Straight arm walking, bent arm running: gait-specific elbow angles

Although humans swing their arms during both walking and running, elbow angle typically differs between the gaits. Walkers use a ‘straight arm’, with the elbow close to full extension. Runners use a ‘bent arm’, with the elbow flexed and the forearm close to perpendicular with the upper arm. Surprisingly, the reason for this difference has been poorly studied. Intuitively, bending the arm when running shortens its length, thus reducing the rotational inertia, making it easier and less costly to swing, especially during running when swing frequency is rapid and muscle torques produced at the shoulder are large. However, reducing the effective length of the arm should benefit both walking and running, so a gait-specific mechanism for the difference must exist beyond simply reducing rotational inertia of the entire arm.

Why humans swing their arms during locomotion has been well established: the reciprocal motions of contralateral arm–leg pairs balance angular momentum about the vertical axis internally by transferring momentum between the limbs via the trunk (Bruijn et al., 2008; Collins et al., 2009; Elftman, 1939; Herr and Popovic, 2008). Internal momentum balance reduces the need for an external ground reaction torque at the foot, which is likely to be metabolically costly (Collins et al., 2009; Li et al., 2001; Umberger, 2008). How humans swing their arms is less well established despite much research. Arm swing can be described as a pendulum operating under a combination of passive and active dynamics (Canton and MacLellan, 2018; Collins et al., 2009; Elftman, 1939; Goudriaan et al., 2014; Kubo et al., 2004; Kuhtz-Buschbeck and Jing, 2012; Meyns et al., 2013). Gravitational torque is a major component of arm swing, as are external driving accelerations that transfer energy from the legs to the arms via the trunk (Collins et al., 2009; Kubo et al., 2004; Pontzer et al., 2009). At the same time, active muscle recruitment develops torques in the trunk, shoulder and elbow joints (Ballesteros et al., 1965; Canton and MacLellan, 2018; Collins et al., 2009; Elftman, 1939; Kuhtz-Buschbeck and Jing, 2012). Neuromuscular control of arm swing is rooted in the central patterns of human gait (Barthelemy and Nielsen, 2010; Cappellini et al., 2006; Dietz et al., 2001), and may be conserved from quadrupedal ancestry (Dietz, 2002).

Arm swing occurs mainly in the parasagittal plane, yet is linked to angular momentum about the vertical axis. The linkage is partly accomplished by the horizontal joint reaction force at the shoulder (JRF_H) that arises from swing. JRF_H causes a transverse plane reaction torque (τ_trv) on the thorax (Fig. 1A), which is further linked to the lower body by trunk torsion to transfer momentum between the upper and lower limbs. In the arm, muscle torques occur at the shoulder (τ_sho) and the elbow (τ_elb), generally opposing angular excursion and acting in a resistive manner (Collins et al., 2009) (Fig. 1A). τ_sho is most simply explained as resembling a rotational spring and acting on a functionally rigid single pendulum arm. Bending the elbow moves the center of mass (CoM) of the pendulum closer to the shoulder pivot, reducing the radius of gyration (R_G) and the required τ_sho (Fig. 1B).

In order to maintain functional approximation of a single pendulum arm, τ_elb must resist external forces that would cause an external torque at the elbow and rotation of the forearm relative to the upper arm. Gravity is one such external force. Pseudoforces from acceleration of the thorax also place external torques on the forearm in the reference frame of the upper arm. Vertical acceleration measured at the shoulder has a much higher magnitude compared with horizontal acceleration in walking (Kubo et al., 2004). Similarly, measurements of linear displacements at the C7 vertebral level indicate larger vertical than horizontal accelerations in both walking and running (Thorstensson et al., 1984). Other forces causing external elbow torques arise from centripetal and tangential accelerations of the elbow joint center in the arm reference frame. The net effect of all these forces is likely a large vertical external force component contributing to the external elbow torque, and a smaller horizontal component. Bending the elbow to reduce arm R_G brings the forearm closer to horizontal, thus increasing the moment arm of the net vertical external force (Fig. 1C). Conversely, maintaining a straight arm places the forearm more parallel with the vertical forces, limiting the external torque they produce and consequently the resistive τ_elb.

We propose a mechanical tradeoff hypothesis that posits a tradeoff between muscle torques at the shoulder and the elbow linked to the average elbow angle. Flexing the elbow, thus shortening the arm's moment of inertia, reduces the shoulder muscle torque but at the cost of increasing the elbow muscle torque. We predict that the energetic consequences of the mechanical tradeoff favor straight arm walking and bent arm running, and that elbow angle is determined by energetic cost for each gait. Studies show that perturbation of normal arm swing, typically by holding or binding the arms to the torso, increases the net energy cost of locomotion by up to ∼10% in both walking (Collins et al., 2009; Ortega et al., 2008; Umberger, 2008) and running (Arellano and Kram, 2014; Egbuonu et al., 1990; Tseh et al., 2008), indicating that normal arm swing is an important cost-saving mechanism. We also predict similar non-trivial energy costs to altering normal elbow angle. We tested our hypothesis and predictions by conducting an experiment with human subjects who walked and ran with both flexed and extended elbows.

Eight healthy subjects (four males and four females, age 26.6±2.5 years, mass 76.6±15.9 kg, mean±s.d.) participated in the experiment. Prior approval was granted by the Harvard University Institutional Review Board, and all subjects gave informed consent. Subjects walked and ran on a split-belt treadmill instrumented with force plates (Bertec Corp., Columbus, OH, USA). Four randomized experimental conditions were conducted in random order: straight arm walking (SW), bent arm walking (BW), straight arm running (SR) and bent arm running (BR). For SW and BR, the subjects were asked to walk and run normally. For BW, subjects were instructed to hold their forearm as they would during running; similarly, the instruction for SR was to hold the forearm as they would during walking. All walking trials were done at a single dimensionless speed (Fr number Fr=0.2, range: 1.30 to 1.44 m s⁻¹), and running trials were also done at a single dimensionless speed (Fr=1, range: 2.90 to 3.22 m s⁻¹). Each condition lasted 3 min, with data collection occurring during the last minute. Six subjects returned within 2 weeks for energetic data collection (see below). All analyses used the Igor Pro software platform (Wavemetrics, Lake Oswega, OR, USA).

Motions of the right forearm, right upper arm and thorax were captured with eight infrared cameras recording at 200 Hz (Qualysis Motion Capture Systems, Gothenburg, Sweden). Reflective markers were placed on the left and right acromia, right humeral epicondyles, and right radial and ulnar styloid processes. The right shoulder joint was estimated to be 3.0 cm (females) or 3.5 cm (males) below the right acromion marker (De Leva, 1996). The elbow joint center was calculated as the midpoint between the humeral epicondyles, and the wrist joint center was calculated as the midpoint between the styloid processes. The radius of the thorax was estimated as half the distance between the left and right acromia. Raw time series were filtered using a 10 Hz low-pass filter.

Analyses were done on the right arm segments in a parasagittal plane. Shoulder angle (θ_sho, rad) was defined as the angle formed by the upper arm and the vertical. Elbow angle (θ_elb, rad) was defined as the angle formed by the forearm and upper arm, with a straight arm being the neutral position. Angles followed the right hand rule, with positive angles representing flexion. Segmental inertias for the forearm and upper arm were estimated using subject metrics and anthropometric tables (De Leva, 1996). Standard inverse dynamics equations were used to calculate joint reaction forces, τ_sho (N m) and τ_elb (N m) (Winter, 2009). JRF_H (N) was multiplied by the radius of the thorax (m) to yield τ_trv (N m). Right heel strikes were used to define strides, and were determined from the vertical force traces under the right foot. Ten consecutive strides were averaged for each subject and condition. Inter-subject stride averages and s.e.m. were then calculated.

Kinetic variables were extracted from the individual stride averages. The magnitude of each torque (Δτ_trv, Δτ_sho and Δτ_elb) was calculated as the difference between the maximum and minimum values across the stride. Δτ_sho and Δτ_elb were normalized to dimensionless muscle torques ΔT_sho and ΔT_elb by dividing by Δτ_trv. Inter-subject means and s.e.m. were calculated for each variable. We normalized by transverse torque because it represents the mechanical link between arm swing in the sagittal plane and angular momentum about the vertical axis, and can be thought of as the relevant output of sagittal plane arm swing. We prefer normalizing by a functional measure rather than standard size dimensions (Hof, 1996) because the method controls for inter-subject variation in the contribution of arm swing to total angular momentum dynamics.

Following the initial experiment, six of the original subjects returned within 2 weeks and repeated the experiment while we collected metabolic data. Energetics were obtained from oxygen consumption, measured using an open-flow respirometry system (Sable Systems, North Las Vegas, NV, USA) and standard equations (Withers, 1977).

Resting oxygen consumption was recorded first, with the subject standing quietly on the treadmill. The four experimental conditions followed in a randomized order. Each condition, including rest, lasted for 5 min. Average oxygen consumption across the last 2 min was extracted to represent steady-state energetics. Oxygen consumption rates were normalized using body mass, and resting metabolism was subtracted from the walking and running conditions to calculate net oxygen consumption, V̇_O2,net (ml O₂ min⁻¹ kg⁻¹).

Comparisons between experimental condition means were done for walking and running separately: SW versus BW and SR versus BR. Repeated measures ANOVA (threshold P=0.05) was used to assess statistical differences between mean values for Δτ_trv, ΔT_sho, ΔT_elb and V̇_O2,net.

In all four conditions, τ_trv showed a consistent pattern of peak clockwise torque near ipsilateral heel strike and peak counter-clockwise torque near contralateral heel strike (Fig. 2A,B), with both occurring mainly at stride frequency. Comparison between the magnitudes of the torques (Fig. 2C) yielded no significant difference within the walking conditions (P=0.29) or the running conditions (P=0.19).

In both walking and running, θ_sho followed a stride-frequency pattern with peak flexion occurring near contralateral heel strike (Fig. 3A,B). The magnitudes of angular excursion tended to be similar within each gait. However, BW tended to shift θ_sho towards extension compared with SW, while BR tended to shift θ_sho towards flexion compared with SR. τ_sho also followed a stride-frequency pattern (Fig. 3C,D), with peak extension torques coinciding with peak shoulder flexion. ANOVA tests showed 33% reduced ΔT_sho in BW compared with SW (P=0.0039), and 32% reduced ΔT_sho in BR compared with SR (P<0.0001) (Fig. 3E).

Consistent with the instructions given to the subjects, θ_elb was substantially more flexed in BW and BR compared with SW and SR (Fig. 4A,B), and the forearm was close to perpendicular (θ_elb=1.57 rad) with the upper arm. Mean θ_elb in SW and BW was 0.62±0.02 and 1.54±0.05 rad, respectively (P<0.0001). Mean angles were similar in running, with 0.61±0.05 and 1.61±0.10 rad in SR and BR, respectively (P<0.0001). Both gaits showed angular excursions occurring at stride frequency. However, unlike in the shoulder, the pattern of θ_elb across the stride differed between straight and bent arm conditions. In SW and SR, the elbow flexed near contralateral heel strike, while in BW and BR, the elbow extended at this point. τ_elb followed stride frequency patterns for SW and SR, but step frequency patterns for BW and BR (Fig. 4C,D). In addition, mean muscle torques were substantially shifted towards flexion in the bent arm conditions (on average, 1.21 N m in walking and 1.60 N m in running), presumably due to increased gravitational torque. Comparison of magnitudes yielded significant increases in ΔT_elb for the bent arm conditions compared with the straight arm conditions in both walking (110% increase, P=0.0037) and running (30% increase, P=0.0096) (Fig. 4E).

Fig. 5A shows the results from the energetics data collection on the six-subject subsample. BW incurred an 11±3% higher V̇_O2,net than SW (P=0.0179), increasing by 0.30 ml O₂ min⁻¹ kg⁻¹ compared with the normal SW condition. In contrast, V̇_O2,net was the same for the SR and BR conditions (P=0.63). Individual oxygen consumption data are presented in Fig. 5B, with the abnormal conditions (BW and SR) expressed as a percentage of the corresponding normal conditions. Five of the six subjects increased their oxygen consumption during abnormal walking; in contrast, four of the six subjects had nearly identical oxygen consumption during abnormal and normal running.

The results from our experiment confirm our hypothesis that there is a mechanical tradeoff between τ_sho and τ_elb when bending the arm at the elbow during locomotion. Bending the arm reduced the relative magnitude of the shoulder muscle moment in both walking and running (Fig. 3E), while simultaneously increasing the relative magnitude of the elbow muscle moment (Fig. 4E). Our hypothesis focuses on the vertical external forces that cause an external torque on the forearm resisted by τ_elb. The stride time series of τ_elb (Fig. 4C,D) shows the effect of bending the elbow and bringing the forearm more perpendicular to the net vertical external force. In BW and BR, τ_elb showed a step frequency pattern similar to vertical accelerations of the trunk (Kubo et al., 2004; Thorstensson et al., 1984). Conversely, τ_elb oscillated at stride frequency in SW and SR, likely due to swinging of the upper arm (Fig. 3A,B) dominating the external torque acting on the forearm.

We predicted that the gait-specific stereotypical behaviors of straight arm walking and bent arm running are driven by the energetic consequences of the mechanical tradeoff, with walking favoring straight arms and running favoring bent arms. The first part of our prediction was supported by our data (Fig. 5), as walking with a bent arm increased V̇_O2,net by 11%, similar to the magnitude of cost increase caused by restricting arm swing (Bruijn et al., 2008; Collins et al., 2009; Umberger, 2008; Arellano and Kram, 2014). However, our results indicate equivalent V̇_O2,net between the two running conditions (Fig. 5), which does not support our energetic hypothesis for running. The existence of an energetic tradeoff favoring bent arms in running cannot be ruled out for several reasons. It is possible the effect size of bending the arm on energetics is too small to be statistically distinguished in our relatively small sample of six individuals. A second possibility is that differences in energetic cost were masked by a shift in metabolic substrate utilization yielding the same oxygen consumption (Fletcher et al., 2009), although the greatest shifts occur at the upper limits of aerobic capacity rather than the comfortable running speed tested here (Goedecke et al., 2000). Finally, we only tested a single dimensionless speed, and it is possible that running becomes less costly with bent arms than straight arms at higher speeds than tested here. Although elbow angle did not affect the net oxygen cost of running, higher torques were generated by the shoulder muscles with straight arms than with bent arms, requiring more activated muscle volume. Larger and costlier motor units tend to be activated as more volume is recruited in muscle contractions (Duchateau and Enoka, 2011), so it is possible that fiber recruitment order affects the tradeoff at faster speeds.

Optimal energetics appears to be the reason why straight arms are stereotyped during walking, but the reason for stereotyped bent arm running remains unclear. Although we have focused on energetic cost as a mechanism in this study, stereotypical bent arm running may result from a non-energetic benefit. For instance, the biceps muscle is thought to link the inertia of the forearm and the head during running for the purpose of head stabilization (Lieberman, 2011); bent arms increases the flexion moment at the elbow and therefore may provide a head stabilization benefit. We must also consider that the stereotyped behavior during running may not provide a benefit at all; there was much greater variation within our sample in average θ_elb for the normal running condition (s.d. of 0.274 rad) than for the normal walking condition (s.d. 0.070 rad), matching our anecdotal observation that runners use quite varied forearm positions.

One potential benefit we did not test in this study is that bent arm running optimizes the relative energetic costs of the shoulder and elbow muscles, independent of the total cost of arm swing. Straight arm running results in greater τ_sho, requiring a greater volume of activated shoulder muscle. More activated volume leads to faster rates of glycogen depletion and lactic acid buildup, both of which are key physiological factors in muscle fatigue (Baker et al., 1993; Maclaren et al., 1989). Therefore, bent arm running may increase time until fatigue in the shoulder muscles even if the total energetic cost of the two arm configurations is the same. The evolution of endurance running in the genus Homo was a major transition in the course of human evolution (Bramble and Lieberman, 2004). The capacity to run very long distances at speeds that force galloping in prey mammals was a critical innovation in hunter–gatherer ecology. Staving off shoulder muscle fatigue may benefit long-distance running and provided the mechanism for the typical human behavior.

Finally, our results have implications for the evolution of arm proportions in hominins. Arm length relative to leg length was greater in Australopithecus and in Homo habilis than in modern humans (Young et al., 2010), as was forearm length relative to upper arm length (Churchill et al., 2013; Richmond et al., 2002). Modern arm proportions emerged in Homo erectus, and coincided with the evolution of endurance running as an important hominin behavior (Bramble and Lieberman, 2004). Reductions in forearm length and total arm length should reduce τ_elb and τ_sho, respectively, and therefore may be signals of selection for lesser arm swing costs during endurance running. Selection for running may have been an important factor shaping the evolution of hominin arms.

We thank Andrew Biewener, Nicholas Holowka, Ian Wallace, Eamon Callison and Victoria Tobolsky for helpful comments at various stages of the project. We also thank the anonymous reviewers for their comments and improvements on the manuscript.