What is a mechanism?
A mechanism is a set of parts that changes an input (a motion and a force you give) into an output (a different motion or force you want). We often draw it as a system: input → process → output.
Mechanisms can do three jobs:
- change the kind of motion (for example turning into sliding);
- change the size of a force or speed;
- change the direction of motion.
Four kinds of motion
- Rotary: turning round in a circle (a wheel, a fan).
- Linear: moving in a straight line in one direction (a train on a straight track, a drawer).
- Reciprocating: moving back and forth in a straight line (a saw blade, a sewing-machine needle, an engine piston).
- Oscillating: swinging back and forth along an arc (a pendulum, a swing).
Levers and mechanical advantage
A lever is a rigid bar that turns about a pivot called the fulcrum. You push with an effort; the lever moves a load.
- Class 1: fulcrum in the middle (see-saw, scissors, crowbar).
- Class 2: load in the middle (wheelbarrow, nutcracker, bottle opener).
- Class 3: effort in the middle (tweezers, fishing rod, your forearm).
Moments balance: effort × effort distance = load × load distance. Mechanical advantage MA = load ÷ effort. If MA > 1 the lever is a force multiplier, but your hand must move further than the load. Velocity ratio = distance moved by effort ÷ distance moved by load.
Gears, gear trains and pulleys
Gears are toothed wheels. The gear you turn is the driver; the one it turns is the driven gear. Two meshing gears turn in opposite directions. A small idler gear placed between them makes the driven gear turn the same way as the driver without changing the ratio.
Gear ratio = teeth on driven ÷ teeth on driver. Output speed = input speed ÷ gear ratio. A ratio above 1 slows things down and increases the turning force (torque).
In a compound gear train two gears are fixed on one shaft; multiply the ratios of each pair to get the total ratio.
Belts and pulleys and chains and sprockets pass turning motion over a distance. Both pulleys turn the same direction (a crossed belt reverses it). Velocity ratio = driven diameter ÷ driver diameter. A belt can slip (safe if jammed); a chain cannot slip.
Other gears: bevel gears turn motion through 90°, a worm and wheel gives a very big reduction, and a rack and pinion turns rotary into linear motion (a car's steering).
Cams, cranks and linkages
A cam is a shaped wheel on a turning shaft. A follower rests on it and is pushed up and down: rotary in, reciprocating out. Cam shapes: circular (eccentric, smooth rise and fall), pear (stays still, then rises fast), snail/drop (slow rise, sudden drop).
A crank and slider links a turning wheel to a rod and a sliding block. It works both ways: in a car engine, the piston (slider) turns the crank; in a pump, the crank drives the piston.
Linkages are bars joined by pivots. They change direction (reverse-motion linkage), keep motion parallel (parallel linkage, a toolbox tray) or change size (a bell-crank turns motion through 90°).
When you build a mechanism: decide the input and output motions, choose the mechanism, work out ratios, make a model (card, wood, a construction kit or a CAD simulation), test, and improve. Reduce friction with lubrication and bearings.
Key formulas and definitions
- Mechanical advantage MA = load ÷ effort
- Velocity ratio VR = distance moved by effort ÷ distance moved by load
- Efficiency = MA ÷ VR × 100%
- Lever balance: effort × effort arm = load × load arm
- Gear ratio = driven teeth ÷ driver teeth
- Output speed = input speed ÷ gear ratio
- Pulley VR = driven diameter ÷ driver diameter
- Compound train ratio = ratio₁ × ratio₂
Worked examples
1. Name the motion: (a) a ceiling fan blade, (b) a swing, (c) a sewing-machine needle, (d) a lift going up.
(a) Rotary, (b) oscillating, (c) reciprocating, (d) linear.
2. A lever lifts a 600 N load with a 150 N effort. Find the MA.
MA = load ÷ effort = 600 ÷ 150 = 4.
3. A load of 300 N sits 0.4 m from the fulcrum. What effort at 1.2 m balances it?
Effort × 1.2 = 300 × 0.4 = 120. Effort = 120 ÷ 1.2 = 100 N.
4. A driver gear with 15 teeth turns a driven gear with 45 teeth at 300 rpm input. Find the ratio and output speed.
Ratio = 45 ÷ 15 = 3 (3 : 1). Output = 300 ÷ 3 = 100 rpm, in the opposite direction.
5. A motor pulley of diameter 50 mm drives a pulley of 200 mm. The motor turns at 1200 rpm. Find the output speed.
VR = 200 ÷ 50 = 4. Output = 1200 ÷ 4 = 300 rpm, same direction.
6. Compound train: gear A (10 teeth) drives B (40). C (12) is on the same shaft as B and drives D (36). Input 800 rpm. Find the output speed.
Ratio AB = 40 ÷ 10 = 4. Ratio CD = 36 ÷ 12 = 3. Total = 4 × 3 = 12. Output = 800 ÷ 12 ≈ 66.7 rpm.
Common mistakes
- Writing gear ratio as driver ÷ driven. It is driven ÷ driver (big over small for a slow-down).
- Thinking a belt reverses the direction. An open belt keeps the same direction; meshing gears reverse it.
- Believing a lever gives free energy. More force means the effort moves a longer distance; work out is never more than work in.
- Mixing up reciprocating and oscillating. Reciprocating is back-and-forth in a straight line; oscillating swings along an arc.