Fundamentals of Engineering

Isometric Sketching and Coordinate Systems

GSMST

2

Objectives

Define 2D and 3D coordinate systemsDetermine coordinates of objects in: 2D views 3D views

Practice drawing isometric from orthographic

Pictorial Sketching:

Coordinate Systems Used to define the locations of points, lines,

and planes in 2 or 3 dimensions.

"Cartesian Coordinate system"

Y

X

4

A 2-D coordinate system locates the origin at the intersection of the X axis (horizontal axis or abscissa) and the Y axis (vertical axis or ordinate).

These are called View Coordinates.

Coordinate Space in 2-D

-5

-4

-3

-2

-1

0

1

2

3

4

5

-5 -4 -3 -2 -1 0 1 2 3 4 5

X-X

-Y

Y

5

-8

-6

-4

-2

0

2

4

6

8

-8 -6 -4 -2 0 2 4 6 8

Determine the Coordinates

point X Y

A

B

C

D

-3 6

-3 -2

6 -2

0 2

A

B C

D

6

In the 3-D coordinate system (world coordinate system) the axes are mutually perpendicular.

The origin (0,0,0) is usually taken at the intersection of these axes.

Coordinate Space in 3-DZ

X

Y

-Z

-X

-Y

(0,0,0)

3-D Coordinate Systems

Consist of three, mutually perpendicular axes used to define space

Positive or negative based on the axes

Right Hand Rule determines if a coordinate system is positive (right-handed) or negative (left- handed)

3-D Coordinate systems are generally positive (right-handed)

Coordinate Systems: Right Hand Rule

Place your fingers in the direction of the positive x-axis and rotate them in the direction of the y-axis. Your thumb will point in the direction of the positive z-axis.

Left or Right-Handed? The systems are right-handed (positive).

Z X

Y

Y Z X

These systems are left-handed (negative). Z X

Y

Y X Z

Orthographic Projection: Missing Views Constructing the third view helps visualization

skills. When constructing the third view, recall: Points project perpendicularly from one view to the

next. bject dimensions (height, width and

depth) are preserved from one view to the next.

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Orthographic Projection: Missing Views Two Solutions

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Pictorial Sketching Used to portray a 3-D object on a 2-D

sheet of paper.

3-D axes appear differently when shown on a 2-D surface.

Standard axes:

Isometric

Oblique

Oblique Sketching

Since one face of the object is undistorted, the most irregular face is usually shown in the plane of the paper.

Oblique Coordinate Axes

Oblique Coordinate Axes Note: Surface parallel to the plane of the paper (the XY plane) is shown in its true shape.

Oblique sketches are made perpendicular to an edge on the object

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Oblique Sketching

Oblique sketch from edge DC:

3 2 Oblique Sketching 1

To draw oblique sketches: 1. Draw the first surface completely 2. Add lines showing the receding dimension (depth) 3. Repeat until the object is complete

Notice: All receding lines are parallel to one another

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Task: Using engineering paper, draw both these coded sketches.

Oblique Practice

4 3

2 1

5 4 6 2

3 3 2 11

Isometric Coordinate Axes

Isometric sketches are made as if you’re looking down a diagonal a cube

Isometric Coordinate Axes Note: all isometric object surfaces will appear distorted.

Square surface appears as a rhombus

Isometric sketches are made as if you were looking down a diagonal of a cube

Isometric Coordinate Axes Isometric grid paper/dot paper is useful for constructing isometric drawings.

We'll use grid paper in class and dot here in the PowerPoint

Coded Plans

Pictorial sketches can be made from coded plans.

Coded plans define the shape of a block building.

"Arrow" shows the corner you are drawing from

Coded Plan Building

Coded Plans: Isometric Sketch From Corner C

Isometric Sketching 1 3

2 1

C Guidelines for constructing isometric drawings:

C Step 4 ... Step 1 & 2 Step 3

0.Draw edge "C“1.Sketch right or left surface. 2.Draw a surface that shares an edge with the surface just drawn. 3.Continue drawing one surface at a time until the object is complete.

Step 4 ...

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Task: Using isometric paper, draw these coded sketches.

Isometric Practice

4 3

2 1

5 4 6 3

3 3 1 0

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Task: Using the world coordinates convention for computers and CAD,determine the values of the coordinates for points in orthographic drawings and isometric drawings. Note the origin (0,0,0) can be set at an any point.

Orthographic and Isometrics Coordinates

X

Z

Y

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B

B B

B

Y

X

Z

X

Z

Y

X Y ZA 0 0 0

A

A A

3 5 5C

CC

C

4 1 2

DDD

D

7 1 0

World Coordinates in Orthographic Projections

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B

B B

B

Y

X

Z

X

Z

Y

X Y Z

A 0 0 0

A

A A

3 5 5C

CC

C

4 1 2

DDD

D

7 1 0

X

Z

YA

D

C

BWorld Coordinates in Isometric Projections

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World Coordinates in the Isometric

X

Z

Y

A

What are the

Coordinates Of this point?X Y Z

3 2 5

Orthographic Projection:

Orthographic Views from Isometric Sketches

Make an orthographic sketch, by sketching top, front and right side views of the object shown below.

2 3 1 1

Orthographic Projection:

Isometric Sketches from Orthographic Views

•Sometimes you are asked to construct isometric sketches from orthographic views.

•Orthographic views develop visualization skills

•The box method is one way to do this.

•For some problems, the box method may not be very helpful.

Orthographic Projection:

Iso. Sketches from Ortho Views 1. Find the object's overall dimensions from

the orthographic views and sketch that size box on isometric dot paper.

W

Orthographic Projection:

Iso. Sketches from Ortho Views 2. Sketch the top, front, and right side

views in their appropriate locations on the box.

Orthographic Projection:

Iso. Sketches from Ortho Views 3. Add/remove lines until the view is complete.