Calculate mechanical advantage for levers and gears using simple ratios, represent gear systems graphically, and break a bicycle gear system into a systems diagram.
Every lever has three key points: the fulcrum (F, the pivot), the load (L, the resistance being overcome) and the effort (E, the force you apply). Which of the three sits in the middle decides the lever's class — and that, in turn, decides what mechanical advantage it can give you.
| Class | Order along the lever | Example | Mechanical advantage |
|---|---|---|---|
| First-class | Load — Fulcrum — Effort (fulcrum in the middle) | See-saw, crowbar, single paper scissors | Can be >1, =1 or <1 depending on arm lengths |
| Second-class | Fulcrum — Load — Effort (load in the middle) | Wheelbarrow, nutcracker, office punch | Always > 1 — the load arm is always shorter than the effort arm |
| Third-class | Fulcrum — Effort — Load (effort in the middle) | Tweezers, fishing rod, light-duty stapler | Always < 1 — trades force for extra speed/distance at the load end |
Mechanical advantage (MA) compares the load a machine lifts or moves to the effort you put in. For levers, we calculate MA using simple ratios — NOT by "taking moments about a point" (that method comes later, in higher grades). At Grade 8 level, use these two equivalent ratio methods:
The effort arm is the distance from the fulcrum to where you apply your effort force. The load arm is the distance from the fulcrum to the load. The longer the effort arm is compared to the load arm, the greater the mechanical advantage.
| Lever example | Class | Mechanical advantage |
|---|---|---|
| Paper scissors (equal blade & handle) | First-class | MA = 1 (no advantage) |
| Secateurs (long handle, short blade) | First-class | MA > 1 |
| Office punch / heavy-duty stapler | Second-class | MA > 1 (always) |
| Light-duty stapler / tweezers | Third-class | MA < 1 (never gives advantage) |
For gears, we calculate MA using the ratio of teeth or the ratio of gear wheel diameters, instead of load and effort arms:
The velocity ratio (VR) works the opposite way around — it tells you how many times the driver must turn to turn the driven gear once:
Gear systems are drawn using circles (for the pitch circles of each gear) drawn with a pair of compasses or circular templates, sized proportionally to the number of teeth. When sketching gear systems you should be able to show:
Any mechanical system can be analysed by breaking it down into three parts: what goes IN, what happens during the PROCESS, and what comes OUT.
A bicycle gearing system is a classic real-world gear train, and CAPS uses specific terminology for it:
| Term | Meaning in a bicycle |
|---|---|
| Master / driver | The chain wheel (attached to the pedals) — the part you put effort into. |
| Slave / driven | The rear cog (attached to the back wheel) — the part that produces the output. |
| Chain wheel | The large front gear turned directly by the pedal cranks. |
| Cogs (sprockets) | The smaller gears at the back wheel, of different sizes for different gear ratios. |
A large chain wheel paired with a small rear cog gives a high velocity ratio — the back wheel spins many times per pedal turn, ideal for speed on flat roads. A small chain wheel paired with a large rear cog gives strong mechanical advantage but a low output speed, ideal for climbing hills.
Switch between a lever and a gear system, enter your own values, and see the mechanical advantage calculated live with a matching diagram.