Madrid PAU Technical Drawing Applied to Arts and Design II study plan
Madrid PAU Technical Drawing Applied to Arts and Design II · Give each week a clear focus.
8 weeks · About 6 hours per week
Plane geometry and geometric constructions applied to design
Construct perpendiculars, parallels and angle bisectors with compass and straightedge, and bisect a given segment without measuring.
Divide a segment into n equal parts using Thales' intercept theorem, and apply it to scale a drawing to a stated ratio.
Draw regular polygons (triangle, square, pentagon, hexagon, octagon) inscribed in a given circle using only construction lines, leaving all auxiliary arcs visible.
Construct a polygon on a given side using the general method based on the semicircle and radial division, and check the result by measuring two independent sides.
Your checkpoint
A single A3 sheet with six solved constructions, each with construction lines kept, a 1-line written procedure, and a scale bar; self-checked against a printed checklist of construction steps.
Plane geometry and geometric constructions applied to design & Tangencies and technical curves (conics and their applications)
Solve external and internal tangency between circles and lines by locating centres with locus intersections (parallel offset lines and concentric circles).
Construct tangent lines to a circle from an external point, and an arc of given radius tangent to two lines at an acute, right and obtuse angle.
Draw an ogee and a reverse curve joining two given parallel lines with two arcs of equal radius, marking all tangent points.
Apply the radical-axis idea to find the centre of a circle tangent to three given circles in a simple case, and justify the construction in writing.
Your checkpoint
One A3 tangency sheet with eight constructions (four line-circle, two line-line arcs, two multi-circle), each with tangent points marked with a small cross and labelled T1, T2.
Tangencies and technical curves (conics and their applications)
Construct an ellipse by the concentric-circle and the trammel methods given both axes, and locate foci and draw the tangent at a chosen point.
Construct a parabola given focus and directrix, and draw the tangent and normal at a point using the reflection property.
Construct a hyperbola given foci and a vertex, and identify its asymptotes.
Sketch three real design objects (a vaulted arch, a satellite dish profile, a cooling-tower outline) and match each to the conic that models it, stating which parameter controls the shape.
Your checkpoint
One A3 sheet: three conics constructed with foci, axes, asymptotes and one tangent/normal each, plus a half-page written comparison of how eccentricity changes the curve family.
Geometric transformations: homothety, similarity, inversion and their applications
Construct the homothetic image of a planar figure given centre and ratio, including negative and fractional ratios, and verify that corresponding sides stay parallel.
Build a similarity transformation mapping one triangle onto another, and state the scale factor and rotation angle.
Construct the inverse of a point, a line and a circle with respect to a given circle of inversion, and explain in writing why a circle through the centre inverts to a line.
Apply homothety to enlarge a logo mark to a required bounding-box size while preserving proportions.
Your checkpoint
One A3 sheet with a homothety, a similarity, three inversions and one applied logo enlargement, each with the ratio or inversion power written next to the figure; checked by measuring two corresponding lengths per figure.
Descriptive geometry: point, line and plane; intersections and distances
Determine true length and true angle of a line by the right-triangle and the change-of-plane methods, and compare the two results.
Find the intersection point of a line and a plane and the intersection line of two planes, deciding visibility in each view.
Construct the true shape of a plane figure by change of plane, and measure the angle between two planes.
Compute the shortest distance from a point to a plane and to a line, and show the perpendicular in projection.
Your checkpoint
A four-view exercise set (two problems, two views each) on A3, with true lengths, true shapes and distances dimensioned numerically and answers verified to within 1 mm of a computed value.
Polyhedra and surfaces; representation of volumes & Descriptive geometry: point, line and plane; intersections and distances
Draw the plan and elevation of a regular hexagonal prism and a square pyramid, and find the true shape of a section cut by an oblique plane.
Construct the intersection curve of a cylinder with a plane and of two cylinders, plotting at least eight points per curve.
Develop the lateral surface of a truncated prism and a truncated cylinder to flat sheet, and state the material allowance needed for a seam.
Model one of these solids as a simple folded card or paper maquette and compare it with the drawing.
Your checkpoint
One A3 sheet with sections and developments plus a physical paper maquette of the truncated cylinder whose measured development matches the drawing within 2 mm.
Orthographic projection, dimensioning and standardization & Axonometric and perspective representation for design
Produce a fully dimensioned orthographic set (plan, elevation, side view) of a small designed object, applying chain and baseline dimensioning without redundancy.
Apply ISO line conventions, arrowheads, dimension text placement and a title block with scale and projection symbol.
Build an isometric axonometric of the same object with correct isometric ellipse construction for circular features.
Construct a two-point perspective of a simple volume from a given station point, picture plane and horizon, including one circle in perspective.
Your checkpoint
Two A3 sheets of the same object: one standardized orthographic set with title block, one isometric plus two-point perspective; peer-checked against a standardization checklist (line weights, arrow style, no double dimensioning).
Graphic communication, sketching and design project representation & Orthographic projection, dimensioning and standardization
Produce a timed 30-minute freehand sketch of a small product with correct proportions, using construction boxes rather than outlines first.
Assemble a one-sheet design presentation: concept sketch, orthographic views, axonometric and a short written specification.
Complete a full past-paper-style mock under exam timing (2 hours) covering one problem from each domain and mark it against a rubric.
List your three weakest construction types from the mock and re-solve each once from memory without notes.
Your checkpoint
A timed 2-hour mock exam script plus a one-sheet design presentation, both self-marked with a written error log naming three weaknesses and the corrective step for each.
Milestones
Week 2: Can complete a line-circle tangency and an arc-of-given-radius construction in under 8 minutes each with all tangent points marked, without referring to notes.
Week 4: Can construct an ellipse given its axes and a homothety with a fractional ratio back-to-back in under 20 minutes, and explain the inversion of a circle through the centre in three sentences.
Week 6: Scores at least 7/10 on a self-marked set of intersection, true-shape and development problems, with numerical answers within 1 mm of computed values.
Week 8: Completes the 2-hour mock within time, with the standardization checklist fully satisfied on the orthographic sheet and a written error log of three named weaknesses.