AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 1

CHAPTER 2CHAPTER 2:

GEOMETRY

AE-1022: AIRCRAFT DRAWING

Outline

Engineering geometry

Coordinate spaces Coordinate spaces

Geometric elements

Points, lines, surfaces & arcs

Conic curves

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 2

Engineering Geometry

Geometric construction: Act of constructing a geometry, especially using hand toolsespecially using hand tools

Engineering geometry: Basic geometric elements and forms

e.g., dividing a line

Engineering geometry: Basic geometric elements and forms used in engineering design

Points, Lines, Surfaces, and Solids

Coordinate Spaces

2-D Cartesian coordinate system

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 3

Coordinate Spaces (con’t)

3-D coordinate system

Coordinate Spaces (con’t)

Display of coordinate axis in a multiview drawing

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 4

Coordinate Spaces (con’t)

Right-hand rule: Used to determine the Used to determine the positive direction of the axes

Note: counter clockwise is positive – default positive rotation of CAD

Coordinate Spaces (con’t)

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 5

Coordinate Spaces (con’t)

Polar coordinates(distance in X-Y plane and angle

Cylindrical coordinates(distance and angle in X-Y plane (distance in X-Y plane and angle

from X axis)(distance and angle in X-Y plane and distance in Z)

Coordinate Spaces (con’t)

Spherical coordinates(angle in two planes and one

Absolute coordinates(referenced to fixed origin)(angle in two planes and one

distance parameter)

( g )

Relative coordinates(referenced to previous point)

World coordinates (referenced back to origin)

Local coordinates(moving system positioned (moving system positioned anywhere in space)

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 6

Coordinate Spaces (con’t)

World Coordinates

User Coordiates

Geometric Elements

Manual drafting AutoCAD

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 7

Points, Lines, Surfaces, and Arcs

Point: Theoretical location that has neither width, height, nor depth and describes an exact location in spacedepth and describes an exact location in space

Points, Lines, Surfaces, and Arcs (con’t)

Line: Geometric primitive that has length and that has length and direction but not thickness May be straight, curved, or a

combination

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 8

Points, Lines, Surfaces, and Arcs (con’t)

Tangencies: Exists when a straight line is in contact with a curve at a single point; that is a line is tangent to a circle if it curve at a single point; that is, a line is tangent to a circle if it touches the circle at one and only one point

Points, Lines, Surfaces, and Arcs (con’t)

Circles: Single curved surface primitive, all points of which are equidistant from one point, the center

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CHAPTER 2: GEOMETRY 9

Points, Lines, Surfaces, and Arcs (con’t)

• The elements of a circle are as follows (outlined in previous slide):

Center

Circumference

Radius

Chord

Diameter

Minor arc

Major arc

Central angle

Sector

Quadrant

S t

( p )

Secant

Arc

Semicircle

Segment

Tangent

• The slides that follow provide examples of manualdrafting points, lines, surfaces, and mostly, arcs

Points, Lines, Surfaces, and Arcs (con’t)

Constructing arcs tangent to two

lines

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 10

Points, Lines, Surfaces, and Arcs (con’t)

Constructing an arc tangent to a line and another arc

Points, Lines, Circles, and Arcs (con’t)

Constructing an arc tangent to two given arcs or circles

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 11

Points, Lines, Circles, and Arcs (con’t)

Constructing an arc tangent to two given

arcs

Points, Lines, Circles, and Arcs (con’t)

Constructing an arc tangent to a given arc

AE‐1022: AIRCRAFT DRAWING 10/27/2009

CHAPTER 2: GEOMETRY 12

Points, Lines, Circles, and Arcs (con’t)

Constructing lines tangent to two circles or arcs using a arcs, using a

straightedge (a trial and error

method)

Conic Curves

Parabola: Curve created when a plane intersects a right circular cone parallel to the side (elements) of the conecircular cone parallel to the side (elements) of the cone

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CHAPTER 2: GEOMETRY 13

Conic Curves (con’t)

Parallelogram Parallelogram Method of

Drawing Parabolas

Engineering Applications of Parabolas

Conic Curves (con’t)

Hyperbola: Curve of the intersection created when a plane intersects a right circular cone and makes a smaller angle intersects a right circular cone and makes a smaller angle with the axis than do the elements

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CHAPTER 2: GEOMETRY 14

Conic Curves (con’t)

Ellipse: Single-curved-surface primitive – created surface primitive created when a plan passes through a right circular cone at an angle to the axis that is greater than the angle between the axis and the sides (a circle when viewed sides (a circle when viewed at an angle appears as an ellipse)

Conic Curves (con’t)

Constructing a Foci Ellipse