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Video Analysis of the Inverted Pendulum Model of Walking- A Classroom Activity by Justin Dunlap (jdunlap@pdx.edu) Angela Steichen Crystal Wright Ralf Widenhorn AAPT Winter Meeting 2012

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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

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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 PSUs 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

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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

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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 decreasing

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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

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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 AAPT Winter Meeting 2012

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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

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Video Analysis in LoggerPro- Methods AAPT Winter Meeting 2012

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Video Analysis- the body as an inverted pendulum AAPT Winter Meeting 2012 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 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 Fr= (1.86 m/s) 2 /(0.93m)*(9.8m/s 2 ) = 0.38

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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. AAPT Winter Meeting 2012

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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 pre- health students Inverted pendulum model is a good meeting ground of physics and biomechanics AAPT Winter Meeting 2012

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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! AAPT Winter Meeting 2012

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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_Muybridgehttp://en.wikipedia.org/wiki/Eadweard_Muybridge Mitchell Leslie (May/June 2001). "The Man Who Stopped Time". Stanford Magazine. Retrieved June 21, 2010. ^"The Man Who Stopped Time"^ Williams, Alan Larson (1992) Republic of images: a history of French filmmaking Harvard University PressRepublic of images: a history of French filmmaking 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=OVwqiXJzR80 http://www.youtube.com/watch?v=OVwqiXJzR80 AAPT Winter Meeting 2012

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Treadmill AAPT Winter Meeting 2012

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Inverted pendulum model of walking AAPT Winter Meeting 2012

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Video Analysis in LoggerPro- Methods AAPT Winter Meeting 2012