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 2012

Outline•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

AAPT Winter Meeting 2012

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

AAPT Winter Meeting 2012

Inverted Pendulum- The Physics•Simple Pendulum:

▫Idealized body where a mass is suspended below a massless rigid rod.

v 0a maxKE 0PE max

v maxa 0KE maxPE min

Inverted Pendulum- The Physics

•Inverted pendulum:▫Simple pendulum rotated

180° so mass is now supported above rigid rod.

v mina minKE minPE max

v increasinga increasingKE increasingPE 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:

Kinematics Velocity Acceleration Potential Energy Kinetic Energy Mechanical Energy Harmonic motion Frequency Vector analysis

AAPT Winter Meeting 2012

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

AAPT Winter Meeting 2012

Video Analysis in LoggerPro•Considerations for taking a good video

▫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

AAPT Winter Meeting 2012

Video Analysis- the body as an inverted pendulum

AAPT Winter Meeting 2012

Potential EnergyKinetic Energy in yKinetic Energy in x

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

•A Fr of about 0.5 will be about where it is more efficient to run rather than walk for humans.

AAPT Winter Meeting 2012

lgvFr2

mgl

mvFr

2

Fr= (1.86 m/s)2/(0.93m)*(9.8m/s2) = 0.38

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.

AAPT Winter Meeting 2012

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 pre-health students

•Inverted pendulum model is a good meeting ground of physics and biomechanics

AAPT Winter Meeting 2012

The End• Thank you to the LivePhoto research

project for financial support of this presentation today.

• Thank you for your attention!

AAPT Winter Meeting 2012

References• Inverted 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_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

▫ 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

2012

Treadmill

AAPT Winter Meeting 2012