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● Recognise basic mechanisms that transmit and transform motion.
● Identify simple mechanisms in complex machines.
● Calculate the mechanical advantage for different mechanisms, such as levers, pulleys and gear trains.
● Use a mechanism simulator to reproduce machines using standard symbols.
● Analyse the mechanisms of a machine or system, as well as their functions.
● Make different mechanisms using different materials and techniques (wood, plastic, 3D printing…).
● Design and build machines for a particular task.
YOU WILL LEARN TO…
MECHANISMS
What do you see in the photo?
What are the parts probably made of?
What is the function of each part?
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FINAL TASK
Analysing the parts of a bicycle
Understand
1. Match the numbered parts of the bicycle with the words below.
2. Which parts of a bicycle are moving parts? Which ones are not?
Analyse
3. Classify the moving parts of a bicycle into two groups: parts that move in a straight line and parts that rotate.
Analysis of a technological device
What do you have to do?1 Identify the different mechanisms in parts of a bicycle. 2 Classify types of mechanisms, how they function and how we use
them. 3 Make a presentation about mechanisms, using photos and
diagrams. 4 Include a section about basic bicycle maintenance and adjustments.
We can find mechanisms all around us. In this unit, you will learn about everyday objects, such as bicycles, that consist of simple mechanisms.
You will also build a simple mechanism and demonstrate how it works.
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Frame Front Wheel Transmission Other parts
crossbar handlebar spokes front gear seat
down tube steering tube hub chain wheel seat post
seat tube suspension rim chain pedal
seat stay front brakes tyre back gear crank
chain stay fork valve sprocket back brake
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1 input force: what we put in2 source: where something starts or comes from
3 receptor: something that receives4 output: the power or energy supplied by a device
1. WHAT IS A MECHANISM? The moving parts of a bicycle are examples of everyday mechanisms that make life easier and more enjoyable:
❚❚ The chain of a bicycle transfers motion to the back wheel.
❚❚ The bar of a seesaw forms a lever that we can use for fun.
❚❚ The gears inside old-fashioned clocks let us measure time
❚❚ The pulley system above a well helps us to bring up water.
Although these mechanisms are quite different, they all have something in common. They make work easier because they transmit and transform force and motion.
All of these mechanisms require an input1 force and motion from some type of source. In the case of a bicycle, our leg muscles are the input source2.
For other mechanisms, the input source might be an animal, an electric motor, the force of running water, or the movement of weights in the case of an antique clock.
Mechanisms transmit motion and force to receptors3 that finally perform the work.
This is the output4 force and motion. In the case of an analogue clock, the output receptors are the hands of the clock that move in circles to show the time.
1.1. The parts of a mechanism
When you ride a bicycle, your legs provide the force and motion. The pedal mechanism transmits input motion to the chain. The chain transmits the motion to the back wheel, which is the output receptor. The wheel does work by moving the bicycle forward.
ê êInput of force and motion
Mechanism Output force and motion
In the case of a bike, the small up-and-down motion of our legs transforms into a long linear movement of our whole body.
Mechanisms transmit and transform force and motion from an input source (motor) to an output receptor. This transmission and transformation lets us perform different types of work with more comfort and less effort.
Some mechanisms: bicycle, seesaw, clock, well
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❚ Mechanisms transfer and transform force and motion from an input source to an output receptor.
❚ Mechanisms can be classified by function: transmitting motion, transforming motion, controlling motion, accumulating energy or making connections.
Key concepts
Understand
4. Look at the photos. What work do the mechanisms do? What provides the input of force and motion? What are the output receptors?
1.2. Classification of mechanisms
We can classify mechanisms by the work that they do and how they function.
Apply
5. In your notebook, make simple drawings of the mechanisms in the chart above. Use books or the Internet to help you.
Transmission of motion
Linear transmission❚❚ Lever❚❚ Pulley❚❚ Block and tackle
Rotary transmission
❚❚ Friction wheels❚❚ Belt drive❚❚ Gears❚❚ Chain drive
Transformation of motion
Rotary-linear
❚❚ Wheel❚❚ Rack and pinion❚❚ Nut and bolt❚❚ Crank
Reciprocating rotary-linear
❚❚ Crank and rod❚❚ Crankshaft❚❚ Cam ❚❚ Eccentric cam
Energy accumulation
Absorption / Dissipation ❚❚ Spring
ConnectionLinkage ❚❚ Clutch
Support ❚❚ Plain bearing
Motion control
Direction control❚❚ Ratchet❚❚ Freewheel
Speed reduction ❚❚ Brake
1.3. Conservation of energy and work in mechanisms
Mechanisms seem to increase force, but they can’t create energy on their own. All mechanisms produce the same amount of work that is done to them, including energy that is lost to friction5 and heat.
If a mechanism increases force, it must decrease motion. Similarly, if a mechanism increases motion, it must decrease force. In this way, energy and work are conserved.
5 friction: the action of one object or material moving against another
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Apply
6. In this type of weighing scales we have to move the counterweight until the bar balances. How much do apples weigh if the counterweight balances the bar at a distance from the fulcrum which is six times that of the plate.
2. LINEAR TRANSMISSION OF MOTION
Linear transmission mechanisms, such as pulleys, use linear motion input to produce linear motion output.
We typically use these mechanisms to transmit force.
2.1. Levers
A lever is a rigid bar that turns around a point called a fulcrum6. Various forces may act on the lever at the same time.
Each force produces a specific torque7, which is the force multiplied by its distance from the fulcrum.
Torque = Force x Distance
Classes of levers
We can divide levers into classes according to the locations of the fulcrum, force and resistance.
Each class of lever has different uses.
Class 2 levers increase the force that we apply.
Class 3 levers increase the distance that the end of the lever moves.
Class 1 levers can do both of those things.
We also use them to compare weights.
When the forces acting on opposite ends of a lever are equal, we say the lever is in equilibrium. We can express this mathematically as the Law of the Lever:
F x d = R x r
F is the force or the effort that we use; d is its distance from the fulcrum; R is the resistance or load that we want to move; and r is its distance from the fulcrum.
Class 1 Class 2 Class 3
The fulcrum is between the force and the resistance.
The resistance is between the fulcrum and the force.
The force is between the fulcrum and the resistance.
The effect of the force applied is increased or decreased.
The effect of the force applied is always increased (d > r).
The effect of the force applied is always decreased (d < r).
R
F
fulcrum
rd
R
F
fulcrum
rd
F
R
fulcrum
dr
d 6d
m = 400 g
F1
F2
MEASUREMENTSIn this unit, we measure force in newtons (N) and distance (d, r) in centimetres (cm).
6 fulcrum: point of support for a lever7 torque: moment of force
Key structure
Expressing purpose
We use pulleys to transmit force.in order to transmit
for transmitting
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Apply
7. In your notebook, draw pictures of the levers on the previous page (seesaw, bottle opener, tweezers) and label the fulcrum, force and resistance. What mechanical advantage does each lever provide?
8. Measure the handlebars of your bicycle. What is the distance from the axis to each end? Imagine the handlebars are three times longer. Would they be easier to turn?
Analyse
9. Locate the fulcrum, force and resistance in the levers above. Identify each type of lever.
Brake levers
Bicycle brakes decrease speed. We control them with levers on the handlebars. These levers pull on cables and the cables activate the brakes on the wheels.
A hand crank
A hand crank has two parts. One is connected to a rotating shaft and the other forms a handle. We can use a hand crank to apply force at a distance from the axis of the shaft. This makes it easier to turn. A crank is a Class 2 lever, so it obeys the Law of the Lever:
F x d = R x r
F is the force that we apply; d is its distance from the axis of rotation.
R is the resistance in the shaft; and r is the radius of the shaft itself.
Uses: We use cranks to make rotation easier in various mechanisms, such as door handles and bicycle pedal systems.
R F
fulcrum force
distance
Bicycle handlebars
The handlebars of a bicycle work like a crank. If we place our hands at the ends of the handlebars, they are easier to turn. If we put our hands near the middle, it’s more difficult to turn the handlebars.
The steering wheel of a car has a circular shape, but it is similar to the handlebars of a bicycle. It is easier to turn a larger steering wheel because there is a larger distance between the outside of the wheel and the axis of rotation in the centre.
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2.2. Pulleys and compound pulley systems
Look at the rope in the picture above. It goes up and down four times through the pulleys. That means the bicycle will rise a distance that is four times less than the length of rope that we pull down.
If we pull down one metre of rope, the bicycle goes up 25 centimetres. This is helpful because we only need one quarter (1/4) of the force. If we don’t use pulleys, we need four times as much force to lift the bicycle.
Pulleys
A pulley is a wheel that rotates around an axis and has a groove. If we pull ropes, belts or chains through pulleys, we can lift objects with less effort. We can divide pulleys into two basic types:
Fixed pulley Movable pulley
The forces are equal because the rope moves the same distance on both sides. We can use gravity and our own weight to help us. It’s easier to lift a weight by pulling down than by pulling up.
F = RForce = Resistance
The rope follows a double path around the pulleys. We need half the force to lift the same weight as with a fixed pulley. We must pull twice as much rope to lift an object to the same height.
F = R / 2Force = Resistance / 2
In a system of pulleys, the equilibrium between the forces depends on the path that the rope follows.
R
F
R
F
Analyse
10. What mechanism are the women using? How does it help them get water from the well?
rope
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Analyse
11. Study the pulley systems on this page. In each case, how much will the load rise if you pull down the rope one meter? How much force will you need to use?
12. Look again at the pulley systems on this page. For each one, how many newtons of load would create a resistance of 900 newtons?
Apply
13. Look at the pulley system on a sailing ship. How many times does the rope go up and down? How much force is needed for a resistance of 400 newtons?
14. Look for more information about block and tackle mechanisms. In addition to pulleys, what other things can they include?
Compound pulley systems
A compound pulley system is a combination of fixed and movable pulleys. It is also called a block and tackle system. The more pulleys there are, the less force we need to lift the load. We can combine the pulleys in various ways:
Vertical system Horizontal system Exponential system
F = R / 2 x n (n = the number of movable pulleys) F = R / 2n
Rescue pulley system
F
F F
R R
We can make block and tackle systems without pulleys. For example, rock climbers use carabiners. They are similar to pulleys because ropes pass through them easily. Some pulley systems are complex, such as systems for elevators or sailing boats. In those cases, it is difficult to count the movable pulleys. However, we can count how many times the rope goes up and down (U) and use the equation F = R / U.
❚ Levers, fixed pulleys, movable pulleys and compound pulley systems are examples of linear transmission.
❚ A lever is in equilibrium when all the opposing moments of rotation acting on the lever are equal to each other.
❚ In a pulley system, the balance between the various forces depends on the path that the rope follows.
Key concept
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Understand
15. Listen to four statements about rotary transmission. Are they true or false?
Analyse
16. Work in groups. List everyday machines that use (1) pulleys and belts (2) gears and sprockets. In each case, what advantage does the mechanism give us?
8 reliable: always good, that you can trust
9 conveyor belt: a moving band of material that transports objects from one place to another
10 home appliance: a machine that does a specific job in the home (e.g. washing machine)
3. ROTARY TRANSMISSION
With a modern bicycle, we can transmit rotary motion from the pedals to the back wheel and increase the speed of rotation easily.
Rotary transmission systems put two rotating elements into contact. These mechanisms have two purposes:
❚❚ Transferring rotary force from an input location to another location.
❚❚ Changing the rotary speed by using rotating elements of different sizes.
We can perform these functions with various mechanisms, such as the following:
Friction wheels Pulleys with belts Interlocking gears Sprockets with chains
The first bicycles had pedals on the front wheel. The front wheel had to be very large so that riders could reach higher speeds. However, this made the bicycles uncomfortable and dangerous.
All of these mechanisms keep the same speed ratios, but each one offers a different advantage. For example, friction wheels are simple but interlocking gears are more reliable8 because they don’t slip easily.
Metal chains are stronger and last longer than rubber or plastic belts, but chains are also more expensive.
Uses: Friction wheels and pulleys are often used in toys and other devices with moving parts, such as industrial rollers or conveyor belt9 systems. Gears are used in clocks, while sprockets and chains are common in home appliances10.
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3.1. Changes in speed
If we want to increase the speed of a rotary system, we must transmit motion from a larger (input) element to a smaller (output) element. However, when we increase the speed we also decrease the rotary force, or torque.
The opposite is true if we want to decrease the speed of a rotary system. We must transmit motion from a smaller (input) element to a larger (output) element. At the same time, we also increase the torque. If the input and output elements are the same size (with the same diameter or with the same number of gear teeth), the rotary speed remains constant. The rotary force will also remain constant11.
Analyse
17. Look at the gears on the right. How many teeth has each gear got? If the bigger gear revolves at 15 rpm, how fast does the smaller gear revolve? If the smaller gear revolves at 50 rpm, what is the speed of the bigger gear?
The relationship between the speeds of the two wheels is inversely proportional12 to their sizes.
N2 =N1
D1
D2
This relationship is called the ratio of transmission, where N is the speed of rotation and D is the diameter of the wheel.
3.2. Speed ratios
If we want to calculate the size ratio of wheels or pulleys, we can compare their diameter, radius (r) or circumference. In the case of gears, we compare the number of cogs or teeth (Z) that each gear has.
Increasing speed system
The input speed (N1) is lower than the output speed (N2).
Constant speed system
The input speed (N1) and the output speed (N2) are equal.
Decreasing speed system
The input speed (N1) is higher than the output speed (N2).
Pulley 1
Pulley 2
D1 > D2 N2 > N1
Pulley 1
Pulley 2
D1 = D2 N2 = N1
Pulley 1
Pulley 2D1 < D2 N2 < N1
Cylindrical gears
MECHANISMS WITH GEARS
Gears are more reliable than friction wheels because gears don’t slip easily and they can transmit more torque. However, gears are noisier and more expensive. They also need lubrication13.
Gears inside a watch
11 constant: always the same12 inversely proportional: corresponding
to the exact opposite13 lubrication: using a substance to
reduce friction
D2 = 10 mmD1 = 30 mm
In the mechanism above, the smaller wheel rotates more quickly than the larger wheel. The difference in speed depends on the relative sizes of the wheels. If the smaller wheel is three times smaller, it rotates three times faster. This happens because the smaller wheel must rotate three times to cover the same linear distance as the big wheel does in only one rotation.
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Analyse
18. Look at the gear train and describe how it moves, the direction and speed of each gear in relation to the one that begins the movement. How fast will each one go if the first one, which is the motor, turns at 60 rpm?
3.3. Belt drives and gear trains
To calculate the ratio of transmission between the first wheel and the last wheel of a belt drive, we must multiply the ratios of transmission of the first pair of wheels and the second pair of wheels
N1 D2 x D4
N4 = D1
x D3
N is the speed of rotation and D is the diameter of the wheel.
We can also find the radius (r) or the circumference of each wheel and use those measurements to calculate the ratio of transmission. For gear trains, we make these calculations using the number of cogs or teeth (Z).
Gear train
A gear train is a system of interconnected gears. In this example, gear 1 transmits motion to gear 2. Gear 3 transmits motion to gear 4. Gears 2 and 3 share the same axis, so they move together. Uses: Tools, cars, robotics, and home appliances, such as a hand mixer or juicer. Gear trains can increase or decrease speed without using large wheels or gears.
1 2 3 4
Apply
19. Count the number of teeth in the gear wheels and sprockets of your bicycle. Then calculate the ratio of transmission for each combination.
Sprocket 1
Sprocket 2
Sprocket 3
Sprocket 4
Sprocket 5
Sprocket 6
Sprocket 7
Wheel 1 ... ... ... ... ... ... ...Wheel 2 ... ... ... ... ... ... ...Wheel 3 ... ... ... ... ... ... ...
If there were more pairs of wheels in this system, we would continue by multiplying the ratio of each pair with the ratio of the next pair.
A belt drive is a system of pulleys connected by belts. Each belt connects a pair of pulleys, so they turn together.
To understand how a belt drive works, we can analyse the example above:
❚ Wheel 1 turns wheel 2, which moves faster because it is smaller. The size ratio between the wheels is D1 / D2 = 1.5. If wheel 1 makes 1 rotation, wheel 2 makes 1.5 rotations.
❚ Wheel 2 and wheel 3 are connected to the same axis, so they turn together. If wheel 2 makes 1.5 rotations, wheel 3 also makes 1.5 rotations.
❚ Wheel 3 turns wheel 4, which moves faster because it is smaller. The size ratio between the wheels is D3 / D4 = 2. If wheel 3 makes 1.5 rotations, wheel 4 makes 1.5 x 2 = 3 rotations.
D1 = 24 mm
D2 = 16 mmD4 = 16 mm
D3 = 32 mm
1
2
3
4
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❚ Rotary transmission mechanisms include friction wheels, pulleys with belts, interlocking gears, and sprockets with chains.
Key concept
3.4. Changes in direction and rotation
We can use various systems to change the direction of rotation or the axis of rotation in a belt drive. We can also vary the distance between the wheels.
Worm drive
Understand
21. Study the picture on the right. The shaft has got three grooves and the gear has got 27 teeth. For each rotation of the shaft, how many teeth does the gear move? If the gear rotates completely, how many times does the shaft turn?
In some gear mechanisms, several cogs or teeth interlock at the same time. These mechanisms are more precise14 and they transmit more rotary force, or torque.
3.5. Worm drive
A worm drive reduces the speed of a rotary system very effectively. A worm drive has two parts: a worm shaft and a worm gear. The shaft has two, three or even more grooves. Each groove interlocks with one tooth of the worm gear.
When the worm shaft makes one rotation, the worm gear moves forward one tooth for every groove on the shaft. Consider the following example, a worm shaft has got two grooves. They interlock with two teeth of a worm gear. The worm gear has got a total of 30 teeth. If the screw makes one rotation, the gear moves forward two teeth. If the screw makes 15 rotations, the gear moves forward 30 teeth, or one rotation. Worm drives are usually non-reversible. The shaft can move the gear, but the gear cannot move the shaft. In this way, the shaft acts as a brake.
Uses: We use worm drives for tuning the strings of a guitar, for elevator mechanisms and for speed reducing systems.
Analyse
20. Study the pictures above. Which pairs of wheels turn in the same direction?
IDLER GEARIn a simple two-gear system, the gears turn in opposite directions. If we want the gears to turn in the same direction, we put an idler gear between them. This gear changes the direction of rotation, but it doesn’t change the ratio of transmission.
Idler gear
With belts, we can change the direction of rotation and the axis of rotation quite easily. However, gear drives require special parts to make these changes. We use different types of gears when two axes are parallel, perpendicular or crossed.
Parallel axes Perpendicular axes Crossed axes
14 precise: exact and accurate
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4. TRANSFORMATION OF MOTION
Some mechanisms transform linear motion into rotary motion. Most of these mechanisms are reversible. They also transform rotary motion into linear motion.
The linear motion can be unidirectional or reciprocating. Reciprocating motions alternate from one side to the other.
4.1. Rotary-linear transformationWheel
A corkscrew with a rack and pinion mechanism
Apply
22. Measure the back wheel of your bicycle. What is the diameter? If the wheel makes one rotation, how far does it move? Repeat this calculation for a children’s bicycle with a wheel that has a diameter of 24 cm.
Analyse
23. Look at the photo of the corkscrew. Locate the rack and the pinion. Where do we apply the input force? What is the output receptor? What work does it do?
24. How is the rotation of a pinion related to the movement of a rack?
Apply
25. A sliding door has got a rack and pinion system. The pinion has a radius of 15 mm. If the door slides two metres, how many times does the pinion rotate?
Wheels are essential parts of bicycles. They let us move more easily because they reduce our contact with the ground and decrease friction. However, if there isn’t enough friction, the wheels can slide out of control.
With each rotation, a wheel moves forward a distance that is equal to its circumference (2πr). As a result, we need less force to move vehicles with larger wheels and they move more quickly.
Rack and pinion mechanism
A rack and pinion mechanism has two parts. The rack is a bar with many teeth and the pinion is a gear with teeth that interlock with the rack. When the pinion rotates, the rack moves in a linear direction. If the mechanism is reversible, the pinion also rotates when the rack moves. Like a wheel, this mechanism transforms rotary motion into linear motion.
Uses: We use rack and pinion mechanisms for sliding doors, conveyor belts and other devices that require precise movements.
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Analyse
27. Study the wooden mechanism above. Locate the winch and crank parts. How does this mechanism work? Why has it got short wooden bars? Why is there one long bar in the centre? What was this mechanism probably used for in the past?
Analyse
26. Look at the scissor jack in the photo. How many nuts and bolts has the scissor jack got? Do the nuts rotate in this mechanism? What happens when we turn the bolt? What mechanism can we use to turn the bolt?
Nut and bolt mechanism
A nut and bolt mechanism transforms rotary motion into linear motion. It has two parts: a bolt or shaft with a spiral groove and a nut that turns around it. We can turn and tighten the nut in order to hold things together. If the nut is held in place, we can turn the bolt to make it move forward. In this way, we can use a nut and bolt mechanism to lift loads because it functions as a reducing system.
Uses: We use nut and bolt mechanisms to hold things together. We also find them in scissor jacks for lifting cars, water tap mechanisms and screw-top bottles.
The increase in force is proportional to the ratio between the radius of the crank and the radius of the winch. These ratios obey the Law of the Lever.
F x d = R x r
We use winch and crank mechanisms to lift or pull heavy loads. These mechanisms should also include a braking system to avoid accidents.
Uses: We use winches for lifting loads. We find them in construction cranes and in the mechanism that raises window blinds in our homes.
dF
r
R
Winch and crank mechanism
A winch is a cylinder that rotates around a horizontal axis. We attach a rope to the winch and to a load. Then we turn the crank to rotate the winch. The rope rolls up around the winch and lifts the load. The crank increases the force and the winch transforms rotary motion into linear motion.
A scissor jack is a nut and bolt mechanism
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4.2. Reciprocating rotary-linear transformation
The pedal mechanism of a bicycle transforms the reciprocating movements of our legs into continuous15 rotary motion. In a similar way, the pistons of a car engine produce a reciprocating linear motion that turns the wheels. Some mechanisms work in the opposite way, transforming rotary motion into reciprocating linear motion.
crankshaft
cranks
rods
wheel
frame
crank
pedal
ball bearings
BB cartridge
lock ringchain
wheel
Analyse
28. In your notebook, copy the illustration of the leg and the bicycle pedal at the top of the page. Label the crank and the rod. What motion does the person’s knee make? What motion does the pedal make?
29. Think of more examples of machines that use cranks and rods. Identify the location of these parts for each machine.
This rod transmits motion to the next wheel
rod steam engine
reciprocating motioncrank wheel
piston
A crankshaft mechanism can synchronise the movements of various parts, such as the multiple pistons of a car engine. In the case of a bicycle, our legs act like connecting rods that turn the crank mechanism of the pedals.
Uses: We use crankshafts for combustion motors that use pistons. We also use them for sewing machines.
In the picture, you can see the parts of a crank and rod mechanism. The piston moves a rod forward and backward. This rod turns the first wheel. The second wheel turns because it is connected to the first wheel by another rod.
Uses: This mechanism was important for the first steam engines. Today we find cranks and rods in internal combustion engines, as well as windscreen wiper16 mechanisms.
Crankshaft mechanism
We can connect multiple rods to one shaft. The rods are connected to cranks, and the cranks are connected to the crankshaft.
15 continuous: without stopping
16 windscreen wiper: a device on the front of a car for keeping the window free of rain
Crank and rod mechanism
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Analyse
31. Think of more examples of machines that use cranks, rods or crankshaft mechanisms. Describe the location and motion of the various parts.
32. Study the camshaft on this page. How many switches could this camshaft operate at the same time? How do you know?
Analyse
33. Many bicycle seats have a quick release clamp. What mechanisms do these clamps include? Describe their movements and functions. What forces are applied? Why are these clamps useful?
Analyse
30. Study the cam mechanism above. What motion will the follower make?
Cam mechanisms
A cam is an irregularly shaped device that rotates on a shaft. When the cam rotates, it pushes a special bar called a follower. The follower can move other parts or it can turn a switch on and off. In some mechanisms, a spring pushes the follower back to its original position.
cam
followerroller
d1 2
spring
Quick release clamp
Uses: We can find camshafts in toys, automatic tools and combustion motors.
Some cams are circular, but with an axis of rotation that is off-centre. These are called eccentric cams because they rotate in an irregular or eccentric way.
Uses: There are often eccentric cams in sewing machines and other devices that transform rotary motion to linear motion.
eccentric cam
follower
roller
axis of rotation
We can put multiple cams on one shaft, called a camshaft. We can use a camshaft to synchronize the movements of various parts, such as the valves of an internal combustion motor. A clockwork music box also has a camshaft mechanism.
There is a metal roller with many tiny bumps. When the roller turns, the bumps act like cams, moving a series of metal teeth that play musical notes.
Camshaft
❚ There are two types of mechanisms that can transform motion: rotary-linear mechanisms (wheels, rack and pinion, nut and bolt, winch and crank) and reciprocating rotary-linear mechanisms (crank and rod, crank shaft, cam and eccentric cam).
Key concepts
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Analyse
34. Study the photos of the bicycle brakes on this page. What class of lever is each type of brake? What type of brake has your bicycle got?
Understand
35. Is the amount of force important when we activate a brake system? What happens if we apply less force or more force?
36. Find information about brake pads and shoes. What materials are used to make them? What are the advantages of these materials?
5. MECHANISMS THAT CONTROL MOTION
5.1. Direction control: ratchets
A ratchet is mechanism that controls the direction of motion. It allows motion in one direction, but not in the other, as you can see in the picture.
Some ratchets are reversible, so they can turn and lock in one direction or another.
Uses: We find ratchets in watches, cable-tensors, and elevator brake systems.
5.2. Speed reduction: brakes
Brakes use friction to reduce speed. They are activated by some type of lever. The lever transmits force to an output receptor, which puts pressure on the wheel. This produces friction, which slows down the wheel.
There are various types of brake systems according to where the friction is produced:
Reversible ratchet
This is a reversible ratchet. It can tighten and loosen nuts in both directions.
Bicycle brake systems
❚ Disc brakes: A disc is connected to an axle. Brake pads apply pressure to the disc.
❚ Band brakes: A drum is connected to an axle. A flexible band applies pressure to the outside of the drum. These brakes were used in carriages and they depended on the strength of the driver.
❚ Drum brakes: A drum is connected to the axle. A pair of brake shoes apply pressure to the inside of the drum.
springs
drum
brake shoes
padsdisc
Disc brakeBand brake
Drum brake
Ratchet
Caliper brake
Cantilever brake
V-brake
❚ Ratchets are mechanisms that control the direction of motion.
❚ Brakes are mechanisms that reduce the speed of motion.
Key concepts
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6. ENERGY ACCUMULATION MECHANISMS
We sometimes need mechanisms that can absorb17, accumulate18 or dissipate19 the energy that they receive. For example, shock absorbers in cars absorb energy that can cause damage or discomfort. They make driving easier on bumpy roads. Other mechanisms, such as watch springs, accumulate energy that can be used later.
6.1. Accumulation: springs
Springs are flexible devices that absorb energy when we apply force to them. Then we can release20 the energy in a controlled way. We use springs with different shapes for various purposes.
❚ We push on compression springs. We find these springs in sofas.
❚ We pull on traction springs. We find them in metallic bed frames.
❚ We bend torsion springs. We see these springs in clothes pins.
Analyse
37. Look at the images of the springs above. Notice their shapes. Can you imagine what type of force we use with these springs? Where can we see springs like these?
Analyse
40. Look at the springs of the bicycle seat. How do they work? What type of force is applied to them? Some bicycle seats have shock absorbers instead of springs. What are the advantages of each system?
Uses: There are often springs in sofas, beds, industrial and domestic machines, spring-operated pens, watches, clocks and toys.
6.2. Dissipation: suspension systems
Car suspension systems are useful because they absorb and dissipate motion when the road is bumpy. This makes driving more comfortable.
❚❚ Shock absorbers are usually made with spiral steel springs.
❚❚ Leaf springs are made with long, curved pieces of steel of different lengths placed on top of each other and joined in the middle.
Analyse
38. There are springs in some pens that we use for writing. Why are they useful? How do we operate these springs? What type of force do we apply to them?
Apply
39. Make a list of objects that have compression springs, traction springs and torsion springs. How do you apply force to these objects?
ENERGY ACCUMULATION MECHANISMS
Some devices have springs that accumulate energy and release it slowly. In the past, watches had springs so people had to wind them every day. Today, most watches use batteries. Some new watches accumulate energy from our body movements.
17 absorb: take in, reduce the effect of18 accumulate: gather gradually and keep19 dissipate: disperse or spread gradually20 release: set free or let go
There are two types of energy absorption mechanisms:
❚ Those that accumulate energy like springs.
❚ Those that absorb and dissipate energy like shock absorbers or suspension.
Key concepts
22
Understand
41. List the main types of couplings. How do they work? What are the similarities and differences between them?
Apply
42. The illustrations show three Cardan joints that form angles of 0 degrees, 30 degrees and 60 degrees. Which joint transmits rotary force more effectively?
30o
60o
0o
A CHANGE OF GEARS
This clutch has various gears. They change the gear ratio, which is a measure of the mechanical advantage.
7. COUPLINGS AND CLUTCHESSometimes we need to transmit rotation from one axis of rotation to another. For example, there may be a distance or an angle between two shafts and they may not be totally aligned21. In these cases, we can use various coupling mechanisms.
❚ Rigid couplings form a permanent connection between two shafts. These shafts may have different diameters, but they must be perfectly aligned.
❚ Clutches form a rigid connection which isn’t permanent. For example, a car has a clutch that engages and disengages the engine and the wheels. This system also permits various combinations that change the gear ratio between the engine and the wheels. This is similar to the gear system of a bicycle.
Friction clutch Jaw clutchThe ends of two shafts come into contact. When one shaft turns, there is friction. This turns the second shaft.
The ends of two shafts are connected by interlocking teeth. A jaw clutch is more reliable because it doesn’t slip easily.
friction surface
Superficiede fricción
❚ Flexible couplings are also useful.
Oldham coupling Cardan joint (Universal joint)An Oldham coupling is used to connect shafts that are not perfectly aligned. The grooves permit lateral movement. Oldham couplings can also connect shafts that have different diameters.
A Cardan joint connects two shafts that are at an angle to each other. Cardan joints are used in cars. They transmit rotary motion from the car’s engine to its back wheels.
Coupling mechanisms include:
❚ Rigid couplings, such as flanges.
❚ Flexible couplings, such as Oldham couplings and Universal joints.
❚ Friction clutches and jaw clutches.
Key concepts
21 align: place in a straight line
23Mechanisms
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8. BEARINGS
The support that holds a rotating shaft is called a bearing. It keeps the shaft in position.
❚ Plain bearings are formed by two rings. One of the rings is connected to the rotating shaft and the other is connected to the support. Plain bearings are made of smooth materials, but they need lubrication to reduce friction. Plain bearings are quiet, but they produce a lot of heat at high speeds.
❚ Antifriction bearings are used in many machines. They reduce the amount of surface contact between the shaft and other parts.
Antifriction bearings have four parts:
❚ The inner ring is in contact with the rotating shaft.
❚ The outer ring is connected to the rest of the mechanism.
❚ The rolling elements are cylindrical rollers or round balls (ball bearings).
❚ The retainer keeps the rolling elements in position.
9. FREEWHEEL
The pedals on the first bicycles were connected directly to the axle of the wheel. As a result, if people pedalled backwards, the bicycle moved backwards too. The pedals also turned very quickly when people rode their bicycles downhill, so they either had to let their feet off the pedals or they had to pedal very quickly.
The invention of the freewheel solved these problems. A freewheel transmits motion in one direction, and turns freely in the opposite direction. As a result, the chain of a modern bicycle can move the wheels when you pedal forward, but not when you pedal backward. The chain cannot transmit motion from the wheels to the pedals.
Uses: There is a freewheel chain mechanism on your bicycle. Cars have also got freewheels in their starting systems.
Freewheel
A freewheel combines the characteristics of sprockets, ratchets and bearings.
Analyse
43. Look at the freewheel. In which direction will the exterior and interior rings turn together? In which direction will only the exterior ring turn?
Roller bearings and ball bearings
❚ A bearing supports a rotating shaft. There are plain bearings and antifriction bearings.
❚ A freewheel transmits motion in one direction and turns freely in the opposite direction.
Key concepts
PROCEDURES
24
Building mechanisms
Mechanisms can be built in many ways, and the techniques that we use are always evolving. However, mechanisms and their parts must be made carefully and precisely, so that they will work properly.
In the workshop, we can make simple mechanisms using a variety of materials, such as wood, nails, cardboard and paper.
MAKING PULLEYS
We can use the following materials and tools to make pulleys:
❚❚ Materials: Cardboard, corrugated paper, construction paper, plywood, chipboard, wooden dowels.
❚❚ Tools: Pencil, compass, protractor, scissors, utility knife, hacksaw.
Pulley A is made from three plywood discs and a wooden dowel. The disc in the centre is smaller and thicker.
Pulley B is made with a strip of corrugated cardboard in the centre. The discs on the sides are made of construction paper.
You can also use thick chipboard or wood to make a pulley. In that case, you must cut a groove around the outside of the disc.
Think of other ways to make pulleys and try them out.
Warning: Try to avoid accidents. Be very careful when you work with sharp tools.
MAKING GEARS
Industrial gears are normally made of metal or plastic. In the workshop, we can make gears from plywood or chipboard. Follow the instructions below:
1. Use a compass and protractor to draw a gear.
2. Use a hacksaw to cut out the gear, following the lines.
3. Sand the teeth. They must be smooth and even.
Pulley A
Pulley B
Apply
44. What other materials could you use to make pulleys or gears? How would you use those materials?
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25Mechanisms
Understand
45. Study the cam above. When it rotates, what motion will its follower make?
Analyse
46. Study the three cams on the right. What type of motion will each cam produce in its follower?
CHANGING THE DIRECTION OF MOTION
There are various ways to change the axis of rotation or the direction of rotation. Here are two examples:
❚ We can use pulleys that are connected by a belt at an angle to each other. This changes the axis of rotation. We can also cross the belt to change the direction of rotation.
❚ We can put two gears at a right degree angle. We use wheels made of chipboard with nails in them. These nails interlock like gear teeth.
45º
MAKING A CAM
It is quite simple to make a cam:
1. Draw a cross with two perpendicular lines on a piece of plywood.
2. Use a compass to draw a circle. The centre must be at the intersection of the two lines. Draw two more lines to divide the circle into eight equal parts.
3. Put the compass needle on point A and the compass pencil on point C. Then draw an arc. Repeat with the needle on point C and the pencil on point A.
4. Put the needle at D and the pencil at E. Draw a line between E and F.
5. Cut out the cam and sand the edges to make them smooth.
AC
F
BE
D
O
MAKING A CARDAN JOINT
As we have seen in this unit, Cardan joints (or universal joints) transmit motion between two axes at an angle.
Study the illustration. Prepare the wire cross, the washers and the two pieces of tin. Then assemble the pieces.
piece of tin
wire cross
washers
piece of tin
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PROCEDURES
26
Printing a pulley with a 3D printer
If you have a 3D printer, you can design parts for your project in three dimensions and then print them.
❚ First of all, we must consider the object that we are going to print. What shape will it have? In this case, the object is a pulley, based on a cylinder.
❚ A pulley has a groove around the outside. We can include this in our 3D design by adding a torus (doughnut shape) around the cylinder of the pulley.
❚ Finally, we can add or remove cylindrical sections around the hole in the centre of the pulley, in order to form the hub.
Analyse
47. Look at the diagram. What are the measurements of the various parts?
Starting to draw
When we open the FreeCAD program, we select Full View to see all of the tools. To make the drawing process simpler and more intuitive, we can trace the figures with the corresponding button and then modify the parameters afterwards.
To draw the cylinder of the pulley and modify its parameters, we click on Data → Value in the pulldown menu on the left, as shown in the image.
Since the cylinder is resting on the horizontal plane, we must raise the torus by 3 mm on the Z axis, until it lines up with the centre of the cylinder’s height.
The easiest way to move an object is to enter Data → Value and choose the Placement option (a button with three dots), where you can change the parameters for inserting new objects.
Next you must remove the section of the cylinder that overlaps with the torus around it. Choose the boolean option, which opens a menu. Then mark the objects that are used in the operation and the action that you want to perform. In this case, it will be ‘difference’.
The next image is the result of the boolean difference operation on the cylinder and torus. This creates a compound object which the program names ‘Cut’ by default.
All the names can be changed by selecting them and then right-clicking on the mouse. In this case, we rename the object as ‘Base’. Using the same menu, we can also change the colour of the object and other viewing options.
Next, we could simply add the hole in the centre of the pulley and then print the design. However, 3D printing material is expensive, so we should remove any excess mass that won’t affect the object’s functionality.
With this program, it is quite easy to create objects by using basic shapes, to which we can gradually add complexity. This gives us absolute control over the resulting object to be printed. In any case, we should save the various stages of our work so that we can use them as the basis for other projects in the future.
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27Mechanisms
Making the piece lighter
To make the pulley lighter, we can remove cylinders from the faces of it. In this case, we can remove a cylinder with a radius of 45 mm from the upper side and another cylinder with a radius of 1.5 mm from the lower side.
The next image is a view of the Base object from below, and the cylinder that has been created on the lower side. We use the boolean difference operation to subtract the new cylinder, in the same way that we removed the torus previously.
We rename the new Cut001 object as Base2 and then repeat the same operation for the cylinder on the upper side of the pulley. To do so, we move 4.5 mm upwards along the Z axis.
The next image shows the result of the previous operations, in which the central area of the pulley is thinner than the grooved edge.
The shapes that we have created are not erased from the program’s memory, even though we cannot see them and they do not form part of the final object that we will print. As a result, we can use these objects again for other projects.
We continue by reinforcing the hub, which is the area in the centre of the pulley. We do this by adding another cylinder with a radius of 10 mm and a height of 6 mm, using the Fusion function. The resulting object is named ‘Fusion’ by the program.
Finally, we remove a cylinder from the centre of the ‘Fusion’ object to make a hole for the pulley’s axle. This hole will have a height of 6 mm and a radius of 2 mm. We do this by using the boolean difference function.
When we have finished designing the pulley, we can save it to make other changes in the future or to use it for other projects. To save the pulley, we use any name that we like, along with the .fcstd extension used by the program. To save the object, we use the menu option File → Save.
FreeCad also lets us save objects with the .stl extension for 3D printing files. To save our work in that format, we select the object that we want to save, which in this case is Pulley. Then we go to File → Export → Type and select Meshformats. We give the file a name with the .stl extenion and then select Save.
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There are computer programs that you can use to experiment with mechanisms. One example is Yenka, which simulates mechanical and electrical components in three dimensions. You can use it to visualize the properties and movements of various mechanisms.
Yenka includes a library of virtual components, which you find in the main menu of the program.
From this library, you can choose input, output and transformation components, as well as presentation options for your project. You can add and modify components as follows:
a) Designing a mechanism
1. Select the plan view and drag components from the library to the workspace.
2. You can use the cursor to move components horizontally. You can move them vertically by changing to the side view or front view.
3. Double-click on components to modify their characteristics. For example, you can change the speed of a motor or the number of teeth on a gear.
4. When all the mechanisms are in position, you can join them with axes. Click on the black box at the top of a component and drag it to the black box on another component. If they are connected properly, they will move.
Start with the motor and the input mechanism. Then add more components. As you work, experiment with different sizes and positions and check your progress.
A virtual demonstration of a mechanism
MECHANISM SIMULATOR
With this programme, you can look at your project from all sides and rotate the perspective to whatever angle you prefer. Start with the plan view, then raised and profile views to situate the parts. Then activate the animated perspective view.
Side view of a motor and wormdrive
Plan view of the axes
VIEW OPTIONS
293. La madera y sus derivados 29Mechanisms
b) Presentation
After you design your mechanism, you can add other elements, such as numbers and graphics, with information about the components and their properties (rotation speed, acceleration, number of gear teeth, etc.).
1. Select an element, such as a number.
2. Drag the target icon to the correct component.
3. Select the property that you want to describe.
Analyse
48. Study the image on this page. Explain how the mechanism works. How does it transmit motion? Which elements are connected? Which ones rotate at the same speed? Does this speed increase or decrease?
49. Use the information about the speeds of the various parts. If gear 1 has got twelve teeth, how many teeth has the worm drive got? How many has gear 2 got?
Apply
50. Use the simulator to reproduce the three bicycle gear combinations that you use most often. You can do this with a motor and a chain drive, and experiment with the characteristics of different gears.
51. Add numbers, explanatory texts and images to your diagram to make it the part you want to explain in the final task.
In this image, you see the speeds if the moving parts in revolutions per minute (rpm).
❚ The motor and the shaft attached to it.
❚ The smaller gear in the gear train.
❚ The larger gear in the chain drive.
The wormscrew transmits motion to the small gear, so they have the same speed. How fast do they rotate?
The graphics show how this property changes over time. It’s interesting to see what happens when you change the sizes of different parts. In this image, you can see the change in speed of the yellow wheel over time. It’s constant since none of the variables of the system have changed during the time period.
You can also add activation buttons, sliding controls, text notes, images and animations, as well as questions and answers. In this way, you can create exercises, tests, explanations with diagrams, etc.
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ANALYSIS OF MECHANISMS
❚ Choosing the right size bicycle
It is important to choose the right size bicycle, so you can ride it properly and avoid problems or injuries. Look at the chart to see the correct size for you.
Check the size of your own bicycle. Stand next to the seat with your left foot on the ground. Then lift your right knee upwards and forwards. The space between your knee and the handlebars should be about the width of your hand.
❚ Adjusting the seat
Your legs should be almost fully extended when you are pedalling your bicycle and your feet are at the closest point to the ground. This will help you to avoid knee injuries. To adjust your bicycle properly, you should: 1. Ask someone to help you get on the bicycle. 2. Put the heel of your foot on the pedal and extend your leg completely. 3. Adjust the seat at that height. When you pedal with your toes, your leg will not be
completely extended. 4. Notice how you sit on the seat. If you are sitting too far backward, the seat is too
low. If you are sitting too far forward, the seat is too high.
❚ Taking off the wheels
In some situations, you will need to remove the front wheel of your bicycle. For example, you might need to change the tyre or the inner tube. Follow these steps: 1. Disconnect the brake system. If you have a disc system, don’t use the handle after
you remove the front wheel. 2. Loosen the nuts on the front axle. Hold the nut on one side in place while you turn
Basic operations with your bicycle
Bicycle sizes by crossbar height
Height (cm) Size
71-773-7475-7879-8283-8485-8889-9091-9293-94
15 15.5
1617
17.51819
19.520
the nut on the other side. If your front wheel has got a quick release system, simply turn the lever. 3. Lift the front of the bicycle and the front wheel should fall out. 4. If you need to remove the back wheel, select the highest gear, so the chain will be on the smallest sprocket. Then
remove the chain and take off the back wheel.
❚ Changing an inner tube
1. Deflate the inner tube completely.2. Lift up one edge of the tyre, starting with the valve, using tyre levers. 3. Leave the tyre on the rim and remove the inner tube. 4. Check the rim and the tyre for any sharp objects. 5. Partially inflate the new inner tube and put it inside the tyre. Start with the valve. 6. Put the tyre back on the rim. 7. Make sure the valve is in the correct position. Inflate the inner tube and then put the wheel back on the bicycle.
❚ Rethreading the chain
If you need to put the chain back onto the chain wheels, follow these steps: 1. Put the chain on the lower part of the smallest sprocket. 2. Lift the back wheel and pedal backward. Thread the chain onto the sprocket. 3. Pedal forward until the chain is completely connected to the gear wheel.
313. La madera y sus derivados 31Mechanisms
❚ Whenever you use your bike.
• Check the tyres and air pressure. You might have a flat or a slow leak.
• Check your brakes. They ensure your safety and the safety of other people.
• Check the lubrication of the chains and gears. In wet areas or in summer, these parts can rust or rub, produce friction and eventually break.
❚ Every month, if you use your bike regularly.
• Check the cables. Are they twisted or broken? Is the tension correct?
• Check the chain wheels and sprockets. Are the teeth in good condition? Does the chain move correctly? Does it jump, slip or rub anywhere? If any of these parts are damaged, you should replace them.
• Check the air pressure of the tyres. The proper pressure is printed on the side of the tyre. You should always carry an air pump and a repair kit.
• Check the lubrication of all the moving parts, including the chain and sprocket mechanisms. You should also lubricate the seat tube, the suspension, the cables or any places where there is friction.
• Check the suspension pressure if your bicycle has got an air or hydraulic suspension system. Are they adjusted correctly for your weight?
• Check the tyres for any cracks, damage or excessive wear.
• Check all the nuts and bolts on your bicycle. Are any of them loose?
• Check the frame of your bicycle. Are there cracks or stress marks on any of the tubes? These problems must be repaired immediately.
Keep your bicycle clean! Dust and dirt cause problems for mechanisms because they cause friction and wear. You should clean your bicycle carefully at least once every three months. After you clean it, you should lubricate the moving parts. If you keep your bicycle in good condition, you will get better use from it for much longer.
Which parts of my bicycle do I have to check?
Analyse
52. Which bicycle parts need lubrication? Why is this necessary? Find information about different lubricants for bicycles. Which type is best for each mechanism (brakes, gear wheels, sprockets, chain, axle, levers, etc.)?
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53. A boy who weighs 30 kilograms sits on one end of a seesaw. On the other end there is a girl who weighs 20 kilograms. The girl is 1.5 metres from the fulcrum. How far from the fulcrum must the boy sit in order to balance the seesaw? How far away must the boy sit if the girl is 3 metres from the fulcrum? What conclusion can you make about the seesaw?
54. How much force do we need to lift the load in the picture? If we apply a force of 30 N, how much weight could we lift?
55. In your notebook, draw diagrams for the three types of lever.
56. Study the diagram and the information that it includes. What is the diameter of the larger wheel? What is the ratio of transmission?
57. Study the gear train below. Calculate the ratio of transmission.
a) How fast does the larger gear turn if the smaller gear turns at 60 rpm? Show the direction of the rotation.
b) If we add another gear between these two gears, will it change the ratio of transmission? Explain.
58. Calculate the output speed of the gear train below. In which directions do gears 2, 3 and 4 rotate? If the output speed of the wheel on the right is 60 rpm, what is the input speed of the wheel on the left?
59. This mechanism is similar to the wheels of an old-fashioned mill. What type of motion does it transmit? If the gear wheel turns clockwise at 60 rpm, how fast will the wheel turn? Will it also turn in a clockwise direction?
60. Study the following mechanism ...
a) Label the various parts of the diagram. How does each part transmit or transform motion? What is the input? What is the output?
b) If gear A turns at 90 rpm, how many times will the output crank move in one hour?
c) Look at gear A in the diagram. In which direction does it turn? In which direction will gear B turn?
d) Is this mechanism reversible? Why? / Why not?
61. Listen and complete the questions. Match the pictures below with the questions and then answer them.
a) Which part provides the _____ motion for the cranks? Is this a _____ mechanism?
b) What type of movement does the _____ make? What force keeps it in contact with the _____?
c) The pinion is turning at 10 rpm and the _____ is moving at 60 cm / min. If each tooth is 2 mm, how many _____ has the pinion got?
d) The crank is 40 cm long and the _____ of the cylinder is one third that distance. How many _____ will the winch lift if we apply 240 N?
CONSOLIDATION
N2 � 560 rpm
D 10 mm
N1 � 70 rpm
200 rpm
Z1 � 36
Z3 � 30 Z4 � 36
Z2 � 18
50 kg
gear
28 nails
7 bars
wheel
gear A
gear B
wheel A
wheel B
ZA � 20
DA � 10
ZB � 30
DB � 15
A
B
C
D
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62. In your notebook, draw a diagram of an eccentric cam. Label the parts and explain how it works. Name two machines that use an eccentric cam.
63. Listen to five sentences. Are they true or false? If a sentence is false, explain why.
64. Analyse the objects below: a music box and the crank system of an awning. Describe the mechanisms that these objects contain. Explain how the various parts work.
33Mechanisms
FINISHING THE FINAL TASK
To finish the task of this unit, make a presentation about the mechanisms that form a bicycle. Follow these steps:
❚❚ Find images or take photos of the various parts of your bicycle, such as the wheels, handlebars, pedals, sprockets, chain, brakes, etc.).
❚❚ Upload the photos to a presentation programme, such as PowerPoint or OpenOffice Impress.
❚❚ Include images from the mechanism simulator that you used in this unit.
❚❚ Add information about basic bicycle maintenance and repair.
Now you know your bicycle better than anyone!
Analysing the parts of a bicycle
STUDY TECHNIQUES
❚❚ Make a summary with information from the Key concept boxes of this unit. Include any other information that you think is important.
❚❚ Make a chart of the key concepts in this unit, following the example below.
❚ Make a technical dictionary. Include definitions for the following terms: mechanism, input source, output receptor, lever, pulley, gear. Then add other terms that you think are important.
such as
Mechanisms
Transmit motion
such as such as
Transform motion Direct and regulate motion
are used to
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