Fundamentals of Descriptive Geometry

(Text Chapter 26)

UAA ES A103Week #12 Lecture

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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.

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.

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

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.

Direct View Method• Reference

plane is used to transfer depth info between related views.

• Length information comes by projection lines from the adjacent view.

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.

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.

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.

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.

Cartesian Coordinate System

• Points are located relative to the origin of the coordinate system.

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.

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).

Multi View Representations of Lines

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.

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.

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

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.

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.

CorollaryAny adjacent view of a point of view of

a line will show the true length of the line.

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.

Not All Points that APPEAR to be on a Line actually are!

• Two orthographic views are required to see where any given point lies.

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.

Plane Definitions

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.

Examples

• Orthographic representations of planes as they appear in the principle views

Principles of Descriptive Geometry Rule #3

Planar surfaces of any shape always appear either as edges or as surfaces of similar

configuration

Principles of Descriptive Geometry Rule #4

If a line in a plane appears as a point, the plane appears as

an edge

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.

Drawing a Plane in Edge View

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.

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.

Finding an Angle