Look at a bicycle and you are looking at almost everything in this course. A chain and two sprockets turn pedalling into driving force. Bearings in the wheels and the pedals let things spin with almost no friction. Bolts clamp the handlebar stem. Springs sit in the saddle and the brakes. A shaft (the axle) carries the wheel's load. And somewhere in the frame, at a weld or a drilled hole, a crack may be growing very slowly with every pedal stroke.
Almost every machine, from a drill to a jet engine to a washing machine, is built from the same short list of standard parts, and from the same short list of ways of failing. Machine design is the craft of choosing, sizing and combining those parts so the machine does its job, for its intended life, without surprises.
Who takes it: mechanical engineers, usually in year 4, and many aerospace and manufacturing engineers.
What it's for: designing real machines out of standard parts, and making sure they don't break.
Comes after: Mechanics of Materials (34/11), Materials Science & Manufacturing (34/13), Engineering Drawing & CAD (34/18).
Leads to: Systems Engineering & the Capstone (34/22), the project where a team designs a whole machine. It leans every day on Dynamics (34/12), Vibrations (34/17) and Control Systems (34/20).
Honest line: you won't be able to certify a gearbox after this; you will see why the shaft has a step in it, why the bolt is tightened so hard, and why the crack starts at the corner.
Power is torque times speed
Every machine moves energy from a source (a motor, an engine, your legs) to a job. The rate at which it does so is power, and for anything that rotates, power is the product of two things: how hard it twists and how fast it turns.
That has a consequence that drives the whole subject: for a fixed amount of power, speed and torque trade against each other. A gear pair is a trade machine. If the driven gear has twice as many teeth, it turns at half the speed and delivers twice the torque, less the small losses in the mesh. A bicycle's low gear does exactly this: slower wheel, more force at the road, so you can climb.
Worked number: a 1 kW motor at 3,000 rpm delivers 3.18 N·m. Through a two-stage reducer of 15:60 teeth and 15:60 teeth, the overall ratio is 4 × 4 = 16, so the output turns at 187.5 rpm and, with about 98% efficiency per mesh, delivers about 48.9 N·m. Power out is about 0.96 kW; the missing 40 W is heat in the oil.
Gear sizes are drawn in proportion to tooth count. Efficiency is taken as 98% per mesh, typical of a well-made gear pair. Gears 2 and 3 share one shaft, so they turn at the same speed (gear 4 is drawn in front of gear 2).
The same idea has other forms. A belt or a chain moves power between shafts that are far apart: a chain or a toothed belt doesn't slip, so the ratio is fixed by the tooth counts; a smooth or V-belt can slip, which can protect the machine and also loses a little. Rough rule of thumb: gears for compact, exact, high-power drives with oil; chains for long, strong, rougher drives; belts for quiet, light, lubrication-free ones.
Shafts and bearings: the parts that turn
A shaft carries torque from one part to another: a motor to a gear, a gear to a wheel. When a shaft twists, the outer fibres are stretched in shear the most, and the stress there is:
The cube is the important thing. Double the diameter and the same torque produces one-eighth of the stress, so a shaft that is 26% fatter (the cube root of 2) carries twice the torque. That is why shafts are thick in the middle where torque and bending are highest, and step down where the loads are lower: material is expensive and heavy, and diameter is a cheap lever.
To size a shaft, find the torque from P = T ω, decide how much stress the material may carry (a fraction of its yield, divided by a factor of safety we'll meet below), and solve for the diameter. Try it. This is the twisting load only; real shafts also bend and have keyways, which is what the later sections are about.
Allowed shear stress = 0.577 × yield strength ÷ factor of safety (the standard distortion-energy estimate). Yields are typical values; the alloy steel is illustrative. Pure twist only.
A bearing lets a shaft turn while something else holds it in place. Bearings don't fail all at once: the steel balls and tracks wear a fatigue pit after so many revolutions. Makers rate each bearing with a load C at which 90% survive a million revolutions, and life scales with a cube for ball bearings:
Halve the load and life goes up eightfold; double it and it drops to an eighth.
Ball bearing, the 90%-survival rating life (L10), no allowance for contamination or lubrication quality. Roller bearings use a different exponent.
A bolt is a spring you stretch on purpose
A spring is simply a part designed to deflect: force equals stiffness times stretch, F = k x, and it stores energy. Two springs side by side add their stiffnesses; two in a chain are softer than either. Now look at a bolt differently: a tightened bolt is a long, thin spring, stretched by the nut, and what it squeezes (the plates) is a short, fat spring, compressed. The two forces are equal and opposite, which is the clamping force, called the preload.
Here is the surprise. When an outside load tries to pull the joint apart, the bolt doesn't carry most of it. The plates are far stiffer than the bolt, so they simply relax a little as the bolt stretches. The bolt's load rises only by its stiffness share C of the outside pull (often around 0.2), while the clamp force falls by the rest. As long as the joint stays clamped, the bolt sees a small fraction of any cycling load, which is why a well-preloaded bolt survives vibration that a loose one would not.
Class 8.8 metric bolts: proof stress 580 MPa up to 16 mm, with standard tensile-stress areas. Torque from the common rule T = 0.2 × F × d; the factor 0.2 varies from about 0.15 to 0.3 with finish and lubrication, so torque is only a rough guide to preload. A common rule is a preload of about 75% of proof load for reusable joints.
Welded joints are the permanent alternative: no preload, no loosening, but the weld and the metal beside it (the heat-affected zone) are often the weakest and most sharply shaped part of the structure, which matters a great deal in the next section.
Factor of safety: a number you choose
Designing against failure starts with the simplest comparison: factor of safety = strength ÷ stress. A part with a yield strength of 300 MPa carrying 100 MPa has a factor of safety of 3. For a steady, static load, that's almost the whole story: stay below yield, with margin.
The margin isn't a law of nature; it is a judgement. It covers loads you can't predict exactly, material scatter, manufacturing error, and what happens if the part fails. A garden chair can take a large one; an aircraft cannot afford to, so it takes a small one with very careful analysis and testing. US rules for large transport aircraft (14 CFR 25.303) apply a factor of 1.5 to the maximum loads expected in service. The same engineers who are generous on a hoist hook are tight on an aircraft wing, and both are rational.
Fatigue and stress concentration: why parts break below their strength
Static design has a trap. A part loaded and unloaded many times can break at a stress far below its strength. This is fatigue. It was first noticed on the railways: in 1842, a locomotive axle broke on the line from Versailles to Paris, near Meudon, and the carriages behind piled into it and caught fire. At least 55 people died (some accounts give far more). The engineer William Rankine, studying axle failures, recognised the importance of stress concentrations, and from about 1860 August Wöhler tested railway axles under repeated loading and showed that the swing in stress matters more than the peak, and that for steel there is a stress swing below which life seems unlimited: the endurance limit. For many steels it is roughly half the tensile strength.
The second half of the trap is stress concentration. Force flows through a part like water through a pipe, and a hole, a sharp corner or a notch makes it bunch up. For a hole in a wide plate in tension, the elastic theory (Inglis, 1913) gives the peak stress at the hole as the average stress times (1 + 2a/b), where a is half the hole's width across the load, b its depth along it. For a round hole (a = b) that is exactly 3. For a thin sharp slit it is enormous. Fatigue cracks always start at such places.
Worked number for steel with a tensile strength of 500 MPa, with its endurance limit set at 250 MPa. A smooth bar swinging ±100 MPa is far below the limit and should last indefinitely. Drill a round hole in it: the peak at the hole is 300 MPa, above the limit, and the bar lasts about 117,000 cycles, which is about 1.3 hours at 25 cycles per second. Same load, same metal, one hole.
A model steel: tensile strength 500 MPa, endurance limit 250 MPa (half), life curve fitted through 450 MPa at 1,000 cycles and 250 MPa at a million. Real parts also lose strength from surface finish, size and temperature, and a real notch is partly smoothed by yielding. The slider is a teaching model, not a design tool.
The de Havilland Comet, the first jet airliner, showed it again. Two Comet 1s broke up in the air in January and April 1954 (35 and 21 people died). Investigators at the Royal Aircraft Establishment pressurised a whole airframe in a water tank, over and over, and it burst after about 3,000 pressurisation cycles (real and simulated flights). The failure began at a fatigue crack growing from a rivet hole at the corner of a window-like cut-out for the direction-finder aerial in the roof, where the stress was concentrated. A popular version of this story blames square passenger windows, but the investigators' report was about those aerial cut-outs, and the passenger windows were not the cause. The real lessons were to design for the stress concentration, to test for fatigue, and to build in ways to stop a crack from running.
The design process: from requirements to prototype
Machine design is not one calculation; it is a loop. Requirements come first, in numbers: how much load, how fast, for how many years, at what size and cost. Then concepts: several ways to do it (gear, chain or belt? bolted or welded?), compared honestly against the requirements. Then analysis: the sizing and fatigue checks above, plus simulation, on the best concept. Then a prototype and test, which will almost always show something the analysis missed. Then round again.
Engineers genuinely differ on the balance. Some favour analysing carefully before building anything; others argue for building and testing cheaply and often, which 3D printing has made easier. Most agree that where a failure kills people, the analysis comes first. The best designs usually come from doing both.
What a graduate just sees
- Power is torque times speed, so gears and belts trade one for the other.
- A shaft's strength goes with diameter cubed; bearing life goes with load to the minus third.
- A bolt is a stretched spring; preload makes it feel a small fraction of the outside load.
- A factor of safety is a decision about what is unknown and what failure costs.
- Repeated stress breaks parts far below their strength; steel has an endurance limit of roughly half its tensile strength.
- A hole concentrates stress by 3, a sharp notch by far more, and fatigue cracks start there.
- Welds, corners and keyways are where machines break.
- Design is a loop of requirements, concepts, analysis and prototype.
Where it shows up next
- Systems Engineering & the Capstone (34/22): choosing a drive train and fastening scheme is the first big decision a capstone team makes.
- Vibrations (34/17) and Dynamics (34/12): rotating shafts have critical speeds, and gear teeth meshing is a vibration source.
- Control Systems (34/20): a motor and gearbox behind a feedback loop; gear backlash and inertia change how the loop behaves.
- Materials Science & Manufacturing (34/13) and Engineering Drawing & CAD (34/18): the steel grade, heat treatment, fits and surface finish you choose appear on the drawing.
- In the real world: why a wind turbine's gearbox is among its most expensive repairs, why cranes are inspected for cracks, why a loose wheel nut is dangerous.
If you want to go deeper
- 📘 Standard texts: Richard Budynas and Keith Nisbett, Shigley's Mechanical Engineering Design (McGraw Hill, 11th edition 2020; a 12th edition is out), the usual course text for everything above. Robert Norton, Machine Design: An Integrated Approach (Pearson), more worked examples and design-case flavour.
- 📘 Gentler: Henry Petroski, To Engineer Is Human: The Role of Failure in Successful Design (1985), how failures teach engineers, in plain language. J. E. Gordon, Structures: Or Why Things Don't Fall Down.
- 🌐 Free course: MIT OpenCourseWare 2.72, Elements of Mechanical Design (bearings, springs, gears, cams, mechanisms, with a lab project).
Machines are built from a short list of parts, each with one governing equation: power is torque times speed, a shaft's strength goes with diameter cubed, a bearing's life with load to the minus third, and a preloaded bolt is a spring that shields itself from the load. Designing against failure means a deliberate factor of safety for steady loads and, for repeated ones, respect for fatigue and above all for notches. Break the part in your head before it breaks in the field.
Try this: look at a pair of scissors, a bicycle crank or a door hinge and find the standard parts in it (shaft, bearing, bolt, spring, gear). Then find where it would crack first: look for a sharp internal corner, a hole, or a weld.
Sources. Versailles rail accident, 8 May 1842 (at least 55 dead; accounts range up to about 200), Rankine and stress concentration, Wöhler's axle tests from about 1860 and 1870 summary: Wikipedia, "Fatigue (material)" and "Versailles rail accident", and the Open University's Tay Bridge materials. Comet: Wikipedia, "de Havilland Comet" (G-ALYP, 10 January 1954, 35 dead, 1,290 pressurised flights; G-ALYY, 8 April 1954, 21 dead, 900 flights; test airframe G-ALYU burst after 3,057 cycles; cause at the ADF window cut-out; square-window account described there as a myth). Inglis stress concentration (1 + 2a/b, 3 for a circle): Wikipedia, "Stress concentration". Endurance limit of steel about 0.5 × tensile strength up to 1400 MPa: Shigley-based lecture notes. Factor 1.5: 14 CFR 25.303. Class 8.8 bolts (proof stress 580 MPa up to M16, M12 stress area 84.3 mm²): ISO 898-1 summaries. T = K F d with K about 0.2 and preload 75% of proof for reusable joints: Shigley as summarised in university case studies and lecture notes. Computed in node: gearbox numbers, shaft diameters (5 kW at 1,500 rpm: 31.8 N·m, 15.0 mm in mild steel at a factor of 3), bearing lives, bolt loads and torques, and the fatigue lives (117,000 and 2,250 cycles).
- 🌐 MIT OpenCourseWare: 2.72 Elements of Mechanical Design
- 📘 Budynas and Nisbett, Shigley's Mechanical Engineering Design
- 📘 Petroski, To Engineer Is Human
- 📘 Norton, Machine Design: An Integrated Approach