Question 3 of 10: Auxiliary View — True Shape of an Oblique/Inclined Face

Question 3: Auxiliary View — True Shape of an Oblique/Inclined Face (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.

Given. The front view shows a block whose top-right corner is cut by an inclined (not vertical, not horizontal) surface; the second view shows the block carries a circular through-hole whose axis is perpendicular to that inclined surface, so the hole appears as an ellipse (foreshortened circle) in both principal views — never its true, round shape.

Find. A primary auxiliary view, projected perpendicular to the inclined edge as it appears (edge-on) in the front view, that shows the inclined face — and the hole through it — in true size and true shape.

Approach. Standard auxiliary-view construction: (1) identify the view in which the inclined surface appears as a line (edge view) — here, the front view, since the incline is perpendicular to the front picture plane; (2) draw a reference/fold line parallel to that edge, offset by any convenient distance; (3) project every point on the incline perpendicular to the fold line, by the same distance each point sits back from the fold line in the adjacent (depth) view, onto the new auxiliary view.

1. Confirm the edge view. In the front view the inclined surface is seen on edge as the slanted line — this is the starting line for every projector.
2. Draw projectors perpendicular to the incline from every significant point on that edge (the two ends of the slanted line, plus the hole's centre) — these projectors define the direction of sight for the auxiliary view.
3. Transfer true depth. The auxiliary view's dimension perpendicular to the projectors (its "depth") is transferred directly from the top view, where that same dimension already appears true length (dividers or a scale carry it across, never estimated).
4. Plot the true outline. Where each projector intersects its transferred-depth position fixes a corner of the true-shape face; connecting them gives the actual (undistorted) outline of the inclined face — here a simple quadrilateral.
5. Plot the hole in true shape. Because the hole's axis is perpendicular to the inclined face, and the auxiliary view looks straight down that axis, the hole projects as a true circle in the auxiliary view — this is the entire point of the construction: the same hole is an ellipse in every other view and only a circle here.
6. Label. Mark the fold line "H/A₁" (horizontal-to-first-auxiliary), and label the new view "AUXILIARY VIEW" per the rubric's explicit labelling requirement.