Inverted Pendulum Model of Walking A Classroom Activity by Justin Dunlap jdunlappdxedu Angela Steichen Crystal Wright Ralf Widenhorn AAPT Winter Meeting 2012 Outline Physics for prehealth students ID: 292696
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Video Analysis of the Inverted Pendulum Model of Walking- A Classroom Activity
by Justin Dunlap (jdunlap@pdx.edu)Angela SteichenCrystal WrightRalf Widenhorn
AAPT Winter Meeting 2012Slide2
OutlinePhysics for pre-health studentsBiomechanics- Rich history of video analysis
The inverted pendulum model of walkingVideo Analysis in LoggerProMethodsResultsFrom galloping horses to robotsConclusion
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Physics for pre-health students
Develop innovative and educational curriculum targeted at pre-health studentsA majority of students taking general physics classes are not physics majors This is true in general and in particular at Portland State UniversityRoughly 50% of students in PSU’s general physics labs are pre-health (larger percentage in algebra based physics, ~80%)
Teach the same core topics taught in all general physics classes but with relevant examples and applications to the pre-health student
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Inverted Pendulum- The Physics
Simple Pendulum:Idealized body where a mass is suspended below a massless rigid rod.
v
0
a
max
KE 0
PE max
v
max
a
0
KE max
PE minSlide5
Inverted Pendulum- The Physics
Inverted pendulum:
Simple pendulum rotated 180° so mass is now supported above rigid rod.
v
min
a
min
KE min
PE max
v
increasing
a
increasing
KE increasing
PE decreasingSlide6
Physics for pre-health students
Relevancy to pre-health students:Video analysis and the inverted pendulum model are used to study sports medicine, physiology, and neurological diseases such as Parkinsons and Multiple SclerosisRelevancy to physics class room:Provides the opportunity to study and discuss:Kinematics
VelocityAccelerationPotential EnergyKinetic Energy
Mechanical Energy
Harmonic motion
Frequency
Vector analysis
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Biomechanics- Rich history of video analysis
Eadweard Muybridge and the galloping horse1872- Leland Stanford (former governor of California) set out to prove horses have all four hooves off of the ground while running- a hotly debated topic at the time Muybridge, set up cameras in a line triggered by a thread as the horse passed to record video of a horse galloping- proving that all the hooves do leave the ground ~1878, essentially inventing video and video analysis in the processMuybridge went on to record many videos of other animals as well as humans doing various activities such as running, boxing,
smithing, leap frogging one another, and carrying water
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Video Analysis in LoggerProConsiderations for taking a good video
Distance between camera and subjectLightingSpeed of walkerSetting the scaleIndicator on center of massBackground noiseKeeping arms up Slide9
Video Analysis in LoggerPro- Methods
AAPT Winter Meeting 2012Slide10
Video Analysis- the body as an inverted pendulum
AAPT Winter Meeting 2012
Potential EnergyKinetic Energy in y
Kinetic Energy in xSlide11
Video Analysis- The Froude NumberFroude Number (Fr)- a dimensionless quantity useful in biomechanics to determine when a land animal changes from one gait to another
Calculated by dividing the centripetal force by the gravitational forceA Fr of about 0.5 will be about where it is more efficient to run rather than walk for humans. AAPT Winter Meeting 2012
Fr= (1.86 m/s)
2
/(0.93m)*(9.8m/s
2
) = 0.38Slide12
From galloping horses to robots
“ In recent decades, there has been a great deal of effort to model and simulate human walking in both the robotics and biomechanics fields.”- Xiang, et al.
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ConclusionVideo analysis of biomechanics has a rich history and potential for future applicationsBasic biomechanics of walking can be taught in a general physics course aimed at engaging pre-health students
Inverted pendulum model is a good meeting ground of physics and biomechanicsAAPT Winter Meeting 2012Slide14
The EndThank you to the
LivePhoto research project for financial support of this presentation today.Thank you for your attention!AAPT Winter Meeting 2012Slide15
ReferencesInverted Pendulum Model-Xiang, Y.,
Arora, J.S. & Abdel-Malek, K. Physics-based modeling and simulation of human walking: a review of optimization-based and other approaches. Structural and Multidisciplinary Optimization 42, 1-23 (2010).Alexander, R.M. The Gaits of Bipedal and
Quadrupedal Animals. The International Journal of Robotics Research 3
, 49 -59 (1984).
Usherwood
, J.R. Why not walk faster?
Biol.
Lett
.
1
, 338-341 (2005
).
Eadweard
Muybridge and the galloping horse-
http://en.wikipedia.org/wiki/Eadweard_MuybridgeMitchell Leslie (May/June 2001). "The Man Who Stopped Time". Stanford Magazine. Retrieved June 21, 2010. ^ Williams, Alan Larson (1992)
Republic of images: a history of French filmmaking
Harvard University Press
Robotics
Kajita
S.
et al.
Biped walking pattern generation by a simple three-dimensional inverted pendulum model.
Advanced Robotics 17, 131-147 (2003).Real time biped walking gait pattern generator for a real robot- http://www.youtube.com/watch?v=OVwqiXJzR80AAPT Winter Meeting 2012Slide16
Treadmill
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Inverted pendulum model of walking
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Video Analysis in LoggerPro- Methods
AAPT Winter Meeting 2012