CHAPTER TWENTY-TWO AXONOMETRIC PROJECTION PROJECTION OBJECTIVES 22 After studying the material in this chapter, you should be able to: 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. AXONOMETRIC 8. Explain why CAD software does not automatically create oblique drawings. Refer to the following standard: • ASME Y14.4M Pictorial Drawing AXONOMETRIC PROJECTION W871 A Portion of a Sales Brochure Showing General Dimensions in Pictorial Drawings (Courtesy of Dynojet Research, Inc.) OVERVIEW Multiview drawing makes it possible to represent the all three principal dimensions using a single drawing complex forms of a design accurately by showing a view, approximately as they appear to an observer. series of views and sections, but reading and interpret- These projections are often called pictorial drawings ing this type of representation requires a thorough because they look more like a picture than multiview understanding of the principles of multiview projec- drawings do. Because a pictorial drawing shows only tion. Although multiview drawings are commonly the appearance of an object, it is not usually suitable used to communicate information to a technical audi- for completely describing and dimensioning complex ence, they do not show length, width, and height in or detailed forms. a single view and are hard for a layperson to visualize. Pictorial drawings are also useful in developing It is often necessary to communicate designs to peo- design concepts. They can help you picture the rela- ple who do not have the technical training to interpret tionships between design elements and quickly gener- multiview projections. Axonometric projections show ate several solutions to a design problem. W872 CHAPTER 22 AXONOMETRIC PROJECTION Visual rays parallel to each Visual rays parallel Plane of other and perpendicular Plane of to each other and projection to plane of projection projection perpendicular to E plane of projection A F A Object B Object A A O Line of B Line of B sight D sight O G 30° C D C C 30° C (a) Multiview projection (b) Axonometric projection (isometric shown) Vanishing point (plane of projection) Picture plane Horizon line Plane of VP Visual rays projection converge at Visual rays parallel to observer’s each other and oblique eye (station to plane of projection E E point SP) F E Line of E F A A sight A A H B F F B B G B D H G C D D D G G C C C Object Object (c) Oblique projection (d) Perspective 22.1 Four Types of Projection UNDERSTANDING AXONOMETRIC PROJECTION Projection Methods Reviewed The four principal types of projection are illustrated in In perspective (Figure 22.1d), the visual rays extend from Figure 22.1. All except the regular multiview projection (Fig- the observer’s eye, or station point (SP), to all points of the ure 22.1a) are pictorial types because they show several sides object to form a “cone of rays” so that the portions of the object of the object in a single view. In both multiview projection that are farther away from the observer appear smaller than the and axonometric projection (Figure 22.1b), the visual rays are closer portions of the object. parallel to each other and perpendicular to the plane of projec- Review Chapter 3 for details on how to create basic picto- tion. Both are types of orthographic projections. rial sketches. In oblique projection (Figure 22.1c), the visual rays are parallel to each other but at an angle other than 90° to the plane of projection. AXONOMETRIC PROJECTION W873 Types of Axonometric Projection The feature that distinguishes axonometric projection from multiview projection is the inclined position of the object with respect to the planes of projection. When a surface or edge of Plane of projection the object is not parallel to the plane of projection, it appears foreshortened. When an angle is not parallel to the plane of Axonometric Object projection, it appears either smaller or larger than the true view angle. To create an axonometric view, the object is tipped to the planes of projection so that all of the principal faces show in a single view. This produces a pictorial drawing that is easy to visualize. But, because the principal edges and surfaces of the object are inclined to the plane of projection, the lengths of the Measurements are lines are foreshortened. The angles between surfaces and edges foreshortened appear either larger or smaller than the true angle. There are an proportionately infinite variety of ways that the object may be oriented with respect to the plane of projection. 22.2 Measurements are foreshortened proportionately The degree of foreshortening of any line depends on its based on the amount of incline. 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 constructed for measuring along these edges or any other edges parallel to them (Figure 22.2). Use the three edges of the cube that meet at the corner nearest your view as the axonometric axes. In Figure 22.1b, the axonometric axes, or simply the axes, are OA, OB, and OC. Figure 22.3 shows three axonometric projections with axes OX, OY, and OZ. Isometric projection (Figure 22.3a) has equal foreshort- ening along each of the three axis directions. Dimetric projection (Figure 22.3b) has equal foreshorten- ing along two axis directions and a different amount of fore- shortening along the third axis. This is because the third axis is not tipped an equal amount to the principal plane of projection. Trimetric projection (Figure 22.3c) has different fore- shortening along all three axis directions. This view is pro- duced by an object whose axes are not equally tipped to the plane of projection. a Z a Z X Z X X a O O O c b c b b c ∠a = ∠b = ∠c Y ∠a = ∠c Y ∠a, ∠b, ∠c unequal Y OX = OY = OZ OX = OY OX, OY, OZ unequal (a) Isometric (b) Dimetric (c) Trimetric 22.3 Axonometric Projections W874 CHAPTER 22 AXONOMETRIC PROJECTION 22.1 DIMETRIC PROJECTION A dimetric projection is an axonometric projection of an object revolved about the axis line PS into the plane of projection, it in which two of its axes make equal angles with the plane of will show its true size and shape as PO′S. If regular full-size projection, and the third axis makes either a smaller or a greater scales are marked along the lines O′P and O′S, and the triangle angle (Figure 22.4). The two axes making equal angles with is counterrevolved to its original position, the dimetric scales the plane of projection are foreshortened equally; the third axis may be divided along the axes OP and OS, as shown. is foreshortened in a different proportion. You can use an architect’s scale to make the measure- Usually, the object is oriented so one axis is vertical. ments by assuming the scales and calculating the positions of However, you can revolve the projection to any orientation if the axes, as follows: you want that particular view. Do not confuse the angles between the axes in the draw- −−2hv22 v4 cos a = ing with the angles from the plane projection. These are two 2hv different but related things. You can arrange the amount that the principal faces are tilted to the plane of projection in any where a is one of the two equal angles between the projections way as long as the two angles between the axes are equal and of the axes, h is one of the two equal scales, and v is the third over 90°. scale. Examples are shown in the upper row of Figure 22.4, The scales can be determined graphically, as shown in where length measurements could be made using an architect’s Figure 22.5a, in which OP, OL, and OS are the projections of scale. One of these three positions of the axes will be found the axes or converging edges of a cube. If the triangle POS is suitable for almost any practical drawing. 22.2 APPROXIMATE DIMETRIC DRAWINGS Approximate dimetric drawings, which closely resemble be obtained with the ordinary triangles and compass, as shown true dimetrics, can be constructed by substituting for the true in the lower half of the figure. The resulting drawings will be angles shown in the upper half of Figure 22.4 angles that can accurate enough for all practical purposes. 1.0 1.0 1.0 .75 .75 .50 106°20’ 152°44’ 131°25’ .75 103°38’ 103°38’ 1.0 97°10’ 131°25’ 126°50’ 126°50’ 1.0 36°50’ 36°50’ 41°25’ 13°38’ 13°38’ 7°10’ (a) (b) (c) Dimetric drawings 1.0 1.0 1.0 .75 .75 .50 .75 1.0 1.0 45° 30° 45° 37°30’ 15° 15° 7°30’ 37°30’ 30° (d) (e) (f) Approximate dimetric drawings 22.4 Understanding Angles in Dimetric Projection 22.2 APPROXIMATE DIMETRIC DRAWINGS W875 22.5 Dimetric Drawings (a) (b) (c) HOW TO MAKE DIMETRIC DRAWINGS 14 STEP 7.5° 28 45° 28 28 28 by STEP 1 To make a dimetric 2 The dimensions for 3 Block in the features 28 drawing for the views the principal face are relative to the surfaces given, draw two intersecting measured full size.