Basque PAU Technical Drawing II flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Thales circle

The locus of points that see a given segment under a right angle is the circle whose diameter is that segment. Used to construct perpendiculars and tangents.

Ellipse focal condition

For an ellipse, the sum of distances from any point to the two foci equals 2a, the major axis. The relation c² = a² − b² links focal distance and semi-axes.

Hyperbola eccentricity

For a hyperbola, eccentricity e = c/a is greater than 1, with c² = a² + b². The absolute difference of focal distances equals 2a for every point.

Tangent length from point

From an external point P to a circle of center O and radius r, the tangent segment length is √(OP² − r²). Both tangent segments from P are equal.

Homothety ratio

A homothety with center O and ratio k maps each point P to P' on ray OP with OP' = k·OP. Parallel lines remain parallel and the center is fixed.

Line traces in dihedral

The horizontal trace is where a line meets the horizontal plane; the vertical trace is where it meets the vertical plane. Both lie on the reference line extensions.

True length by right triangle

Build a right triangle with one leg equal to a segment's projection and the other equal to the difference of the complementary coordinates. The hypotenuse is the true length.

Line perpendicular to plane

A line is perpendicular to a plane when its horizontal projection is perpendicular to the plane's horizontal trace and its vertical projection is perpendicular to the vertical trace.

Plane traces

A plane is represented by its traces, the lines where it intersects the horizontal and vertical projection planes. Both traces meet on the reference line.

Cone lateral development

The lateral surface of a right cone unrolls into a circular sector whose radius equals the slant height g and whose angle is 360°·r/g.

Cylinder development

The lateral surface of a right cylinder unrolls into a rectangle whose width equals the base circumference 2πr and whose height equals the cylinder height.

Sphere plane section

A plane cutting a sphere of radius R at distance d from its center produces a circle of radius √(R² − d²). A plane through the center gives a great circle.

Cone conic sections

A plane parallel to a cone's base gives a circle; oblique to the axis gives an ellipse; parallel to one generatrix gives a parabola; steeper gives a hyperbola.

Truncated cone development

The lateral surface of a truncated cone unrolls into an annular sector. Use similar triangles on the extended generatrices to find the inner and outer radii.

Change of plane rule

In a change of plane, the new plane is perpendicular to one existing plane. The coordinate measured perpendicular to the replaced plane is preserved in the new view.

True shape by two changes

To obtain the true shape of a plane figure, first change the plane so the figure projects edge-on, then change again to a plane parallel to the figure.

Rotation about perpendicular axis

Rotating a point about an axis perpendicular to a projection plane moves the point on a circle in that view; the coordinate perpendicular to the plane stays constant.

Dihedral angle by edge-on view

Successive changes of plane bring the intersection line of two planes to a point. In that view, the angle between the traces equals the dihedral angle.

Isometric foreshortening

In true isometric axonometry the three axes are at 120° and all foreshortening coefficients equal 0.816. Isometric drawing uses 1 for convenience.

Cavalier projection

Cavalier perspective draws the front face true size, with the receding axis at a chosen angle and a reduction factor of 1/2 or 2/3 to reduce distortion.

Isometric circle ellipse

A circle of diameter d appears in isometric projection as an ellipse with major axis about 1.22d and minor axis about 0.71d, oriented along the appropriate diagonal.

Vanishing point

In conical perspective, a vanishing point is where a line through the eye parallel to a family of object edges meets the picture plane. Parallel edges share it.

One-point perspective

When the front face of an object is parallel to the picture plane, edges perpendicular to it converge at the principal point, giving a one-point perspective.

First-angle projection

In first-angle (European) projection the object lies between observer and plane; the top view is placed below the front view and the left view on the right.

Hatching in sections

Cut surfaces are hatched with thin parallel lines, usually at 45°, uniformly spaced. Adjacent parts use different hatching directions or spacing to distinguish them.

Half section

A half section shows one half of a symmetric object in section and the other half in exterior view, separated by a thin chain line representing the axis.

ISO fit notation

ISO fits use uppercase letters for holes and lowercase for shafts, e.g. H7/h6 for a clearance fit. The number is the tolerance grade.

Golden ratio

The golden ratio φ equals (1+√5)/2 ≈ 1.618. A rectangle with sides a and b satisfies it when (a+b)/a equals a/b.

Rule of thirds

Divide the picture frame into a 3×3 grid. Placing key elements on the grid intersections or along the lines gives a balanced composition.

ISO A series format

ISO 216 A0 has an area of one square metre with a √2 side ratio. Each subsequent size halves the area; A4 measures 210 × 297 mm.

ISO line weights

Visible outlines are drawn thick (about 0.5–0.7 mm); hidden edges are thin dashed; center lines are thin chain; dimension and extension lines are thin.

Freehand circle method

Sketch a light bounding square or center cross first, then draw arcs through the marked points. For ellipses, use a bounding parallelogram with both axes marked.