Spain 2º Bachillerato Technical Drawing II
Chapters: 4
1. Geometric foundations
Geometry in modern architecture and engineering · Homology and affinity · Power of a point and radical axis · Conic curves
- Architecture: How Buildings Stand, Look and Feel – Architecture is the art and science of designing buildings and spaces for people. Every building must carry its load to the ground: by post and lintel, by the arch, vault and dome, or by a steel and concrete frame. Each age had its style: Egyptian, Greek and Roman, Byzantine, Romanesque, Gothic, Renaissance, and modern. Architects plan with drawings (plan, elevation, section), models and CAD, and design space, light and access so that places work and feel good for everyone.
- Transformations: Slide, Flip, Turn and Resize a Shape – A transformation moves a shape to a new place. Translation slides it, reflection flips it in a mirror line, rotation turns it about a centre, enlargement changes its size from a centre. The first three keep size and shape (congruent image). Enlargement keeps shape but changes size (similar image). Each has a simple coordinate rule.
- 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.
- Conic Sections (Class 11): Circle, Parabola, Ellipse and Hyperbola – Cutting a double cone with a plane gives a circle, an ellipse, a parabola or a hyperbola; a cut through the vertex gives a point, a line or a pair of lines (degenerate conics). Circle: (x − h)² + (y − k)² = r². Parabola y² = 4ax: focus (a, 0), directrix x = −a, latus rectum 4a, e = 1. Ellipse x²/a² + y²/b² = 1 (a > b): c² = a² − b², foci (±c, 0), e = c/a < 1, latus rectum 2b²/a, PF₁ + PF₂ = 2a. Hyperbola x²/a² − y²/b² = 1: c² = a² + b², e = c/a > 1, latus rectum 2b²/a, |PF₁ − PF₂| = 2a.
2. Projective geometry
Advanced dihedral system · Axonometric figures and solids · Dimensioned planes: roofs and terrain · Conical perspective of solids
- 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.
- 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.
3. Standardisation and project documentation
Industrial part drawings · Design, ecology and sustainability · Collaborative engineering projects · Assembly drawings
- Machine Drawing: Making and Reading Detail Drawings – A machine drawing is an exact picture of one part, made so a factory can build it without asking any questions. A detail (working) drawing shows the views of the part, section views for hidden insides, every size (dimension), how much each size may vary (tolerance), the surface finish, the material and a title block.
- Sustainable Design: Products That Are Kind to People and Planet – Sustainable design means making products that meet our needs while harming nature and people as little as possible. Every product has a life cycle: materials, making, transport, use and end of life. A life cycle assessment adds up the ecological footprint (energy, CO₂, water, waste) at each stage. The social footprint is the effect on workers and communities: pay, safety, child labour, fair trade. Designers use the six Rs (rethink, refuse, reduce, reuse, repair, recycle), design for maintenance, repair and disassembly, and avoid planned obsolescence. Ecodesign also weighs the economic side: a product must be affordable and profitable, so the best designs balance environment, society and economy.
- Project Management – A project is a one-time piece of work with a clear goal, a start and an end. Project management means planning and controlling it so it meets its scope on time and within cost. The life cycle runs initiate, plan, execute, monitor and close. Planners break the work into tasks (WBS), place them on a Gantt chart, find the critical path, manage risks and review lessons learned at the end.
- Assembly Drawings: How Parts Fit Together – An assembly drawing shows many parts joined together as one product. It tells you which parts there are (balloons and a parts list, also called a bill of materials), where each one goes, and how they are joined: with bolts and screws you can undo, or with rivets and welds that stay for good.
4. CAD systems
CAD applications
- 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.