3.1: Auxiliary views

Learning Objectives

By the end of this section, learners will be able to

1. Describe the purpose and application of primary and secondary auxiliary views.
2. Distinguish between depth, width, and height in auxiliary views.
3. Explain the role of the reference plane and demonstrate how to place it effectively to simplify the construction of auxiliary views.
4. Identify and represent hidden edges in auxiliary views.
5. Create a primary auxiliary view of a surface or a complete object.

Auxiliary views are orthographic views that are not standard views (top, front, and side views). They are used to visualize inclined or oblique surfaces in their true shape and size.

A surface appears in its true shape only when it is projected onto a plane that is parallel to it using perpendicular projectors. As discussed in Module B, section 2.6: Normal, inclined, and oblique surfaces, a normal surface appears true shape and size on the plane it is parallel to, while inclined and oblique surfaces appear foreshortened. An auxiliary plane is a plane of projection that is inclined or oblique relative to the standard planes, and it is used to describe inclined or oblique surfaces in their true shape and dimensions.

Figure 3.1.1 illustrates the glass box with one plane replaced by an auxiliary plane.

Figure \(\PageIndex{1}\): Auxiliary plane visualized in the glass box.

In a primary auxiliary view, the plane of projection is inclined to two standard planes and perpendicular to the third. Primary auxiliary views are projected from the perpendicular standard view and are used to show inclined surfaces in their true shape and dimensions.

Secondary auxiliary views are projected from primary auxiliary views and are used to show oblique surfaces in their true shape and size. Succeeding auxiliary views can be drawn from secondary auxiliary views.

This section focuses on primary auxiliary views.

Depth, width, and height auxiliary views

Auxiliary views are named according to the dimension that is transferred onto the auxiliary plane and shown in the resulting auxiliary view: depth, width, or height. Understanding depth, width, and height auxiliary views is essential for interpreting and creating auxiliary views.

A primary auxiliary plane is an inclined plane of projection; by definition, it is tipped relative to two principal planes and perpendicular to the third standard plane of projection.

• A depth auxiliary view is perpendicular to the frontal plane, and the dimension shown on the auxiliary view is the depth. Figure 3.1.2 shows the glass box with a depth auxiliary plane highlighted (in red) perpendicular and hinged to the frontal plane. A depth auxiliary view is projected from the front view, and the unfolded glass box shows how the depth can be transferred from the top view to the auxiliary plane. Although Figure 3.1.2 shows one example of a depth auxiliary plane, an infinite number of planes perpendicular to the front view could be constructed.

Figure \(\PageIndex{2}\): Depth auxiliary plane.

• A width auxiliary view is perpendicular to the profile plane, and the dimension shown on the auxiliary view is the width. Figure 3.1.3 shows the glass box with a width auxiliary plane (in red) perpendicular to and hinged to the profile plane. A depth auxiliary view is projected from the right-side view, and the unfolded glass box shows how the width can be transferred from the front and top views on the auxiliary plane. As with depth, infinitely many width auxiliary planes could be drawn.

Figure \(\PageIndex{3}\): Width auxiliary plane.

• A height auxiliary view is perpendicular to the horizontal plane, and the dimension shown on the auxiliary view is the height. Figure 3.1.4 shows the glass box with a height auxiliary plane (in red) perpendicular to and hinged to the horizontal plane. A height auxiliary view is projected from the top view. The unfolded glass box shows how the height can be transferred from the front view to the auxiliary plane. Similar to the depth and width auxiliary views, there are an infinite number of auxiliary planes perpendicular to the top view.

Figure \(\PageIndex{4}\): Height auxiliary plane.

The reference plane

Another important concept in creating auxiliary views is the reference plane. The reference plane is always parallel to the plane of projection and perpendicular to the auxiliary plane. It is positioned so that it either touches or passes through the object.

The reference plane is used to transfer the depth, width, or height onto the auxiliary plane. The advantage of using a reference plane is that it reduces the number of measurements needed, since some vertices lie directly on the reference plane.

• In a depth auxiliary view, the reference plane is parallel to the frontal plane. It can be located at any position in space along the depth direction (the y-coordinate in the figure below). It appears as a horizontal edge in the top view and as an edge perpendicular to the line of sight in the auxiliary view.

Figure \(\PageIndex{5}\): Reference plane shown in a depth auxiliary view.

• In a width auxiliary view, the reference plane is parallel to the profile plane. It can be located at any position in space along the width direction (the x-coordinate in the figure below). It appears as a vertical edge in the front view and as an edge perpendicular to the line of sight in the auxiliary view..

Figure \(\PageIndex{6}\): Reference plane shown in a width auxiliary view.

• In a height auxiliary view, the reference plane is parallel to the horizontal plane. It can be located at any position in space along the height direction (the z-coordinate in the figure below). It appears as a horizontal edge in the front view and as an edge perpendicular to the line of sight in the auxiliary view.

Figure \(\PageIndex{7}\): Reference plane shown in a height auxiliary view.

Example

The example below shows a step-by-step procedure for constructing an auxiliary view.

The interactive model shows the setup for this example, including the glass box, the auxiliary plane, and the reference plane. An object, shown in green, is placed inside the glass box. The object has one inclined surface (P), and the auxiliary plane is aligned parallel to this surface. In this case, the reference plane (shown in red) is positioned against the object’s rear face. Rotating the model makes it possible to view the object, the reference plane, the glass box, and the auxiliary plane in three dimensions. The QR code in the lower-right corner can be used to open the visualization on an external device.

Interactive Element

This box will NOT print up in pdfs.

1. Define the line of sight: Figure 3.1.8 shows a top and front view of the object. In this example, the line of sight is chosen perpendicular to the inclined surface P. Surface P is an inclined surface, perpendicular to the frontal plane, and appears as a full length edge in the front view.

Figure \(\PageIndex{8}\): Front and top views and direction of site for auxiliary view.

2. Identify the type of auxiliary view: Determine whether the auxiliary view is a depth, width, or height view. In this example, the frontal plane is the projection plane that is perpendicular to the auxiliary plane. Therefore, this exercise illustrates a depth auxiliary view.

Figure \(\PageIndex{9}\): Vertices are projected on the auxiliary plane from the front view using projectors parallel to the line of sight.

3. Place the reference plane: There is not a single correct way to position a reference plane, but it is typically placed so that several vertices of the object lie on it. In this example, the reference plane is positioned against the rear surface, with vertices 3, 10, 4, 6, and 8 lying on the plane. Because the reference plane is parallel to the frontal plane, it appears as a horizontal edge in the top view. In the auxiliary view, the reference plane is shown perpendicular to the line of sight.

Figure \(\PageIndex{10}\): Reference plane seen as an edge on top and auxiliary views.

4. Project vertices from the plane of projection and transfer depth: In this example, the frontal plane is the plane of projection. The vertices of surface P are projected from the front view; for instance, vertices 7 and 8 lie along the same projector. To determine their exact positions along the projector, the depth must be transferred from the top view. The reference plane can be used to measure depth. For example, vertex 8 lies on the reference plane, so its location is at the intersection of the projector and the reference plane. Vertex 7 is located along the same projector at a distance equal to the object’s depth. Similarly, vertices 6 and 5 lie on the same projector, with vertex 6 on the reference plane and vertex 5 positioned at a distance corresponding to the object’s depth from the reference plane and vertex 6.

Figure 3.1.11 shows the inclined surface P in its true shape and size as seen in the auxiliary view.

Figure \(\PageIndex{11}\): Surface P seen true shape and size on auxiliary view.

5. Repeat for all vertices and identify hidden edges: This process is repeated for all vertices to represent the entire object in the auxiliary view. Any edges that are not visible in the view should be shown as hidden lines. For example, the edge connecting vertices 9 and 10 appears hidden behind surface P in the auxiliary view.

Figure \(\PageIndex{12}\): Complete object seen on auxiliary view.

Note 1

The reference plane can also be positioned in different locations, such as against the front surface or cutting through the object. The image below shows a reference plane cutting through a symmetric object. The placement of the reference plane is at the drafter’s discretion; however, it must be consistent across all views.

Figure \(\PageIndex{13}\): Placement of reference plane in a symmetric object.

Note 2

The reference plane should always be shown on the standard view that is not the plane of projection, as well as on the auxiliary view. Regardless of its placement, the reference plane appears as a horizontal edge on the top view in depth auxiliary views, as a vertical edge on the front view in width auxiliary views, and as a horizontal edge on the front view in height auxiliary views.