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Lesson
6: Ellipse Geometry |
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Technical Illustration essentially is an art and
a science of taking orthographic views and creating
a three dimensional image.
There are three standard isometric views and you
will be exploring these views in this lesson. With
some illustrations and depending upon certain characteristics
of a model one view might be used better than another.
Along with our Standard views come the 'un standard'
views where ellipses have to be modified; in terms
of the minor and major axis. Isometric ellipses are
set at 35 degrees but non standard can vary from this
value. In this lesson you will learn how using ACAD
to determine and draw a non standard ellipse. These
kind of ellipses are found on sloping surfaces
A Draftsman not only makes the blueprint but their
responsibilities also lie in being able to present
the print so others can visualize what the model looks
like. In this lesson the Draftsman has to make the
choice as to what Isometric view would best be suited
to illustrate the model in question. But, what about
using a 3d model in place of an isometric drawing.
Are they both as accurate. We will explore in this
lesson drawing and comparing the Isometric with the
3d.
Connecting Your Learning
As you work your way through this lesson, you should
reflect on the following questions:
What is the function is of the iso ellipse command
and the ellipse command in determining the major and
minor axis of an ellipse?
How can I project an ellipse on an angled surface?
What type of Isometric view is used to show the bottom
of an object?
What are Isometric lines?
What are Non isometric lines?
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The State of Arizona has assembled Drafting
standards to make sure that Instruction is thorough
and well thought out by the instructor. By clicking
on the hyperlink below will upload to your browser window
the entirety of these standards. The standards that
are addressed in this lesson are below the hyperlink.
1.0 USE BOARD DRAFTING EQUIPMENT,
INSTRUMENTS AND MEDIA.
2.0 DEMONSTRATE SKETCHING, LETTERING,
AND LINE SKILLS.
- 2.1 Demonstrate freehand sketching skills for drafting
applications.
- 2.2 Demonstrate lettering skills.
- 2.3 Demonstrate line work.
6.0 DEMONSTRATE GEOMETRIC CONSTRUCTIONS
- 6.1 Measure Geometric Constructions.
- 6.2 Develop Geometric Constructions.
8.0 APPLY BOARD DRAFTING SKILLS TO COMPUTER-AIDED
DESIGN/DRAFTING (CADD)
- 8.1 Demonstrate computer skills for a CADD system.
- 8.2 Create dimensional CADD entities.
- 8.3 Create 3 dimensional CADD drawings.
The State of Arizona has also assembled Math
standards and many of these apply directly to
the vocational subject area of Drafting. Drafting
is a very precise discipline and the use of mathematics
is integral to design and manufacturing. Below are
the math standards that are involved in this lesson
1M-P1. Compare and contrast
the real number system and its various subsystems
with
regard to their structural characteristics
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PO 2. Compare subsets of the
real number system with regard to their properties
(commutative, associative, distributive, identity,
inverse and closure properties)
1M-P2. Construct, interpret and
demonstrate meaning for real numbers and absolute
- PO 3. Solve real-world distance problems using
absolute value
- PO 4. Determine, among the solutions to a real-world
problem, which, if any, is reasonable
- PO 2. Define absolute value as the distance from
the origin
4M-P1. Interpret and draw three-dimensional
objects
- PO 1. Sketch prisms, pyramids, cones, cylinders
and spheres
- PO 2. Classify prisms, pyramids, cones, cylinders
and spheres by base shape and lateral surface shape.
- PO 3. Recognize the three-dimensional figure represented
by a two-dimensional drawing.
- PO 5. Make a model of a three-dimensional figure
from a two-dimensional drawing and make a two-dimensional
representation of a three-dimensional object (models
and representations include scale drawings, perspective
drawings, blueprints or computer simulations)
4M-P4. Deduce properties of,
and relationships between, figures from given
assumptions
- PO 1. Find similarities and differences among
geometric shapes and designs using a given attribute
(e.g., height, area, perimeter, diagonals and angle
measurements)
- PO 2. Identify arcs, chords, tangents and secants
of a circle
- PO 3. State valid conclusions using given geometric
definitions, postulates and theorems
- PO 4. Represent pi as the ratio of circumference
to diameter
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Lesson
Objectives
By the end of this lesson you should
be able to:
1. Draw an ellipse using the Iso Ellipse
command in the CADD software.
2. Rotate a standard Isometric view to reversed axis
and long axis views.
3. Sketch Isometric models using an Isometric Grid.
4. Adjust line weights in ACAD for easier viewing
of the constructed model.
5. Draw an ellipse from an Iso Ellipse using projection
lines and determining the major and minor axis.
6. Project and ellipse on an angled surface using
an isometric ellipse.
7. Maintain approximate proportions using "boxing
in" also called the "Glass box Technique"
8. Using an Ellipse to project another ellipse that
is not isometric
Key
Terms
"click
on the key on any of these terms and it will hyperlink
to the course glossary"
isometric |
long
axis |
ellipse |
orthographic |
projection
lines |
hex
bolt |
reverse
axis |
ellipse |
isometric
lines |
line
weight |
glass
box |
dimension |
| Iso Ellipse |
proportion |
ellipse |
Boxing-in |
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The following
are the models that will be used for Lesson 6:
- Lesson 6:
[drawing
figure 4.12 on page 47 of the Thomas Text]
For
this model you will be drawing the isometric view
of the above model as a sketch and then using an
Isometric ellipse to project lines onto the sloping
surface of this model. After our model is constructed
we will discover our dimensions and create a 3d
model of figure 4.12 and compare both in isometric
perspective.
I will
explain this further in the lesson 6 media disc.
Please insert the media disk and listen to lesson
6.
*Note:
The Lessons are best viewed with real player and you
can download the latest version by clicking on the
words real
player.
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Below are two examples of Lesson 6; one being
an isometric and the next screen capture jpeg is the precise
3d model of the very same model. Remember you must turn in
each of these views separately as indicated in the assessment
section of this lesson.
Your
Text Book and Reading Assignments
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Text:
Technical Illustration by Thomas
Use
Chapter 4"Isometric Drawing''
Pages 42-55, as a reading reference.
Lesson 6 assessment comprises:
-
Lesson 6a figure 4.12 ; regular isometric
view.(20 pts.)
- Lesson 6b figure 4.12; 3d model.(20 pts.)
Rubrics for Grading: The drafting
standards for assessing the quality and accuracy of your drawings
are as follows: Neatness, Accuracy and Lines and Lettering.
One half of one point (.5) will be taking off your score in
relation to NALL.
Submit by email attachment all of
the above lessons as dwg. files and send to your Instructor whose
mail address is. losimilar@yahoo.com
Your Instructor will grade your
drawings within 24 hours and email you back the grade/assessment
of your work. You should take allot of pride in your work.
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