The Hole Normal to an Inclined Face
A candidate is drawing, at scale 1:1, the first-angle orthographic views of a machined clevis bracket. The body is 90 mm long, 60 mm high and 40 mm deep. The top right-hand corner is cut away by a flat face inclined at 40° to the horizontal; this face is perpendicular to the frontal plane, so it appears as a straight line in the front view. A Ø16 mm hole is drilled right through, normal to that inclined face, with its axis on the mid-depth plane and its centre 25 mm up the slope from the lower edge of the face. The candidate has finished the front view, drawn the hole in the plan as a true 16 mm circle, and drawn the hole in the front view as a rectangle with vertical sides 16 mm apart. The teacher marks the plan circle wrong, says the front-view sides are wrongly inclined, and asks for a third view the candidate has not yet attempted.
1. Which view shows the Ø16 mm hole as a true circle, and what should the plan actually show?
Read the worked answer
A circular edge projects as a true circle only when the line of sight is along the hole axis, so the true circle appears in an auxiliary view taken perpendicular to the inclined face; it does not appear in any of the three principal views.
The axis is normal to a face inclined at 40° to the horizontal, so the axis stands 40° from the vertical. Because that face is perpendicular to the frontal plane, the 40° tilt lies in the frontal plane and affects only the length direction of the bracket. In the plan the line of sight is vertical and meets the axis at 40°, so the opening projects as an ellipse:
- major axis = 16 mm, measured across the 40 mm depth, where the surface is not tilted relative to the line of sight;
- minor axis = 16 cos 40° = 12.3 mm, measured along the length of the bracket, in the direction of the tilt.
The candidate's 16 mm circle would only be correct for a vertical hole. The error is serious because it also misplaces the visible outline of the hole relative to the inclined face in the plan.
2. How should the two sides of the hole be drawn in the front view, and how does the mouth of the hole appear there?
Read the worked answer
The two visible sides are the silhouette of the cylindrical wall, so they must be parallel to the hole axis and 16 mm apart measured perpendicular to that axis.
The axis lies in the frontal plane at 40° to the vertical, so the sides are drawn at 40° to the vertical (50° to the horizontal), leaning the same way as the inclined face - not vertical as the candidate drew them. Vertical sides would describe a vertical hole through the bracket, which is a different part and would not meet the inclined face square.
The mouth of the hole is a circle lying in the inclined face. That face contains the depth direction, so in the front view the circle collapses onto a straight segment 16 mm long lying along the inclined face line, centred on the axis. It must not be drawn as an ellipse or as a rounded rectangle. The lower end of the hole is therefore bounded by the inclined face line itself, and the two silhouettes stop on it.
3. Describe how the missing third view is set up and what it proves.
Read the worked answer
It is an auxiliary view projected at right angles to the inclined face, i.e. viewing along the hole axis.
- Draw a reference line parallel to the inclined face line in the front view.
- Project lines from every point of the front view at right angles to that reference line (the direction of the hole axis).
- Transfer depths from the plan, measured from the mid-depth plane (the centre line of the 40 mm width), at right angles to the reference line.
- In first angle the auxiliary view is placed on the opposite side of the reference line from the direction of viewing, and it is projected from the front view, not from the plan.
Result: the inclined face appears true shape. The hole is a true Ø16 mm circle with its centre 25 mm up the slope from the lower edge, and the slope length of the face reads true. This view is the only one in which the hole can be measured or marked out on the machine.