# Control and Function of Arm Swing in Human Walking and Running

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4 Arm swing in walking and running 525 A Controller Energy Mass Movement k c Mass 2 Position of mass Mass alone With mass 2 attached Time B Passive arm swing model C Active arm swing model Head Head Arms Arms x y Energy Torso Pelvis Torso Pelvis Energy Energy Legs Legs Fig.. Schematic diagram of passive and active arm swing hypotheses. (A) Simple mass damper (see Soong and Dargush, 997). Oscillating forces applied by a controller (red element) to the principle Mass will tend to move it (solid line in position plot); the attachment of an auxiliary Mass 2 using a damped spring can decrease the amplitude of movement of Mass (dashed line in position plot); the effectiveness of the damping is a function of the spring stiffness k and damping constant c, and is proportional to Mass 2. (B) In the passive arm swing model, oscillating moments from the swinging legs tend to accelerate the pelvis and other body segments in turn; all energy in the system is generated by the legs. The arms act as an auxiliary mass which damps movement of the torso (and head). Shoulder and arm accelerations are predicted to increase with angular displacement of the trunk (y) and shoulder (x), respectively. (C) In the active arm swing model, energy into the system comes from both the swinging legs and the shoulder muscles driving the arms. Accelerations of the pelvis and torso are expected to be negatively correlated (i.e. in opposition). Since forces of the shoulder muscles will accelerate both the arm and torso masses, albeit in opposing directions, arm acceleration is predicted to be negatively correlated with shoulder acceleration. In both passive and active models, oscillation of the torso and head will increase if arms are removed. Note that these systems (B and C) are rotational in nature, but are rendered as linear systems here for clarity. element will increase, resulting in greater acceleration of the shoulder girdle. Second, the angular acceleration of the arm is predicted to increase with angular displacement at the shoulder (i.e. the angle of the upper arm segment relative to vertical), just as the force generated by a spring increases with its displacement (Fig. B). In this way, rotation of the shoulders in the transverse plane is expected to result in arm swing in the sagittal plane. For example, as the shoulder girdle rotates and the right shoulder translates anteriorly, the arm will tend to remain in place following Newton s first law. Thus, the right arm will appear to swing posteriorly relative to the right shoulder, until the angular displacement of the shoulder is sufficient to swing the arm forward (protraction). As the right arm swings forward, the right shoulder will begin to translate posteriorly as the torso rotates with the next step, resulting again in angular displacement of the shoulder and acceleration of the arm. The shoulder musculature is expected to act as a spring-like element, translating angular displacement into torque. Thus a third prediction of the passive model is that the anterior and posterior portions of the deltoid will fire together, acting to stabilize the shoulder. Active arm swing model The active arm swing hypothesis proposes that arm swing is an active mass damping mechanism in which the arms (an auxiliary mass) are driven by the shoulder muscles acting as controllers in order to decrease the amplitude of torso rotation (Fig. B). Since the arm and torso are attached at the shoulder, anterior acceleration of the arm in the sagittal plane will lead to posterior acceleration of the shoulder and torso following Newton s third law: protraction of the right arm will tend to accelerate the right shoulder posteriorly, while retraction of the left arm will force the left shoulder anteriorly, thereby translating sagittal plane accelerations of the arms into

6 Arm swing in walking and running 527 Arm rotation (+) * α ( ) Head rotation (+) (yaw) Shoulder rotation (+) Pelvis rotation (+) et al., 98); the system was calibrated daily and checked for leaks using a known flow rate of pure nitrogen. The resting rate of oxygen consumption was first measured with the subjects standing on the treadmill. Next, the subjects performed two.5ms walking trials, and two 3.ms running trials. In one walking trial and one running trial the subjects walked or ran normally, as in the control condition; in the other walking and running trial, they walked or ran with arms folded tightly across their chest as in the no arms condition. The order of conditions was varied, so that half of the subjects performed the control trials first, and half performed the no arms condition first. Each metabolic trial lasted at least 6min, and mean oxygen concentration from the final 2 min of each trial was used to calculate the rate of oxygen consumption. Only trials in which oxygen consumption visibly reached a plateau (less than % change over the final 2min) were used for analysis. For each subject, the resting rate of oxygen consumption was subtracted from the rate of consumption while walking or running in order to calculate a net cost of locomotion. This net cost was then divided by body mass and then by speed to give the mass-specific cost of transport (ml O 2 kg m ) for each speed in each condition. y Step width x z Fig. 2. Schematic diagram of the reference frame and kinematic variables. Rotation of the head, shoulders and pelvis in the transverse (x y) plane about the vertical (z) axis was measured using reflective markers (gray circles) with reference to the x-axis; arrows indicate positive rotation. Trunk torsion was measured as the rotation of the pelvis relative to the shoulders. Arm rotation was measured in the sagittal (y z) plane using the reconstructed arm center of mass (*) and shoulder relative to vertical; arrow indicates positive rotation. Angular displacement of the shoulder (α) was defined as negative when the arm was retracted (as shown), positive when protracted. Step width was measured as the difference in x-position of successive heel strikes. the maximum difference was set as the threshold for the lowest muscle activity. All values below this threshold (e.g. values lower than random muscle activity) were removed from the original signal. Metabolic cost of locomotion After the kinematic trials described above, a subset (N=6, four male, two female, 7.2±5.9kg) of subjects performed a set of metabolic trials in order to determine the effect of arm restraint on locomotor cost. For these trials, oxygen consumption was measured using the open-flow method described previously (Fedak et al., 98; Pontzer, 27). Subjects wore a light mask through which air was pulled at 25 l min. This air was sub-sampled continuously, scrubbed of water vapor and carbon dioxide, and analyzed for oxygen concentration using a paramagnetic analyzer (Sable Systems, Las Vegas, NV, USA). Oxygen concentration was monitored in near-real time and recorded at 3Hz in Vicon Nexus software. Oxygen concentration was then used to calculate the rate of oxygen consumption (ml O 2 s ) following Fedak et al. (Fedak Hypothesis testing Filtered kinematic and thextonized EMG data were used to examine predicted relationships. Segment velocities and accelerations were calculated using the finite differences method described in Winter (Winter, 25). Predictions were considered to be supported if the correlation between two kinematic variables (e.g. shoulder displacement and arm acceleration) had a Pearson s R greater than.5 or less than.5, and in the predicted direction, following Cohen s index for a large effect size (Cohen, 992). This effect size (R=±.5) recognizes the complexity of the multi-segment, multimuscle system being analyzed, and anticipates variability within the system and between subjects. It should be noted that the conventional criterion for statistical significance, a P-value of <.5 or <., is inappropriate in determining the biological or biomechanical significance of these segment correlations due to the large number of data points generated by high-speed kinematic data. With a capture rate of 2 frames s, three strides generate approximately 6 data points, because each frame produces a position, velocity and acceleration estimate for a given segment. With a sample of 6 points, even small correlations of R=±. become significant at P<.; however, such small correlations indicate that only % of the variance in the dependent variable is explained by the independent variable. Therefore the criterion for a large effect size (R=±.5) (Cohen, 992), while admittedly arbitrary, is preferable to a calculated P-value for these correlations. To determine the effect of the no arms condition on locomotor cost, we compared the net mass-specific cost of locomotion in the control and no arms condition during walking and running for each subject using Student s one-tailed, paired t-test. Similarly, we used Student s one-tailed, paired t-test to compare mean contact times, stride frequencies, head yaw amplitude and footfall variability for each subject walking at.5ms and running at 3.ms in each condition. Note that using a one-tailed test was deemed appropriate here, since the direction of the predicted difference is known a priori. We discuss the effect of using a one-tailed test below. Lag time between shoulder and pelvis rotation and footfall variability were also compared between conditions using Student s paired t-tests. As pelvis and shoulder rotation occur with similar frequency but with different times of peak amplitude, we calculated the phase difference between pelvis and shoulder movement in order

7 528 H. Pontzer and others to determine the effect of increasing or decreasing the moment of inertia of the upper body. The phase difference between peak pelvis rotation (t pelvis ) and peak shoulder rotation (t shoulder ) was calculated as phase difference=36deg. ( t pelvis t shoulder /stride period). The closest shoulder and pelvis peaks were compared, so that the maximum phase difference was 8 deg. To test for differences in footfall variability, the medio-lateral position of the heel at heel strike was recorded for eight consecutive steps at each speed (Fig. ). The medio-lateral distance between successive steps, hereafter termed step width, was measured, and the coefficient of variation (a sizecorrected measure of variance) was determined for each subject at each speed. Coefficients of variation (c.v.) were then compared using Student s paired t-test. Shoulder rotation amplitude (deg.) A B Arm weights Control No arms RESULTS Kinematics Kinematic analyses revealed correlated movements of the pelvis, shoulder and arm which support the hypothesis that the arms act as mass dampers, decreasing the amplitude of upper body rotation. Changing the moment of inertia of the arms (and hence the upper body) generally resulted in the predicted effects on the amplitude of upper body rotation (measured as shoulder rotation; Fig. 3A) and of the head (measured as the amplitude of head yaw; Fig.3B), although this effect was stronger during running. For walking trials at.5ms, shoulder rotation was generally low, and there were no significant differences between no arms (mean±s.d. 8.6±.9 deg.) and control (8.±2.5 deg.) conditions (P=.2), or between control and arm weights (9.±3. deg.) conditions (P=.33; Fig. 3A). In contrast, during running at 3.ms, the amplitude of shoulder rotation was significantly greater (P<.) and changes in arm inertia had expected effects on shoulder rotation. Decreasing the moment of inertia of the arms in the no arms condition resulted in greater shoulder rotation (35.68 deg.) than in control trials (23.75 deg., P<.; Fig. 3A), while increasing the moment of inertia of the arms in the arm weights condition resulted in decreased shoulder rotation (7.8 deg.) compared with control trials, although this relationship barely met the significance criterion (P=.9). The amplitude of head rotation was significantly lower than that of the shoulder in all conditions, both walking and running (P<. all comparisons; Fig. 3B). Still, changes in head yaw between conditions generally followed the pattern of shoulder rotation. During walking, head yaw was lowest in arm weights trials (5.±.7 deg.), slightly greater in control trials (5.2±. deg.) and greatest in no arms trials (6.±.6 deg.). Significant differences were found between no arms and control trials (P=.6), and between no arms and arm weights trials (P=.), but differences between control trials and arm weights (P=.32) and no arms trials were not significant. During running, head yaw was lowest in arm weights trials (5.3±.5 deg.), slightly greater in control trials (6.±.6 deg.) and greatest in no arms trials (.3±3. deg.). The difference between no arms and both arm weights (P<.) and control trials (P<.) was significant, but the difference between control and arm weights conditions (P=.26) was not. For all conditions, head yaw tended to be greater during running than during walking, but this difference was only significant for the no arms condition (P<.). Lag time between pelvis and shoulder rotation increased with greater moment of inertia of the upper body as predicted (Fig.3C), with the greatest phase differences between pelvis and shoulder rotation during arm weights trials for both walking (57.6±22.deg.) and running (7.±35.8deg.). Phase differences in control trials were slightly lower (walking 9.2±.5deg., running 93.9±6.9deg.) but Head yaw amplitude (deg.) Phase difference (deg.) Pelvis versus shoulder rotation C Walking Running Fig. 3. Mean ± s.d. (A) shoulder rotation, (B) head yaw and (C) phase differences between peak shoulder rotation and peak pelvis rotation. *Significant difference compared with control trials (P<.5). Significant difference compared with arm weights trials (P<.5). Significant difference compared with both arm weights and control trials (P<.5). * these differences were not significant (walking P=., running P=.6). Phase differences were smallest in the no arms trials (walking 93.9±6.9 deg., running 33.±23.3 deg.), significantly smaller than control trials for both gaits (walking P=., running P<.), and significantly smaller than arm weights trials during running (running P<., walking comparison approach significance at P=.55). For each condition, phase differences were significantly greater during walking (P<., walking versus running trials, all comparisons). Passive arm swing predictions were strongly supported by kinematic results. During walking and running, angular acceleration of the shoulders in the transverse plane was consistently, positively correlated with torsion of the spinal column, measured as the difference in angle between the shoulder and pelvis in the transverse plane (mean Pearson s R=.59; Table ; Fig. ). Similarly, for both walking and running trials, angular acceleration of the arm in the sagittal plane was strongly correlated with angular displacement of the shoulder, with greater retraction associated with greater anterior

8 Arm swing in walking and running 529 Table. Correlations (Pearson s R) between body segments during normal walking and running Passive arm swing Active arm swing Pelvis shoulder angle versus shoulder acceleration Speed/gait Mean s.d.. m s walk.5.3 (.387,.736).5 m s walk..5 (.2,.667) 2. m s walk..97 (.7,.7) 2. m s run (.266,.82) 2.5 m s run.75. (.562,.887) 3. m s run.75.8 (.589,.835) Walking.5.6 (.7,.736) Running.7.33 (.266,.98) All (.7,.98) Arm angle versus arm acceleration (Min., max.) Mean s.d (.889,.57) (.955,.672) (.952,.758).8.8 (.889,.773).8.5 (.895,.776).85.8 (.93,.778).83.2 (.955,.57).8. (.93,.773).8.85 (.955,.57) (Min., max.) Mean s.d. Pelvis acceleration versus shoulder acceleration..9 (.8,.266).5.92 (.,.8) (.7,.29) (.385,.22)..259 (.365,.33) (.3,.33)..5 (.7,.266)..238 (.3,.33)..97 (.3,.33) Arm acceleration versus shoulder acceleration (Min., max.) Mean s.d (Min., max.) (.229,.365) (.286,.72) (.55,.667) (.8,.58) (.9,.598) (.22,.65) (.286,.667) (.8,.7) (.286,.7) acceleration (mean Pearson s R=.59; Table ; Fig. ). These results are consistent with the passive arm swing prediction that the spinal column and shoulder effectively act as springs, with greater displacement leading to greater acceleration. Active arm swing predictions were generally not supported by kinematic analyses. Angular accelerations of the pelvis and shoulder were not correlated (mean Pearson s R=.; Table ; Fig. ). Further, while arm acceleration was weakly correlated with the angular acceleration of the shoulder (mean Pearson s R=.27; Table ; Fig. ), the positive direction of correlation was opposite to that of the active arm swing hypothesis, which predicts that anterior acceleration of the arm will lead to posterior acceleration of the ipsilateral shoulder. Comparing walking and running (Table ), it is evident that Pearson s correlations between shoulder acceleration and both arm acceleration and spinal torsion are greater during running. The significance of this change and the underlying mechanism are unclear. In both cases, the greater ground forces encountered during running may lead to greater stabilizing muscle activity, and therefore a stronger linkage (i.e. a stiffer spring ) between the pelvis, shoulder and arm. Stiffer springs may also be necessitated by the greater stride frequencies used in running, since stiffer springs would increase the natural frequencies for the body segments involved. For example, a stiffer spring in the shoulder will increase the natural frequency of the swinging arm. Finally, the greater angular excursions seen in running (Fig. 3A,B) may lead to a stronger correlation of movement between segments. Muscle activity Patterns of muscle firing were generally consistent with predictions of the passive arm swing hypothesis, although some alternating activity in the anterior and posterior deltoid was observed. When compared with the clear alternating pattern of anterior and posterior deltoid activity seen in the arm pump trials (Fig.5A), firing of these muscles during both walking and running was largely simultaneous. This suggests that the deltoid is acting to stabilize the shoulder as predicted by the passive arm swing hypothesis, rather than to drive it anteriorly or posteriorly as predicted by the active arm swing hypothesis. However, some alternating activity was observed, particularly in walking trials (Fig. 5B), indicating that the deltoid does drive arm swing at least occasionally for some individuals. During running, firing of the anterior and posterior portions of the deltoid was almost exclusively co-contraction (Fig. 5C). Overlaying the angular velocity and acceleration of the shoulder in the sagittal plane on EMG activity (Fig.6), it appears that many, perhaps most, of the deltoid contractions are eccentric, with the anterior deltoid firing while the arm moves posteriorly, and the posterior deltoid firing while the arm moves anteriorly. These eccentric contractions are consistent with the view of the shoulders as spring-like linkages. Further, while contraction of the anterior or posterior deltoid is typically associated with predictable accelerations at the shoulder, there are also periods in which arm acceleration and deltoid activity are in opposition, with anterior acceleration of the arm associated with posterior deltoid activity (Fig. 6A), even when the lag time between activation and force production are considered. Similarly, periods of arm acceleration are also seen when the deltoid muscles are quiet (Fig. 6B). These patterns suggest that forces, in addition to those from the deltoid, are acting on the arm. These results are consistent with the mass damping hypothesis, in which forces acting on the arms are primarily derived from the legs via the trunk. Gait characteristics Stride period during no arms trials (walking.5±.6 s, running.7±. s) was similar to that in control (walking.5±.7 s, running.75±. s) and arm weights trials (walking.±.5 s, running.76±.8 s). These differences were not significant for walking or running (P>.5) with the exception of the control no arms comparison for running (P<.). However, this difference was small (. s, or.3%) and probably biomechanically unimportant. Contact times during no arms trials (walking.68±.5s, running.3±.3s), control trials (walking.68±.5s, running.3±.3 s) and arm weights trials (walking.68±.5 s, running.32±.3 s) were similar (P>.5 all comparisons).

9 53 H. Pontzer and others A Shoulder angular acceleration (deg. s 2 ) Sub. 3. m s Walking Running Trunk torsion (deg.) 2 Sub m s B C 3 5 D 3 Arm angular acceleration (deg. s 2 ) E Shoulder angular acceleration (deg. s 2 ) Sub. 2 Sub. 2. m s 3. m s 5 Sub. 9.5 m s Shoulder displacement (deg.) Pelvis angular acceleration (deg. s 2 ) Sub m s F Count (trials) G Shoulder angular acceleration (deg. s 2 ) Sub..5 m s Sub m s H 5 6 Arm angular acceleration (deg. s 2 ) Pearson s R Fig.. Kinematic results. (A D) Predictions of the passive arm swing hypothesis (see Fig. 2B); (E H) active arm swing predictions (see Fig. 2C). Plots are representative results for walking and running and list the subject (Sub.) and speed shown. Histograms are Pearsonʼs R-values for all speeds and subjects, walking and running combined. Hatched areas in histograms indicate predicted values for passive (B,D) or active (F,H) hypotheses. Footfall variation and metabolic cost During walking at.5ms, variation in step width during no arms trials (mean c.v..53±.26) was greater than for control trials (.±.2) although this difference was only marginally significant (P=.39). There was no difference between control and arm weights (.56±.3) conditions, or between no arms and arm

10 Arm swing in walking and running 53 A Arm pump Anterior deltoid Posterior deltoid 2 2 scaled Adelt Sub. 2 Sub. 3 scaled Pdelt B Walking,.5 m s Normalized muscle activity Sub. 2 scaled Adelt scaled Pdelt 2 Sub. 7 scaled Adelt scaled Pdelt C Running, 3. m s 2 2 scaled Adelt Sub. 8 Sub. scaled Pdelt Time (s) Fig. 5. Representative anterior and posterior deltoid activity for (A) arm pump, (B).5 m s walking, and (C) 3. m s running trials. EMG data have been processed as described in the text and normalized to the maximum activation within a trial. The subject from whom data were obtained is listed. weights conditions (P>. both comparisons; Fig. 7A). During running at 3.ms, there were no differences between no arms (.59±.2), control (.53±.8) and arm weights trials (.8±.7; Fig. 7A). Restricting arm swing in the no arms condition had no effect on the mass-specific energetic cost of transport (ml O 2 kg m ). Locomotor costs during no arms trials (walking.3±.3 ml O 2 kg m, running.2±.ml O 2 kg m ) and control trials (walking.2±.2ml O 2 kg m, running.2±.ml O 2 kg m ) were similar (walking P=., running P=.; Fig. 7B). DISCUSSION Arms as mass dampers Our results support the hypothesis that the arms act as mass dampers during human walking and running, although the evidence is clearest for running. In running trials, the amplitude of shoulder

11 532 H. Pontzer and others Normalized EMG Normalized EMG A Posterior deltoid Anterior deltoid.5 m s walk Subject B 3. m s run Subject Posterior deltoid Anterior deltoid Angular velocity (deg. s ) 3 Angular velocity (deg. s ) 3 Angular acceleration (deg. s 2 ) Angular acceleration (deg. s 2 ) 3 3 Fig. 6. Representative angular velocity (red line) and angular acceleration (blue line) for the arm at the shoulder, overlaid on normalized anterior and posterior deltoid activity, during (A) walking at.5 m s and (B) running at 3. m s. Deltoid activity is processed and shown as in Fig. 5. Periods of apparent eccentric contraction are indicated (red arrows), as are periods in which shoulder acceleration is in opposition to prevailing muscle activity (blue arrows) or occurs without substantial deltoid activity (black arrows). Not all such periods are indicated. rotation clearly increased when the moment of inertia of arms decreased (Fig. 3A), just as movement the principle mass of a massdamped system should increase with a decrease in the auxiliary mass (Fig. A) (Soong and Dargush, 997). While this relationship was not observed for walking (Fig.A), this does not mean that a massdamper view of the arms should be rejected; the effectiveness of a mass damper and the effect of changing its inertial properties depend upon the magnitude and frequency of the external forces acting on the system (Soong and Dargush, 997). The magnitude and frequency of forces from the lower body may simply be too low during walking to elicit a significant change in torso movement with the manipulations of arm inertial properties used here. The magnitude of head yaw was less than that of the shoulders, but changes in head yaw across experimental conditions generally followed the pattern of shoulder movement, supporting the view of the head as a mass attached via a damped spring. Finally, phase lag between the lower body and upper body decreased when the moment of inertia of the arms was decreased during both walking and running (Fig.C), as predicted for a mass-damped system. The view of the arms as mass dampers is consistent with previous work (e.g. Hinrichs, 987; Hinrichs, 99; Li et al., 2; Herr and Popovic, 28) indicating that angular acceleration in the upper and lower body tend to cancel, resulting in near-zero net moments about the vertical axis. However, while the results of this study fit predictions of a mass-damper model, the tests here are certainly not exhaustive, and future work might test other predictions of a mass-damper hypothesis in order to determine whether this model alone is sufficient for explaining upper body movement, particularly during walking. Passive versus active arm swing The passive arm swing hypothesis proposes that upper body movement is driven by movement in the legs and pelvis, with force transferred to the shoulders and arms via spring-like elements (ligaments and muscles) in the spine and shoulder. This differs from an active arm swing hypothesis, which proposes that upper body movement is driven primarily by swinging the arms using the shoulder muscles. As predicted by the passive arm swing hypothesis, angular acceleration of the shoulders was correlated with increased trunk torsion, and arm acceleration was strongly correlated with angular displacement of the shoulder (Fig. ). In contrast, angular acceleration of the shoulders and pelvis were not inversely correlated, nor was shoulder acceleration inversely correlated with arm acceleration, as predicted by the active arm swing hypothesis (Fig. ). EMG recordings of the anterior and posterior deltoid suggest that, while these muscles may play a limited role in driving arm swing, they act primarily to stabilize the shoulder through cocontraction or eccentric contractions (Figs 5 and 6). Taken together, the kinematic and EMG results support the passive arm swing hypothesis. Additional support for the passive arm swing model comes from the metabolic comparisons of control and no arms conditions. As noted above, upper body movement during running increases in the no arms condition by approximately 5% compared with control trials (Fig. A). If upper body movement is actively driven by trunk and arm musculature as in the active arm swing model, the larger displacements of the torso should require a corresponding increase in oxygen consumption. Instead, energy use is similar to that in the control condition, indicating that greater movement of the torso in

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