· Web viewObjective: At the completion of this exercise, you will demonstrate the effects of mechanical advantage regarding the use of levers. …

Robotics Engineering

DoDEA Career and Technical EducationSimple and Compound Machines

Exercise 1a Levers

Objective: At the completion of this exercise, you will demonstrate the effects of mechanical advantage regarding the use of levers. Youll build models of the different lever classes and then calculate, test, and verify the results of your lever machines.

Deliverables: Copy and paste the required deliverables to another document for submission. All deliverables must be word processed with the required student ID information in the footer of the document. The header of the document should contain the title of the assignment. Both the question and answer must be included in the deliverable with the answers highlighted. All work must be complete and accurate to receive credit.

1. Detailed definitions for each of the terms found in the Nomenclature section.

2. Detailed answers to the queries listed in the Questions section.

3. Completed table from the Materials Lab.

Information: Archimedes of Syracuse was a Greek astronomer, mathematician, physicist, engineer and inventor. He lived during the Classical Period between 287BC and 212BC. He is regarded as one of the leading scientists of the ancient Greco-Roman world focusing much of his work upon the machines of warfare. In fact, he was killed during a siege on his hometown. His greatest achievement in physics is probably his explanation of the mathematical principles of the lever. He once said, Give me a lever long enough, and a prop strong enough, I can single-handed move the world. The lever is the simplest of the simple machines. However, knowing how a lever works reveals the principles of how other simple machines reduce effort and Isnt that the reason why we build machines to begin with?

The Math:

Terms -

W = Work

F = Force

d = Distance

MA = Mechanical Advantage

Equations -

W = Fd

Load x d1 = Effort x d2

MA = length of effort arm / length of load arm

We define work as applying force to move an object through to a distance. Mathematically, we can express this as Work = Force x Distance or W = Fd. For instance: If a stack of books weighs 18 pounds and we lift them from the floor 3 feet up to a shelf, we will have performed 54 foot-pounds of work (54 ft-lb = 18 lb x 3 ft). This is also true when using a lever. When force is applied to the Effort Arm, the Resistance Arm will lift the Load a specific distance. The amount of Work performed is the product of the weight of the Load and the distance the Load is lifted.

In physics and engineering, mechanical advantage (MA) is the factor by which a machine multiplies the force put into it. One reason we invent machines is to multiply force (or make work easier). The mechanical advantage of a lever can be calculated using the equation MA = length of Effort Arm / length of Resistance Arm. However, to determine the amount of Effort required to lift the Load, we will have to incorporate this equation into the ratio Load d1 = Effort d2, where d1 represents the length of the Effort Arm and d2 represents the length of the Resistance Arm. Algebraically manipulating the equation will allow the solution of any single term in the equation.

Research Resources: The WWW changes all the time. If the listed links do not work, first inform your instructor then use a search engine to research information regarding the described subject.

Web Site

Description

http://iqa.evergreenps.org/science/phy_science/ma.html

Math for all simple machines

http://www.enchantedlearning.com/physics/machines/Levers.shtml

Explains different classes of levers and how they work

http://www.cosi.org/files/Flash/simpMach/sm1.html

Describes levers and how they multiply force

http://ronleigh.com/ivytech/_ref-levers.htm

Applies math to levers with sample problems

http://www.vernier.com/products/sensors/force-sensors/dfs-bta/

Vernier Dual-Range Force Sensor information

Nomenclature: Research and develop a detailed (two to three sentences) definition for each of these terms. Its important to realize that many words have multiple definitions. Some of which may have nothing to do with this course of study. Make sure your definitions fall within the context of this lesson.

Work

Lever

Pivot

Fulcrum

Levers of the 1st Class

Force

Distance

Newton

Foot-Pound

Levers of the 2nd Class

Load

Resistance

Effort

Mechanical Advantage

Levers of the 3rd Class

Questions:

1. Research and develop a detailed definition for each of the terms found in the Nomenclature section of this document.

2. You and a friend come upon a teeter-totter in a neighborhood playground. You weigh 135 lbs and your friend weighs 220 lbs. Determine how you would have to change the location of the pivoting point so that the teeter-totter is balanced with both of you on it. Show the math.

3. Youre helping your neighbor move 16 bags of concrete from the floor to the top of a workbench in his garage. Each bag weighs 25 Kg and the surface of workbench is 1 M off the floor. You neighbor had already stacked half the bags. How much Work did you perform? Show the math.

4. Create a table listing several examples of tools that fall into each of the three classes of levers.

5. What were the circumstances of Archimedes death? What were his last words?

Procedure: In this activity, youll closely examine the mechanical advantage inherent to the lever. Youll build a study model of a lever and then use lab equipment to measure the multiplied force of the simple machine. Finally, youll load your measurements into a Excel mathematical model to compare and contrast the results between the measured and calculated values.

Required Materials and Equipment: Get these materials and tools from your instructor.

Lego NXT Mindstorms Kit

Vernier Dual-Range Force Sensor

Ring Stand or Other Support

Rubber Band

Steps: Complete each of the following steps in the assigned order:

1. ()Build a model of a lever similar to the one shown in Figure 1.

2. () Setup the test apparatus as shown in Figure 2. For reliable readings, insure that the connected components are tight and stable. The rubber band applies a relatively constant force to the Effort end of the lever. The Load end of the lever is situated pressing up against the rubber cap of the Force Sensor. More detailed photos are available on the website.

3. (Figure 1. Lever Model)( )Connect the Force Sensor to the NXT Intelligent Brick using the NXT adapter and can cable. Youll also have to connect the Brick to the USB port of the computer. Note: You may have to download and install the Vernier NXT drivers using the Block Import/Export feature found in the Tools tab of the NXT Programming program.

4. ( )Launch the NXT Data Logging program and turn on the brick. Start a New Experiment, Select the Vernier Force Sensor 50 Newtons and the connected port (You may want to name the experiment.).

5. ( )Start with levers fulcrum in the center of the bar. With the rubber band pressing down on the Effort end of the lever, click the green download and run button in the data logging software.

6. ( )Move the fulcrum to the 4th hole on the Load end of the bar, setup the test apparatus and click the download and run button to record the results.

7. ( )Move the fulcrum to the 2nd hole on the Load end of the bar, setup the test apparatus and again click the download and run button to record the results.

8. ( )Record your results in the Levers Excel spreadsheet and analyze the graphic model comparing calculated data to your measurements.

9. (Figure 2. Lever Test Apparatus)()Use the courses website and the parts found in your NXT Mindstorms kit to build models of a wheelbarrow and pliers study models. Experiment by moving the load closer to and further from the pivoting point of each machine. Discuss your observations regarding the amount of effort required to operate the model with the instructor.

10. ( )Disassemble and properly store your materials and tools.

Conclusion: In completing this exercise you built models of 1st, 2nd, and 3rd class levers. You used an electronic sensor to measure the amount of force generated with a 1st class lever depending on the position of the pivoting point (fulcrum). By recording your results into a spreadsheet, you used a mathematical model to graph the performance of your machine, and as a result, determined that when the load is closer to the fulcrum, the amount of effort required to lift the load is reduced by a proportion determined by the length of the Effort Arm as related to the Resistance Arm. Finally, you verified your results by doing the math and found that although the performance pattern was similar, measured results are seldom the same as the calculated results. Welcome to the real world.



Exercise 1b Levers

Objective:

At the completion of this exercise, you will demonstrate how lever systems can be modified to alter mechanical advantage and you will be able to apply the use of levers in complex machines.




3. Completed table from the Levers Activity below.

Information: The Great Pyramid of Giza is built of approximately 2.3 million stone blocks with the largest among them weighing between 20 and 80 metric tons. How was it possible to move these massive boulders over 5000 years ago? The answer lies in simple machines. One example of a simple machine is a lever. Levers use significantly less effort to move large weights by placing the weight on one side and applying pressure to the other while a fulcrum is positioned underneath to act as a pivoting point. See-saws, wheelbarrows bicycle hand-brakes are examples of levers.


Web Site

Description

http://www.technologystudent.com/forcmom/lever1.htm

Website showing classification of levers

http://ocw.mit.edu/index.htm

M.I.T. Open Courseware -Search engine for high school level physics/engineering information.


Lever

Fulcrum

Load

Effort

Force

Work

Questions:

1. Research and develop a detailed definition for each of the terms found in the Nomenclature section.

2. Explain how levers allow people to lift heavy objects that they would normally be unable to lift.

3. Classify the three types of levers drawing a simple diagram of how they work.

4. List several practical examples of levers in everyday life.

5. From the data you collected in web based activity below:

a. How does a lever produce a mechanical advantage for moving the obelisk?

b. How did moving the fulcrum affect the mechanical advantage?

c. How did moving the object affect the mechanical advantage?

d. How did changing the length of the bar affect the mechanical advantage?

Procedure: In this activity, youll conduct a virtual experiment regarding the simple machine known as the lever. Youll closely examine the relationship between the fulcrum and bar, as well as the position of the fulcrum in relation to the effort and load. Follow the instructions carefully.


Computer with Internet Access

Shockware Software Installed

Steps:

1. Link to http://www.pbs.org/wgbh/nova/egypt/raising/ and navigate through the Nile Site Map showing how scientists attempted to lever an obelisk. Use your Learning Log to record notes.

2. Now, go to www.pbs.org/wgbh/nova/egypt/raising/leverwave.html and launch the lever simulation.

3. Before you begin, complete Table 1 below describing how you plan to raise the obelisk.

4. Put your plan into action and record the results in the cells provided, paying careful attention to the calculations provided in the simulation. The goal of this activity is to understand the mechanical advantage which levers provide.

5. Improve your plan in Table 2 and compare the results between the two tables.

Table 1: Plan for Raising the Obelisk

Step

Object Used

Location

Mechanical Advantage Data

Work = Force x Distance

Result

Lever Side

W=FxD

=,

Obelisk Side

W=FxD

How did obelisk move?

1

2

3

4

5

6

7

8

9

10

Table 2: Improved Plan for Raising the Obelisk

Step

Object Used

Location

Mechanical Advantage Data

Work = Force x Distance

Result

Lever Side

W=FxD

=,

Obelisk Side

W=FxD

How did obelisk move?

1

2

3

4

5

6

7

8

9

10

Conclusion: Were you able to lift the obelisk? This is a virtual simulation to what the Egyptians had to deal with but they had to incorporate gravity into their solution as well. Used properly, levers can change the amount of effort needed to a fraction or what would be required without using this simple machine. The amount of force applied times the distance an object moves is equal the amount of work performed. In completing this exercise you can now understand how levers used to build huge structures like the pyramids at Giza can be also be applied to the miniature mechanism found in robot design.



Exercise 2 Inclined Plane, Wedge and Screw

Objective: At the completion of this exercise, you will demonstrate the effects of mechanical advantage regarding the use of inclined planes, wedges and screws. Youll build models of these simple machines and then calculate, test, and verify the results of your inclined plane machines.




3. Completed Spreadsheet Math Model for the Inclined Plane.

Information: The inclined plane is ancient simple machine. It was used for more than a millennium before Archimedes and Heron of Alexandria first theorized its physical operations and discovered how it provided for mechanical advantage. Over 1000 years later, inclined planes might have been used to place the largest blocks at Stonehenge. Another 1000 years later, inclined planes in the form of ramps were used to build the Great Pyramid at Giza.

An inclined plane is a flat surface (plane) that slopes at an angle (inclined) to provide a path to move an object from one level to another. Examples of inclined planes include ramps, graded roads, or a playground slide. Wedges are an example of double inclined plane and a screw is an inclined plane thats wrapped around an axis. Examples of wedges would be an axe, chisel or doorstop. Worm gears, screw jack, and a screw (duh) are examples of the simple machine known as a screw.

Research Resources: Use your search engine to research information on Inclined Planes, Math and Simple Machines.

Web Site

Description

http://www.slideshare.net/jbishopgcms/planewedgescrew

Explains different types of Inclined Planes

http://www.cosi.org/downloads/activities/simplemachines/sm1.html

Describes Inclined Planes and how they reduce force

http://zonalandeducation.com/mstm/physics/mechanics/forces/inclinedPlane/inclinedPlane.html

Apply math to Inclined Planes


Mass

Gram

Centimeter

Joule

Slope

Thread

UNC

UNF

TPI

Foot Pounds

Questions:


2. Who is Hero (Heron) of Alexandria? What do you feel were his most significant contributions to engineering?

Procedure:


Lego NXT Mindstorms Kit

String: 1 Meter

Vernier Dual Force Sensor

Steps: Complete each of the following steps in the assigned order:

Inclined Plane: Theres always a trade-off when using simple machines to perform work. With inclined planes you choose to lift an object a short distance using more force, or can use a ramp to lift the same object the same height, but over a longer distance using less force. The mass of the object and the work accomplished stays the same it just takes more time (distance) to get the job done. You should consider this relationship of proportions as you build and test the Inclined Plane model.

The Math:

Terms -

M = Mass

W = Work

F = Force

d = Distance

MA = Mechanical Advantage

Equations -

W = Fd

MA = d2/d1

F = Mass/MA

Joule = Newton-Meter

As before, we define Work as applying force to move an object a certain distance. An inclined plane reduces the effort necessary to move the load by distributing the force required to perform the task over the distance of the inclined plane. Reducing effort is a good thing, but we do sacrifice having to exert the reduced Force over a greater distance. Theres always a trade-off.

If we wanted to lift an 80 lb. bag of concrete from the floor up to a tabletop 3 ft. up we could calculate the Work required as W = Fd or The Work is equal to 80 pounds multiplied by 3 ft. for a total of 240 foot-pounds of Work.

When we use an inclined plane to do the same task, it takes the same amount of Work to perform the task. However it takes less Force to get the Work done because of the Mechanical Advantage provided by the inclined plane. In an inclined plane, Mechanical Advantage is equal to the Slope Length divided by the Slope Height or MA = d2/d1. If we used a 12 foot long ramp to move a bag of concrete up to the same height of 3 feet, the equation for Mechanical Advantage would be MA = 12 ft./3ft. or 4 ft. To determine how much force is actually required to move the bag of concrete up the (frictionless) ramp we would apply the formula F = Mass/MA or F = 80 lb./4 or 20 foot-pounds. Heres the sequence of calculations:

Step 1. W=Fd240 foot-pounds = 80 lb x 3 ft.

Step 2.MA=d2/d14 ft. = 12 ft. / 3 ft.

Step 3.F = Mass/MA20 foot-pounds = 80 lb / 4 ft.

Using an incline plane 12 ft. long and 3 ft. high, it now takes only 20 lbs. of Force to move an 80 lbs. bag of concrete.

1. ( ) Carefully examine the model of the Inclined Plane and Trolley shown in Figure 1. Construct a model similar to the one shown in the photograph. The trolley must slide easily up and down the model of the Inclined Plane.

2. ( )Tie one end of the string to the Trolley as shown and tie a loop on the opposite end. Place the Trolley onto the rail of the model of the Inclined Plane with the rollers facing down. Secure a load to the Trolley in a way that wont interfere with its travel on the rail and route the string from the Trolley over the pulley hanging freely off the edge of a table or bench.

3. ( )Measure the dimensions of the Inclined Plane and use the Excel model to calculate the Mechanical Advantage for the first version of the Inclined Plane.

4. (Figure 1. Inclined Plane Model with Trolley)( )Attach the looped end of the string to a number of wheels, gears and tires that (when combined) will allow the weighed trolley to ride slowly and continuously up the Inclined Plane without assistance.

5. ( )Measure the amount of force exerted on the trolley by the string and counter weight with a force sensor.

6. ( )Modify the Inclined Plane model making it a little longer by adding one more section of Studless Technic Beams. Repeat the force and distance measurements. Operate the Inclined Plane in the new configuration noting any difference in the machines behavior.

7. ( )Modify the Inclined Plane model again adding one more section of Studless Technic Beams. Repeat the measurements and then the experiment noting any difference in the machines behavior.

Wedge: The basic difference between an Inclined Plane and a Wedge is that a Wedge moves and an Inclined Plane does not. Wedges can be either single-sloped like a doorstop or double-sloped like an axe or knife. The mathematical analysis of wedges is essentially the same as with Inclined Planes. Instead of using the term Height, well use the term Thickness. The Mechanical advantage is determined by dividing the length of the slope by the thickness of the wedge (MA = d2/d1). The shaper the angle of the wedge, the less effort is needed to operate it.

The Math:

Terms -

d2 = Slope Length

d1 Thickness

Equations -

MA = d2/d1

Lets look at the cross-section of a wedge. youll notice it is really nothing more than a triangle. Applying the equation MA = d2/d1, you should notice that the relationship between the length of the wedge (d2) and the thickness of the wedge (d1) are considered inversely proportional because d2 is being divided by d1. This means that the smaller the thickness of the wedge compared to its length, the more mechanical advantage it can deliver. The opposite is also true. As d1 increases, mechanical advantage is reduced if the length of the wedge remains the same.

(Figure 2. Wedge Model and Test Apparatus)

(Figure 3. Long Wedge Inserted into the Test Apparatus.)

1. () Carefully examine the model of the Wedge and the test apparatus shown in Figure 2. Construct a model similar to the one shown in this photograph.

2. ( )Secure a load to the lift platform on the test apparatus in a way that wont interfere with its travel on the two vertical support rails.

3. ( )Measure d1 and d2 on the wedge and then calculate the mechanical advantage if the longest slope of the Wedge is used to lift the load as shown in Figure 3.

4. ( )Measure d1 and d2 on the wedge and then calculate the mechanical advantage if the Shortest slope of the Wedge is used to lift the load.

5. ()Alternately push the long and the short slope of the Wedge through the test apparatus making note of the difference in the force required to perform the work.

Screw: A screw is an Inclined Plane where the plane is wrapped around an axis like a cylinder. The threads of the screw act as a single plane while the spacing between the threads form the slope of the plane. The greater the spacing of the threads means the greater the angle of the Inclined Plane requiring greater effort to drive the screw. The finer the threads indicate a smaller angle of the Inclined Plane and subsequently, the lesser effort to drive the screw. The trade-off again Although Mechanical Advantage increases, more turns will be required to do the same amount of work with a screw with fine threads as the one with larger thread spacing. The relationship between the number of threads and a specific distance is called the Pitch. The screws that come with the Tetrix robotics kit are identified as #6-32 and #10-32 screws. Although both screws have a pitch of 32 Threads Per Inch (TPI), the diameters of the screws are different as indicated by the first number. Its important to note that these screws are not interchangeable.

The Math:

Terms -

Pitch = 1/Threads Per Unit of Measure (TPI)

= Pi

FP = Foot Pounds

r = Radius

= Inch

Equations -

MA = 2r / Pitch

The English and Metric systems of measurement are used to determine the specifications of lots of things including hardware like screw, nuts and bolts. The Metric system is based on the Meter as the standard unit of measure and is considered to be more logical because its based upon decimal units. A Meter is divided into 10 equal parts called decimeters, 100 equal parts called centimeters or 1000 equal parts called millimeters. The English system, also known as the inch system or the Imperial system is based on the Foot measurement. A foot is divided into 12 equal parts called inches. However, when we consider threads on a bolt like the one shown to the right were not talking about inches. Were really talking about very small measurements like 1/16, 1/32 and 1/64.

This bolt is a in diameter. Its a course thread (UNC) bolt 1 long with a Pitch of 20 TPI. To determine the Mechanical Advantage of this simple machine well simple apply the formula. Before we start, youll need to know that the radius is half the diameter. Since the diameter of this bolt is , to find half of any fraction, simply multiply its denominator by two or 2 x 4 is 8 equaling 1/8 for the bolts radius.

1. MA = 2 r / Pitch

2. MA = 2 x x 1/8 / (1/20)

3. MA = 2 x 3.14 x .125 / .05

4. MA = 15.7

This means that this screw will multiply the turning force 15.70 times. So if we apply 14 foot pounds of force to turning this bolt, the tightening force of the nut will be 14 ft lb x 15.7 resulting in 219.8 ft lb of energy. 14 lb of effort results in 219.8 lb of force using this simple machine called a screw. Thats pretty impressive.

1. () Carefully examine the model of the Screw Machine shown in Figure 4.

2. ( )To build the model of the Screw Machine you can refer to the photographs of this model youll find in the photo gallery on the courses webpage.

3. (Figure 4. Model of a Screw Machine)( )Take a closer look at the part of this machine that resembles the threads of a screw. This is also called a worm gear primarily because it sort of looks like a worm when its turning. Now heres a tricky question: How many teeth does this worm gear have? Did you think it has ten or perhaps twelve teeth for its entire length? Would you believe it has only one tooth? Its one tooth that continuously spirals around the axis of the worm gears axle. As the handle is turned clockwise and counterclockwise it will drive the tiny non-spinning worm drive gear from one side of the machine to the other.

4. ()Use a ruler to measure the number of threads this worm gear has in one inch. This will be the screws pitch or threads per inch (TPI).

5. ()Now How many turns of the handle does it take to make the little worm drive gear travel one inch?

6. ()Do you see the relationship between the screws pitch and the turns needed for it to drive one inch?

7. ()Refer to the Math section for the Screw and calculate the Mechanical Advantage for this machine.

Conclusion:

Inclined planes, wedges and screws seem like they may be different types of machines but theyre really all the same simple machine but in different forms. The math used to determine how they work is closely related to each machine as well. Thats easier to see when comparing the math used to calculate mechanical advantage using an inclined plane with that of a wedge. After all, a wedge is really just a mobile version of an inclined plane. The math is a little harder to see when determining the Mechanical Advantage of a screw. The relationship in the equation MA = 2r / Pitch is clearer to see if you realize that 2r represents the slope length of an incline plane for one revolution of the screw or its circumference. The Pitch is the height of the slope or the thickness as it relates to a wedge.

Like in all applications of simple machines, there is always a trade-off between the effort made to make the machine operate and the amount of actual work it performs. In simple machines, as the amount of effort is reduced and the amount of work stays the same, then the distance must increase to get that work done.



Exercise 4 Wheel and Axle

Objective: At the completion of this exercise, you will demonstrate the mechanical advantage inherent to the wheel and axle combination. Youll measure the diameters of wheels and axles and develop a mathematical model describing their relationship.




3. (Figure 1 Mechanics work at the axle as they assemble and maintain a huge Ferris Wheel.)Completed spreadsheet defining the mechanical advantage for various wheels and axle combinations.

Information: The wheel Its been around since the dawn of man. Its hard to pinpoint when it was invented or what culture invented it. It seemed to simultaneously appear in Central Europe, the Caucasus and Mesopotamia during the Copper Age (about 4000 BC) give or take a millennium or two. Were talking ancient history here.

(Figure 3 Hundreds drag a stone sculpture thats secured to a sledge.) (Figure 2 Wooden rollers are swapped-out one at a time as a heavy stone block towed along.)

(Figure 5 By the courtesy of Freds own two feet. Even as a kid I always wondered how that back roller just didnt fall off.) (Figure 4 Stone grinding wheel with axle for grinding grain or minerals.)Before wheels, people would move very heavy objects using tree logs as rollers. They also used sledges (big sleds) to slide stuff around. Sledges worked well on low-friction surfaces like ice, snow and sand but not as well on grass and rock. When the going got too tough When they couldnt get the sledge to budge, someone had the great idea to combine the roller and the sledge. They discovered as the rails of the sledge cut deep grooves into the rollers, they didnt need to use as many rollers to keep the sledge moving. That was good, because it wasnt a lot of fun swapping-out rollers every two or three second to keep the sledge moving. Larger rollers were heavier and more difficult to reposition as well, but they also made it easier to roll the sledge. If there was only a way to reduce the weight of the larger rollers and secure it to the sledge so it didnt have to be swapped-out all the time. At first they just carved out the center portion of the roller making it a single piece construction of the wheels and axle. The axle was pegged into a fixed position on sledge and thus the wheeled cart was invented. Later enhancements included spoke wheels to make them lighter and repairable. As new materials have been developed, wheels and axels have improved significantly. When methods were developed to apply force to the wheel or to the axle, mechanical advantage became part of this simple machines engineering importance. The wheel and axle has become the most prevalent and significant invention in the history of mankind.

The Math:

Terms -

MA=Mechanical Advantage

Dw = Diameter Wheel

Da = Diameter Axle

C = Circumference

R = Radius

Lb-ft = Foot Pound

RPM = Revolutions Per Minute

D = Diameter

Equations -

MA = Dw/Da (Input at Wheel)

MA = Da/Dw (Input at Axle)

R = D/2

C = 2R

One way to look at a wheel is to consider it as a continuous lever of the 2nd class. The axle would be the fulcrum and the radius at any point would be the bar. Like the lever, turning the steering wheel in a car will multiply the force at the axle. The bigger the steering wheel, the greater the leverage and the more rotational effort (torque) would be applied to the axle. An automobiles wheels are different. The effort is applied at the axle. Therefore, the effort at the axle is divided as it reaches out to the roads surface. Mathematically, this is represented by the equation MA = Dw/Da if the input effort is at the wheel and MA = Da/Dw if the input effort is at the axle.

Tire sizes for my Jeep Wrangler go from 27 to 44 in diameter. The size that came stock with the vehicle are 28. The axle that drives each of the wheels has a diameter of about one inch. With the stock tires, the MA is 1/28 or .036. Slap on a set of 44 inchers, the MA would be 1/44 or .023. So what does that mean?

If the engine applied 222 lb-ft of torque at the axle, I would lose about 2.88 lb-ft of torque if I changed my wheels from the stock 28 to the oversized 44 tires. In essence, I would lose power but my Jeep would look awesome! Heres the application:

1. MA28 = .036

2. MA44 = .023

3. .036 - .023 = .013

4. 222 lb-ft x .013 = 2.88 lb-ft difference

As with all applications of mechanical advantage, there is a trade-off. The smaller the tire, the more force is transferred to the where the rubber hits the road. Since the tire is smaller, its circumference is too. That means the wheel will have to make more revolutions to acquire the same speed using the larger tires. Youll get more power at the wheels, but your top-end speed will be reduced.

The circumference of a 28 inch diameter wheel is calculated using the equation C = 2R and results in 2 x 3.141 x 14 or about 88 inches. One rotation of the 28 wheel would push the Jeep 88 inches down the road. Using the 44 tires, that application of the same equation (C = 2 x 3.141 x 22) would result in a circumference of about 138 inches. One rotation of the axle would push the vehicle over 10 feet down the road. Although the larger tire would require fewer rotations to travel a specified distance and the vehicle would have a higher top-end speed, it would require more torque to perform the task. Theres always a trade-off.


Web Site

Description

http://library.thinkquest.org/C004203/science/science02.htm

Ancient Civilizations Invention of the Wheel

http://en.wikipedia.org/wiki/Wheel_and_axle

Wiki on the Wheel and Axle

http://en.wikipedia.org/wiki/Caliper

How to Use Calipers

http://www.ehow.com/how_2273770_read-metric-ruler.html

How to Use a Metric Ruler


RPM

Foot - Pound

Wheel and Axle

Caliper

Questions:


2. The drive system of a robot features drive wheels that have a diameter of 3. If the robots gear box has rotated the drive wheels 10 revolutions About how far has the robot traveled?

3. The wheels of a drive system for a robot are 64mm in diameter. The maximum speed for the motors gearbox at the axle is a 160 RPM. If the robot is driven at its highest speed for 30 seconds How far will it have traveled in meters?

4. Repeat the same calculations as in question 3 replacing the wheels with ones that are 128mm in diameter.

5. Calculate the maximum feet-per-minute for a robot that uses 8 drive wheels attached to a direct drive gearbox with a maximum output speed of 400 RPM.

Procedure: In the following activity youll have to measure the diameter of an axle and various sizes of wheels. The best tool to perform this task is a vernier caliper. These calipers come in dial and digital varieties but youll have to make sure your measurements are in millimeters and not inches for this activity. Hopefully you have access to one of these nifty measurement tools. If not, you might also be able to transfer the measurements using an outside caliper, but it takes some effort to make accurate measurements. As a last resort, you can directly measure the diameter of the axle and wheels using a metric ruler, but youll also throw the concept of accuracy out the window. There are informative links in the Research Resources section describing how to use calipers and rulers. The most important consideration is accuracy Learn how to use the tools, make accurate measurements, but verify your results. I understand that the precise dimensions of many LEGO components can be found on the Internet if all else fails.


Mindstorms Robotics Kit

Mindstorms Resource Set

Tetrix Robotics Kit

Outside Caliper

Linear Caliper

Metric Scale

Steps: Refer to these figures as you take your measurements. Complete each of the following steps in the assigned order:

Tetrix Omni Wheel

Tetrix 3 Wheel

LEGO Tractor Wheel

Balloon Tire

Diameter: mm

Diameter: mm

Diameter: mm

Diameter: mm

Tire Ring

Small Tire

Bushing, Grey

Bushing, Small

Axle

Diameter: mm

Diameter: mm

Groove Diameter: mm

Groove Diameter: mm

Diameter: mm

1. ()Measure and record the diameters of each of the wheels ( and axel) shown above.

2. () Enter the measured information into the Wheel and Axle Excel Model following the instructions posted on the models worksheet.

3. ()Make a temporary mark somewhere on the circumference of one of the larger wheels. Place the wheel with that mark positioned on a flat surface. Making a temporary mark at that point on the flat surface. Carefully roll the wheel precisely one revolution making another mark on the surface at that point. Measure the distance between the marks on the flat surface. Does this measurement match the circumference the model calculated for that wheel?

(Figure 4 - Digital vernier caliper used to measure inside and outside diameters in either inches or millimeters at a press of a button.)Conclusion: In completing this exercise you discovered that the mechanical advantage of a wheel and axel can be determined by dividing the diameter of the input by the diameter of the output. Driving this simple machine by the wheel multiplies effort at the axle while driving it by its axle divides the effort at the wheel. You also discovered that the circumference of the wheel and its number of rotations per unit of time determines the distance the wheel can travel in a specified period of time. Thats speed baby and speed takes into consideration this simple machines mechanical advantage when it comes to converting effort into motion and determining the trade-offs needed to get work done.



Exercise 5 Belt and Chain Drives

Objective: At the completion of this exercise, you will demonstrate the proper application of belts/pulleys and chains/sprockets when building drives and transmissions. You will compare and contrast belt and chain drives while experimenting with various sprocket and pulley wheel sizes. In addition, youll describe the advantages and disadvantages of slippage in belt and chain drive design.




3.

Information: Think about riding a 10-speed bicycle through the hills and hollers of the wide-open countryside. The sun shines warmly your face on a remarkable spring day. The tall grass seems to whisper in the air as a soft breeze blows across an adjacent wheat field. Youre stopped at the base of a hill studying the long and winding path as it gradually scales the incline that lies ahead.

You mistakenly start out in 5th gear pushing down with all your might just to get yourself moving. You quickly shift down into 3rd gear where you dont have to struggle nearly as much to peddle. As the grade of the road increases its getting harder to peddle so you shift down again and then again. Youre now in 1st gear and youre peddling like crazy. Its certainly easier to peddle, but youre just crawling along going nowhere fast. Panting like German shepherd, you crest the ridge and start downhill, you shift up into 5th gear and now youre rolling along at an incredible clip, but your legs are moving like Wile E. Coyote chasing the Roadrunner. You decide to shift the front derailleur to the outer ring and suddenly youre peddling much slower while careening downhill at close to light speed. Weeeeee!

What a marvelous machine a 10-Speed bike is. Although biking enthusiasts know how to use gear combinations well enough to tackle even the steepest hills, not many riders know how gears, sprockets, chains and belts work to reduce the effort needed to get work done.

When effort is applied to a bikes crank with the chain on the smaller ring, less effort is required to produce torque, but youll have to peddle more times to travel a certain distance. This setting on a 10-Speed bike is used for gears 1 through 5. These are the low gears typically used for climbing hills. When the chain is moved to the outer ring on the crank, more effort is required to produce torque. Its harder to peddle, but youll peddle fewer times to travel the same distance. This larger outer ring on the crank covers gears 6 through 10 on a 10-speed bike and is used to obtain some exhilarating downhill speed.

So The mechanical advantage of any simple machine is the relationship between input effort and output force. Mechanical advantage on the 10-speed bike is achieved by combining different sizes of wheels. Since (simple machine) The Wheel also includes components like pulleys, sprockets, cogs, and gears its important to come up with a systematic way to determine the size of the wheels were combining to more complex machines. We can us wheel measurements like the circumference, diameter, and radius but most often we simply count the number of teeth on a sprocket, cog or gear to represent its size. The chain simply transfers the effort exerted on the crank ring to the gear cassette on the bikes back wheel. The relationship between the chain and the sprocket or cog is their matching pitch. The pitch is the spacing of the teeth on the bikes cogs and the links of the chain. On modern bicycles, the pitch is . The pitch of the chain and the sprocket must match for the drive train to work.

Belt drive systems are very similar to chain drives. The major difference between chains and belts is that belts are designed to slip and they break easier than chains. Belts are also lighter and quieter, but again The primary difference is slippage. Belts slip Chains dont. In fact, many drive belts are designed with teeth to keep them from slipping unless theres a malfunction. Then they break. Engineers use belts in their designs as a safety precaution. After all, its much cheaper to replace a broken belt than the components theyre driving.

The mechanical advantage in belt drive systems is determined the same as those using chains. If teeth are part of the design, you can determine the gear ration by simply counting teeth. Otherwise, you can measure the wheels circumference, diameter, or radius to obtain the information necessary to calculate mechanical advantage. Understanding how to calculate the mechanical advantage of chain and belt drive systems will help you determine the torque required to operate the system as well as the speed it will deliver.

Terms -

Equations -

Application

Insert a table and picture of gear sizes here:

Gear

Teeth

39 Tooth Ring

52 Tooth Ring

1

28

1.39

1.86

2

24

1.63

2.17

3

20

1.95

2.60

4

17

2.29

3.06

5

14

2.79

3.71

The Math:


Web Site

Description

http://www.technologystudent.com/gears1/pulley1.htm

Describes a system of pulleys and belts

http://www.technologystudent.com/gears1/chain1.htm

Describes a system of sprockets and chains


Belt

Chain

Sprocket

Slippage

Questions:


2. Compare and contrast gears and sprockets.

3. Compare and contrast belts and chains.

4. What are some advantages and disadvantages of slippage?

Procedure: In this activity, youll conduct a hands-on experiment regarding this topic area. Youll closely examine


Mindstorms NXT Trainer

Tetrix Robotics Trainer

Chains and Sprockets Set

Steps: Refer to figures as you construct Complete each of the following steps in the assigned order:

1. ()Refer to the first webpage above. Build a similar system of pulleys and belts.

2. ()Determine, on your model, which is the driver pulley and which is the driven pulley and calculate the velocity ratio. Repeat with twice with varying sized pulleys

3. ()Record all calculations on the data table provided.

4. ()Refer to the second webpage above. Build a similar system of sprockets and chains.

5. ()Determine which is the driver sprocket and which is the driven sprocket and calculate the gear ratio. Repeat with various sized sprockets.

6. ()Record all calculations on the data table provided.

7. ()Using what you have learned above, construct two vehicles; one with a belt drive and one with a chain drive.

8. ()Calculate and measure the mechanical advantage of each.

Gear (Sprocket) Ratio

Distance moved by the driver (effort)

Distance moved by the driven (load)

Effort/Load

Ratio

Velocity Ratio of Pulleys

Diameter of Driven Pulley (A)

Diameter of Driver Pulley (B)

A/B

Ratio

Discussion:

In your vehicles, which system provided the greater mechanical advantage? Why? Would you use a belt or chain drive in a full sized vehicle? Use your data to support your answer.

Conclusion: In completing this exercise you have demonstrated that you can apply the principles of belts and chains when building drives and transmissions. By building vehicles using both belt and chain drives, you then were able to calculate and measure the mechanical advantage of the vehicles drive train. Gear/Velocity ratios give you the information you need to be able choose the mechanisms to help you move mountains.



Exercise 6 Gears and Gear Ratios

Objective: At the completion of this exercise, Students will demonstrate how gear drives are used to alter mechanical advantage in simple machines. Calculating mechanical advantage, students will determine the effect that gear ratio has upon torque and rate of rotation. Demonstrating their knowledge of gears and gear trains, student will construct simple machines using gear, compound gear, and worm gear transmissions. Using crown and bevel gears, students will demonstrate methods of changing the angle of transmission. To demonstrate their competence, students will design and construct a working 2-speed gearbox using their robot trainer.




3.

Information: A gear is a wheel with teeth that mesh together with other gears. Gears change the speed, torque (rotational force) direction of rotating axles. Different types of gears: spur, idler, worm, bevel, and crown. Always remember gear ration is the ratio of the number of teeth on one gear to the number of teeth on the other gear. Finding Mechanical Advantage with Gears: (Example) Take a 40 tooth gear paired with a 8 teeth gear the gear ratio = 40 to 8 or, simplifying, MA = 5 to 1.

The Math:

Terms -

Equations -

Application


Web Site

Description

http://www.technologystudent.com/gears1/geardex1.htm

Website click on Index page: click on Gears & Pulleys

http://technicopedia.com/fundamentals.html

Excellent resource of gears and geartrains.


Gears

Spur gear

Worm gear

Bevel gear

Crown gear

Gear box

Transmission

Questions:


2. Explain how gears change speed, torque and direction of rotation axles.

3. Explain what is meant by a gear ratio? Show a velocity ratio problem to demonstrate gear ratio.

4. Explain torque or (rotational force) and show an example how we can change angle of transmission



Mindstorms NXT Kit

Tetrix Robotics Kit


1. ()Go to http://www.technologystudent.com/gears1/gearat3.htm

2. ()http://www.dynamicscience.com.au/tester/solutions/hydraulicus/gearforceexe.htm :Use this site to help calculate mechanical advantage for gear systems.

3. ()Before you begin, write a plan for how you will create a two speed gear box using your Lego kit.

4. ()Put your plan into action.

5. ()Draw a picture first of your design before you build. Show how you will create two speeds?

6. ()Show your work for all problems in Step two.

7. ()What is the MA of your transmission (gear box)?

8. ()Whats the difference between the automatic and the standard transmission.

Conclusion: At the completion of this exercise, Students will demonstrate how gear drives are used to alter mechanical advantage in simple machines. Calculating mechanical advantage, students will determine the effect that gear ratio has upon torque and rate of rotation. Demonstrating their knowledge of gears and gear trains, student will construct simple machines using gear, compound gear, and worm gear transmissions. Using crown and bevel gears, students will demonstrate methods of changing the angle of transmission. To demonstrate their competence, students will design and construct a working 2-speed gearbox using their robot trainer.



Exercise 7 Gear Trains

Objective: At the completion of this exercise, you will demonstrate




6.

Information: One of the problems that engineers

The Math:

Terms -

Equations -

Application


Web Site

Description

http://www.nxtprograms.com/transmission/steps.html

3-Speed Transmission with Clutch


Vocabulary Words

Questions:


2. Explain




1. ()

2. ()

Conclusion: In completing this exercise



Exercise 8 Pulleys and Pulley Systems

Objective: At the completion of this exercise, you will demonstrate how pulleys are used in simple machines. You will apply the concept of the block and tackle, together with gears and levers to build machines that significantly alter mechanical advantage to lift heavy loads. At the completion of this exercise, you will demonstrate how pulleys are used in simple machines. You will apply the concept of the block and tackle, together with gears and levers to build machines that significantly alter mechanical advantage to lift heavy loads.




3.

Information: An urban legend circulated some years ago that describe the insurance claim of a bricklayer after an accident occurred. The story goes like this, I am a bricklayer by trade. On the day of the accident, I was working alone on the roof of a new six-story building. When I completed my work, I found I had some bricks left over which when weighed later were found to weigh 240 lbs. Rather than carry the bricks down by hand, I decided to lower them in a barrel by using a pulley which was attached to the side of the building at the sixth floor. Securing the rope at ground level, I went up to the roof, swung the barrel out and loaded the bricks into it. Then I went down and untied the rope, holding it tightly to insure a slow descent of the 240 lbs of bricks. You will note on the accident reporting form that my weight is 135 lbs.

Due to my surprise at being jerked off the ground so suddenly, I lost my presence of mind and forgot to let go of the rope. Needless to say, I proceeded at a rapid rate up the side of the building. In the vicinity of the third floor, I met the barrel which was now proceeding downward at an equally impressive speed. This explains the fractured skull, minor abrasions and the broken collarbone, as listed in Section 3 of the accident reporting form. Slowed only slightly, I continued my rapid ascent, not stopping until the fingers of my right hand were two knuckles deep into the pulley which I mentioned in Paragraph 2 of this correspondence. Fortunately by this time I had regained my presence of mind and was able to hold tightly to the rope, in spite of the excruciating pain I was now beginning to experience. At approximately the same time, however, the barrel of bricks hit the ground, and the bottom fell out of the barrel. Now devoid of the weight of the bricks, the barrel weighed approximately 50 lbs. I refer you again to my weight.

As you might imagine, I began a rapid descent down the side of the building. In the vicinity of the third floor, I met the barrel coming up. This accounts for the two fractured ankles, broken tooth and severe lacerations of my legs and lower body. Here my luck began to change slightly. The encounter with the barrel seemed to slow me enough to lessen my injuries when I fell into the pile of bricks and fortunately only three vertebrae were cracked. I am sorry to report, however, as I lay there on the pile of bricks, in pain, unable to move and watching the empty barrel six stories above me, I again lost my composure and presence of mind and let go of the rope.

Pulleys and pulley systems can be used to lift heavy weights that humans would not normally be able to lift. What do you think is the difference between a pulley and a pulley system? Pulleys and pulley systems can be used to lift heavy weights that humans would not normally be able to lift. Block and tackle pulley systems are used to hoist sails on ships and lift an engine from a vehicle. A block and tackle can have as many pulleys as you want as long as there arent too many. Why do you think there might be a system of too many pulleys?

The Math:

Terms -

Equations -

Application


Web Site

Description

www.ocw.mit.edu

High School physics information

www.library.thinkquest.org/27948/pulley.html

An applet with a pulley where pulley systems with various numbers of pulleys can be studied and calculations of necessary force observed.

http://www.swe.org/iac/lp/pulley_03.html

Clearly details the mechanical advantage of different pulleys and pulley systems.

www.ocw.mit.edu

High School physics information

http://www.swe.org/iac/lp/pulley_03.html

Clearly details the mechanical advantage of different pulleys and pulley systems.

http://science.howstuffworks.com/transport/engines-equipment/pulley.htm

Details how a block and tackle works.


Pulley System

Block and Tackle


Newtons

Pulley System

Block and Tackle


Questions:


2. What is the difference between a pulley and a pulley system?

3. How does a single pulley affect mechanical advantage?

4. How does a pulley system affect mechanical advantage?

5. What is the difference between a pulley and a pulley system?

6. How does a single pulley affect mechanical advantage?

7. How does a block and tackle affect mechanical advantage?

8. What happens if you have too many pulleys in a block and tackle system?



Robot Trainer

String

Spring scales

Ring stands (chemistry) with rings

Weights that can be hooked/tied to string

Computers with internet access


1. ()Find the resistance force of the mass by attaching it to the spring scale and observing the gravitational pull.

2. ()Attach a pulley to a ring stand. Run string across the top of the pulley. Attach the weight on one end of the string and the spring scale to the other end.

3. ()Find the force required to lift the weight by reading the spring scale as it is being pulled downward.

4. ()Attach one end of the string to the ring stand and the other end to the spring scale. Position the pulley in between. Attach the weight to the pulley.

5. ()Find the force required to lift the weight by reading the spring scale as it is being pulled upward.

6. ()Use the internet to find at least three examples of pulley systems.

7. ()Set up your model to match the diagrams. Draw the diagrams in your engineering journal or notebooks.

8. ()Measure the resistance force with the spring scale in each instance.

9. ()Create a table documenting your findings in steps 1, 3, 5, and 8.

10. ()Go to http://www.swe.org/iac/lp/pulley_act.html and check your knowledge on pulley systems. Correct answers will activate the pulley. Incorrect answer will show a try againmessage.

11. ()Discuss how pulley systems impact mechanical advantage.

12. ()Find the resistance force of the mass by attaching it to the spring scale and observing the gravitational pull.

13. ()Create a block and tackle pulley system. Draw the diagram of the system on this handout or in your engineering journal or notebook.

14. ()Measure the resistance force with the spring scale.

15. ()Discuss how a block and tackle pulley systems impact mechanical advantage.

Conclusion: In completing this exercise you will have a greater understanding of the effect of pulleys and pulley systems on mechanical advantage. The amount of force needed to lift an object is varies with the number and distribution of pulleys. In conclusion, how would you advise the bricklayer to set up his pulley system in the future to avoid this type of injury reoccurring? In completing this exercise you will have a greater understanding of the effect of pulleys and pulley systems on mechanical advantage. The amount of force needed to lift an object is varies with the number and distribution of pulleys. In conclusion, if you moved into a two story home with narrow stairways and big windows, what type of pulley system might you create to get your furniture up to the second floor?



Exercise 9 Transmission of Motion

Objective: At the completion of this exercise, you will demonstrate the various forms of motion that affect the operation of simple machines. You will construct models that change linear, reciprocal, and rotary forms of motion through an angle.




3.

Information: What good would a lever be if it didnt move? How useful would this pulley be? Motion is an essential part of all machines. You will deal with linear motion (motion in a straight line), reciprocal motion (also called reciprocating motion- back and forth), and rotary motion (circular). Conversion from one type to another produces mechanisms we have at our disposal every day. OK, lets get a move on!

The Math:

Terms -

Equations -

Application


Web Site

Description

http://www.flying-pig.co.uk/mechanisms/pages/linear.html

Site providing clear definitions with moving images explaining types of motion and conversions and transformations.

www.ocw.mit.edu/index.htm

Physics information for high school students.

http://www.physicsclassroom.com/Class/newtlaws/

Concise information on Newtons Laws of Motion

www.howstuffworks.com/sewing-machine.htm

Details how sewing machines work by showing combined mechanisms


Linear Motion

Reciprocal/Reciprocating Motion

Rotary Motion

Piston

Bell-Crank

Rack-and-Pinion Mechanism

Gear

Chain

Crank

Inertia

Force

Newtons Three Laws of Motion

Questions:


2. Compare and contrast the three types of motion in the nomenclature above.

3. Identify at least four types of mechanisms. Describe their parts. Give at least one practical use for each.

4. Construct examples to explain each of Newtons three laws of motion.



Computer with internet access

Robot Trainer

Stack of coins of varying denominations

6 similarly sized food cans (preferably closed)

Set of3-6various balls (ex. Tennis, ping pong, wiffle, dodgeball, baseball, basketball, etc)

Triple beam balance

1 L plastic soda bottle

Cork that fits plastic bottle

Vinegar

Aluminum foil

Baking soda

Graduated beaker/cylinder


Lab A: Newtons First Law

1. ()Bend your elbow with the palm of your hand facing the ceiling and your forearm parallel to the ground.

2. ()Take one coin and put it on your elbow.

3. ()Quickly straighten your arm and catch the coin.

4. ()Add a second, third, fourth, coin and repeat. Repeat with different coins of various sizes.

5. ()Have a team member watch the coins movement carefully.

6. ()Reverse roles and repeat.

7. ()Describe the movement of the coins. Were some easier to do than others? Why do you think this? How does this represent Newtons First Law? Give another example of Newtons First Law.

Lab B: Newtons Second Law

Safety Note: Be sure cans cannot fall on peoples toes.

1. ()Find the mass of each of the balls to be used.

2. ()Stack the cans of food in a pyramid.

3. ()Gently toss on ball at the cans and measure how far the farthest can moved from its original position.

4. ()Reset the cans and repeat with other balls. Measure the distance the farthest can travels. Record your results in a table.

Note: It is IMPERATIVE that EACH ball be thrown in exactly the same fashion with the same amount of force.

5. ()Describe the difference in each toss. What is the variable in this experiment that caused the results to vary? Give another example of Newtons Second Law.

Lab C: Newtons Third Law (best do do this on a hard surface outside)

Safety Note: Be sure the cork is not pointing toward anyone.

1. ()Pour 100 ml of vinegar into the bottle. Put the cork into the bottle

2. ()Make a small funnel shaped envelope out of foil.

3. ()Put 1-2 tablespoons of baking soda in the foil.

4. ()Carefully and quickly place baking soda pouch into the bottle. Do not agitate the bottle so the two dont mix.

5. ()Replace the cork.

6. ()Lay bottle on its side and quickly spin the bottle so the ingredients mix.

7. ()Observe the movement of both the bottle and the cork.

8. ()How does each of these elements (bottle and cork) represent NewtonsThird Law? Give another example of Newtons Third Law.

Lab D: Motion and Mechanisms

1. ()Go to http://www.flying-pig.co.uk/mechanisms/pages/bellcrank.html. Look at each of the mechanisms identified. Using your robot trainer, build each of the mechanisms to observe the movements. How does each of these mechanisms represent Newtons Laws? Prepare a chart similar to the one at the end of this activity in your engineering journal or notebook.

2. ()Construct a sewing machine according to the pictures on the How Stuff Works website.

Lab D:

Mechanism

Parts

Motion conversion

Practical Use

Conclusion: Now werent those moving experiences? Newtons Laws are the basics on which the principles of motion stand. Mechanisms are made of individual pieces that work together demonstrating Newtons Laws. These mechanisms exhibit the various forms of motion to make machines useful in our everyday lives. Can you develop of a machine that uses several of these mechanisms on this list? What mechanisms would it included and what does it do?



Exercise 10 Centrifugal Force and Motion





6.


The Math:

Terms -

Equations -

Application


Web Site

Description


Vocabulary Words

Questions:


2. Explain




1. ()

2. ()




Exercise 11 Steering Mechanisms





3.


The Math:

Terms -

Equations -

Application


Web Site

Description


Vocabulary Words

Questions:


2. Explain




1. ()

2. ()




Exercise 12 Compound Machines





3.


The Math:

Terms -

Equations -

Application


Web Site

Description


Vocabulary Words

Questions:


2. Explain




1. ()

2. ()




Exercise 13 Forms of Energy

Objective: At the completion of this exercise, you will demonstrate the properties of potential and kinetic energy by building and launching model trebuchet made from materials found in your robot trainers and rubber bands. At the completion of this exercise, you will demonstrate the properties of potential and kinetic energy by building and launching model catapults made from materials found in your robot trainers and rubber bands.




3.

Information: In olden days, catapults/trebuchets were used as weapons in the defense of a kingdom or castle. Large rocks or other objects were hurled at an approaching enemy. The various types of catapults all share common characteristics. There must be a solid base on which to stand the catapult and a moveable arm with receptacle attached to hold, load and hurl the projectile. The tension produced when the arm is pulled back will, along with the angle at which the projectile is launched, and weight of the projectile, determine the distance the projectile will travel. This is a clear example of the relationship between potential and kinetic energy.

In olden days, catapults were used as weapons in the defense of a kingdom or castle. Large rocks or other objects were hurled at an approaching enemy. The various types of catapults all share common characteristics. There must be a solid base on which to stand the catapult and a moveable arm with receptacle attached to hold, load and hurl the projectile. The tension produced when the arm is pulled back will, along with the angle at which the projectile is launched, and weight of the projectile, determine the distance the projectile will travel. This is a clear example of the relationship between potential and kinetic energy.

The Math:

Terms -

Equations -

Application


Web Site

Description

http://monsterguide.net/how-to-build-a-trebuchet

Website gives step by step process on how to build a trebuchet.

www.howstuffworks.com/transport/engines-equipment/question127.htm

Explains the different types of mechanical devices which function like catapults.


Potential Energy

Kinetic Energy

Projectile

Questions:


2. Explain the relationship between the catapult and trebuchet as to their kinetic and potential energy.

3. Discuss the factors that affect the distance a projectile travels from the catapult and trebuchet.

4. Which do you feel does the best job at sending a projectile? Why?

5. Explain the relationship between kinetic and potential energy.

6. Discuss the factors that affect the distance a projectile travels.



Materials from robot trainer, Rubber bands, Projectiles (Marshmallow, ping pong balls)


1. ()Construct model Trebuchet

2. ()Launch projectile. Plot data on paper (distance vs. trail)

3. ()Vary angle, tension, and load, re-launch.

4. ()Collect and report data that shows the comparison of distances traveled by projectiles.

5. ()Which does a better job catapult or trebuchet for launching projectiles from data collected.

6. ()Construct model catapult.

7. ()Launch projectile.

8. ()Vary angle, tension, and load, re-launch.

9. ()Collect and report data.

Conclusion: At the completion of this exercise, you will demonstrate the properties of potential and kinetic energy by building and launching models of both catapult and trebuchet. Can you think of a battle where you would use just a catapult? How about a trebuchet? In completing this exercise you will have a greater understanding of the relationship between potential and kinetic energy. Energy can never be created or destroyed, only changed from one form to another and the projectile initially contained more potential energy than kinetic energy as it was pulled back and when released, the potential energy was converted to kinetic energy as it moved across the space. Can you think of other examples of situations where potential energy is converted to kinetic energy?



Exercise 3 Resistance

Objective: At the completion of this exercise, you will demonstrate how friction can be measured to alter mechanical advantage and Students will demonstrate how to reduce friction and resistance when moving loads using simple machines. Using their robot trainer, they will construct various types of conveyor systems (rolling and belt) and then contrast and compare each machines operation. Finally, they will construct an aerial cableway and modify it so a load can be moved up a steep incline

Dragster racing friction or hook.




3.

Information: Friction is a very common (and sometimes troublesome) force. How does it work? What does the force of friction depend on? You will probably not be surprised to know that some aspects of the behavior of friction are quite surprising.

Lubricants:

The Math:

Terms -

Equations -

Application


Web Site

Description

http://www.foriauto.com

Click on Products Conveyors and Material Handling

http://tablemountain.net/about/the_table_mountain_aerial_cableway/

Table Mountains Aerial Cableway

http://www.bergbahn-heidelberg.de/englisch/index.html?haupt.html

Heidelberg, Germanys Funicular (Incline) Railway

http://www.cablecarmuseum.org/index.html

San Francisco Cable Car Museum


Friction

Resistance

Static friction

Rolling friction

Fluid friction

Load

Questions:


2. Explain how friction resistance is removed from a conveyor system?

3. What are the three types of friction?

4. Compare and contrast rolling and belt conveyors.



String For Cable Way

Lego Mindstorms NXT Kit

Tetrix Robotics Kit


1. ()Go to http://tablemountain.net/about/the_table_mountain_aerial_cableway/

2. ()Before you begin, write a plan for how to build an aerial cableway.

3. ()Put your plan into action.

4. ()Demonstrate to the class your simple aerial cableway. Show how you can move a load from one place to another. What is your limit?

5. ()Show a faster way to move your load along on the cableway.

Conclusion: In completing this exercise, you demonstr

Documents

· Web viewObjective: At the completion of this exercise, you will demonstrate the effects of mechanical advantage regarding the use of levers. …