Compensations for increased rotational inertia during human cutting turns

Maneuverability is necessary for locomotion in natural environments (Jindrich and Qiao, 2009). Maneuvers involve behaviourally generated changes to speed, direction and/or body orientation. Animals must maneuver to forage, negotiate uneven terrain or escape predation, with direct impacts on fitness (Demes et al., 1999; Dunbar, 1988; Howland, 1974; Losos and Irschick, 1996). Performance depends on morphology, behavior and motor control (Aerts et al., 2003; Alexander, 2002; Carrier et al., 2001; Dial et al., 2008; Eilam, 1994; Jindrich et al., 2006; Jindrich and Full, 1999; Jindrich et al., 2007; Van Damme and van Dooren, 1999). For humans, turns alone comprise up to 50% of walking steps during daily living (Glaister et al., 2007), and can cause injuries directly by increasing the forces and moments experienced by the legs, and indirectly by decreasing stability and causing falls (Besier et al., 2001; Colby et al., 2000; Cross et al., 1989; Kawamoto et al., 2002; McLean et al., 2004; Stacoff et al., 1996). Maneuvering performance reflects dynamic interactions among mechanics, musculoskeletal physiology and motor control (Biewener and Daley, 2007; Dickinson et al., 2000; Full et al., 2002; Jindrich and Qiao, 2009). Determining the principles governing unsteady locomotion therefore requires assessing both the mechanical requirements and behavioral compensations associated with maneuvers.

Two common aspects of maneuvers are changing movement direction and body re-orientation. Changing movement direction requires a force impulse with a component orthogonal to the initial movement direction (imd). Body re-orientation does not require external moments if large limb motions are used (Kane and Scher, 1970). However, moments due to external forces will also cause rotation if resultant forces are not directed through the center of mass (COM). For example, a simple mathematical model based on the assumptions that (1) rotational moments are primarily due to external forces and (2) body rotation should align with velocity direction at the end of a turning step can predict horizontal-plane ground reaction forces (GRFs) used during maneuvers in insects, ostriches and humans (Jindrich and Qiao, 2009). The model relates several morphological (i.e. body mass, M; yaw moment of inertia, I_zz), task (i.e. velocity direction change, θ_d; amount of body rotation, θ_r; and speed, V_AEP,imd) and behavioral (i.e. fore–aft foot placement, P_AEP,imd; lateral foot placement, P_p; and stance duration, τ) parameters (Fig. 1A). The model was used to express the hypothesis that braking forces, i.e. deceleratory forces in the initial velocity direction that occur during the turning step, act to control body rotation during running turns (Jindrich et al., 2006). Specifically, the model suggests that braking forces prevent body over-rotation in humans, in part because of an orthograde posture and a high ratio of M to I_zz. This hypothesis was supported by the 7- to 20-fold increases in braking forces during turns relative to constant-average-velocity running, the approximate doubling of average braking forces with an increase in turn magnitude from 28 to 42 deg, and the high (r²=0.7) correlation between measured and model-predicted peak braking forces for both sidestep and crossover cuts (Jindrich et al., 2006).

Additional support was provided by the model's prediction that braking forces for ostriches, ancestrally cursorial runners with a pronograde posture and a lower ratio of M to I_zz relative to humans, may not be necessary to prevent over-rotation (Jindrich et al., 2007). As predicted by the model, ostriches made sidestep cuts using braking forces that were, on average, close to zero. Although the lower M to I_zz ratio could explain some of the low braking forces observed in ostriches, differences in several other parameters also contributed (Jindrich and Qiao, 2009). Although measured peak braking forces were tightly correlated to predictions (r²=0.7), forces also showed substantial variance across trials, suggesting that braking forces may still contribute to trial-by-trial control of body rotation.

In addition to braking forces, other behavioral parameters could also contribute to successfully matching changes in body orientation

to changes in velocity direction during running turns. For humans, turns of increasing magnitude were associated with increases in stance duration (τ) and foot placement in the anterior–posterior (P_AEP,imd) and mediolateral (P_p) directions. However, these changes were not as closely associated with turn magnitude as were braking forces (Jindrich et al., 2006). Moreover, several parameters that could affect turning were not included in the analysis or model. For example, body rotation could be directly affected by initial pre-rotation angle (θ_i) and initial body rotational speed (ω₀; Fig. 1A). Rotation due to free moments (θ_Tz), i.e. rotation due to moments directly generated by the foot in contact with the ground, were small during normal running turns, but could potentially be recruited under different or perturbed turning conditions. Consequently, whether adjustments to one, or some combination, of these parameters are used to control body rotation during running turns remains a question.

One difference among parameters that could affect their role is the point in the stride cycle at which each parameter can be altered. Changes to braking force, free moment or stance duration involve alterations to forces or moments generated by the leg during stance. Changes to other parameters (e.g. P_AEP,imd, P_p, θ_i or ω₀) involve altering leg or body kinematics during previous steps or the flight period before stance. Anticipation can involve adjustments to muscle activity associated with changes in foot placement and GRFs (Bencke et al., 2000; Houck, 2003; Rand and Ohtsuki, 2000). However, passive factors such as coupling among parameters (i.e. foot placement and GRFs) could also contribute to changes prior to turning steps. For simplicity, we will term ‘anticipatory’ any parameters that are determined before the turning step, whether passive (mechanical) or active factors primarily cause a change. Furthermore, observed anticipatory changes may not necessarily be involved in the trial-level control of individual turns, but could instead reflect task-level adjustments associated with the shift from constant-average-velocity running to turning (Besier et al., 2003). Consequently, the role of anticipatory adjustments relative to changes that occur during the stance period of a turning step remains unclear.

Our overall goal is to better characterize the behavioral strategies used by legged animals to perform turning maneuvers, to identify the parameters used to turn and determine how and when they are modulated to make successful turning maneuvers despite variability and perturbations. Specifically, we sought to test the hypothesis that human runners use braking forces alone to maintain appropriate body rotation during running turns under different mechanical conditions that affect body rotation. This hypothesis would be supported if perturbations that affect body rotation result in proportional changes to braking forces during stance, but do not affect other behavioral parameters. If braking forces do not change then the hypothesis is rejected, and this presents the question of whether anticipatory adjustments, within-step changes or a combination are used to compensate for perturbations to rotation.

To test this hypothesis, we sought to perturb body rotation requirements while minimally changing other aspects of turning (i.e. requirements for movement direction or linear momentum change). To this end, we used a harness system that enabled up to 400% increases in rotational inertia with substantially less (15–17%) change to body mass. If the magnitude of braking forces alone is adjusted to control body rotation, the turning model predicts that increases in I_zz would progressively decrease peak braking forces and even result in acceleratory forces. Threefold increases in I_zz would decrease peak braking forces to zero and, similar to ostriches, humans would turn using primarily the average lateral forces necessary for movement deflection.

Increasing rotational inertia did not change most aspects of turning performance. On average, participants made sidestep cuts with COM deflection angles (θ_d) and body rotational angles (θ_r) that were not significantly different among conditions (Table 1). However, participants did not fully deflect their movement direction by 45 deg during the turning step, but by only 25–27 deg (Table 1). This was primarily because of partially changing movement direction (relative to global) before the primary turning step. Forces in both the ML and AP directions [F_p(t) and F_imd(t), respectively] were also not significantly different (Fig. 2AB). There was no significant difference between COM initial speed (V_AEP,imd) and final speed (V_f) (P=0.99; Table 1). Increased force impulses associated with 15–17% increases in mass were achieved by 10–16% increases in stance duration (τ; Table 1). Consequently, because participants were able to achieve similar performance in all conditions, turns with and without the harness and under different M and I_zz conditions were considered comparable.

Leg effectiveness number (ε) decreased significantly as rotational inertia increased (P<0.01; Table 1). Measured decreases in ε caused the predicted peak braking force, F_hmax, to decrease significantly and to predict acceleratory forces at M17%I3.5 and M17%I4 (P<0.01; Fig. 3A, Table 1).

However, measured peak braking force, β, was not significantly different among rotational inertia conditions (P=0.08; Table 1). Moreover, GRF impulse in the AP direction was also not different (P=0.21; Fig. 3B). Consequently, the hypothesis that increasing rotational inertia would decrease measured peak braking force was rejected.

The consistent braking forces across M and I_zz conditions resulted in unchanged leg orientation with respect to GRF (1.5 deg) during stance. The GRF direction relative to the virtual leg connecting the COM and the center of pressure (COP) at 50% of stance phase was unchanged during sidestep cutting turns with different I_zz (P=0.19; Fig. 4A). Relative angles during straight running under different I_zz also remained the same (P=0.48; Fig. 4B). A factorial repeated-measures ANOVA comparing the effects of gait (factor A, TURN and RUN) and I_zz (factor B) on body orientation relative to GRF revealed no main effects (p_A=0.9, p_B=0.2; Fig. 4C).

Increased I_zz was associated with both changes to parameters describing the turning step and anticipatory adjustments. Significant increases in stance duration occurred during the turning step (τ, P<0.01; Table 1). ML foot placement (P_p), which reflects changes that primarily occur before the turning step, decreased 8–15% relative to non-harness (NH; M0%I1) turning. However, AP foot placement (P_AEP,imd) did not differ significantly among conditions (P=0.15; Table 1). Changes to P_p were partially due to shifts of the COP under the foot. When either P_AEP,imd and P_p were determined from the toe or heel markers, there was no significant difference among inertia conditions (P_AEP,imd, P=0.13; P_p, P=0.32).

All other parameters being equal, decreases in P_p would be expected to require increased peak braking force (β) (see Eqn 5 in Materials and methods). However, the decreases in P_p were more than offset by 10–16% increases in τ that would be expected both to decrease ε (see Eqn 4) and directly decrease β (see Eqn 5). Consequently, changes to the modeled parameters P_p and τ could not explain the unchanged peak braking forces among different rotational inertia conditions.

Increasing I_zz revealed that a balance among several previously un-modeled parameters resulted in unchanged β across conditions. A more complete model of turning (see  Appendix) showed that perpendicular turning forces (F_p) and braking forces were not the only contributors to body rotation. Both the normally observed deceleratory/acceleratory AP force (the α component of F_imd) and its interaction with F_p resulted in substantial body rotations (θ_α and θ_αFp, respectively; Table 1). For example, in the NH condition these force components together resulted in net body rotations of −25 deg, i.e. against the overall turn direction. This rotation, θ_α+θ_αFp, was almost completely offset by initial body rotational velocity (ω₀) acting over the stance period, and initial body rotation (θ_i) at TD, that together contributed 26 deg of body rotation towards the turning direction. Therefore, for the NH condition, the small amount (~1 deg) of net body rotation resulting from the sum of these parameters (θ_α+θ_αFp+θ_i+ω₀τ) did not substantially affect the ability of the simple model of Eqns 4 and 5 to predict β with F_hmax (Jindrich et al., 2006).

Increasing I_zz significantly reduced both θ_α and θ_αFp, resulting in a combined effect of −6 to −7 deg of rotation against the turn direction for threefold and greater increases in I_zz. Without θ_α+θ_αFp opposing ω₀ and θ_i, the potential for body over-rotation would be expected to increase. Preventing over-rotation during the turning step could be achieved by increasing peak braking forces relative to the NH condition (the opposite of the hypothesis from the simple turning model) to maintain θ_r close to θ_d. Instead, participants employed an anticipatory strategy, significantly decreasing ω₀ (P<0.05; Table 1). However, ω₀ did not drop to zero but decreased only by 33–49%. Therefore, rotation due to ω₀ and θ_i balanced rotation due to fore–aft forces, allowing for anticipatory adjustments to initial rotation conditions to maintain nearly constant braking forces among conditions.

Contrary to the hypothesis that increasing I_zz would decrease braking force, we found that anticipatory changes to initial rotational speed were associated with maintaining average braking forces that did not differ among rotational inertia conditions during running turns. Consistent turning performance was maintained across fourfold increases in I_zz using relatively minor changes to behavioral parameters: 8–15% decreases in ML foot placement (P_p), 10–16% increases in stance duration (τ) and 33~49% decreases in initial rotational angular speed (ω₀). Moreover, the opposing rotation of multiple dynamic parameters provided humans with several behavioral options when compensating for morphological changes.

Based on the turning model and the relatively small braking forces observed in ostriches, we predicted that humans would decrease peak braking forces when the requirements for preventing body over-rotation were relaxed. Humans instead maintained similar peak braking forces and GRF orientation relative to the leg across fourfold changes to rotational inertia. There was a trend for decreases in β with increased inertia that may have been non-significant because of limited sample size. However, the ~50% decreases in measured β would have been insufficient to explain the 150% decreases in F_hmax predicted to control body rotation with braking forces alone. The maintenance of similar leg forces across conditions may limit the changes in motor output required for different maneuvers. Similar to ostriches, where cutting turns involved few changes to joint moments relative to straight running (Jindrich et al., 2007), humans may organize maneuvers in part to reduce functional changes at the joint or muscle level.

Therefore, although movement parameters are related in a way that results in appropriate body rotation and can be predicted by Eqns 2 and 3, we cannot conclude that these relationships reflect active control of body orientation. Additional experiments will be necessary to determine how movement is organized to satisfy several task objectives of potentially different importance, including controlling body rotation, maintaining speed, maximizing stability, reducing injury risk, minimizing energetic cost, or reducing sensorimotor demands.

Whether the strategies used by bipeds for maneuvers are also employed by other animals also remains an important question. Quadrupeds or polypeds that step with more than one leg may have fewer constraints and more options for maneuvering strategies than bipeds (Jindrich and Full, 1999). For example, additional legs may allow for rotation and translation to become partially de-coupled (Walter, 2003).

Anticipatory adjustments contributed to appropriate body rotation. Increasing I_zz resulted in significant differences in anticipatory (ML foot placement, P_p, and initial angular speed, ω₀) parameters and to parameters describing the turning step (stance duration, τ). However, observed increases in τ could be primarily due to increases in body mass (M) resulting from the harness and weights. Although our original intent for using two separate levels of added mass was to directly test the effects of M on turning, constraints on the length of the harness bars limited our values of M to differing by only 2%. Longer galvanized steel bars substantially increased M and offset the benefit of requiring less added weight to increase I_zz. However, as M and I_zz increased, τ increased by 15–20% even in the RUN condition (P<0.05; Table 2). Similarly, increasing M alone by 10% or 20% was found to result in 5% or 8% increases in τ during constant-speed treadmill running at 3 m s⁻¹ (Chang et al., 2000). Therefore, it is reasonable to conclude that the increases in τ are associated with increased M and not I_zz.

If increases in stance duration reflected compensations for increased mass, compensations for increased I_zz principally involved significant changes in two parameters that were both primarily determined before the turning step: ML foot placement (P_p) and initial body rotational speed (ω₀). For all turning conditions, humans increased their lateral leg placement relative to straight running (RUN), where P_p averages ~4 cm (Jindrich et al., 2006). The higher P_p observed during turns compared with RUN could reduce the braking forces necessary to prevent over-rotation, and would therefore be consistent with the hypothesis that humans reduce braking forces when less necessary because of increased I_zz. However, increases in I_zz were instead associated with decreased P_p relative to the NH condition, consistent with the alternative hypothesis that humans use anticipatory adjustments to maintain unchanged braking forces during running turns.

In contrast to changes in ML foot placement, decreases in ω₀ with increased I_zz relative to the NH condition would be expected to decrease peak braking forces. However, the values of ω₀ were high in the NH condition (65 deg s⁻¹) and remained positive despite 33–49% decreases with increased I_zz (Table 1). Therefore, along with pre-rotation (θ_i), ω₀ continued to cause rotation in the trial turn direction. Overcoming rotation due to ω₀ contributed to required braking forces in all conditions. Without decreases in ω₀, peak braking forces in the increased I_zz conditions could even have increased relative to NH values. Therefore, the decreases in ω₀ relative to the NH condition were also consistent with the hypothesis that humans use anticipatory adjustments to maintain unchanged peak braking forces during running turns. Anticipatory adjustments that reflect behavioral strategies are consistent with research on walking turns (Jindrich and Qiao, 2009). For example, anticipation in walking turns affects foot placement (Orendurff et al., 2006; Patla et al., 1999), and changes to ω₀ and θ_i are initiated before the turning step in walking (Taylor et al., 2005). The finding that anticipatory compensations are used during both walking and running could therefore suggest that humans use some feed-forward strategies to execute anticipated maneuvers.

However, because initial rotational speed reflects the dynamics of strides before the turn that could be affected by increased I_zz, we cannot determine whether decreases in ω₀ were due to behavioral adjustments or stemmed passively from changes in running dynamics associated with higher M and I_zz. Decreases in ω₀ in the RUN condition (Table 2) for increased I_zz suggest that the compensations necessary to maintain unchanged braking forces may arise passively, or be part of a more general strategy for compensation for increased inertia. Future experiments may be able to distinguish between robustness of the mechanical system and behavioral strategies that allow modest changes to initial conditions to compensate for large morphological perturbations.

A running, segmented system involves many morphological and behavioral factors that are extensively coupled. Coupling can involve both passive mechanisms (due to changes in movement dynamics) and active coupling, where adjustments are made to achieve task requirements and mechanical or energetic objectives (Hackert et al., 2006). For example, decreased AP foot placement (P_AEP,imd) would be predicted to decrease body rotation (see Eqns 4, 5, and Eqn A10 in the  Appendix). However, decreasing P_AEP,imd could result in transfer of potential to kinetic energy, COM acceleration and increased speed (McGowan et al., 2005; Qiao and Jindrich, 2012). Changes to stance duration could alter both translational and rotational momentum changes about all three axes, potentially altering movement dynamics (Herr and Popovic, 2008).

We hypothesize that adjusting initial rotational speed is advantageous because changes to ω₀ can directly affect body rotation, depending only on stance duration (see Eqn A10). However, this presents the question of why humans did not change pre-rotation to compensate for increased I_zz, as θ_i can also directly change net body rotation. Changes in θ_i may not have been used because θ_i influences the orientation of the leg relative to the body at TD, potentially requiring substantial changes in muscle activity to ensure that leg forces remain appropriate, and that resultant leg forces are minimally affected by turning.

Perturbing locomotion by increasing I_zz demonstrated that several simplifying assumptions made in the original model (see Eqns 4, 5) were not appropriate for a general description of horizontal-plane maneuvers.

First, the model simplified COM motion in the initial movement direction by assuming constant speed. This allowed foot movement relative to the COM to be described as P_imd(t)=P_AEP,imd–V_AEP,imd·t (Jindrich et al., 2006). Accounting for accelerations during stance caused by forces in the initial movement direction (see Eqn A3 in the  Appendix) resulted in two additional terms, θ_α and θ_αFp (Eqn A10). The net effect of θ_α+θ_αFp would be rotation against the turning direction, leading to predictions of lower peak braking forces.

Second, the original model neglected initial body rotation conditions, initial rotational speed (ω₀) and pre-rotation (θ_i). Both ω₀ and θ_i were positive, towards the trial turn direction, and would be expected to contribute to over-rotation and lead to a prediction of increased peak braking forces.

Third, the model also assumed that body rotation (θ_r) matched movement deflection (θ_d) at the end of the turn. However, total body rotation was less than movement deflection at TO across all conditions, suggesting that humans may prefer to consistently under-rotate during stance (Table 1, Fig. 6). Maintaining under-rotation would be predicted to require increased peak braking forces. Finally, the original model did not account for moments generated by the foot, θ_Tz.

Increased rotational inertia is often assumed to limit maximal turning performance (Carrier et al., 2001; Eilam, 1994). However, we found that increasing I_zz up to fourfold during sub-maximal turns did not affect performance, and could be compensated with changes to a limited number of parameters. Compensations for increased I_zz were facilitated by the opposite contributions of several factors to body rotation. The initial conditions (ω₀ and θ_i), and the preference for under-rotation during the turning step (θ_f), opposed the effects of rotation due to fore–aft and perpendicular forces, θ_α+θ_αFp (Fig. 6B, Table 1). Consequently, when increased I_zz decreased rotation due to forces and their resulting moments, force directions relative to the leg could be maintained by decreased ω₀. Therefore, the opposition of rotations due to θ_α+θ_αFp, ω₀ and θ_i contributed to the robustness of the maneuvering system by allowing substantial increases to I_zz to be overcome by modest changes to initial rotational speed. The robustness and stability gained from maintaining a balance of opposing factors may be analogous to the observation of increased muscle co-activation with increasing movement accuracy demands (Gribble et al., 2003).

Humans maintained unchanged braking forces and consistent force direction relative to the leg across I_zz conditions by altering initial conditions, ML foot placement (P_p) and initial body rotational speed (ω₀). These findings suggest that humans are able to modulate several parameters to maintain specific aspects of movement invariant, on average. However, the ability to maintain consistent peak braking force (β) across rotational inertia conditions does not explain the large variance in many parameters, including β, across trials. For example, across-trial variability in β was 83% of the average, s.d./mean. However, the large variance observed in individual parameters contrasts with lower variance when the coupling among movement parameters described by Eqns 2 and 3 is accounted for (Fig. 7). The observation of a relationship among parameters that is maintained despite large variance in values of the parameters themselves is analogous to the pattern observed in joint coordination during several types of movements (Scholz and Schöner, 1999). For example, during hopping, joint redundancy is used to maintain task-level parameters such as leg length, orientation or force invariant (Auyang et al., 2009; Yen and Chang, 2010). Redundancy among several factors that contribute to body rotation could be exploited to maintain desired orientation relative to movement direction at the end of the turning step. However, the underlying source of the considerable intra-trial variability remains to be determined.

All procedures used for these experiments were approved by the Institutional Review Board of Arizona State University.

Predicted and measured deceleratory forces, F_hmax and β, were defined to be negative and acceleratory forces positive. Assumptions of this model include: (1) successful turns involve body rotation (θ_r) matching θ_d at the end of the turning step; and (2) initial body pre-rotation angle (θ_i) and angular speed (ω₀) are zero (Fig. 1A).

For humans, the ε during running cuts ranges from ~2 to ~4 (Jindrich et al., 2006). Consequently, during turns, the difference (1–ε) in Eqn 5 is typically negative, resulting in negative (‘braking’) F_hmax. Increasing I_zz would be expected to reduce ε, in turn reducing 1–ε and therefore reducing the braking forces required for θ_r to match θ_d at the end of the step.

Seven participants [age=22.5±1.5 years; body mass (M)=68.2±4.0 kg; body height=174.9±4.2 cm, leg length=96.1±4.6 cm, five males; means ± s.d.] participated in the study. Anthropometric data for individual participants were estimated using allometric scaling from a reference human model, assuming identical density and segment mass percentage (Herr and Popovic, 2008; Huston and Passerello, 1982). The principal moments of inertia of each segment in yaw, roll and pitch directions were then scaled. Whole body moment of inertia tensor relative to the COM in the stance posture, as a function of M and body height, was calculated using the parallel axis theorem. This resulted in body rotational inertia, I_zz, scaling with M^5/3 (Carrier et al., 2001). The participant's body rotational inertia about the vertical axis was validated by having participants make stationary turns on a force platform, and calculating I_zz using a least-squares fit to free moment and rotation angular acceleration [validation R²=0.72 (Jindrich et al., 2007)].

A customized harness (8.3 kg) based on previous designs was built using galvanized steel bars and a rigid plastic frame (Carrier et al., 2001). The harness was used to change I_zz by adding equally balanced weights (tiny lead balls contained in a bag) both anterior and posterior to the COM (Fig. 1B). The dimensions of the harness were 0.7×1.5×0.8 m (ML×AP×z). Treated as a rigid body, its principal moments and products of inertia were 1.35 (ML), 0.100 (ML, AP), 0.463 (ML, z), 0.601 (AP), 0.0972 (AP, z) and 1.38 (z) kg m², determined by measuring swinging periods about principal axes and the parallel axis theorem (Jindrich and Full, 1999).

Five different harness mass and I_zz increment combinations were applied: M0%I1 (control, no harness, NH), M15%I3 (mass increased by 15% and body inertia to threefold), M15%I3.5, M17%I3.5 and M17%I4. To change I_zz, mass was attached to the horizontal bars symmetrically about the COM of the combined human and harness. The added weight was selected so that the total weight with the harness was a set percentage (15% or 17%) of the participant's M. Both weight and position were changed to achieve the target body mass and I_zz increments. For example, for the M15%I3.5 condition, less weight was placed further from the COM, while for the M17%I3.5 more weight was placed closer. The specific weights and positions were calculated separately for each participant.

Participants ran at 2.98±0.08 m s⁻¹, and performed both straight running (RUN) and left 45 deg sidestep cutting turns (TURN). Turning direction was indicated by tape on the floor. In each condition, five trials were collected. The order of the conditions (RUN and all TURN conditions) was randomized. Participants were given instructions to make turns in a natural way, but were not instructed to maintain constant speed during the turn.

We used a 3-D motion tracking system (VICON, model 612, Oxford Metrics, Oxford, UK) to record the kinematics of 37 reflective markers at 120 Hz. To compensate for the harness, we replaced the markers on the anterior and posterior superior iliac spines in the standard marker set with markers on the left and right greater trochanter (LGT and RGT). Two force platforms (400×600 mm, model FP4060-NC, Bertec Corporation, Columbus, OH, USA) embedded in the ground were used to record GRF at 3000 Hz. The inertial coordinate system was defined as in Fig. 1A. The AP and ML directions were defined as parallel and perpendicular, respectively, to the horizontal projection of COM velocity at TD (i.e. the initial movement direction; Fig. 1C). Forces in the AP direction can be decomposed into full-sine (α) components similar to those observed during constant-speed running, and half-sine (β) components only observed during turning (Jindrich et al., 2006). The α and β components in F_imd(t) were determined by multiple linear regression using αsin(2π t/τ) and βsin(π t/τ), respectively.

The COM was calculated by segmental average, and its velocity was tuned with the GRF using a path-finding algorithm (McGowan et al., 2005). Specifically, the initial velocity that minimized the Euclidean distance between the tuned and un-tuned COM trajectories was chosen. Body rotation (θ_r) was defined as the change in the vector connecting the hip markers (LGT and RGT; Fig. 1A) over the turning step. We also tuned rotational angle with resultant vertical moment to determine the initial rotational angular speed (ω₀) at the beginning of a turn. The correlation between tuned and un-tuned rotational angle trajectories was 0.99.

Because the harness was at the height of the pelvis, LGT and RGT markers were not visible in some of the trials. Those trials were excluded from analysis, but at least one trial for each participant at each condition was available. Only two participant/condition sets had only one trial as a result of marker placement. Eighty-three percent of the participant/condition sets contained five trials. For turning, 284 trials were successful out of 420.

Kinematic data were interpolated to the same sampling frequency as GRF using a spline fit. The instant of TD was determined as the first sample after which raw vertical GRF continuously increased for 5 ms (Qiao and Jindrich, 2012). An equivalent criterion was used to identify the last 5 ms of force decrease to identify TO. Because the COP location at TD can be noisy because of impact transients, we used the average COP location during stance relative to the toe marker to calculate P_AEP,imd and P_p (Jindrich et al., 2006). Kinetics/kinematics were filtered by a fourth-order zero-lag low-pass Butterworth digital filter at 30/11 Hz.

To compare the effect of rotational inertia (different M and I_zz combinations) on turning performance, we used repeated-measures ANOVA with participants as the repeated factor (Keppel and Wickens, 2004). To compare the effects of gait and rotational inertia on the gait parameters, a factorial repeated-measures ANOVA was employed with gait (TURN versus RUN) as factor A and the levels of different rotational inertias as factor B. Post hoc analysis was based on the Bonferroni procedure with Šidák correction {P<[1−(1−α)^1/c], where c=(a−1)·a/2 and a is the number of I_zz levels; this resulted in P<0.0051}.

All calculations were performed using MATLAB (R2012a, MathWorks, Natick, MA, USA). All values within the text and tables are means ± s.d. except as indicated.

This research would not have been possible without the support of the Arizona State University (ASU) Kinesiology Program, School of Life Sciences and Graduate College. We are grateful to James Abbas and the ASU Center for Adaptive Neural Systems for use of laboratory facilities. Furthermore, we thank Carolyn Westlake for valuable input and contributions to experimental design.