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14 - Modeling human walking as an inverted pendulum of varying length

Published online by Cambridge University Press:  10 August 2009

By
Jack T. Stern ,
Brigitte Demes  and
D. Casey Kerrigan
Edited by
Fred Anapol ,
Rebecca Z. German  and
Nina G. Jablonski
Jack T. Stern
Affiliation:
Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA
Brigitte Demes
Affiliation:
Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA
D. Casey Kerrigan
Affiliation:
Department of Physical Medicine and Rehabilitation, School of Medicine, University of Virginia, Charlottesville, VA 22908-1007 USA
Fred Anapol
Affiliation:
University of Wisconsin, Milwaukee
Rebecca Z. German
Affiliation:
University of Cincinnati
Nina G. Jablonski
Affiliation:
California Academy of Sciences, San Francisco
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Summary

Symbols and abbreviations

  1. Ac axial (centripetal or centrifugal) acceleration of the mass

  2. ΔC forward translation of the substrate contact point

  3. COM center of mass

  4. D instantaneous horizontal distance traveled by the mass since t = 0

  5. Dh the total horizontal distance traveled by the mass during one swing of the inverted pendulum, i.e., the step length

  6. f stride frequency

  7. Fc centripetal force required to keep the mass on a circular path

  8. GRFv vertical component of the ground reaction force

  9. H instantaneous value of the height of the point mass (or COM)

  10. H height of the point mass (or COM) at the middle of the first double-support phase

  11. H height of the point mass (or COM) at the middle of the second double-support phase

  12. H height of the point mass (or COM) at the middle of the single-support phase

  13. ΔH maximum vertical excursion of the point mass (or COM) from MDS to MSS

  14. I moment of inertia of the mass about the pivot point of the inverted pendulum

  15. Lc the axially directed force exerted on the virtual stance limb (VSL) by the mass

  16. -Lc the axially directed force exerted on the mass by the virtual stance limb (VSL)

  17. M mass

  18. MDS middle of double-support phase

  19. MSS middle of single-support phase

  20. R the length of the virtual stance limb (from substrate contact-point to the point mass or its surrogate) at any moment in time

  21. R length of the virtual stance limb at MDS

  22. R length of the virtual stance limb at MSS

  23. S stature

  24. t time

  25. t half the duration of the swing of the inverted pendulum

  26. V velocity of the mass

  27. Vc axial (centripetal or centrifugal) velocity of the mass

  28. Vo orbital (tangential) velocity of the mass

  29. […]

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Chapter
Information
Shaping Primate Evolution
Form, Function, and Behavior
 , pp. 297 - 333
Publisher: Cambridge University Press
Print publication year: 2004

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References

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  • Modeling human walking as an inverted pendulum of varying length
    • By Jack T. Stern, Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA, Brigitte Demes, Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA, D. Casey Kerrigan, Department of Physical Medicine and Rehabilitation, School of Medicine, University of Virginia, Charlottesville, VA 22908-1007 USA
  • Edited by Fred Anapol, University of Wisconsin, Milwaukee, Rebecca Z. German, University of Cincinnati, Nina G. Jablonski, California Academy of Sciences, San Francisco
  • Book: Shaping Primate Evolution
  • Online publication: 10 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511542336.019
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  • Modeling human walking as an inverted pendulum of varying length
    • By Jack T. Stern, Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA, Brigitte Demes, Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA, D. Casey Kerrigan, Department of Physical Medicine and Rehabilitation, School of Medicine, University of Virginia, Charlottesville, VA 22908-1007 USA
  • Edited by Fred Anapol, University of Wisconsin, Milwaukee, Rebecca Z. German, University of Cincinnati, Nina G. Jablonski, California Academy of Sciences, San Francisco
  • Book: Shaping Primate Evolution
  • Online publication: 10 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511542336.019
Available formats
×

Save book to Google Drive

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  • Modeling human walking as an inverted pendulum of varying length
    • By Jack T. Stern, Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA, Brigitte Demes, Department of Anatomical Sciences, School of Medicine, Health Sciences Center, Stony Brook University, Stony Brook, NY 11794-8081, USA, D. Casey Kerrigan, Department of Physical Medicine and Rehabilitation, School of Medicine, University of Virginia, Charlottesville, VA 22908-1007 USA
  • Edited by Fred Anapol, University of Wisconsin, Milwaukee, Rebecca Z. German, University of Cincinnati, Nina G. Jablonski, California Academy of Sciences, San Francisco
  • Book: Shaping Primate Evolution
  • Online publication: 10 August 2009
  • Chapter DOI: https://doi.org/10.1017/CBO9780511542336.019
Available formats
×