Gear Systems: Simple, Compound, Worm, Rack & Pinion, Bevel

This lesson covers the main types of gear systems used in mechanical products. Gears are a core topic in AQA GCSE Design and Technology (8552), Section 3.1.5, and are essential for understanding how machines control speed, force and direction.

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What Are Gears?

Gears are toothed wheels that mesh together to transmit rotary motion and force from one shaft to another. Gears can:

• Change the speed of rotation
• Change the direction of rotation
• Multiply force (torque) at the expense of speed, or vice versa

Key Gear Terminology

Term	Definition
Driver gear	The gear connected to the input (motor/handle) — provides the effort
Driven gear	The gear connected to the output — receives the motion
Teeth	The interlocking projections on the gear circumference
Gear ratio	The ratio of teeth on the driven gear to teeth on the driver gear
Meshing	When two gears are engaged (teeth interlocked)
Idler gear	A gear placed between the driver and driven gears to change direction without affecting the gear ratio
Gear train	A system of two or more meshing gears

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Simple Gear Train

A simple gear train consists of two or more spur gears meshing together. Each gear in the train meshes with the next.

The diagram below shows how meshing gears transmit motion, with the direction of rotation reversing at each gear:

graph LR
    A["🔵 Driver Gear\n(Small — 20 teeth)\nClockwise ↻"] -- "Teeth mesh" --> B["🔴 Driven Gear\n(Large — 60 teeth)\nAnticlockwise ↺"]
    B -- "Speed decreases\nTorque increases" --> C["Output:\nSlower rotation,\nMore force"]

Key Rule: Direction of Rotation

When two spur gears mesh:

• They rotate in opposite directions.
• Adding an idler gear between them causes the output to rotate in the same direction as the input.

Configuration	Driver Direction	Output Direction
Two gears (no idler)	Clockwise	Anticlockwise
Three gears (with idler)	Clockwise	Clockwise

Speed and Force Relationship

Scenario	Effect on Speed	Effect on Torque (Force)
Small driver → Large driven	Speed decreases	Torque increases
Large driver → Small driven	Speed increases	Torque decreases
Equal-sized gears	Speed unchanged	Torque unchanged

AQA Exam Tip: Remember the trade-off: gearing down (large driven gear) gives more torque but less speed — like cycling uphill in a low gear. Gearing up (small driven gear) gives more speed but less torque — like cycling on a flat road in a high gear.

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Compound Gear Train

A compound gear train has two or more gears mounted on the same shaft. This allows much larger gear ratios in a compact space.

How It Works

1. Gear A (driver) meshes with Gear B.
2. Gear B and Gear C are on the same shaft — they rotate together at the same speed.
3. Gear C meshes with Gear D (output).

The overall gear ratio is the product of the individual ratios:

$\text{Overall GR} = \text{GR}_1 \times \text{GR}_2$Overall GR=GR1​×GR2​

Worked Example

Gear	Teeth	Role
A (driver)	20	Input
B	60	Meshes with A
C (on same shaft as B)	15	Meshes with D
D	45	Output

$GR_1 = \frac{60}{20} = 3$GR1​=2060​=3

$GR_2 = \frac{45}{15} = 3$GR2​=1545​=3

$\text{Overall GR} = 3 \times 3 = 9$Overall GR=3×3=9

If the input speed is 900 RPM:

$\text{Output speed} = \frac{900}{9} = 100 \text{ RPM}$Output speed=9900​=100 RPM

Real-World Example

A hand-cranked drill uses a compound gear train. The slow rotation of the hand crank is geared up to spin the drill bit at high speed.

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Worm and Worm Wheel

A worm and worm wheel (or worm gear) uses a screw-like worm that meshes with a toothed worm wheel.

Properties

Property	Detail
Very high gear ratio	One turn of the worm advances the wheel by one tooth
Direction change	Axes are at 90°
Self-locking	The worm wheel cannot drive the worm — the system locks in place when the input stops
Compact	Large gear ratios in a small package

Gear Ratio Calculation

$GR = \frac{\text{Number of teeth on worm wheel}}{\text{Number of starts on worm}}$GR=Number of starts on wormNumber of teeth on worm wheel​

For a single-start worm and a 40-tooth worm wheel:

$GR = \frac{40}{1} = 40:1$GR=140​=40:1

This means 40 turns of the worm produce 1 turn of the wheel.

Applications

Application	Why Worm Gear Is Used
Guitar tuning pegs	Precise, small adjustments; self-locking prevents strings de-tuning
Stairlift	Self-locking prevents the platform sliding down when the motor stops
Car steering (older systems)	Converts rotary motion of the steering wheel to controlled turning
Hoist / winch	Self-locking holds the load securely when the handle is released

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Rack and Pinion

A rack and pinion converts rotary motion into linear motion (or vice versa).

• The pinion is a small circular gear.
• The rack is a flat, straight bar with teeth along its length.

How It Works

• When the pinion rotates, its teeth mesh with the rack's teeth, pushing the rack in a straight line.
• Conversely, pushing the rack linearly causes the pinion to rotate.

Applications

Application	How It Works
Car steering	Turning the steering wheel (rotary) moves the rack left/right (linear), steering the wheels
Pillar drill	Turning the handle (rotary) lowers the drill bit (linear) into the workpiece
Sliding gate	A motor drives a pinion that moves the gate along a rack
Railway (rack railway)	A pinion on the train engages a rack between the rails for steep climbs
3D printer axis	Stepper motor with pinion drives the print head along a rack

AQA Exam Tip: Rack and pinion is one of the most commonly examined mechanisms. The key fact to remember: it converts rotary motion to linear motion. Car steering is the classic example.

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Bevel Gears

Bevel gears are cone-shaped gears that transmit rotary motion between shafts at an angle — most commonly 90°.

Properties

Property	Detail
Angle change	Typically 90° but can be other angles
Speed change	If bevel gears have different numbers of teeth, speed and torque change
Direction	Both gears rotate, but their axes are at an angle

Applications

Application	How Bevel Gears Are Used
Hand drill	Handle turns a vertical shaft; bevel gears redirect motion to a horizontal drill bit
Car differential	Changes the direction of rotation from the driveshaft (longitudinal) to the axle (transverse)
Helicopter rotor	Engine power is redirected from horizontal to vertical axis

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Summary