PAU Technical Drawing II (Castilla y León) flashcards

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

Euler line

In any non-equilateral triangle, the circumcentre, centroid and orthocentre are collinear; the centroid divides the segment from circumcentre to orthocentre in ratio 1:2.

Cyclic quadrilateral condition

A quadrilateral can be inscribed in a circle if and only if its opposite angles sum to 180°. This is the necessary and sufficient condition.

Thales' theorem

An angle inscribed in a semicircle is a right angle. Conversely, the locus of points seeing segment AB under 90° is the circle with diameter AB.

Regular polygon interior angle

For a regular polygon with n sides, each interior angle equals (n − 2) × 180° / n, and each exterior angle equals 360°/n.

Golden ratio in pentagon

In a regular pentagon, the diagonal d and side a satisfy d = a·φ with φ = (1 + √5)/2 ≈ 1.618; pentagram intersections divide diagonals in golden ratio.

Locus equidistant from two points

The set of points equidistant from two given points A and B is the perpendicular bisector of segment AB. It is a straight line.

Locus equidistant from two lines

The locus of points equidistant from two intersecting lines is the pair of angle bisectors of the lines, which are perpendicular to each other.

Tangent from external point

From point P outside a circle with centre O, the tangent points lie on the circle with diameter OP, by Thales' theorem.

Grashof condition

A four-bar linkage has at least one fully rotating link when shortest + longest link lengths ≤ sum of the other two link lengths.

Number of common tangents

Two separate circles have four common tangents (two external, two internal); externally tangent circles have three; overlapping circles have two; nested circles have none.

Ellipse equation and foci

For x²/a² + y²/b² = 1, foci lie at (±c, 0) with c² = a² − b²; eccentricity e = c/a is less than 1.

Parabola focus and directrix

For y² = 2px, the focus is at (p/2, 0) and the directrix is x = −p/2; every point is equidistant from both.

Hyperbola asymptotes

For x²/a² − y²/b² = 1 with c² = a² + b², the asymptotes are y = ±(b/a)x and the eccentricity e = c/a exceeds 1.

Ellipse tangent property

The tangent to an ellipse at point P bisects the exterior angle between the focal radii FP and F'P; focal radii make equal angles with the tangent.

Parabola optical property

The tangent to a parabola at P reflects the focal radius FP parallel to the axis; this is the basis of parabolic reflectors and headlights.

Trammel ellipse construction

A segment of fixed length slides with its ends on two perpendicular axes; a marked point on the segment traces an ellipse.

Dihedral system planes

Two perpendicular planes, horizontal (PH) and vertical (PV), intersect at the ground line; projections are the horizontal and vertical views of each element.

Projecting line

A line perpendicular to a projection plane projects as a single point on that plane and appears in true length on the other plane.

Line perpendicular to plane

A line is perpendicular to a plane when it is perpendicular to two non-parallel lines of that plane; its projection is perpendicular to the plane's traces.

Line–plane intersection method

Pass an auxiliary projecting plane through the line, find its intersection line with the given plane, then intersect that line with the original line.

Euler polyhedron formula

For any convex polyhedron, vertices minus edges plus faces equals 2: V − E + F = 2. It holds for all five regular polyhedra.

True shape by rabatment

Rotate the section plane about its trace until it is parallel to a projection plane; the section then appears in true size.

Cone development angle

A right cone of base radius r and slant height g develops into a sector of radius g and angle α = 360°·r/g.

Sphere section radius

A plane cutting a sphere of radius R at distance d from its centre produces a circle of true radius √(R² − d²).

Isometric axes

Isometric projection uses three axes at 120° to each other with equal foreshortening; isometric drawing uses full scale along all three axes.

Cabinet perspective

A cavaliera (cabinet) projection draws the frontal face in true shape, with the receding axis at 45° and a reduction factor of 1/2.

Perspective vanishing point

In central (conical) perspective, families of parallel lines in space converge at a common vanishing point on the horizon line.

ISO 5455 scale definition

Scale is the ratio of drawing dimension to real dimension; preferred scales include 1:2, 1:5, 1:10, 1:50, 1:100 and enlargements 2:1, 5:1, 10:1.

Hidden edge line type

Hidden edges are drawn with thin dashed lines (ISO 128); visible edges use continuous thick lines and centre lines use thin dash-dot lines.

Broken-out section

A partial section bounded by a freehand or irregular break line, used to show internal detail without sectioning the whole view.

Metric thread designation

M10×1.5 denotes a metric thread of nominal diameter 10 mm and pitch 1.5 mm; coarse pitch is omitted (M10). LH marks left-hand thread.

Surface roughness Ra

Ra is the arithmetic mean deviation of the roughness profile; lower values mean smoother surfaces, with 0.8, 1.6, 3.2 and 6.3 µm being common.

CAD relative polar entry

In CAD, @length<angle enters a point at a given distance and angle from the previous point; @dx,dy enters a relative rectangular offset.