### Summary

Students learn about gear ratios and power by operating toy mechanical cranes of differing gear ratios. They attempt to pick up objects with various masses to witness how much power must be applied to the system to oppose the force of gravity. They learn about the concept of gear ratio and practice calculating gear ratios on worksheets, discovering that smaller gear ratios are best for picking objects up quickly, and larger gear ratios make it easier to lift heavy objects.*This engineering curriculum meets Next Generation Science Standards (NGSS).*

### Engineering Connection

Gears are incorporated into almost all mechanical machines. From cars to cranes, different gear ratios provide ways to increase or decrease torque depending on the task at hand. Engineers figure out what torque is needed for each situation and the corresponding gear ratio for a fixed power.

### Pre-Req Knowledge

A familiarity with the mathematical operation of division, the concepts of speed and energy, and how to use measuring tools, such as rulers.

### Learning Objectives

After this activity, students should be able to:

- Measure gear diameters.
- Compute gear ratios used in a simple machine.
- Describe the characteristics of different gear ratios, including speed and torque.

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###
Educational Standards
Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

Each *TeachEngineering* lesson or activity is correlated to one or more K-12 science,
technology, engineering or math (STEM) educational standards.

All 100,000+ K-12 STEM standards covered in *TeachEngineering* are collected, maintained and packaged by the *Achievement Standards Network (ASN)*,
a project of *D2L* (www.achievementstandards.org).

In the ASN, standards are hierarchically structured: first by source; *e.g.*, by state; within source by type; *e.g.*, science or mathematics;
within type by subtype, then by grade, *etc*.

###### NGSS: Next Generation Science Standards - Science

- Make observations and/or measurements of an object's motion to provide evidence that a pattern can be used to predict future motion. (Grade 3) Details... View more aligned curriculum... Do you agree with this alignment?

###### Common Core State Standards - Math

- Multiply and divide within 100. (Grade 3) Details... View more aligned curriculum... Do you agree with this alignment?
- Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Use the four operations with whole numbers to solve problems. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?

###### International Technology and Engineering Educators Association - Technology

- Tools, materials, and skills are used to make things and carry out tasks. (Grades 3 - 5) Details... View more aligned curriculum... Do you agree with this alignment?

###### New York - Math

- Multiply and divide within 100. (Grade 3) Details... View more aligned curriculum... Do you agree with this alignment?
- Use the four operations with whole numbers to solve problems. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?
- Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. (Grade 4) Details... View more aligned curriculum... Do you agree with this alignment?

###### New York - Science

- Make observations and/or measurements of an object's motion to provide evidence that a pattern can be used to predict future motion. (Grade 3) Details... View more aligned curriculum... Do you agree with this alignment?

### Materials List

Each group needs:

- The Claw Worksheet, one per student

To share with the entire class:

- LEGO parts to make three cranes with differing gear ratios (See Figures 1 and 2)
- 9 objects with varying masses (for the cranes to lift)
- string
- 3 hooks

### Introduction/Motivation

Who has been to Chucky Cheese's or a fair? If you have been to an arcade, carnival or Chucky Cheese's, you know about the crane game! Picture that game with the big glass box that contains toys, stuffed animals, or loads of candy, and gives kids a chance to win any prizes they can grasp by maneuvering a metal claw.

Who has seen the movie "Toy Story?" That movie includes a similar toy called The Claw. The Claw is quite the mystical device to the Pizza Planet Aliens, but does anyone know how it works? (Listen to student ideas.)

The crane that picks up candy and other objects uses pulleys and gears. (Draw a diagram on the classroom board of two gears, and show how one can make the other rotate.) These simple machines enable an operator to use different amounts of power, depending on the rigging, to pick up an object. Imagine power as the amount of energy put in to crank the gears over a certain amount of time.

Today, we will experiment with small cranes that can pick up objects like those in "Toy Story" or an arcade! By using the cranes, we can find out how different set-ups of gears lift objects differently. Then, we will learn to calculate gear ratio, which is the ratio of diameters of the gears, and see which ratios work best for specific tasks. We can then see which set-up helps you lift objects the fastest or makes it the easiest to crank the gears!

### Vocabulary/Definitions

angular velocity: Rotational speed about a point.

crane: A machine for hoisting and moving heavy objects by means of cables.

diameter: A straight line passing through the center of a circle or sphere and meeting the circumference or surface at each end.

gear: A disc or wheel with machined teeth on the circumference that transfer force and movement when meshed with other gears.

gear ratio: The ratio of the diameters or teeth of any two meshing gears.

idler gear: Gear that transfers power between input and output gear.

input gear: Gear that is driven by the motor.

output gear: Gear that is driven by the input gear and does work.

power: Work done or energy transferred per unit of time.

speed: The rate at which position is changed.

torque: Applied force multiplied by a distance from a specific point.

work: An applied force multiplied by the distance an object moves in the same direction.

### Procedure

Background

Using three LEGO cranes with differing gear ratios, students pick up objects of different masses and make observations about speed and the amount of effort it takes to crank the gears. They learn about the concept of gear ratio and practice calculating gear ratios on worksheets. Students find out that smaller gear ratios are great for picking objects up quickly, and larger gear ratios can make it easier to lift heavy objects.

Before the Activity

- Build three basic LEGO cranes with differing gear ratios (see Figure 2). A simple design consists of two gears, with each gear containing an axle through its center. Have one gear have a spool connected to the axle, and the other gear have a handle that allows it to be turned easily. Placing the axles in the holes of the long LEGO channel pieces ensures a strong hold and easy means of rotation. Anchor the channels to a base structure. Make sure the base structure sits evenly on a surface and can provide stability. Consider using a turntable LEGO piece so that students can rotate the crane. If not enough pieces, make a handheld crane like a fishing rod. Crane designs can vary and need not be complicated. Use long channels jutting from the base as a guide for the string wrapped around the spool.
- Find three each of three different objects with differing masses that can be used to demonstrate a substantial change in power when picked up by a LEGO crane. For example, objects that are 3, 6 and 9 grams work well.
- Put one of each object at each crane station.
- Make copies of The Claw Worksheet, one per student.

With the Students

- Review the terms associated with gears (
**input**and**output gear**,**idler**, ratio). - Teach students
**how to compute gear ratio**: Establish input and output gear, measure diameter or number of teeth on each gear, compute ratio (output/input). - Explain the basic meaning of power in terms of torque and angular velocity:
**power = torque x angular velocity**. - Review other background information with students. Make sure students understand the
**diameter**of the circle to be a straight line passing through the center of the circle between two points on the circle or d = c/π, where, c, is the circumference. Make sure they understand the concept of a**ratio**, meaning a comparison of the magnitude of quantities relative to one another. Also make sure students are familiar with the concept of**power**and its relation to**work**, P = W/t, where t is time and W is work. - Have students practice drawing circles and measuring their diameters.
- Direct students to draw a circle and then cut a piece (one-fourth) out of it. This gives them a sense of the ratio of the piece they just cut out compared to the entire circle. Show them that the piece they cut out can be seen as another circle, so they see that the ratio still pertains to two circles.
- Direct students to complete the worksheets to practice what they learned so far.
- Draw two gears with differing diameters interlocked by teeth.
- Explain that if one gear is turned, the other gear turns as a result.
- Explain the set-up of the cranes (handle connected to one gear, another gear connected to a spool that changes the size of the rope hanging off the crane).
- Divide the class into three groups, assigning each to one of the three crane stations.
- Allow enough time for students in each group to pick up the three objects at their station with the crane.
- Have students write down observations about lifting masses with the crane. Was there a difference in speed when lifting the various masses? How much effort did it take to crank the gears?
- Have groups rotate to another crane station and pick up the three objects at that station.
- Have students write down observations about lifting masses with the second crane.
- Have groups rotate to the third crane station and again pick up the three objects.
- Have students write down observations about lifting masses with the third crane.
- After students finish documenting their observations, instruct them to measure the gear diameters.
- As a class, compute gear ratios for the three cranes.
- Using student observations, come up with a class list of characteristics for each gear ratio (speed, energy used to turn gear).

### Attachments

### Safety Issues

- Do not let youngsters put crane pieces in their mouths.
- Remind students not to swing the crane arm excessively, as it could injure surrounding students.

### Assessment

Pre-Activity Assessment

*Discussing Terms:* Ask students to tell you what they know about gears and gear ratios. Listen to their answers to gauge their familiarity with the terms.

Activity Embedded Assessment

*Worksheet:* Have students complete the activity worksheet; check their answers to gauge their levels of understanding.

*Evaluating Observations: *Circulate the classroom while students are working and look at the observations they made about the various cranes.

Post-Activity Assessment

*Concept Understanding:* At activity end, ask the students:

- Give students real-life situations in which they would need to choose a specific gear ratio. Ask them what gear ratio they would choose and why. What could happen if they used another ratio?
- If I want to pick something up fast, what gear ratio do I use? (Answer: Gear ratio smaller than 1:1, such as 1:2.)
- If I want to pick something up easily, what gear ratio do I use? (Answer: Gear ratio larger than 1:1, such as 2:1.)
- Can I have a lot of speed and torque when using a gear ratio? (Answer: No. A gear ratio increases torque and decreases speed at the same time and vise versa, but never both.)

### Contributors

Zachary Nishino; Marissa H. Forbes### Copyright

© 2013 by Regents of the University of Colorado; original © 2012 Polytechnic Institute of New York University### Supporting Program

AMPS GK-12 Program, Polytechnic Institute of New York University### Acknowledgements

This activity was developed by the Applying Mechatronics to Promote Science (AMPS) Program funded by National Science Foundation GK-12 grant no. 0741714. However, these contents do not necessarily represent the policies of the NSF, and you should not assume endorsement by the federal government.

Additional support was provided by the Central Brooklyn STEM Initiative (CBSI), funded by six philanthropic organizations.

Last modified: February 9, 2018

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