1. AXONOMETRIC PROJECTION
C H A P T E R F I F T E E N

2. OBJECTIVES
1. Sketch examples of an isometric cube, a dimetric cube, and a
trimetric cube.
2. Create an isometric drawing given a multiview drawing.
3. Use the isometric axes to locate drawing points.
4. Draw inclined and oblique surfaces in isometric.
5. Use projection to create an axonometric drawing.
6. Use offset measurements to show complex shapes in oblique
drawings.
7. Add dimensions to oblique drawings.
8. Describe why CAD software does not automatically create
oblique drawings.

3. Axonometric projections
Axonometric projections show all three principal dimensions using a single
drawing view, approximately as they appear to an observer. Pictorial drawings are also useful in developing design concepts. They can help you picture the relationships between design elements and quickly generate several solutions to a design problem.
Axonometric projection
(isometric shown)
These projections are often called pictorial drawings because they look more like a picture than multiview drawings do. Because a pictorial drawing shows only the appearance of an object, it is not usually suitable for completely describing and dimensioning complex or detailed forms.

4. Projection Methods Reviewed
The four principal types of projection

5. Types of Axonometric Projection
Isometric projection
Dimetric projection
The degree of foreshortening of any line depends on its angle to the plane of projection. The greater the angle, the greater
the foreshortening. If the degree of foreshortening is determined for each of the three edges of the cube that meet at one corner, scales can be easily constructed for measuring along these edges or any other edges parallel to them
Trimetric projection

6. DIMETRIC PROJECTION
Adimetric projection is an axonometric projection of an object in which two of its axes make equal angles with the plane of projection, and the third axis makes either a smaller or a greater angle.

7. APPROXIMATE DIMETRIC DRAWING
Approximate dimetric drawings, which closely resemble true dimetrics, can be constructed by substituting for the true angles.
The resulting drawings will be accurate enough for all practical purposes.

8. TRIMETRIC PROJECTION
A trimetric projection is an axonometric projection of an object oriented so that no two axes make equal angles with the plane of projection.
Because the three axes are foreshortened differently, each axis
will use measurement proportions different from the other two.
Ellipses in Trimetric. (Method (b) courtesy of Professor H. E. Grant.)

9. TRIMETRIC ELLIPSES
The trimetric centerlines of a hole, or the end of a cylinder, become the conjugate diameters of an ellipse when drawn in trimetric.
In constructions where the enclosing parallelogram for an ellipse is available or easily constructed, the major and minor
axes can be determined
(Method (b) courtesy of
Professor H. E. Grant.)
(b)
When you are creating a trimetric sketch of an ellipse, it works great to block in the trimetric rectangle that would enclose the ellipse and sketch the ellipse tangent to the midpoints of the rectangle.

10. AXONOMETRIC PROJECTION USING INTERSECTIONS
Note that if the three orthographic projections, or in most cases any two of them, are given in their relative positions, the directions of the projections could be reversed so that the intersections of the projecting lines would determine the axonometric projection needed.

11. Use of an Enclosing Box to Create an Isometric Sketch using Intersections
To draw an axonometric projection using intersections, it helps to make a sketch of the desired general appearance of the projection.
Even for complex objects the
sketch need not be complete, just an enclosing box.

12. COMPUTER GRAPHICS
Pictorial drawings of all sorts can be created using 3D CAD.
The advantage of 3D CAD
is that once you make
a 3D model of a part
or assembly, you can
change the viewing direction
at any time for orthographic,
isometric, or perspective views.
You can also apply different materials to the drawing objects and shade them to produce a high degree of realism in the pictorial view.
(Courtesy of
Robert Kincaid.)
(Courtesy of PTC)

13. OBLIQUE PROJECTIONS
In oblique projections, the projectors are parallel to each other but are not perpendicular to the plane of projection.

14. Directions of Projectors
The directions of the projections BO, CO, DO, and so on, are independent of the angles the projectors make with the plane of projection.

15. ELLIPSES FOR OBLIQUE DRAWINGS
It is not always possible to orient the view of an object so that all its rounded shapes are parallel to the plane of projection.
Both cannot be simultaneously placed parallel to the plane of projection, so in the oblique projection, one of them must be viewed as an ellipse.

16. Alternative Four-Center Ellipses
Normal four-center ellipses can be made only in equilateral parallelogram, so they cannot be used in an oblique drawing where the receding axis is foreshortened. Instead, use this alternative four-center ellipse to approximate ellipses in oblique drawings.
Draw the ellipse on two centerlines. This is the same method as is sometimes used in isometric drawings, but in oblique drawings it appears slightly different according to the different angles of the receding lines…

17. OFFSET MEASUREMENTS
Circles, circular arcs, and other curved or irregular lines can be drawn using offset measurements.
Draw the offsets on the multiview drawing of the curve and then transfer them to the oblique drawing…

18. OBLIQUE DIMENSIONING
You can dimension oblique drawings in a way similar to that used for isometric drawings.
For the preferred unidirectional system of dimensioning, all dimension figures are horizontal and read from the bottom of the drawing. Use vertical lettering for all pictorial dimensioning.

19. COMPUTER GRAPHICS
Using CAD you can easily create oblique drawings by using a snap increment and drawing in much the same way as on grid paper. If necessary, adjust for the desired amount of foreshortening along the receding axis as well as the preferred direction of the axis.
(Autodesk screen shots reprinted with the permission of Autodesk, Inc.)