Basque PAU Technical Drawing II common mistakes
Basque PAU Technical Drawing II · Understand the traps and how to avoid them.
When a tangency problem asks for circles tangent to two given lines and passing through a point on one of them, the candidate draws one solution and stops, ignoring the second family of circles on the opposite side of the angle bisector.
Textbook tangency procedures are usually memorised as a single construction (bisector + perpendicular), so the candidate treats the first valid circle as the answer and never checks the symmetric or external case; the habit comes from school exercises that only asked for one solution.
What to do instead
Before drawing, list the solution families explicitly: for two lines plus a point, there are generally two circles (internal and external to the angle). Use the locus method (bisector of the angle, plus the locus of centres equidistant from the point and the line) and construct both centres, then label each with its radius. As a final check, verify tangency numerically: distance from centre to each line equals the radius.
In an ellipse construction, the candidate marks the major and minor axes but places the foci at the ends of the minor axis or at half the major axis, and the resulting curve does not pass through the minor-axis vertices.
The relation c² = a² − b² is confused with c = a/2 because the focal distance is memorised as 'half of something'; the candidate also mixes up which axis is major when the ellipse is drawn in a rotated frame.
What to do instead
Write the invariant on the sheet before constructing: the sum of distances from any point to the foci equals the major axis 2a, and the foci lie on the major axis at distance c from the centre with c² = a² − b². Construct the foci by striking an arc of radius a from a minor-axis vertex onto the major axis. Verify by checking that the curve passes through all four vertices and that a string-and-pins check gives the same curve.
A homothety or rotation is applied to a figure but the candidate transforms only the outline, leaving the centre, the axis, or the corresponding points of an inscribed circle untransformed, so the image is internally inconsistent.
Transformations are treated as 'redrawing the shape in a new place' rather than as a point-by-point mapping; the candidate works from visual similarity instead of from the defining correspondence.
What to do instead
Always fix the transformation data first (centre and ratio, or centre and angle, or axis), then transform at least three defining points and the centre of any circle, and construct the image from those. For a circle under homothety, transform the centre and multiply the radius by the ratio; for rotation, the image centre is the rotated centre with the same radius. Check that ratios of corresponding segments and angles are preserved.
In dihedral projection, the candidate draws the vertical and horizontal traces of a plane without checking that they meet the ground line at the same point, and then constructs true lengths from a plane that is not actually a plane.
The traces are drawn as two independent lines because the candidate thinks of them as separate data; the condition that both traces of a plane intersect the ground line at a common point (unless the plane is parallel to the ground line or to a projection plane) is not applied as a check.
What to do instead
After drawing any plane, immediately verify the trace condition: the horizontal and vertical traces must meet on the ground line at a single point. If they do not, the plane definition is wrong - recompute from the given points or lines. Only then proceed to true-length constructions, and re-verify the condition after any change of plane.
When finding the intersection of a line and a plane, the candidate uses an auxiliary plane that contains the line but is chosen arbitrarily (for example, a plane parallel to a projection plane that does not actually contain the line), and the intersection point lands off the line in one projection.
The auxiliary-plane method is remembered as a sequence of steps without the key requirement that the auxiliary plane must contain the given line; the candidate picks a convenient plane and forces the construction.
What to do instead
State the requirement aloud: the auxiliary plane must contain the line. The easiest valid choice is a projecting plane through the line, whose trace coincides with one projection of the line. Find the intersection of that plane with the given plane (a line), then intersect that line with the original line. Verify the result lies on both projections of the original line.
In a section of a solid by an oblique plane, the candidate constructs the section polygon by joining points that look adjacent in one view, producing a section that is not planar or that misses a face.
The section is drawn from the visual outline rather than from the intersections of the cutting plane with each edge of the solid; with an oblique plane the projected section is distorted, so adjacency in one view is misleading.
What to do instead
Work face by face: intersect the cutting plane with every edge of the solid, collect the true intersection points, and join only points that lie on the same face. Then obtain the true shape by a change of plane or rotation so the cutting plane becomes a projection plane. Cross-check the number of section vertices against the number of edges actually cut.
A development (unfolding) of a prism or cylinder is drawn with the lateral edges spaced at the chord lengths of the base rather than the true arc or edge lengths, so the developed surface is short and does not close.
The candidate measures along the projected base in the view where the base is foreshortened, or divides the circle into chords and treats them as arc lengths; the difference is small on each segment but accumulates at the closure.
What to do instead
Obtain the true length of the base perimeter first: for a prism, use the true lengths of the base edges from the plan or an auxiliary view; for a cylinder, divide the circle into equal arcs and lay out the corresponding arc lengths (or use the calculated circumference) on the development. Always check closure: the first and last generators must coincide.
In a change of plane, the candidate moves the ground line but keeps the distances of points from the old ground line instead of transferring the correct coordinate perpendicular to the new ground line.
The rule 'distances from the ground line are preserved' is misapplied: what is preserved is the distance from the point to the plane being replaced, measured perpendicular to the new ground line, and the candidate transfers distances along the wrong direction.
What to do instead
Use a fixed procedure: draw the new ground line, drop perpendiculars from each point's retained projection to the new ground line, and lay off on those perpendiculars the same distance the point had from the old ground line (measured perpendicular to the old ground line). Do it for two or three points first and check that a known true length appears before completing the figure.
In isometric drawing, the candidate scales all three axes by the same factor as the true lengths and also draws ellipses for circles with the major axis horizontal regardless of the face the circle lies in.
Isometric is conflated with a simple oblique or cavalier projection; the candidate forgets the isometric scale (about 0.816 of true length, or the conventional full-scale reduction) and the rule that the ellipse major axis is perpendicular to the axis normal to the circle's plane.
What to do instead
Fix the convention at the start: state whether the drawing uses true isometric scale or the conventional isometric drawing at full scale along the axes. For every circle, identify its plane, draw the ellipse with the major axis perpendicular to the third axis, and set the major/minor ratio to about 1.22/0.71 of the diameter. Check one circle against its enclosing isometric square.
In a multi-view drawing, the candidate omits hidden-line representation of internal features on the views where they are not visible, and then adds a section that contradicts the views.
The candidate treats each view as an independent outline drawing and does not maintain the projection correspondence; hidden edges are seen as clutter, and the section is drawn as a separate exercise rather than as a cut through the same object.
What to do instead
Establish correspondence first: project every feature across all views using alignment lines before adding detail. Draw hidden edges as dashed lines wherever an edge is not visible, and use the section only to replace hidden detail on the cut view, keeping all other views consistent. Hatch only the material actually cut by the plane, at 45°, and leave the sectioned hole or void unhatched.
Dimensioning is done by adding numbers that match a measured drawing rather than by specifying the feature: duplicated dimensions, dimensions to hidden lines, and chains that leave the overall size undefined.
The candidate dimensions what is easy to measure on the sheet instead of what a manufacturer needs; standards for dimension placement (no closed chains unless one dimension is reference, no dimensions on hidden edges, overall dimensions given once) are not applied as a checklist.
What to do instead
Before writing numbers, decide the datum and the functional dimensions: give overall length, width and height once, then locate each feature from a datum rather than chaining. Never dimension a hidden line; add a section or a local view instead. Remove any dimension that can be derived from others, and mark a deliberately duplicated dimension as a reference dimension in parentheses.
The candidate produces a technically correct construction with faint, unlabelled lines: no distinction between construction lines and final solution, no lettering of key points, and no statement of the result, so the marker cannot follow the reasoning.
Under exam time pressure the candidate treats the drawing as scratch work and skips annotation; the habit comes from practising only the construction and never practising the presentation of the solution.
What to do instead
Adopt a fixed presentation protocol: construction lines thin and light, final solution thick, all constructed points lettered (A, B, O, T for tangency points), and a one-line written statement of the result with its radius or true length. Reserve the last five minutes of every practice problem to tidy and label, so the protocol is automatic under exam conditions.