PAU Technical Drawing II (Castilla y León) key terms

Locus of points from which a given segment is seen under a fixed angle; constructed by drawing the two arcs symmetric about the segment whose inscribed angle equals the given one.

Set of all points that satisfy one geometric condition; the standard loci are the circle, the perpendicular bisector, the angle bisector, parallels at a fixed distance and the conics.

Line perpendicular to a segment at its midpoint; it is the locus of points equidistant from the two endpoints and the centre line of every circle through them.

Line dividing an angle into two equal parts; it is the locus of points equidistant from the two sides, and the three bisectors of a triangle meet at the incentre.

Transformation that maps each point onto another on the same ray from a fixed centre, scaled by a constant ratio; used to enlarge polygons and to solve tangency problems.

Contact between two curves or a curve and a line at a single point where they share the same tangent; in construction problems the centre lies on a locus determined by the given elements.

Point shared by two tangent figures; it lies on the line joining the centres for two circles, or on the perpendicular to the tangent line from the centre of a circle.

Closed plane curve whose points are all at the same distance from a fixed centre; the basic element for locus, tangency and polygon construction work.

Point where the three angle bisectors of a triangle meet; it is the centre of the inscribed circle and is equidistant from the three sides.

Point where the three perpendicular bisectors of a triangle's sides meet; it is the centre of the circumscribed circle and may lie outside an obtuse triangle.

Polygon with all sides and all interior angles equal; it is inscribed in a circle whose centre is also the centre of the polygon, and its exterior angle equals 360° divided by the number of sides.

Five-sided polygon; the regular pentagon is built from a circle by dividing the radius in golden section and is linked to the golden ratio in its diagonal-to-side proportion.

Division of a segment into two parts such that the whole is to the larger part as the larger is to the smaller; the ratio is approximately 1.618.

Closed conic section whose points have a constant sum of distances to two fixed foci; it has major and minor axes and is generated by cutting a cone with a plane oblique to its axis.

Open conic section whose points are equidistant from a fixed focus and a fixed directrix; obtained when the cutting plane is parallel to a generator of the cone.

Open conic with two branches whose points have a constant absolute difference of distances to two foci; produced when the cutting plane cuts both nappes of the cone.

Fixed line used with the focus to define a conic: the parabola has equal distances to focus and directrix, and the ellipse and hyperbola have a constant ratio of those distances.

Number describing the shape of a conic as the ratio of the distance to the focus over the distance to the directrix; below one for an ellipse, one for a parabola, above one for a hyperbola.

Straight line that a curve approaches without ever reaching; the hyperbola has two asymptotes through its centre, used to draw the curve and its tangents.

Line touching a conic at one point; from an external point two tangents exist, found through the focal circle or by the polar construction depending on the conic.

Projection system that represents a point by its horizontal and vertical projections onto two perpendicular planes, related by a reference line and by equal distances from it.

View of an object or point onto the horizontal plane in the dihedral system; it is paired with the vertical projection and both share the same distance from the ground line.

Rotation of a plane about one of its traces onto a projection plane so that figures lying in it appear in true shape and size.

Actual size of a segment, angle or figure, obtained by abatement, change of projection plane or auxiliary views when it is not parallel to a projection plane.

Flat pattern obtained by unfolding the faces of a solid onto a plane; used for prisms, pyramids, cylinders and cones to transfer true lengths to the drawing.

Figure produced where a cutting plane intersects a solid; its true shape is found by abatement or by a change of plane, and it defines the cut surface in sectional views.

Point common to a line and a plane; found in dihedral projection by containing the line in an auxiliary plane, intersecting it with the given plane and projecting the result.

Relationship between two lines, two planes or a line and a plane meeting at 90°; in dihedral projection right angles appear true only when one side is parallel to the projection plane.

Axonometric projection with the three axes equally inclined to the picture plane, so the three scales are equal; angles between axes are drawn at 120°.

Oblique axonometric projection in which one face of the object is drawn true shape parallel to the picture plane and the receding axis is drawn at an angle, usually 45°.

Parallel projection system that shows a solid on a single picture plane with three axes, giving a three-dimensional view without vanishing points.

Central projection in which parallel lines converge at vanishing points; the picture plane, the station point and the horizon line determine the result.

Point on the horizon where the images of a family of parallel lines meet in conical perspective; one-point and two-point perspectives use one or two such points.

Systematic placing of dimensions on a drawing using dimension lines, extension lines, arrowheads and figures, following standard rules so the size is stated once and clearly.

Ratio between a length on the drawing and the corresponding real length; a scale of 1:50 means one unit on paper represents fifty units in reality.

View in which part of the object is imagined cut away to reveal internal form; the cut surface is hatched and hidden lines behind the cut are normally omitted.

Broken-out section that removes only a small part of a view to show a local internal feature; the break is bounded by a thin irregular freehand line.

Standard screw thread with a triangular profile and a 60° angle, designated by M followed by the nominal diameter and pitch, for example M10x1.5.

Permissible variation in a dimension, given as upper and lower deviations or as an ISO code such as H7, so that parts fit and interchange without losing function.

Specification of the micro-geometry of a surface, indicated by the roughness symbol with a Ra value in micrometres and any required machining process.