VCE Systems Engineering (Year 12) · Unit 3 — Ethical Systems Design · 15m read

Mechanical Systems — Levers, Moments, Gears, Pulleys and Mechanical Advantage

Mechanical principles appear in every integrated system — from the gearbox on a robot to the pulley on a lift. These calculations are reliable exam marks.

Learning objective: Analyse mechanical systems using moments, mechanical advantage, velocity ratio, efficiency and gear ratios.

By the end of this lesson you can:

• I can classify levers and calculate moments.
• I can calculate mechanical advantage, velocity ratio and efficiency.
• I can calculate gear ratios and output speed and torque.

Machines trade force for distance. A lever or gear lets a small force move a big load — but you pay by moving further or turning more.

Levers and moments

LEVER CLASSES (by what is in the middle):
• Class 1 — FULCRUM in the middle (see-saw, scissors).
• Class 2 — LOAD in the middle (wheelbarrow, bottle opener).
• Class 3 — EFFORT in the middle (tweezers, fishing rod).

MOMENT = force × perpendicular distance from the pivot (N m).
In balance: clockwise moments = anticlockwise moments.

Mechanical formulas

• Moment: M = F \times d
• Mechanical advantage: MA = \dfrac{\text{load}}{\text{effort}}
• Velocity ratio: VR = \dfrac{\text{distance moved by effort}}{\text{distance moved by load}}
• Efficiency: \eta = \dfrac{MA}{VR} \times 100\%
• Gear ratio: GR = \dfrac{\text{teeth on driven gear}}{\text{teeth on driver gear}} (Output speed = input speed ÷ GR; output torque ≈ input torque × GR (ignoring losses))

Worked example (Medium)

A motor turning at 3000 rpm drives a 12-tooth gear that meshes with a 48-tooth gear. Find the gear ratio, output speed and the effect on torque.

1. Gear ratio. Driven ÷ driver. GR = 48 / 12 = 4
2. Output speed. Input speed ÷ GR. 3000 / 4 = 750\ \text{rpm}
3. Torque. Torque increases by about the same factor (ignoring friction). \approx 4 \times \text{input torque}

Answer: Gear ratio 4 : 1, output 750 rpm, with roughly four times the torque.

Worked example (Medium)

A pulley system lifts a 600 N load with a 200 N effort. The effort moves 4 m while the load rises 1 m. Find MA, VR and efficiency.

1. MA. Load ÷ effort. 600 / 200 = 3
2. VR. Effort distance ÷ load distance. 4 / 1 = 4
3. Efficiency. MA ÷ VR × 100%. 3/4 \times 100\% = 75\%

Answer: MA = 3, VR = 4, efficiency = 75% (losses due to friction and pulley weight).

Common mistakes

• Inverting the gear ratio It is driven over driver. Fix: Write the definition before substituting.
• Expecting 100% efficiency Friction always causes losses. Fix: MA is less than VR in real machines.

Practice questions

1. A wheelbarrow is which class of lever?

   1. Class 1
   2. Class 2
   3. Class 3
   4. Not a lever

   (1 marks)

2. A 20-tooth driver gear meshes with a 10-tooth driven gear turning at 100 rpm input. Find the output speed.

   (2 marks)

3. A 30 N force acts 0.4 m from a pivot. What force at 0.6 m on the other side balances it?

   (2 marks)

Summary

• Lever classes depend on what is in the middle.
• Moment = F × d; balance clockwise and anticlockwise moments.
• MA = load/effort, VR = distance ratio, efficiency = MA/VR.
• Gear ratio = driven/driver; speed down, torque up.