Representation systems
A drawing is a language: it turns a three-dimensional object into flat figures that any workshop in the world can turn back into the object. The first thing to learn is how to project.
01Projecting
Representing a three-dimensional object on paper requires choosing how to project it. The two families that matter in engineering are:
| System | How it projects | What it is for |
|---|---|---|
| Orthographic projection (views) | Parallel rays, perpendicular to the plane | Manufacturing: it preserves true measurements |
| Axonometry (isometric) | Parallel rays, oblique to the object | Understanding: it shows all three dimensions at once |
| Cavalier (oblique) | One face seen head-on and the depth drawn at an angle | Quick freehand sketch |
| Perspective (central projection) | Rays that converge at a viewpoint | Presentation: it looks like what the eye sees |
In a perspective drawing lengths are distorted and you cannot measure on the drawing. In orthographic projection, on the other hand, every face parallel to the projection plane appears at true size: what you measure on the drawing, with its scale, is what the part measures.
02The six views and the three that suffice
If you imagine the object inside a glass cube and project onto each face, you get six views: front view, top view, left side view, right side view, bottom view and rear view. In practice three are almost always enough: front, top and one side view.
The front view is the main view and should be the one that gives the most information about the shape, normally with the part in its working or machining position. A poor choice forces you to draw more views than necessary.
And there is a rule that organizes the whole drawing: the views line up. The top view shares widths with the front view, and the side view shares heights. This correspondence lets you deduce a missing view and detect errors.
Choose a part and see how its views are arranged in each system. Switching between first- and third-angle projection does not change the views: it changes where they are placed.
03First-angle and third-angle projection
There are two conventions for placing the views on the sheet, and confusing them mirrors the drawing:
| First-angle projection (ISO-E) | Third-angle projection (ISO-A) | |
|---|---|---|
| Idea | The object is between the observer and the plane | The plane is between the observer and the object |
| Top view | Below the front view | Above the front view |
| Left side view | To the right of the front view | To the left |
| Used in | Argentina, Europe, ISO and IRAM | United States, Canada, Japan |
The title block carries the projection symbol: a truncated cone seen from the front and from the side. Without that symbol, a drawing that is manufactured in the other hemisphere may come out mirrored. It is one of the classic costly errors in industry.
04Hidden edges, sections and symmetry
- Dashed line: edges that exist but cannot be seen from that view.
- Section: the part is assumed to be cut by a plane to show the interior; the cut material is hatched at 45°. It avoids filling the drawing with dashed lines.
- Half view and half section: for symmetrical parts, the outer half is drawn and the other half in section.
- Centerline: a chain of dashes and dots, it marks axes of revolution and centers; it is not an edge.
A common case in electronics: the drawing of a metal enclosure includes the flat pattern of the sheet metal before bending, with the views and a section that shows the housing for the circuit board.
05Isometric projection
In isometric projection the three axes form 120° with each other and the three directions are drawn at the same scale. You cannot dimension it accurately, but it is understood at a glance: that is why assembly manuals use it, and why a CAD 3D viewer shows something similar by default.
Today the normal flow is the reverse of the historical one: first the solid is modeled in three dimensions and the program generates the views and sections. But to choose which views to request, check them and dimension them, you have to understand the system: the program does not decide for you.
06In the lab
Take three objects from the workshop—a heat sink, an L bracket, an enclosure cover—and sketch their three views in first-angle projection, keeping the views aligned.
Given two views, draw the third and the isometric. It is the exercise that trains spatial visualization the most, and it is best done before touching the computer.
Draw an asymmetric part in first-angle and in third-angle projection and compare. Check that the symbol in the title block changes and understand what would happen if it were manufactured with the wrong symbol.
07Common mistakes
- Not aligning the views. The top view goes right below the front view, with no offsets.
- Drawing more views than necessary. If two are enough, the third is redundant.
- Omitting the projection symbol in the title block.
- Using a continuous line for hidden edges or the other way around.
- Dimensioning on the perspective instead of on the views.
- Choosing a poor view as the front view, which forces you to add views to understand the part.
08Self-assessment
In first-angle projection, where does the top view go?
Below the front view. In third-angle projection it goes above.
Why does the manufacturing drawing not use central perspective?
Because it distorts lengths and you cannot measure on the drawing; orthographic projection preserves true size.
What does a chain line of dashes and dots mean?
It is a centerline or line of symmetry: it marks centers and axes of revolution, not edges.
How many views are enough to define a cylinder with a through hole?
Two: one showing the diameter and another showing the height, with the corresponding centerlines.
What angle do the axes form in an isometric drawing?
120° with each other, that is, 30° from the horizontal for the two inclined axes.
What is a section for?
To show the interior of the part without filling the view with dashed lines; the cut material is hatched at 45°.
09Further reading
- Frederick E. Giesecke et al. Technical Drawing with Engineering Graphics. 14th ed. (Spanish edition, “Dibujo técnico con gráficas de ingeniería”), Pearson, 2013. The university classic: projections, views, sections and standardization, with hundreds of exercises.
- Thomas E. French and Charles J. Vierck. Engineering Drawing and Graphic Technology. (Spanish edition, “Dibujo de ingeniería y tecnología gráfica”), McGraw-Hill, 1988. Widely used in Argentine universities; a good development of spatial visualization.
- Instituto Argentino de Normalización (Argentine Standardization Institute). IRAM 4502 (Lines) and IRAM 4501 (Representation of views). IRAM. The standards themselves: it is worth reading them once to know exactly what they say.