Isometric pictorial from an orthographic projection: 04-BS-15, May 2015, Q1

Question 1: Isometric pictorial from an orthographic projection

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.

The three given views (top, front, right-side) describe a stepped mounting block: a tall front section carrying two cylindrical bosses (each with a vertical through-hole) joined by a diagonal reinforcing web, stepping down to a lower shelf at the right-hand end. The top view’s two circles are the boss holes; its solid/hidden diagonal pair is the web’s visible top edge and hidden lower edge. The front view’s paired arches are the two bosses seen face-on, and the stepped right-side view confirms the shelf drop.

Approach. Block in the overall envelope first (length × depth × height) using the isometric axes (vertical, and two axes at 30° to the horizontal, 120° apart), then add the step, the two bosses (with their holes as isometric ellipses built by projecting the true circle point-by-point onto the two axes), and finally the diagonal web.

Lay out the box. Mark off length along the right-going axis and depth along the left-going axis at 30° above horizontal; mark height along the vertical axis. This preserves true measurements along all three isometric axes.
Cut the step. Drop the right portion of the block down to the shelf height, transferring the step location from the top view along the length axis.
Add the bosses and holes. Project each hole’s true circle onto the top face as an isometric ellipse (four-centre or point-plot method); the through-hole is drawn as a hidden ellipse below the visible boss-top ellipse.
Add the diagonal web. Its top edge is visible (solid), its lower edge is hidden behind the bosses (dashed), matching the top view.

Fig. Q1 — isometric pictorial built by the box method from the given three views.

Item	Result
Sketch scale	1:1 (full size) — the given orthographic was drawn at half size
Construction	Isometric box method, axes at 120°

The grading rubric marks view selection, projection technique and proportion — not an exact replica of the freehand original.

Topic: Isometric pictorials from multiview drawings

Key relations: Isometric axes are drawn vertical + 2×30° from horizontal (120° apart); true lengths are measured only along these three axes, never along a sloped or curved edge.

Why this works: Because the isometric axes are the three mutually-perpendicular part edges rotated equally about the line of sight, distances along them stay undistorted (isometric = "equal measure"), so the box method lets every feature be located by simple offsets from the envelope.

Common pitfall: Students often measure a diagonal or a curve directly on the isometric sketch; only edges parallel to the three isometric axes may be measured true-length — circles must be plotted point-by-point (or four-centre ellipse method), never drawn as a true circle.

Source: Bertoline & Wiebe, Technical Graphics Communication, ch. on the topic below.

Question 1 of 9: Isometric pictorial from an orthographic projection

Question 1: Isometric pictorial from an orthographic projection