Madrid PAU Technical Drawing Applied to Arts and Design II common mistakes
Madrid PAU Technical Drawing Applied to Arts and Design II · Understand the traps and how to avoid them.
When a tangency problem gives two circles and a point, the candidate draws an approximate circle through the point that merely looks tangent, instead of constructing the centers as the intersection of the perpendicular-distance loci (parallel offset lines/arcs at distance r), so the tangency is only visual and the point of contact is not on the line joining centers.
Tangency is taught as a drawing operation (sliding a compass until it 'touches'), and the underlying locus definition - the center is equidistant from the given elements by exactly the radius - is not internalized, so no construction is planned before drawing.
What to do instead
Before drawing, write the locus statement for the unknown center (e.g. 'equidistant from line L by r and from circle C by R±r'), construct the two loci as thin construction lines, mark the intersection as center, then drop the perpendicular to the line or draw the center-to-center line to locate the contact point. Verify the contact point lies on that line as a self-check.
On conic construction, the candidate plots many points but never draws the tangent at the vertex or uses the directrix–focus definition, producing an ellipse that is flattened at the ends or a hyperbola branch that crosses its asymptote; eccentricity and the focal parameter are never checked numerically.
Point-by-point plotting is memorized as the only method, and the defining ratio (distance to focus / distance to directrix = e) is treated as theory rather than a construction and verification tool.
What to do instead
Construct the conic from its definition: set the focus, directrix and eccentricity, then generate points by the ratio, and draw the tangent at the vertex perpendicular to the axis as a control. After drawing, measure three points and confirm the focus/directrix ratio equals e, and confirm the curve stays inside (ellipse) or outside (hyperbola) the asymptote lines.
In a homothety or similarity problem, the candidate computes the center by joining corresponding points with lines that are nearly parallel and then guesses the intersection off the sheet, or applies a ratio without deciding whether it is positive or negative, so the image lands on the wrong side of the center.
Corresponding-point pairs are chosen arbitrarily and the sign convention of the ratio k is not connected to the geometric meaning (negative k gives the image on the opposite ray through the center).
What to do instead
Choose two well-separated corresponding point pairs so their joining lines meet at a healthy angle; state the sign of k first (k>0 same side, k<0 opposite side) and the position of the center relative to the figures (interior for k<0, exterior for k>0, k≠1). Then verify by checking that every corresponding pair lies on a line through the center and that all distances scale by |k|.
In inversion problems the candidate inverts points but forgets that a line not through the center inverts to a circle through the center (and vice versa), so the image of a straight edge is drawn as a straight line, and the inversion circle's radius is not stated.
Inversion is reduced to the formula OP·OP'=r² and the global incidence rules (circles/lines through the center map to lines/circles) are not rehearsed, so the type of the image is misidentified before construction.
What to do instead
Classify each element first: through the center or not, circle or line. Then construct using the invariant points on the inversion circle and the rule that the center is the limit image. State r explicitly, and check one point numerically with OP·OP'=r².
In dihedral (descriptive geometry) problems, the candidate draws the auxiliary plane or change-of-plane line without projecting every vertex, so the true shape of a section or the true distance comes out distorted; the reference line is placed arbitrarily rather than perpendicular to a line in true length.
The rule 'a plane is seen in true shape when the reference line is parallel to a line of the plane in true length' is memorized as a phrase but not applied as a sequence of projection steps, and vertices are omitted for speed.
What to do instead
Work vertex by vertex with a table of coordinates (x, y, z) so nothing is dropped. For a true-shape section, first find a line of the cutting plane in true length, then set the new reference line parallel to it, and project all section vertices. Check that the new view's extents match the expected dimensions.
When finding the intersection of a line and a plane or of two planes, the candidate uses an auxiliary plane that is not perpendicular to a projection plane, or picks it so the auxiliary trace coincides with the given line, making the intersection point indeterminate and the answer a guess.
The auxiliary-plane method is applied mechanically without checking the degeneracy condition; the candidate does not test whether the chosen plane gives a clean, non-coincident trace.
What to do instead
Choose the auxiliary plane as a projecting plane containing the line (so its trace coincides with the line's projection), find where that plane cuts the given plane, and intersect that line with the original line. If the trace coincides with the given line's projection, choose a different projecting plane (e.g. the other projection direction). Verify the point lies on both the line and the plane in both views.
In orthographic projection of a solid, the candidate draws only the visible edges and omits hidden edges, center lines and symmetry axes, and mixes first-angle and third-angle symbol conventions so the views are placed on the wrong sides.
The view layout is copied from memory of a textbook page rather than from the projection symbol, and hidden-line discipline is seen as cosmetic rather than as information needed to reconstruct the solid.
What to do instead
Draw the projection symbol first to fix the angle of projection, then place the views accordingly. Use a consistent line hierarchy: continuous thick for visible edges, dashed for hidden, chain thin for axes and center lines. As a check, count the edges of the solid and account for each one in every view as visible or hidden.
In dimensioning, the candidate dimensions the same length twice (chain and baseline together), places dimensions inside the hatched section, omits the diameter symbol on cylindrical features or the radius symbol on arcs, and leaves no gap between the dimension line and the extension line.
Standardization rules (ISO/UNE conventions on symbols, no redundant dimensions, dimensions outside the outline where possible) are treated as decoration, and the candidate has not internalized that every dimension must be measurable and non-contradictory.
What to do instead
Apply a checklist: each feature dimensioned once; Ø before diameters, R before radii, □ for squares, SR for spherical radii; extension lines with a small gap from the object and a small overrun past the dimension line; dimensions outside the hatched area; no dimensions on hidden lines. Re-read the drawing and ask whether a machinist could make the part from the dimensions alone.
In axonometric or perspective representation, the candidate uses arbitrary angles for the axonometric axes and arbitrary vanishing points, so the drawing looks plausible but does not correspond to any projection; in perspective the station point and picture plane are never fixed, so the horizon and vanishing points are inconsistent.
Freehand '3D sketching' habits are carried into technical axonometric work, and the relationship between the station point, picture plane, horizon line and vanishing points is not used as a construction sequence.
What to do instead
For axonometric, fix the axes from the chosen projection (isometric axes at 120°, or the appropriate dimetric/trimetric angles) and apply the corresponding foreshortening or the isometric scale. For perspective, place the picture plane, station point and horizon first, then construct vanishing points from lines parallel to the object's edges through the station point, and check that all lines of one direction converge to the same point.
In a design-project sketch, the candidate produces a single rendered view with no construction geometry, no proportional grid and no dimension or scale note, so the drawing cannot be read as a technical proposal and proportions drift between views.
Sketching is treated as an artistic illustration rather than as graphic communication, and the candidate does not establish a proportional framework or a consistent scale before detailing.
What to do instead
Start with a light construction framework (bounding box, axis lines, proportional grid) and keep it visible. Establish a scale and note it. Produce at least the views needed to define the object, keep shared dimensions consistent across views, and annotate materials, dimensions and key construction lines so the sketch functions as a communicable project document.