Catalogue axonometric of a bearing bracket: scale, ellipses and choice of oblique system
A catalogue view is required of a cast-aluminium bearing bracket: a rectangular base 80 × 50 × 12 with two Ø10 fixing holes, a vertical web, and a Ø40 boss with a Ø22 through bore whose axis is horizontal and parallel to the 80 mm side. A junior drafter has produced an "isometric" with every edge laid off at full measured length on 30° axes, has drawn the front face of the boss as a true circle, has included the hidden lines of the bore, and has written "Ø40" along the ellipse with an arrow. The client also wants a second, quicker oblique view for a patent figure and has asked whether cavalier or cabinet is better. A colleague has measured the 80 mm base edge on the isometric print with a rule, obtained 80 mm and declared the drawing correct at 1:1.
1. Explain the isometric scale and state what the Ø40 boss face and the Ø22 bore become on this drawing. Comment on the colleague's measurement of 80 mm.
Read the worked answer
In a true isometric projection the three axes are equally inclined to the picture plane, so every length parallel to them is foreshortened by cos 35.26° = 0.816. Circles on the three coordinate planes become ellipses with major axis 1.22d perpendicular to the isometric axis normal to that plane, and minor axis 0.71d.
No one wants to multiply every dimension by 0.816, so the standard practice is an isometric drawing: true lengths are laid off along the 30° axes, which makes the picture the true projection enlarged by 1/0.816 = 1.22. On this drawing, therefore:
- the Ø40 boss face becomes an ellipse with major axis ≈ 1.22 × 40 = 48.8 mm and minor ≈ 28.3 mm;
- the Ø22 bore becomes an ellipse with major ≈ 26.8 mm and minor ≈ 15.6 mm.
On a true projection built on the isometric scale, the major axis of a circle's ellipse comes out equal to the diameter - 40 mm - which is a neat check on which convention is in use.
The colleague's measurement proves nothing: measuring 80 mm on a full-scale isometric means the part has been enlarged 1.22 times, so the print is not 1:1 and must never be scaled. Axonometrics are illustrative; dimensions belong in the orthographic views.
2. Identify the representation errors in the junior's isometric and state what should be drawn instead.
Read the worked answer
Three errors, plus one bad habit.
- The boss face drawn as a circle. In isometric no coordinate plane is parallel to the picture plane, so no circle stays a circle. The boss face is normal to the 80 mm direction, so it must be an ellipse whose major axis is perpendicular to the isometric line of that 80 mm axis, with major 1.22 × 40 ≈ 48.8 mm and minor ≈ 28.3 mm. Use the four-centre approximation for speed, but remember it is only accurate near the mid-points and sags at the ends - fair the curve if the boss is prominent.
- Hidden lines of the bore. Axonometrics omit hidden lines unless the shape is otherwise ambiguous; here the bore is fully described by the visible ellipse and the boss outline. Drawing the hidden bore clutters the view and, worse, invites the reader to interpret the thin hidden lines as thread or groove features.
- "Ø40" written along the ellipse with an arrow. A dimension on an axonometric runs along a foreshortened direction and cannot be measured; if dimensions must appear at all, they go on one face parallel to a principal plane, and normally they are simply left to the orthographic views. Delete it.
Bad habit: two continuous thick circles or a thick runout indicate the drafter is copying orthographic habits; check line weights throughout, since axonometrics rely on a clean thick/thin hierarchy to read as solids.
3. Advise the client on cavalier versus cabinet for the patent figure, giving reasons, and state the practical drawing rules for whichever you recommend.
Read the worked answer
Both are oblique (frontal) projections: the front face is parallel to the picture plane and is therefore drawn true shape and true size, with a single receding axis, typically at 45° (30° and 60° are also used, never 90°). The difference is the receding scale.
- Cavalier: full scale on the receding axis. Simple and directly measurable in all three directions, but a deep object looks stretched and unnatural, because the eye foreshortens depth heavily.
- Cabinet: receding axis at half scale. The apparent distortion is much closer to visual experience and the figure reads as a solid rather than a sheared block.
For a patent or catalogue figure, recommend cabinet, with the receding axis at 45° and depths halved. Practical rules: orient the part so the face carrying the circular features - here the boss and bore - lies in the front plane, so they stay true circles and need no ellipse construction at all, which is the main labour saving; keep the same line hierarchy as orthographic drawings (thick visible edges, thin construction lines only where needed); omit hidden lines unless the shape demands them; and never place dimensions along the receding axis. If the figure must be measurable in all three directions, cavalier is the honest choice - but then say so, and still do not scale it.