A3.3 — Introduction to mechanical systems (HL)

Key concepts

A mechanical system transmits and transforms motion and force. Mechanisms convert input (usually rotary motion from a motor, pedal, or handle) into the specific motion the product needs — linear, rotary, oscillating, or reciprocating.

Types of motion

• Linear — motion in a straight line. Example: drawer sliding open, lift cabin.
• Rotary — motion around a fixed axis. Example: wheels, drills, clock hands.
• Oscillating — rotating back and forth through a limited arc. Example: pendulum, windscreen wiper.
• Reciprocating — back-and-forth linear motion. Example: piston, sewing machine needle.

Mechanisms convert between these motion types.

Gears

Gears transmit rotary motion between shafts. The gear ratio is the ratio of teeth (or diameters) between driver and driven gears.

Gear ratio = teeth on driven gear / teeth on driver gear

• A large driver turning a small driven gear → speed up, torque down (ratio < 1).
• A small driver turning a large driven gear → speed down, torque up (ratio > 1).

Common gear types: - Spur gears — parallel shafts, simple teeth. Efficient but noisy. - Helical gears — angled teeth, smoother and quieter. - Bevel gears — transmit motion between shafts at an angle (typically 90°). - Worm gears — high reduction ratios in a compact space; can be self-locking. - Rack and pinion — converts rotary motion into linear (car steering, train rails).

Levers

A lever is a rigid bar pivoting about a fulcrum. The three classes are:

• Class 1 — fulcrum between effort and load (seesaw, scissors).
• Class 2 — load between fulcrum and effort (wheelbarrow, bottle opener).
• Class 3 — effort between fulcrum and load (tweezers, fishing rod).

Mechanical advantage (MA) = load / effort = effort arm length / load arm length.

Class 1 and 2 typically amplify force; class 3 amplifies movement at the cost of force.

Linkages

A linkage connects members with pivots to produce complex motion paths. The simplest is the four-bar linkage — two cranks joined by a connecting rod, producing oscillating or tracing motions. Used in umbrella mechanisms, parallelogram desk lamps, bicycle gear derailleurs.

Cams and followers

A cam is a rotating shaped profile that drives a follower in reciprocating or oscillating motion. Cams convert rotary motion into non-uniform motion with precise timing. Used in engine valve gear, textile machines, automatic toys, door-closers.

Mechanical advantage and velocity ratio

Mechanical advantage (MA) = load / effort. A 5:1 MA means 1 N input produces 5 N output.

Velocity ratio (VR) = distance moved by effort / distance moved by load. If effort moves 5 cm and load moves 1 cm, VR = 5.

Efficiency = MA / VR × 100%. A perfect machine would have MA = VR, efficiency = 100%. Friction ensures real machines never reach this.

Friction and efficiency

Friction converts mechanical energy into heat, reducing efficiency. Strategies to reduce friction:

• Lubrication — oil, grease, dry lubricants (PTFE, graphite)
• Bearings — ball, roller, or plain bushings that provide low-friction pivots
• Surface finish — smoother surfaces reduce adhesion and asperity contact
• Material pairing — dissimilar materials with low friction coefficients (steel on bronze, nylon on steel)

Case studies

Bicycle drivetrain — chainring, chain, cassette. Gear ratios across the cassette (e.g. 11–32 tooth cogs) let the rider choose between speed (high ratio) and torque (low ratio) to suit terrain. Classic example of applied mechanical advantage.

Windscreen wipers — four-bar linkage converts continuous motor rotation into oscillating wiper arm motion, sweeping a specified arc without needing a reversing motor.

Combustion engine valve train — cams on a camshaft push followers that open valves. Cam profile determines valve lift, duration, and timing. Precise mechanical timing critical to engine performance.

Staple remover — class 1 lever pair pivoting on a common fulcrum, amplifying hand effort to extract staples.

Glossary

• Mechanism — an assembly of moving parts that transmits or transforms motion.
• Gear ratio — the ratio of teeth between driven and driver gears.
• Lever — a rigid bar pivoting about a fulcrum.
• Fulcrum — the pivot point of a lever.
• Mechanical advantage (MA) — the ratio of output force to input force.
• Velocity ratio (VR) — the ratio of input distance to output distance.
• Efficiency — MA divided by VR, expressed as a percentage.
• Cam — a shaped rotating element that drives a follower.
• Follower — the member that moves in response to a cam's profile.
• Linkage — connected bars pivoting to produce complex paths of motion.
• Friction — resistive force opposing relative motion between surfaces.

Check your understanding

1. Calculate the gear ratio when a 10-tooth driver meshes with a 40-tooth driven gear. Explain what this means for speed and torque.

Gear ratio = 40 / 10 = 4:1. The driven gear turns at one quarter the speed of the driver but with four times the torque (ignoring losses). This is a reduction gear — trading speed for force. Commonly used to drive wheels from a high-speed motor at a usable torque.

2. Identify the lever class and explain the trade-off for tweezers, a wheelbarrow, and scissors.

Tweezers are class 3 — effort between fulcrum and load; mechanical advantage is less than 1, so they amplify movement at the cost of force (precise positioning). A wheelbarrow is class 2 — load between fulcrum and effort; MA greater than 1, so less effort moves a heavy load. Scissors are class 1 — fulcrum between effort and load; can be configured for either force or speed depending on blade/handle lengths.

3. Define mechanical advantage and velocity ratio and explain what their ratio tells you.

Mechanical advantage (MA) is the ratio of output force to input force. Velocity ratio (VR) is the ratio of input distance moved to output distance moved. If there were no friction, MA would equal VR. Efficiency = MA/VR × 100%. A large gap between MA and VR indicates heavy frictional losses — energy going to heat instead of useful work.

4. Explain how a cam-and-follower mechanism can produce non-uniform motion from a uniform rotary input, and give a product application.

As the cam rotates at constant speed, its shaped profile pushes the follower outward by varying amounts — the follower moves quickly where the profile rises steeply, slowly where it rises gently, and dwells where the profile is concentric. This lets one rotation produce a custom timed motion sequence. In a car engine camshaft, each cam opens its valve at the correct instant, lifts to a specified amount, holds it open briefly, then closes it — all from uniform crankshaft rotation.