lec 11 descriptive geometry
TRANSCRIPT
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Fundamentals of Descriptive Geometry
(Text Chapter 26)
UAA ES A103
Week #12 Lecture
Many of the materials provided in this lecture are provided by
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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Introduction
• Most of the concepts of this chapter have already been touched on in prior lectures and exercises.
• The intent of this lecture to provide another view of the principles and concepts from an analytical standpoint.
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Descriptive Geometry
• Descriptive geometry is the graphic representation of plane, solid, and analytical geometry used to describe real or imagined technical devices and objects.
• It is the science of graphic representation in engineering design.
• Students of technical or engineering graphics need to study plane, solid, analytical, and descriptive geometry because it forms the foundation or grammar of technical drawings.
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Uses of Descriptive Geometry• Descriptive geometry principles are used to
describe any problem that has spatial aspects to it.
• For example the application of descriptive geometry is used in:– The design of chemical plants. For the plant to
function safely, pipes must be placed to intersect correctly, and to clear each other by a specified distance, and they must correctly intersect the walls of the buildings.
– The design of buildings– The design of road systems– The design of mechanical systems
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Methods of Descriptive Geometry
• There are three basic methods– Direct View– Fold Line– Revolution
• The differences is in how information is transferred to adjacent views.
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Direct View Method
• Reference plane is used to transfer depth info between related views.
• Length information comes by projection lines from the adjacent view.
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Fold-Line Method
• A variation on the Direct View method.
• The reference line is moved between the views to represent the folds in a glass box.
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Revolution Method
• The projectors from the adjacent view are not parallel to the viewing direction (as related to the object)
• Need to rotate the length information about an axis before projecting it to the new adjacent view.
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Reference Planes• The reference
plane is perpendicular to the line of sight project lines. It appears as a line in related views.
• Gives a reference for measuring depth information for related views.
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Basic Elements
• The basic elements used in descriptive geometry include:– Points– Lines– Planes
• Coordinate systems are mathematical tools useful in describing spatial information– Cartesian coordinate systems are the most
commonly used.
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Cartesian Coordinate System
• Points are located relative to the origin of the coordinate system.
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Points
• A point has no width, height, or depth.
• A point represents a specific position in space as well as the end view of a line or the intersection of two lines.
• The graphical representation of a point is a small symmetrical cross.
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Lines
• Lines represents the locus of points that are directly between two points.
• A line is a geometric primitive that has no thickness, only length and direction.
• A line can graphically represent the intersection of two surfaces, the edge view of a surface, or the limiting element of a surface.
• Lines are either vertical, horizontal, or inclined. A vertical line is defined as a line that is perpendicular to the plane of the earth (horizontal plane).
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Multi View Representations of Lines
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True Length Lines
• A true length line is the actual straight-line distance between two points.
• In orthographic projection, a true-length line must be parallel to a projection plane in an adjacent view.
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True Length Lines
• True length lines are ALWAYS parallel to the reference plane in ALL adjacent views.
• To find the true length of a line, draw a view of the line where the reference plane is parallel to an adjacent view of the line.
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Principles of Descriptive Geometry Rule #1
If a line is positioned parallel to a projection plane and the line
of sight is perpendicular to that projection plane, then the line will appear as true length
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Point View of a Line
• What you see when you look down the length of a line.
• Experiment:– Take a pencil and
look at it from various directions, keeping in mind the rotations between line of sight directions.
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Principles of Descriptive Geometry Rule #2
If the line of sight is parallel to a true-length line, the line will appear as a
point view in the adjacent view.
Corollary
Any adjacent view of a point of view of a line will show the true length of the
line.
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Points on a Line
• If a point is on a line, it will appear on the line in all views and be at the same location on the line.
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Not All Points that APPEAR to be on a Line actually are!
• Two orthographic views are required to see where any given point lies.
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Planes
• Planes are surfaces that can be uniquely defined by:– Three non-linear points in space,– Two non-parallel intersecting vectors,– Two parallel vectors, or– A line and point not on the line.
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Plane Definitions
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Plane Classifications
• Planes are classified as– Horizontal– Vertical
• Profile• Frontal
– Inclined (perpendicular to a principle plane)– Oblique (not perpendicular to a principle
plane)
• Horizontal and Vertical planes are principle planes.
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Examples
• Orthographic representations of planes as they appear in the principle views
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Principles of Descriptive Geometry Rule #3
Planar surfaces of any shape always appear either as edges or as surfaces of similar
configuration
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Principles of Descriptive Geometry Rule #4
If a line in a plane appears as a point, the plane appears as
an edge
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Principles of Descriptive Geometry Rule #5
A true-size plane must be perpendicular to the line of sight and must appear as an edge in all adjacent views.
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Drawing a Plane in Edge View
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A Corollary to Rule #5
If a plane is true-size then all lines in the plane are true
length and all angles are true.
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Finding the Angle Between Two Intersecting Planes
• The key is to create a view where BOTH planes are in edge view.– The common line between the planes is the
intersecting line. – Create a view where the intersecting line
appears as a point.• Start by drawing a view of the line in true length
• Then draw the desired view.
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Finding an Angle