Transcript Video Analysis of the Inverted Pendulum Model of Walking

Video Analysis of the
Inverted Pendulum Model of WalkingA Classroom Activity
by Justin Dunlap ([email protected])
Angela Steichen
Crystal Wright
Ralf Widenhorn
AAPT Winter Meeting 2012
Outline
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Physics for pre-health students
Biomechanics- Rich history of video analysis
The inverted pendulum model of walking
Video Analysis in LoggerPro
▫ Methods
▫ Results
• From galloping horses to robots
• Conclusion
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Physics for pre-health students
• Develop innovative and educational curriculum targeted
at pre-health students
• A majority of students taking general physics classes
are not physics majors
• This is true in general and in particular at Portland
State University
• Roughly 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 min
Inverted Pendulum- The Physics
v min
a  min
KE  min
PE max
• Inverted pendulum:
▫ Simple pendulum rotated
180° so mass is now
supported above rigid rod.
v increasing
a  increasing
KE  increasing
PE decreasing
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 Sclerosis
• Relevancy to physics class room:
▫ Provides the opportunity to study and discuss:
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Kinematics
Velocity
Acceleration
Potential Energy
Kinetic Energy
Mechanical Energy
Harmonic motion
Frequency
Vector analysis
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Biomechanics- Rich history of video analysis
• Eadweard Muybridge and the
galloping horse
▫ 1872- 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 process
▫ Muybridge 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 LoggerPro
• Considerations for taking a good video
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Distance between camera and subject
Lighting
Speed of walker
Setting the scale
Indicator on center of mass
Background noise
Keeping arms up
Video Analysis in LoggerPro- Methods
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Video Analysis- the body as an inverted pendulum
Potential Energy
Kinetic Energy in y
Kinetic Energy in x
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Video Analysis- The Froude Number
• Froude 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 force
mv 2
2
v
l
Fr 
Fr 
mg
Fr= (1.86 m/s)
lg 2/(0.93m)*(9.8m/s2) = 0.38
• A Fr of about 0.5 will be about where it is more
efficient to run rather than walk for humans.
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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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Conclusion
• Video analysis of biomechanics has a rich history
and potential for future applications
• Basic biomechanics of walking can be taught in a
general physics course aimed at engaging prehealth students
• Inverted pendulum model is a good meeting
ground of physics and biomechanics
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The End
• Thank you to the LivePhoto research project for
financial support of this presentation today.
• Thank you for your attention!
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References
• Inverted Pendulum Model▫
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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▫
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http://en.wikipedia.org/wiki/Eadweard_Muybridge
Mitchell 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
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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 robothttp://www.youtube.com/watch?v=OVwqiXJzR80
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Treadmill
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