Isometric sketch from a given multiview (chamfered, notched cube): 04-BS-15, May 2018, Q2

Question 2: Isometric sketch from a given multiview (chamfered, notched cube) (10 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

[Figure not reproduced: source figure. See the official exam paper or the cited reference text.]

Source figure (exam p. 3), reproduced for reference.

Reading the views. In third-angle projection the view above the Front view is the Top view, and the view to its right is the Right-side view. The upper sketch is therefore the Top view, the lower-left the Front and the lower-right the Right side. All three are orthographic. Their short diagonal lines are the ends of chamfers, not receding isometric edges. The three outlines are equal squares, so the object is essentially a cube; call its side 10 units.

A notch 5 × 5 × 5 is removed from the top-front-right corner. It appears as the upper-right square in the Front view, the lower-right rectangle in the Top view (its floor) and the upper-left rectangle in the Side view (its left wall). Its width, height and depth all measure half the cube.
45° chamfers of about 1 unit run round every edge of the L-shaped front face: its outer edges and the two edges where it meets the notch. This produces the inset L outline with corner diagonals in the Front view, the band along the front edge of the Top view, and the band down the front edge of the Side view.
One more chamfer runs along the top-right edge of the rear block, behind the notch. It is the diagonal at the top-right corner of the Front view, the line just inside the right edge of the Top view behind the notch, and the band along the top of the Side view behind the notch.

Checking each feature in all three views, as above, confirms one consistent solid. Each line in one view must project to a line or a point in the others.

Approach

Box in the 10 × 10 × 10 cube on the three isometric axes: vertical, and 30° either side of horizontal. Measure only along those axes, where isometric keeps a constant scale. Next cut the 5-unit notch from the top-front-right corner by stepping in 5 units along each axis. Then locate each chamfer by its two end points, 1 unit along the adjoining faces on each side of the edge it replaces, and join them. Chamfer lines are not parallel to an isometric axis, so they are never measured directly. Finally, darken only the visible edges; hidden lines are omitted in an isometric sketch.

Fig. Q2 — isometric of the chamfered, notched cube, consistent with all three printed views.

The finished pictorial shows the L-shaped front face framed by its chamfers, and the notch's floor, left wall and back wall, with the chamfered corner clipped into the top of the back wall. The top face is L-shaped around the notch and meets the rear top-right chamfer. The right face is L-shaped as well, stepping down in front of the notch. Its bottom-front corner shows the thin chamfer strip.

Topic: Isometric pictorial construction from orthographic views

Key relations: Isometric axes are drawn 120° apart (30° above horizontal, left and right, plus vertical); true lengths are measured only along lines parallel to one of the three isometric axes — any other line is foreshortened or elongated on the sketch and must never be measured directly.

Why this works: An isometric projection is an axonometric projection in which the three principal axes are foreshortened equally, so laying off true (unforeshortened) lengths along the isometric axes reproduces the object's proportions with a single, constant scale factor, letting a solid be built corner-by-corner from an orthographic multiview without a separate projection construction for every edge.

Common pitfall: Sketching a curved or angled edge from the orthographic view as if it were still a straight isometric-axis line (or vice versa) — and, on this paper, mistaking a multiview's chamfer diagonals for isometric receding lines. The view positions (Top above Front, Side to its right) settle which view is which before any line is interpreted.

Source: Bertoline & Wiebe, Technical Graphics Communication, ch. on axonometric/isometric pictorials.

Question 2 of 5: Isometric sketch from a given multiview (chamfered, notched cube)

Question 2: Isometric sketch from a given multiview (chamfered, notched cube) (10 marks)

Approach