Key Idea: MA = load ÷ effort — a ratio of FORCES. VR = effort distance ÷ load distance, or input speed ÷ output speed — a ratio of DISTANCES, fixed by geometry.\n\nEfficiency = MA ÷ VR × 100%, and the gap between them is friction as heat.\n\nEverywhere: driven ÷ driver, in teeth for gears and diameters for belts. Stages in series multiply, and so do efficiencies.\n\nA cam turns rotary into reciprocating, and its profile is the specification — lift, lobes and dwell.\n\nA lever obeys one equation: effort × effort arm = load × load arm, both measured from the fulcrum.
Paper 1 — multiple choice
- Calculate an MA, a VR or an efficiency
- Find an output speed from a ratio
- Identify what an idler does to a ratio
- Read a cam lift or count its lobes
Paper 2 — analysing a product
- Work a multi-stage ratio through a real product
- Design a gear train to a stated speed
- Analyse a cam system and its timing
- Calculate on a lever and recommend a change
Carried into the design project
- Criterion D — a ratio claim must be measured on your model
- Record the effort your user actually has to apply
- Friction losses are evidence: measure them, do not assume them
MA, VR and efficiency are confused constantly, and the confusion is always the same one: forces against distances. Keeping them apart is most of the topic.
| Quantity | What it compares | Where it comes from |
|---|---|---|
| Mechanical advantage | FORCES: load ÷ effort | Measured on the real machine, and always lower than the geometry promised |
| Velocity ratio | DISTANCES or SPEEDS: effort ÷ load, or input ÷ output | Pure geometry — tooth counts, diameters, arm lengths |
| Efficiency | The two against each other: MA ÷ VR × 100% | The friction that took the difference, as heat |
Both ratios worked on the same three mechanisms, so the difference stops being abstract.
🔒 Interactive diagram
Explore the labelled diagram, charts and maps for this topic in study mode.
Important: The ratio upside down — it is always driven ÷ driver, and load ÷ effort.\n\nAdding stage ratios instead of multiplying them: 15 and 6 give 90, not 21.\n\nCounting an idler in the arithmetic, when it changes only the direction.\n\nRecommending less friction on a worm drive or a screw jack, where the friction is what holds the load.
| What to read | Where | What it decides |
|---|---|---|
| Cam lift | Largest radius minus smallest | How far the follower moves — the stroke of the needle, valve or arm |
| Rises per revolution | The number of lobes | One for pear, circular or eccentric; two for oval; three for triangular |
| Dwell | A stretch of constant radius | The follower holds still while the shaft keeps turning |
| Lever class | Whichever of F, L and E is in the middle | Second always multiplies force; third always multiplies movement |
| Lever ratio | Effort arm ÷ load arm, from the fulcrum | The MA, and the distance the effort end must travel |
Each profile beside the motion it produces — the graph is computed from the same shape.
🔒 Interactive diagram
Explore the labelled diagram, charts and maps for this topic in study mode.
Driven ÷ driver, always.\n\nSeries ratios multiply, and so do efficiencies.\n\nAn idler changes direction, never the ratio.\n\nA worm cannot be back-driven — which is why it is only 50% efficient and why that is deliberate.\n\nF, L, E for first, second and third class levers.
A winch uses a 1,500 rpm motor, a 4:1 belt drive and a 25:1 worm gearbox, and lifts a 3,000 N load with a 20 N effort at the motor. Apply the three ratios to find the drum speed, the MA, the VR and the efficiency.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A display turntable must rotate once every 20 seconds from a 2,400 rpm motor. Construct a suitable drive and justify it.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
A hand-operated rotary can opener becomes hard to turn after a year. Analyse the likely causes.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
What is the difference between MA and VR?
What happens to ratios and efficiencies in series?
What does an idler gear do?
Why is a worm drive only 50-70% efficient, and why is that wanted?
What three things identify a cam?
State the lever equation and its check.
Exam tips
- Write driven ÷ driver and load ÷ effort before substituting anything.
- Multiply stage ratios and efficiencies; never add them.
- Leave an idler out of the arithmetic and use it only for direction.
- Check every efficiency is below 100% — above it means a figure is wrong.
- For a cam, give the lift, the lobes and the dwell.
- For a lever, classify by what is in the middle before calculating.