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Effective leg stiffness increases with speed to maximize propulsion energy
Dynamics & Energetics of Human Walking
Seyoung Kim and Sukyung Park, “Leg stiffness increases with speed to modu-late gait frequency and propulsion energy”, Journal of Biomechanics, Vol.44(7): 1253-1258, 2011
Human Gait Research
Seyoung Kim, PhD
Model based balance & gait analysis
• Mechanical model-based human gait analysis– Periodic gait cycle [ Mcgeer 1990; Garcia et al. 1998 ]
– Lateral stability [ Kuo 1999 ]
– Advantage of curved foot [ Adamczyk et al. 2006 ]
– Collision dynamics [ Jin and Park 2011 ]
Research background
[ Kuo 2001 ][ Geyer et al. 2006 ]
Model based balance & gait analysis
Spring-like leg behavior to human gait dynamics
• Lower limb stiffness was introduced in order to account for walking dynamics.
spring-like leg mechanics
[ Geyer et al. 2006; Whittington and Thelen 2009; Kim and Park 2011 ]
Leg stiffness
The relationship between Leg stiffness change w/ speed and energetic
benefitHas not been investigated.
Model based balance & gait analysis
• Objective : – We examined whether humans may benefit from spring-
like leg mechanics during walking.
• Hypothesis : [1] Human walking may take advantage of resonance
characteristics of the spring-like leg.[2] Humans may change their leg stiffness to obtain max-
imum propulsion energy as walking speed changes.
Research objective
Model based balance & gait analysis
• Subjects – Eight healthy young (7M/1F, 23±2y)– 1.68±0.06 m / 66.7±10.9 kg
• Protocols– Three sets of four randomly ordered frequency– Self-selected natural speed and maximum walking speed
• Measurement– Kinematics : sacrum and both ankles by Motion capture
system– Kinetics : Ground reaction forces (GRFs) by three force
plates
• Center of mass (CoM) estimation– Twice integrating the accelerations obtained from the
GRFs data [ Donelan et al. 2002b; Yeom and Park 2010 ]
Walking experiment
@ Biomimetics Lab
Model based balance & gait analysis
Compliant walking model
• M : body mass• R : curved foot radius• θ : leg angle• L : spring leg length• K : spring constant• C : damping constant
[ Equation of motion ]
][ L,,L,x:state Heel-strike force
Motion
Push-off force
Model based balance & gait analysis
• Double support phase (DS)– DS begins when the leading leg (L1) hits the ground.– DS continues until the trailing leg (L2) spring reaches its
slack length (L0), where the single support phase begins. – During the DS, the CoM motion is constrained by two
compliant legs.
• Single support phase (SS)– The trailing leg is repositioned ahead of the body’s CoM
at a given inter-leg angle and becomes the leading leg for the next step.
– When the leading leg hits the ground, i.e., touchdown, SS is finished.
Mechanism of the walking modelL1L2
Model based balance & gait analysis
• Spring and damping constants from an optimiza-tion (Matlab®) that minimized the least square error between the GRF data and the model simu-lation over one step gait cycle, which consists of double and single support phases.
Estimation of leg stiffness by model simulation
[ Compliant walking model ]
[ Vertical leg stiffness ]
Model based balance & gait analysis
• Fitting results• Model parameter change with gait speed• Mechanical resonance characteristics• Mechanical energy analysis
Results and Discussion
Model based balance & gait analysis
Fitting result: goodness of fit (avg. 0.81±0.06)
[ S. Kim and S. Park, Journal of Biomechan-ics (2011) ]
Model based balance & gait analysis
Model parameter (K, z) change with gait speed
A B
• Humans increase joint stiffness as gait speed increases. • The increase in joint stiffness could be achieved by in-
creased muscle forces that reduce the range of joint motion.
[ S. Kim and S. Park, Journal of Biomechan-ics (2011) ]
93.14x16.30y
026.0x048.0y
Why the leg stiffness increases with gait speed ?
Is there any energetic or dynamic benefit ?
Model based balance & gait analysis
• The duration of single support phase ≈ the period from damped natural frequency of the leg.
The duration of the single support phase and the period of oscillation of the compliant leg
[ S. Kim and S. Park, Journal of Biomechan-ics (2011) ]
∆t
d
[ Video clip uploaded by moogyxo,Youtube .com (2007) ]
Driving frequency: 1Hz
Natural frequency: 1.6, 1, 0.63 Hz
Human walking may take advantage of reso-nance ?
Analysis in the view of mechanical energy
Model based balance & gait analysis
Parameter study: energetic benefits of human walking
Propulsion energy as a function of leg stiffness (14 ~ 28 kN/m) and walking speed (0.8 ~
2.2 m/s)
Model based balance & gait analysis
20propulsion )LL(K
2
1E
Leg stiffness to store max. propulsion energy
[ S. Kim and S. Park, Journal of Biomechan-ics (2011) ]
Model based balance & gait analysis
• Humans emulate spring-like leg mechanics, and modu-late the apparent stiffness at a given walking speed.
Conclusion
• Leg stiffness increases with speed to modulate gait frequency and propulsion energy.
• Application: • Quantifying parameter changes among different walking condi-
tion and/or subject groups• Gait performance assessment for the elderly or patients• Development of walking assist device• Multi-joint stiffness to whole leg stiffness
Model based balance & gait analysis
• The compliant walking model does not require an energy input mechanism to maintain steady walk-ing. However, human walking requires active pos-itive and negative muscle work [ Donelan et al., 2002 ].
• Multi-joint stiffness characteristics were lumped into whole-leg stiffness. Thus, the compliant walk-ing model does not specify how changes in leg stiffness might be attributed to changes at each joint.
Limitations
Model based balance & gait analysis
• Funds– Postural control study was supported by a Basic Research Fund
of the Korea Institute of Machinery and Materials, the second stage of the Brain Korea 21 Project, and a National Institute on Aging.
– Walking research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Tech-nology (#2010-0013306) and the Unmanned Technology Re-search Center (UTRC) at the Korea Advanced Institute of Sci-ence and Technology (KAIST), originally funded by DAPA, ADD.
• Collaborators– Fay B. Horak (Oregon Health & Science University)– Patricia Carlson-Kuhta (Oregon Health & Science University)– Chris G. Atkeson (Carnegie Mellon University)
Acknowledgement
The oscillatory behavior of the CoM facilitates mechanical energy balance between push-off
and heel strike
Dynamics & Energetics of Human Walking
Seyoung Kim and Sukyung Park, “The oscillatory behavior of the CoM facilitates mechanical en-ergy balance between push-off and heel strike”, Journal of Biomechanics, Vol.44(7): 1253-1258, 2011
Human Gait Research
Seyoung Kim, PhD
Model based balance & gait analysis
• The least costly gait is achieved when the push-off propulsion fully compensates for the collision loss during the double support phase, during which the redirection of the center of mass (CoM) occurs [ Jin and Park 2011; Kuo 2002 ].
• The duration of the CoM redirection can also be defined based on changes in work or velocity, and those durations are greater than that of the dou-ble support phase.
• The purpose of this study was to examine whether different definitions of the step-to-step transition (SST) would affect the mechanical en-ergy balance between push-off and heel strike during gait.
Introduction
[ Adamczyk and Kuo 2009 ]
Model based balance & gait analysis
• The observed robustness of energetic optimality may be attributable to the seemingly symmetric oscillatory behavior of the CoM during the step-to-step transition. – Recent studies have described the motion of the CoM of
the body during the gait cycle as the oscillation of the inertia on a compliant leg.
– Due to the intrinsic symmetry of the mechanical power of an oscillatory mechanism around the minimum and maximum heights of the CoM, the mechanical powers of the mass before and after the mid point of the double support phase are approximated to be the same in mag-nitude but opposite in sign, showing energetic symme-try.
Conclusion
Model based balance & gait analysis
• Funds– This research was supported by the Basic Science Re-
search Program through the National Research Founda-tion of Korea (NRF) funded by the Ministry of Education, Science and Technology (#2010-0013306) and the Un-manned Technology Research Center (UTRC) at the Ko-rea Advanced Institute of Science and Technology (KAIST), originally funded by DAPA, ADD.
Acknowledgement
