Year 10 Design & Technologies · Technologies Contexts · 12m read

Mechanical Systems — Levers, Gears, Pulleys and Mechanical Advantage

Bikes, cranes and wind-up toys all use simple machines to trade force for distance or speed. Year 10 adds the calculations — a bridge to VCE Systems Engineering.

Learning objective: Calculate mechanical advantage and gear ratios and apply mechanisms in designs.

By the end of this lesson you can:

• I can calculate mechanical advantage.
• I can calculate gear and pulley ratios.
• I can choose mechanisms for motion and force.

Mechanisms multiply your strength. A lever lets a child lift an adult on a see-saw. Gears and pulleys trade distance or speed for force — that's mechanical advantage.

Mechanical Systems — Levers, Gears, Pulleys and Mechanical Advantage

TYPES OF MOTION:
• Rotary, linear, oscillating, reciprocating.

LEVERS:
• Mechanical advantage (MA) = load ÷ effort.
• MA > 1 means less effort is needed.

GEARS:
• Gear ratio = teeth on driven gear ÷ teeth on driver gear.
• Ratio > 1 → output slower, more torque. Ratio < 1 → output faster, less torque.
• Idler gears change direction, not ratio.

PULLEYS:
• Velocity ratio = driven pulley diameter ÷ driver pulley diameter.

CONVERTING MOTION:
• Cams, cranks and sliders, rack and pinion.

| Mechanism | Formula | Example |
|---|---|---|
| Lever | MA = load ÷ effort | Crowbar |
| Gear ratio | Driven teeth ÷ driver teeth | Bike gears |
| Pulley | MA ≈ number of supporting ropes | Crane |
| Velocity ratio | Distance effort ÷ distance load | Pulley systems |

Key ideas at a glance

• MA > 1 = force gain: Less effort.
• Gear ratio trades speed for torque: Big driven gear = slower, stronger.
• Friction reduces efficiency: Real systems.
• Show calculations: With units.

Key formulas

• Mechanical advantage: MA = \dfrac{\text{load}}{\text{effort}}
• Gear ratio: \dfrac{\text{driven teeth}}{\text{driver teeth}}

Worked example (Medium)

A 12-tooth driver gear turns a 36-tooth driven gear. Find the gear ratio and output speed if the driver turns at 90 rpm.

1. Ratio. 36 ÷ 12 = 3 (3:1)
2. Output speed. 90 ÷ 3 = 30 rpm
3. Effect. Slower output with three times the torque.

Answer: Ratio 3:1; output 30 rpm.

Worked example (Medium)

A 10-tooth gear drives a 40-tooth gear. Find the ratio and effect.

1. Ratio. 40 ÷ 10 = 4:1.
2. Effect. Output 4× slower, ~4× torque.

Answer: 4:1 — slower output, more torque.

Common mistakes

• Dividing the wrong way Ratio is driven ÷ driver. Fix: Write the formula first.

Practice questions

1. A lever lifts a 600 N load with 200 N of effort. MA =

   1. 0.33
   2. 3
   3. 400
   4. 800

   (1 marks)

2. What mechanism converts rotary to linear motion in a car steering system?

   (2 marks)

3. A pulley system with 4 supporting ropes has an ideal MA of:

   1. 1
   2. 2
   3. 4
   4. 8

   (1 marks)

4. Calculate MA if a 600 N load is lifted with 150 N effort.

   (2 marks)

Summary

• MA = load ÷ effort.
• Gear ratio = driven ÷ driver.
• Mechanisms convert motion types.
• MA, gear ratios, pulleys.