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Engineering Graphics and CAD · Lesson 10 of 35

Auxiliary views and true shape

Show the true shape of an inclined surface that no principal view can show without distortion.

Readiness check

Learning objectives

By the end of this lesson you can:

Explain why inclined surfaces foreshorten in principal views.
Construct a primary auxiliary view projected from an inclined face.
Transfer true-length and true-shape information into the auxiliary view.
Dimension features in the auxiliary (true-shape) view rather than a foreshortened one.
Decide when an auxiliary view is necessary.

Check your starting point

Five to ten minutes.

If a flat face is tilted away from you, does it look its true size, or smaller?
To see a tilted face truly, from what direction must you look at it?
If a hole sits on a slanted face, which view should carry its true spacing dimensions?

Interpretation.

Q1: Smaller (foreshortened), because you see it at an angle. This is the whole reason for auxiliary views.
Q2: Straight on, perpendicular to that face. That is what an auxiliary view provides.
Q3: The view that shows the face truly, the auxiliary, not a distorted principal view. Skill 10.4 covers this.

You need L5-L6 (projection and view reading).

0 or 1 weak itemsContinue with this lesson.

2 weak itemsReview Lesson 5, Lesson 6, then return.

3 or more weak itemsWork through the prerequisite examples before continuing.

The core idea

What it is. An auxiliary view is a view projected onto a plane parallel to an inclined surface, so that surface appears in its true shape. It is taken looking perpendicular to the inclined face, not along a principal direction.

Why an engineer needs it. Many parts have surfaces slanted to all three principal planes. In every principal view such a face foreshortens (appears smaller and distorted), so its true shape and the true positions of features on it cannot be seen or dimensioned there. The auxiliary view is the only way to show them truly.

What problem it solves. It gives the true shape of an inclined face and the true spacing of features on it, which principal views cannot.

What goes wrong when it is ignored. Dimensioning an inclined face in a foreshortened principal view gives wrong distances; features drilled to those wrong distances land in the wrong place. The part fails to assemble or function.

A simple mechanical example. A bracket has a face cut at an angle, and two holes are drilled perpendicular to that slanted face. In the front and side views the slanted face is a foreshortened line or a squashed shape, and the hole spacing appears shortened. An auxiliary view, looking square at the slanted face, shows the face true and the holes at their real spacing.

How an auxiliary view is made:

Identify the inclined face and the principal view where it appears as an edge (a line).
Set a reference (fold) line parallel to that edge.
Project perpendicular to the inclined face (perpendicular to that edge) into the new view.
Transfer depths from the related principal view, measured from the reference line.
The inclined face now appears in true shape; dimension features here.

Part 2: Internal and inclined geometry.

Check: explain the decision in your own words before using a CAD command.

The concept. Project perpendicular to the inclined face so its foreshortened shape becomes true size and the circular feature becomes a true circle.

The skills, taught in order

Skill 10.1 - Recognize foreshortening

Concept. A face not parallel to a principal plane never shows true shape in that view. Terminology. Foreshortening is the apparent shortening of a surface seen at an angle. An inclined surface is tilted to one or more principal planes. Procedure. For each face, ask whether it is parallel to a principal plane. If not, expect it to foreshorten in the principal views. Reasoning. Only faces parallel to the viewing plane show true shape; tilted faces compress. Failure mode. Treating a foreshortened face as true size and dimensioning it there. Check. Identify which face on a part foreshortens in all principal views.

Skill 10.2 - Find the edge view and set the reference line

Concept. An auxiliary is projected from the principal view where the inclined face appears as an edge (a line). Terminology. The edge view of a face is the view where it appears as a line. The reference (fold) line is drawn parallel to that edge. Procedure. Locate the view where the inclined face is a straight line. Draw the reference line parallel to that line, offset to where the auxiliary will sit. Reasoning. Projecting perpendicular to the edge view yields the true shape; the reference line anchors depth transfer. Failure mode. Projecting from a view where the face is not an edge, which does not give true shape. Check. Identify the edge view of the inclined face before projecting.

Skill 10.3 - Project perpendicular and transfer depth

Concept. Project perpendicular to the inclined edge and transfer depths from the related principal view. Terminology. True length is an edge shown at actual length; true shape is a face shown at actual shape. Procedure. Draw projectors perpendicular to the edge view into the auxiliary. Take each point's depth from the related principal view, measured from the reference line, and mark it along its projector. Reasoning. Perpendicular projection removes foreshortening; consistent depth transfer places every point correctly. Failure mode. Measuring depths inconsistently, distorting the true shape. Check. Confirm depths in the auxiliary match the related principal view.

Skill 10.4 - Dimension in the true-shape view

Concept. Features on the inclined face are dimensioned in the auxiliary, where they are true. Terminology. A functional dimension locates a feature by what it must achieve; here it must be placed where the geometry is true. Procedure. Place size and location dimensions for the inclined face and its features in the auxiliary view, not in the foreshortened principal views. Reasoning. Dimensions taken in a foreshortened view are wrong; the true-shape view gives correct values. Failure mode. Dimensioning the hole spacing in a squashed principal view, producing wrong distances. Check. Confirm the inclined-face dimensions appear only in the auxiliary.

Worked example 1: true shape of an inclined face with a hole

Problem. A wedge-shaped block has one face inclined at 30 degrees to the base. A hole of diameter 10 is drilled perpendicular to that inclined face, centred on it. In the front view the inclined face appears as an edge (a slanted line); in the top view it foreshortens. Build the auxiliary view that shows the inclined face true and the hole round and correctly placed.

Planning. Use the front view (edge view of the face). Set a reference line parallel to the slanted edge, project perpendicular to it, and transfer depths from the top view.

Solution.

Edge view. In the front view, the inclined face is a straight slanted line: this is its edge view.
Reference line. Draw a reference line parallel to that slanted edge, offset to where the auxiliary will sit.
Project perpendicular. Draw projectors from the ends of the slanted edge, perpendicular to it, into the auxiliary region.
Transfer depth. The face has a depth (its width into the part), read from the top view. Transfer that depth from the reference line along the projectors, marking the face's true outline.
The hole. The hole axis is perpendicular to the inclined face, so in the auxiliary (looking square at the face) the hole appears as a true circle of diameter 10 at the face centre. In the foreshortened top view it would appear as an ellipse.
Result outline. The inclined face appears in true shape (its real rectangle) with a true round hole centred on it.

Result. The auxiliary view shows the 30-degree face at true size with the hole as a true 10-diameter circle, neither of which the principal views show correctly.

Why the method works. Looking perpendicular to the face removes foreshortening, so the face and the hole appear at their real shape and size.

How to verify independently. The hole in the auxiliary must be a true circle (equal width and height). If it comes out elliptical, the projection was not perpendicular to the face, and the construction needs correcting.

Worked example 2: dimensioning an inclined slotted boss

Problem. A part has an inclined boss (a raised pad tilted to all principal planes) carrying a slot and two holes that must locate a mating part. A colleague dimensions the slot length and hole spacing in the front view. Show why that is wrong, build the true-shape auxiliary, and place the functional dimensions there. The complication is that the functional dimensions must be true, and only the auxiliary makes them true.

Planning. Establish the edge view, build the auxiliary, and compare the (wrong) foreshortened dimensions with the (correct) true-shape dimensions.

Solution.

Why the front-view dimensions are wrong. In the front view the inclined boss foreshortens, so the slot length and hole spacing appear shorter than they really are. A maker building to those values would cut the slot too short and space the holes too closely, and the mating part would not fit.
Edge view and auxiliary. Find the view where the boss face is an edge, set the reference line parallel to it, and project perpendicular to build the auxiliary true-shape view of the boss.
Transfer features. Bring the slot and the two holes into the auxiliary by depth transfer, so they sit at true positions.
Dimension in the auxiliary. Place the slot length and the hole spacing in the auxiliary view, where they are true. These are the functional dimensions the mating part depends on.
Leave the principal views for other dimensions. The overall block sizes can be dimensioned in the principal views; only the inclined-face features move to the auxiliary.

Comparison of approaches. Dimensioning in the front view is convenient but wrong (foreshortened). Dimensioning in the auxiliary is the only correct option for the inclined-face features. The small extra effort of the auxiliary prevents a non-assembling part.

Result. The functional slot and hole dimensions belong in the true-shape auxiliary; the front-view values were foreshortened and would have produced a part that does not fit.

Independent check. Compare the slot length in the front view and the auxiliary: the auxiliary value is larger (true), the front value smaller (foreshortened). The true value is the one to build to.

Misconceptions and diagnostics

Misconception	Why it seems reasonable	Why it is wrong	Evidence that reveals it	Correction	Diagnostic question
"The side or top view shows the slanted face at true size."	It is a standard view.	An inclined face foreshortens in every principal view; only an auxiliary shows it true.	The face appears smaller and a hole on it appears elliptical.	Build an auxiliary perpendicular to the face.	"Is this face parallel to the viewing plane? If not, it foreshortens."
"Dimension features wherever it is convenient."	Any view seems fine.	Dimensions in a foreshortened view are wrong; the true-shape view gives correct values.	Foreshortened hole spacing is smaller than the true spacing.	Dimension inclined-face features in the auxiliary.	"Is this dimension placed in a true-shape view?"
"A hole always looks round."	Holes are round.	On a foreshortened face a round hole projects as an ellipse.	The hole is elliptical in the top view but round in the auxiliary.	Read and dimension the hole in the auxiliary where it is round.	"In which view is this hole actually round?"

Practice ladder

Level A - Recognition

Task. For six parts, identify which surface needs an auxiliary view and in which principal view it appears as an edge. Deliverable. Six short answers. Success criteria. At least five inclined faces and their edge views correctly identified. Answer guidance. The auxiliary is projected from the view where the face is a line. Common errors. Choosing a view where the face is not an edge. Difficulty. Low.

Level B - Guided application

Task. Project an auxiliary view of a given inclined face with the reference line and one projector provided. Deliverable. The completed auxiliary showing true shape. Success criteria. Perpendicular projection; depths transferred; face true; any hole round. Answer guidance. Measure depths from the reference line, consistent with the related principal view. Common errors. Non-perpendicular projectors distorting the shape. Difficulty. Medium.

Level C - Independent application

Task. Build a full auxiliary view of an inclined-face part from scratch, including features on the face. Deliverable. The auxiliary with features at true position. Success criteria. True shape achieved; features round/true; consistent depth transfer. Answer guidance. Find the edge view first; everything else follows. Common errors. Forgetting to transfer depth, flattening the view. Difficulty. Medium to high.

Level D - Transfer and design

Task. For a part with an inclined functional face, decide whether an auxiliary is required; if so, produce it and place the functional dimensions there, justifying why the principal views cannot carry them. Deliverable. The auxiliary (if needed) plus a justification. Success criteria. Correct decision; functional dimensions in the true-shape view; justification references foreshortening. Answer guidance. If the face is inclined to all principal planes and carries functional features, an auxiliary is required. Common errors. Dimensioning the inclined features in a principal view. Difficulty. High.

Working with AI, and proving it yourself

Use AI as a tutor

Useful AI support:

Ask it to explain why a face foreshortens and confirm with your part.
Ask it to outline the auxiliary-view steps and follow them.
Ask for practice inclined-face parts.

Limits:

A text assistant cannot verify your projection is perpendicular or your depths are consistent.
It may suggest dimensioning in a principal view.

Verify AI output against: the perpendicular-projection rule, the depth-transfer check, and the true-shape dimensioning rule (round hole must be round in the auxiliary).

Prove it yourself

A plausible but incorrect AI answer, and how to catch it. You ask, "Where should I dimension the holes on the slanted face?" and the assistant replies: "Put them in the front view; it is the main view, so its dimensions are authoritative."

This is wrong when the face is inclined. Detect it with the foreshortening rule: the slanted face compresses in the front view, so hole spacing there is smaller than true. The evidence is direct: measure the spacing in the front view and in the auxiliary; they differ, and the auxiliary value is the true one. Correct conclusion: dimension inclined-face features in the true-shape auxiliary, not the foreshortened principal view.

Retrieval and spaced review

Why does an inclined face foreshorten in principal views?
From which view is an auxiliary projected, and in what direction?
How are depths placed in the auxiliary?
Which view carries the functional dimensions of an inclined face?
What shape is a round hole on a foreshortened face in a principal view?
When is an auxiliary view necessary?
Cumulative (L5): How does the reference (fold) line in an auxiliary relate to the fold lines of the glass box?
Reconstruction task: From memory, sketch the wedge from Worked Example 1 and its auxiliary showing a true round hole.

Answers. 1: because it is not parallel to the viewing plane, so it appears compressed. 2: from the view where the face is an edge, projecting perpendicular to that edge. 3: transferred from the related principal view, measured from the reference line. 4: the true-shape auxiliary. 5: an ellipse. 6: when a face is inclined to all principal planes and its true shape or feature positions are needed. 7: it is another fold line, parallel to the inclined edge rather than a principal direction.

Suggested review intervals. 1 day, 3 days, 7 days. Rebuild an auxiliary from a fresh inclined-face part at day 7.

Reference mapping and next step

Read further

Giesecke ch.8
ISO 128-3:2022.

Standards details must be checked against the current official edition used by your institution or employer.

Finish the lesson

You can now: recognize foreshortening; find the edge view; project an auxiliary perpendicular to an inclined face; transfer depths; and dimension features in the true-shape view.

Self-assessment checklist.

I can spot a face that foreshortens in all principal views.
I project auxiliaries perpendicular to the inclined edge.
I transfer depths from the related principal view.
A round hole comes out round in my auxiliary.
I dimension inclined-face features in the auxiliary.

Next lesson: L11 - Dimensioning principles and presentation (Part III begins). Why it follows: you can now produce every kind of view (principal, section, auxiliary) needed to show a part's geometry. Part III turns to defining that geometry with size, starting with the ISO 129-1 rules for placing dimensions clearly and unambiguously, including on the section and auxiliary views you just learned.

Required files or submissions: submit your Level C auxiliary view. Optional extension: find a part with an angled face (a clamp jaw, a chamfered block) and produce the auxiliary that would carry its true-shape dimensions.

End of Part II (L8-L10). Part III (Dimensioning and technical definition) begins with L11-L17 in the file 12-part3-lessons.md.

# Engineering Graphics and CAD - Phase 4: Full Lesson Content, Part III (Dimensioning and Technical Definition), L11-L14

Lessons L11-L17 make up Part III. This file holds L11-L14 (dimensioning principles, functional dimensioning, tolerances, and limits and fits). L15-L17 are in 13-part3-lessons-cont.md. Same MechCompass structure and conventions. All arithmetic is checked and shown. Normative table values (ISO 286 deviations, IT grades) are used illustratively and flagged for verification against the official standard, per the course accuracy policy. No em dashes.