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Mechanisms & Drive Systems
How machines move — the four types of motion, gears and gear trains, belt and chain drives, friction, and the drive-system calculations.
Motion and mechanisms Exam
A mechanism is a part of a machine that changes one type of motion into another, or transfers force from one place to another. Mechanisms make machines safer, easier to use and more efficient.
| Type of motion | Meaning | Engineering example |
|---|---|---|
| Rotary | turning round and round | electric motor shaft, drill chuck |
| Linear | moving in a straight line in one direction | conveyor belt, lift cage |
| Reciprocating | moving back and forth in a straight line | piston in an engine, jigsaw blade |
| Oscillating | swinging back and forth around a pivot | pendulum, windscreen wiper arm |
Levers Enrichment
Enrichment — N4 progression. Levers are useful background, but the lever classes are not on the National 5 assessment list. For N5 revision, prioritise motion, gears, belt/chain drives and friction.
A lever is a rigid bar that pivots about a point called the pivot (or fulcrum). Levers change the size or direction of a force. The three parts are the effort (E — the force you apply), the load (L — the force you are moving) and the pivot (F).
| Class | Order | Engineering example |
|---|---|---|
| Class 1 | pivot in the middle (E — F — L) | pliers, scissors, see-saw, claw hammer |
| Class 2 | load in the middle (F — L — E) | wheelbarrow, bottle opener, nutcracker |
| Class 3 | effort in the middle (F — E — L) | fishing rod, tweezers, robot arm |
Linkages Enrichment
Enrichment — N4 progression. Linkages are good breadth, but are not part of the National 5 assessment list. Focus your N5 revision on the gear, drive-system and friction content below.
A linkage is made from rigid bars (links) joined by pivots. Engineers use linkages to change the direction or position of a movement.
| Linkage | Function |
|---|---|
| Reverse motion | changes the direction of motion (input one way, output the other way) |
| Push/pull | transmits motion in a straight line, in the same direction |
| Bell crank | changes the direction of motion through 90° |
| Parallel motion | keeps the output moving parallel to the input |
Gears and gear trains ExamAssignment
The driver gear is connected to the input (the motor); the driven gear is the output. An idler between them reverses the direction of rotation but does not change the ratio or the speed.
Use the data-booklet method. For any gear, belt or chain drive:
input speed × input size = output speed × output size. "Size" means teeth for a gear
or sprocket, and pulley diameter for a belt. Markers reward this relationship — candidates who
invent a "movement-multiplier" ratio instead tend to score less.
Gear ratio
gear ratio = N2N1
driven teeth ÷ driver teeth · a ratio (e.g. 3 : 1)
Drive relationship
n1 N1 = n2 N2
input speed × input size = output speed × output size
Velocity ratio
VR = n1n2
input speed ÷ output speed · a ratio
A gear ratio greater than 1 means the output turns more slowly than the input. A ratio less than 1 means the output turns faster. Speeds are in revs min⁻¹.
Gear ratio — gear ratio = N2 ÷ N1
Worked example — substitute & solve
Substitute & solve
A driver gear has 20 teeth. The driven gear has 60 teeth. Calculate the gear ratio.
gear ratio=N2 ÷ N1
gear ratio=60 ÷ 20
gear ratio=3 (3 : 1)output 3× slower
Worked example — ratio less than 1 (speed increase)
Substitute & solve
A driver gear has 60 teeth and the driven gear has 20 teeth. Calculate the gear ratio and state the effect on speed.
gear ratio=N2 ÷ N1
gear ratio=20 ÷ 60
gear ratio=0.33 (1 : 3)ratio < 1 = faster
The output turns 3 times faster than the input.
Output speed — n1 N1 = n2 N2
Worked example — substitute & solve
Substitute & solve
A 20-tooth driver gear turns at 600 revs min⁻¹ and meshes with a 40-tooth driven gear. Calculate the output speed.
n1 N1=n2 N2
600 × 20=n2 × 40numbers in first
n2=12 000 ÷ 40now rearrange
n2=300 revs min⁻¹
Worked example — rearrange (find the teeth)
Rearrange — numbers in first
A 30-tooth driver gear turns at 800 revs min⁻¹. The output must turn at 200 revs min⁻¹. Calculate the number of teeth needed on the driven gear.
n1 N1=n2 N2
800 × 30=200 × N2numbers in first
N2=24 000 ÷ 200now rearrange
N2=120 teeth
Compound gear trains
In a compound gear train, two gears share the same shaft, so they turn at the same speed. The output of the first gear pair becomes the input of the next. Work through the train one pair at a time.
Worked example — two-stage compound train
Substitute & solve — stage by stage
A motor turns gear A at 1200 revs min⁻¹. Gear A (10 teeth) meshes with gear B (40 teeth). Gear B is on the same shaft as gear C (20 teeth), which meshes with gear D (60 teeth). Calculate the speed of gear D.
Stage 1 — A drives B:
1200 × 10=nB × 40
nB=12 000 ÷ 40 = 300 revs min⁻¹
Stage 2 — C (same shaft as B, so 300 revs min⁻¹) drives D:
300 × 20=nD × 60
nD=6000 ÷ 60 = 100 revs min⁻¹
Simulate it — NoStrainSim Drive Trains Assignment
Your booklet's ▶ SIMULATE IT tasks use the free NoStrainSim — Drive Trains builder — no kit needed. Predict first with the data-booklet method, then run the sim and compare.
▶ Simulate it 1
Driver, driven and the idler
- Build a gear pair (driver + driven). Run it and note the direction of each gear.
- Change one thing: add an idler gear between them and run again. What happens to the direction? To the RPM?
- Predict, then test: does a second idler change the speed?
▶ Simulate it 2
Gear ratio and output speed
- Motor at 600 rev/min, 20-tooth driver meshing a 40-tooth driven gear. Predict the output with n₁N₁ = n₂N₂ before you run.
- Change one thing at a time — driven gear to 60 teeth, then 10 teeth, then motor to 1200 rev/min — predicting each result first.
- Discuss: when is the output slower than the input, and when is it faster?
▶ Simulate it 3
Build and verify a compound train
- Build the worked example above: motor 1200 rev/min → A (10T) drives B (40T); C (20T) shares B's shaft and drives D (60T). Predict D's speed first (you should get 100 rev/min).
- Change one thing: swap C for a 10-tooth gear. Predict, then check the new speed of D.
- Use Export Image to save your train as evidence for the Booklet 8 assignment.
Assignment link. When you design and justify a drive system in your assignment (Task 3: gear train, velocity ratio and a compound design), see Booklet 8 — Assignment Skills: work out VR from the speeds you actually recorded, aim for a speed reduction, and justify each specification point with a direction, a calculation or a gear type.
Belt and chain drives Exam
A belt drive transmits drive by friction between the belt and the pulleys — smooth and quiet, but it can slip. A chain drive locks onto toothed sprockets — it cannot slip and transmits large forces, but is noisier and needs lubrication.
| Belt drive | Chain drive | |
|---|---|---|
| How it works | flexible belt loops two pulleys; friction transmits the drive | metal chain locks onto toothed sprockets |
| Advantages | smooth, quiet, can slip safely if overloaded | does not slip; reliable; transmits large forces |
| Disadvantages | can slip and waste energy; wears out | noisier; needs lubrication; can stretch and wear |
Belt and chain drives use the same data-booklet relationship as gears — input speed × input size = output speed × output size — with the pulley diameter (belt) or sprocket teeth (chain) as the size. Unlike meshing gears, the output turns in the same direction as the input.
Worked example — belt drive (substitute & solve)
Substitute & solve
A driver pulley of 50 mm diameter turns at 1000 revs min⁻¹. The driven pulley has a diameter of 200 mm. Calculate the output speed.
n1 d1=n2 d2
1000 × 50=n2 × 200numbers in first
n2=50 000 ÷ 200now rearrange
n2=250 revs min⁻¹
Worked example — chain drive (substitute & solve)
Substitute & solve
A bicycle has a chainwheel with 40 teeth and a rear sprocket with 20 teeth. The chainwheel turns at 80 revs min⁻¹. Calculate the speed of the rear wheel.
n1 N1=n2 N2teeth as the size
80 × 40=n2 × 20
n2=3200 ÷ 20
n2=160 revs min⁻¹faster — smaller sprocket
Worked example — rearrange (find the diameter)
Rearrange — numbers in first
A 60 mm driver pulley turns at 1500 revs min⁻¹. A fan must turn at 500 revs min⁻¹. Calculate the diameter of the driven pulley needed.
n1 d1=n2 d2
1500 × 60=500 × d2numbers in first
d2=90 000 ÷ 500now rearrange
d2=180 mm
▶ Simulate it 4
Belt and chain drives
- Build a belt drive, then a chain drive. Compare the output direction with a meshing gear pair — what is different?
- Change one thing: make the driven pulley 3× the driver's diameter (60 mm → 180 mm). Predict the output at 900 rev/min, then check (you should get 300 rev/min).
- Discuss: a belt can slip, a chain cannot. Which suits (a) a quiet office printer, (b) a bicycle?
▶ Extension sims — changing the type of motion, and speed vs turning effort
- Sim 5 — Rotary → linear. Add a rack and pinion, then swap it for a lead screw. Both convert rotary → linear; the lead screw moves the load more slowly for the same motor speed — engineers use it for high force and precision. A worm & wheel turns the axis through 90°.
- Sim 6 — Speed vs turning effort. A worm acts like a 1-tooth gear, so a worm driving a 40-tooth wheel gives about a 40 : 1 reduction. Big speed reduction ⇒ large turning effort — that's why winches and hoists use worm drives.
- ★ Design brief — hit the target. From a 1000 rev/min motor, design a drive whose output turns at roughly 100 rev/min in the same direction as the motor. (Hint: a belt or chain keeps the direction; a gear reduction does the slowing.) Save the .json and Export Image as assignment evidence.
British Standards drive-system symbols
Engineers use the standard BS symbols from the data booklet so a drive-system drawing means the same thing to everyone. Learn to recognise them and use them in your own designs.
Spur gear
A toothed wheel on a shaft that meshes with another to transmit drive.
Gear train
Two or more meshing gears shown together on parallel shafts.
Belt & pulley drive
Two pulleys linked by a belt; drive transmitted by friction.
Chain & sprocket drive
Toothed wheels linked by a chain (dashed line); drive cannot slip.
Shaft
A rotating bar that carries gears or pulleys.
Bearing
A support that lets a shaft turn with low friction.
Friction Exam
Friction is a force that opposes motion between two surfaces in contact. In a mechanism it wastes energy as heat and sound, reduces efficiency, causes wear of moving parts and can cause overheating.
| Method of reducing friction | How it helps |
|---|---|
| Lubrication (oil or grease) | separates the two surfaces so they do not rub |
| Bearings | replace sliding contact with rolling contact |
| Smooth surfaces | reduce roughness and so reduce friction |
| Lighter loads | less force pressing the surfaces together |
Friction is not always bad. On a bicycle it is helpful at the brakes and where the tyres grip the road — and wasted energy in the chain, bearings and axles. "Explain" questions want a cause and a related effect: friction → heat → wasted energy → lower efficiency.
Common mistakes — watch out for these in the exam
- Using a made-up "movement multiplier" instead of the data-booklet relationship input speed × input size = output speed × output size.
- Mixing up driver and driven — the driver provides the input, the driven is the output.
- Thinking an idler changes the gear ratio — it only changes the direction of rotation.
- Forgetting the unit revs min⁻¹ on a speed answer.
- "Explain" questions: give one cause and one related effect, not just a single statement.
Check your booklet work
Try each task in your booklet first, then open the matching answer. Calculations show the final value — full worked methods use n1N1 = n2N2 throughout.
Task 1 — Identify the motion §1
- Blade of an electric jigsaw — reciprocating
- Output shaft of a motor — rotary
- Child swinging on a swing — oscillating
- Lift moving up a shaft — linear
- Needle of a sewing machine — reciprocating
- Hands of a clock — rotary
Task 2 — Identify the lever class §2
- Pliers — class 1 · Wheelbarrow — class 2 · Tweezers — class 3
- Bottle opener — class 2 · See-saw — class 1 · Fishing rod — class 3
Task 3 — Identify the linkage §3
- Bicycle brake (motion at 90°) — bell crank
- Toolbox lid staying parallel — parallel motion
- Control rod, output same way — push/pull
- Toy crocodile, opposite handles — reverse motion
Try This — final answers
Try This — Gear ratio §4
- 45 ÷ 15 = 3 (3 : 1)
- 20 ÷ 60 = 0.33 (1 : 3) — the output turns faster
- 90 ÷ 30 = 3 (3 : 1)
Try This — Output speed §4
- (800 × 25) ÷ 50 = 400 revs min⁻¹
- (100 × 60) ÷ 20 = 300 revs min⁻¹
- (1200 × 30) ÷ 90 = 400 revs min⁻¹
Try This — Compound gear trains §4
- nB = (900 × 20) ÷ 40 = 450; nD = (450 × 10) ÷ 30 = 150 revs min⁻¹
- nB = (1200 × 10) ÷ 50 = 240; nD = (240 × 20) ÷ 40 = 120 revs min⁻¹
- nB = (1500 × 15) ÷ 30 = 750; nD = (750 × 20) ÷ 60 = 250 revs min⁻¹
Try This — Belt and chain drives §5
- (900 × 60) ÷ 180 = 300 revs min⁻¹
- (80 × 40) ÷ 20 = 160 revs min⁻¹
- (1500 × 75) ÷ 150 = 750 revs min⁻¹
Section practice — final answers
Practice — Motion and Mechanisms §1
- A part of a machine that changes one type of motion into another, or transfers force.
- Rotary.
- Linear is a straight line in one direction; reciprocating is back and forth in a straight line.
- Any two: pendulum, swing, windscreen wiper, swinging arm.
- Linear.
- Reciprocating.
- Rotary.
- To change motion or transfer force — making the machine safer, easier to use or more efficient.
- Any two: drill, fan, motor, clock, wheel.
- A crank and slider (or cam) — e.g. the piston in a car engine, a jigsaw blade.
Practice — Levers §2 · enrichment
- The fixed point the lever turns about (the fulcrum).
- Class 2.
- Class 3.
- Class 1.
- Class 2.
- Class 3.
- Class 1 has the pivot in the middle; class 3 has the effort in the middle.
- Load = the nail; effort = your hand on the handle; pivot = where the hammer head rests on the wood.
- e.g. a wheelbarrow — the load sits between pivot and effort, so a large load is moved with a small effort.
- The effort is closer to the pivot than the load, so the effort must be larger than the load — the trade-off is a large movement at the tip.
Practice — Linkages §3 · enrichment
- Rigid bars (links) joined by pivots that transfer or change movement.
- Bell crank.
- Reverse motion linkage.
- Keeps the output moving parallel to the input.
- Transmits motion in a straight line, in the same direction.
- Bell crank.
- Parallel motion.
- Two bars crossing at a central fixed pivot; input arrow one way, output arrow the opposite way.
- e.g. a bicycle brake — the cable's pull is turned through 90° to press the brake pad.
- A parallel motion linkage keeps the board level (parallel) as it moves; a push/pull rod would let it tilt.
Practice — Gears and Gear Trains §4
- gear ratio = N2 ÷ N1 (driven teeth ÷ driver teeth).
- 80 ÷ 20 = 4 (4 : 1)
- (600 × 30) ÷ 60 = 300 revs min⁻¹
- (1200 × 40) ÷ 10 = 4800 revs min⁻¹
- Reverses the direction of the driven gear; does not change the ratio or output speed.
- nB = (1200 × 10) ÷ 50 = 240; nD = (240 × 20) ÷ 40 = 120 revs min⁻¹
- 4 times slower.
- 800 ÷ 5 = 160 revs min⁻¹
- It reverses the direction of the driven gear; the ratio and output speed are unchanged.
- nB = (960 × 12) ÷ 48 = 240; nD = (240 × 15) ÷ 60 = 60 revs min⁻¹
Practice — Belt and Chain Drives §5
- Friction between the belt and the pulleys transmits the drive.
- Does not slip / transmits larger forces / more reliable.
- Noisier / needs lubrication / can stretch and wear.
- (1200 × 80) ÷ 240 = 400 revs min⁻¹
- (600 × 50) ÷ 100 = 300 revs min⁻¹
- (60 × 48) ÷ 16 = 180 revs min⁻¹
- Chain — it cannot slip and transmits the large pedalling forces reliably.
- Belt — it runs quietly and smoothly.
- A belt can slip if the machine jams or is overloaded, protecting the motor and the operator.
- (600 × 20) ÷ 40 = 300 revs min⁻¹
Practice — Friction §6
- A force that opposes motion between two surfaces in contact.
- It wastes energy as heat and causes wear — lowering the efficiency (cause + effect).
- Any two: lubrication, bearings, smoother surfaces, lighter loads.
- Friction converts useful energy to heat/sound, so less of the input becomes useful output — lower efficiency.
- Bearings give rolling (not sliding) contact, so there is less friction — less wear and a freer spin.
- Lubrication reduces friction and wear and stops the chain seizing.
- A worn gear has a rougher, looser contact, so there is more friction — more energy is turned into heat.
- The brakes / the tyres gripping the road / the pedal grip.
- The chain, bearings or axles (anywhere friction resists rotation).
- Over time friction causes wear and heat (energy loss, looseness); engineers reduce them with lubrication, bearings and smoother surfaces.
▶ Simulate It 1–6 — expected results §4–5
- Sim 1 (idler): one idler flips the driven gear's direction back; the RPM is unchanged. A second idler flips it again — speed still unchanged. An idler changes direction, never ratio or speed.
- Sim 2 (ratio/output): baseline 600 → 300. Driven 60T → 200; driven 10T → 1200 (faster than the motor); motor 1200 with 20/40 → 600.
- Sim 3 (compound): D = 100 rev/min; with C = 10T, D = 200 rev/min.
- Sim 4 (belt/chain): a gear pair turns the output the opposite way; belt and chain keep it the same way. 60 → 180 mm at 900 gives 300 rev/min.
- Sims 5–6 (extension): rack & pinion and lead screw both give rotary → linear; the lead screw is slower, for high force and precision. A worm & 40T wheel ≈ 40 : 1 reduction with the axis turned 90° — big speed reduction means a big turning effort (winches, hoists).
Check yourself
Ready for exam questions? Open the
Past Paper Finder
and look for the mechanisms and drive-system questions.
Sources & credits: The Topic 5 booklet © R Stewart, 2026. NoStrainSim Drive Trains is a free simulator by R Stewart. The Past Paper Finder is compiled by Mr McDonald, 2024; past-paper questions © Qualifications Scotland (SQA). The N4/N5 data booklet is reproduced for educational use, © Qualifications Scotland (SQA).