Spain 1º Bachillerato Technical Drawing I
Chapters: 4
1. Geometric foundations
History and fields of technical drawing · Origins of geometry · Loci and capable arc · Proportionality, equivalence and similarity · Triangles and polygons construction · Basic tangencies and technical curves · Rigour and precision in drawing
- Technical Drawing: Communicating Design Ideas – Technical drawing is a shared visual language for showing the exact shape and size of an object. Designers start with freehand sketches, then use pictorial views (isometric, oblique) to show the object in 3D, and orthographic projection (front, top and side views) with standard lines, dimensions in millimetres and a scale so that anyone can make it. Today most drawings are made with CAD software.
- History of Mathematics – Mathematics grew over thousands of years in many places. People first counted with tally marks. Egypt and Babylon used geometry for land and building, and Babylon counted in 60s. Greek thinkers such as Thales, Pythagoras, Euclid and Hypatia turned geometry into proofs. India gave place value with zero, scholars in Baghdad built algebra, and the ideas reached Europe. Women and men from every continent have shaped maths, often against unfair barriers.
- Locus: The Path of a Point That Follows a Rule – A locus is the set of ALL points that obey one rule, and no other points. Fixed distance from one point gives a circle. Equal distance from two points gives the perpendicular bisector. Equal distance from two crossing lines gives the angle bisector. Where two loci meet, you find points that obey both rules, like the centre of the circumcircle. Points that see a segment at a fixed angle lie on an arc, called the capable arc.
- Similar Triangles – Two figures are similar when they have the same shape but maybe a different size. Two triangles are similar if their matching angles are equal and their matching sides are in the same ratio. Basic Proportionality Theorem (BPT): a line parallel to one side of a triangle cuts the other two sides in the same ratio; its converse is also true. You can prove similarity with AA, SSS or SAS.
- Geometric Constructions: Drawing Exactly with Compass and Straightedge – A geometric construction draws a figure exactly using only a compass and a straightedge (a ruler used for straight lines). Key constructions: the perpendicular bisector of a segment, the bisector of an angle, a perpendicular from a point to a line, angles of 60°, 30°, 90° and 45°, a triangle from three sides (SSS), two sides and the included angle (SAS) or two angles and a side (ASA), and regular polygons such as the hexagon. Each works because equal compass arcs make equal lengths, which give congruent triangles.
- Tangent to a Circle – A tangent is a line that touches a circle at exactly one point. At that point it makes a 90° angle with the radius, and two tangents drawn from one outside point are always equal in length.
- Circles and Tangents: How to Draw Them and Why They Work – A tangent touches a circle at one point and is at 90 degrees to the radius. From an outside point P you can draw two equal tangents of length √(D² - r²). Two circles have up to four common tangents. A circle can join two lines smoothly, and arcs with changing centres make spirals. Power of a point says PA x PB = D² - r² for every line through P. The radical axis is the straight line of points that have equal power for two circles.
2. Projective geometry
Basics of projective geometry · Dihedral system: point, line, plane · Dihedral relations · Axonometric systems · Dimensioned plane system · Conical perspective
- Projections: Central, Parallel and Orthogonal – A projection draws a 3D object on a flat surface using straight rays. If all rays start at one point (a lamp, your eye) it is a central projection: images change size with distance and give perspective. If all rays are parallel (sunlight) it is a parallel projection: sizes do not depend on distance. If the parallel rays are at 90° to the screen it is an orthogonal projection: faces parallel to the screen show their true size. Engineers use orthogonal views, artists use perspective.
- Orthographic Views of Solids – An orthographic view shows a solid as seen straight on from one direction, with no perspective. The three main views are the front view (front elevation), the top view (plan) and the side view (side or end elevation). Each view loses one dimension, so we usually need all three to fix the shape. Views are arranged in a standard layout: first-angle projection (plan below the front view; used in India, Europe and ISO standards) or third-angle projection (plan above; used in the USA). Visible edges are thick continuous lines, hidden edges are dashed, and centre lines are chain lines. A net is the flat pattern that folds into a solid, and a cross-section is the shape you see when you cut through it.
- Isometric Projection and Axonometric Drawing – An axonometric drawing shows a solid in one picture with three axes: width, depth and height. In isometric projection the three axes are 120° apart and every axis is shortened equally (scale ≈ 0.82). An isometric drawing uses full lengths instead. Dimetric shortens two axes the same, trimetric all three differently. Oblique (cavalier, cabinet) keeps the front face true size and draws depth at 45°, full length (cavalier) or half (cabinet). Circles on faces become ellipses.
- Topographical Maps – Topographical maps are large-scale maps that show both natural and human features of a small area in detail, using agreed signs and colours. In India they are made by the Survey of India in a nested sheet series (1:1,000,000 → 1:250,000 → 1:50,000 → 1:25,000). Relief is shown by contours; their spacing and shape tell slope and landform, and a cross-section turns them into a side view.
3. Standardisation and project documentation
Scales · Paper formats and folding · Standardisation and norms · Views, lines and dimensioning
- Technical Drawing: Communicating Design Ideas – Technical drawing is a shared visual language for showing the exact shape and size of an object. Designers start with freehand sketches, then use pictorial views (isometric, oblique) to show the object in 3D, and orthographic projection (front, top and side views) with standard lines, dimensions in millimetres and a scale so that anyone can make it. Today most drawings are made with CAD software.
- National and International Standards in Design – A standard is an agreed document that sets sizes, quality, safety or test methods so products fit, work safely and can be traded. ISO and IEC write world standards; regional (EN) and national bodies such as BIS, BSI, DIN, UNE and ANSI adopt them. Marks like CE, ISI and the Kitemark show conformity. ISO 216 A-series paper starts at A0 = 1 m², halves at each size and keeps a 1 : √2 ratio. Drawing standards fix line types, scales, dimensions, title blocks and how to fold sheets to A4.
- Orthographic Views of Solids – An orthographic view shows a solid as seen straight on from one direction, with no perspective. The three main views are the front view (front elevation), the top view (plan) and the side view (side or end elevation). Each view loses one dimension, so we usually need all three to fix the shape. Views are arranged in a standard layout: first-angle projection (plan below the front view; used in India, Europe and ISO standards) or third-angle projection (plan above; used in the USA). Visible edges are thick continuous lines, hidden edges are dashed, and centre lines are chain lines. A net is the flat pattern that folds into a solid, and a cross-section is the shape you see when you cut through it.
4. CAD systems
2D and 3D vector applications · 3D part design basics · Box modelling · Collaborative CAD assemblies
- CAD Modelling: From a Sketch to a 3D Part – CAD (computer-aided design) means using a computer to draw and build exact models of objects before they are made. A design starts as a freehand sketch. In CAD it becomes a 2D sketch with constraints and dimensions. 3D tools such as extrude, revolve and cut turn the sketch into a solid. Each step is saved in a feature tree, so changing one size rebuilds the whole model. Parts are joined in assemblies, tested by simulation, shared as drawings and sent to 3D printers, laser cutters or CNC machines.
- 3D Modelling: From a Cube to a Printed Object – A 3D model is a shape stored in a computer as points (vertices) joined by edges into flat faces: a mesh. We build models by starting from simple shapes (primitives), moving, rotating and scaling them, and pulling faces out (extrude). Then we add materials and lights and the computer renders a picture. The same model can be sliced into thin layers and built by a 3D printer, or used in games, films, VR and product design.