The Effects Of Arm Swing On Human Gait Stability-Books Pdf

The effects of arm swing on human gait stability
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3946 S M Bruijn and others, motion increased with the arms swinging outward when swinging has an effect comparable to that of bumping into somebody while. forward Collins et al 2001 These findings suggest that arm swing walking This kind of perturbation occurs commonly in daily life. may at least influence global gait stability Still it remains to be but has not received much attention in the literature To allow for. shown how well these model findings translate to real human generalizability of our results to a broad range of walking speeds. walking Also these studies do not reveal how arm swing affects we measured subjects at three different walking speeds. local and global gait stability Based on the results of Collins and colleagues Collins et al. A recent study by Pijnappels and colleagues on the effect of arm 2009 and Pijnappels and colleagues Pijnappels et al 2010 we. swing in the recovery phase following an actual trip did provide hypothesized that 1 arm swing has no effect on the local stability. additional insight into the effects of arm swing on global gait stability of steady state gait 2 the initial phase of global gait stability. Pijnappels et al 2010 In their study the effects of angular indicates that walking with normal arm swing is less stable and 3. momentum generated by the arms were examined using simulations the reactive phase of global gait stability indicates that walking with. In the first simulation all momentum of the arms at the instant of normal arm swing leads to a better recovery following an external. tripping was transferred to the body as if the subjects arrested all perturbation as quantified by the rate of return to normal walking. arm movement at that instant and the arms were removed thereafter pattern. while in the second simulation all momentum carried by the arms. was simply regarded as lost as if the subjects had lost their arms MATERIALS AND METHODS. and thus all arm momentum at the instant of the trip Using actual Subjects. angular momenta derived from experimental data the position that Eleven healthy male subjects age 27 7 3 3 years mass 75 5 9 0 kg. the body would have assumed at the instant of recovery foot height 1 80 0 06 m means s d participated in the study None. placement was calculated Compared with the actual measured of the participants had an orthopedic or neurological disorder Before. position the simulations in which the angular momentum of the participating subjects signed an informed consent form The. arms was transferred to the body as would occur with normal arm protocol was approved by the ethical committee of the Faculty of. swing led to a less favorable position From this Pijnappels and Human Movement Sciences of VU University Amsterdam. colleagues concluded that angular momentum of the arms at the. instant of tripping is detrimental to recovery foot placement Procedures. Pijnappels et al 2010 These findings suggest that the absence of Neoprene bands with clusters of three infrared light emitting diodes. arm swing might enhance rather than diminish the initial phase of LEDs were attached to the trunk over the level of T6 and the. global gait stability heels The LEDs were used for movement registration with a 3D. The study by Pijnappels and coworkers Pijnappels et al 2010 optoelectronic system Optotrak Northern Digital Inc Waterloo. also suggested that corrective arm movements are made in the ON Canada consisting of a 2 3 camera array i e two. reactive phase thus postponing the transfer of angular momentum measurement units holding three sensors each Kinematic data were. to the trunk that would occur with normal arm swing so that the sampled at 50 samples s 1. actual foot placement is much more favorable than would be Subjects walked on a treadmill at three different speeds 0 56. expected from simulations in which such corrective movements are 1 12 and 1 68 m s 1 At each speed they walked for 5 min with. absent Thus in the reactive phase corrective arm responses likely normal arm swing and 5 min with arm swing restricted by a belt. make up for the negative effects of normal arm swing on the initial attached at pelvis height All six conditions were performed twice. phase of global gait stability Nonetheless the role of arm once without perturbations steady state walking trials and once. movements in stabilizing human gait needs to be elucidated further with perturbations perturbation trials The perturbation consisted. In the current study the local stability of steady state gait was of a pull to the trunk in the direction of walking Approximately. assessed using maximum time finite Lyapunov exponents Bruijn 20 perturbations were applied per perturbation trial during. et al 2009a Bruijn et al 2009b Dingwell and Cusumano 2000 quasi randomly selected strides determined by the experimenter. Dingwell et al 2008 Rosenstein et al 1993 which quantify the All conditions were performed in random order Subjects were told. average logarithmic rate of divergence after infinitesimally small whether or not the upcoming trial would be a perturbation trial but. perturbations Since such infinitesimally small perturbations occur they could not know which strides would be perturbed. naturally during steady state gait i e due to neuromuscular and. external noise this measure can be used to quantify the local Perturbation device. stability of steady state gait and may thus serve to capture the effects A custom made device see Figs 1 3 was used to apply the. of arm swing on the local stability of steady state gait perturbations to the subjects while they walked on the treadmill The. To gain more insight into the effects of arm swing on global gait device consisted of pneumatic pistons latches ropes pulleys and. stability responses to an external perturbation were analyzed in detail force transducers and was controlled on the basis of kinematic data. in the present study This analysis was based on a clear distinction When a predefined cue in the kinematic signal was detected see. between an initial phase which also contains information on the Fig 3 the previously free running ropes attached to the subject were. preceding steady state of the system and the recovery phase in which blocked by a pneumatic latch and the piston would go down. the efficacy of corrective actions performed to return to the normal causing via the pulleys a shortening of the rope by 0 2 m However. gait pattern could be quantified Of course such a distinction can because of the elasticity of the rope and movements of the harness. only give an indication of the difference between these two different relative to the subject the actual displacement of the subject was. phases as the phases themselves may interact and overlap always less than this The delay between detection of the kinematic. In summary the present study sought to elucidate the effect of cue and force onset was approximately 100 ms see Fig 3. arm swing on the local and global stability of gait Our analysis Forces during the perturbations were recorded at 200 samples s 1. was focused on trunk motions as maintaining stability of the upper using uni directional force transducers The force transducers were. body is a critical aspect of human locomotion MacKinnon and calibrated before each measurement session The perturbations. Winter 1993 The perturbation used was a pull to the trunk which were timed to occur just before heel strike on the basis of a lateral. THE JOURNAL OF EXPERIMENTAL BIOLOGY,Arm swing in human walking 3947. Fig 2 Top view of the harness the subjects were wearing and the ropes. attached to it rope attachments are indicated by A When a perturbation. D occurred the left rope would be pulled just before the right heelstrike and. vice versa Arrow B indicates the walking direction while arrow C indicates. the direction of the force during a perturbation on the left side. Pre processing, Trunk cluster marker 3D linear velocity data V were obtained by. C differentiation of the average position of the three trunk markers. while rotational velocities of the trunk cluster marker were. calculated as described in previous studies e g Berme and Capozzo. Fig 1 The set up used to perturb the subject A subject is shown wearing. 1990 All analyses were performed on the velocity time series to. the safety harness To this harness two ropes were attached see also minimize the effects of non stationarity in the position data i e. Fig 2 which were free running with some tension by means of the device wandering around on the treadmill. in A When a perturbation was delivered the device B would block the. ropes from running freely and a pneumatic piston C would go down. causing a shortening of the rope by 20 cm A uni directional force. transducer D was used to record the forces,250 Force N. Trunk marker lateral position mm,Trunk marker lateral position mm.
Foot marker vertical position mm,200 Foot marker vertical position mm. velocity reversal of the trunk markers with a force of about 200 N. and a duration of 200 ms and were applied contralateral to the 150. heel strike in the forward direction see Fig 3 It should be noted. that with increasing walking speed step times decrease which. given the fixed delay in the system meant that perturbations at. different speeds occurred at slightly different moments within the 50. stride cycle As a consequence any effect of speed reported in. the present study is actually a combined effect of speed and the 0. timing of the perturbation in the stride cycle Since the system. was position controlled the force exerted by the pistons provided 50. information on the compliance of the subject during the. perturbation and thus on the initial phase of global gait stability. We therefore registered maximum forces during each perturbation 0 6 0 4 0 2 0 0 2 0 4 0 6 0 8 1 0 1 2 1 4. The median of these forces within a trial was used for further Time s. statistical analysis Fmax, Fig 3 Plot showing the timing delay and variability of a series of. Calculations perturbations for one subject The perturbations were timed on the basis of. the change in lateral trunk velocity lateral trunk motions are shown as. Heel strikes, dotted lines The delay between the trigger signal vertical dotted line and. To allow time normalization of the data heel strikes were detected force onset vertical solid line was approximately 100 ms so that the. as the local minima in the vertical position of the heel marker Stride perturbation would occur just before heelstrike of the contralateral foot i e. times were then calculated as the average time between two the local minimum in the vertical signal of the heel marker depicted here. consecutive heel strikes by the dashed vertical line. THE JOURNAL OF EXPERIMENTAL BIOLOGY,3948 S M Bruijn and others. Local dynamic stability Heelstrike just after perturbation. Local dynamic stability expressed as maximum time finite Time to maximum distance. Lyapunov exponents was calculated from the unperturbed walking. Maximum distance from attractor B, trials only To this end state spaces were reconstructed from V and 16.
The first 140 strides of the signals were selected and then time. Distance from attractor,standard deviations, normalized using a spline interpolation so that each state space 12. consisted of 14 000 samples Bruijn et al 2009a England and D i A B A e i. Granata 2007 12D state spaces Bruijn et al 2010b Dingwell et 10. al 2007 Kang and Dingwell 2006a Kang and Dingwell 2006b 8. Kang and Dingwell 2008 Kang and Dingwell 2009 were then 6. First recovery heelstrike, reconstructed using these time normalized signals and their 25 Distance at first. samples delayed copies Next the average logarithmic divergence 4 heelstrike Dhc. was calculated using well documented methods Dingwell and Relaxation 2. distance A, Cusumano 2000 Rosenstein et al 1993 nearest neighbors were 0. calculated for each point and the distance between the trajectories 50 100 150. from these points over time was determined These differences were Time of stride. Perturbation onset, averaged and the logarithm was then taken to obtain a divergence. curve From this curve the maximum time finite Lyapunov Fig 4 Parameterization of the perturbation. exponents were calculated as the linear slopes from 0 to 0 5 strides. lS and from 4 to 10 strides lL Bruijn et al 2010b Bruijn et. where D refers to the Euclidian distance between the perturbed gait. Perturbation measures cycle and the average limit cycle A refers to the relaxation distance. Linear V and angular velocity time series of all trials were defined as the average value of D from i 100 to i 150 B refers. first time normalized using a spline interpolation so that every stride to the size of the initial perturbation and refers to the rate of. consisted of exactly 100 samples Then V and angular velocity return to the limit cycle Higher values of indicate a faster return. time series of the steady state trials were combined to construct an to the normal gait pattern Next the distance from the average limit. average limit cycle for each subject and trial NW normal cycle i e the attractor at the first recovery heel contact was. walking Furthermore for each percentage in this limit cycle the calculated Dhc For statistical analysis the median values of each. normal variability for each dimension was calculated as the standard parameter per condition per subject were used. deviation vNW All calculations were performed using custom made MatLab. Normalized Euclidean distances between the gait cycles during programs The MathWorks Inc Natick MA USA. the perturbation trials PW and the average limit cycle were then. calculated as Statistical analysis, D k 100 i k 0 n 1 The effects of condition arm swing vs no arm swing and speed.
i 1 100 as well as their interaction were tested using repeated measures. ANOVA for all variables i e the control variables number of. perturbations in a trial stride time stride time variability mdNW. NW i d PW k 100 i d vNW i d 2 1, and the dependent variables lS lL Fmax A B t and Dhc. where D k 100 i is the normalized distance in standard RESULTS. deviations for i of stride k 1 with n representing the maximum Stride times. number of strides in PW d is the dimension number NW is the There were no significant main effects of arm swing on average. limit cycle PW is the state of the perturbed walking trial and vNW stride time P 0 3 see Fig 5A and stride time variability P 0 5. is the variance of the limit cycle To examine to what extent the see Fig 5B nor were there significant interactions of speed. changes in perturbation parameters see below were dependent upon with arm swing P 0 2 for both stride time and stride time. changes in vNW we calculated the mean deviation from NW across variability These results imply that the time normalization of. the gait cycle as mdNW strides we used in our analysis of the perturbation parameters. did not bias our results with regard to the effects of arm. swing As expected both stride time and stride time variability. vNW i d 2 2 decreased significantly P 0 001 for both with increasing. walking speed, The start of a perturbation was determined as the last sample. before the force exceeded 40 N see also Fig 3 We used 40 N as Local dynamic stability. a cut off as there was already some tension in the ropes which For steady state gait lS showed larger values when walking with. given the noise would otherwise lead to false positive perturbation normal arm swing however this difference was not significant. detections The time to the maximum D after each perturbation P 0 06 see Fig 6A There was a significant effect of speed on lS. started was detected t see also Fig 4 From then on the P 0 01 with increasing walking speed leading to lower values. exponential decay or relaxation to the limit cycle was quantified of lS There was no significant effect of arm swing on lL P 0 2. using see Post et al 2000 see also Fig 4 see Fig 6B but again there was a significant effect of walking speed. P 0 01 with higher walking speeds leading to higher values of. D i A B A e i t 3 lL,THE JOURNAL OF EXPERIMENTAL BIOLOGY. Arm swing in human walking 3949, 2 Stride time 0 1 Stride time variability 1 4 A Normal arm swing 0 07 B. A Normal arm swing B No arm swing,1 8 No arm swing 0 09.
Stride time variability s,Stride time s,1 2 0 06 0 8 0 04. 0 4 0 02 0 2 0 01,0 0 0 56 1 12 1 68 0 56 1 12 1 68. 0 56 1 12 1 68 0 56 1 12 1 68 Walking speed m s 1,Walking speed m s 1. Fig 6 Local dynamic stability measures Error bars represent standard. Fig 5 A Stride time P 0 05 for speed all other effects P 0 2 and B errors A The Lyapunov exponent calculated from the slope of the. stride time variability P 0 05 for speed all other effects P 0 2 Error bars divergence curve at 0 0 5 strides lS P 0 06 for arm swing P 0 01 for. represent standard errors speed B The Lyapunov exponent for the slope at 4 10 strides lL P 0 2. for arm swing P 0 01 for speed There were no significant interaction. effects for any of the variables P 0 8 for all, Perturbation parameters Inspection of Fig 7A suggested reduced local stability when. The average number of perturbations applied within a trial ranged walking with normal arm swing however this effect was not. from 15 for those at 0 56 m s 1 to 21 for those at 1 68 m s 1 a variation significant which confirmed our first hypothesis that arm swing. that resulted in a significant effect of speed P 0 05 There was would have no effect on the local stability of steady state gait. no significant effect of arm swing P 0 4 and arm swing speed Perturbation parameters revealed that arm swing was. P 0 3 on the number of perturbations There was also no accompanied by a lower force exerted by the pistons Fmax and a. significant effect of arm swing or walking speed on mdNW rendering shorter time to reach the same maximum distance from the attractor. it unlikely that differences in variability of the unperturbed gait t for perturbed walking implying a greater acceleration Taken. pattern influenced the perturbation parameters together these findings are in agreement with our second hypothesis. There were no significant interaction effects for any of the that walking with normal arm swing leads to a decreased. dependent variables implying that the effects of condition were the performance in the initial phase of global gait stability. same for all speed levels In support of our third hypothesis arm swing allowed for more. Fmax was significantly lower in the arm swing condition P 0 05 effective recovery reactions to large external perturbations as. see Fig 7A Moreover the time that elapsed before the maximum indicated by higher values of the exponential return parameter. distance from the attractor was reached t was significantly shorter More importantly we found lower values of the distance to the. in the arm swing condition P 0 01 see Fig 7C while this attractor at first heel strike Dhc when walking with normal arm. maximum distance B was not different between conditions swing suggesting that in total global gait stability increased when. P 0 32 see Fig 7B Of the perturbation parameters quantifying walking with arm swing. the initial response to the perturbation only t showed a significant Increases in walking speed led to conflicting results regarding. effect of walking speed with higher values of t for the higher the local and global stability of gait with significant decreases in. walking speeds P 0 01 lS suggesting increased local stability significant increases in lL. In the recovery phase the exponential decay towards the limit suggesting decreased local stability significant increases in t. cycle was faster in the condition with arm swing P 0 05 see suggesting an increased performance in the initial phase of global. Fig 7D while the relaxation distance A was not different between gait stability significant decreases in suggesting a decreased. the two arm swing conditions P 0 72 see Fig 7E which rendered performance in the recovery phase of global gait stability and. the distance at the first recovery heel strike Dhc significantly smaller significant increases of Dhc suggesting an overall negative effect. when walking with arm swing P 0 01 see Fig 7F All parameters of increased walking speed on global gait stability. quantifying the recovery phase showed significant effects of walking. speed decreased while A and Dhc increased with increasing The effects of arm swing. walking speed P 0 01 for all Regarding both local gait stability and the initial phase of global. gait stability the effects of arm swing found in the present study. DISCUSSION contradict the conclusion of Ortega and colleagues that arm swing. In the present experiment we examined the effect of arm swing on plays a positive role in stabilizing steady state gait Ortega et al. the local and global stability of human gait In doing so we 2008 Instead our findings are more in line with those of Collins. partitioned the global stability into two phases an initial response and coworkers who reported no effects of arm swing on local. which also contains information on the steady state gait and a stability of steady state gait Collins et al 2009 and those of. recovery phase Pijnappels and colleagues who concluded that arm swing. THE JOURNAL OF EXPERIMENTAL BIOLOGY,3950 S M Bruijn and others.
Fig 7 Perturbation parameters Error bars, 300 A 14 B 30 C represent standard errors A Perturbation. force Fmax B Maximum distance from the,Normal arm swing. 250 12 25 No arm swing,attractor B C Time to maximum distance. B standard deviations,10 t D Exponential decay E Relaxation. 200 20 distance A F Distance at first heelstrike,8 Dhc Significant effects of arm swing were.
150 15 found for Fmax t and Dhc and significant,6 effects of walking speed were found for t. 10 A and Dhc There were no significant,4 interaction effects for any of the variables. P 0 1 for all,0 09 3 5 7,Dhc standard deviations,A standard deviations. 0 06 2 5 5,0 04 1 5 3,0 01 0 5 1,0 56 1 12 1 68 0 56 1 12 1 68 0 56 1 12 1 68. Walking speed m s 1, decreases performance in the initial phase of global gait stability The decreased performance in the initial phase of global gait.
Pijnappels et al 2010 While the effects of arm swing on lS stability when walking with normal arm swing may perhaps be. were not significant it should be kept in mind that this measure explained in terms of increased inertia When the hands are tied to. has limited statistical precision Bruijn et al 2009a Interestingly the body the upper body has a greater effective inertia and is. like in previous studies Bruijn et al 2010a Su and Dingwell thus more resistant to perturbations This hypothesis of greater. 2007 the effect of arm swing on lS was similar to the effect on steady state gait stability due to greater effective inertia may be. measures of the initial phase of global gait stability such as the tested experimentally by having subjects walk with their arms fixed. perturbation force and the initial response to the perturbation as away from the body so that arm swing is restricted while rotational. quantified by t and B which in part also reflect the steady state inertia is further increased Another explanation would be that. gait stability Of course these findings may be confounded by the restricting arm swing also causes different trunk muscle activation. fact that the reactive phase of the response is already present in patterns We are unaware of literature reporting this effect and did. these measures However since recovery was faster in the arm not measure muscle activity. swing condition higher values of and lower values of Dhc this When a perturbation occurs to the upper body with the arms tied. would attenuate the effects found The higher values of and the constrained upper body will tend to behave more like an inverted. more importantly the lower values of Dhc indicate an overall pendulum than the unconstrained upper body and will be less able. positive effect of arm swing on global gait stability The overall to recover from a perturbation The present results thus suggest that. picture that emerges from these results is thus consistent with the from a stability point of view the optimal strategy would be to walk. work of Pijnappels and colleagues who predicted that arm with the hands alongside the body until a perturbation occurs Still. momentum in the horizontal plane at the instant of a trip during it may be that ongoing arm movements are needed to perform the. mid stance would have a detrimental effect on the initial phase rapid arm movements required for successful recovery Future. after a perturbation but that subsequent reactions of the arms were experiments in which the hands are tied to the body and released. likely to counteract this initially detrimental effect Pijnappels et at the instant of a trip or other perturbation are required to test this. al 2010 It should be noted that we found an overall positive idea It should be noted in this context that while this strategy of. effect of arm swing on global gait stability i e lower values of holding the arms alongside the body until a perturbation occurs may. Dhc when walking with normal arm swing whereas Pijnappels be optimal with respect to stability it is certainly not optimal in. and coworkers did not find such an effect Pijnappels et al 2010 terms of energy costs Collins et al 2009 Ortega et al 2008. The reason for this difference may be that we used a position Umberger 2008 which may explain why humans do not normally. controlled rather than a force controlled perturbation had we used walk like this Interestingly however non human primates. force controlled perturbations values of A might have been higher displaying bipedal gait seem to be doing exactly this see figure 2. for walking with normal arm swing resulting in equal values of in Mori et al Mori et al 2006 but this has never been explicitly. Dhc reported Nonetheless even if this observation were to be confirmed. THE JOURNAL OF EXPERIMENTAL BIOLOGY,Arm swing in human walking 3951. it remains to be investigated whether this constitutes a strategy to unperturbed walking which is indicative of the local stability of. optimize stability the entire gait cycle yielded results although non significant that. were in line with performance in the initial phase of global gait. The effects of walking speed stability As there is some evidence that local stability may be. Interestingly walking speed led only to significant main effects and correlated to global stability of the gait pattern Bruijn et al 2010a. no interaction effects which suggests that the effects of arm swing Su and Dingwell 2007 this would suggest that our findings. were similar or at least not very different for all walking speeds regarding the initial phase of global gait stability are valid for the. Still like in previous studies Bruijn et al 2010b Bruijn et al entire gait cycle Lastly because our perturbation occurred after a. 2009b Fallah Yakhdani et al 2010 increasing walking speed led fixed delay and was not infinitely short it started and ended at. to a significant decrease in lS and a significant increase in lL Note different times in the gait cycle for different walking speeds These. that only lS has been shown to be related to global stability i e the considerations imply that the effect of arm swing was the same for. probability of falling in modeling studies Bruijn et al 2010a Su slightly different perturbations at different walking speeds Here it. and Dingwell 2007 In line with this t increased significantly with appears likely that the effects of arm swing were similar for slightly. increasing walking speed also suggesting an increased performance different perturbations at the same walking speed which supports. in the initial phase of global gait stability with increasing walking the idea that our findings may at least be generalized to perturbations. speed Higher walking speeds however also led to a decreased applied at different times in the gait cycle. performance in the recovery phase of global gait stability as The perturbation applied in the current study was a forward pull. indicated by a slower exponential decay All in all larger to the thorax with a slight rotational component Since in daily life. distances from the attractor Dhc at the first recovery heelstrike with perturbations in other directions may also occur a full assessment. increasing walking speed indicated a decrease in global gait stability of the functional importance of arm swing to human gait requires. However all results derived from perturbation parameters must be that perturbations in these other directions are studied as well We. treated with great caution as perturbations were not infinitely short are not aware of published experiments showing that arm swing. and started and ended after some delay which automatically caused decreases performance in the initial phase of global gait stability. a perturbation to end later in the gait cycle for the faster walking while facilitating the recovery phase of global gait stability in the. trials medio lateral direction and thus do not know to what extent our. results generalize to this direction Ortega and colleagues claimed. Limitations of the present study that arm swing has a stabilizing effect on steady state gait in this. The present study has several limitations Firstly our sampling rate direction Ortega et al 2008 but the reduction in energy. was relatively low 50 samples s 1 which may have reduced the consumption due to lateral stabilization that they found for the no. precision of the perturbation data but is unlikely to have caused arm swing condition may have been caused by the medio lateral. any bias Secondly we carried out the experiments only on healthy stabilization counteracting the angular momentum about the vertical. male subjects which limits the generalizability of our results Lastly Collins et al 2009 Ortega et al 2008 In the mechanical model. it is known that a novel task Milner and Cloutier 1993 or of Collins and coworkers Collins et al 2001 non human like arm. expectation of a perturbation Lavender and Marras 1995 Lavender swing with arms swinging outwards while moving forwards helped. et al 1989 may lead to increased co contraction Increased co to stabilize the model However arms in their model were passive. contraction would probably lead to a higher perturbation resistance and fully coupled to the motions of the legs rendering it questionable. Stokes et al 2000 van Die n et al 2003 possibly confounding whether this finding can be extrapolated to human walking Thus. the results However conditions were offered in random order so further studies into the de stabilizing effects of arm swing in other. co contraction due to expectation is likely to have played little or movement directions are clearly required. no role in the reported effects of arm swing Still co contraction. may have been increased in all conditions which may have limited CONCLUSION. the generalizability of our results to real life unexpected The present study showed that contrary to what is commonly. perturbations Moreover it seems unlikely that co contraction was believed arm swing does not only stabilize gait However the results. higher in the no arm swing condition because of the relative novelty also indicate that recovery actions of the arms may help recovery. of that task walking with the hands alongside the body may not be of gait stability following a perturbation. a very new task to subjects as people can only walk while doing. different things with the arms and subjects had to walk with the LIST OF SYMBOLS AND ABBREVIATIONS. hands alongside the body for 6 5 min A relaxation distance. B size of the initial perturbation, Generalizability of results to other perturbations d dimension number. We only investigated perturbations occurring at one specific time D distance between perturbed gate cycle and average limit cycle. Dhc distance from average limit cycle at first recovery heel contact. interval and in one specific direction leaving it uncertain whether. Fmax maximum force, our results can be generalized to perturbations at other phases of i percentage of stride. the gait cycle and in other directions k stride number. While we perturbed only at one instance in the stride cycle just LED light emitting diode. before heel strike our results regarding the initial and recovery mdNW mean deviation from normal walking. phases of global gait stability are consistent with those of Pijnappels n maximum number of strides in perturbed walking. and colleagues in which a trip was applied at mid stance Pijnappels NW normal walking. PW perturbed walking, et al 2010 The effects of arm swing on recovery after a vNW variability in normal walking. perturbation further agree with findings in slipping experiments V linear velocity. Marigold et al 2003 in which a slip was induced at mid stance rate of return to limit cycle. Moreover our local dynamic stability analysis particularly lS of lL Lyapunov exponent for the slope at 4 10 strides. THE JOURNAL OF EXPERIMENTAL BIOLOGY,3952 S M Bruijn and others.
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