Mechanical systems: levers, linkages, gears, pulleys, cams, cranks

Systems and Control – Mechanical Systems Overview

In this unit we explore the main mechanical components that make machines work: levers, linkages, gears, pulleys, cams and cranks. Think of them as the “muscles and joints” of a machine, each with a special job to do.

Levers

A lever is a simple machine that amplifies force. Imagine a seesaw: the fulcrum is the pivot point, the effort is the weight you put on one side, and the load is the weight you lift on the other side. The basic principle is $F_1 d_1 = F_2 d_2$, where $F$ is force and $d$ is distance from the fulcrum.

• First‑class lever – fulcrum between effort and load (e.g., scissors).
• Second‑class lever – load between fulcrum and effort (e.g., wheelbarrow).
• Third‑class lever – effort between fulcrum and load (e.g., tweezers).

Exam tip: When asked to calculate the load a lever can lift, remember to keep the distances on the same side of the fulcrum and use the equation above.

Linkages

Linkages connect multiple levers to produce a desired motion. Think of a car’s steering system: turning the wheel moves a series of rods that turn the wheels. Linkages can be rigid (fixed length) or flexible (allow some play).

1. Identify the pivot points.
2. Determine the direction of motion for each link.
3. Use the principle of virtual work to predict the final motion.

Exam tip: Sketch the linkage and label all forces; this helps you spot hidden constraints.

Gears

Gears transfer rotational motion. The key relationship is $n_1 r_1 = n_2 r_2$, where $n$ is the number of teeth and $r$ is the radius. This means the product of teeth and radius is constant for meshing gears.

• Spur gears – straight teeth, used for parallel shafts.
• Helical gears – angled teeth, smoother operation.
• Planetary gears – one central gear with several outer gears, great for compact designs.

Exam tip: To find gear ratio, divide the number of teeth on the driven gear by the driver gear. Remember that a larger gear slows down speed but increases torque.

Pulleys

Pulleys change the direction of a force and can multiply it. A single pulley is a simple block and tackle. A compound system uses multiple pulleys to reduce effort.

• Fixed pulley – changes direction only.
• Movable pulley – reduces the required effort.
• Block and tackle – combination of fixed and movable pulleys.

Exam tip: Calculate the mechanical advantage by counting the number of rope segments supporting the load.

Cams

A cam is a rotating or sliding piece that converts rotary motion into linear motion. Think of a heart‑shaped cam that pushes a piston up and down in an engine. Common cam shapes include eccentric, flat‑topped, and circular.

Exam tip: When given a cam profile, sketch the follower path and identify the timing of the motion.

Cranks

A crank converts linear motion into rotary motion or vice versa. In a car engine, the piston’s up‑and‑down motion is turned into the crankshaft’s rotation. The radius of the crank determines the torque output.

Exam tip: To find the torque produced by a crank, multiply the force on the piston by the crank radius: $\tau = F \times r$.

Summary Table

Exam Tips & Study Checklist

• Always sketch the mechanism before calculations.
• Label all forces, distances and directions clearly.
• Check units – Newtons for force, meters for distance.
• Practice converting between gear ratios, torque and speed.
• Use the analogy of everyday objects (seesaw, car steering) to remember concepts.
• Time yourself on past exam questions to build confidence.