A Comparison of Computation Methods for Leg Stiffness During Hopping

2014 ◽  
Vol 30 (1) ◽  
pp. 154-159 ◽  
Author(s):  
Hiroaki Hobara ◽  
Koh Inoue ◽  
Yoshiyuki Kobayashi ◽  
Toru Ogata
Keyword(s):  
Ground Reaction Force ◽  
Stance Phase ◽  
Center Of Mass ◽  
Reaction Force ◽  
Sine Wave ◽  
Phase Method ◽  
Leg Stiffness ◽  
Mass Displacement ◽  
Male Subjects ◽  
Oscillation Method

Despite the presence of several different calculations of leg stiffness during hopping, little is known about how the methodologies produce differences in the leg stiffness. The purpose of this study was to directly compareKlegduring hopping as calculated from three previously published computation methods. Ten male subjects hopped in place on two legs, at four frequencies (2.2, 2.6, 3.0, and 3.4 Hz). In this article, leg stiffness was calculated from the natural frequency of oscillation (method A), the ratio of maximal ground reaction force (GRF) to peak center of mass displacement at the middle of the stance phase (method B), and an approximation based on sine-wave GRF modeling (method C). We found that leg stiffness in all methods increased with an increase in hopping frequency, butKlegvalues using methods A and B were significantly higher than when using method C at all hopping frequencies. Therefore, care should be taken when comparing leg stiffness obtained by method C with those calculated by other methods.

Differences in Spring-Mass Characteristics Between One- and Two-Legged Hopping

2013 ◽  
Vol 29 (6) ◽  
pp. 785-789 ◽  
Author(s):  
Hiroaki Hobara ◽  
Yoshiyuki Kobayashi ◽  
Emika Kato ◽  
Toru Ogata
Keyword(s):  
Ground Reaction Force ◽  
Center Of Mass ◽  
Reaction Force ◽  
Training Methods ◽  
Plyometric Training ◽  
Vertical Ground Reaction Force ◽  
Mass Model ◽  
Leg Stiffness ◽  
Mass Displacement ◽  
Vertical Ground

Although many athletic activities and plyometric training methods involve both unilateral and bilateral movement, little is known about differences in the leg stiffness (Kleg) experienced during one-legged hopping (OLH) and two-legged hopping (TLH) in place. The purpose of this study was to investigate the effect of hopping frequencies on differences inKlegduring OLH and TLH. Using a spring-mass model and data collected from 17 participants during OLH and TLH at frequencies of 2.0, 2.5, and 3.0 Hz,Klegwas calculated as the ratio of maximal ground reaction force (Fpeak) to the maximum center of mass displacement (ΔCOM) at the middle of the stance phase measured from vertical ground reaction force. BothKlegandFpeakwere found to be significantly greater during TLH than OLH at all frequencies, but type of hopping was not found to have a significant effect on ΔCOM. These results suggest thatKlegis different between OLH and TLH at a given hopping frequency and differences inKlegduring OLH and TLH are mainly associated with differences inFpeakbut not ΔCOM.

Effect of Hopping Frequency on Bilateral Differences in Leg Stiffness

2013 ◽  
Vol 29 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Hiroaki Hobara ◽  
Koh Inoue ◽  
Kazuyuki Kanosue
Keyword(s):  
Ground Reaction Force ◽  
Center Of Mass ◽  
Reaction Force ◽  
Human Movement ◽  
Vertical Ground Reaction Force ◽  
Mass Model ◽  
Lower Extremity Injuries ◽  
Leg Stiffness ◽  
Significant Difference ◽  
Bilateral Differences

Understanding the degree of leg stiffness during human movement would provide important information that may be used for injury prevention. In the current study, we investigated bilateral differences in leg stiffness during one-legged hopping. Ten male participants performed one-legged hopping in place, matching metronome beats at 1.5, 2.2, and 3.0 Hz. Based on a spring-mass model, we calculated leg stiffness, which is defined as the ratio of maximal ground reaction force to maximum center of mass displacement at the middle of the stance phase, measured from vertical ground reaction force. In all hopping frequency settings, there was no significant difference in leg stiffness between legs. Although not statistically significant, asymmetry was the greatest at 1.5 Hz, followed by 2.2 and 3.0 Hz for all dependent variables. Furthermore, the number of subjects with an asymmetry greater than the 10% criterion was larger at 1.5 Hz than those at 2.2 and 3.0 Hz. These results will assist in the formulation of treatment-specific training regimes and rehabilitation programs for lower extremity injuries.

scholarly journals Estimates of Running Ground Reaction Force Parameters from Motion Analysis

2017 ◽  
Vol 33 (1) ◽  
pp. 69-75 ◽  
Author(s):  
Gaspare Pavei ◽  
Elena Seminati ◽  
Jorge L.L. Storniolo ◽  
Leonardo A. Peyré-Tartaruga
Keyword(s):  
Motion Analysis ◽  
Ground Reaction Force ◽  
Center Of Mass ◽  
Reaction Force ◽  
The Body ◽  
Vertical Force ◽  
Vertical Stiffness ◽  
Leg Stiffness ◽  
Force Peak ◽  
Body Center

We compared running mechanics parameters determined from ground reaction force (GRF) measurements with estimated forces obtained from double differentiation of kinematic (K) data from motion analysis in a broad spectrum of running speeds (1.94–5.56 m⋅s–1). Data were collected through a force-instrumented treadmill and compared at different sampling frequencies (900 and 300 Hz for GRF, 300 and 100 Hz for K). Vertical force peak, shape, and impulse were similar between K methods and GRF. Contact time, flight time, and vertical stiffness (kvert) obtained from K showed the same trend as GRF with differences < 5%, whereas leg stiffness (kleg) was not correctly computed by kinematics. The results revealed that the main vertical GRF parameters can be computed by the double differentiation of the body center of mass properly calculated by motion analysis. The present model provides an alternative accessible method for determining temporal and kinetic parameters of running without an instrumented treadmill.

scholarly journals Effects of Tendon Release Surgery on Inter-Limb Leg Stiffness Control in Children with Spastic Diplegic Cerebral Palsy during Gait

2021 ◽  
Vol 11 (10) ◽  
pp. 4562
Author(s):  
Chien-Chung Kuo ◽  
Hsing-Po Huang ◽  
Hsuan-Yu Lu ◽  
Tsan-Yang Chen ◽  
Ting-Ming Wang ◽  
...  
Keyword(s):  
Cerebral Palsy ◽  
Stance Phase ◽  
Reaction Force ◽  
Bilateral Symmetry ◽  
Healthy Controls ◽  
Leg Stiffness ◽  
Characteristic Features ◽  
Total Leg ◽  
Analysis System ◽  
Single Limb Support

Impaired motor control and musculotendon tightness in the lower extremities are characteristic features of patients with diplegic cerebral palsy (CP). Tendon release surgery (TRS) helps improve joint and leg stiffness, but the effects of TRS on inter-limb coordination in terms of the total leg stiffness, and the bilateral symmetry in leg stiffness during gait, remain unknown. Ten children with spastic diplegic CP scheduled for TRS and ten healthy controls participated in this study. The inter-limb sharing of total leg stiffness during double-limb support phase and bilateral leg stiffness symmetry during stance phase of gait were calculated using the kinematic and ground reaction force data measured by a motion analysis system. Before TRS, the patients with diplegic CP walked with a decreased share of total leg stiffness during weight-acceptance (p < 0.05) and with increased bilateral leg stiffness asymmetry during single-limb support and weight-transfer during gait (p < 0.05) when compared to healthy controls. After TRS, the bilateral leg stiffness asymmetry was significantly reduced in the CP group, especially in the terminal stance phase, with inter-limb sharing of total leg stiffness becoming similar to that in controls (p > 0.05). The surgery seemed to improve the lower limb control and increased the bilateral limb symmetry during gait.

Mechanical power output during running accelerations in wild turkeys

2002 ◽  
Vol 205 (10) ◽  
pp. 1485-1494 ◽  
Author(s):  
Thomas J. Roberts ◽  
Jeffrey A. Scales
Keyword(s):  
Power Output ◽  
Ground Reaction Force ◽  
Center Of Mass ◽  
Reaction Force ◽  
Mechanical Power ◽  
Force Vector ◽  
Instantaneous Power ◽  
Hindlimb Muscle ◽  
Wild Turkeys ◽  
Running Mechanics

SUMMARYWe tested the hypothesis that the hindlimb muscles of wild turkeys(Meleagris gallopavo) can produce maximal power during running accelerations. The mechanical power developed during single running steps was calculated from force-plate and high-speed video measurements as turkeys accelerated over a trackway. Steady-speed running steps and accelerations were compared to determine how turkeys alter their running mechanics from a low-power to a high-power gait. During maximal accelerations, turkeys eliminated two features of running mechanics that are characteristic of steady-speed running: (i) they produced purely propulsive horizontal ground reaction forces, with no braking forces, and (ii) they produced purely positive work during stance, with no decrease in the mechanical energy of the body during the step. The braking and propulsive forces ordinarily developed during steady-speed running are important for balance because they align the ground reaction force vector with the center of mass. Increases in acceleration in turkeys correlated with decreases in the angle of limb protraction at toe-down and increases in the angle of limb retraction at toe-off. These kinematic changes allow turkeys to maintain the alignment of the center of mass and ground reaction force vector during accelerations when large propulsive forces result in a forward-directed ground reaction force. During the highest accelerations, turkeys produced exclusively positive mechanical power. The measured power output during acceleration divided by the total hindlimb muscle mass yielded estimates of peak instantaneous power output in excess of 400 W kg-1 hindlimb muscle mass. This value exceeds estimates of peak instantaneous power output of turkey muscle fibers. The mean power developed during the entire stance phase increased from approximately zero during steady-speed runs to more than 150 W kg-1muscle during the highest accelerations. The high power outputs observed during accelerations suggest that elastic energy storage and recovery may redistribute muscle power during acceleration. Elastic mechanisms may expand the functional range of muscle contractile elements in running animals by allowing muscles to vary their mechanical function from force-producing struts during steady-speed running to power-producing motors during acceleration.

Carrying loads with springy poles

1991 ◽  
Vol 71 (3) ◽  
pp. 1119-1122 ◽  
Author(s):  
R. Kram
Keyword(s):  
Oxygen Consumption ◽  
Ground Reaction Force ◽  
Oxygen Consumption Rate ◽  
Consumption Rate ◽  
Reaction Force ◽  
Load Carriage ◽  
Vertical Ground Reaction Force ◽  
Suspension Systems ◽  
Vertical Ground ◽  
Male Subjects

People throughout Asia use springy bamboo poles to carry the loads of everyday life. These poles are a very compliant suspension system that allows the load to move along a nearly horizontal path while the person bounces up and down with each step. Could this be an economical way to carry loads inasmuch as no gravitational work has to be done to lift the load repeatedly? To find out, an experiment was conducted in which four male subjects ran at 3.0 m/s on a motorized treadmill with no load and while carrying a load equal to 19% body wt with compliant poles. Oxygen consumption rate, vertical ground reaction force, and the force exerted by the load on the shoulders were measured. Oxygen consumption rate increased by 22%. The same increase has previously been observed when loads are carried with a backpack. Thus compliant poles are not a particularly economical method of load carriage. However, pole suspension systems offer important advantages: they minimize peak shoulder forces and loading rates. In addition, the peak vertical ground reaction force is only slightly increased above unloaded levels when loads are carried with poles.

scholarly journals Dynamic Balancing Responses in Unilateral Transtibial Amputees Following Outward-Directed Perturbations During Slow Treadmill Walking Differ Considerably for Amputated and Non-Amputated Side

2021 ◽  
Author(s):  
Andrej Olenšek ◽  
Matjaž Zadravec ◽  
Helena Burger ◽  
Zlatko Matjačić
Keyword(s):  
Stance Phase ◽  
Center Of Pressure ◽  
Center Of Mass ◽  
Reaction Force ◽  
Dynamic Balancing ◽  
Transtibial Amputation ◽  
Control Subjects ◽  
Foot Strike ◽  
Transtibial Amputees ◽  
Proprioceptive Function

Abstract BackgroundDue to disrupted motor and proprioceptive function lower limb amputation imposes considerable challenges associated with balance and greatly increases risk of falling in case of perturbations during walking. The aim of this study was to investigate dynamic balancing responses in unilateral transtibial amputees when they were subjected to perturbing pushes to the pelvis in outward direction at the time of foot strike on non-amputated and amputated side during slow walking.MethodsFourteen subjects with unilateral transtibial amputation and nine control subjects participated in the study. They were subjected to perturbations that were delivered to the pelvis at the time of foot strike of either the left or right leg. We recorded trajectories of center of pressure and center of mass, durations of in-stance and stepping periods as well as ground reaction forces. Statistical analysis was performed to determine significant differences in dynamic balancing responses between control subjects and subjects with amputation when subjected to outward-directed perturbation upon entering stance phases with non-amputated or amputated side.ResultsWhen outward-directed perturbations were delivered at the time of foot strike of the non-amputated leg, subjects with amputation were able to modulate center of pressure and ground reaction force similarly as control subjects which indicates application of in-stance balancing strategies. On the other hand, there was a complete lack of in-stance response when perturbations were delivered when the amputated leg entered the stance phase. Subjects with amputations instead used the stepping strategy and adjusted placement of the non-amputated leg in the ensuing stance phase to make a cross-step. Such response resulted in significantly higher displacement of center of mass. ConclusionsResults of this study suggest that due to the absence of the COP modulation mechanism, which is normally supplied by ankle motor function, people with unilateral transtibial amputation are compelled to choose the stepping strategy over in-stance strategy when they are subjected to outward-directed perturbation on the amputated side. However, the stepping response is less efficient than in-stance response. To improve their balancing responses to unexpected balance perturbation people fitted with passive transtibial prostheses should undergo perturbation-based balance training during clinical rehabilitation.

scholarly journals Estimation of leg stiffness using an approximation to the planar spring–mass system in high-speed running

2020 ◽  
Vol 17 (1) ◽  
pp. 172988141989071
Author(s):  
Wei Guo ◽  
Changrong Cai ◽  
Mantian Li ◽  
Fusheng Zha ◽  
Pengfei Wang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
High Speed ◽  
Stance Phase ◽  
Center Of Mass ◽  
Critical Role ◽  
Line Center ◽  
Motion Model ◽  
Mass System ◽  
Leg Stiffness ◽  
Wide Range

Leg stiffness plays a critical role in legged robots’ speed regulation. However, the analytic solutions to the differential equations of the stance phase do not exist, of course not for the exact analytical solution of stiffness. In view of the challenge in dealing with every circumstance by numerical methods, which have been adopted to tabulate approximate answers, the “harmonic motion model” was used as approximation of the stance phase. However, the wide range leg sweep angles and small fluctuations of the “center of mass” in fast movement were overlooked. In this article, we raise a “triangle motion model” with uniform forward speed, symmetric movement, and straight-line center of mass trajectory. The characters are then shifted to a quadratic equation by Taylor expansion and obtain an approximate analytical solution. Both the numerical simulation and ADAMS-Matlab co-simulation of the control system show the accuracy of the triangle motion model method in predicting leg stiffness even in the ultra-high-speed case, and it is also adaptable to low-speed cases. The study illuminates the relationship between leg stiffness and speed, and the approximation model of the planar spring–mass system may serve as an analytical tool for leg stiffness estimation in high-speed locomotion.

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