A7esigning Gear Machines GD MAT H - Frey Scientific€¦ · y Whiteboard Resources y Animation: Engineering Cycle y Science Content Video: Simple and Complex Machines y Student Reading:

A7INVESTIGATION

A7 Designing Gear MachinesKey Question: How can you design machines with different gear ratios?

y 2 aluminum spacers

y 2 threaded knobs

y 2 sheets of cardstock*

y 4 meters of masking tape*

y Scissors*

y Ping pong ball**provided by the teacher

Online ResourcesAvailable at curiosityplace.com

y Equipment Video: Gears

y Skill and Practice Sheets

y Whiteboard Resources

y Animation: Engineering Cycle

y Science Content Video: Simple and Complex Machines

y Student Reading: Mechanical Advantage

Vocabularyconstraints – design limitations such as cost, time, size, and materials

criteria – the standards a product or process must meet in order to be successful

engineering cycle – a process used by designers and engineers to develop solutions

prototype – a model used by engineers to test possible design solutions

In this investigation, students use the skills they have learned to design gear machines. They begin with a simple number theory exercise to determine which gear ratios are possible using the CPO gears. Next, they design their own gear machines using mathematic principles. Finally, they build and test their own gear machines.

Learning Goals ✔Use number theory to determine which gear ratios are possible using CPO gears.

✔Design and test a compound gear machine.

✔Use the engineering cycle to design a ping pong ball launcher using CPO gears.

GETTING STARTED

Time 100-150 minutes

Setup and Materials1. Make copies of investigation sheets for students.

2. Watch the equipment video.

3. Review all safety procedures with students.

Materials for each group

y Physics stand*

y Gears set

y 2 short thumbscrews

y 2 long thumbscrews

NGSS Connection This investigation builds conceptual understanding and skills for the following performance expectation.

MS-ETS1-2. Evaluate competing design solutions using a systematic process to determine how well they meet the criteria and constraints of the problem.

Science and Engineering Practices Disciplinary Core Ideas Crosscutting Concepts

Engaging in Argument from Evidence ETS1.B: Developing Possible Solutions Systems and System Models

TECH

NOLO

GY

ENGINEERING

MATH

SCIENCE

Simple Machines 45

DESigning gEAr MAchinES

BACKGROUND

Engineers use science, math, and technology to solve problems. Some solutions result in new products, such as more fuel-efficient cars. Other solutions may be processes, such as recycling compost so that it can be used to make biomass fuels. In each case, engineers employ a range of methods and practices to reach their solutions.

The engineering cycle summarizes these practices for students by breaking the design process into steps. The cycle helps students to identify and explain their background knowledge, to identify criteria and constraints, to explore and plan for testing activities, and to plan communication of results.

Com

mun

icate R

esearch Specify

Ref ine Prototype S

olut i

ons

Requirements

Test and B

rain

stor

m

IDENTIFYA NEED

IDENTIFYA NEED

The Engineering Cycle

Identify a Need is the triggering component of the cycle. This phase asks students to state the main problem that needs to be solved or process that needs to be improved.

Research involves organizing background knowledge that is useful in solving the problem. It can include the process of acquiring additional information through web searches, interviews with experts, etc.

Criteria, constraints, and trade-offs are all part of Specify Requirements. Criteria are the standards a successful product or process must meet. Student should be encouraged to break down the design goals into objectives that can be measured and achieved. Next, the student should list constraints to the design process. Constraints are limitations such as time, cost, availability of materials, and size of product. When considering limits on time and resources, students should identify strategic trade-offs.

The remaining steps of the engineering cycle involve creation, construction, and testing of the design. In Brainstorm Solutions, students think about designs and share their ideas with their groups. Sometimes a group may describe several possible designs and select design features to merge into a single prototype. In other cases, the group may choose the design they believe is most likely to meet the criteria. Once a design is chosen, it is assembled in the Prototype phase and then tested in Test and Refine. Often students move back and forth between these phases of the engineering cycle as design features are tested, evaluated, and improved. Finally, students share their ideas with an audience during the Communicate phase.

46

A75E LESSON PLAN

EngageType “rotary egg beater” into an internet search engine or shopping site. You will find photos of a wide variety of egg beaters, from inexpensive models with plastic gears to high-quality, ergonomically designed stainless steel models. Show photos of two different designs to the class. Ask them to think about the process that went into designing each one. Which one is probably the least expensive? Can students identify possible criteria/constraints that the designer of each tool may have been working with? For whom would each tool be the best choice?

This investigation will give students an opportunity to practice designing their own gear machines. They will figure out which gear ratios are possible within the constraints of the available gear sizes, and then choose to build one of the possible designs.

ExploreHave students complete Investigation A7, Designing Gear Machines. In this investigation, students use the skills they have learned to design gear machines. They begin with a simple number theory exercise to determine which gear ratios are possible using the CPO gears. Next, they design their own gear machines using mathematical principles. Finally, they build and test their own gear machine that will launch a ping pong ball.

ExplainRevisit the Key Question to give students an opportunity to reflect on their learning experience and verbalize understandings about the science concepts explored in the investigation. Curiosityplace.com resources, including student readings, videos, animations, and whiteboard resources, as well as readings from your current science textbook, are other tools to facilitate student communication about new ideas.

Science Content Video Simple and Complex

Machines

Animation Engineering Cycle

ElaborateInvite several different types of engineers to speak to your classes in a round-table discussion format. Some interesting fields include electrical, mechanical, aerospace, civil, chemical, and biomedical engineering. Ask each to explain how they use the engineering process in their work. What do they enjoy most about their work? What are some of the challenging constraints of their current project? Can they describe a significant design change they have made to a project? How is teamwork important in their field?

Evaluate y During the investigation, use the checkpoint

questions as opportunities for ongoing assessment.

y After completing the investigation, have students answer the assessment questions on the Evaluate student sheet to check understanding of the concepts presented.

Simple Machines 47


A7 Designing Gear MachinesSimple Machines

Copyright © CPO ScienceCan be duplicated for classroom use

A7 Explore INVESTIGATION

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A7 Designing Gear MachinesHow can you design machines with different gear ratios?

How many different gear ratios can you make from gears with 36, 24, and 12 teeth? In this investigation, you will determine the possible gear ratios and then, using the engineering cycle, design and build a gear machine with a ratio of your choosing. You’ll use what you learned from this process to design your own ping pong ball launcher.

Which gear ratios can you make?

The three gears have numbers of teeth in the ratio of 36:24:12. Because all the numbers in the ratio are divisible by 12, this ratio can be reduced to 3:2:1. This means that you can only build gear machines with ratios that are multiples of the numbers 1, 2, and 3.

a. How many numbers between 1 and 20 can you make by multiplying the numbers 1, 2, and 3 together? You can use the same number more than once. The group of numbers that make up your answer is an example of a set. A set is a group of numbers that are all related. For example, the number 8 belongs to this set because 8 = 2 × 2 × 2. Find all of the numbers between 1 and 20 that are included in this set and write them below.

The set of numbers that can be used to create ratios for CPO gears includes:

1 2 3 4 6 8 9 12 16 18

Materials: ✔ Physics stand

✔ Gears set

✔ 2 short thumbscrews

✔ 2 long thumbscrews

✔ 2 aluminum spacers

✔ 2 threaded knobs

✔ 2 sheets of cardstock

✔ 4 meters of masking tape

✔ Scissors

✔ Ping pong ball

Name ____________________________________________ Date ________________________

SCIENCE AND MATH

Prime factorization In order to determine which gear ratios are possible using a certain set of gears, students need to be able to determine the prime factorization of the number of teeth in each gear. Students may benefit from a quick review of prime factorization. Here is a simple review exercise:

To find the prime factorization of a number, try the “birthday cake” method.

1. Write the starting number as the first layer of your cake:

42

7 42

7 426

3 6

2 21

Prime factorization = 7×3×2

2. To the left of the first layer, write a prime number that will divide evenly into the starting number.

42

7 42

7 426

3 6

2 21


3. Divide and write your answer as the second layer of the cake.

42

7 42

7 426

3 6

2 21


4. To the left of the second layer, write a prime number that will divide evenly into this number.

42

7 42

7 426

3 6

2 21


42

7 42

7 426

3 6

2 21


5. Divide. Repeat until you get the number 1 at the top. Think of the 1 as a “birthday candle” and celebrate that you’re done! The prime factors are the numbers listed to the left of your cake.

42

7 42

7 426

3 6

2 21


42

7 42

7 426

3 6

2 21


42

7 42

7 426

3 6

2 21


Which gear ratios can you make? Some groups may come to a point where they have filled some, but not all, of the ten boxes for multiples of 1, 2, and 3 and then say that they can’t think of any others. At that point, encourage them to take a systematic approach: Consider each whole number from 1-20 in order. Ask yourselves, “Can I multiply some combination of 1, 2, and/or 3 to make this whole number?” If so, add it to your table. If not, move on to the next whole number.

Guiding the INVESTIGATION

42

7 42

7 426

3 6

2 21


48

A7




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Each of these numbers can be part of a gear ratio for a machine that you can build using the gears. Pick one number from the set for the numerator (top number) and another for the denominator (bottom number) of a gear ratio. Express the gear ratio as a fraction and a number (divide the numerator by the denominator).

Example :

Gear ratio = 34⎧⎨⎩

⎫⎬⎭

= 0.75

fraction number

Design and build your own gear machine

In the last investigation, you learned to build a compound gear machine by stacking gears on top of each other and using multiple axles. You also learned to calculate the gear ratio of the machine by multiplying the gear ratios of the pairs of gears that mesh.

Now, try designing and building your own gear machine with gear ratios that contain any combination of the numbers from your set in Part 1. You may need to combine with other groups in the class to get enough gears to build the machines you design. If possible, each group in the class should choose a different gear ratio to build.

Use the chart on the next page to create your design. Try using the fewest pairs of gears to get the final gear ratio.

a. Use the numbers from your set in Part 1 to choose a gear ratio that only your group will build.

Gear ratio =⎧⎨⎩

⎫⎬⎭

=

fraction number

Sample answer: Gear ratio = 18/1 = 18




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b. Use the table below to record your design. Each axle can have a gear in the inner position and/or the outer position. Use the table to write down the number of teeth in the gear you have in each position. You can also use the spacers in places where you do not wish to use gears. Put an X in the spaces where there are no gears. Circle the pairs of gears that mesh.

Sample data table:

Table 1: Your gear machine

AxleInner position

X or number of teeth

Outer position

X or number of teeth

1 36 X

2 12 36

3 24 12

4 12 X

5

6

Note: In this sample setup, the 24-tooth gear at the third axle goes under

the 36-tooth gear at the second axle. The 24-tooth gear does not mesh with the 12-tooth gear on the second axle in this arrangement.

c. Each place where gears mesh defines a gear ratio. Use the space below to write down the gear ratios in your machine as fractions. Multiply the ratios to calculate the total gear ratio. This number should be equal to the gear ratio in step a.

d. Build your machine and test it. Did the machine have the same gear ratio as the design?

Yes, our machine had a gear ratio of 18:1, just like our design.

3

1×3

1×2

1=18

1

SCIENCE AND TECHNOLOGY

In this investigation, students move from a scientific activity (learning how gears work) to a technology-focused activity (using gears to accomplish a task). This is a good time to discuss the differences between science and technology.

Science is the process of building knowledge about the physical world through observation and experimentation. Technology is the application of science to solve problems or accomplish useful tasks. Technology includes all of the inventions and techniques humans have developed over the years, such as cars, microwave ovens, and smartphones. It also includes processes such as laparoscopic surgery for gall bladder removal, which uses a much smaller incision and has a faster recovery rate than traditional open surgery.

To guide students in distinguishing between science and technology, read aloud each statement below. Have students tell whether it is a description of science or technology.

1. The teacher displayed pictures of types of plant life commonly found in tropical rainforests. (science)

2. The new building is in an area prone to hurricanes. Therefore it was constructed to withstand wind speeds of up to 250 kilometers per hour. (technology)

3. The president of the company was excited about new manufacturing methods that increased production from 30 widgets per hour to 75 widgets per hour. (technology)

4. A student observed that a steel nail placed in a jar of water began to rust after six days. (science)

Simple Machines 49





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b. Now, Specify the Design Requirements for your launcher. First, list the criteria. These are the standards a product must meet in order to be successful. As a class, brainstorm the criteria by which you will evaluate the launcher. Write your criteria here.

Sample answer: The launcher should enable the ping pong ball to travel the greatest horizontal distance, measured from the outermost point of the launch device to the spot where the ball first hits the floor.

c. Next, list the constraints. These are limits to your design such as cost, time, size, and materials. Brainstorm the list with your entire class, so that each team is working under the same constraints.

Sample answer: Some part of the physics stand must touch the floor. Only one gears kit may be used. A maximum of 4 meters of masking tape and 2 sheets of 8.5 x 11 inch cardstock may be incorporated into the design. Human power may be used only to turnthe input gear.

d. Brainstorm Solutions: With your group, discuss design possibilities for your launcher. Select the best possible design and sketch it in the space below.

Answers will vary.

e. Build your prototype (a model used to test possible design solutions) based on your selected design.

f. Test and Refine your design. Use the engineering design log provided by your teacher to record changes. You may go through this step many times until you determine that you have arrived at the best possible design to launch the ping pong ball. See 3f sample data table.

g. Communicate: Prepare a presentation for the class that documents your procedures and results.




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Design and build a ping pong ball launcher

You and your group will use a process called the engineering cycle to design and build a ping pong ball launcher. The engineering cycle will guide you through the problem-solving process. The steps of the engineering cycle are shown in the diagram below.

Com

mun

icate Research Specify

Requirements

Test and Bra

inst

orm

IDENTIFYA

NEED

Present yourresults to others.

Test your prototype, collectdata, identify problems, and

consider trade-o�s.Repeat this step until you

have the best possible design.

Develop a problem statement.

Find information about existing solutions and identifyimportant characteristics your solution must possess.

Identify criteria and constraints. Make a list of

design requirements.

Brainstorm solutionsand select the bestpossible solution.

Create a working modelthat can be tested.

The Engineering Cycle

Your first step, Identify a Need, asks you to develop a problem statement that will help you stay focused on the goal. In this case, your problem statement has been defined for you:

Using one physics stand, one gears kit, four meters of masking tape, and two sheets of cardstock, develop a ping pong ball launcher that enables the ball to travel the greatest horizontal distance before hitting the floor.

a. Your first task as a team is Research. Rather than looking up a topic on the internet, take a look at the gear machines around the classroom. Each one has a different gear ratio. Turn the input gear on each one. Observe the output gear. Use this information to choose a gear ratio for your launcher. Please note that you may be limited to one gears kit. Which gear ratio will you use? Give a reason for your answer.

Sample answer: We will use a 6:1 ratio in order to get the highest possible output speed with one kit.

Design and build a ping pong ball launcher

In question d., students reach the Brainstorm Solutions phase. Depending on what works best with your class, you may wish to ask students to create individual designs and then choose the best one by a vote. Alternatively, you can ask students to present their designs to their group and then have the group identify the most useful parts of each design and synthesize these parts into a single prototype. The second approach requires more complex thinking than the first approach, but it may result in a stronger initial prototype. Additionally, it requires students to practice interpersonal skills and to be able to listen and respond to feedback.

Guiding the INVESTIGATION TEACHING TIP

Use the Engineering Design Log found at the back of this Teacher’s Guide to help your students record their design process. Investigation A7 may be conducted over as many as three 50-minute class periods. Students will be better able to review

their progress and break down the investigation into manageable parts by referring to a graphic organizer. Show students a sample filled-in Engineering Design Log or complete some of the initial design steps as a class in order to demonstrate how to use the log.

Engineering Design Log


Engineering Design Log

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Why Keep an Engineering Design Log?People who are trying to meet a need or solve a problem often follow an approach called the engineering cycle. The engineering cycle divides the design process into a series of stages that can be repeated as needed. Engineers often use a design log to keep track of their work. As you develop your own designs, keep a log to describe your ideas, gather information, ask questions, sketch plans, record results, and share fi ndings. Your log should include the following stages:

1. Identify a NeedWhat problem are you trying to solve? What process are you trying to improve?

2. ResearchPart of research is identifying what you know about a topic or closely related topics that may help you to design your solution. Then you may think about any additional information you need to gather and where you can fi nd that information. What do you know about this topic? What additional information do you need?

3. Specify Requirements The requirements of a design process include criteria, constraints, and trade-offs. Criteria are the standards a product or process must meet in order to be successful. Constraints are rules that limit the design of your product and include cost, availability of materials, and time. A trade-off is a compromise that exchanges one idea with another that may not be as good but still achieves the design requirements. For this design challenge, what are the design criteria and constraints? Can you identify any trade-offs at this stage? (Trade-offs often become more apparent during subsequent stages of the design process.)

4. Brainstorm SolutionsDescribe the different ways you could solve the problem. Which solution should you explore fi rst? Can you make a plan or blueprint of your solution?

5. Prototype Now that you have chosen a solution, build your prototype. At this stage, you may need to gather some materials and/or tools. Did you learn something new as you constructed your prototype?

6. Test and RefineHow will you test your design and what data will you record? Once you have your prototype and other materials set up and you are ready to record your observations, conduct your tests. Construct a data table to record and analyze your data. Considering the results of your tests, what improvements should you make to your design?

7. CommunicateScientists and engineers share their ideas within communities so that others may benefi t from their work and review their conclusions. How will you share your design with others? What suggestions do others have for your design?

8. Reflect and ReviseThe design process does not have to end when the results are communicated. What new information could you fi nd that would help your design? Is there another type of test you could perform on your design, or an idea you weren’t able to investigate in the fi rst round of the process? Review your notes and refl ect on these questions.

50

A73f sample data table

Trial Distance traveled by ping pong ball (meters) Design change made

1 0.36

Our first design uses a 6:1 gear ratio. We made a small 3-sided box with loose flaps to hold the ping pong ball. We thought centrifugal force would fling the ball out of the launcher box but the ball didn’t travel very far. The physics stand is laying on its side with a threaded knob used to prop up the pole so that the gears are horizontal. We used tape to hold it in place but it was still wobbly.

2 0.85

We changed to a T-ball approach. We dismantled our first design. We made a small bat that we taped to the output gear’s peg. We made a stand for the ball. When you turn the input gear, the bat swings around and knocks the ball off of the stand. We need to find a better way to attach the bat because it gets loose every time it hits the ball.

3 1.12

We cut a notch in the bottom of the bat so that we could slide the bat over the peg on the output gear. Then we taped the bat down again. We also adjusted the location of the ball’s stand so that the bat would hit the center of the ball.

batping pong ball

3-sided box

ping pong ball

bat on peg

Simple Machines 51


TEACHING TIP

Rationales for Evaluate answers Question 2: Choice B is correct because the 20- and 10-tooth gears can be combined to produce a gear ratio of 2:1 or 1:2. The 40- and 20-tooth gears can be combined to produce a 2:1 or 1:2 ratio as well. The 40 and 10-tooth gears can be combined to produce a ratio of 4:1 or 1:4.

It is only possible to combine these three gears into sets that form multiples of 2 or 1/2. Any other numbers require additional gears not included in the set.

Choice A is incorrect because the ratio 2:3 is not possible.

Choice C is incorrect because its ratios are made using 12, 24, and 36-tooth gears (those found in the CPO set). Students who choose this answer may not understand the significance of the numbers of teeth on a gear, or they may have difficulty applying the rules about gears to new situations.

Choice D uses the numbers of teeth in the gears, but only the 40/20 ratio is possible. A one-tooth gear would be required to create the ratios with the number 1 in the denominator.



Name ____________________________________________ Date ________________________

Evaluate INVESTIGATION A7

1. You have a kit that contains many gears with 12, 24, and 36 teeth.

a. Can you make a gear ratio of 8:3? Why or why not?

You can make an 8:3 gear ratio with these gears. Given these gears, combinations of 2:1, 1:2, 3:1, 1:3, 3:2, and 2:3 are available. Since the prime factors of 8 are 2 × 2 × 2, you can use a 2:1 followed by a 2:1 followed by a 2:3 to make an 8:3.

b. Can you make a gear ratio of 60:1? Why or why not?

You cannot make a 60:1 gear ratio with these gears. The prime factors of 60 are 5 × 3 × 2 × 2. You need at least one additional gear with a 5:1 ratio to one of the other gears (or a combination of other gears). For example, a 60-tooth gear combined with a 12-tooth gear would give a 5:1 ratio. Similarly, a 20-tooth gear combined with a 12-tooth gear would give a 5:3 ratio, which could be followed by a 3:1 combination to produce the required 5:1 ratio.

2. Challenge! You have a collection of gears with 10, 20, and 40 teeth. Using only these gears, which one of the following sets of gear ratios is possible?

A. 14

, 11

, 23

, 41

, 161

B. 18

, 12

, 21

, 41

, 161

C. 1224

, 1236

, 2412

, 3624

, 3612

D. 110

, 101

, 201

, 401

, 4020

B is the correct answer.

WRAPPING UP

Have your students reflect on what they learned from the investigation by answering the following questions:

1. You have a set of three gears: A 24-tooth gear, a 36-tooth gear, and a 48-tooth gear. Can you build a gear machine with a 5:1 gear ratio? If so, how? If not, why not?

2. You have one set of CPO gears, which includes one 36-tooth gear, one 24-tooth gear, and two 12-tooth gears. What is the lowest gear ratio you can make?




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Answers will vary. Presentations should include descriptions of the group’s design process and results. At the end of the presentation, the group should demonstrate their launcher for the class.

Extending your knowledge

a. How did your final design compare with other designs in your class? What are the similarities and differences?

Answers will vary.

b. Using what you learned from the presentations, describe one further change you could make to improve your design.

Answers will vary.

52

A7esigning Gear Machines GD MAT H - Frey Scientific€¦ · y Whiteboard Resources y Animation: Engineering Cycle y Science Content Video: Simple and Complex Machines y Student Reading:

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