Sectional and Auxiliary Views

Introduction

Orthographic views describe external geometry effectively, but hidden internal features and inclined surfaces can remain difficult to interpret. Excessive hidden lines may make a drawing ambiguous, while an inclined surface appears foreshortened unless viewed perpendicular to its plane. Sectional and auxiliary views address these limitations.

A sectional view represents an object as though it were cut by an imaginary plane and the material between the observer and that plane were removed. An auxiliary view is an orthographic projection onto a plane other than a principal projection plane. Together, these methods communicate cavities, bores, ribs, cable passages, inclined mounting faces and other engineering features clearly.

In electrical engineering practice, they are particularly useful for motor housings, switchgear enclosures, busbar supports, heat sinks, connector bodies, cable glands, sensor mounts and power-electronic assemblies.

Learning Objectives

After completing this chapter, students should be able to:

• distinguish cutting planes, section views and section lining;
• construct full, half, offset, broken-out and revolved sections;
• apply accepted conventions for ribs, webs, fasteners and adjacent parts;
• select suitable cutting planes and viewing directions;
• construct primary auxiliary views showing true lengths and true shapes;
• construct secondary auxiliary views through successive projection;
• dimension sectional and auxiliary views without unnecessary duplication; and
• evaluate manually or digitally generated views for geometric correctness.

1. Principles of Sectional Representation

1.1 Cutting planes and viewing direction

A cutting plane is an imaginary plane passing through selected features. Its trace is identified in another view by a cutting-plane line, commonly a thick chain or designated line according to the governing drawing standard. Arrowheads indicate the direction from which the section is viewed. All arrows associated with one straight cutting-plane trace must indicate the same viewing direction and must be normal to that trace.

The resulting section is usually identified by matching letters, such as SECTION A–A. The letters identify the cutting plane and do not represent physical points on the component.

Figure: A full-section cutting plane with both viewing arrows directed downward, normal to the horizontal trace.

The arrows in the figure are parallel to each other, not opposed. The section below is therefore the view obtained while looking downward across plane A–A.

1.2 Section lining

The thin lines drawn over cut material are called section lines or hatching. General conventions include:

• use thin, uniformly spaced lines, commonly at 45° to the main outlines;
• change the angle or spacing for adjacent components in an assembly;
• use the same pattern for separated regions belonging to one component;
• interrupt hatching around dimensions or notes when necessary for legibility;
• avoid spacing so close that hatching appears as a solid tone; and
• follow organization-specific material patterns only when the pattern is defined in the drawing or referenced standard.

Hatching does not mean that the component is physically made from diagonal layers. It is a symbolic indication that the cutting plane intersects solid material.

1.3 Visible and hidden detail

Visible boundaries behind the cutting plane are normally shown. Hidden lines are generally omitted from sectional views because the purpose of sectioning is to eliminate visual clutter. A hidden line may be retained when it communicates an important feature that cannot be shown more clearly elsewhere.

Centerlines remain appropriate for bores, shafts and symmetric features. A cutting-plane line is not reproduced in the resulting section unless it has another necessary function.

2. Types of Section

2.1 Full section

A full section results when one cutting plane passes completely through the object. It is suitable when major internal features lie in a common plane. Typical applications include bearing housings, terminal-block bodies and cylindrical cable-entry components.

Construction procedure:

1. Choose a plane that passes through the important internal features.
2. Draw and identify its trace in an adjacent view.
3. Place consistent viewing arrows normal to the trace.
4. Imagine the material in front of the plane removed.
5. Project the remaining boundaries into the sectional view.
6. Hatch only the material physically intersected by the plane.
7. Add centerlines, dimensions and necessary annotations.

2.2 Half section

A half section is used mainly for objects symmetric about one or more center planes. Two perpendicular cutting planes conceptually remove one quarter of the object. One half of the resulting view shows internal geometry, while the other half shows the exterior.

The dividing boundary is normally a centerline, not a visible object line. Hidden lines are generally omitted on both halves unless indispensable. A half section should not be used for a substantially asymmetric object because it could imply symmetry that does not exist.

2.3 Offset section

An offset section uses a cutting plane that changes direction so it can pass through several features that do not lie in one straight plane. The bends are shown on the cutting-plane trace, but the sectional view is conventionally drawn as though the cutting plane were a single plane. The bend locations are therefore not shown as edges in the section.

This technique is useful for a flange containing non-collinear holes or an enclosure with cable passages at different transverse positions. Offsets should be arranged so that the projected feature order remains understandable; arbitrary offsets can create a misleading apparent geometry.

2.4 Broken-out section

A broken-out section removes only a local portion of a view to reveal a nearby internal feature. Its boundary is drawn as an irregular freehand or zigzag break line in accordance with the applicable standard. It does not require a cutting-plane trace or viewing arrows.

The depth must be evident from geometry, a centerline, another feature or a note. Broken-out sections are efficient for showing a keyway, local wall thickness or shallow counterbore without sectioning the entire component.

2.5 Revolved section

A revolved section shows the cross-sectional shape of a slender feature directly on its main view. A cutting plane is imagined perpendicular to the feature’s axis, and the resulting cross-section is rotated 90° into the plane of the drawing.

Revolved sections are used for arms, spokes, busbars, structural rails and shafts with non-circular profiles. Their outlines are conventionally thin when superimposed on the view, subject to the selected drawing standard. If superposition would obscure detail, a removed section may instead be placed elsewhere and identified.

3. Special Sectioning Conventions

Engineering conventions sometimes depart from a literal physical slice to improve communication.

3.1 Ribs, webs and spokes

A thin rib, web or spoke is normally not hatched when the cutting plane passes longitudinally through it. Hatching it would falsely suggest a much greater thickness. Its outline is still shown. When the cutting plane passes transversely across the same feature, it is hatched normally.

3.2 Standard fasteners and shaft-like parts

In assembly sections, bolts, nuts, washers, screws, pins, rivets, keys, shafts and similar standard parts are commonly left unsectioned when the cutting plane passes longitudinally through them. They may be sectioned when cut transversely or when a detailed part drawing specifically requires it. The applicable ISO, ASME or organizational convention must be followed consistently.

3.3 Thin features

Very thin cut regions may be filled solid instead of hatched when normal section-line spacing would be unreadable. A visible gap should separate adjacent solid-filled components so that they do not merge graphically.

3.4 Assemblies

Adjacent components require distinguishable hatch angles or spacings. Areas belonging to the same component should retain the same hatching. This visual continuity is important when complex electrical assemblies contain insulation, conductors, housings and mechanical supports.

4. Geometric Basis of Auxiliary Views

The six principal orthographic views project onto mutually perpendicular principal planes. If a surface is inclined to a principal plane, it appears foreshortened in that view. A true-shape view is obtained by projecting onto an auxiliary plane parallel to the surface.

Let a point have position vector \mathbf{p}, and let an auxiliary projection plane pass through \mathbf{p}₀ with unit normal \mathbf{n}. Its orthogonal projection onto the plane is

Here, \mathbf{p}' is the projected point. The equation applies to orthogonal projection and requires \mathbf{n}\cdot\mathbf{n}=1. If a non-unit normal is used, the subtracted term must be divided by \mathbf{n}\cdot\mathbf{n}. Coordinates must use one consistent unit.

For a line of true length L making angle \alpha with the projection plane, the projected length is

This relationship assumes orthogonal projection. When the line is parallel to the projection plane, \alpha=0° and L_p=L. When the line is perpendicular to the plane, \alpha=90° and it projects as a point.

Worked Example: Foreshortened length

A 75 mm edge makes an angle of 35° with a principal projection plane. Its orthographic projected length is

Thus, approximately 61.4 mm is seen in the principal view. An auxiliary plane parallel to the edge would display its true 75 mm length.

For a planar area A projected orthogonally onto another plane, the projected area is

where \beta is the angle between the normals of the two planes. This formula applies to a single planar region. If the auxiliary plane is parallel to the feature plane, their normals are parallel, \beta=0°, and the true area is obtained.

5. Primary Auxiliary Views

A primary auxiliary view is projected directly from a principal view. The selected inclined plane must first appear edge-on in the source view. A new reference or fold line, commonly designated x₁, is drawn parallel to that edge view. Projectors are then drawn perpendicular to x₁.

Figure: The reference line x₁ is parallel to the inclined edge AB; auxiliary projectors are perpendicular to x₁.

5.1 Manual construction procedure

1. Identify a principal view in which the required surface appears as an edge.
2. Draw x₁ parallel to that edge, leaving adequate space for the auxiliary view.
3. Draw light projectors from every required vertex perpendicular to x₁.
4. From a companion principal view, measure each point’s perpendicular distance from the original principal reference line.
5. Transfer those distances onto the corresponding auxiliary projectors, preserving the correct side of x₁.
6. Connect points in their topological order.
7. determine visible and hidden boundaries from the viewing direction.
8. Darken final lines, add centerlines and dimension only true-size geometry.

The location of x₁ affects drawing layout but not the size or shape of the auxiliary view. Errors usually arise from making x₁ perpendicular rather than parallel to the edge view, or from transferring distances from the wrong principal view.

Worked Construction: Inclined mounting plate

An inclined rectangular mounting face has true dimensions 60 mm × 35 mm and contains a central hole of diameter 20 mm. In the front view, the face appears edge-on.

• Draw x₁ parallel to the 60 mm edge view.
• Project its four corners and hole center perpendicular to x₁.
• Transfer the four corresponding depths from the top view.
• Join the corners to obtain the 60 mm × 35 mm true-shape rectangle.
• Draw the hole as a true circle of diameter 20 mm.

In a principal view the hole may appear elliptical because its circular plane is inclined. It is dimensioned most clearly in the auxiliary view, where its true circular shape is visible.

6. Secondary Auxiliary Views

A primary auxiliary view is not always sufficient. A surface may be oblique to all principal planes and fail to appear edge-on in any principal view. Two successive transformations are then required:

1. a primary auxiliary view makes the required surface appear edge-on; and
2. a secondary auxiliary view looks perpendicular to that surface, revealing its true shape.

Figure: Successive projection for a secondary auxiliary view. Each new reference line is parallel to the edge view used at that stage.

6.1 Detailed secondary construction procedure

Assume the target plane is oblique in all principal views.

Stage A—create the primary auxiliary view

1. Select a line lying in the target plane that can be made true length in a suitable principal or auxiliary construction.
2. Establish x₁ parallel to the appropriate edge or reference direction.
3. Project perpendicular to x₁.
4. Transfer depths from the companion principal view. The resulting primary auxiliary view must make the target plane appear as one straight edge, designated CD in the figure.
5. Verify that every point belonging to the target plane lies on edge CD. If not, the plane has not yet been obtained edge-on.

Stage B—construct the secondary auxiliary view

1. In the primary auxiliary view, draw x₂ parallel to edge CD.
2. Draw projectors from all target-plane points perpendicular to x₂.
3. For each point, measure its signed perpendicular distance from x₁ in the source view used to generate the primary auxiliary view.
4. Transfer that same distance along the corresponding secondary projector from x₂. Keep points on the correct side of the fold line.
5. Connect the transferred points in their original sequence.
6. Add circles, slots and other features using transferred center points and boundary points. A circle should appear circular only if its plane is parallel to the secondary auxiliary plane.
7. Check closure, symmetry, equal lengths and feature relationships before darkening the view.

“Signed distance” means that the side of a reference line is retained rather than transferring only an unsigned magnitude. This prevents reflected or inside-out constructions.

6.2 Verification methods

A secondary auxiliary construction is credible when:

• x₂ is parallel to the target plane’s edge view;
• all projectors are perpendicular to x₂;
• transferred distances correspond point by point;
• the final polygon closes;
• known parallel edges remain parallel;
• a known rectangle has right angles and its specified dimensions; and
• a circular feature in the target plane appears as a circle of true diameter.

7. Dimensioning and Drawing Selection

Dimensions should be placed in the view that shows a feature most clearly and, where possible, in true size. A hole on an inclined face should normally be located and sized in its true-shape auxiliary view. Internal diameters, counterbores and wall thicknesses are usually clearest in sections.

Avoid:

• dimensioning to hidden lines;
• repeating the same dimension in several views;
• placing dimensions on heavily hatched regions when clearer space exists;
• using a sectional or auxiliary view that adds no information; and
• showing an entire auxiliary view when a partial auxiliary view would suffice.

A partial auxiliary view may show only the inclined surface and its directly related features. A break line can indicate the omitted portion.

8. Applied Case: Power-Electronics Enclosure

Background

This is an illustrative case. A design team is developing an aluminium enclosure for a power converter. The enclosure contains an inclined connector face, two internal cable passages, cooling fins and mounting ribs.

Problem

The initial three-view drawing contains numerous hidden lines. The connector face appears foreshortened, making the location of four threaded holes difficult to inspect. Two cable passages lie on different center planes, and a longitudinal section through a mounting rib makes the rib appear undesirably thick.

Analysis

No single conventional view communicates all features effectively:

• the internal cable passages require sectioning;
• their centerlines are not collinear, favouring an offset section;
• the connector face requires an auxiliary true-shape view;
• the mounting rib requires the longitudinal-rib convention; and
• a local gasket recess requires only limited exposure.

Approach

The team prepares:

1. an offset section passing through both cable passages;
2. a primary auxiliary view normal to the inclined connector face;
3. a broken-out section around the gasket recess;
4. an unhatched longitudinal representation of the mounting rib; and
5. a revolved section of one cooling fin to specify its tapered profile.

The auxiliary view shows the connector face as a true rectangle. The four threaded-hole centers are dimensioned from two mutually perpendicular datums on that face. The offset section shows both passages without retaining unnecessary hidden lines.

Outcome

The revised drawing reduces ambiguity during CNC setup and inspection. Hole positions can be checked directly from true-shape dimensions, while the section views distinguish cable passages from cooling and mounting features. The drawing package also records the applicable projection method, units, scale, material and revision.

Learning Points

• Different view types solve different communication problems.
• A minimum-view strategy is preferable to adding views indiscriminately.
• Conventional exceptions, such as not hatching a longitudinal rib, prevent false geometric impressions.
• Auxiliary dimensions should be tied to functional datums rather than arbitrary drawing edges.

9. CAD, Model-Based Definition and Automated Checking

Modern CAD systems generate sections and auxiliary views from three-dimensional models. A user typically selects a parent view, defines a cutting line or inclined edge, specifies a direction and places the derived view. Associativity allows views to update after model changes.

Automation does not remove the need for engineering judgment. Common digital errors include reversed section arrows, incorrect hatch assignment, accidental display of hidden lines, inappropriate rib sectioning and auxiliary views derived from the wrong edge. CAD output should be checked geometrically rather than accepted because it was generated automatically.

Model-based definition may attach dimensions and tolerances directly to a 3D model, but 2D derived views remain widely used in manufacturing, maintenance, education and contractual documentation. AI-assisted drafting can identify clutter or suggest cutting planes, yet safety-critical drawings require accountable human review and controlled revision.

10. Standards, Governance and Professional Practice

Section and projection conventions vary in detail among ISO, ASME and organizational standards. A drawing should clearly state whether first-angle or third-angle projection is used and should not mix conventions.

Professional practice requires:

• traceable revisions and approvals;
• consistent line types, symbols and terminology;
• correct units, scale and tolerancing;
• protection of controlled or security-sensitive design data;
• verification that a section does not imply nonexistent material; and
• independent checking for safety-critical electrical equipment.

Ambiguous drawings may lead to machining errors, inadequate insulation clearances, compromised enclosure protection or unsafe assembly. Clear graphic communication is therefore an engineering responsibility, not merely a drafting preference.

11. Common Errors and Best Practices

A sound workflow first identifies the communication problem, then selects the simplest valid view. The final drawing should be inspected as a manufacturing document rather than merely as a geometric exercise.

Chapter Summary

Sectional views reveal internal geometry by representing an imaginary cut through an object. Full sections expose extensive interior detail; half sections combine internal and external information for symmetric objects; offset sections pass through non-collinear features; broken-out sections reveal local details; and revolved sections display transverse profiles of slender members. Correct hatching, viewing-arrow direction and special conventions for ribs, webs, spokes and fasteners prevent misleading representations.

Auxiliary views are orthographic projections onto non-principal planes. A primary auxiliary view is constructed with a reference line parallel to the edge view of the inclined surface and projectors perpendicular to that reference line. A secondary auxiliary view uses successive projection to reveal the true shape of a plane oblique to all principal planes. Accurate point correspondence, signed-distance transfer and geometric verification are essential in both manual and CAD workflows.

Key Terms

Auxiliary plane: A projection plane other than a principal horizontal, frontal or profile plane.

Auxiliary view: An orthographic view projected onto an auxiliary plane.

Broken-out section: A local section bounded by an irregular break line.

Companion view: A related view supplying distances unavailable in the source view.

Cutting plane: An imaginary plane used to expose internal geometry.

Cutting-plane line: The line showing the location and direction of a cutting plane.

Edge view: A projection in which a plane appears as a line.

Fold line: A reference line representing the intersection or conceptual hinge between projection planes.

Foreshortening: Reduction of apparent size caused by inclination to a projection plane.

Full section: A sectional view produced by a plane passing completely through an object.

Half section: A view combining one sectional half and one exterior half of a symmetric object.

Offset section: A section created by a cutting plane that changes direction to include several features.

Orthogonal projection: Projection using rays perpendicular to the projection plane.

Primary auxiliary view: An auxiliary view projected directly from a principal view.

Revolved section: A cross-section rotated into the plane of the main view.

Secondary auxiliary view: An auxiliary view projected from a primary auxiliary view.

Section lining: Thin lines identifying solid material intersected by a cutting plane.

Signed distance: A transferred distance that retains which side of a reference line contains the point.

True shape: The undistorted shape seen when the projection plane is parallel to the feature plane.

Viewing arrow: An arrow indicating the direction from which a sectional or derived view is observed.

Review Questions

Short Answer Questions

1. Why must viewing arrows be normal to a straight cutting-plane trace and point in a consistent direction?
2. When should a longitudinal rib be left unhatched?
3. What distinguishes a broken-out section from a full section?
4. Why is the first auxiliary reference line drawn parallel to the surface’s edge view?
5. What is meant by signed-distance transfer in auxiliary construction?

Long Answer Questions

1. Explain the procedure for constructing and checking a full sectional view of a component containing two aligned bores.
2. Compare full, half, offset, broken-out and revolved sections with suitable engineering applications.
3. Describe the construction of a primary auxiliary view, including the role of the companion principal view.
4. Explain, step by step, how a secondary auxiliary view reveals the true shape of an oblique plane.
5. Discuss how standards, CAD associativity and human review affect the reliability of sectional and auxiliary drawings.

Analytical / Application Questions

1. An enclosure contains three non-collinear cable passages and a longitudinal strengthening web. Select an appropriate sectional method and explain how the web should be represented.
2. A 100 mm line appears 86.6 mm long in an orthographic view. Assuming orthogonal projection, determine its acute angle with the projection plane and identify how an auxiliary view could display its true length.
3. An inclined circular mounting face appears elliptical in every principal view. Develop a view-selection strategy to show its true diameter and locate four equally spaced holes clearly.

Multiple Choice Questions with Answers

Question 1

Which statement correctly describes the viewing arrows for one straight cutting-plane trace?

A. They point in opposite directions along the trace.

B. They point consistently in one direction normal to the trace.

C. They are parallel to the trace and face inward.

D. Their direction is unrelated to the resulting section.

Correct Answer: B. They point consistently in one direction normal to the trace.

Question 2

Which sectional method is most suitable for showing several important holes whose axes do not lie in one straight cutting plane?

A. Offset section

B. Half section

C. Revolved section

D. Broken-out section

Correct Answer: A. Offset section

Question 3

When a cutting plane passes longitudinally through a thin rib, the rib is normally:

A. removed completely from the view.

B. shown only by hidden lines.

C. shown in outline but not hatched.

D. hatched with double spacing.

Correct Answer: C. shown in outline but not hatched.

Question 4

What boundary normally separates the sectioned and exterior halves of a half section?

A. A cutting-plane line

B. A centerline

C. A hidden line

D. An irregular break line

Correct Answer: B. A centerline

Question 5

In constructing a primary auxiliary view, reference line x₁ should be drawn:

A. parallel to the edge view of the required surface.

B. perpendicular to the edge view of the required surface.

C. parallel to every auxiliary projector.

D. through the centroid of the component only.

Correct Answer: A. parallel to the edge view of the required surface.

Question 6

A 50 mm line makes an angle of 60° with an orthographic projection plane. What is its projected length?

A. 25 mm

B. 43.3 mm

C. 50 mm

D. 100 mm

Correct Answer: A. 25 mm

Question 7

What is the principal purpose of a secondary auxiliary view?

A. To add hatching to a full section

B. To show the true shape of a plane oblique to the principal planes

C. To replace all principal orthographic views

D. To show only the exterior of a symmetric object

Correct Answer: B. To show the true shape of a plane oblique to the principal planes

Question 8

After a target plane appears edge-on as CD in a primary auxiliary view, the second reference line x₂ is drawn:

A. perpendicular to CD.

B. at 45° to CD.

C. parallel to CD.

D. through CD without regard to direction.

Correct Answer: C. parallel to CD.

Question 9

Which section is most appropriate for revealing only a local counterbore while retaining the remainder of the exterior view?

A. Full section

B. Offset section

C. Half section

D. Broken-out section

Correct Answer: D. Broken-out section

Question 10

Which feature confirms that an auxiliary view is parallel to the plane of a circular hole?

A. The hole appears as a true circle.

B. The hole appears as a straight line.

C. The hole appears as a parabola.

D. The hole disappears from the view.

Correct Answer: A. The hole appears as a true circle.