Gear & Pulley - Part II

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BETI 3423ACTUATORS & DRIVESby : Mr Mohamad Haniff bin HarunEmail : [email protected]

Chapter 5 : Gear & pulley(Part ii)11Mohamad Haniff bin Harun18/2/2014Learning OutcomeBy the end of this chapter, students will be able to explain model, types, architecture & operations related to actuators and drives2BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA

Chapter ContentsGearIntroductionTypes of gearsSpur gearsHelical gearsBevel gearsWorm gearsRack and pinion gearsExample Calculation

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BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA PulleyIntroductionFixed PulleyMovable PulleyCombined PulleyPulley SystemsExample Calculations

3Mohamad Haniff bin Harun18/2/2014Gears4IntroductionGears are a means of changing the rate of rotation of a machinery shaft. They can also change the direction of the axis of rotation and can change rotary motion to linear motion.

Gears are of several categories, and can be combined in a multitude of ways.

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BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA

5Mohamad Haniff bin Harun18/2/2014How Gears Work6

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Gears are used in tons of mechanical devices. They do several important jobs, but most important, they provide a gear reduction in motorized equipment. This is key because, often, a small motor spinning very fast can provide enough power for a device, but not enough torque. For instance, an electric screwdriver has a very large gear reduction because it needs lots of torque to turn screws, but the motor only produces a small amount of torque at a high speed. With a gear reduction, the output speed can be reduced while the torque is increased.

6Mohamad Haniff bin Harun18/2/2014Introduction7

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Another thing gears do is adjust the direction of rotation. For instance, in the differential between the rear wheels of your car, the power is transmitted by a shaft that runs down the center of the car, and the differential has to turn that power 90 degrees to apply it to the wheels.There are a lot of intricacies in the different types of gears. In this topic, we'll learn exactly how the teeth on gears work, and we'll talk about the different types of gears we can find in all sorts of mechanical gadgets.

7Mohamad Haniff bin Harun18/2/2014Basics8

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA On any gear, the ratio is determined by the distances from the center of the gear to the point of contact. For instance, in a device with two gears, if one gear is twice the diameter of the other, the ratio would be 2:1. One of the most primitive types of gears we could look at a wheel with wooden pegs sticking out of it.

8Mohamad Haniff bin Harun18/2/2014Types of Gears9


1. Spur gearsSpur gears are the most common type of gears. They have straight teeth, and are mounted on parallel shafts. Sometimes, many spur gears are used at once to create very large gear reductions.

Figure 1: Spur gears 9Mohamad Haniff bin Harun18/2/2014Types of Gears10


1. Spur gearsSpur gears are used in many devices that we can see all over, like the electric screwdriver, dancing monster, oscillating sprinkler, windup alarm clock, washing machine and clothes dryer. But we won't find many in the car.

This is because the spur gear can be really loud. Each time a gear tooth engages a tooth on the other gear, the teeth collide, and this impact makes a noise. It also increases the stress on the gear teeth.

To reduce the noise and stress in the gears, most of the gears in the car are helical.

10Mohamad Haniff bin Harun18/2/201411




2. Helical gearsThe teeth on helical gears are cut at an angle to the face of the gear. When two teeth on a helical gear system engage, the contact starts at one end of the tooth and gradually spreads as the gears rotate, until the two teeth are in full engagement.

Figure 2: Helical gears 12Mohamad Haniff bin Harun18/2/2014Types of Gears13


2. Helical gearsThis gradual engagement makes helical gears operate much more smoothly and quietly than spur gears. For this reason, helical gears are used in almost all car transmissions. Because of the angle of the teeth on helical gears, they create a thrust load on the gear when they mesh. Devices that use helical gears have bearings that can support this thrust load. One interesting thing about helical gears is that if the angles of the gear teeth are correct, they can be mounted on perpendicular shafts, adjusting the rotation angle by 90 degrees.



Figure 3: Crossed helical gears 2. Helical gears


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA 3. Bevel gearsBevel gears are useful when the direction of a shaft's rotation needs to be changed. They are usually mounted on shafts that are 90 degrees apart, but can be designed to work at other angles as well. The teeth on bevel gears can be straight, spiral or hypoid. Straight bevel gear teeth actually have the same problem as straight spur gear teeth -- as each tooth engages, it impacts the corresponding tooth all at once.

Figure 4: Bevel gears 15Mohamad Haniff bin Harun18/2/2014Types of Gears16


3. Bevel gearsJust like with spur gears, the solution to this problem is to curve the gear teeth. These spiral teeth engage just like helical teeth: the contact starts at one end of the gear and progressively spreads across the whole tooth.

Figure 5: Spiral Bevel gears 16Mohamad Haniff bin Harun18/2/2014Types of Gears17


3. Bevel gearsOn straight and spiral bevel gears, the shafts must be perpendicular to each other, but they must also be in the same plane. If you were to extend the two shafts past the gears, they would intersect. The hypoid gear, on the other hand, can engage with the axes in different planes.

Figure 6: Hypoid Bevel gears in a car differential 17Mohamad Haniff bin Harun18/2/2014Types of Gears18


3. Bevel gearsThis feature is used in many car differentials. The ring gear of the differential and the input pinion gear are both hypoid. This allows the input pinion to be mounted lower than the axis of the ring gear.

Figure 6 shows the input pinion engaging the ring gear of the differential. Since the driveshaft of the car is connected to the input pinion, this also lowers the driveshaft. This means that the driveshaft doesn't intrude into the passenger compartment of the car as much, making more room for people and cargo.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA 4. Worm gearsWorm gears are used when large gear reductions are needed. It is common for worm gears to have reductions of 20:1, and even up to 300:1 or greater.

Figure 7: Worm gears 19Mohamad Haniff bin Harun18/2/2014Types of Gears20


4. Worm gearsMany worm gears have an interesting property that no other gear set has: the worm can easily turn the gear, but the gear cannot turn the worm. This is because the angle on the worm is so shallow that when the gear tries to spin it, the friction between the gear and the worm holds the worm in place.

This feature is useful for machines such as conveyor systems, in which the locking feature can act as a brake for the conveyor when the motor is not turning.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA 4. Rack and Pinion gearsRack and pinion gears are used to convert rotation into linear motion. A perfect example of this is the steering system on many cars. The steering wheel rotates a gear which engages the rack. As the gear turns, it slides the rack either to the right or left, depending on which way you turn the wheel.

Figure 8: Rack and pinion gears from a household scale21Mohamad Haniff bin Harun18/2/2014Planetary Gear Sets & Gear Ratios22


Any planetary gearset has three main components: The sun gear The planet gears and the planet gears' carrier The ring gear Each of these three components can be the input, the output or can be held static. Choosing which piece plays which role determines the gear ratio for the gearset. Let's take a look at a single planetary gearset. One of the planetary gearsets from our transmission has a ring gear with 72 teeth and a sun gear with 30 teeth. We can get lots of different gear ratios out of this gearset.

22Mohamad Haniff bin Harun18/2/2014Planetary Gear Sets & Gear Ratios23


ABCInputSun (S)Planet Carrier (C)Sun (S)OutputPlanet Carrier (C)Ring (R)Ring (R)StationaryRing (R)Sun (S)Planet Carrier (C)Calculation1 + R/S1 / (1 + S/R)-R/SGear Ratio3.4:10.71:1-2.4:1Also, locking any two of the three components together will lock up the whole device at a 1:1 gear reduction. The first gear ratio listed above is a reduction the output speed is slower than the input speed. The second is an overdrive the output speed is faster than the input speed. The last is a reduction again, but the output direction is reversed. 23Mohamad Haniff bin Harun18/2/2014Planetary Gear Sets & Gear Ratios24

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA There are several other ratios that can be gotten out of this planetary gear set, but these are the ones that are relevant to our automatic transmission. You can try these out in the animation below:

24Mohamad Haniff bin Harun18/2/2014Planetary Gear Sets & Gear Ratios25


So this one set of gears can produce all of these different gear ratios without having to engage or disengage any other gears.

With two of these gearsets in a row, we can get the four forward gears and one reverse gear our transmission needs.

We'll put the two sets of gears together in the next section. 25Mohamad Haniff bin Harun18/2/2014Details on Involute Gear Profiles26


On an involute profile gear tooth, the contact point starts closer to one gear, and as the gear spins, the contact point moves away from that gear and toward the other. If you were to follow the contact point, it would describe a straight line that starts near one gear and ends up near the other. This means that the radius of the contact point gets larger as the teeth engage. The pitch diameter is the effective contact diameter. Since the contact diameter is not constant, the pitch diameter is really the average contact distance.

26Mohamad Haniff bin Harun18/2/2014Details on Involute Gear Profiles27


As the teeth first start to engage, the top gear tooth contacts the bottom gear tooth inside the pitch diameter. But notice that the part of the top gear tooth that contacts the bottom gear tooth is very skinny at this point.Figure 9: Animation of Involute Gear27Mohamad Haniff bin Harun18/2/2014Details on Involute Gear Profiles28


As the gears turn, the contact point slides up onto the thicker part of the top gear tooth. This pushes the top gear ahead, so it compensates for the slightly smaller contact diameter. As the teeth continue to rotate, the contact point moves even further away, going outside the pitch diameter but the profile of the bottom tooth compensates for this movement. The contact point starts to slide onto the skinny part of the bottom tooth, subtracting a little bit of velocity from the top gear to compensate for the increased diameter of contact. The end result is that even though the contact point diameter changes continually, the speed remains the same. So an involute profile gear tooth produces a constant ratio of rotational speed. 28Mohamad Haniff bin Harun18/2/2014Example Calculation29


Example 1 (Question)In examinations one of the first questions will probably for you to work out the 'gear ratio' (sometimes called velocity ratio). As a guide - always assume that the larger gear revolves one revolution. The number of rotations of the second gear has then to be worked out.

In the example below, the DRIVER has 60 teeth and because it is the largest we say that it revolves once. The DRIVEN gear has 30 teeth. Simply divide 60 teeth by 30 teeth to work out the number of revolutions of the driven gear.

29Mohamad Haniff bin Harun18/2/2014Example Calculation30


Example 1 (Answer)

Work out the Velocity Ratio (Gear Ratio);30Mohamad Haniff bin Harun18/2/2014Example Calculation31


Example 2 (Question & Answer)Work out the Velocity Ratio (Gear Ratio);



Example 3 (Question & Answer)Work out the Velocity Ratio (Gear Ratio);



Example 4 (Question)Below are examples of the way to work out 'revolutions per minute', or RPM as it is usually called. In the example below the DRIVER gear is large than the DRIVEN gear. The general rule is - large to small gear means 'multiply' the velocity ratio by the rpm of the first gear. Divide 60 teeth by 30 teeth to find the velocity ratio. Multiply this number (2) by the rpm (120). This gives an answer of 240rpm.If A revolves at 120 revs/min what is B ? (Remember large gear to small gear increases revs)



Example 4 (Answer)



Example 5 (Question)In the example below the DRIVER gear is smaller than the DRIVEN gear. The general rule is - small to large gear means 'divide' the velocity ratio by the rpm of the first gear. Divide 75 teeth by 25 teeth to find the velocity ratio. divide the 60rpm by the velocity ration (3). The answer is 20rpm.If A revolves at 60 revs/min what is B? (Remember small gear to large gear decreases revs)



Example 5 (Answer)



Example 6 (Question & Answer)If A revolves at 100 revs/min what is B ? (Remember small gear to large gear decreases revs)


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Example 7 (Question)When faced with three gears the question can be broken down into two parts. First work on Gears A and B. When this has been solved work on gears B and C.The diagram above shows a gear train composed of three gears. Gear A revolves at 60 revs/min in a clockwise direction. What is the output in revolutions per minute at Gear C?In what direction does Gear C revolve ?

GEAR A

GEAR B

GEAR C

20 TEETH

60 TEETH

10 TEETH



Example 7 (Answer)First work out the speed at Gear B.

Next, take B and C. C is smaller, therefore, revs/minute will increase and rotation will be faster.

What direction does C revolve ? A is clockwise, B consequently is anti-clockwise and C is therefore clockwise.

(Remember B is larger than A therefore, B outputs less revs/min and is slower)39Mohamad Haniff bin Harun18/2/2014Example Calculation40


Example 8 (Question)Gear A revolves at 90revs/min. What is the output and direction at Gear C.

GEAR AGEAR B

GEAR C

30 TEETH90 TEETH

15 TEETH



Example 8 (Answer)First work out the speed at Gear B.

Next, take B and C. C is smaller, therefore, revs/minute will increase and rotation will be faster.

What direction does C revolve ? A is clockwise, B consequently is anti-clockwise and C is therefore clockwise.

(Remember B is larger than A therefore, B outputs less revs/min and is slower)141Mohamad Haniff bin Harun18/2/2014Example Calculation42


Example 9 (Question)Below is a question regarding 'compound gears'. Gears C and B represent a compound gear as they appear 'fixed' together. When drawn with a compass they have the same centre. Two gears 'fixed' together in this way rotate together and at the same RPM. When answering a question like this split it into two parts. Treat gears A and B as one question AND C and D as the second part.

This is an example of a compound gear train. Gear A rotates in a clockwise direction at 30 revs/min. What is the output in revs/min at D and what is the direction of rotation ?

GEAR A

GEAR B

GEAR C

GEAR D

120 T

40 T

80 T

20 T



Example 9 (Answer)First find revs/min at B;

Next find revs/min at D

B is smaller therefore it rotates faster and revs/min increase. C is fixed to B and therefore, rotates at the same speed. 90 REVS/MIN at CD is smaller than C, therefore rotates faster (increased revs/min).43Mohamad Haniff bin Harun18/2/2014Example Calculation44


Example 9 (Answer)

A revolves in a clockwise direction, B is therefore anti-clockwise, C is fixed to B and is also anti-clockwise, which means D revolves in a clockwise direction.



Example 10 (Task)Try the following question:

45Mohamad Haniff bin Harun18/2/2014Pulley46Introduction47

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA What is pulleysA pulley is a simple machine made with a rope, belt or chain wrapped around a wheel. The pulley is usually used to lift a heavy object (load).

What does a pulley do?A pulley changes thedirection of the force, making it easier to lift things.

Are all pulleys the same?No, they are not. There are three types of pulleys:Fixed Pulley Movable Pulley Combined Pulley


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA A single pulley changes the direction of the lifting force.

For example, if you are lifting a heavy object with a single pulley anchored to the ceiling, you can pull down on the rope to lift the object instead of pushing up. The same amount of effort is needed as without a pulley, but it feels easier because you are pulling down.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA A fixed pulley is the only pulley that when used individually, uses more effort than theload to lift the load from the ground. The fixed pulley when attached to an unmovable object e.g. a ceiling or wall, acts as a first class lever with the fulcrum being located at the axis but with a minor change, the bar becomes a rope. The advantage of the fixed pulley is that you do not have to pull or push the pulley up and down. The disadvantage is that you have to apply more effort than the load


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA A movable pulley is a pulley that moves with the load. The movable pulley allows the effort to be less than the weight of the load. The movable pulley also acts as a second class lever. The load is between the fulcrum and the effort.The main advantage of a movable pulley is that you use lesseffort to pull the load. The main disadvantage of a movable pulley is that you have to pull or push the pulley up or down.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA A combined pulley makes life easier as the effort needed to lift the load is less than half the weight of the load. The main advantage of this pulley is that the amount of effort is less than half of the load.The main disadvantage is it travels a very long distance.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA If you add a second pulley, the amount of effort to lift the heavy object is much less .

For example, to lift a box weight of150 N, one would need to exert 150 N of force without the help of pulleys.

However, by using just two pulleys, the person would only need to use 50 N of force.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The pulley system consists of one or more pulleys and a rope or a cable. The number of pulleys used may increase or decrease the mechanical advantage of the system. Generally, the higher the mechanical advantage is, the easier it is to lift the object that is being lifted.

Pulley systems are used when there is a need to transmit rotary motion. The diagram 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.53Mohamad Haniff bin Harun18/2/2014Pulley Systems54

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA 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.

54Mohamad Haniff bin Harun18/2/2014Pulley Systems55

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA 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 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.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Velocity Ratio & Revolution per minuteThe system shown has a driver pulley attached to a motor. When the motor is switched on the driver pulley revolves at 20 rpm. The diameter of the driver pulley wheel is 200mm and the driven pulley wheel is 400mm. This means for every single revolution of the larger driven pulley wheel, the smaller driver pulley wheel rotates twice. This is due to velocity ratio. The ratio can be worked out mathematically in different ways.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The two most likely methods to determine the velocity ratio are shown below


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA This means that the larger pulley wheel (the driven pulley wheel) revolves half as fast compared to the smaller driver pulley wheel. In effect the driven pulley wheel is slower and revolves half as many times as the driver. This means if the rpm of the driver pulley wheel is divided by 2, the output rpm of the driven pulley wheel will be found.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Another example:The diameter of the driver pulley wheel is 200mm and the driven pulley wheel is 600mm. This means for every single revolution of the larger driven pulley wheel, the smaller driver pulley wheel rotates three times. This due to velocity ratio. The ratio can be worked out mathematically in different ways. The two most likely methods are :


Pulley Systems60

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA This means that the larger pulley wheel (the driven pulley wheel) revolves a third of the rpm compared to the smaller driver pulley wheel. In effect the driven pulley wheel is slower and revolves a third as many times as the driver. This means if the rpm of the driver pulley wheel is divided by 3, the output rpm of the driven pulley wheel will be found.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The diameter of the driver pulley wheel is 600mm and the driven pulley wheel is 200mm. This means for every single revolution of the larger driver pulley wheel, the smaller driven pulley wheel rotates three times. This due to velocity ratio. The ratio can be worked out mathematically in different ways. The two most likely methods are shown below. Please note, the driver pulley wheel is placed on top of the equation as it is the larger number of distance.


Pulley Systems62

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA This means that the larger pulley wheel (the driver pulley wheel) revolves a third of the rpm compared to the smaller driven pulley wheel. In effect the driver pulley wheel is slower and revolves a third as many times as the driven. This means if the rpm of the driver pulley wheel is MULTIPLIED by 3, the output rpm of the driven pulley wheel will be found.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Reversing RotationSometimes it is necessary to reverse the rotation of the driven pulley wheel in relation to the driver pulley. If the driver is rotating in an anti-clockwise direction the driven pulley may be required to rotate in a clockwise direction.This is achieved by twisting the belt as shown in the diagram. Care must be taken when this is done as the belt can rub where it crosses and this may increase friction or damage it.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Example

A system of four pulley wheels are set up as shown in the diagram above. The driver pulley rotates in an anti-clockwise direction. In what direction does the output pulley wheel revolve ?

If pulley A (driver) rotates at 60 rpm what is the output rpm at F.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA AnswerLook at the animation below. The final output of pulley F is a clockwise movement.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA AnswerTo answer the question, split the pulleys into pairs and work out the velocity rotation of each pair. Treat the pairs of pulleys as separate questions.Use the diameters when dividing and place the largest number on the top of the division.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Pulley wheel A has an rpm of 60. Pulley B is larger and so revolves at a lower rate than A. This means that the rpm of A is divided by the ratio of 2.

Pulley wheel C has the same rpm as pulley B because they form a compound pulley. Pulley D is larger and so revolves at a lower rate than C. This means that the rpm of C is divided by the ratio of 1.2


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Pulley wheel E has the same rpm as pulley D because they form a compound pulley. Pulley F is smaller and so revolves at a higher rate than E. This means that the rpm of E is multiplied by the ratio of 1.3


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Pulleys and liftingPulley systems can be used to lift weights safely and effectively. The diagram shows a pulley attached to a beam. The rope is pulled on the effort side and the weight being lifted is on the right hand side, called the load. In general a single pulley is useful as it allows the laborer to lift the weight without bending his back. This means it is much safer to lift the weight.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The diagrams below show how a pulley can be compared to a lever. First draw a fulcrum in the centre of the pulley wheel. Then draw a beam across the centre, balancing on the fulcrum. The comparison with a lever can now be seen clearly. Pulleys are a type of lever.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Pulleys and liftingWhen using pulleys for lifting the formulas for mechanical advantage and velocity ratio are very important. The formulas are shown below.

FORMULAS RELATING TO MECHANICAL ADVANTAGEMechanical advantage is defined as the ratio of load to effort. Pulley systems rely on this important relationship between load and effort. The higher the mechanical advantage, the easier it is to lift a weight. 71Mohamad Haniff bin Harun18/2/2014Pulley Systems72

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The formula 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.

In the example the LOAD and the EFFORT is equal and consequently there is no mechanical advantage with this single pulley.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The pulley to the left is suspended and as a consequence the mechanical advantage is increased. This happens because the rope on the left and right of the pulley are both lifting the LOAD, they each lift half its weight. The load is split into 2. The calculation is shown below.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA FORMULAS RELATING TO VELOCITY RATIOVelocity 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 is also best understood by writing it within a triangle.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Using the same example from previous slide. If the load is lifted 2 meters, above the pulley wheel - the rope on the right hand side must be shortened by one meter and this also applies to the left hand side. Therefore, the effort can be seen to move twice as far as the load.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Please note, as one of the pulleys is a fixed pulley, the mechanical advantage and velocity ratio is still calculated as if only the moving pulley exists. The velocity ratio and the mechanical advantage remains 2.When dealing with a fixed pulley and a moving pulley, as shown in the diagram, always work out which of the efforts move about the movable pulley. When the load is lifted, two efforts (e1) and (e2) move. The strain of the load is divided into two whilst one final effort lifts the entire load.A pulley system with the effort applied from previous slide is very difficult to use. The most comfortable way to use a single moving pulley is combine it with a fixed pulley, seen below. This allows the effort to be applied downwards.

76Mohamad Haniff bin Harun18/2/2014Example Calculation (Example 1)77

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA A simple pulley system is shown as the figure. A 40N effort is used to move a 80N load. The final effort moves 2 meters and at the same time the load moves 1 meter.

Determine the mechanical advantage and velocity ratio for this pulley systemWork out the efficiency of this pulley system.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Answer

It is important to remember that NO pulley system is 100% efficient. This is due to friction of the ropes against the pulley wheels and the friction of the bearings of the pulley wheels as they rotate. 100% efficiency is only theoretical.78Mohamad Haniff bin Harun18/2/2014Example Calculation (Example 2)79

BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Determine the mechanical advantage and velocity ratio for this pulley systemWork out the efficiency of this pulley system.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The pulley opposite has four pulleys which support the load by dividing it into four lengths. Each part of the rope equally supports the load. The mechanical advantage is 4. This means lifting a load with this arrangement of pulleys allows the lifting of 4 times a normal maximum load.

Each of the efforts (e1, e2, e3, e4) has to move in order for the load to move and calculating the velocity ratio is seen below.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA What effort is required to lift the 100N load?

How far does the load move in compared to the 4m movement of the final effort?


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA The pulley system opposite has 1:4 ratio (effort : load). An effort of 25N can lift a load of 100N.

1. Draw a pulley system that is capable of lifting 150N.

2. Work out the velocity ratio, the mechanical advantage and the efficiency of the system.


BETI 3423 ACTUATORS & DRIVESFAKULTI TEKNOLOGI KEJURUTERAANUNIVERSITI TEKNIKAL MALAYSIA MELAKA Answer


Gear & Pulley - Part II

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Transcript of Gear & Pulley - Part II