Choosing the Pictorial for a Catalogue Page
A small design studio must supply a single pictorial illustration for a printed parts catalogue. The part is a wall bracket: a rectangular block 70 mm wide, 40 mm high and 25 mm deep, with a 45° chamfer cut across one vertical corner of the front face, two Ø10 mm fixing holes through the front face, and one Ø10 mm hole in the top face. The illustration must let a customer see at a glance that the front-face holes are round, must show the 45° chamfer at its true angle, and must fit into an A5 space on the page, drawn with compass, set squares and a scale rule only. A junior draughtsperson proposes an isometric on a 30° grid. The senior illustrator rejects this and proposes cabinet oblique at half scale on the receding axis.
1. Justify the senior illustrator's choice using the geometry of the two projections.
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In isometric projection no face of the block is parallel to the picture plane. All three axes are foreshortened equally (to about 0.816 of true length, drawn full length by convention), every square face becomes a rhombus, and every circle becomes an ellipse with major axis 1.22D and minor axis 0.71D. For Ø10 that is 12.2 mm by 7.1 mm, which needs the four-centre construction and still reads as an oval at catalogue size - the exact opposite of what the brief asks. The 45° chamfer on the front face is also a non-isometric line, so its angle cannot be set out with a protractor at all.
In cabinet oblique the front face is parallel to the picture plane, so it is drawn true shape at full size: the 70 × 40 rectangle, the two Ø10 circles struck with a compass, and the chamfer at a true 45°. Only the receding axis foreshortens, and at half scale the 25 mm depth is drawn 12.5 mm along a 45° line. Cavalier (full depth on the receding axis) would show the depth more strongly but looks obviously distorted at 45°, so cabinet is the correct compromise here.
2. The top-face Ø10 mm hole still has to be added. Explain how it is constructed in cabinet oblique and why it cannot simply be struck as a circle.
Read the worked answer
Only surfaces parallel to the picture plane keep circles round. The top face recedes to the 45° axis, so it is not parallel to the picture plane and its Ø10 hole must be drawn as an ellipse.
Construction:
- Set out the top face as a parallelogram: 70 mm along the horizontal and 12.5 mm (half of 25) along the 45° receding axis, drawn from the two top corners of the front face.
- Draw the two centre lines of the face: one parallel to the horizontal, one parallel to the receding axis, crossing at the hole centre, which is positioned by its two coordinates along these axes.
- Inscribe the ellipse in the parallelogram so that it touches the mid-points of the four sides, using the four-centre approximation (locate the mid-points, draw the two axes of the ellipse at the crossing of the centre lines, find the four centres on the long axis and its perpendicular, and strike the four arcs).
A compass circle of radius 5 mm would represent a hole parallel to the picture plane and would read as a hole drilled into the front face, not the top.
3. Explain why the 45° chamfer cannot be set out with a set square in isometric, and give the correct method.
Read the worked answer
Isometric projection preserves true length only along the three isometric axes and distorts every other length and every angle. The chamfer line is a non-isometric line: it runs across the front face from the top edge to the vertical corner edge, so neither of its ends is measured along a single axis direction and neither its true length nor its true 45° survives.
Drawing it with a 45° set square produces a line that is not 45° on the actual object, so the model would be wrong even if it looks plausible on the sheet.
Correct method - set out by coordinates along the isometric axes:
- On the top edge of the front face, measure the chamfer intercept (say 15 mm) from the corner, along the 30° isometric axis.
- On the vertical corner edge, measure the same intercept, along the vertical isometric axis.
- Join the two points. The drawn line will appear at roughly 60° on paper, not 45°, and this is correct - it must never be scaled or measured from the drawing.
Any additional point on the chamfer is located the same way: two coordinates taken along the isometric axes from the corner.