Abstract

VideoPointä is a video analysis software package for both Macintoshä and Windowsä based computers that allows one to collect position and time data from digital video images in the form of "video points". This User’s Guide describes a VideoPointä project that investigates how a bicycle’s speed depends on the pedaling gear. The gear ratio dictates how much power a cyclist can transmit to the rear wheel of a bike. This project utilizes two different methods to measure gear ratios. The first method determines the gear ratio by simply counting the number of teeth on the driver and driven gears. The second method determines the gear ratio by using VideoPointä to measure the angular velocities of the rear wheel and pedals. Preliminary analyses indicate that both methods yield consistent results. The extensive use of technological tools, computer software, and data analysis routines makes this project a viable activity for technical physics students. Movie files and VideoPointä files on the accompanying CD-ROM give the instructor the opportunity to present this activity as an interactive lecture demonstration.

^* The Two-Year College Physics Workshops for the 21^st Century Project is a collaborative effort of Joliet Junior College (Joliet, IL), Lee College (Baytown, TX), and the National Science Foundation. It is supported by NSF Grant #9950062 from the Division of Undergraduate Education of the Advanced Technological Education Program.

Abstract Cover

A. Instructional Notes 1

Motivation for this Activity 1

How this Activity Will Impact the Physics Curriculum 1

Materials Found in this User’s Guide 2

B. Description of VideoPointä Analysis of Bicycle Motion 3

C. Apple Video Player, QuickTimeä , Movie Player, & VideoPointä Software 4

D. Pre-Recorded Movies for 27 Bicycle Gear Ratio Combinations 5

Gear Ratio Combinations 5

 

3-Speed Front Chain Ring 5

9-Speed Rear Freewheel 5

Movie Files Ready for Student Analysis 6

VideoPointä Files (*.vpt) Ready for Instructor Use 7

E. Laboratory Activity: VideoPointä Analysis of Bicycle Motion 9

Purpose 9

Preliminary Exercises 9

Method 1: Determining Gear Ratios by Counting Gear Teeth 12

 

Supplies Needed 12

Procedure 12

Method 2: Determining Gear Ratios by Measuring Angular Velocities 13

 

Supplies Needed 13

Procedure 14

Analysis of Results 15

Project Reports 16

F. Guide to Video Capture, Movie Making, and Digital Video Analysis 17

Supplies Needed 17

Minimum Macintoshä Requirements 17

Minimum Windowsä Requirements 17

Equipment Setup 18

Video Capture with the Apple Video Player Software 20

Making and Editing Digital Movies with the Movie Player Software 23

An Introduction to Digital Video Analysis: The VideoPointä Software 24

Overview 24

An Introduction to VideoPointä Features 24

"video points" 25

Coordinate Systems 25

Scale Factors 26

Calculations Based on Video Points 26

Movies and VideoPointä Files 26

Fundamental Concepts of Uniform Circular Motion 27

Angular Measure 27

Angular Speed 27

Using VideoPointä to Determine the Angular Velocity w of a Rotating Object 28

Opening VideoPointä 28

The Movie Window 29

The Coordinate Systems Window 29

The Table Window 30

Playing the Movie 30

Scaling the Movie 31

Moving the Origin 32

Labeling the New Origin 33

Labeling the "video point" on the Moving Object 33

Taking Data: Using "video points" to Track the 2-D Motion of a Rotating Object 33

Graphing Data and Determining Angular Position 34

Fitting a Mathematical Function to the Data and Determining Angular Velocity 35

Relating the Graph to the Movie 35

Live Updating 36

Viewing the Data in a Table 36

Saving Your Work and Quitting VideoPointä 36

Additional VideoPointä Analyses 36

Using VideoPointä to Calculate the Gear Ratio 36

G. Sample Laboratory Activity: VideoPointä Analysis of Bicycle Motion 37

Sample Results: Front Gear = 44 Teeth, Rear Gear = 16 Teeth 37

Results from the 27 Pre-Recorded Bicycle Movies on the Accompanying CD-ROM 39

Motivation for this Activity

My knowledge and fascination with the bicycle stems from both a scientific and a recreational foundation. While attending graduate school at UCLA, I raced on the UCLA cycling team for three years. In 1992 I completed a 3300-mile cross-country bicycle ride from San Diego to Virginia Beach. I have also completed other long-distance bicycle treks from Washington, D.C. to Memphis and along the California coast.

Based upon my physics teaching experience, I have noticed that students have difficulties making the distinction between linear quantities that describe translational motion and the corresponding angular quantities used to characterize rotational motion. This observation holds true for all levels of physics students. As a group, technical physics students often find themselves in the workplace environment actively using and seeing physics more than their conceptual / algebra / calculus-based-physics peers. Consequently, technical physics students have different needs that can be met by the proper design and integration of hands-on instructional activities. This project addresses this need by using technological instructional tools to reinforce a student’s understanding and distinction between translational and rotational motion. A knowledge and appreciation for these facts is useful in an industrial workplace that utilizes rotating machinery, gears, pulleys, or other equipment that seeks to use the principles of mechanical advantage to increase efficiency, work output, or cost savings.

How this Activity Will Impact the Physics Curriculum

The teaching of physics, particularly technical and vocational physics, faces many challenges. These include the motivation of students, the lack of instructional materials which students see as relevant or connected to their common experiences, and the general belief that science seems too abstract to be of any use to the average individual in everyday life. This project aims to enrich the science and technology curricula by having students actively learn physics as they study the bicycle.

Most people, regardless of gender, geographical location, or economic level, have experienced the physical sensations associated with riding a bike. Riding a bike is an interactive experience between the rider and the machine. Studying the bike can also be an interactive activity between the student and the bicycle, too. Despite the steady encroachment of video game technology and virtual worlds into the lives of college students, the physical sensation of riding a bicycle continues to be a concrete experience that students bring into the classroom. The basic science and technology of the bicycle can be seen and understood by most students.

This project seeks to take advantage of this sensory awareness by engaging students in an inquiry-based approach to learning that will leave a lasting impression on their attitudes towards physics. My goal in designing this project has been to develop an activity that students can use to make the connections between the sensory experience of riding a bike, the physics that can be used to describe the motion, and the extensions of this exercise to the technical workplace. While performing this investigation, students use technological tools to measure, collect, manipulate, and predict physical quantities. As such, the bicycle offers the technical physics student the opportunity to study an inexpensive, familiar device that has the proper mix of simplicity and complexity.

This project requires students to develop a team approach to learning and problem solving, rather than merely acting as individuals doing a laboratory exercise. As students do this project, they are actively involved in the learning process as they work with fellow team members. Physics education research shows that students learn more by doing than by listening. The skills and knowledge acquired by active learners are more readily transferred to other problems in other areas. Project-based science helps make students active learners and involves them in problem-solving teams. By constructing their own experiments, collecting and analyzing data, and identifying relationships through hands-on activities, students are able to relate real-world phenomena to abstract physical laws. This type of thinking is important in today’s technical workplace where a multitude of physical variables often govern a complex process.

A long-range goal is to develop this project as a self-contained curricular unit that is amenable to a variety of levels of expertise and instructional styles. This project should be adaptable to the precise needs and interests of the entire range of students who are likely to work with it. The project lends itself not only to the study of the physics of the bicycle, but also to engineering, materials design, and biomechanical considerations. Students from a wide variety of technical disciplines can find something of interest in this bicycle project. Additionally, there exist a number of bicycle educational materials in print and video format that can further supplement student interests in the subject.

Materials Found in this User’s Guide

This User’s Guide consists of the following materials for both student and instructor use:

1.  
2. Section B describes the activity, providing the instructor with a methodology and suggestions on how to best implement this work in the physics classroom.

    

3. Section C briefly describes features of the Apple Video Player, QuickTimeä , Movie Player, and VideoPointä software packages. Students use these routines to make and edit their own digital movies, which are then analyzed to perform rotational motion studies.

    

4. Section D describes a series of pre-recorded movies that can be used to complete this activity, without requiring students to bring their bicycles to class or make their own movies. Two VideoPointä files accompany each movie, providing the instructor with video analysis results that can be used to benchmark measured angular velocities. These movie files and VideoPointä files (*.vpt) are included on the accompanying CD-ROM. Institutions that do not have video capture equipment can use these pre-recorded movies with the VideoPointä software to perform interactive lecture demonstrations.

    

5. Section E contains the laboratory activity that may be copied and used for student instruction.

    

6. Section F is a step-by-step guide to video capture, movie making, and digital video analysis.

    

7. Section G contains a sample laboratory activity that serves as an Instructor’s Resource. These lab results can be reproduced using movie files found on the accompanying CD-ROM.

In an effort to develop technical skills and increase the technological awareness of physics students, I developed the laboratory activity VideoPointä Analysis of Bicycle Motion. In this activity, students make the connections between the sensory experience of pedaling a bicycle, the physics used to describe the motion, and the extensions of this exercise to the technical workplace. While performing this investigation, students learn how to use technological tools (video capture equipment, data acquisition devices), computer software (Apple Video Player, QuickTimeä , Movie Player, VideoPointä ), and graphical analysis routines.

To begin this project, I divide the class into teams of three to four students. Student teams share hypotheses about how the role of gear selection influences the power transmission system used in the bicycle. They explore how their pedaling effort depends on the bicycle gear. The physics concepts of work, energy, and power; simple machines, mechanical advantage, and gear ratios; rotational motion and the correlation between linear and angular quantities are discussed and reviewed. Students are encouraged to look at factors in addition to the gear ratio that influence a cyclist’s ability to biomechanically transfer power to the rear wheel. Through a guided discussion, they learn that energy leaving the bicycle is proportional to the applied pedaling force and the distance the bicycle travels. The concept of the bicycle’s chosen gear ratio is discussed to demonstrate how the applied pedaling force and the distance the bicycle travels are correlated to one another.

For a hands-on application, student teams measure the gear ratio of the bicycle in two different manners. Students bring their own bicycles to perform this activity, which adds a bit of personal flair to their work. To broaden their database, each team is encouraged to select gear combinations that other teams are not investigating.

In the first measurement, students count the number of teeth on the selected front chain ring gear that the chain passes over, as well as the number of teeth on the chosen rear freewheel gear. From a physics standpoint, the front chain ring gear is the driver gear, while the rear freewheel gear is the driven gear. The gear ratio is determined by simply dividing the number of teeth on the front chain ring gear by the number of teeth on the rear freewheel gear.

In the second measurement, student teams use a video camera to record the rotational motion of the rear wheel and pedals of a stationary bicycle. The bicycle movie is then transferred to a computer, then edited to select the desired video footage. The VideoPointä software package is used next to analyze this rotational motion and measure the angular velocities of the rear wheel and pedals. The gear ratio is then calculated by dividing the angular velocity of the rear wheel by the angular velocity of the pedals.

To assess the accuracy of their VideoPointä results, teams compare their two gear ratio measurements by computing the percent error between the accepted gear ratio (from the first measurement) and the measured gear ratio (from the second measurement). Project reports are written which document the hypotheses, procedure, results, and analyses of each team. Discrepancies in the accepted versus measured gear ratio values are noted and explained, using the students’ current knowledge of physics, science, and technology.

This project utilizes two different methods to measure bicycle gear ratios. In the first measurement, students count the number of teeth on the selected front chain ring gear that the chain passes over, as well as the number of teeth on the chosen rear freewheel gear. The gear ratio is determined by simply dividing the number of teeth on the front chain ring gear by the number of teeth on the rear freewheel gear.

In the second measurement, the gear ratio is calculated by dividing the angular velocity of the rear wheel by the angular velocity of the pedals. To measure these angular velocities, students use a video camera to record the rotational motion of the rear wheel and pedals of a stationary bicycle. The bicycle movie is then transferred to a computer, then edited to select the desired video footage. The VideoPointä software package is then used to analyze this rotational motion and measure the angular velocities of the rear wheel and pedals.

If you have access to video capture equipment, I highly encourage you and your students to make your own bicycle movies and perform the resulting video analysis. Appleâ Macintoshä computer systems readily lend themselves to this very straightforward process and only require the use of the following four pieces of software:

· Apple Video Player

· QuickTimeä

· Movie Player

· VideoPointä

Windowsä based systems can also be used; however, the Laboratory Activity and the Guide to Video Capture, Movie Making, and Digital Video Analysis discussed in Sections E and F of this User’s Guide only describe detailed procedures for Macintoshä systems. Whatever system you use, your goal is to produce a short QuickTimeä movie that captures the rotational motion of the bicycle’s rear wheel and pedals. VideoPointä can open QuickTimeä movies made via both systems, thus enabling you to analyze the rotational motion and determine angular velocities.

On Macintoshä systems, the Apple Video Player software allows one to view and capture video camera images through the computer. To do this, one simply connects the video camera’s VIDEO OUT port to the computer’s VIDEO IN port, then plays the video camera images into the computer. Apple Video Player allows one to view the image the video camera is currently recording (or playing back) on the computer’s monitor. Apple Video Player allows one to record this video playback on the computer and save it as a QuickTimeä movie. The Movie Player routine is then used to edit this QuickTimeä movie, cutting out unwanted frames. The final result is a short (about 10 to 20 frames) QuickTimeä movie that only contains the relevant motion of interest.

To analyze the relevant motion, one opens the QuickTimeä movie in the VideoPointä software, then performs the resulting video analysis. This procedure is more fully described in the Guide to Video Capture, Movie Making, and Digital Video Analysis discussed in Section F.

Gear Ratio Combinations

Gear ratios are shown for a 2000 model year Cannondale F800 mountain bike. The bicycle has a 3-speed front chain ring and a 9-speed rear freewheel. This creates 27 different gear ratio combinations. The number of teeth in each gear is shown in the following charts:

 

3-Speed Front Chain Ring

 

Gear	# of Teeth, FG
1	44
2	32
3	22

9-Speed Rear Freewheel

Gear	# of Teeth, RG
1	32
2	28
3	24
4	21
5	18
6	16
7	14
8	12
9	11

The gear ratio is determined by dividing the number of teeth on the front chain ring gear (FG) by the number of teeth on the rear freewheel gear (RG). The 27 gear ratio combinations are:

FG = # of Teeth

in Front Chain RG = # of Teeth in Rear Freewheel Gear

Ring Gear

Movie Files Ready for Student Analysis

The accompanying CD-ROM contains 27 movies. Each movie highlights the rotational motion of the rear wheel and pedals of the Cannondale F800 mountain bike in one of its 27 possible gear combinations. Institutions that do not have video capture equipment can use these pre-recorded movies with VideoPointä to perform interactive lecture demonstrations. In this manner, students do not have to bring their bicycles to class or have to make their own movies.

Each movie has a title that is indicative of the bicycle’s gear ratio. For instance, if the bicycle chain is in the 44-teeth front chain ring gear (FG = 44) and the 16-teeth rear freewheel gear (RG = 16), then the gear ratio is FG/RG = 44/16 = 2.75. The CD-ROM file that contains this footage is called

FG 44, RG 16, Gear Ratio 2.75

The following chart contains a list of all the movie files available on the CD-ROM.

VideoPointä Files (*.vpt) Ready for Instructor Use

Using the movie files listed in the previous section, the VideoPointä software package has been used to analyze the rotational motion of the rear wheel and pedals of the Cannondale F800 mountain bike. Each movie file was analyzed twice: once to determine the angular velocity of the rear wheel (w _{Rear Wheel}), and once to determine the angular velocity of the pedals (w _Pedals). The gear ratio is calculated by dividing the angular velocity of the rear wheel by the angular velocity of the pedals; that is, Gear Ratio = (w _{Rear Wheel}) / (w _Pedals).

Two VideoPointä files accompany each movie file, providing the instructor with video analysis results that can be used to benchmark measured angular velocities. These VideoPointä files have the extension (*.vpt) and are included on the accompanying CD-ROM. Each VideoPointä file has a title that is indicative of the bicycle’s gear ratio and the rotating object of interest. For instance, if the bicycle chain is in the 44-teeth front chain ring gear (FG = 44) and the 16-teeth rear freewheel gear (RG = 16), and the motion of the rear wheel is desired, then the CD-ROM file that contains this analysis is called

FG 44, RG 16, Rear Wheel.vpt

If the motion of the pedals is desired, then the CD-ROM file that contains this analysis is called

FG 44, RG 16, Pedal.vpt

The following chart contains a list of all the VideoPointä files available on the CD-ROM.

FG	RG	Gear Ratio	VideoPointä File Name Rear Wheel Analysis	VideoPointä File Name Pedal Analysis
22	11	2.00	FG 22, RG 11, Rear Wheel.vpt	FG 22, RG 11, Pedal.vpt
22	12	1.83	FG 22, RG 12, Rear Wheel.vpt	FG 22, RG 12, Pedal.vpt
22	14	1.57	FG 22, RG 14, Rear Wheel.vpt	FG 22, RG 14, Pedal.vpt
22	16	1.38	FG 22, RG 16, Rear Wheel.vpt	FG 22, RG 16, Pedal.vpt
22	18	1.22	FG 22, RG 18, Rear Wheel.vpt	FG 22, RG 18, Pedal.vpt
22	21	1.05	FG 22, RG 21, Rear Wheel.vpt	FG 22, RG 21, Pedal.vpt
22	24	0.92	FG 22, RG 24, Rear Wheel.vpt	FG 22, RG 24, Pedal.vpt
22	28	0.79	FG 22, RG 28, Rear Wheel.vpt	FG 22, RG 28, Pedal.vpt
22	32	0.69	FG 22, RG 32, Rear Wheel.vpt	FG 22, RG 32, Pedal.vpt
32	11	2.91	FG 32, RG 11, Rear Wheel.vpt	FG 32, RG 11, Pedal.vpt
32	12	2.67	FG 32, RG 12, Rear Wheel.vpt	FG 32, RG 12, Pedal.vpt
32	14	2.29	FG 32, RG 14, Rear Wheel.vpt	FG 32, RG 14, Pedal.vpt
32	16	2.00	FG 32, RG 16, Rear Wheel.vpt	FG 32, RG 16, Pedal.vpt
32	18	1.78	FG 32, RG 18, Rear Wheel.vpt	FG 32, RG 18, Pedal.vpt
32	21	1.52	FG 32, RG 21, Rear Wheel.vpt	FG 32, RG 21, Pedal.vpt
32	24	1.33	FG 32, RG 24, Rear Wheel.vpt	FG 32, RG 24, Pedal.vpt
32	28	1.14	FG 32, RG 28, Rear Wheel.vpt	FG 32, RG 28, Pedal.vpt
32	32	1.00	FG 32, RG 32, Rear Wheel.vpt	FG 32, RG 32, Pedal.vpt
FG	RG	Gear Ratio	VideoPointä File Name Rear Wheel Analysis	VideoPointä File Name Pedal Analysis
44	11	4.00	FG 44, RG 11, Rear Wheel.vpt	FG 44, RG 11, Pedal.vpt
44	12	3.67	FG 44, RG 12, Rear Wheel.vpt	FG 44, RG 12, Pedal.vpt
44	14	3.14	FG 44, RG 14, Rear Wheel.vpt	FG 44, RG 14, Pedal.vpt
44	16	2.75	FG 44, RG 16, Rear Wheel.vpt	FG 44, RG 16, Pedal.vpt
44	18	2.44	FG 44, RG 18, Rear Wheel.vpt	FG 44, RG 18, Pedal.vpt
44	21	2.10	FG 44, RG 21, Rear Wheel.vpt	FG 44, RG 21, Pedal.vpt
44	24	1.83	FG 44, RG 24, Rear Wheel.vpt	FG 44, RG 24, Pedal.vpt
44	28	1.57	FG 44, RG 28, Rear Wheel.vpt	FG 44, RG 28, Pedal.vpt
44	32	1.38	FG 44, RG 32, Rear Wheel.vpt	FG 44, RG 32, Pedal.vpt

It should be noted that the 27 sets of movie files and VideoPointä files on the accompanying CD-ROM give the instructor the opportunity to present the entire VideoPointä Analysis of Bicycle Motion activity as an interactive lecture demonstration. The movie files themselves can be opened in VideoPointä and individually analyzed. Additionally, the previously analyzed VideoPointä files can serve as preliminary materials used to discuss and highlight the rotational characteristics of the bicycle’s rear wheel and pedals.

Purpose

The laboratory activity VideoPointä Analysis of Bicycle Motion has been designed to develop technical skills and increase the technological awareness of physics students. In this activity, you will make the connections between the sensory experience of pedaling a bicycle, the physics used to describe the motion, and the extensions of this exercise to the technical workplace. While performing this investigation, you will learn how to use technological tools (video capture equipment, data acquisition devices), computer software (Apple Video Player, QuickTimeä , Movie Player, VideoPointä ), and graphical analysis routines.

The purpose of this activity is to compare two different methods used to measure the gear ratio of a bicycle. The gear ratio dictates how much power a cyclist can transmit to the rear wheel of a bike and ultimately, the bicycle’s speed. This project utilizes two different methods to measure gear ratios. The first method determines the gear ratio by simply counting the number of teeth on the driver and driven gears. The second method determines the gear ratio by using VideoPointä to measure the angular velocities of the rear wheel and pedals. VideoPointä is a video analysis software package for both Macintoshä and Windowsä based computers that allows one to collect position and time data from digital video images in the form of "video points". Your final results will indicate how well the two gear ratio measurement methods agree.

Preliminary Exercises

Your instructor will lead a guided discussion through these Preliminary Exercises. Fill in the blanks where indicated. Take notes in the spaces provided as your instructor discusses concepts and topics important to this activity.

1.  
2. To begin this project, your instructor will divide your class into teams of three to four students. Write the names of your team members in the space below:

    

   ______________________________ ______________________________

    

   ______________________________ ______________________________

    

    

3. With your team members, discuss how the pedaling gear influences the power transmitted to a bicycle’s rear wheel. Discuss how one’s pedaling effort depends on the bicycle gear, and what impact this has on the bicycle’s speed.

    

    

    

    

    

    

   For items 3-8, your instructor will review the following physics concepts with your class, or may request that each team provide their own summaries in the spaces below:

    

    

4. Work, energy, and power

    

    

    

    

    

    

    

    

5. Simple machines

    

    

    

    

    

    

    

    

6. Mechanical advantage

    

    

    

    

    

    

    

    

7. Gear ratio

    

    

    

    

    

    

    

    

8. Rotational motion

    

    

    

    

    

    

9. Correlation between linear motion and angular rotation quantities

    

    

    

    

    

    

    

    

10. With the rest of your team members, discuss other factors in addition to the gear ratio that influence a cyclist’s ability to biomechanically transfer power to the rear wheel.

     

     

     

     

     

     

     

     

11. Your instructor will lead a guided discussion that demonstrates that the energy leaving a bicycle is proportional to the applied pedaling force and the distance the bicycle travels. The concept of the bicycle’s chosen gear ratio will be discussed to demonstrate how the applied pedaling force and the distance the bicycle travels are correlated to one another.

Method 1: Determining Gear Ratios by Counting Gear Teeth

In this first measurement method, you will determine the gear ratio of a bicycle by counting the number of teeth on a selected front chain ring gear that the chain passes over, as well as the number of teeth on a chosen rear freewheel gear. From a physics standpoint, the front chain ring gear is the driver gear, while the rear freewheel gear is the driven gear. The gear ratio is determined by dividing the number of teeth on the front chain ring gear (FG) by the number of teeth on the rear freewheel gear (RG):

Supplies Needed:

· Bicycle

· Calculator

Procedure:

1.  
2. Put the bicycle in a chosen gear.

    

    

3. Count the number of teeth in the Front chain ring Gear, FG. FG = __________

    

    

4. Count the number of teeth in the Rear freewheel Gear, RG. RG = __________

    

    

5. Calculate the Gear Ratio to two decimal places. Gear Ratio = FG/RG = __________

    

    

6. Repeat steps 1-4 for other gear selections. Put your results in the table below:

Method 2: Determining Gear Ratios by Measuring Angular Velocities

In this second measurement method, you will use a video camera to record the rotational motion of the rear wheel and pedals of a stationary bicycle. The bicycle movie is then transferred to a computer, then edited to select the desired video footage. The VideoPointä software package is used to analyze this rotational motion and measure the angular velocities of the rear wheel and pedals. The gear ratio is calculated by dividing the angular velocity of the rear wheel (w _{Rear Wheel}) by the angular velocity of the pedals (w _Pedals):

Supplies Needed:

· Solid color tablecloth or sheet, masking tape

· Bicycle

· Ruler

· Index cards, wide felt-tip marking pens

· Video Camera (with a blank videotape or cassette for storing digital movies)

· Tripod or other suitable stand, to support video camera

· Appleâ Macintoshä computer system

· Cable (to connect video camera’s VIDEO OUT port to the computer’s VIDEO IN port)

· Apple Video Player, QuickTimeä , and Movie Player software (used to make and edit digital movies with the Appleâ Macintoshä computer system)

 

· VideoPointä software (used to analyze the digital movies and measure the angular velocities of the rear wheel and pedals)

· Calculator

List other supplies needed for your specific laboratory conditions:

· ______________________________

· ______________________________

· ______________________________

· ______________________________

· ______________________________

Procedure: (Complete details of this procedure can be found in Section F)

1.  
2. Put the bicycle in a chosen gear.

    

    

3. Setup the video camera and record the rotational motion of the rear wheel and pedals. You only need to record two or three complete revolutions of the wheel and/or pedals.

    

    

4. Transfer the bicycle movie to the computer using the Apple Video Player software. Apple Video Player allows one to record this video playback on the computer and save it as a QuickTimeä movie.

    

    

5. Use the Movie Player routine to edit this QuickTimeä movie, cutting out unwanted frames. The final movie should be short (about 10 to 20 frames) that only contains the relevant motion of interest. Save your movie file with a meaningful name and perhaps a *.mov extension.

    

    

6. Use the VideoPointä software to open the QuickTimeä movie. Use VideoPointä to perform a digital video analysis of the rotational motion of the rear wheel. Determine the angular velocity of the rear wheel, (w _{Rear Wheel}).

   w _{Rear Wheel} = __________ rads/s

    

    

7. Once again, use the VideoPointä software to open the QuickTimeä movie. This time VideoPointä will be used to perform a digital video analysis of the rotational motion of the pedals. Determine the angular velocity of the pedals, (w _Pedals).

   w _Pedals = __________ rads/s

    

    

8. Calculate the Gear Ratio

   to two decimal places. Gear Ratio = w _{Rear Wheel} / w _Pedals = __________

    

    

9. Repeat steps 1-7 for other gear selections. Put your results in the table below:

Analysis of Results

To assess the accuracy of the two gear ratio measurement methods, you will compute the percent error between the accepted gear ratio (from Method 1: Counting Gear Teeth) and the measured gear ratio (from Method 2: Measuring Angular Velocities). The percent error is defined as

Noting that

(Accepted Gear Ratio) = (FG / RG)

(Measured Gear Ratio) = (w _{Rear Wheel} / w _Pedals)

then the Percent Error can be expressed as

Determine the Percent Error in your gear ratio measurements by completing the table below:

Selectn #		FG	RG	Accepted Gear Ratio, FG/RG		w Rear Wheel (rads/s)	w Pedals (rads/s)	Measured Gear Ratio, w Rear Wheel / w Pedals		Percent Error (%)
1
2
3
4
5
6
7
8
9
10

Project Reports

Each team will prepare a project report that documents their work. Discrepancies in the accepted versus measured gear ratio values should be noted and explained, using your current knowledge of physics, science, and technology. At a minimum, each report should contain the following sections:

· Background

· Purpose

· Hypotheses

· Procedure

· Results

· Analysis

· Conclusions

6.  
7.  

    

    

8. Guide to Video Capture, Movie Making, and Digital Video Analysis

This Section provides a step-by-step guide to video capture, movie making, and digital video analysis. For the first-time user, this information will serve as a prerequisite to the laboratory activity presented in Section E.

Supplies Needed

· Solid color tablecloth or sheet, masking tape

· Bicycle

· Ruler

· Index cards, wide felt-tip marking pens

· Video Camera (with a blank videotape or cassette for storing digital movies)

· Tripod or other suitable stand, to support video camera

· Appleâ Macintoshä computer system^*

· Cable (to connect video camera’s VIDEO OUT port to the computer’s VIDEO IN port)

· Apple Video Player, QuickTimeä , and Movie Player software (used to make and edit digital movies with the Appleâ Macintoshä computer system)

 

· VideoPointä software (used to analyze the digital movies and measure the angular velocities of the rear wheel and pedals)

· Calculator

^* The movie files and VideoPointä files on the accompanying CD-ROM were created on an Appleâ Power Macintoshä 5500 series computer system with a PowerPC 250 MHz processor. If you attempt this activity on a different system, note that VideoPointä requires the following:

Minimum Macintoshä Requirements for the VideoPointä Software

· Any Macintoshä capable of running QuickTimeä

· System 7.0 or later

· 2.5 MB of free RAM

· 3 MB of free storage space on the hard drive

· 13² or larger monitor recommended

· CD-ROM drive (for installation)

Minimum Windowsä Requirements for the VideoPointä Software

· Windows 3.1 or Windows95

· 8 MB of free RAM

· 3 MB of free storage space on the hard drive

· VGA monitor with 256 colors

· CD-ROM drive (for installation)

Equipment Setup

The following suggestions will help the user setup a bicycle, a video camera, and other relevant equipment so that high-quality movies can be produced for digital video analysis. On the accompanying CD-ROM, the movie file

Equipment Setup.mov

shows the setup used for the bicycle movies. Using this image as a guide, proceed as follows:

1.  
2. The key to making movies that are easy to analyze is the background. Simpler is better, and good contrast between object and background is important. The background should be a royal blue for recording light-colored objects or a plain light gray for the motion of dark-colored objects.

    

   Sometimes the external lighting can make a big improvement. Provide good lighting! This lighting needs to be diffuse enough to avoid specular reflections. Good halogen flood light sets with reflectors and stands are now available from video and photo equipment suppliers. With these facts in mind, find an area in your lab that is free of clutter and harsh lighting. Avoid getting too close to windows, and make sure the area is free of shadows and glare.

    

    

3. If you look at the movie file (Equipment Setup.mov) on the accompanying CD-ROM, you will notice that a video camera is mounted on a jack stand, ready to videotape the motion of a bicycle that is leaning against a table. To produce a similar setup, drape the solid color tablecloth or sheet over a table. Use masking tape to secure the edges of the tablecloth to the top of the table so that the tablecloth forms a uniform, wrinkle-free, vertical background against which the bicycle will be filmed. It is useful to crawl on the floor and pull the bottom edge of the tablecloth back, taping this edge to the floor, so that the rotating bicycle pedals do not rub against the tablecloth during the activity.

    

   If a table is not available or desired, a wall or room partition may also be used for the background. Again, it is highly recommended that one tape a solid color tablecloth or sheet to the wall or partition to create a uniform background.

    

    

4. After setting up the uniform background, position the bicycle in front of the background. In the movie file (Equipment Setup.mov), the bicycle is leaning against a table in a vertical, upright position. It is important to keep the bicycle vertical so that the rear wheel and pedals can rotate in a vertical plane perpendicular to the video camera’s viewing axis. If the bicycle leans at a significant angle, the camera will see a point on the rear wheel move in an elliptical path, rather than a circle, making it extremely difficult to measure accurate angular velocities.

    

   To allow the rear wheel and pedals to rotate freely, the rear tire of the bicycle is raised off the floor. This is done by placing a stack of spacers (like books, boxes, or small boards) under the bicycle’s bottom bracket (the metal part of the bicycle frame where the pedals attach). This can be a rather tricky procedure. Most students avoid this and simply turn the bicycle upside down, resting the bicycle on its seat and handlebars. Although I find the motion a bit more intuitive to analyze when the bicycle is upright, from a digital video analysis standpoint, the key to good results is keeping the bicycle vertical. It does not matter if the bike is upright or upside down.

    

    

5. When one videotapes the bicycle’s motion, it will be useful to indicate the gear ratio used. Using index cards and wide felt-tip marking pens, make a series of cards that indicate the number of teeth on each gear. The bicycle in the movie file (Equipment Setup.mov) has three gears on the front chain ring and nine gears on the rear freewheel. Three index cards were made for the front chain ring gears (22 Teeth, 32 Teeth, 44 Teeth) and nine index cards were made for the rear freewheel gears (11 Teeth, 12 Teeth, 14 Teeth, 16 Teeth, 18 Teeth, 21 Teeth, 24 Teeth, 28 Teeth, 32 Teeth). In the movie file, the chain is in the 44 Teeth front gear and the 18 Teeth rear gear; this is indicated by positioning the 44 Teeth and the 18 Teeth cards as shown in the movie. Make sure these cards are positioned so that they do not block the camera’s view of the rear wheel or the rotating pedals.

    

    

6. In order for a digital video analysis software program to convert video images from screen units (pixels) to actual length units (like centimeters, feet, meters, etc.), a known length must be marked in the video image. Any distant object or known length that is present in a movie frame can be used for scaling. This enables one to properly scale objects in the movie with real units. In the movie file (Equipment Setup.mov), a 1-foot long ruler is placed on the floor in front of the rear wheel. When this movie is analyzed with VideoPointä , this known length will be used to scale the movie. To avoid scaling distortions, the ruler, rear wheel, and pedals should all lie in the same vertical plane, the same distance away from the camera.

    

    

7. After preparing the background and the bicycle, you will now position the video camera. Almost any type of video camera available for the consumer market (e.g., 8mm, Hi-8, VHS, or S-VHS) can be used. The camera should have an adjustable shutter speed. Set it at 1/500^th of a second or less for sharp images. Note that good lighting is important when using such a fast shutter speed.

    

   Mount the camera on a tripod or other suitable stand. Position the camera and adjust the zoom so that the entire rear wheel and the full circular motion of the pedals appear in the viewfinder. Make sure the camera axis is at right angles to the vertical plane of motion. Although distortions are usually negligible in modern zoom lens systems, the zoom lenses in some low cost cameras may cause radial image distortions. Radial distortions can give a pincushion and/or barrel shape to a rectangular image. These distortions can be minimized if the camera is located fairly far away from the object of interest and then the zoom is set about halfway in so the motion fills about _ of the screen.

    

    

8. When filming the bicycle motion, we will study the rotation of the rear wheel about the rear wheel axle, and the rotation of the pedals about the pedal axle. To readily identify these objects, place a piece of masking tape or a brightly colored dot on the following points: at any point on the side of the rear tire, on the rear axle, on the pedal spindle, and on the pedal axle. These points are clearly marked in all of the movie files and VideoPointä files included on the accompanying CD-ROM. Make sure the video camera can "see" these highlighted points throughout the rotation of the rear wheel and pedals.

Video Capture with the Apple Video Player Software

After completing the Equipment Setup, your next step is to videotape the bicycle motion, followed by a video capture process to convert this recording into a digital movie file for computer analysis. The movie file (Equipment Setup.mov) on the accompanying CD-ROM shows the video camera mounted on a jack stand, ready to videotape the motion of a bicycle that is leaning against a table. Notice that the video camera is not connected to a computer … this allows one flexibility, minimizes cable clutter, and enables one to collect video data outside the lab. Some users may prefer to connect the video camera to the computer during the videotaping process, with the live feed from the camera going directly into a video screen box on the computer’s monitor. Unless one has a portable laptop computer, this live-feed technique limits one’s activity to the area where the computer is located. The following description assumes the video camera and computer are separated during the videotaping process.

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2. With the equipment setup properly, turn on the video camera. Remember, with the camera’s zoom set about halfway in, the camera should be positioned in front of the bicycle so that the motion of the rear wheel and the full rotational motion of the pedals fills about _ of the screen.

    

    

3. After turning on and positioning the camera, set the camera’s IMAGE ZONE SHOOTING MODE. Most cameras have selector dials or switches that allow you to choose an image zone shooting mode. These modes automatically set all camera functions such as shutter speed and aperture settings to optimum values for the existing conditions. The four most common image zone shooting modes are the portrait mode (indicated with a face-like icon), the landscape mode (indicated with a mountain-like icon), the close-up mode (indicated with a flower-like icon), and the sports mode (indicated with a runner-like icon). The sports mode is used for recording images of fast-moving objects. Thus, set the camera’s IMAGE ZONE SHOOTING MODE to the SPORTS MODE.

    

   For easier analysis, we also want to manually focus the camera in order to have the same size video image for each frame. Most cameras have a FOCUS MODE switch that allows one to set the lens in automatic focus (AF) mode, or manual (M) focus mode. Find this switch on the camera and set the camera’s FOCUS MODE to the MANUAL (M) focus mode. Focus the lens so that the bicycle’s rear wheel and pedals appear sharp and clear in the viewfinder.

    

    

4. With the camera turned on, properly positioned, and set in the correct modes, you are now ready to begin videotaping the bicycle motion. Position yourself near the front wheel of the bicycle so that you can turn the pedal on the back side of the bicycle with your hand. Whether the bicycle is upright or upside down, make sure your arm and body do not interfere with the camera’s view of the rear wheel and pedal. The camera must be able to record the complete, unobstructed rotational motion of the rear wheel and the pedals.

    

   Begin rotating the back side pedal in a "forward" direction so that the front chain ring gear engages the chain and causes the rear wheel to rotate "forward". As you rotate the pedal, make sure your hand does not rub against the tablecloth and cause the tablecloth to flap, creating a moving background in the videotaped images. Finally, make sure the bicycle remains stationary and does not rock forwards or backwards during the videotaping. If the bicycle is mounted upside down, this is not usually a problem; however, if the bicycle is in an upright position with its bottom bracket resting on top of some spacers, the bicycle may be prone to rocking. Maintaining a uniform background and keeping the bicycle stationary simplify the video analysis portion of this activity that follows.

    

   You only need to videotape three or four full rotations of the rear wheel and pedals. This will be edited later with the Movie Player software. As you rotate the pedals, keep an even tension on the chain. It does not matter whether you rotate the pedals fast or slow; the key is to keep the front chain ring gear and the rear freewheel gear intimately connected throughout the rotational process. The movie files on the accompanying CD-ROM illustrate this technique.

    

    

5. After videotaping three or four full rotations of the rear wheel and pedals, stop the videotape recorder. Rewind the tape, playback the video, and check the footage for correctness: make sure you can see the front chain ring gear and rear freewheel gear labels, make sure the ruler or other known scale length is clearly visible, ensure the rear wheel and pedals make three or four full rotations, and make sure the masking tape or brightly colored dots are easily seen on the side of the rear tire and on the pedal spindle. If you have a good recording, rewind the tape once again and proceed to the next step. If not, correct your mistakes and try again.

    

    

6. You now want to transfer the videotape recording to the computer. In order to make your own digital movies (that can be later analyzed by a digital video software program like VideoPointä ), you will need to have a digitizing board or a video capture card installed in your computer. A video capture card allows you to convert an analog video signal from a camera, VCR, LaserDisc, or other common video source to a digital file on a computer. Cards are available for both PC-compatible and Macintoshä computers. Many Macintoshä computers come with video capture capabilities (the Apple Video Player software) built in.

    

   At present, digital video files can be created in many different formats. The most common format for computers operating under Windowsä is the .AVI format while QuickTimeä is the standard format for Appleâ Macintoshä computer systems. The software that comes with commercially available MAC and PC capture cards will usually allow you to digitize video frames in several different formats. The VideoPointä digital video analysis software uses QuickTimeä as the standard format for digital video files because properly digitized QuickTimeä movies can be played back on both Macintoshä and PC-compatible computers. Many Macintoshä computers come with QuickTimeä . If you are using a Windowsä operating system on a PC computer, you can get a Video For Windowsä to QuickTimeä converter from the VideoPointä web site at http://www.lsw.com/videopoint.

    

   The movie files and VideoPointä files on the accompanying CD-ROM were created on an Appleâ Macintoshä PowerPC 5500/250 computer system with the Apple Video Player software. To transfer the videotape recording to the computer, connect the video camera to the computer with an RCA cable. The cable connects the video camera’s VIDEO OUT port to the computer’s VIDEO IN port. After connecting the video camera to the computer, turn on the computer, find the Apple Video Player software, then start the Apple Video Player.

    

7. When the Apple Video Player software is activated, two screens will appear: a VIDEO screen and a CONTROLS screen. If the CONTROLS screen does not appear, click on the WINDOWS selection on the Appleâ menu bar and activate "Show Controls Window". Using your mouse, click on the CONTROLS screen to make it active.

    

   Three icons on the left side of the CONTROLS screen enable you to capture movies. The camera icon at the top allows you to capture a single picture or to capture a movie (a series of video frames). The computer-screen icon in the middle allows you to adjust the brightness, sharpness, contrast, and color of the video source you are recording from. The movie projector icon at the bottom allows you to control the movie playback when an MPEG movie is present on a mounted CD or hard disk.

    

   Your goal is to use the Apple Video Player to capture a movie, so click on the camera icon on the top left side of the CONTROLS screen. If the video camera is turned on and properly connected to the computer, you should see the live feed from the camera on the Apple Video Player’s VIDEO screen. Make sure the VIDEO screen window size is set to NORMAL (if not, other size windows may result in multiple images of your subject). To set the VIDEO screen window size to NORMAL, click on the WINDOWS selection on the Appleâ menu bar and activate "NORMAL SIZE".

    

    

8. You are now ready to capture a movie with the Apple Video Player. With the videotape properly cued, start playing the video camera through the Apple Video Player’s VIDEO screen. On the CONTROLS screen, click on the "Capture Movie: Record" button to begin recording on the computer. When you are ready to stop recording, click on the "Capture Movie: Stop" button. Make your computer movie short! If it is too long, you will not be able to save it or use it.

    

    

9. After you click on the "Capture Movie: Stop" button, you will then be asked to save your movie. Choose a name that represents your class, your lab partners, and/or a short description of your activity. This series of video frames that you have captured and saved are now stored as a QuickTimeä movie. QuickTimeä is a system extension that gives your computer the capability to use digitized video and audio files.

    

    

10. Quit the Apple Video Player by clicking on the FILE selection on the Appleâ menu bar and activating "QUIT". You may now turn off the video camera. If other groups need to borrow the video camera for their own studies, you may disconnect the video camera from the computer.

Making and Editing Digital Movies with the Movie Player Software

Once a videotape movie has been captured and saved as a QuickTimeä movie, you need to edit it, cutting out unwanted video frames. Appleâ Macintoshä computer systems use the Movie Player software to edit such digital movies.

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2. After quitting the Apple Video Player, start the Movie Player software. The computer screen will not appear to change. To access a QuickTimeä movie for editing, click on the FILE selection on the Appleâ menu bar and activate "OPEN …". If the QuickTimeä movie’s file name does not show up immediately, it may be located on the computer’s hard drive. Once you locate the desired file name, open the movie.

    

    

3. When the QuickTimeä movie is opened in the Movie Player software, the first video frame of the movie appears on the computer screen. You can play the movie by clicking on the triangle at the bottom left-hand corner of the Movie Window. As the movie plays, a rectangular slider bar moves from left to right across the bottom of the Movie Window. The two arrows in the bottom right-hand corner of the Movie Window (to the right of the slider bar) advance the movie one frame at a time.

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2. When you have finished editing your movie, save it by clicking on the FILE selection on the Appleâ menu bar and activate "SAVE AS …". You may wish to include in the new file name the letters "ed", indicating that the movie has been edited. The movie may be saved normally or self-contained by selecting the "Save normally (allowing dependencies)" button or the "Make movie self-contained" button. Select "Make movie self-contained" if you want to make the movie playable on non-Appleâ computers. After saving the movie, quit the Movie Player by clicking on the FILE selection on the Appleâ menu bar and activate "QUIT". You now have an edited movie, ready for digital video analysis.

An Introduction to Digital Video Analysis: The VideoPointä Software

The VideoPointä software will be used to analyze the QuickTimeä digital bicycle motion movie files that you have created. VideoPointä will be used to measure the angular velocities of the rear wheel and pedals, which can then be used to determine the corresponding gear ratio. No special hardware is needed when VideoPointä is used to analyze digital movies in the QuickTimeä format. The following serves as a brief introduction to digital video analysis and Version 2.0 of the VideoPointä software.

Overview

VideoPointä is designed to help you analyze the motion of features or objects of interest in digital video movies. This software will allow you to define characteristics of a series of points you would like to examine on each video frame. These characteristics include the name, the size, and the shape of the marker; the mass; and the coordinate system each point series is associated with. You will also be able to specify the length of objects or distances between features in frames for scaling purposes. In addition to obtaining data via the selection of features or objects of interest on frames, you will be able to define calculated data points such as the location of the center of mass of a system of features or objects. Data that are obtained can be graphed as they are located or calculated. Data can be saved in an electronic file or copied for use with other types of analysis software such as spreadsheets and graphing programs. VideoPointä runs on both the Windowsä and Macintoshä computer platforms.

An Introduction to VideoPointä Features

The VideoPointä software allows you to collect coordinate data from digital video images by clicking a mouse on locations of interest in the video image. This allows you to study two-dimensional motions by locating, displaying, and analyzing coordinate data obtained from sequences of digitized video frames. You can also study individual electronic images saved as QuickTimeä movies to determine geometric relationships or count objects of interest. The software has a number of innovative features, many of which are not found in other video analysis packages. It can be operated from either menus or a toolbar.

"video points"

A "video point" is defined as a location of a feature or object of interest on a single QuickTimeä movie frame. The software initially stores the x, y, and t values of a video point. Here x is the distance from the left side of the Movie Window (in pixels), y is the distance from the bottom of the Movie Window (in pixels), and t is the elapsed time (in seconds) since the first frame in the movie was recorded. By themselves, video points are not very interesting. However, the VideoPointä software allows you to make calculations based on these video points. It should be noted that VideoPointä refers to the name of the software program, while the term "video point" refers to a point you have located on the frame of a QuickTimeä movie.

Video points are designated by you. For example, if you are looking at a movie of a ball toss, you might be interested in measuring the position of the ball in each movie frame. In order to do this, you would set up the VideoPointä software for one video point per frame, and then click on the location of the ball in each frame in the movie. VideoPointä then stores the information for the series of video points corresponding to the selected locations.

Since the data set, consisting of a series of video point coordinates, is stored in screen units (pixels) relative to the arbitrary origin at the bottom left of the movie, it is not terribly useful for analysis. However, you have the ability to define new coordinate systems. You can then associate the video points with a specific coordinate system and determine the position coordinates and graphs in the new system they are associated with.

Coordinate Systems

A VideoPointä coordinate system is two-dimensional and consists of an origin, an orientation, and an optional scale factor. In addition, you can designate a coordinate system as either Cartesian or polar. By default, VideoPointä opens a movie with two coordinate systems present. The first coordinate system is known as the default system and is initially named the "Origin 1" system. It is a Cartesian system with horizontal and vertical axes and a pre-selected origin (i.e., "Origin 1") near the lower left corner of the Movie Window. Initially the units of the coordinates in this system are in pixels. You can easily change the name of this system or scale it so that video points you locate have coordinates in meters or centimeters. You can also move the default system origin and rotate the coordinate axes if you choose.

The second coordinate system is VideoPoint’sä native system, the "Video Origin" system. This is a Cartesian coordinate system with horizontal and vertical axes and no scaling. The coordinates of the video points located in this system are always in pixels, and the "Video Origin" is always at the bottom-left of the Movie Window. You cannot change the "Video Origin" system in any way.

Each video point series that you define has to be associated with a coordinate system. Video points that are associated with the "Origin 1" coordinate system have (x, y, t) data saved as coordinates in the "Origin 1" coordinate system.

Scale Factors

Data stored in pixels is only useful for computers. In order to collect data in "real" units (e.g., meters), each coordinate system must be scaled. In a sample movie, a meter stick might appear to be about 200 pixels tall. During the scaling process, you need to click on both ends of the meter stick and tell the VideoPointä software that the distance between these two video points (which VideoPointä sees as 200 pixels) is actually 1.00 meters. VideoPointä would then assign a scale factor of 200 pixels per meter. You can then associate the scale factor with any of the coordinate systems you have defined. With the combination of the origin location and the scale factor, video point data can be reported in "real" units relative to any coordinate system.

Calculations Based on Video Points

You can specify the standard calculation based on two coordinates or two or more video points associated with a given coordinate system. These calculations include:

Distance The distance between any two video points on a frame.

 

Scale Ratio of a known length (in meters or centimeters) to the distance in pixels between two video points.

 

 

Center of Mass Calculated center of mass of a collection of video points based on masses associated with a series of video points. Each series of video points can be assigned a different mass.

 

Angle Angle made by lines conn