MECHANISMS INTRODUCTION

Transcription

1 MECHANISMS INTRODUCTION Early man discovered that work could be made easier by using a mechanical device to control movement and force rather than his bare hands. Today mechanisms are an integral part of our lives, so much so that we take them for granted. However complex, all mechanisms have two things in common: 1. An input motion and force 2. An output motion and force Consider the mechanical devices below: Page 1

2 DEFINITION A mechanism is a device which changes an input motion and force into a desired output motion and force. INPUT MOTION & FORCE MECHANISM OUTPUT MOTION & FORCE MOTION There are four principal types of motion: 1. Linear 2. Reciprocating 3. Rotary 4. Oscillating Linear Motion This is motion in a straight line and can be represented by an arrow like this: Although the wheels of the bicycle in the picture above are going around, the overall motion is linear in nature as the man moves forward along the road. Reciprocating Motion This is forward and backwards motion in a straight line. It can be represented by a double arrow like this: The engine piston opposite reciprocates up and down continuously. It does not move at a constant speed as it has to change direction at the highest and lowest positions. Engine crankshaft and piston Rotary Motion This is motion in a circular direction and may also be called circular motion. It is a very common form of motion and can be represented by a curve with an arrow head like this: The chuck of a drill moves in a circular motion Page 2

3 Oscillating Motion Oscillating motion is essentially reciprocating motion along an arc. It can be represented by an arc with an arrow head at both ends. A common example is the pendulum in a clock which oscillates continuously back and forth. In this case the pendulum is instrumental in the time keeping of the clock. A child on a swing moves back and forth through an arc as the swing hangs from a pivotal point. The input and output motions associated with particular mechanisms may or may not be the same. Consider the examples below: The paper punch has both a linear input and a linear output motion The T-Bar clamp has a rotary input motion and a linear output motion THE WEDGE Generally mechanisms are used to afford the user a mechanical advantage. In other words by putting in a small force we can get a larger force out. The wedge is one of the earliest known mechanisms known to man which afforded him this advantage. From splitting logs to pulling loads up a ramp the wedge or inclined plane became one of early mans best friends. Wedge Inclined Plane Page 3

4 Calculations Velocity Ratio Consider the man opposite pulling a load up the inclined plane. The velocity Ratio produced by this inclined plane can be found using the formula: h Effort Load Velocity Ratio = Distance moved by effort Distance moved by load If the length of the ramp is s and the height is h then the man must pull the load a distance of s in order to raise it through the height h. Hence the Velocity Ratio = s/h If for example s = 10m and h = 4m then the Velocity Ratio = 10/4 or 2.5 In this way the man must move his effort force 2.5 time further than the load is lifted. In doing this he gets a Mechanical Advantage. It can be shown that this mechanical advantage is also 2.5 (ignoring frictional forces in the wheels of the cart). Mechanical Advantage = Load Effort = s h If the load in this example was 1000N then the effort force would be 2.5 times smaller, i.e. 400N We can learn from this that if the effort is moved over a greater distance than the load then the effort force will be smaller than the load and a mechanical advantage is afforded to the person doing the work. This mechanical advantage is paid for by the person having to move his/her smaller force over a greater distance (2.5 times more in this example). Screw Threads If an inclined plane type triangle is wrapped around a cylinder the long edge of the triangle produces a helix. This is the curve which is used in the manufacture of screw threads. Screw threads produce considerable mechanical advantage due mainly to the shallow angle at which the helix slopes. Helix Consider the car jack opposite. By using a crank handle to turn the threaded bar of the jack the jack rises thereby lifting the vehicle. The distance moved by the effort is considerably greater than the height through which the car rises. Hence the velocity ratio is very high and so too the mechanical advantage. The screw thread plays a large roll in converting the small input force of the person s hand into a large output force at the top of the jack. Page 4

5 Drill vices are very useful items in a workshop. By turning the handle of the vice very large forces can be applied to the object in the vice thereby securing it while it is being drilled. The lever handle and the screw thread combined are responsible for the mechanical advantage afforded by the vice. Drill Vice LEVERS A lever is a rigid rod pivoted about a fixed point/axis called a fulcrum. Levers may be used to produce a small output motion from a large input motion. In so doing the output force will be much greater than the input force, hence producing a mechanical advantage. The brake on the soapbox cart and the car handbrake illustrate this use of a lever. Small movement Large force Large movement Small force Large movement Small force Small movement Large force Levers as force amplifiers Velocity Ratio As with the inclined plane the ratio of the amount of movement made by the effort to that amount made by the load is called the Velocity Ratio. Velocity Ratio = Distance moved by effort Distance moved by load If in the illustration below the man pushes the lever down a distance of 1m and the load rises by 0.5m, then the Velocity Ratio is: Load Effort = 2 Load Effort Fulcrum Lever Diagram Fulcrum Assuming that the lever in this example does not bend and there is no friction at the fulcrum, then the Mechanical Advantage will be equal in value to the Velocity Ratio. In other words if the weight is 1000N then the effort force will be 500N (the weight of the lever is ignored in these basic calculations). Page 5

6 LEVER TYPES Levers are divided into three classes depending on the relative positions of the load, effort and fulcrum. The lever diagrams below illustrate these three classes: Effort Effort Effort Fulcrum Fulcrum Fulcrum Load Load Load Class 1 Class 2 Class 3 Provided the effort is further from the fulcrum than the load in the Class 1 lever, the Velocity Ratio will be greater than 1 and consequently the Mechanical Advantage will be greater than 1. In the Class 2 lever the Mechanical Advantage will always be greater than 1 as the effort is always further from the fulcrum than the load. In Class 3 there is a Mechanical disadvantage as the load is further from the fulcrum than the effort. To balance the lever the effort force must be greater than that of the load. A practical example of each of the three classes is given below: E E F E L F E F L L Class 1 Class 2 Class 3 MOMENTS Consider a person s hand applying a force to a spanner as shown opposite. The product of the effort force and the distance from the effort force to the fulcrum (a nut in this case) is referred to as a turning moment or simply a moment. It is measured in Newton metres (Nm). The Law of the Lever (Principle of Moments) The Law of the lever tells us that when a lever is in equilibrium the sum of the clockwise moments is equal to the sum of the anti-clockwise moments. Sum of clockwise moments = Sum of anti-clockwise moments Page 6

7 PROBLEM The diagram illustrates a lever microswitch. The spring loaded button of the microswitch exerts a force on the lever at the point of the button amounting to 0.5N. Calculate the effort force required to depress the lever and so activate the switch. 5mm F L 0.5N 45mm E Note: Always convert dimensions to metres! The Law of the Lever tells us that the: Sum of the clockwise moments = the sum of the anti-clockwise moments Hence: E x 0.05 = 0.5 x.005 E x 0.05 = E = /.05 E = 0.05N The result tells us that the effort force is ten times smaller than the load force. This makes sense since the effort force is acting over a distance ten times greater than the distance over which the load is acting. LINKAGES A linkage is an assembly of components (generally linear in form) which are designed to act together and allow forces and motion to be transmitted to where they are needed. There is an input force and motion and an output force and motion. The output force may be bigger or smaller than the input force and it may have a different direction. The input and output motion may differ in a similar manner. The examples to follow illustrate some of the basic types of linkages: Center Pivot/fulcrum Input motion and force is equal in size to the output motion and force. The Mechanical Advantage and Velocity Ratio are therefore equal to 1 Offcentre Pivot In this case the input motion is greater than the output motion, however the output force is greater than the input force. Given that the input is the effort and the output the load, the Velocity Ratio and Mechanical Advantage will be greater than 1 Output Output Pivot Pivot Reverse Motion Linkages Input Input Parallel Linkage In a parallel motion linkage the opposite sides of the parallelogram remain parallel even when it is pushed out of shape. The lazy-tongs below uses this principle to good effect as it stretches in length as the handles are brought closer together. It is used to pick up objects which are dangerous or inaccessible. Lazy-tongs Page 7

8 Bell Cranks The calliper brakes of a bicycle illustrate the use of bell crank levers to change a pull into a push and take motion around a corner. The brake cable, when pulled causes the bell cranks to move in opposite directions and to push the brake blocks against the wheel rim. The friction generated brings the bicycle to a halt. Treadle Linkage This linkage can convert oscillating motion into rotary motion and vice versa. Old foot operated sewing machine used this mechanism. PULLEYS One of the methods used in technology to transmit motion and torque between parallel shafts is to use a pulley and belt drive. A pulley is a wheel with a grooved rim. Pulley wheels Parallel shafts Graphic symbol for a pulley drive Motor Consider the pulley drive opposite. The motor has a large pulley wheel mounted on its shaft and this in turn is driving a small pulley which is mounted on a shaft which is parallel to the motor shaft. The Driver pulley on the motor shaft is referred to as the driver ( effort ) and the other pulley is referred to as the driven ( load ). In this case the driven pulley Driven must be rotating faster than the driver. If the driver has a diameter of 80mm and the driven pulley diameter is 40mm then the driven will rotate at twice the speed of the driver but with only half the torque. We are already familiar with the formula: Velocity Ratio = Distance moved by effort Distance moved by load Since the diameter of a wheel is directly proportional to its circumference the formula for Velocity Ratio must be: Velocity ratio = Diameter of driven pulley = 40mm = 1:2 Diameter of driver pulley 80mm This means that one revolution of the driver produces two revolutions of the driven. Hence the driver rotates at half the speed of the driven. Page 8

9 VELOCITY If the rotary velocity of the motor in the previous example is 1000 revs/min what then is the rotary velocity of the driven pulley? Solution: Common sense tells us that if the driver rotates at half (Velocity ratio = ½) the speed of the driven then the driven speed must be 2000 revs/min. A formula is generally used to calculate the driven speed. Rotary Velocity of driven pulley = Rotary velocity of driver Velocity Ratio = 1000/0.5 = 2000 revs/min Consider the pulley arrangement opposite. If the rotary velocity of the driven pulley is 300 revs/min, calculate the rotary velocity of the motor shaft. Driver Pulley 30mm dia. Velocity ratio = Diameter of driven Diameter of driver = 75 = From the formula above: 300 = Rotary velocity of driver 2.5/1 Driven pulley 75mm dia. 300 x 2.5 = Rotary velocity of driver Rotary velocity of driver = 750 revs/min Jockey Pulleys A problem which may arise with pulley drives is that any slackness in the belt may cause the belt to slip. To overcome this problem a jockey pulley is often used. This pulley engages with the belt as shown opposite and keeps the belt in firm contact with the driver and driven pulleys. They are used on many belt drives such as in the band-saw of your school workshop. Jockey Pulley CHAIN & SPROCKET Another method of transmitting motion and torque between parallel shafts is to use a chain and sprocket mechanism. This system provides a non-slip positive drive due to the traction between the chain and the sprockets. Chain and sprockets are used widely in technology, the most common example being the chain drive on a bicycle. Chain Sprocket Page 9

10 PROBLEMS Velocity Ratio To calculate the Velocity Ratio for a chain and sprocket drive the number of teeth on the gears must be taken into account. Driven 20 teeth Driver 30 teeth V.R. = Number of teeth on driven sprocket Number of teeth on driver sprocket In the example opposite the Velocity Ratio is: V.R. = 20/30 V.R. = 2/3 or 2:3 If the rotary velocity of the driver is 600 revs/min, what would the rotary velocity of the driven sprocket be? GEARS Rotary Velocity of Driven Sprocket = Rotary Velocity of Driver Sprocket Velocity Ratio Rotary Velocity of driven = 600 = 600 x 3 = 900 revs/min Gears are toothed wheels which mesh together and like pulleys and chain and sprocket mechanisms can transmit rotary motion and torque from one shaft to another. The pair of gears opposite are referred to as Spur Gears. The smaller gear is called the pinion and the larger gear the wheel. They form a Simple Gear Train. The shafts rotate in opposite directions and at different speeds since the gears are different sizes. If the driver gear has 15 teeth and the driven 45 teeth calculate the Velocity Ratio. Driver 15 teeth Driver Driven V.R. = No. of teeth on driven gear = 45 No. of teeth on driver gear 15 = 3/1 or 3:1 Driven 45 teeth This means that 3 revolutions of the driver are required to make 1 revolution of the driven and that the driver rotates 3 times faster than the driven. To get the driver and driven gear to rotate in the same direction an Idler Gear is introduced between both driven and driver. This changes the direction of the driven gear. It does not affect the Velocity Ratio of the gear train and is ignored in Velocity Ratio calculations IDLER Page 10

11 COMPOUND GEAR TRAINS To achieve greater velocity ratios with gears a Compound Gear train may be used. This involves meshing 2 or more pairs of gears as shown opposite. The two middle gears in the illustration are fused together and rotate at the same speed. To calculate the total velocity ratio we obtain the product of the velocity ratios for each pair of gears. In the graphic symbol illustration of a compound gear train A has 10 teeth, B has 25 teeth, C has 10 teeth and D has 20. Driven Driver Driver Driven Compound Gear Train V.R. = 25 x 20 = 5 10 x 10 1 C In other words A rotates 5 times faster than D. A Driver B D WORM GEARS To achieve a large velocity ratio with just one pair of gears a worm and wormwheel may be used. The worm has a helical groove cut into it like a screw thread and the worm wheel is similar to a spur gear. One revolution of the worm causes one tooth of the wormwheel to be moved. Hence the Worm can be treated as a gear with one tooth. Worm V.R. = No. of teeth on wormwheel 1 If the wormwheel has 60 teeth then the Velocity ratio will be 60/1 Unlike a simple gear train the shafts of the worm and wormwheel are at 90 to each other. This may or may not be an advantage. These gears are widely used in industry as they are very compact and give such large velocity ratios. They also have the advantage that the worm cannot be turned by the wormwheel. This makes them very suitable as the drive mechanism of a lifting system. One such crank operated lifting device is shown opposite. Worm & Wormwheel Worm gear unit with MM28 motor Graphic symbol Page 11

12 BEVEL GEARS As With worm gears bevel gears involve the transmission of motion between shafts which are at 90 to each other. By using bevel gears of different sizes the driver and driven shafts will rotate at different speeds. TORQUE RACK & PINION Torque (the turning force in a shaft) is an important consideration in rotary type mechanisms. Where a mechanism results in a reduction in speed from the driver to the driven shaft, this speed reduction is compensated for by an increase in torque. The compound gear train on page 11 resulted in a velocity ratio of 5:1. This gave rise to a five fold reduction in speed from the driver to the final driven shaft. Ignoring losses of energy due to friction, noise etc. the torque in the final driven shaft will be five times greater than that in the driver shaft. This is why one puts a bicycle or car in a low gear when going up a hill. Rack and pinion gears involve changes in motion from linear to rotary or the other way round. A common use of a rack and pinion is the drill feed mechanism of a pillar drill. Pinion Graphic Symbol Rack Drill Feed Mechanism RATCHET & PAWL To lock a mechanism so that it does not slip when under load a mechanism known as a ratchet and pawl may be used. As the ratchet rotates the pawl, which is usually spring loaded clicks into the teeth of the ratchet preventing it from rotating in the opposite direction. Winches, spanners, screw drivers and fishing reels are examples of devices which use ratchet and pawl mechanisms. Pawl Pawl Ratchet Manually operated winch Page 12

13 PULLEY LIFTING SYSTEMS The Illustration opposite shows a man raising a bucket up a scaffolding using a rope and single pulley. Ignoring friction in the mechanism the effort force applied by the man to the rope is equal to the load force produced by the bucket. This system does not produce a mechanical advantage and the velocity ratio is one. Mech. Advantage = load/effort Velocity Ratio = Distance moved by effort Distance moved by load By using more than one pulley a mechanical advantage can be obtained. Consider the pulley arrangement shown here. The load of 400N is split evenly between both parts of the cable holding the lower moving pulley wheel. Hence the force in each part of the cable is 200N. The tension force in the cable is the same at every point and so the effort force (which is the tension force) must be 200N. The mechanical advantage is then 2:1. 1m Effort = 200N 0.5m Another way of looking at this is to consider the Velocity Ratio. If the load was raised through a height of 0.5m then the effort would have to move through a distance of 1m. This is because both elements of the cable holding up the moving pulley must shorten by 0.5m. The velocity ratio is therefore 2:1 Load = 400N The system opposite uses 4 pulleys with two movable pulleys. This time the load force splits evenly between 4 parts of the cable and so the tension in each part is 250N. Again the tension is the same throughout the cable and so the effort force is 250N. The mechanical advantage and velocity ratio is therefore 4:1. In all these systems we treat the pulleys and cables as having no weight and we assume that the cable does not stretch. Strictly speaking these factors would have to be taken into account when real systems are being designed by engineers. Load 1000N Lifting system using 4 pulleys Effort 250N Page 13

14 CAMS Cams are shaped pieces of metal or plastic which are part of or fixed to a shaft. A follower presses against the cam as it rotates causing the follower to follow the profile of the cam. Follower The diagram opposite shows the different terminology associated with cams. This cam is a pear shaped cam and it causes the follower to move up and down (reciprocate) continuously. The height through which it moves is referred to as the stroke. The rise and fall motion of the follower is the same due to the symmetry of the cam. For half of the revolution of the cam the follower is in the dwell position and does not move. Pear shaped cams are often used to control the valves in an engine. Cam shapes Different cam shapes produce different follower movements. The shapes opposite are pear, eccentric circular and heart shape. Eccentric circular cams are used in some fuel pumps and heart shaped cams in bobbins for winding threads and wools. Fall Dwell Cam Terminology Stroke Rise Rotation clockwise Cam follower shapes Followers may be weighted or spring loaded to ensure that they follow accurately the shape or profile of the cam. Radial arm follower Roller follower Knife follower Point follower Flat follower CRANK SLIDERS Crank slider mechanisms are used to convert rotary motion into reciprocating motion and vice versa. Guide Slider Connecting Rod A car engine is a very good example of a crank slider mechanism. The diagram shows the crankshaft of a 4 cylinder engine. As the pistons move up and down the crankshaft rotates. Hence reciprocating motion is being converted into rotary motion. Crank Page 14

15 LEVERS - 1 Identify the class of lever for each of the following practical levers and label its load, effort and fulcrum. (the first three are worked examples.) Load Fulcrum Class 2 Lever Load Fulcrum Fulcrum Load Effort Effort Effort Class 1 Lever Class 3 Lever (a) Arm (b) Nutcracker (d) Claw Hammer (c) Crow Bar Page 15

16 EVERS - I LEVERS 2 (e) Foot Brake (f) Scissors (g) Spanner (h) Spade (i) Forged Tongs (k) Wheelbarrow (j) Weighing Scales (l) Microswitch Page 16

17 LEVERS - 3 Question 1. (a) Calculate the Mechanical Advantage for the lever shown if a Load of 60 Newton s can be raised using an Effort of just 16 Newton s. (b) Calculate the Velocity Ratio between the two movements if the Load moves through 300mm and the Effort moves through 1200mm. (c) Calculate the Efficiency of the above lever. Efficiency = MA x 100% VR (d) Explain why levers in principle are never 100% Efficient? Page 17

18 LEVERS 4 Question 2. Calculate the Force applied to the lever micro switch at X in the sketch. 10mm 40mm 0.3N X Question 3. For the two levers shown below attempt the following: (a) State its Class of lever. (b) Find the size of the Effort given that the Load in each case is 36N. (c) What is the Mechanical Advantage for the lever? (i) 3M E F 1M Load (ii) 4M 2M E F L Page 18

19 PULLEY SYSTEMS - 1 Question 1. Fill in the missing blanks for the following two sentences: (a) Machine shaft (b) Driven Driven Motor Motor (a) (b) Driver Driver When the motor pulley has a large diameter and the machine shaft driven pulley has a small diameter we have a speed. When the motor pulley has a small diameter and the machine shaft driven pulley has a large diameter we have a speed. Question 2. The arrangement of pulleys shown in the diagram is called a stepped cone pulley system. What are the advantages of this system? On which machine in the Technology workshop can it be located? Question 3. Calculate the Velocity Ratio for the Pulley System? Driven ø 75 Driver ø 15 Page 19

20 PULLEY SYSTEMS - 2 Question 4. In the diagram shown, is a Hoover brush cylinder fitted with a 30mm diameter pulley and is being driven by a 90mm diameter pulley. Driven (i) (ii) Motor Calculate the Velocity Ratio Calculate the Cylinder speed when the motor shaft is rotating at 1000rpm. Driver (i) (ii) Question 5. Calculate for the Pulley systems the (i) Velocity Ratio & (ii) Mechanical advantage. Effort 15N 1M Load 30N 0.5M 1N - Effort 4N - Load Load Page 20

21 CHAIN AND SPROCKET Question 1. Shown in the picture is a bicycle. (a) (b) (c) (d) Name two working parts of the bicycle, which are levers? State three advantages a chain and sprocket drive over a belt and pulley drive in this application. Identify four areas where friction is encountered in a bicycle, two of which are of benefit to the cyclist and two of which are a disadvantage to the cyclist. Suggest how the undesirable friction can be removed. On the bicycle above, the driver sprocket (pedal) has 36 Teeth and the driven sprocket (back wheel) has 12 Teeth, calculate: (i) The Velocity Ratio. 12T 36T (ii) Determine the road speed of the bicycle in metres/second (m/s) if the pedal sprocket (Driver) rotates at 15 revs/minute? The circumference of the wheel is 2.4 Metres in length. Page 21

22 GEAR SYSTEMS - 1 Question 1. The illustrations show simple gear trains in mesh. State: (i) A train that will not rotate, (ii) A train that gives no change in direction, (iii) A train that gives no increase in speed, (iv) A train that decreases speed, (v) A train that does not alter speed. (i) (ii) (iii) (iv) (v) Answers: (The rotational arrow indicates the driver for each gear train). Gear Train 1 Gear Train 2 Gear Train 3 Gear Train 4 Question 2. Name the mechanisms below. Identify their main features? Name two practical applications of each: one used in industry, the other from everyday life. (a) (b) (c) Page 22

23 GEAR SYSTEMS - 2 Question 3. Calculate the number of turns Of the handle are required to Rotate the drum three times. 32 Teeth Drum Handle 8 Teeth Question Driven Driver A simple gear train is shown. (A symbolic representation of the two gears in mesh is also shown). Calculate the following: (i) The gear ratio? (ii) If the driver gear operates at 200 rpm at what speed will the driven gear rotate? A B Question 5. Shown is a compound gear train Which has two pairs of meshed Gears: A and B, and C and D. A C Gear A has 30 Teeth Gear B has 20 Teeth Gear C has 40 Teeth Gear D has 20 Teeth The Driver Gear D rotates at 240rpm B D Driver Gear rpm (i) (ii) What is the gear ratio? Calculate is the rotary Speed of gear A? Page 23

24 GEAR SYSTEMS - 3 Question 6. Identify the gear arrangements shown. Give a practical example of each. Fill in your answers on the blank spaces provided: (b) (c) (a) (d) (e) Question 6. A Rack has 200 teeth per metre, which is meshed with a 20T Pinion gear. If the pinion is rotated through one revolution, how far will the rack go? Rack 200 Teeth Per Metre Pinion 20 Teeth Page 24

25 EXAMINATION QUESTIONS - 1 Question 1. If an additional 18 tooth gear Wheel is placed between the Driving and driven gears, what Effect will this have on: Driven 54T (i) (ii) (i) The speed of the driven gear? Driving 18 T (ii) The direction of the driven gear. Question 2. Question 3. Identify clearly on the bicycle shown, two areas where bearings are used. Name this Mechanism? Question 4. In the pulley system shown it was found that an effort of 50N moving 2 Metres could lift a load of 80N through a distance of 1 Metre. Using the formula shown calculate the efficiency of the system. Efficiency = Work got out Work put in. 50N 80N Question 5. Name a mechanism, which will achieve The direction change shown. Mechanism Page 25

26 EXAMINATION QUESTIONS - 2 Question 6. The sketches below show mechanisms that may be used for lifting loads. 40T 20T 40T 10T 40T Mechanism B Y X Z LOAD Mechanism A LOAD 10T 40T (i) If the axle X in Mechanism A rotates at 50rpm, calculate the speed of the motor. The speed of this motor, stated in a component catalogue, is 800rpm. Explain the difference between the catalogue speed and the calculated motor speeds. (ii) Name the gear arrangement Y in mechanism B. Calculated the speed of axle Z, if the motor in Mechanism B turns at 3200rpm. (iii) State two advantages of mechanism B over mechanism A. Answers: Page 26