Unit 3

Mechanisms

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Mechanisms A mechanism is the arrangement of connected parts in a machine. A bicycle, a car, a corkscrew are all mechanisms. Types of motion Rotary motion is motion in a circle the starting point for many mechanisms. It is the type of motion provided by dc motors. Oscillation is back and forth motion about a pivot point. It is measured in terms of both the angle of throw (amplitude) and the period of time for one complete cycle (periodic time) or the number of cycles in a given time (frequency). Linear motion is the most basic of all motions. Uninterrupted objects will continue to move in a straight line indefinitely. Under every day circumstances gravity and friction conspire to bring objects to rest. Reciprocating motion is back and forth motion. In the example below the reciprocating motion of the piston is converted to the rotary motion in the crank.

http://www.flying-pig.co.uk/mechanisms/pages/reciprocate.html The flying-pig website is a fantastic resource for demonstrating the different forms of motion. It can provide solutions for many different mechanical problems encountered when designing systems

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Levers “If you had a lever long enough and a suitable fulcrum you could move the earth”. The lever is the most basic mechanism and has been used for thousands of years. There are three classes of levers, and each one performs a particular job. Class 1 Lever

Load

Effort

Fulcrum

Products made from this class of lever.

The crowbar is a single lever but the pliers make use of two levers joined together at the fulcrum. Activity: In this space can you draw another product that makes use of the class 1 lever?

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Class 2 Lever Load

Fulcrum Effort You will notice the arrangement has altered in this case. The fulcrum is on the end, and load in the middle. The Effort or force is on the end.

Activity Draw in the space below a product that makes use of a class 2 lever.

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Class 3 lever Load Effort

Fulcrum

In the case above the load and effort change places. Can you think of a product that makes use of a class 3 lever? Draw your thoughts below.

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Mechanical Advantage (Leverage) Levers are used to change the direction, distance or velocity of movement or to decrease the effort required to lift a load. This latter reduction of effort was called leverage. Nowadays and in terms of the WJEC syllabus it is known as MECHANICAL ADVANTAGE. Mechanical advantage is the RATIO of the LOAD in measured NEWTONS and the EFFORT required to lift the LOAD also measured in NEWTONS. Mechanical Advantage

=

LOAD EFFORT 1N

10N

10cm

100cm

In the example above the FORCE (EFFORT) of 1Newton is required to lift a load of 10N. So Mechanical advantage is: LOAD EFFORT 10 1 Therefore this system has a MA of 10. There are no units because it is a ration of the same units

MOMENTS To design a lever to lift a particular load you will need to know about MOMENTS. These are a way of calculating what effect a force will have when it is applied to a lever. A MOMENT is calculated by multiplying the FORCE with the DISTANCE the FORCE is from the fulcrum. For a lever to be balanced, the clockwise moments and the anti-clockwise moments must be the same. In that condition the lever is said to be in equilibrium.

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Try this experiment. Take a lever 1200mm long place a fulcrum somewhere in the middle and balance the lever with a 10N Load with a 2N Effort. 2N 10N

D2 _______cm

D1 _______cm

When the lever is in EQUILIBRIUM (balanced) the CLOCKWISE moments equals the ANTI-CLOCKWISE moments. F1 x d1 = F2 x d2 10 x ______ = 2 x ________ You can use this method to find an unknown quantity when designing a leveroperated system. For example what force is required to open the lid of a tin of paint?

100N

Effort in N

200mm

5mm Clock wise moments = Anticlockwise Moments

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Conventions When you draw a lever as a parallel line then you will need to follow the correct conventions or symbols. For example a lever can be bent through 90 degrees and connected to a backboard, see below. In the diagram the type of lever is called a bell crank lever. It is designed to move linear motion through 90 degrees. The FREE or moving pivots can be seen as a The FIXED pivot however is seen

non-shaded circle.

as a shaded circle.

This pivot passes through the backboard and connects the lever securely to the backboard

Backboard

Push/ Pull

FIXED PIVOT

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Exam Question Activity

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HINT – think about ratios

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CAMS

Direction of rotation Rise

Fall

Dwell

Cams are used to convert rotary motion into reciprocating motion. The motion created can be simple and regular or complex and irregular. As the cam turns, driven by the circular motion, the cam follower traces the surface of the cam transmitting its motion to the required mechanism. Cam follower design is important in the way the profile of the cam is followed. A fine pointed follower will more accurately trace the outline of the cam. This more accurate movement is at the expense of the strength of the cam follower. Snail CAM The snail cam will produce a gradual ‘rise’ and then a sudden fall during it’s rotation. The dwell is extremely small as the CAM is lifting almost as soon as it falls.

Follower height

One full rotation

Cam Rotation Cam Rotation

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Pear shaped cam

Heart shaped cam

Eccentric Cam

Pear Shaped cam will produce a regular rise and fall with a dwell for approximately 180 degrees during rotation. The rise and fall will not be regular, instead there will be a rapid rise and fall which relates to the shape of the cam. One full rotation

Fall

Rise

Dwell

Rise

Follower height

Fall

Steady fall

long dwell

steady rise

Cam Rotation

Dwell

Heart shaped cam will produce a linear rise and fall but with no dwell time and the follower path will be a rising and falling continually. Rise

Follower height

Fall

Linear rise

no dwell

linear rise

Cam Rotation 12

The eccentric cam or circular cam produces a regular rise and fall with no acceleration of rise or fall. There will be a uniform follower action.

Activity Design and make a cam in 2D design and cut out on the laser cutter with the following specifications. A snail cam with a dwell diameter 30mm and a peak diameter of 50mm; the first 90 degrees drops from radius of 25 to 22, to 180 degrees it drops from radius of 22mm to 20mm, to 270 degrees the radius drops to 18 and finally to a radius of 15mm.

360o

90o

270o

180o

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Specific Mechanisms Crank and Slider Connecting rod Crank

Rotary

Reciprocating

Slider

The crank and slider mechanism can convert rotary motion into reciprocating motion and vice versa. Rotary to reciprocating – The input turns the shaft that causes the slider to move forwards and backwards. Examples of reciprocating motion used are the drive systems for saws or the pumping system for hydraulic or pneumatic systems. Reciprocating to Rotary – The input pushes the slider that causes the crank to turn. The crank must be away from the bottom dead centre (BDC) if the mechanism is to start. These systems make use of a flywheel. A flywheel is a disc with a large mass so that when the slider is pushed the flywheel builds up inertia which keeps the system running.

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Gears The gear wheel is a toothed disc that engages or meshes with another toothed disc. A gear wheel is a basic mechanism. Its purpose is to control and transmit ROTARY motion. A shaft passes through the centre of a gear wheel and the gear is connected to a shaft by using a key.

Keyed onto shaft

Gear wheels that mesh together are known as a gear train. The gears that are shown are called SPUR gears. It is extremely difficult to draw two gears with teeth meshing as in the diagram below and to the left. In order to draw gears more accurately it is necessary to draw their symbols, the diagram to the right. Meshing Centre lines

Symbols for Spur Gear Spur gears 12 per gear NON symbolic

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Transmitting Rotary Motion The figure below shows two meshed gears. Gear A is the DRIVER and turns clockwise. EFFORT

Gear B is the DRIVEN and turns anticlockwise. LOAD

Gear A has 12 teeth.

Gear B has 12 teeth.

When the DRIVER gear rotates once all of its 12 teeth mesh with all 12 of the DRIVEN gear’s teeth and so the driven gear will also rotate once. In this gear train the DRIVER transmits the effort while the DRIVEN gear is the load. Velocity Ratio is given as =

=

distance moved by effort (RPM) distance moved by load (RPM) 1 revolution 1 revolution

Therefore the velocity ratio of this gear train is 1:1 NOTE that for this train of two gears the velocity ratio can also be given as Gear Ratio =

number of teeth on DRIVEN number of teeth on DRIVER =

12 12

=

1:1

Note the VELOCITY RATIO of a gear train is sometimes called the ‘GEAR RATIO’, and they are EQUAL. Sometimes you will see VR written as 1 but it is more common to write it as 1:1 1 Now the next example shows how the speed of the transmitted motion can be controlled. VELOCITY RATIO = GEAR RATIO

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Controlling the speed

Gear A is the DRIVER and turns clockwise.

Gear B is the DRIVEN and turns anticlockwise.

Gear A has 10 teeth and turns at 20rpm

Gear B has 20 teeth. What speed will the DRIVEN gear turn at?

What is the Gear Ratio for this system? Gear Ratio = Gear Ratio = Therefore the Gear Ratio is _______________ •

or

____:_____

Put the formula for Velocity Ratio in…

But Velocity Ratio is also given by = The distances moved are referred to in the Revolutions made Per Minute (RPM)

So VR =

2 1

=

20 rpm ? rpm

Cross multiply ? rpm =

•

20 rpm x 1 2

Therefore the speed the driven gear rotates at is 10 rpm

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An easier way of representing this formula is to combine the Velocity Ratio and Gear Ratio calculations in one Remember GEAR RATIO and VELOCITY RATIO are EQUAL So the formula can be used as follows:

Rpm of DRIVER x Teeth on DRIVER = RPM of DRIVEN x Teeth on DRIVEN

This one formula can be used with gear train calculations. YOUR TURN Calculate the speed of the driven gear.

Gear A is the DRIVER and turns clockwise.

Gear B is the DRIVEN and turns anticlockwise.

Gear A has 15 teeth and turns at 1500rpm

Gear B has 45 teeth. What speed will the DRIVEN gear turn at?

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IDLER GEARS What do Idler gears do?

IDLER

Driver

Driven

The idler gear will change the direction of motion of a gear box, which enables the output DRIVEN gear to rotate in the same direction as the input DRIVER gear. Does it matter how many teeth there are on the IDLER gear? 1. Using the gears board shown below set up a DRIVER and DRIVEN gear so that the gears mesh together. 2. Next move the Driven gear out and introduce the IDLER gear. 3. Try different sized gears for the idler. What are the results?

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SAQ Exam Questions – Have you really got it?

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Compound Gears The TEP gearbox shown makes use of a compound gear train. This consists of two pairs of meshed gears where the gear shafts are parallel. The gear train has a driver gear and driven gear, but the intermediate gears are fixed together on one common shaft. The gears are not idle since one becomes the driver and the other the driven. They will affect the output speed of the gear train. When calculating velocity for a compound gear, calculate the gear ratios and multiply them to give an overall gear ratio for the gearbox. Use this to calculate the overall velocity ratio.

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Transmission of FORCE Gears are not only used to transmit motion they also need to transmit force. But, the force acts at a distance from the centre of rotation. Consider a spanner used to tighten a nut below. Force applied F

distance r

When a spanner tightens a nut a force F is applied by hand at a distance r from the centre of the nut (centre of rotation). The turning moment on the nut is the product of force F x distance r. The Turning moment F x r is called TORQUE. Torque is measured in Newton Metres because the applied force is in NEWTONS and the distance is measured in METRES. The formula for TORQUE is: Torque = F x radius What would happen to the ‘tightness’ of the nut if the spanner was made longer? If the spanner was longer …………………………………………….……….

So when gears mesh they also transmit torque. Look at the example a small gear with a small radius transmits its force to the larger gear. Now the force is transmitted further away from the centre of rotation, and so the torque is increased. The more gears, the more torque. The less gears the less torque. So the compound gearbox bought from TEP will ________________ the torque applied to output shaft. However an increase in torque means a ____________ in speed.

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Designing Gearboxes Input

Process

DC Motor No load speed 240rpm

Gearbox

Output 10 rpm to turn an advertising display

So the gearbox must produce a velocity reduction of 240rpm to 10rpm, i.e. a velocity reduction of 240:10 or 24:1 Solution 1 A small driver pinion and a large driven wheel. The pinion could have 10 teeth and the driven wheel _______ teeth?

The problem with this solution is that only one transmission of force is taking place and so the TORQUE of this system will be ________(high or low) Solution 2 By finding the PRIME factors of 24 a gearbox with more than one transmission of force can be designed which will increase the torque of the system. The prime factors of 24 are 4 x 3 x 2. A velocity reduction of 4:1, followed by 3:1 followed by 2:1 would provide an overall reduction of 24:1 and provide 3 transmission of force which in turn increase output torque. 3:1 2:1 4:1

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Other mechanisms using gears Worm and Wheel A worm is used to reduce speed. For each complete turn of the worm shaft the gear shaft advances only one tooth of the gear. In this case, with a twelve-tooth gear, the speed is reduced by a factor of twelve. Also, the axis of rotation is turned by 90 degrees. Unlike ordinary gears, the motion is not reversible, a worm can drive a gear to reduce speed but a gear cannot drive a worm to increase it. As the speed is reduced the power to the drive increases correspondingly. Worm gears are a compact, efficient means of substantially decreasing speed and increasing power. This is ideal for use with small electric motors. Symbol for the Worm and Wheel.

A gear that has one tooth is called a worm. The tooth is in the form of a screw thread. A wormwheel meshes with the worm. As the worm acts like a single toothed gear the, so the ratio of the worm and

Wormwheel =

number of teeth on wormwheel 1

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Rack and Pinion

The rack and pinion is used to convert between rotary and linear motion. The rack is the flat, toothed part, the pinion is the gear. Rack and pinion can convert from rotary to linear of from linear to rotary. The diameter of the gear determines the speed that the rack moves as the pinion turns. Rack and pinions are commonly used in the steering system of cars to convert the rotary motion of the steering wheel to the side to side motion in the wheels. Rack and pinion gears give a positive motion especially compared to the friction drive of a wheel in tarmac. In the rack and pinion railway a central rack between the two rails engages with a pinion on the engine allowing the train to be pulled up very steep slopes. In the space below draw the symbol for Rack and Pinion.

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Bevel Gears These gear wheels have teeth cut on a cone instead of a cylinder. They are used in pairs to transmit rotary motion and torque where bevel gear shafts are at right angles (90 degrees) to each other. A hand drill makes use of a bevel gear arrangement to transmit the turning action of the crank to the chuck.

Here a DC motor is used with bevel gears to transmit motion through 90 degrees. In this case no velocity change is taking place.

Draw the symbols for bevel gears here.

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Ratchet and Pawl The ratchet can be used to move a toothed wheel one tooth at a time. The part used to move the ratchet is known as the pawl. The ratchet can be used as a way of gearing down motion. By its nature motion created by a ratchet is intermittent. By using two pawls simultaneously this intermittent effect can be almost, but not quite, removed. Ratchets are also used to ensure that motion only occurs in only one direction, useful for winding gear that must not be allowed to drop. Ratchets are also used in the freewheel mechanism of a bicycle, and on the handbrake lever of a car.

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SAQ

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Pulley Systems Pulleys can be used to transmit motion instead of gear wheels. Pulleys offer an advantage over gear wheels in that the pulley belt can slip across the pulley when transmitting motion. This can be useful if a motor is connected to a pulley driving the chuck of a pillar drill. If the drill bit becomes stuck in the material being drilled the motor can still drive and the belt will slip. If gear wheels are used then the motor could stall, which might burn out the coils of the motor, or the teeth could be stripped off of the gear wheels themselves. DRIVER

DRIVER

Speed increase

Speed decrease

Straight connection Same rotation Belt drives are also used with lawnmowers for the same reason. The picture above illustrates the action of the pulley and its effect on driving speed. Pulleys are attached to the shafts (axles) of motors in a similar way to attaching gears, i.e. by using a KEY. Here we can see a V pulley system where the keyway is shown cut out of the pulley. This keyway would engage with a KEY attached (brazed or welded) to the shaft.

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Pulley Symbols

N

DRIVE 10 rpm 80 mm dia

R

DRIVE 20 rpm 40 mm dia

When the DRIVER pulley rotates 20 times the DRIVEN pulley will only rotate for the 20 x circumference of the Driver pulley, 10rpm. In this pulley drive the DRIVER transmits the effort while the DRIVEN gear is the load. Velocity Ratio is given as =

=

distance moved by effort distance moved by load 20 revolutions 10 revolutions

=

2 1

Therefore the velocity ratio of this gear train is 2:1, velocity reduction NOTE that for this pulley drive the velocity ratio can also be given as Pulley Ratio

=

Diameter of DRIVEN Diameter of DRIVER

=

80 40

=

2:1

=

2 1

Since velocity ratios are the same then this formula can be used to calculate an unknown quantity in a pulley drive system.

Rpm of DRIVER x Dia of DRIVER = RPM of DRIVEN x Dia of DRIVEN

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Activity Design a pulley drive system. Specification for your design • • •

VR of 4:1 Driver pulley is 25mm diameter Distance between the centres of the pulleys is 85mm

Use a compass and ruler and draw your system here.

If the DRIVER pulley rotates at 240rpm calculate the speed the DRIVEN pulley will rotate at.

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Chain Drive Systems We have all seen chain drive systems on our bikes. The crank (pedal) is the driver sprocket and the chain transmits this motion to the wheel where we can select different sprockets, which in turn will select different speeds. Chains combine the positive, nonslip, drive of the gear wheel, with the flexibility of positioning driver and driven a distance apart without the need for any additional idler gears.

Activity In this table list the advantages and disadvantages of the different types of drive system.

Pulleys

Gears Advantages

Disadvantages

Advantages

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Disadvantages

SAQ – Exam Questions

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