007

30. Pop Quiz – What Type of
Sketch?

31. Pop Quiz – What Type of
Sketch?
ISOMETRIC
Source:
http://toolboxes.flexiblelearning.net.au/demosites/series12/12_05/toolbox12_05/fpicot3204a_sketch
es_and_drawings/3204a_30_producing_drawings/3204a_35_drawing_in_3d.htm

32. Pop Quiz – What Type of
Sketch?

33. Pop Quiz – What Type of
Sketch?
OBLIQUE
Source: http://chestofbooks.com/crafts/machinery/Shop-Practice-V2/Oblique-Projection.html

34. Pop Quiz – What Type of
Sketch?

35. Pop Quiz – What Type of
Sketch?
ISOMETRIC
Source: http://www.brynmawr.edu/cities/Cities/imgb/071/071m.html

36. 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.

37. AXONOMETRIC
Various types of
DRAWINGS
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, a
rchitectural
design, and in
furniture design; and
for ideation sketching.
Axonometric
(Courtesy of Douglas Wintin.)

38. 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

39. 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

40. 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

41. 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

42. 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?

43. 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.

44. Group Project
• Draw an isometric cube
• Label the angles

45. 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

46. 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

47. ISOMETRIC DRAWINGS steps…

48. 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

49. 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

50. 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

51. 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

52. Isometric Drawings of Inclined
Surfaces
• 54mm is not along an isometric axis
• Start sketching out the isometric lines: 44 mm, 18mm,
and 22mm

53. 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

54. 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

55. 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

56. 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

57. 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

58. 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

59. 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

60. 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

61. Visualization Exercise
• http://www.wisc-
online.com/objects/ViewObject.aspx?ID=ENG20004

62. 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”

63. 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?

64. 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

65. 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.

66. 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.

67. 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

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

69. 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?

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