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10.1.1 Define mechanical advantage, velocity ratio and efficiency
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T. Ford. April 2008. GENERIC 1 International Baccalaureate Organization (IBO) -_ Name: TG: 1 AHL Topic 10 Mechanical Design (8 hours approx. 7 lessons) Design Technology. 2 Topic 10 – Mechanical Design. Contents: □ 10.1 General concepts. □ 10.2 Mechanical Motion □ 10.3 Conversion of motion 2 3 Students please note: Tick each section as you go. Use the checklist at the end to make sure you have learned the unit. Your teacher may not necessarily cover each stage in this order and some stages take longer than others to learn. You are expected to keep your own folder of notes and portfolio of work related to this unit which you must bring to every lesson. This booklet is designed as a guide only – studying is where the learning takes place! Bring this booklet with you to every lesson. 10.1 General concepts. 10.1.1 Define mechanical advantage, velocity ratio and efficiency. Here’s a quick workshop demonstration to help you understand this topic: You will be given a piece of metal to bend and cut by hand. The bend must be to a 90 degree angle and the cut must completely shear the metal in two. How can it be done? Try opening a tinned food product using three different types of tin opener. Discussion: Why are some methods easier than others? Why is this when we are still only using human muscle power to carry out the same task? We use mechanisms to help make every day tasks easier to perform. However, we can’t simply create energy from nowhere to do these jobs – so where does this extra ‘power’ come from? The following sections will help you to understand. Look at these pictures: The tin opener has to do two distinct things: 1) Pierce or cut the top of the can 2) Remove the lid by slicing the steel. The picture on the right shows the small cutting wheel doing this. Let’s examine each process in turn: To pierce the can, two levers are pushed together which forces the cutting wheel to pierce the lid. How? Where does it get its power? The answer is in the lever. Your hand is moving a long distance. The fulcrum (pivot) is moving a small distance (shown by the length of the red arrows). The total energy that you put into the lever over this long distance is concentrated into a very small distance. In fact, the cutter only moves a few millimetres but your hand moves much, much further. 3 4 So; 1) The distance moved changes from large to small 2) The power produced changes from small to large. 3) The total amount of energy put in by the hand is the same total amount of energy given out by the cutting wheel! Let’s look at the second stage; removing the lid. The smaller lever is rotated which turns two small cogs (teeth with wheels). The cogs grip the edge of the can. They drive the cutting wheel along the metal, slicing it away. This is also a lever. It is in fact two levers on opposite sides of the fulcrum. The outside edges move through a greater distance than the centre, so it’s the same principle. Lever 1 Lever 2 All mechanisms do this. They convert energy by collecting it up over a long distance and concentrating it, or by taking concentrated energy and spreading it out over a longer distance. It is always about converting energy and movement. In fact, all mechanisms are actually levers! It will be interesting to see if you can identify the levers in this unit – they are very well disguised! 10.1.2 Calculate mechanical advantage (MA), velocity ratio (VR) and efficiency for simple mechanical systems. Don’t be put off by these scientific terms. They actually mean very simple things: Mechanical Advantage or MA : How much easier work is to do when you use a mechanism. Velocity Ratio or VR: How much difference there is between the distances moved. Efficiency: How well all the energy is converted to do the job needed. There are also formulae for calculating these things exactly. Sorry – but you need to learn them! Let’s work through some examples, they are actually very simple as long as you understand everything said so far. 4 5 The Load is the work that is being done. In this case, it’s the force needed to cut the paper. Force is measured in Newtons (N). The Effort is the force needed to be exerted by the hands to cut the paper. We would expect the effort to be less than the load – the scissors are meant to make the job easier after all. Suppose the effort was 1N and the load was 5N MA = Load / Effort. MA = 5/1 MA = 5 There are no units because it is a RATIO (a comparison). This means the scissors make the job 5 times easier to do! Simple. But where’s the trade off? We have gained power but what have we lost? Can you work it out? You’ve probably guessed that the distances moved have something to do with it. This is where the Velocity Ratio (VR) comes in. It compares the distances moved. In this example, the hands must have moved 5 times further than the blades at the point where they cut the paper. Suppose the hands moved 150MM and the blades moved 30MM: VR = distance moved by effort / distance moved by load VR = 150/30 VR = 5 Again, there are no units because it is a RATIO (a comparison). This means the hands move 5 times further than the blades at the point where they cut the paper. Efficiency = MA/VR Efficiency = 5/5 Efficiency = 1. That means that the total energy you put in is exactly what you get so no energy is wasted. You can multiply it by 100 to get a percentage. However, in reality, products are never 100% efficient. Energy can be converted into heat and sound if there is a lot of friction at the fulcrum or if the cutting edges are not sharp. A number which is less than 1 means that it is not 100% efficient. Here’s another example: The hand truck makes it easier to lift heavy loads. To lift the box up by a small distance, the handles need to be pushed down by a much longer distance. Here is the data you need to work out MA, VR and efficiency: 5 6 Load: 50 N Effort: 5 N Distance moved by effort: 550 MM Distance moved by load: 50 MM Calculate MA, VR, Efficiency and how much energy has been lost: (teachers note: The answers are in white text below, click, drag and change font colour to reveal the answers). Answers: MA = 50/ 5 = 10 VR = 550/50 = 11 Efficiency = MA/VR = 10/11 = 0.91 or 91% Energy lost = 9% Summary: If you understand this then everything else is straightforward. Always remember that energy cannot appear or disappear, it has to be converted. All mechanisms convert energy and motion – but the total amount put in and the total amount we get out is always the same. Because MA and VR are ratios, you can also work them out by comparing speed. This is important to remember when we look at gears. A really good revision website is at: http://www.designandtech.com/resistantmaterials/#mechanisms 10.1.3 Describe first, second and third-class levers and 10.1.4 Discuss the relevant efficiencies of the three classes of lever. There are three types of lever. The only difference between them is the relative positions of the Load, effort and Fulcrum: First class: Second class: Third class: Using page 136 of Design and Technology (Caborn, Mould & Cave), label clearly the positions of the load and the effort in the diagrams above. The third class lever may look a little strange but all will become clear… For each type of lever shown below, try to work out which class of lever it is. Be careful, some objects may have multiple levers! 6 7 (teachers note: The answers are in white text below, click, drag and change font colour to reveal the answers). Example: Class (1st, 2nd or 3rd )? Scissors… First class. Fulcrum in centre, load and effort on opposite sides. Bottle opener… Second class. The fulcrum is at the end, The lid (load) is pushing down against the opener, the hand (effort) is pushing up. Broom… Third class. The fulcrum is provided by the wrist or elbow at one end of the broom. The effort is provided by the hand further along. The load resists the effort. Rickshaw… Second class. The fulcrum is at the end (wheel), The load (passengers and box) are pushing down, the effort is pushing up. Fishing rod… Third class. The fulcrum is provided by the wrist or elbow at one end of the rod. The effort is provided by the hand further along. The fish is the load pulling down while the effort tries to pull up. Crowbar… First class. Fulcrum in centre (the point where the crowbar makes contact with the ground), load and effort on opposite sides ( the load is the wood resisting being moved, the effort is provided by the arm moving downwards). See-saw… First class. Fulcrum in centre, load and effort on opposite sides (like the scissors). Tweezers… Third class. The fulcrum is provided at one end. The effort is provided by the fingers in the centre which push together. The load resists the effort by pushing out. Nutcrackers… Second class. The fulcrum is at the end, the load (nut) is pushing against the effort. Question: 7 8 Many people would say first class because they are the only levers with a fulcrum in between the load and effort so that’s an acceptable answer. However, both the first and second class levers give a mechanical advantage, they make work easier to do by moving the load smaller distances. The third class lever does not! It actually decreases mechanical advantage and makes the load feel even heavier! But why…? Look at the fishing rod. The fish will ‘feel’ much heavier and is hard to lift out of the water. However, a small movement form the hand (effort) produces a larger movement further along the fishing rod, making it much easier to control the fish when it is in the water. The tweezers need to grip small objects tightly. A small movement form the effort results in a larger movement where the tweezer grips are, making it much easier to accurately use. Finally…sweeping up is hard work and now we know why: The broom can be accurately controlled using only small movements form the arm – we can sweep a larger area without needing to move much. However, the effort we need to put in is large. The better answer = third class. Your arm is a third class lever too. Which class of lever do you think is the ‘odd one out’ and why? Think carefully before you commit yourself. Answers on above (teachers note: The answers are in white text in the box above, click, drag and change font colour to reveal the answers) 10.1.5 Explain that, when a lever is in equilibrium, the net moment is zero. What is a moment? …we all have them. A moment in mechanical terms is a turning force. Look at the picture below: Moment = Force X Distance A moment is the product of the force exerted by the load (Newtons or N) and the distance it is from the fulcrum (in Metres). Suppose the man exerts a force of 100N and is 1.5M away from the fulcrum. He produces a moment (turning force) of 100 X 1.5 = 150 Newton Metres (NM) Question: Suppose the little girl exerted a force of 40 N. How far from the fulcrum will she need to be to make the see-saw balance? See if you can work it out before checking the answer below. Answer: Moment = Force X Distance 150NM = 40 X Distance Distance = 150/40 Distance = 3.75M The girl will need to be 3.75 metres from the fulcrum to make the see-saw balance 8 9 The NET MOMENT is the difference between the moments on the left and the moments on the right. In this example, the net moment is 0 and the see saw balances. What would happen if the girl was 3M from the fulcrum? Again see if you can work it out before checking the answer below. Answer: Moments on the left = 40 X 3 = 120NM Moments on the right = 100 X 1.5 = 150NM The net moment is 30 NM to the right so the man will go down and the girl will go up. 10.1.6 Calculate mechanical advantage and effort for first-, second- and third class levers. You can do some revison on this topic at: http://www.bbc.co.uk/schools/gcsebitesize/design/systemscontrol/mechanismsrev1.shtml Calculate the missing element in each example (teachers note: The answers are in white text below, click, drag and change font colour to reveal the answers) MA = 0.5 Load = 2N Effort = ? Effort = Load/MA = 2 / 0.5 = 4N Remember to include the units – NEWTONS (N) MA = ? MA = Load / Effort Load = 10N = 10/33 Effort = 33N = 0.30 No units – it’s a ratio. MA = ? MA = Load / Effort Load = 48N = 48/12 Effort = 12N = 4 No units – it’s a ratio. MA = ? Load = 13 Effort = 3 MA = Load / Effort = 13/3 = 4.33 9 10 No units – it’s a ratio. MA = 0.35 Load = 0.5 Effort = ? Effort = Load/MA = 0.5/0.35 = 1.43N Remember to include the units – NEWTONS (N) MA = 2 Load = 187 Effort = ? Effort = Load/MA = 187/2 = 93.5N Remember to include the units – NEWTONS (N) 10 11 Gears 10.1.7 Describe gear systems. A gear system is a collection of different gears mounted so that they contact (mesh) their teeth together. The diameter of the gears can be changed to increase / decrease rotary speed. A gear system can transfer the input rotary energy from a shaft or axle to a different angular direction (bevel gear) and or rotate it in a different direction (clockwise / anti clockwise) the speed of rotation along with the torque level can also be adjusted (faster / slower rotation). A number of gears together is called a gear train. Some simple gear types: Simple Gear Train Bevel Gear Gears ‘meshed’ Compound Gear Timber windmill gears Gear systems or ‘gear trains’ are designed for specific applications. • • Basically: The smaller the gear the faster the rotational velocity (but with lower torque). (the easier it would be stop using your brakes) The larger the gear the slower the rotational velocity (but with higher torque). If you require high torque you need larger gears… (the harder it would be to stop using your brakes) Think about a car or bicycle…. • • 11 12 • high gear (small gears low torque) for high speed on level ground. • low (large gears, max torque) for going up hill GEARS AND GEAR SYSTEMS V. Ryan © 2001 GEAR TRAINS This is a good example of a ‘gear train’. A gear train is usually made up of two or more gears. The driver in this example is gear ‘A’. If a motor turns gear ‘A’ in an anticlockwise direction; Which direction does gear ‘B’ turn ? Which direction does gear ‘C’’ turn ? Does gear ‘C’ revolve faster or slower than gear ’A ? explain your answer.’ So far you have read about ‘driver’ gears, ‘’driven’ gears and gear trains. An ‘idler’ gear is another important gear. In the example opposite gear ‘A’ turns in an anticlockwise direction and also gear ‘C’ turns in an anticlockwise direction. The ‘idler’ gear is used so that the rotation of the two important gears is the same. Is the speed of gears A and B the same ? 12 13 In one sentence below explain what an ‘idler’ gears does. DRAWING GEARS It would be very difficult to draw gears if you had to draw all the teeth every time you wanted to design a gear system. For this reason a gear can be represented by drawing two circles. 13 14 10.1.8 Calculate velocity ratio for gear systems. THE BASICS - GEAR RATIO (VELOCITY RATIO) V. Ryan © 2003 Many machines use gears. A very good example is a bicycle which has gears that make it easier to cycle, especially up hills. Bicycles normally have a large gear wheel which has a pedal attached and a selection of gear wheels of different sizes, on the back wheel. When the pedal is revolved the chain pulls round the gear wheels at the back. Look at the gear wheel with the pedal attached and compare it in size to the gear wheels in the centre of the back wheel. What do you notice about them? Can you name any other machines that use gears? Most people have cycled a bicycle up a hill. The steeper the hill gets the more difficult it is to pedal and normally a cyclist will change gears to make it easier. When the cyclist changes gear, the chain moves from a small gear to a larger gear with more teeth, making it easier to push the pedals round. The more teeth the back gear has, the easier it is to cycle up hill although the bicycle moves forward more slowly. What will happen if a cyclist going up a hill changes gear from a larger to a smaller gear wheel? Will it be easier or harder to pedal? GEAR RATIO (VELOCITY RATIO) The reason bicycles are easier to cycle up a hill when the gears are changed is due to what is called Gear Ratio (velocity ratio). Gear ratio can be worked out in the form of numbers and examples are shown below. Basically, the ratio is determined by the number of teeth on each gear wheel, the chain is ignored and does not enter the equation. 14 15 EXAMPLE: If the pedal gear revolves once how many times will the sprocket gear revolve? The example above shows that every time the pedal gear revolves once the sprocket gear on the back wheel revolves twice making it easier to cycle up hill. 15 16 10.1.9 Describe the function of different types of gears in a range of objects. Use rack-and-pinion, bevel and worm gears. Different types of gears carry out different jobs within a gear train principally to change direction or speed of rotation, change direction of drive, increase or decrease torque of final drive or change the speed or to change a rotary to other required movement. Rack and pinion: A very simple arrangement with a gear (pinion) mounted and in contact with a rack (a strip of metal with corresponding teeth on the top, just like a gear but in one long strip) the strip is mounted in a sliding carriage to allow it to freely move in one direction and then back again. This movement is linear but also reciprocating. This simple mechanism has been used for centuries and can be found in applications where a horizontal or vertical movement is required that can be precisely and easily controlled. Eg steering system on a car, table movement on a pillar drill. RACK AND PINION A ‘rack and pinion’ gears system looks quite unusual. However, it is still composed of two gears. The ‘pinion’ is the normal round gear and the ‘rack’ is straight or flat. The ‘rack’ has teeth cut in it and they mesh with the teeth of the pinion gear. If gear ‘A’ rotates how would you describe the movement of the rack ? The pinion rotates and moves the rack in a straight line - another way of describing this is to say ‘rotary motion’ changes to ‘linear motion’. A good example of a ‘rack and pinion’ gear system can be seen on trains that are designed to travel up steep inclines. The wheels on a train are steel and they have no way of gripping the steel track. Usually the weight of the train is enough to allow the train to travel safely and at speed along the track. However, if a train has to go up a steep bank or hill it is likely to slip backwards. A ‘rack and pinion’ system is added to some trains to overcome this problem. A large gear wheel is added to the centre of the train and an extra track with teeth is added slope, this is called a ‘rack’. As the train approaches a steep hill or slope the gear is lowered to the track and it meshes with the ‘rack’. The train does not slip backwards but it is pulled up the steep slope. 16 17 A good example of a ‘rack and pinion’ train is the Nilgiri mountain railway in India. . RACK AND PINION - DRILLING MACHINE V. Ryan © 2002 Opposite is an example of a rack and pinion as seen in the school workshop and machine shops throughout the world. As the handle is turned the table moves up and down the central pillar of the drill. This makes it easy to move the table and takes the minimum of effort. This is a simple but interesting application of a rack and pinion mechanism. The less well designed machine drills do not have this and consequently brute force is needed to move the table up and down. Often this is difficult and requires some strength. The rack and pinion reduces the force needed to move the table and most importantly protects the machine operator and his/her back from excessive strain. 17 18 Above is one of the less well designed machine drills. The table on these machines can weigh a significant amount and if they are used often by the same operator damage to the back can occur. A well designed mechanism such as the rack and pinion is precise and saves effort and time. Sometimes it is a good idea to invest in a slightly more expensive piece of machinery especially as health and safety is very important. 18 19 GEAR MODELS - RACK AND PINION MODEL V. Ryan © 2003 Rack and pinion gear systems involve the use of a round gear called a pinion and a flat gear called a rack. A simple model of this type of gear system is shown below. Using the same or similar gear modelling kit (lego technic), set up the arrangement of gears shown in the photographs. 1. Put the back board and base in position. 2. Add the pinion (round gear) and rotate by hand. 3. Add the ‘gauge’ above the pinion. This will be used later to measure how far the gear moves. Check the pinion can still rotate. 4. Add the ‘rack’ (flat gear) so that it meshes with the pinion. Check the pinion can still rotate. If the pinion revolves in a clockwise direction which way does the rack move? (Left or right). If the pinion revolves in a anticlockwise direction which way does the rack move? (Left or right). 19 20 Using the ‘gauge’ - if the pinion moves three teeth, how many teeth does the rack move? 5. Explain one use of a rack and pinion gear system. Draw a diagram to help explain your answer. 20 21 Bevel drive: BEVEL GEARS V. Ryan © 2002 Bevel gears can be used to change the direction of drive in a gear system by 90 degrees. A good example is seen as the main mechanism for a hand drill. As the handle of the drill is turned in a vertical direction, the bevel gears change the rotation of the chuck to a horizontal rotation. A TYPICAL HAND DRILL ENLARGED VIEW OF THE BEVEL GEARS OF A HAND DRILL MECHANISM The bevel gears in a hand drill have the added advantage of increasing the speed of rotation of the chuck and this makes it possible to drill a range of materials. With the aid of diagrams and notes explain how a bevel gear is used as part of a mechanism/machine you have seen or used. 21 22 Worm drive This is the slowest method of driving a gear and consists of two components, the worm drive, a horizontal or vertically mounted shaft driven casting which meshes with a correspondingly cast gear. A very accurate, slow method of drive. Due to the angle of the driving faces this system can only move in one direction. WORM GEARS V. Ryan © 2002 The arrangement of gears seen left is called a worm and wormwheel. The worm, which in this example is brown in colour, only has one tooth but it is like a screw thread. The wormwheel, coloured yellow, is like a normal gear wheel or spur gear. The worm always drives the worm wheel round, it is never the opposite way round as the system tends to lock and jam. The picture to the right is a typical set-up for a motor and worm gear system. As the worm revolves the worm wheel (spur gear) also revolves but the rotary motion is transmitted through a ninety degree angle. 22 23 The gear ratio of a worm gear is worked out through the following formula: number of teeth on wormwheel number of teeth on worm The worm acts as a single toothed gear so the ratio is; number of teeth on wormwheel 1 EXAMPLE: If the wormwheel has 60 teeth: 60 1 Gear Ratio = 60:1 (Rotary velocity is also reduced by 60:1) Quite simply, this means a worm gear reduces the speed of the spur gear by sixty times. If you need a gear system whereby the speed is reduced by a considerable amount - a worm and wormwheel are worth considering. 1. Describe how a worm and wormwheel could be used as part of a design for a mechanical device or toy. Use diagrams and notes. 2. If the wormwheel has 80 teeth, what is the gear ratio ? Show your working below. 23 24 10.1.10 Explain a design context in which a compound rather than a simple gear train would be appropriate. Consider the gearing system on a metal lathe designed to be changed to cut a specific type of thread. Consider ratios, mechanical advantage and changes. A compound gear is essentially two different diameters of gears joined together in one component and this means that from one input an additional ,different ratio, output can be achieved without the requirement for an additional gear to be placed in the gear train, this is desirable as less gears means less drive or gear train ‘slack’ in the system as each gear does not mesh absolutely perfectly and this minute misalignment adds up over a gear train. 10.1.10 Explain a design context in which a compound rather than a simple gear train would be appropriate Compound gear trains involve several pairs of meshing gears. They are used where large speed changes are required or to get different outputs moving at different speeds. Centre lathes, like the ones found in school workshops have compound gear trains that transmit rotary motion from an electric motor through to the headstock spindle. The lead screw, which allows the tool post to travel on automatic feed, also operates from this compound gear train. Compound gear trains often have two or more gears mounted on the same shaft. A good example of this is a car gear box, which has to fit into a confined space, has to allow the driver to select various gear ratios and also has to change from forward to reverse. Gear ratios (or velocity ratios, VR) are calculated using the same principle as for simple gear trains, i.e. VR = number of teeth on the driver gear divided by the number of teeth on the driven gear. However, the velocity ratio for each pair of gears must then be multiplied together to calculate the total velocity ratio of the gear train: Total VR = VR1 x VR2 x VR3 x VR4 etc. 24 25 10.1.11 Discuss the function of different types of gears in a range of objects. Use rack-and-pinion, bevel and worm gears. Rack and pinion: A traditional method of creating a steering mechanism Consider other uses for this type of movement within a mechanical system Bevel gear: A method of transferring drive through 90 degrees Consider other uses for this type of movement within a mechanical system Worm drive: The slowest method of transferring high speed rotary drive to manageable speed. Typically used for speed reduction from electric motor to final drive in toy vehicles. In the table below write the most common use for each method of mechanical movement transfer. Rack and pinion Bevel gear Worm Drive 25 26 Belts 10.1.12 Describe a belt or chain drive system. Consider profile, load, changes in load, and speed. Pulley systems use a belt to transmit motion and force from the driver shaft to the driven shaft. The continuous V-belt is the most common type used. It fits tightly into the groove on the pulley wheels to keep slipping to a minimum. V-belts come in a variety of widths and thicknesses as shown on the left. Also shown are the two construction methods of V-belts. The belt drives or is driven by the pulley via friction, the angled sides of the belt fit exactly into the groove on the pulley and it is these two surfaces that drive not the flat underside of the belt. Belt drives also provide a built in protection to the mechanism if too much torque is created (ie the machine encounters a blockage) the belts will slip slightly. Speed changes are made by using different size pulleys on the driver and driven shafts. By comparing the size of the two pulleys you can calculate the velocity ratio of the system. 10.1.13 Calculate velocity ratio for belt or chain drive systems. Driver pulley 35 diameter Driven pulley 140 diameter 26 27 Velocity ratio= Jkj Driven pulley diameter Driver pulley diameter VR = 4:1 VR = 140 35 VR Ratio 10.1.14 Compare belt or chain drives and gear systems Consider profile, load, changes in load, and speed. Belt drives One problem with belt drives is that the belt can slip, causing driven shaft to rotate slower than expected. Where it is vital that the rotation of the driven shaft is kept in sequence with the driver shaft a toothed belt can be used. Chain drives These use a chain to transmit rotary motion from the driver shaft to the driven shaft. Sprockets are the toothed wheels on which the chain runs on. Unlike some pulley systems the chain and sprocket cannot slip. Bicycles and motorbikes use a chain and sprocket system because of its strength and because they do not slip. For example: Driver sprocket has 15 teeth and the Driven sprocket has 60 teeth No. of teeth on driven sprocket 60 ______________________________ No. of teeth on driver sprocket VR RATIO = or 4:1 or 4 High torque low speed 15 VR = = Gear systems Gears are toothed wheels, fixed to the driver and driven shafts, which mesh together. A number of gears connected together are called a gear train. 27 28 There are several types of gear systems all designed to turn the shaft at set calculated speeds. The shafts will turn in opposite directions and as the gears are different sizes they will turn at different speeds. To get them to turn in the same direction, a third gearwheel has to be fitted between them. This is called an idler gear. Compound gear trains involve several pairs of meshing gears. They are used where it is necessary to make large speed changes or to get different outputs moving at different speeds. 28 29 10.1.15 Design a system to provide belt tension to a belt-and-pulley system. Without tension between the pulleys the belt cannot function therefore a method of tension adjustment is required via moving the idler wheel Sketch a simple method of adjusting the idler pulley so it can create more or less tension on the belt. Outer frame of mechanism Belt Idler pulley 29 30 10.1.16 Describe a pulley system. PULLEY SYSTEMS - 1 V. Ryan © 2004 Pulley systems are used when there is a need to transmit rotary motion. The diagram below shows a simple system comprised of two pulley wheels and a belt. It is a simple mechanical device to winch up and down a rope. When the motor is turned on it revolves the driver pulley wheel. The belt causes the driven pulley wheel to rotate as well, winding out the rope. Pulley wheels are grooved so that the belt cannot slip off. Also, the belt is pulled tight between the two pulley wheels (in tension). The friction caused by this means that when the driver rotates the driven follows. Below sketch a side and end view of a belt rotating around a pulley, annotate to show the faces of the pulley where the belt is driven. 30 31 Most pulley wheels have a central shaft on which they rotate. To keep the wheel firmly attached to the shaft it is usual to use what is called a ‘key’. The diagrams to the left shows a keyed shaft which is pushed through the centre of the pulley wheel. A small rectangular key is then ‘tapped’ into position, holding the shaft and the pulley wheel together. This fitting means that the pulley wheel cannot slip on the shaft. 10.1.17 Calculate mechanical advantage for pulley systems. PULLEYS AND LIFTING - IMPORTANT FORMULAS V. Ryan © 2004 When using pulleys for lifting the formulas for mechanical advantage and velocity ratio are very important. The formulas are shown below. FORMULAS RELATING TO MECHANICAL ADVANTAGE Mechanical advantage is defined as the ratio of load to effort. Pulley systems rely on this important relationship between load and effort. The formula seen below is best understood by writing it within a triangle. This helps when it is necessary to change the formula to find either; mechanical advantage or the load or the effort. In this way three formulas can be generated from the single formula inside the triangle. 31 32 FORMULAS RELATING TO VELOCITY RATIO Velocity Ratio (sometimes called movement ratio)- is defined as the ratio of the distance moved by the effort to the distance moved by the load. The formula seen below is best understood by writing it within a triangle. This helps when it is necessary to change the formula to find either; velocity ratio or the distance moved by the load or the distance moved by effort. In this way three formulas can be generated from the single formula inside the triangle. 32 33 Inclined plane 10.1.18 Describe an inclined plane. Consider inclined planes, screw threads and wedges. An inclined plane is a surface where there is a slope on the end points, or in other words on a surface where the height is different It is one of the six simple mechanisms. We all know that work done is force and distance, and by moving an object gradually on an inclined plane, less force is needed than lifting it up vertically. An inclined plane can be used in many ways to make a job easier. In the simple example shown above, the load can be raised to the top either by pulling it up the slope or by lifting it vertically. Screw Thread Screw threads make use of the inclined plane principle. The diagrams show how by wrapping an inclined plane around a cylinder you get the helix form as on a screw thread. The threads are used in several different ways: • To provide powerful movements (car jacks) • To hold things in place (bolts and screws) • To position things accurately (binoculars) 33 34 Wedges When cutting hard materials, you can of course choose to crush it. However, to gain more precision and using less effort, a wedge can be used. Saws and wedges transfer the circular or linear motions of such inclined planes to the surface being cut and multiply the force being applied. Holes drilled for wedges Steel wedges inserted Wedges hammered in Wedges start to split the stone Large 3000kg stone block is split The action of hammering the wedge into the stone with a linear action forces the inclined planes of the wedge sides to push the material apart. The force applied by hammering the wedge in is multiplied by the small surface point and inclined planes. 10.1.19 Explain the advantage of an inclined plane. One famous use of inclined planes is the building of the pyramids. It is believed that the Egyptians used slopes to lower the force needed to move the huge rock blocks. It transfers horizontal forces eventually into vertical forces in the sacrifice of a longer distance needed. The mechanical advantage is also very high as it can be adjusted to the needs. Mechanical advantage= For the ideal machine, the work input = work output There is no friction; hence there is 100% efficiency in converting the work done by the effort into the work done on the resistance. 34 35 An example is shown below Two ropes laid down a ramp attached to a raised platform. A barrel is rolled onto the ropes and the ropes are passed over the barrel and handed to two workers at the top of the ramp. The workers pull the ropes together to get the barrel to the top. The barrel is a movable pulley and the MA = 2. Try the simple experiment above , using some string and a heavy cylinder, use the cylinder as a moveable pully. If the there is enough friction where the rope is pinched between the barrel and the ramp, the pinch point becomes the attachment point. This is considered a fixed attachment point because the rope above the barrel does not move relative to the ramp. Alternatively the ends of the rope can be attached to the platform. Inclined plane: MA = length of slope ÷ height of slope Generally, the mechanical advantage is calculated thus: MA = (the distance over which force is applied) ÷ (the distance over which the load is moved) The Force exerted IN to the machine × the distance moved IN will always be equal to the force exerted OUT of the machine × the distance moved OUT. For example; using a block and tackle with 6 ropes, and a 600 pound load, the operator would be required to pull the rope 6 feet, and exert 100 pounds of force to lift the load 1 foot, therefore: (force IN 100 × distance IN 6) = (force OUT 600 × distance OUT 1) or, WORKin = WORKout” http://moodle.student.cnwl.ac.uk/moodledata_shared/CDX%20eTextbook/dswmedia/ brakes/brake/funda/leveradvantage.html 35 36 10.2 Mechanical motion 2 hours 10.2.1 Describe linear, rotary, intermittent, oscillating, reciprocating and irregular motion Linear Motion Linear motion is motion in a straight line. Steady linear motion is known as velocity (uniform motion in a straight line). An example of linear motion is the cutting arm of a paper guillotine (photo below) as it travels from one side of the machine to the other. Rotary Motion Motion in a circle is called rotary motion. The number of complete revolutions made per minute (rpm), is called rotary velocity. Intermittent Motion Intermittent motion is motion which starts and stops regularly. For example, in a cinema projector the film needs to be moved on one frame at a time then held stationary while the light projects it onto the screen. This is usually done with a Geneva stop as shown here. Intermittent motion is usually the end result of a mechanism rather than the starting point for conversion. http://www.flyingpig.co.uk/mechanisms/pages/intermittent.html Oscillating Motion Oscillating motion is motion backwards and forwards in a circular arc. E.g. playground swings (photo) and clock pendulums. Reciprocating Motion Reciprocating motion is linear motion backwards and forwards in a straight line. Sewing machines make use of this type of motion. Jigsaws and scroll saws which are often used in school workshops have blades that cut by reciprocating motion. 36 37 Irregular Motion Irregular motion is motion which has no obvious pattern to its movement. It is often needed in automata to recreate the movements of living things. Irregular motion is usually created using a cam or series of cams Irregular motion is not often used as the starting point for a mechanism. It can, however be translated and transformed as shown below. http://www.flyingpig.co.uk/mechanisms/pages/irregular.html 10.2.2 Explain how linkages can be used to change the direction of motion of components. A linkage in combination with a fulcrum can easily be used to change the direction of motion. The input motion be it linear, reciprocating or rotary can be converted to provide an output motion that is different. If you want to change the direction of movement or force through 90° you can use a linkage device called a bell crank (so called because it was used in victorian times in linkages used to operate doorbells and servants bells). A common device which uses this mechanism is the brakes of a bicycle. Here the force from the handlebar lever is turned through 90° to squeeze the brake block against the wheel rim. If the fulcrum is at an equal distance from the input and output then the movement of the output will be equal to the movement of the input. Otherwise the movement will be different and the system will have some degree of mechanical advantage This mechanism is composed of three important parts: The crank which is the rotating disc, the slider which slides inside the tube and the connecting rod which joins the parts together. 37 38 As the slider moves to the right the connecting rod pushes the wheel round for the first 180 degrees of wheel rotation. When the slider begins to move back into the tube, the connecting rod pulls the wheel round to complete the rotation. One of the best examples of a crank and slider mechanism is a steam train. Steam pressure powers the slider mechanism as the connecting rod pushes and pulls the wheel round. The cylinder of an internal combustion engine is another example of a crank and slider mechanism REVERSE MOTION LINKAGE: As the top rod moves to the left the bottom rod moves to the right. The bars move in opposite directions. Another way of describing this linkage is the direction of movement in one rod is reversed in the other rod. The fixed pivot is the centre of rotation. PARALLEL MOTION LINKAGE: As the large rod at the top of the diagram moves to the left the two small rods at the bottom move to the right. All the rods are parallel to each other. CRANK AND SLIDER LINKAGE: The rods move forwards and backwards in slider. The fixed pivot anchors the linkages to one place. BELL CRANK LINKAGE: This linkage allows horizontal movement to be converted to vertical movement. It also works the opposite way round. A practical example of this is the brake mechanism on a bicycle. 38 39 10.2.3 Discuss mechanical motion in a range of contexts. Consider a hydraulic digger, a bicycle, a car jack and a hand drill. Mechanical motion transfers movement from one input motion to another output motion. Along with the concept of mechanical advantage, velocity ratio and experience, humans have developed mechanical methods to achieve tasks that would otherwise be incredibly difficult or impossible by other means. Early, in fact prehistoric man most likely used the first lever to gain mechanical advantage over a much larger load, imagine the Egyptians and thousands of slaves pulling a huge block of stone for pyramid construction and some one having the idea of putting it on rollers….much easier! This development and refinement has continued over centuries driven by physical needs, food, agriculture and also due to conflict and war. One of the major advances in the refinement of precision engineering came about due to the requirement of watch manufacture and the need to create a time piece that was accurate and could be used for naval navigation see John Harrison http://www.royalnavalmuseum.org/info_sheets_john_harrison.htm In modern terms the majority of mechanisms we see around us are refinements of historic designs that have been adapted to fit a different or more modern requirement. Most mechanisms or mechanical solutions in modern terms are broadly designed to make tasks physically easier or quicker, enable the use of less labour or make a task more cost effective. It is a modern fact that in the majority of developed or developing countries the operation of a machine is more efficient that relying on human labour. The original power source for any mechanism was obviously human however we now have numerous power sources available such as electric motors and petrol / diesel powered engines. These provide the motive power through connection to gears, linkages and other mechanical connections to achieve mechanical advantage and complete tasks. One modern aspect of mechanical motion is the combination of fluid (hydraulic), pneumatic (air) technologies and more traditional linkages, this can be illustrated within a mechanical excavator but as a starting point a basic understanding of how hydraulic systems work is required. Hydraulic systems can exert a large amount of pressure or force from a relatively small input. Hydraulic systems basically work on the fact that it is impossible to compress a fluid and within a closed system when the fluid is compressed it displaces to another part of the system and can operate a piston. This linear action can be transferred mechanically by linkages to many outputs. 39 40 In a car braking system when the brake pedal is depressed the fulcrum turns the pedal into a 2nd class lever and exerts pressure on the piston which transfers the fluid via displacement to the wheel piston which puts pressure on the pads which press onto the brake disc, as the pressure increases on the pedal the pressure increases on the pads which creates more friction and slows the vehicle. In a similar way the mechanical excavator transfers motive power via displacement of fluid in flexible pipes to a piston which is linked to a lever which then operates a digging arm or ‘boom’ and or the final digging ‘bucket’. The log splitter works by the engine E, powering a hydraulic motor D, which transfers oil via Brake pedal, brake light switch, brake booster, Brake master cylinder a valve C, to the cylinder or Brake pedal, brake light switch, brake booster, Brake master cylinder piston B this extends the wedge (inclined plane) into the log and splits it, the piston can then be retracted by operating the valve and oil direction the other way. Fulcrum Bucket Hydraulic cylinder Bell crank Linkage Boom Hydraulic cylinder The use of a bell crank enables a much greater range of rotational movement from a relatively small input motion. Hydraulic or fluid powered machines offer high powered, compact, flexible and reliable transfer of power. It would be difficult or potentially impossible to achieve these capabilities using purely mechanical means. 40 41 10.2.4 Define torque. A rotational force commonly measured in units of newton metres. Torque is best defined as a ‘twisting’ force. The act of twisting or being twisted is known as torsion. Torque is an important force in anything that is driven, the higher the torque the more force used to move a rotating object. Torque wrench used to set the correct torque measurement in newton metres. Water wheel low torque required to power it. Output (small, high torque) Rotating shaft 41 42 The larger the wheel ie. The larger the lever the easier it is to move or rotate the output from this is transmitted via a shaft to a much smaller output wheel which is higher torque and is moving much faster. 10.2.5 Discuss the design features of a ratchet and pawl system. A ratchet and pawl is the most basic refinement of an early winch. By the additional of a simple lever which locates into wedge shaped angled planes on the ratchet it turns the simple winch into a device which locks incrementally and allows the operator to move the load in a much safer stage by stage manner, if the handle is released the load will only lower a very small amount until the pawl locks. To lower the load the pawl is simply retracted which allows the ratchet to free wheel. 42 43 10.2.6 Describe simple cam shapes and their advantages. Cam shapes essentially must be smooth and allow the follower to pass over them easily. There are two major types of cam design: Lobe cam Pivot point Eccentric cam The eccentric cam is simply a circular disc that is rotated off its central natural axis which therefore gives a wider range of movement. The nearer the axis to the edge of the disc the greater the movement but also the more difficult it is to move the follower. A lobe cam is rotated around its central axis and the perimeter of the disc is shaped to create defined movement in the follower. Lobe cams can also take the shape of a heart or snail to provide different types of repetitive movement. A snail cam allows a slow build and increase in height of the follower then a sudden drop A heart cam provides 3 seperate up and down movements. 10.2.7 Identify cam followers and state their use. 10.2.8 Explain the use of a series of cam and follower mechanisms to achieve a set purpose. Below is a mechanical toy based on a CAM mechanism. As the handle on the eccentric cam is turned the top part of the egg shell lifts to reveal a face. The basic construction of the toy is also shown below. The ‘flat’ follower moves upwards and downwards as the cam rotates. Although the design is simple it must be made accurately or the mechanism will stick. 43 44 10.3 Conversion of motion 2 hours 10.3.1 Identify how mechanisms allow conversion of one form of motion to another. For example, rack and pinion, bell cranks, toggle clamps, linkages and levers. Mechanisms cannot be seen as individual entities, the component parts (cams, sliders, bell cranks, gears) and power sources are connected to perform whatever task is required. It is this use of known ‘standard’ components with design adjustments that allows the engineer to create mechanisms to perform specific tasks. Some examples of simple known mechanisms are below: Rack and pinion: 44 45 Describe what happens in technical terms in the above mechanism. Bell crank Describe what happens in technical terms in the above mechanism. Toggle clamp: Describe what happens in technical terms in the above mechanism. 45 46 Levers First class: Describe what happens in technical terms in the above mechanism. Second class: Describe what happens in technical terms in the above mechanism. Third class: Describe what happens in technical terms in the above mechanism. 46 47 Linkages: Describe what happens in technical terms in the above mechanism. Describe what happens in technical terms in the above mechanism. 47 48 10.3.2 Identify the mechanisms in a bicycle. Consider chain drive, levers, linkages and gears. 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 48 49 BICYCLE BRAKES: Look at the diagram carefully. As the brake lever on the bike is pulled the cable moves upwards and forces the brake blocks against the rim of the wheel. Explain the type of linkage involved - using notes and diagrams. Look at the page 'linkages' to help you decide. 49 50 10.3.3 Design combinations of mechanisms to achieve specific tasks. Consider the following tasks:• alter the axis of rotation • change the type of movement • increase force and decrease speed • decrease force and increase speed. Experiment with the lego kits provided and then build a copy of one of the mechanisms and adjust the design to trial changes. Lego and identify and make. 50 51 51 52 10.3.4 Discuss how designers make use of simple mechanisms in the home. Consider water tap, garlic crusher and foot operated trash/rubbish bin. Identify mechanisms in the home: Sketch the images below and identify the mechanisms and linkages, fulcrum, class of lever etc. 1) 52 53 2) 3) 53 54 4) 5) You should now be able to identify a range of mechanisms, look around your home or around your immediate environment to see how mechanism s help you ! 54 55 55
Mechanisms are devices that have been designed to make jobs easier. They all have certain things in common:
They involve some kind of
They involve some kind of
They must have some kind of input to make them work.
They produce some kind of output.
If we connect mechanisms together we can build mechanical systems called machines.
Machines help to make our lives easier and more comfortable.
The tin opener has to do two distinct things:
1) Pierce or cut the top of the can
2) Remove the lid by slicing the steel.
The picture on the right shows the small cutting wheel doing this. Let’s examine each process in turn:
1) The distance moved changes from large to small
2) The power produced changes from small to large.
3) The total amount of energy put in by the hand is the same total amount of energy given out by the cutting wheel!
Let’s look at the second stage; removing the lid.
The smaller lever is rotated which turns two small cogs (teeth with wheels). The cogs grip the edge of the can. They drive the cutting wheel along the metal, slicing it away. This is also a lever. It is in fact two levers on opposite sides of the fulcrum. The outside edges move through a greater distance than the centre, so it’s the same principle.
All mechanisms do this. They convert energy by collecting it up over a long distance and concentrating it, or by taking concentrated energy and spreading it out over a longer dis
tance. It is always about converting energy and movement. In fact, all mechanisms are actually levers! It will be interesting to see if you can identify the levers in this unit – they are very well disguised!
10.1.2. Calculate mechanical advantage (MA), velocity ration (VR) and efficiency for simple mechanical systems
MA = Load / Effort
Class 1 and 2 levers produce mechanical advantage. This means that you can move a large load using a small amount of effort.
In the diagram below (class 2 lever) a 100N effort will move a 300N load.
Example taken from Focus on Mechanisms
The mechanical advantage of any mechanism can be calculated the same way.
The mechanical advantage for a simple gear train equals the number of teeth on the driven gear divided by the number of teeth on the driver gear.
VR = distance moved by effort / distance moved by load
When calculating mechanical advantage it may appear that you are getting something for nothing. That you are moving a large load using a small effort.
What is in fact happening is that the load is being moved just a small distance compared to the distance moved by the effort.
By comparing the two distances you get the velocity ratio (see diagram below).
Example taken from Focus on Mechanisms
Velocity ratios for pulley systems can be calculated by comparing the diameters of the pulley wheels.
Velocity ratios for gear chains and sprockets and chain systems can be calculated by comparing the number of teeth on the gear wheels or sprockets.
Efficiency = MA / VR
A machine which moves a load by a certain distance can be said to be doing 'work'. In real machines, more work (or energy) is put in than is got out.
The efficiency of a machine is the ratio of the useful output of work to the total input of work.
Efficiency can also be expressed in terms of mechanical advantage and velocity ratio.
Example taken from Focus on Mechanisms
In real life mechanisms never run 100% efficiently. This is because parts twist, bend and rub against each other making them less efficient.
Lego Mechanical Design Task
Creating practical examples using Lego - Collect the Lego kits and working in pairs, watch the presentation below and select one of the following task sheets (numbers 4, 6, 7, 12, 13, 18) to build a mechanism. When you have completed the model take a photo and annotate it related to the work you have been doing in this topic.
You are expected to complete 2-3 models during the lesson:
10.1.3 First, Second and Third Class Levers
You should be able to identify load (L), effort (E) and fulcrum (F)
in first class levers (E-F-L) for example: seesaw, crowbar, scissors
in second class levers (E-L-F) for example: wheelbarrow, bottle opener, nutcrackers
in third class levers (L-E-F) for example: tweezers broom, fishing rod
10.1.4 Relevant efficiencies of the three classes of lever
10.1.5 When a lever is in equilibrium, the net moment is zero
10.1.6 Calculate mechanical advantage and effort for first, second and third-class levers
10.1.7 Gear Systems - what are they?
Test the size of gears using this website
10.1.8 Calculate velocity ratio for gear systems
10.1.9 Describe the function of different types of gears in a range of objects
rack and pinion
Rack & Pinion
Rack & Pinion jacks for lifting, lowering,
adjusting or fixing of mechanical components,
machines, windows, sluice gates etc.
10.1.10 Explain a design context in which a compound rather then a simple gear train would be appropriate
Consider the gearing system on a metal lathe designed to be changed to cut a specific type of thread
Consider ratios, mechanical advantage and changes
10.1.11 Discuss the function of different types of gears in a range of objects
Which use the the following gears:
rack and pinion
10.1.12 Describe a belt or chain drive system
Consider the profile, the load, changes in the load and the speed.
10.1.13 Calculate velocity ratio for belt or chain drive systems
10.1.14 Compare belt or chain drives systems with gear systems
Consider the profile, the load, changes in the load and the speed, considers the merits of each of the systems.
Design a system to provide belt torsion to a belt-and-pulley system
10.1.16 Describe pulley systems
Here is another explanation and take the test - I know its written for P2-4s but hey it comes with a
10.1.17 Calculate mechanical advantage for pulley systems
Use this site and check out the pulley's section
10.1.18 Describe an inclined plane
The inclined plane is a plane surface set at an angle, other than a right angle, against a horizontal surface. The inclined plane permits one to overcome a large resistance by applying a relatively small force through a longer distance than the load is to be raised.
Consider inclined planes, screw threads, and wedges. look at the images above (General Concepts)
10.1.19 Explain the advantages of an inclined plane
The science explained behind the calculations of mechanical advantage of inclined planes
10.2.1 Linear, Rotary, intermittent, oscillating, reciprocating and irregular motion
What are mechanisms?
is a device which transmits energy in the form of movement.
changes an input force and movement into an output force and movement.
If we connect
together we can build
which we call machines that make our lives easier or more comfortable.
The technological advances humans have made through the ages, have been closely linked with their ability to harness energy and use it to perform
Although humans are very clever creatures, our size, structure and muscles put severe limitations on what we can do.
All mechanisms are based on what ancient philosophers called the
Five Basic Machines
. The five basic machines are the five simplest machines which form the basis of all the other machines developed throughout human history.
To understand machines we need to look at the mechanisms used to build them.
Mechanisms use one of these four basic movements, either on their own or combined
There are four types of motion:
is the motion in a straight line
is the motion in a circle
is motion backwards
and forwards in an arc
is motion backwards
and forwards in a straight line
For some more information and examples of mechanisms clink on the links below:
Test your knowledge with the following site:
Machines that help people contain a
. Mechanical advantage is the amount of effort that a machine helps one to do ones work.
The larger the mechanical advantage, the easier one's work is. The formula for Mechanical Advantage is Resistance force divided by the Effort Force.
The Resistance force is the force applied by the machine, and the Effort Force is the force applied to the machine by the human.
Good examples such as motors and pulleys:
For futher examples click on the links below:
10.2.2 How linkages can be used to change the direction of motion of components
10.2.3 Mechanical motion in a range of contexts
A car jack
10.2.5 Design features of a ratchet and pawl system
10.2.6 Simple Cams and their advantages
is a device which can convert
(movement in a straight line). A cam is a specially shaped piece of material, usually metal or hard wearing plastic, which is fixed to rotating
can have various shapes eg. round, oval, heart shaped. A
is a mechanism which is designed to move up and down as it follows the edge of the cam.
Many machines which have moving parts use cams. A good example is the motor car engine which has cams to open and close valves and contact breaker points and operate fuel pumps.
There are several different types of cams but most of these can be placed into two groups, rotary and linear. Rotary cams change rotary motion into reciprocating (backwards and forwards) motion. the cams come in several shapes including egg-shaped and snail cams, these cams are called "lobed cams" because they have additions to the circular shape known as lobes. As the cam rotates, the follower moves accordingly. The exact distance it moves depends on the shape of the cam and this is know as a the
. The movement of the different cams can be described as smooth.
One complete revolution of the cam is called a cycle. As the cam rotates there will be one distinct event per revolution for each lobe. The timing of the events will depend on the speed of rotation. Cams have the ability to store information. Another way to look at cams is as the mechanical version of a computer program. The information is stored in the shape of the cam. As the cam turns, the information is retrieved by the cam follower. The follower tracks the movement of the cam's profile (shape) and reproduces the same movement for each
Testing your cams watch the video! Click to the next page:
Look at the following resources:
10.2.7 Cam followers and their uses
10.2.8 Using a series of cams and followers to achieve a set purpose
Use this link and read through the site and build some cams
Conversion of Motion
10.3.1 How mechanisms allow conversion of one form of motion to another
Rack and pinion
10.3.2 Identify the mechanisms in a bicycle
Can you identify the chain drive, the levers, the linkages and the gears?
10.3.3 Design a combination of mechanisms to achieve the following specific tasks:
Alter the axis of rotation
Change the type of movement
Increase force and decrease speed
Decrease force and increase speed
10.3.4 How do designers make use of simple mechanisms in the home?
Consider the following:
Foot operated trash/rubbish bin
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