Supported by the Two-Year College Physics Workshops for the 21st Century Project *
Chuck Stone
Department of Physics
Forsyth Technical Community College
2100 Silas Creek Parkway
Winston-Salem, NC 27103
Phone: (336) 734-7266
FAX: (336) 761-2399
Email: cstone@forsyth.cc.nc.us
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 21st 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:
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
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9-Speed Rear Freewheel
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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
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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.
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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.
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Rear Wheel Analysis |
Pedal Analysis |
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Rear Wheel Analysis |
Pedal Analysis |
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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.
______________________________ ______________________________
______________________________ ______________________________
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:
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:
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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)
w Rear Wheel = __________ rads/s
w Pedals = __________ rads/s
to two decimal places. Gear Ratio = w Rear Wheel / w Pedals = __________
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(rads/s) |
(rads/s) |
w Rear Wheel / w Pedals |
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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:
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Selectn # |
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Gear Ratio, FG/RG |
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(rads/s) |
(rads/s) |
Gear Ratio, w Rear Wheel / w Pedals |
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Error (%) |
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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
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:
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.
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.
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.
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.
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.
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.
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.
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.
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".
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.
The natural frame rate for videotapes is 30 frames per second. In general, the motions filmed in a physics lab can be completed in a second or less. Thus, our movie sequences are rarely longer than 30 frames. The QuickTimeä movie that you made in the previous step is often made from a videotape recording that is much longer than one second long. When you edit this QuickTimeä movie, be sure to eliminate all the frames taken before the motion starts and after it ends. Usually the analysis of 10 to 15 video frames, all showing motion of interest, tells the whole story. Analyzing more than 20 frames is often boring.
When you videotaped the bicycle motion, it was suggested that you videotape three of four full rotations of the rear wheel and pedals. Three or four full rotations will give you plenty of good footage to edit. With the Movie Player software, select the best one single rotation of the rear wheel or pedals that can be used for future digital video analysis studies.
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 connecting three video points.
Designated Point Point at a location specified by relative distances between any two video points.
Movies and VideoPointä Files
Movies are sequences of still images that have been digitized and saved in the QuickTimeä format. Each image is called a frame. Each frame has a time associated with it that represents the elapsed time since the first frame of the movie was recorded.
Information derived by VideoPointä can be saved in more than one way. The entire data set, along with the current window arrangement (including movies, data tables, and graphs) can be saved as a VideoPointä file with the extension *.vpt.
VideoPointä files contain coordinate data as well as the name and location of the movie. It does NOT save the movie itself in the file, nor does it ever edit the movie. Thus, if you want to open a VideoPointä file later, the movie associated with it must also be present.
Fundamental Concepts of Uniform Circular Motion
In the VideoPointä Analysis of Bicycle Motion activity, the VideoPointä software is used to analyze the rotational motion of the rear wheel and the pedals of a bicycle. VideoPointä allows one to measure the angular velocities of the rear wheel and pedals, which are then used to calculate the gear ratio. The following concepts of uniform circular motion are presented as a prelude to the next section that describes how one uses VideoPointä to actually measure these angular velocities.
Angular Measure: If the circle below has radius r and the arc cut by the angle q is s, then the angle in radians is given by
Angle q = (Arc Length, s) ¸ (Radius, r)
q ® [rads]
s ® [cm]
r ® [cm]
VideoPointä refers to q as angular position.
Angular Speed: If a rotating body turns through the angle q in the time t, its average angular speed w is
Angular Speed w = (Angular Measure, q ) ¸ (Time, t)
w ® [rads/s]
q ® [rads]
t ® [s]
VideoPointä refers to w as angular velocity.
Using VideoPointä to Determine the Angular Velocity w of a Rotating Object
Section E of this User’s Guide contains the laboratory activity VideoPointä Analysis of Bicycle Motion. The second method of this activity requires one to determine the gear ratio of a bicycle by measuring the angular velocities of the rear wheel and pedals.
To measure these angular velocities, one will use VideoPointä to analyze a digital movie that features the rotational motion of the rear wheel and pedals. Recall that the easiest type of movie to analyze is a movie with a single feature of interest that was taken with a camera that does not move or zoom during filming. Thus to determine the gear ratio, the same movie will be analyzed twice: once for the rotational motion analysis of the rear wheel, and once for the rotational motion analysis of the pedals. Each analysis produces a VideoPointä file (*.vpt) that contains the angular velocity of the rotating object.
The following five bullets summarize the basic procedure for determining the angular velocity of a fixed, rotating object with the VideoPointä software:
· Use VideoPointä to analyze the two-dimensional motion of the rotating object.
· Select an origin that is located on the axis of rotation of the rotating object.
· Use "video points" to track angular position q of the rotating object as a function of time t.
· Plot the angular position q of the rotating object as a function of time t.
· Since the angular position, q , is given by q = w t, the slope of the q vs. t graph will be the angular velocity, w , of the rotating object.
The following presents a step-by-step approach of performing a typical analysis for the situation in which the bicycle chain is in the 44-teeth front chain ring gear and the 16-teeth rear freewheel gear (i.e., FG=44 and RG=16).
Opening VideoPointä
The VideoPointä software should be installed on your computer. For details on the installation procedure, consult the VideoPointä manual that came with the software or the VideoPointä web site at http://www.lsw.com/videopoint. To open VideoPointä , double click on the VideoPointä icon, a blue circle around eight hatched lines. The icon will be labeled with a legend like "VideoPoint 2.0.3" which indicates Version 2.0.3 is installed on your computer.
Once VideoPointä opens, a title screen will appear with the header "ABOUT VIDEOPOINT" at the top. Click anywhere on this screen to reveal the "STARTUP" screen. To start, click on the "Open Movie …" button to open the movie you want to analyze. In the example discussed here when the chain is in the 44-teeth front chain ring gear and the 16-teeth rear freewheel gear, you should open the movie file
FG 44, RG 16, Gear Ratio 2.75
Once the movie opens, a screen showing the first frame of the movie should appear. This screen has the header title "NUMBER OF POINTS". On this screen you are asked to enter the "Number of features or objects to be located". This is simply the number of moving points that you want to locate on each movie frame. We will begin by studying the rotational motion of a single point on the rear wheel of the bicycle. Thus, enter the number "1" in the "Number of features or objects to be located" box, then click the "OK" button.
Three windows should now appear on your computer monitor. The Movie Window appears in the upper left hand corner, with the header label "FG 44, RG 16, Gear Ratio 2.75" that describes the movie to be analyzed. The Coordinate Systems Window appears in the upper right hand corner, with the header label "COORDINATE SYSTEMS". The Table Window appears in the lower left hand corner, with the header label "TABLE". To make a window active, click on the window once with the mouse.
The Movie Window
Activate the Movie Window which is titled "FG 44, RG 16, Gear Ratio 2.75". You will notice in the movie that the front chain ring gear and rear freewheel gear labels are clearly seen, as well as the ruler used to mark the known scale length. None of these obstruct the view, or the motion, of the rear wheel or pedals. Masking tape was used to highlight the rear axle and the pedal axle, as well as a point on the side of the rear tire and the pedal spindle. These four points are easily seen in the Movie Window.
A yellow rectangular box appears in the upper right hand corner of the Movie Window with the label "1 of 26" on it. This indicates that this is the first frame of a movie with a total of 26 frames. A set of vertical and horizontal lines intersect in the lower left corner of the Movie Window, defining the "Origin 1". If you move the mouse over the active movie area, you see the cursor has been replaced by a white circle with the label "Point S1". This white circle allows you to specify the location of "video points" on each movie frame. Since you entered the number "1" in the "Number of features or objects to be located" box on the "NUMBER OF POINTS" screen, this white circle cursor will be used to specify one "video point" on each of the 26 frames in this movie. The position of the white cursor on the frame is specified by x and y coordinates (measured in pixels) as indicated in the lower left corner of the Movie Window. As the mouse moves, the white circle cursor moves, and the x and y coordinates change accordingly.
The Coordinate Systems Window
Initially the Coordinate Systems Window shows two Cartesian coordinate systems. The first is the "Origin 1" coordinate system, while the second is the "Video Origin" coordinate system, both shown in the window. A single video point series called "Point S1" has been placed in the "Origin 1" coordinate system. "Point S1" will record all of its data relative to the "Origin 1" coordinate system.
The Table Window
The Table Window will record all of the time and motion data for each movie frame. If you activate the Table Window, you can scroll down the left hand column and see that 26 rows appear, numbered from 1 to 26. Each row will store the time and motion data for each of the 26 movie frames that make up this movie. As you use the white circle cursor to specify the relevant "video point" for each movie frame, the x and y position coordinates for this "video point" will be saved in the table. VideoPointä uses this position and time data to calculate velocities and accelerations which are then used to calculate linear quantities (such as momentum, net force, kinetic energy, potential energy, and total energy) as well as rotational quantities (such as angular position, angular velocity, and angular acceleration). As you perform a VideoPointä analysis and graph these results, this additional motion data is calculated and tabulated in the Table Window in data columns to the right of the position data.
The first column in the Table Window contains the frame number. The second column contains the time (in seconds) associated with each frame in the movie. The third and fourth columns contain the x and y position data (in pixels) for the "Point S1" video points. When the movie is scaled, these coordinates will have "real" units associated with them.
It should be noted that the times in the Table Window do not increase in a linear manner. This is due to the "dropped frame" artifact that sometimes occurs when a video capture card converts the analog video information to a digital format. The capture card "drops frames" because it cannot keep capturing at the intended rate. Instead of falling behind, it simply drops the frame it is working on and captures the next one. If you are using a QuickTimeä movie with the VideoPointä software, this is not a problem. The time at which each frame is recorded is stored with the digital information that defines the frame. Thus even though a movie may appear to be "choppy", the times associated with each movie frame are correct.
Playing the Movie
To play the movie, activate the Movie Window with the mouse, then click on the triangular shaped button on the bottom of the Movie Window to the left of the movie controller slide bar. The movie plays each frame in sequence, finally stopping on the final (in this movie, the 26th) frame. Notice that the rear wheel and pedals both rotate in a "forward" direction (in this movie, a clockwise direction). The person turning the pedals did not let his arm or body obstruct the camera’s view of the pedals, so the full rotation can be clearly seen.
To rewind the movie, drag the slider on the movie controller slide bar back to the beginning of the controller. You can also rewind the movie by clicking on the MOVIE selection on the Appleâ menu bar and activating "REWIND".
Scaling the Movie
Before we begin the video analysis of the movie, we should scale the movie so that our x and y coordinate positions can be measured in "real" values instead of pixels. The process of scaling the movie tells VideoPointä how many screen units (pixels) in the Movie Window are in a meter, a centimeter, a millimeter, etc. in the actual scene. Conveniently, a one-foot long ruler was placed in the "FG 44, RG 16, Gear Ratio 2.75" movie; this will be used to scale the movie.
To start the scaling process, click on the Scale Icon in the toolbar. The toolbar is a vertical column of icons on the far left hand side of your computer screen. The sixth icon from the top of the toolbar is the Scale Icon, a blue rectangle that resembles a ruler. After clicking on the Scale Icon, a dialog box appears that has the header label "SCALE MOVIE". The length of the scale object (in this case, the one-foot long ruler) is known to be 1.00 ft. Enter this value into the "Known Length" box. Since we want to scale the coordinate system relative to "Origin 1", select "Origin 1" in the "Scale Origin" pop-up menu. Since the camera did not zoom during the time the movie was made, choose a "Fixed" scale type in the "Scale Type" box.
Once these values have been set, you are ready to begin the scaling process. Click on the "Continue" button in the bottom right hand corner of the "SCALE MOVIE" dialog box. A "MOVIE MESSAGE" window may appear on your screen, which can be ignored. With your mouse, click on one end of the ruler with the set of cross-hairs (which now appears as the new cursor). Release your finger off the mouse, move the cross-hairs cursor to the other end of the ruler, and click again. The "MOVIE MESSAGE" window will disappear, and a line will appear on the ruler which tells VideoPointä how many pixels are in the one-foot known length.
Note that three new rows appear on the Coordinate Systems Window (before, only the "Origin 1" row was present). Two rows, "Scale1 A" and "Scale1 B", specify the ends of the object that you clicked on. The third row, called "Scale1", stores the ratio of the length of the object relative to the distance between "Scale1 A" and "Scale1 B".
These two video points, "Scale1 A" and "Scale1 B", are used by the VideoPointä program to determine the number of pixels between the ends of an object or the distance between two features used for scaling on a video frame. If the actual distance between the "Scale1 A" and "Scale1 B" video points is known, then a scale factor can be determined for the frame. This scale factor is calculated as the ratio between the number of pixels between "Scale1 A" and "Scale1 B" and the actual distance between these points specified by you. Moving either of the two scaling video points closer together will decrease the scale factor and moving them farther apart will increase the scale factor.
You have now scaled this coordinate system by telling VideoPointä that 1.00 foot is equivalent to the distance (in pixels) between the two video points that you just clicked on. In the Table Window, the x and y position coordinates are now measured in the "real" units of meters instead of pixels. Even though the known length in this movie was measured in the "real" unit of the foot, VideoPointä converts all such units to meters for use in the Table Window.
Moving the Origin
When you first open the VideoPointä software, a set of vertical and horizontal lines intersect in the lower left corner of the Movie Window, defining the "Origin 1". This is where the x and y positional coordinates have the values of (x = 0 pixels, y = 0 pixels), or if the movie has been scaled, (x = 0 m, y = 0 m). Since this origin does not lie on the axis of rotation of either the rear wheel or the pedals, the position of some fixed point on either the rear wheel or the pedals will have a sinusoidal relationship over time as the rear wheel and pedals rotate. In other words, if x(t) represents the horizontal position of some fixed point on the rotating object at time t, then
x(t) = A sin (w t + f ) + B
where
x(t) = the horizontal position of the fixed point on the rotating object at time t (m)
A = the amplitude of the sinusoidal oscillation (m)
w = the angular velocity of the rotating object (rads/s)
t = the time (s)
f = the phase constant of the sinusoidal oscillation (rads)
B = a factor which accounts for how far the axis of rotation is located from the coordinate system’s origin (m)
A similar expression can be written for the fixed point’s vertical position, y(t).
On the other hand, if the coordinate system’s origin coincides with the rotating object’s axis of rotation, then the angular position q (t) of a point of interest on the rotating object will be a linear function of the object’s angular velocity w . That is,
q (t) = w t
Consequently, when one analyzes the rotational motion of the bicycle’s rear wheel, one should move the origin over the rear axle. Similarly, when analyzing the rotational motion of the bicycle’s pedals, one should move the origin over the pedal axle.
After scaling the movie in the previous step, one should move the origin in the following manner. To start the "moving the origin" process, click on the Pointer Icon in the toolbar. The toolbar is a vertical column of icons on the far left hand side of your computer screen. The second icon from the top of the toolbar is the Pointer Icon, a black arrow. After clicking on the Pointer Icon, position the mouse on the Movie Window. Use the mouse to click on the video point where the origin lines intersect, then drag the origin to the new desired location. If you are analyzing the motion of the rear wheel, then drag the origin to the rear wheel axle. If you are analyzing the motion of the pedals, then drag the origin to the pedal axle.
Labeling the New Origin
It will be instructive to label the new origin with a meaningful name. For instance, if the rear wheel axle is the new origin, an appropriate name would be "Rear Axle". If the pedal axle is the new origin, an appropriate name would be "Pedal Axle". All of the VideoPointä files on the accompanying CD-ROM label these two origins as "Origin 1: Rear Axle" and "Origin 1: Pedal Axle".
To label the new origin with a meaningful name, activate the Coordinate Systems Window with the mouse. Using the Pointer Icon, click one time on the "Origin 1" labeled row. This will darken the row. Label the new origin by simply typing in the name in the darkened area. The new name becomes permanent once you hit the RETURN key on the keyboard, click the mouse in the Coordinate Systems Window, or activate the Movie Window with the mouse.
Labeling the "video point" on the Moving Object
It will also be instructive to label the "video point" on the rear wheel or the pedal spindle with a meaningful name. For instance, if the rotational motion of a fixed point on the rear wheel is to be analyzed, then an appropriate name would be "Rear Wheel". If the rotational motion of the pedal spindle is to be analyzed, then an appropriate name would be "Pedal". All of the VideoPointä files on the accompanying CD-ROM label these two points of interest as "Point S1: Rear Wheel" and "Point S1: Pedal".
To label the "video point" that is to be analyzed with a meaningful name, activate the Coordinate Systems Window with the mouse. Using the Pointer Icon, click one time on the "Point S1" labeled row. This will darken the row. Label the "video point" that is to be analyzed by simply typing in the name in the darkened area. The new name becomes permanent once you hit the RETURN key on the keyboard and click the mouse in the Movie Window, or directly activate the Movie Window with the mouse.
Taking Data: Using "video points" to Track the 2-D Motion of a Rotating Object
At this point in the video analysis process, you should be ready to start taking data. Begin with the analysis of the rear wheel. In the Movie Window, the origin should be positioned on the rear axle and labeled accordingly. In the Coordinate Systems Window, the single video point that will be tracked should be labeled with the name "Rear Wheel".
To begin taking data, click on the "video point" Icon in the toolbar. The toolbar is a vertical column of icons on the far left hand side of your computer screen. The first icon at the top of the toolbar is the "video point" Icon, a blue circle. After clicking on the "video point" Icon, position the mouse on the Movie Window. You should now see a white circle with the label "Rear Wheel" appearing in the Movie Window, as well as the italicized text "Rear Wheel" in the bottom right of the Movie Window. The white circle allows you to specify the location of "video points" on each movie frame. Since you entered the number "1" in the "Number of features or objects to be located" box on the "NUMBER OF POINTS" screen, this white circle cursor will be used to specify one "video point" on each of the 26 frames in the "FG 44, RG 16, Gear Ratio 2.75" movie.
Using the white circle, click the mouse one time in the very center of the marker taped to the rear wheel. The more precise you are in the data collection step, the better your data will be for analysis. After clicking the mouse, the movie will automatically advance to the next frame. Continue clicking on the location of the marker in each frame until the last frame of the movie. To see video points you have marked, you can turn on "trails" by clicking on the eleventh icon from the top of the toolbar (a series of four red dots). You can remove the "trails" by clicking on the same icon.
You have now collected data that describes the rotational motion of the rear wheel about the rear axle. In particular, the x and y positions of the rear wheel "video points" have been collected as a function of time and catalogued in the Table Window. This data must now be converted to angular position data so that the angular velocity of the rear wheel can be determined.
It should be noted that you will perform a similar procedure at the pedal axle when the rotational motion of the pedals is studied.
Graphing Data and Determining Angular Position
To investigate the rotational motion of the rear wheel or pedals, you will use VideoPointä to convert the x and y rectilinear position data (stored in the Table Window) into angular position data. VideoPointä will do this for each movie frame and then graph the angular position, q , as a function of time, t. You can then fit a mathematical function to the angular position data and determine the angular velocity, w , of the rotating object.
To begin this process, click on the Graph Icon in the toolbar. The toolbar is a vertical column of icons on the far left hand side of your computer screen. The eighth icon from the top of the toolbar is the Graph Icon, a set of horizontal and vertical axes with four blue "+ shaped" symbols. After clicking on the Graph Icon, a dialog box appears that has the header label "PLOT SERIES". Two lists appear in this dialog box. The left list allows you to select the quantity to graph on the "Horizontal Axis", while the right list allows you to select the quantity to graph on the "Vertical Axis". From the left list, use the pop-up menu to choose the one value that you want as your horizontal (domain) axis. For the bicycle motion studies, you will choose "Time". You can then choose one or more values in the right list for the vertical (range) axis. For the bicycle motion studies, choose "Rear Wheel" (if analyzing the motion of the rear wheel) or "Pedal" (if analyzing the motion of the pedals) from the pop-up menu located just below the "Vertical Axis" heading. In the adjacent pop-up menu, select "angle". A list now appears below these two pop-up menus with the items "Angular Position", "Angular Velocity", and "Angular Acceleration". Use the mouse to select "Angular Position" from this list. Click the "OK" button with the mouse to create the graph. This will produce a Graph Window with the header "Theta vs. Time" that plots the angular position, q , as a function of time, t, for the selected points series.
Fitting a Mathematical Function to the Data and Determining Angular Velocity
If all has gone well, your graph of the angular position, q , as a function of time, t, for the rotational motion of the rear wheel or pedals should be a straight line. The key to getting this linear graph is to have your origin properly located on the axis of rotation &emdash; either the rear axle (for the rear wheel) or the pedal axle (for the pedals). To adjust the location of your origin, use the mouse to click on the Movie Window, then click on the video point where the origin lines cross. Drag the origin to the new desired location. The graph will change as the origin moves.
If your graph is a straight line, VideoPointä allows you to fit a linear curve to your data so that you can determine the angular velocity of the rotating object. To do this, recall that the angular position, q , is given by q = w t if the origin is located on the axis of rotation. The slope of the q vs. t graph will be the angular velocity, w , of the rotating object. To find the slope of your data, use VideoPoint’sä automatic curve-fitting feature.
With the Graph Window active, click on the Curve Fitting Icon in the upper right hand corner of the Graph Window. The second icon from the top is the Curve Fitting Icon, a red letter "F" in a box. After clicking on the Curve Fitting Icon, a dialog box appears that has the header label "CURVE FIT". In the "Type of Fit" pop-up menu select the "Linear" option. Check the "Update Automatically" option so that VideoPointä will update the fit automatically every time that you move a video point on the movie. Click the "OK" button with the mouse to fit a line to the data. At the top of the graph, the fit is given by
F: m x + b r^2=*.***
where
F = the linear fit expression for the angular position q of the fixed point on the rotating object at time t (rads) m = the slope of the linear fit; here, the angular velocity w of the rotating object (rads/s)
x = the independent variable on the horizontal axis; here, the time t (s)
b = the value of F when x = 0; that is, where the line intercepts the vertical axis (rads)
r^2 = a correlation value that indicates how "good" the line fits the data; the closer r^2 is to 1.000, the better the fit
It should be noted that the actual "fit" will have numerical values for m, b, and *.***. For example, the VideoPointä file "FG 44, RG 16, Rear Wheel.vpt" has m = w = - 5.43, b = - 2.25, and r^2 = 1.000. This indicates that the rear wheel has an angular velocity of w = - 5.43 rads/s.
Relating the Graph to the Movie
One of the great features of video analysis is the ability to replay the situation. Activate the Movie Window by clicking on it, then play the movie by clicking on the triangular play button or moving the rectangular slider bar. Watch the graph while the movie plays. A circle should move along the graph points indicating the current time of the movie on the graph.
Live Updating
VideoPointä has the capability of performing "live" graph updates while you move "video points" around on the movie. Activate the Movie Window by clicking on it, then click and drag the "video point" marker with the mouse. The Graph Window simultaneously updates the graph.
Viewing the Data in a Table
The position, time, and motion data that you have taken during your video analysis work is stored in the Table Window. If you want to view this data, activate the Table Window by clicking on it. You can select and copy any portion of this data. To select a specific data entry, click on the entry with the mouse. To select all of the data in an entire column, click on the column header. To copy the data, click on the EDIT selection on the Appleâ menu bar and activate "COPY". This process will copy the highlighted data into a buffer area where it can then be pasted into other types of analysis software such as spreadsheets and graphing programs.
Saving Your Work and Quitting VideoPointä
To save your VideoPointä analysis study, click on the FILE selection on the Appleâ menu bar and activate "SAVE AS …". A dialog box appears which allows you to save your results with a specific file name. Each file should be saved with a *.vpt extension. The information saved with each file consists of all your data and open windows, as well as the name and location of the movie file analyzed. It does NOT contain or change the movie file. This keeps the VideoPointä file sizes small and allows files to be associated with movies that are stored on "read-only" networks.
At this point, you have successfully analyzed and saved a movie with VideoPointä . To quit the program, click on the FILE selection on the Appleâ menu bar and activate "QUIT".
Additional VideoPointä Analyses
After analyzing the motion of the rear wheel, you will want to perform a similar VideoPointä analysis on the pedals. To do so before quitting the VideoPointä program, click on the FILE selection on the Appleâ menu bar and activate "NEW STARTUP …" (to start a new analysis) or "OPEN MOVIE …" (to open a new movie). Follow the same procedures as before.
Using VideoPointä to Calculate the Gear Ratio
To calculate the gear ratio with VideoPointä , you must perform two analyses: one to determine the angular velocity of the rear wheel (w Rear Wheel), and the other to determine the angular velocity of the pedals (w Pedals). The gear ratio is then Gear Ratio = (w Rear Wheel) / (w Pedals).
Section G provides a brief look at sample laboratory results that one might obtain during the VideoPointä Analysis of Bicycle Motion activity. Section E contains all of the handout materials that students should complete when doing the activity. The following comments are made in regards to the various subsections within Section E.
The Purpose of the activity is to compare two different methods used to measure the gear ratio of a bicycle. This is clearly explained at the beginning of the lab, however, instructors should reiterate this fact. Do not let students be overwhelmed by the physics studied or the technological tools used in this lab.
The Preliminary Exercises provide students and instructors ten items that will build a knowledge base leading into the activity. I have not provided answers to these exercises because such answers will vary, depending on the nature and level of your students. As an instructor, I encourage you to let your students spend class time discussing these exercises, and I trust you will fill in the gaps with guided discussion when appropriate. These exercises stimulate creative thinking, avoid the "plug-and-chug" atmosphere of traditional labs, and provide a technical foundation for the Project Reports that culminate this activity. These reports should be a team effort and can serve as the basis for in-class presentations if desired.
Results from the Two Methods for Determining Gear Ratios, and the Analysis of these results, are discussed in the next subsection.
Sample Results: Front Gear = 44 Teeth, Rear Gear = 16 Teeth
These sample results will assume that the bicycle chain is in the 44-teeth front chain ring gear (FG = 44) and the 16-teeth rear freewheel gear (RG = 16). Using Method 1: Determining Gear Ratios by Counting Gear Teeth, the accepted gear ratio is found to be
To find the measured gear ratio for these same conditions, the bicycle is put in the appropriate gear and a movie is made of the rotational motion of the rear wheel and pedals. The bicycle movie is then transferred to a computer, then edited to select the desired video footage. The CD-ROM that accompanies this activity contains a movie file called
FG 44, RG 16, Gear Ratio 2.75
that shows the rear wheel and pedal motion when the bicycle chain is in the 44-teeth front chain ring gear and the 16-teeth rear freewheel gear. One can open this movie in the VideoPointä software package, analyze this rotational motion, and measure the angular velocities of the rear wheel and pedals. The measured 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). As an instructor, you can analyze this movie with your students to showcase the features of VideoPointä .
The CD-ROM also contains two VideoPointä analysis files that accompany the previously mentioned movie. The VideoPointä file that contains the analysis for the rotational motion of the rear wheel is called
FG 44, RG 16, Rear Wheel.vpt
Open this file and one finds the angular velocity of the rear wheel to be w Rear Wheel = - 5.43 rads/s.
The VideoPointä file that contains the analysis for the rotational motion of the pedals is called
FG 44, RG 16, Pedal.vpt
Open this file and one finds the angular velocity of the pedals to be w Pedals = - 2.02 rads/s. Using Method 2: Determining Gear Ratios by Measuring Angular Velocities, the measured gear ratio is found to be
To assess the accuracy of the two gear ratio measurement methods, compute the percent error between the accepted gear ratio and the measured gear ratio. Percent error is defined as
½ (2.75) - (2.69) ½ (0.06)
- (2.75)
The Percent Error in the gear ratio measurements is 2.2%. This is an acceptable value, due to the visual limitations in actually defining the precise "video points" of interest during the digital video analysis work.
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.
Results from the 27 Pre-Recorded Bicycle Movies on the Accompanying CD-ROM
The following table showcases the results from the 27 pre-recorded bicycle movies on the accompanying CD-ROM. The following abbreviations are used:
FG = # of Teeth in Front Chain Ring Gear
RG = # of Teeth in Rear Freewheel Gear
w Rear Wheel = Angular Velocity of Rear Wheel (rads/s)
w Pedals = Angular Velocity of Pedals (rads/s)
(FG / RG)
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FG |
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Gear Ratio, FG / RG |
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(rads/s) |
(rads/s) |
Gear Ratio, w Rear Wheel / w Pedals |
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Error (%) |
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Summary: The Percent Error in the gear ratio measurements ranges from 0.0 to 5.8%. This is acceptable, due to the visual limitations in actually defining the precise "video points" of interest during the digital video analysis work.