Isometric Drawing of a Bearing Bracket
A candidate must draw an isometric view of a cast-iron bearing bracket. The base is 100 mm × 60 mm × 12 mm, the vertical web is 60 mm × 12 mm × 50 mm, and a boss of outside diameter 40 mm with a 20 mm bore projects from the web. The candidate sets out the 30° isometric axes at 1:1, then multiplies every measurement by 0.816 because “isometric projection is smaller,” but labels the drawing “full size.” The boss is drawn as a true circle on the top face, and a 45° chamfer is drawn as a line at 30° to the horizontal. The result is visibly undersized and the circular features look wrong. The examiner wants the candidate to separate isometric drawing from isometric projection and to correct the ellipse and the non-isometric chamfer.
1. Distinguish isometric drawing from isometric projection and state which scale the candidate should use for a 1:1 sheet. Calculate the size factor.
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In isometric projection, the three axes are equally inclined to the plane of projection, so every length along an isometric axis is foreshortened by cos 35.26° = 0.816. The isometric axes are drawn at 120° to one another, normally 30° to the horizontal. In an isometric drawing, the same axes are used but true lengths are measured along them; the 0.816 factor is omitted. The isometric drawing is therefore 1/0.816 = 1.225 times the corresponding isometric projection. For a 1:1 sheet the candidate should use true lengths along the 30° axes, not multiply everything by 0.816. If the examiner specifically asks for an isometric projection, apply 0.816 to all isometric-axis dimensions and label it accordingly. The candidate has done the opposite: applied the projection factor but labelled the sheet full size, so the bracket is about 81.6% of the intended size. The 1.22 factor belongs to ellipse major axes, not to every measurement.
2. Correct the boss circle on the top face. Give the major and minor axes and their orientation, and describe a four-centre construction.
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A circle on the top face is parallel to HP and appears as an ellipse. Its major axis is horizontal on the sheet and equals 1.22d = 1.22 × 40 = 48.8 mm. Its minor axis is vertical and equals 0.71d = 0.71 × 40 = 28.4 mm. For the four-centre construction, draw an isometric square (a rhombus) of side 40 mm about the centre using the 30° axes. The two obtuse corners of the rhombus are centres for the large arcs. Draw lines from those corners to the midpoints of the opposite sides; their intersections with the short diagonal give the two small centres. Draw the two large arcs and the two small arcs tangent to them. The result is a close approximation to the ellipse. A true circle is wrong because the top face is foreshortened in isometric. If the same boss were on a vertical face, the major axis would be oriented along the other isometric direction, not simply copied from the top face.
3. How should the 45° chamfer be drawn, and why can’t its line be set at 30°?
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The chamfer edge is a non-isometric line: it is not parallel to any of the three isometric axes. Its direction is therefore not preserved in the isometric view, and its length cannot be scaled directly along a 30° axis. Draw it by locating its endpoints from known corners using offsets along the isometric axes, then join the endpoints. For example, if the chamfer cuts 10 mm along one edge and 10 mm along an adjacent edge, step off those offsets along the two isometric directions from the corner, mark the two endpoints, and connect them. Do not draw the chamfer at 30° merely because the isometric axes are at 30°, and do not measure its sloping length with an isometric scale. The same box-and-offset method applies to any oblique edge, curve or intersection that is not parallel to an isometric axis.