Wheels, pulleys and gears

The Wheel Possibly the most important mechanical invention ever made. From the tiny gears in a watch to cars and computers, nearly every machine constructed since the Industrial Revolution (in the early nineteenth century) uses a wheel in its design. Earliest known application was a potter’s wheel, used in Mesopotamia (modern day Iraq) around 3500 BC. Probably first used for transportation on chariots in this region around 3200 BC.

Wheels can be levers A wheel on an axle is actually a special kind of lever. The wheel acts as a lever and the pivot is the centre of the axle. Wheels can act as force multipliers or speed multipliers. Steering wheels are force multipliers, the larger the steering wheel, the easier the axle will be to turn. Car wheels operate as speed multipliers in the opposite manner to the steering wheel. A large force is supplied to the axle of the wheel by the motor which makes the wheel move faster.

Pulleys A pulley is like a wheel with a groove around it into which a cable or rope can fit. It also acts like a lever, with its axle as the pivot. Simple pulleys allow us to lift upwards by pulling downwards. They do not alter the size of the force applied, just the direction.

Pulleys To increase the size of the force, we need to use a system involving more than one pulley. We need to apply a force over a greater distance, but multiple pulleys allow us to lift large loads with minimal effort. They act as a force multiplier. The multiple pulley system shown in the picture is called a ‘block and tackle’. The ‘block’ is the outer casing around the pulley wheels, and the ‘tackle’ is the cable or rope connecting them.

Using pulleys To calculate the effort required to lift the load we divide the load by the number of ropes (do not count the rope that goes to the effort). The image on the right shows a four pulley system. The person lifting the 200kg load experiences a pull equal to only 50kg (200kg/4).

Pulley question 1 What is the maximum load that can be lifted with this system? For every 2 metres the rope is pulled through what height does the load rise off the ground? What is the mechanical advantage?

Pulley question 2 What is the minimum effort that must be applied to lift the load? For every 2 metres the rope is pulled through what height does the load rise off the ground? What is the mechanical advantage?

Pulley question 3 What is the maximum load that can be lifted with this system? For every 2 metres the rope is pulled through what height does the load rise off the ground? What is the mechanical advantage?

Gears Gears or cogs are like wheels with teeth that mesh together. When one gear turns, the one it interlocks with also turns, but in the opposite direction. Sometimes gears are joined by a chain, such as in a bicycle or the overhead cam shaft in some car engines.

Driving and Driven Gears The cog that turns first is called the driving gear. Gears that are made to turn by this are called driven gears. If the driving gear is smaller than the driven gear, the system acts as a force multiplier. If the driving gear is larger than the driven gear, then the system acts as a speed multiplier.

Idler Gears An idler gear can be used in a gear combination to make the driving and driven gears rotate in the same direction.

Bevelled Gears Bevelled gear wheels are positioned at right angles to each other This changes the plane of rotation. Used in hand-drills and in many other machines.

Rack and pinion gears Rack and pinion gears are made up of a row of teeth (called the rack), and a gear wheel that rolls on top of this. One use of this type of system is to stop mountain trains slipping on steep slopes.

Bicycle Gears A bike with twenty-one gears gives us a choice of twenty-one possible gearing combinations. The front chain wheel has three sprockets and the rear wheel has seven. To select the lowest gear, we use the largest rear sprocket and the smallest chain wheel sprocket. This combination of gears makes it easier to go up hills. To select the highest gear, we use the largest chain wheel sprocket and smallest rear wheel sprocket. The combination of a large front sprocket and a small rear sprocket makes the bike go faster.

Bicycle Gears The gears used in a bicycle are called sprockets. The pedal and crank are attached to a gear sprocket called the chain wheel. A chain connects this to the rear sprocket. Pedalling turns the chain wheel, which turns the rear wheel, via the chain.

Gear Ratios Are calculated by dividing the number of teeth on the driving sprocket by the number of teeth on the driven sprocket. GR = teeth on driver teeth on driven gear Example: If the driving gear has 9 teeth and the driven gear has 3 GR=9/3=3

Gear ratio question 1 Gear "B" has 36 teeth and gear "A" has 12. Calculate the gear ratio of this gear train if "B" is the driver.

Gear ratio question 2 Look at the image on the right. Gear "B" has 12 teeth and gear "A" has 24. Calculate the gear ratio of this gear train if "B" is the driver.