Buy a shelf bracket, and the screw holes line up with the studs in your wall. Buy a replacement bearing for a bicycle, a car, a washing machine, and it fits a shaft that was made in a different factory, on a different continent, years earlier. Nobody phoned anyone. What made all that work is a sheet of paper, or these days a file, that says: make it exactly like this, to within this much.
That sheet is an engineering drawing, and it is the quietest important idea in mechanical engineering. A graduate looks at one and reads it the way you read a sentence: the views, the numbers, the little symbols. The skill sounds dull until you see how many ways a part can come back wrong when a drawing is vague.
Who takes it: mechanical, aerospace and civil engineers, and anyone in product design, usually in year 1.
What it's for: saying precisely what shape a part is, how exact it must be, and then turning that into a model that can be analysed and made.
Comes after: nothing; it needs only geometry.
Leads to: Machine Design (34/19), where every part you design is communicated by a drawing; it also supports Materials Science & Manufacturing (34/13), Mechanics of Materials (34/11) and the Capstone (34/22).
Honest line: you won't learn a CAD package here (those change every decade); you will learn what every package is asking you to say.
A drawing is a contract
A drawing is not an illustration. It is the document the designer hands to the maker, and it is what the buyer pays against. If the maker builds exactly what is drawn and it doesn't work, the question "whose fault is that?" is settled by reading the drawing. If the maker builds something different and it fails, that is settled by the same document.
This is why engineers insist on one rule: if it matters, it is on the drawing. Not in an email, not in a phone call, not "everyone knows". A change that isn't on the drawing doesn't exist, and a change that is on it has to be checked by someone who understands what it does.
The sad proof is the Hyatt Regency walkways in Kansas City, which collapsed in 1981 and killed 114 people (some sources say 113). The contract drawings showed the hanger rods holding two walkways as single long rods. The steel fabricator's shop drawings changed that to two sets of shorter rods, which roughly doubled the load on the critical connection. The US National Bureau of Standards investigation found two problems: the original connection was already inadequate (it would have reached only about 60% of the capacity the building code expected), and the change made it far worse. The lesson isn't that someone was careless with a pencil. It is that a drawing carries a decision, and an unchecked change to a drawing is an unchecked change to a building.
A drawing says what to make, how exactly, and who is responsible when it isn't.
Three flat views tell you a solid
A 3D object has to be described on flat paper. The method used for roughly two centuries is orthographic projection: imagine the object inside a glass box, and look straight at each face from far away. Projection lines are parallel, there is no perspective, and so a length on the drawing is a true length: parallel edges stay parallel, and a hole that is 12 mm across is drawn 12 mm across in the view where you look down its axis.
Usually three views are enough: front, top and right side. The front and top share the same widths, the front and side share the same heights, and from any two you can find the third. Edges you can't see are drawn dashed. If the inside matters, you imagine slicing the part and drawing the cut face with hatching, a section view. Several parts together appear in an assembly drawing, often with an exploded view and a numbered parts list.
There are two conventions for where the views go on the sheet. Third angle (used in the US and Canada) puts the top view above the front. First angle (used in most of Europe and Asia) puts it below. Same views, different layout; a small symbol in the title block says which one you are reading. Try it below: the three views come from a real 3D model, projected live, with hidden lines worked out by ray-casting.
The part is an L-bracket, 60 × 40 × 40 mm, with a 12 mm vertical hole in the base, a 10 mm horizontal hole through the upright and a notch in one corner. Solid lines are visible edges and dashed lines are hidden ones. Drag the picture to rotate it.
Every dimension is a range: tolerance and stack-up
No machine makes anything exactly 25.000 mm, and nothing needs to. What matters is how far off is still acceptable. A tolerance is that allowed range: 25 ± 0.1 mm means anything from 24.9 to 25.1 is good. Tight tolerances cost money (more careful machines, more inspection, more scrap), so the designer's job is to give each dimension the loosest tolerance that still works.
The trouble is that tolerances add up. Put three parts in a housing: the gap left over is the housing size minus all three parts, so every ± feeds into the gap. Adding the extremes gives the worst case, which is safe but costly. But it is very unlikely that every part lands at its extreme in the same direction. If you treat each ± as three standard deviations of a bell curve, the combined spread is the square root of the sum of the squares, the statistical (root-sum-square) stack:
Worked number: a 100 mm housing holds parts of 30, 40 and 28 mm, leaving a 2 mm gap. With tolerances ±0.30, ±0.20, ±0.20 and ±0.15 mm, worst case is ±0.85 mm (gap 1.15 to 2.85 mm). The statistical range is ±0.44 mm. That 2:1 difference is why statistical stacks let designers loosen tolerances; it is also a bet that your manufacturing really is centred and random.
The statistical figure assumes each tolerance is three standard deviations of a normal distribution and the parts are independent. Check this against real inspection data before relying on it.
One more everyday consequence: how you dimension decides how tolerances add. Dimension a row of holes as a chain (each from the last) and the errors accumulate along the chain. Dimension them all from one datum edge and each hole only inherits its own tolerance. Good drawings dimension from the surfaces that matter, and never make the machinist do arithmetic.
Fits, and GD&T in plain words
When a shaft goes into a hole, what matters is the gap between them. A fit is a standard pairing of tolerances chosen for the job. ISO 286 names them with letters and numbers: a capital letter for the hole, a lowercase one for the shaft, and a number for the tolerance grade. For a 25 mm size, H7 for the hole means 25.000 to 25.021 mm. Pair it with g6 and the shaft runs freely; with k6 you may get either a small gap or a small squeeze (a transition fit); with p6 you must press the shaft in (an interference fit), and the parts then grip by friction alone.
Deviations are for the 18 to 30 mm size band from ISO 286 tables (H7: 0 to +21 µm, g6: −20 to −7, h6: −13 to 0, k6: +2 to +15, p6: +22 to +35). A micrometre is a thousandth of a millimetre; a human hair is very roughly 50 to 100 of them.
A ± size tolerance only controls the size at each point. It says nothing about whether the hole is straight, round, square to the face, or in the right place. Geometric dimensioning and tolerancing (GD&T) is a language of symbols for exactly that: flatness, perpendicularity, roundness, and above all position. Each rule reads like a short sentence: "this hole's axis must lie within a 0.2 mm circle, measured from datum surfaces A, B and C." The datums are the three flat faces that sit the part on a table, against one wall, and against another; they are how a maker and an inspector agree on where "measure from" is. A circular position zone also holds more good parts than a square ± box with the same corner reach: a ±0.1 mm square has area 0.040 mm², and the circle through its corners (0.283 mm across) 0.063 mm², about 57% more. In the US the rulebook is ASME Y14.5 (the 2018 edition, reaffirmed in 2024); ISO has its own set.
Parametric CAD: you draw the intent, not the shape
Computer-aided design began as an electronic drafting board. Ivan Sutherland's Sketchpad, in the early 1960s, let a person draw with a light pen and have the computer keep the lines connected. Modern CAD went further: since the late 1980s (PTC's Pro/ENGINEER shipped in 1988), mainstream CAD records how you built the shape. You draw a 2D sketch, add constraints (this line is horizontal, that circle is 12 mm, these two are equal), then extrude or cut it into a solid. Every step goes into a feature tree and every number is a parameter, so changing one rebuilds the part.
The point is design intent: the rules you chose say what must stay true when something changes. Widen this plate: should the hole stay 30 mm from the wall, or stay in the middle? Both are legitimate, and they are different parts. Try it.
Tap constraints on and off. The plate sketch is a rectangle (8 coordinates) and a circle (3 numbers) = 11 degrees of freedom. Each constraint removes some.
From the model to simulation and the shop floor
Once a part exists as a precise digital solid, two things become cheap. First, you can simulate it. The standard tool is the finite element method (FEA): chop the part into thousands of little elements, write the equations of stiffness for each one, and solve all of them together for how the part deforms and where the stress is. It is a numerical answer, and the discipline is to ask how wrong is it? The way to find out is to refine the mesh and see whether the answer settles. The bar below is a real, tiny finite-element model: a tapered aluminium bar, pulled with 10 kN at the thin end.
Bar: 100 mm long, cross-section tapering from 200 mm² at the wall to 50 mm² at the free end, E = 70 GPa, 10 kN axial load. Each element has linear displacement, so its stress is one constant number. The exact answers come from integrating the load over the taper.
Look at the two errors. Movement settles quickly; stress, which depends on the slope of the movement, converges much more slowly, and the worst stress is usually where it matters most. A graduate never trusts a coloured stress plot with one mesh. Second, the same model feeds manufacturing. CAM (computer-aided manufacturing) turns the solid into toolpaths: a list of moves for a CNC machine (often G-code) to cut the part from stock. For 3D printing the model is sliced into layers and each layer into a toolpath. The drawing doesn't disappear: the tolerances, fits and datums are still what the inspector checks, even if the model carries them.
What a graduate just sees
- A drawing is a contract: if it matters, it is on the drawing, and a change needs a check.
- Any object can be read from two or three orthographic views; hidden features are dashed.
- Every dimension is a range, and tolerances cost money.
- Tolerances stack: worst case is the sum, statistical is the root-sum-square, and datum dimensioning stops errors accumulating.
- A fit is a pairing of two tolerances, and "clearance, transition, interference" is a ladder from sliding to pressed.
- A size tolerance doesn't say the part is straight or in the right place; GD&T does.
- A CAD model is a record of intent, with sketch, constraints and a feature tree; what you constrain is what stays true.
- A simulation is a number with an error bar, and you check it by refining the mesh.
Where it shows up next
- Machine Design (34/19): every shaft, gear and bolted joint you design ends up as a dimensioned drawing, with fits for the bearing seats.
- Materials Science & Manufacturing (34/13): the process (casting, machining, printing) sets the tolerances you can realistically ask for.
- Mechanics of Materials (34/11): FEA is the numerical cousin of the beam and stress formulas.
- Systems Engineering & the Capstone (34/22): interface drawings are how subsystems built by different teams agree to fit.
- In the real world: product design, a car's body panels fitting with an even gap, an aircraft's thousands of parts matching across suppliers.
If you want to go deeper
- 📘 Standard texts: Giesecke and co-authors, Technical Drawing with Engineering Graphics (Pearson, 15th edition; a 16th is listed), the usual first-year text. Gene Cogorno, Geometric Dimensioning and Tolerancing for Mechanical Design (McGraw Hill, 3rd edition), for GD&T. The standard itself is ASME Y14.5-2018.
- 📘 Gentler: the free MIT OpenCourseWare short course How to CAD Almost Anything (RES.16-002), a hands-on introduction to parametric modelling through reverse engineering.
- 🌐 Free course: NPTEL: Engineering Graphics and Design (IIT Delhi, Profs. Naresh Datla and S. R. Kale).
A drawing is the contract between a designer and a maker: views to say the shape, dimensions and tolerances to say how exactly, fits and GD&T to say how parts meet. Tolerances add up, so you stack them deliberately. CAD records your intent so changes rebuild correctly, and simulation and manufacturing both read the same model, which is why you check each by asking how wrong it could be.
Try this: pick any small object with a few parts (a hinge, a jar lid) and sketch its front, top and side views. Then guess which two dimensions matter most for it to work, and what a ±1 mm error on each would do.
Sources. Hyatt Regency collapse: US National Bureau of Standards, NBSIR 82-2465 (1982) and its NIST-hosted summaries; the Linda Hall Library notes (114 deaths; NIST pages and UPI report 113). Third/first angle: ISO 128 and ASME Y14.3 as summarised by Xometry and Peachpit. ISO 286 fits for 18 to 30 mm: ISO 286-2 values as reproduced by cadforum.cz (H7, g6, h6, k6, p6). ASME Y14.5-2018 (R2024): ASME and ANSI webstore listings. Pro/ENGINEER commercial shipments from January 1988: PTC history summaries. Sketchpad (Sutherland, early 1960s): PTC/NovEdge history summaries. Numbers computed in node: the three views and hidden lines by ray-casting; stack-up (worst case 0.85, statistical 0.439); the p6 and g6 limits; position-zone areas (0.040 and 0.063 mm²); and the tapered-bar finite-element model checked against its exact integral (exact tip movement 0.13203 mm).
- 🌐 NPTEL: Engineering Graphics and Design
- 🌐 MIT OpenCourseWare: How to CAD Almost Anything
- 📘 Giesecke et al., Technical Drawing with Engineering Graphics
- 📘 Cogorno, Geometric Dimensioning and Tolerancing for Mechanical Design