# The counter-rotating mechanism makes a substantial contribution to balance-movement coordination during the anticipatory period of gait initiation

Romain Bechet, Romain Tisserand, Laetitia Fradet, Floren Colloud

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Romain Bechet, Romain Tisserand, Laetitia Fradet, Floren Colloud. The counter-rotating mechanism makes a substantial contribution to balance-movement coordination during the anticipatory period of gait initiation. Journal of Biomechanics, 2025, 190, pp.112860. 10.1016/j.jbiomech.2025.112860. hal-05176655

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The counter-rotating mechanism makes a substantial
contribution to balance-movement coordination during
the anticipatory period of gait initiation

**Abstract**

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Maintaining balance during gait initiation is essential for mobility and
functional independence. The transition from a postural state to steady-state
gait relies on two mechanisms to accelerate the whole-body centre of mass
(WBCOM): moving centre of pressure (CoP); and counter-rotating segments
to modulate internal whole-body angular momentum (H<sub>M</sub>). While the mov-
ing CoP mechanism is well-understood and known to generate mechanical
instability, the role of the counter-rotating mechanism is less clear. There-
fore, the present study *quantified* the contribution of the counter-rotating
mechanism and *explored* its coordination with the moving CoP mechanism
during the anticipatory period of gait initiation. Based on a sample of 13
healthy participants, we computed the time evolution of CoP, H<sub>M</sub>, the coef-
ficient of cancellation (i.e., the extent to which segmental angular momenta
counterbalance each other), and the relative contribution of each mechanism
to WBCOM acceleration. We tested whether the contribution of the counter-
rotating mechanism was significantly different from zero using a Statistical
Parametric Mapping *t*-test. In the frontal plane, the counter-rotating mecha-
nism did not appear to play a substantial role. However, in the sagittal plane,
we found that: 1) the period of mechanical instability was longer than the
period that have been identified based on the moving CoP mechanism alone;
2) rotational instability was reduced in anticipation of unipedal support;
and 3) the counter-rotating mechanism significantly contributed to WBCOM
forward acceleration. Overall, our findings emphasise the critical role of the
counter-rotating mechanism in the sagittal plane for balance-movement coor-
dination. Considering the counter-rotating mechanism appears important for
understanding, assessing, and developing interventions for individuals with
balance impairments.

Keywords: Transition, Anticipation, Coordination, Balance, Movement
# 1. Introduction

The ability to move safely is essential, both for independence and overall well-being, making it a critical public health concern. In particular, poor balance increases the risk of falling during daily movements, leading to a loss of confidence, social isolation, and, ultimately, a decline in quality of life, in parallel with high the cost to society (Selikson et al., 1988; Schoene et al., 2019).

Research on balance has primarily focused on steady-state conditions, such as maintaining posture or walking at constant velocity. However, transitions, defined as movement phases that modify whole-body centre of mass (WBCOM) acceleration (Bechet et al., 2025b), are predominant in daily life (Orendurff et al., 2008). Crucially, the ineffective execution of these transitions may be a leading cause of falls among older adults (Robinovitch et al., 2013).

Gait initiation, a transition from a postural state to steady-state gait, can be used to assess balance-movement coordination. A characteristic of gait initiation is that once the foot is lifted, the whole-body is thought to follow a ballistic trajectory (Lyon and Day, 2005; Bancroft and Day, 2016). Thus, anticipatory adjustments (i.e., the adjustments that occur between the onset of forward WBCOM acceleration and the first foot lifting) are essential because they provide favourable conditions to support both the initiation of the movement and the maintenance of balance (Yiou et al., 2017). However, the characteristics of these favourable conditions, and how they are achieved during the anticipatory period remain only partially understood.

Earlier research proposed two complementary mechanisms regulate WB-
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CoM acceleration: moving centre of pressure (CoP) and counter-rotating segments (Hof, 2007; Bechet et al., 2025b). The moving CoP mechanism consists in misaligning the CoP with the WBCoM, and accelerating the WB-CoM in the opposite direction. The counter-rotating mechanism refers to the rotation of body segments, which modulates internal whole-body angular momentum ($H_M$), whose time derivative ($\dot{H}_M$) is directly linked to WBCoM acceleration.

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The moving CoP mechanism has been extensively studied during gait initiation: first, the CoP moves both backward and toward the future swing lower-limb until it reaches a maximal backward position (Brenière et al., 1987), termed the *max CoP* event (Mickelborough et al., 2004). This movement is thought to generate mechanical instability, represented by an increase in the distance between the WBCoM and the CoP. After *max CoP*, the CoP moves laterally, with the aim to help maintain balance in the frontal plane, by decreasing the mediolateral distance between the WBCoM and the CoP (Mickelborough et al., 2004; Yiou et al., 2017).

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After the first CoP movement, the whole-body rotates in a forward direction, characterised by a decrease in $H_{ML}$ (i.e., $H_M$ around the mediolateral axis). Then this rotational mechanical instability is controlled by a whole-body backward-directed rotation, limiting the absolute value of $H_{ML}$ (Begue et al., 2019; Bechet et al., 2025a). We define the moment that characterises the shift from forward- to backward-directed rotation as *momentum reversal*. However, it is unknown whether these two events (*max CoP* and *momentum reversal*) occur simultaneously, and how the moving CoP and counter-rotating mechanisms are coordinated.
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Although the counter-rotating mechanism has received much less attention in the literature (Bechet et al., 2025b), $H_M$ regulation has been proposed as an indicator of whole-body balance (Neptune and Vistamehr, 2019). The use of segment counter-rotating to regulate $H_M$ can be evaluated using a coefficient of cancellation ($\kappa$), which represents the degree to which the angular momenta of the body's segments compensate for each other (Bennett et al., 2010). This coefficient ranges from 0, indicating no segment cancellation for balancing purposes (all segments rotate in the same direction) to 1, indicating perfect cancellation and balance regulation.

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The time evolution of $H_M$ is linked to WBCOM acceleration through its time derivative $\dot{H}_M$ (Hof, 2007). Although it seems reasonable to assume that changes in $H_M$ due to counter-rotation might contribute to WBCOM acceleration, this relationship has not yet been quantified in the anticipatory phase of gait initiation. Moreover, the link between the time evolution of $H_M$, and both balance maintenance and movement initiation makes this a useful metric to better-understand balance-movement coordination. However, it is not yet clear whether the counter-rotating mechanism helps in stabilising the whole-body and/or contributes to WBCOM acceleration during gait initiation.

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The aim of this study was therefore to investigate the role of the counter-rotating mechanism, and its coordination with the moving CoP mechanism during the anticipatory period of gait initiation. First, we examined whether *max CoP* and *momentum reversal* events occurred at the same time. Next, we quantified the time evolution of $H_M$ and $\kappa$ to determine how the counter-rotating mechanism changed the amplitude of $H_M$ and, thus, how it might
contribute to balance regulation. Earlier work has described a backward ori-
ented $H_{ML}$ and a stance lower-limb directed $H_{AP}$ (i.e., $H_M$ around the
anteroposterior axis) at the end of the anticipatory period of a stepping task
(Begue et al., 2019), we therefore hypothesised an increase in both $H_{ML}$ and
$\kappa_{ML}$ before foot-off. Similarly, we hypothesised a decrease in $H_{AP}$ toward
the stance lower-limb side, along with an increase in $\kappa_{AP}$ before foot-off, in-
dicating a role of whole-body balance regulation. Finally, we quantified the
contribution of the counter-rotating mechanism to WBCOM acceleration, in
order to determine whether it substantially contributed to movement initia-
tion. Based on reported values of $\dot{H}_M$ during a stepping task (Begue et al.,
2019), we hypothesised that the increase in $H_{ML}$ contributes to forward
WBCOM acceleration, while the decrease in $H_{AP}$ is not sufficient to accel-
erate the WBCOM laterally.

## 2. Methods

### 2.1. Participants

Thirteen healthy participants (4 females, mean ± standard deviation, 23.4± 4.2 years old; 1.72 ± 0.1 m; 65.5 ± 8.8 kg) were recruited on a voluntary basis from the student population of the local university for this study. Inclusion criteria required participants to be young adults (18-35 years old) in good general health (i.e., no condition that could affect balance) and the ability to walk without assistive device. Exclusion criteria were the presence of any musculoskeletal injury of the lower-limb during the six months preceding the experiment, and any neurological impairment that could affect balance and coordination. All procedures were declared in accordance with
the institutional guidelines set by the Declaration of Helsinki and approved
by the University Ethics Committee (CER-TP 2022-04-02). All participants
gave informed consent to the protocol before the experiment.

## 2.2. Measurements and Procedure

Fifty-four reflective markers were placed by the same experienced
experimenter (five years of experience in marker placement) on each partici-
pant's body, 36 on anatomical body landmarks and 18 as technical markers
(Fig. 1a). Their three-dimensional trajectories were recorded by an optoelec-
tronic system composed of 19 cameras (T40, Vicon, Oxford, UK) sampled at
200 Hz. The participants first performed a series of functional movements,
rotating each degree of freedom of the hip, knee, shoulder, lumbar, spine and
neck in order to compute joint centres. Then, participants completed three
gait initiation trials. Each foot was positioned on a force plate (400 x 600
mm, Sensix, Poitiers, France), which recorded ground reaction forces and
moments at 2000 Hz. Participants stood upright maintaining a hip-width
stance, with their arms alongside their bodies. After a five-second period
of quiet standing, they were verbally instructed to start walking with their
preferred lower-limb, and continue walking for five meters (Fig. 1b). The
initial foot position was marked on each force plate to ensure consistency in
the starting position, and the same experimenter checked that the first step
was a consistent length between trials.

## 2.3. Data Analysis

Ground reaction forces and moments, and marker trajectories were fil-
tered using a critically damped zero-phase low pass filter at 20 and 10 Hz,
respectively (Robertson and Dowling, 2003). The global CoP was then computed in the global reference frame. The CoP representation was normalised by the length and width of the base of support (Fig. 1c). WBCOM horizontal acceleration was computed using ground reaction forces (Eq. 1). See Nomenclature (Table 1) for definition of all variables.

$$a_{MAP} = \frac{F_{GAP}}{m}; a_{ML} = \frac{F_{GML}}{m} \qquad (1)$$

Recordings from the functional movement trials were used to compute joint centres. Hip joint centres were determined according to Halvorsen (2003). Knee joint centres were defined as the midpoint of the femoral condyles, projected onto the axis of flexion (Ehrig et al., 2007). Ankle, elbow, and wrist joint centres were defined as the midpoints of the malleoli, humeral epicondyles, radial and ulna styloid processes, respectively. Lumbar, neck and shoulder joint centres were determined using the SCoRe method (Ehrig et al., 2006). Markers and joint centres were used to construct a 13-segment whole-body model (excluding hands). The centre of mass and inertia of each segment were computed from anthropometric tables (Dumas et al., 2007), the WBCOM as the weighted sum of all segment positions (Winter, 2009), and $H_M$ as the sum of angular momentum of each segment relative to the WBCOM (Herr and Popovic, 2008) (Eq. 2).

$$\overrightarrow{H_M} = \sum_{i=1}^{n} \overrightarrow{H_M^i} = \sum_{i=1}^{n} [i_i \cdot \overrightarrow{\omega}_i + (\overrightarrow{OM}_i - \overrightarrow{OM}) \times m_i \cdot (\overrightarrow{v}_{M_i} - \overrightarrow{v}_M)] \quad (2)$$

The coefficient of cancellation $\kappa$ was computed from segment angular momenta (Eq. 3) by dividing the amount of cancelled segment angular mo-
mentum by the total magnitude of segment angular momentum (Bennett et al., 2010).

$$ \kappa_j = \frac{\sum_{i=1}^{n} |H_{M_j}^i| - |H_{M_j}|}{\sum_{i=1}^{n} |H_{M_j}^i|} \quad (3) $$

The figures presented in the results represent gait initiation with a left swing lower-limb. Thus, for participants who initiated gait with the right lower-limb, frontal plane curves were negated.

## 2.4. Temporal Analysis

The anticipatory period was defined as starting when WBCOM acceleration exceeded the mean plus three standard deviations, calculated during the one-second interval with the smallest WBCOM acceleration during the quiet standing period (0%) (Fig. 1d), and ending at the first foot-off, when the vertical ground reaction force under the swing lower-limb was less than 10 N (100%). We then computed the timings of the two events that occurred during the anticipatory period: 1) max CoP, which occurs when the CoP is the most backward, and directed toward the swing lower-limb (Halliday et al., 1998; Crenna et al., 2006) (Fig. 1c); and 2) momentum reversal, defined as the first instant when $\dot{H}_{MML}$ becomes positive, and leads to the maximal value of $\dot{H}_{MML}$ (Fig. 1e). To reduce the time variability between trials, we used curve registration (Sadeghi et al., 2000) to align curves with the momentum reversal event.
## 2.5. Contribution of the moving CoP and counter-rotating mechanisms to WBCOM acceleration

We quantified the contribution of the moving CoP ($a_{MAP}^{CoP}$ and $a_{ML}^{CoP}$) and the counter-rotating ($a_{ML}^{HM}$ and $a_{ML}^{HM}$) mechanisms to WBCOM acceleration using equations from a linearised inverted pendulum (Eqs 4-5) (Hof, 2007; Bechet et al., 2025b).

$$a_{MAP}^{CoP} = \frac{(OP_{AP} - OM'_{AP})F_{GVert}}{m.l}; a_{ML}^{CoP} = \frac{(OP_{ML} - OM'_{ML})F_{GVert}}{m.l} \quad (4)$$

$$a_{MAP}^{HM} = \frac{\dot{H}_{ML}}{m.l}; a_{ML}^{HM} = \frac{\dot{H}_{MAP}}{m.l} \quad (5)$$

The effective pendulum length $l$ was set at 1.34 times the participant's lower-limb length (Hof et al., 2007).

## 2.6. Statistical Analysis

All statistical tests were performed using Matlab (MathWorks, version 2024a). The normality of the timing of each event was checked using Shapiro-Wilk test. These data were found to be normally distributed, and we therefore tested whether max CoP and the momentum reversal occurred at the same time using a paired-samples t-test. Time evolution data were not normally distributed, we therefore performed non-parametric one-sample t-test using Statistical Parametric Mapping (Pataky, 2010), to test whether $a_{M}^{HM}$ was significantly different from zero (the null contribution) along each axis, and thus determine whether the counter-rotating mechanism contributed to WBCOM acceleration. We computed the Pearson correlation coefficient ($r$) between experimental acceleration $a_{M}$ and the sum of the contribution of
## 3. Results

Momentum reversal occurred significantly later than max CoP (510.8 ± 126.6 ms vs. 418.8 ± 125.5 ms, p<0.001), indicating that whole-body forward rotation continued after the max CoP event. At the same time, $\kappa_{ML}$ decreased and reached its minimum during the interval between max CoP and momentum reversal (91.2 ± 61.3 ms) (Fig. 2, left panel). After momentum reversal, both $H_{ML}$ and $\kappa_{ML}$ increased until the end of the anticipatory period. During the last 20% of this period, $H_{ML}$ approached 0 and $\kappa_{ML}$ neared 1.

In the frontal plane, $H_{MAP}$ increased toward the stance lower-limb side, reached its maximum close to momentum reversal, and decreased until the end of the anticipatory period. $\kappa_{AP}$ decreased until max CoP, then increased until the end of the anticipatory period.

In the sagittal plane, forward WBCOM acceleration increased during the whole anticipatory period, with the moving CoP mechanism making the major contribution (Fig 3, left panel). The contribution of the counter-rotating mechanism was significantly greater than 0 m.s⁻² between 69% and 96% of the anticipatory period.

In the frontal plane, WBCOM was accelerated toward the stance lower-limb during the first 95% of the anticipatory period, and then accelerated toward the swing lower-limb side, with the moving CoP mechanism making a very large contribution (Fig. 3, right panel). The contribution of the
counter-rotating mechanism was only significantly different from 0 m.s⁻² for short periods of time, as detailed in Fig. 3.

## 4. Discussion

Several studies have investigated the anticipatory period of gait initiation, focusing solely on the moving CoP mechanism, omitting the contribution of the counter-rotating mechanism (Bechet et al., 2025b). Since the counter-rotating mechanism may have a substantial contribution to the WBCOM acceleration and balance maintenance, we quantified the counter-rotating mechanism and its consequence to both balance and movement initiation. We also quantified the moving CoP mechanism and characterised the coordination between the two. We found that: 1) the whole-body continued to rotate forward after the *max CoP* event; 2) the counter-rotating mechanism regulated whole-body rotational instability; and 3) the counter-rotating mechanism significantly contributed to forward WBCOM acceleration. Overall, our findings suggest that the counter-rotating mechanism makes a substantial contribution to balance-movement coordination during the anticipatory period of a transition from a postural state to steady-state gait.

### 4.1. Both moving CoP and counter-rotating mechanisms define mechanical instability

Our results showed that the whole-body rotation continued in the forward direction after the *max CoP* event, when the majority of body segments rotated forwards (i.e., small $\kappa_{ML}$, Fig 2, left panel). These findings support the idea that the moving CoP mechanism initiated mechanical instability (Brenière et al., 1987), but clarify that this mechanical instability was not
257 maximal at, but 91.2 ms on average after, the *max CoP* event. Therefore, 258 it appears necessary to quantify the time evolution of *H*<sub>ML</sub> and κ<sub>ML</sub> to 259 accurately determine the period of mechanical instability during the antici- 260 patory period of gait initiation, when there is little segment counter-rotating 261 to regulate the whole-body rotation.

262 The origin of the *momentum reversal* event remains to be investigated.
263 The average timing of 91.2 ms after *max CoP* event is long enough to be per- 264 ceived and integrated by the central nervous system as feedback (Pruszynski 265 and Scott, 2012). It has to be confirmed by future studies as it could provide 266 valuable information on the conditions required to perform the transition.
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Our findings suggest that the period of maximal mechanical instability
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268 should be defined as the period between the *max CoP* event and *momentum reversal*, when the whole-body is rotating forward and *κML* is small.
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270 The identification of this period is relevant in order to evaluate movement
271 initiation impairments in populations such as older adults, individuals with
272 Parkinson's disease, stroke survivors, and those with multiple sclerosis. Ear-
273 lier work has established that in these populations, the backward CoP move-
274 ment is smaller, but lasts longer (Halliday et al., 1998; Polcyn et al., 1998). It
275 has been suggested that this prolonged duration compensates for the reduced
276 efficiency of the backward CoP movement, and/or to reach a large enough
277 velocity while avoiding the period of mechanical instability with small κML.
278 However, since the time evolution of κML has not been quantified in these
279 populations, it is not known whether balance deficits can lead to κML (i.e.,
280 segment regulation) differing from healthy participants during the period of
281 mechanical instability, and this point needs further research.
## 4.2. The role of the counter-rotating mechanism in balance

Our findings showed that after the period of mechanical instability, there was a period when the whole-body balance seemed to be regulated, characterised by an increase in both $H_{ML}$ and $\kappa_{ML}$ (Fig. 2, left panel, after the vertical red line). Moreover, we found a large decrease in the standard deviation of $\kappa_{ML}$ after momentum reversal and continuing until foot-off, which suggests that the counter-rotating mechanism was used similarly by all participants. It has been suggested that the whole-body falls ballistically once the foot is lifted, with no regulation of WBCOM acceleration (Lyon and Day, 2005). Therefore, the transition from a bipedal to a unipedal base of support, with a combination of forward oriented $H_{ML}$ and forward WBCOM acceleration is expected to be consistent with an excessive forward fall of the whole-body. We therefore suggest that the backward oriented $H_{ML}$ enables the person to anticipate the upcoming forward rotation of the whole-body around the stance lower-limb, and avoids placing the whole-body in a configuration with excessive rotational mechanical instability about the mediolateral axis.

An earlier study with older adults during a stepping task found that backward-oriented $H_{ML}$ was smaller at foot-off, resulting in larger forward-oriented $H_{ML}$ once the foot was lifted (Begue et al., 2019). Therefore, rotating body segments (the counter-rotating mechanism) contributes to maintaining balance before foot lift, especially if there is an absence of regulation once the foot is lifted, as suggested by other work (Bancroft and Day, 2016; Lyon and Day, 2005).

With respect to the anteroposterior axis, $H_{AP}$ was first directed toward
the stance lower-limb, as a result of the CoP movement toward the swing lower-limb, with small $\kappa_{AP}$ before the max CoP event (Fig. 2, right panel). However, there was no clear segment counter-rotating, and the increase in $\kappa_{AP}$ was smaller and more variable than in the sagittal plane. These findings suggest that the counter-rotating mechanism does not play a major role in frontal plane balance regulation during the anticipatory period of gait initiation. Nevertheless, $H_{MAP}$ regulation is present during walking, especially step-to-step transitions (Nott et al., 2014), and may be present just before foot strike during gait initiation.

Additionally, our results suggested that the counter-rotating mechanism appears to contribute very little to mediolateral WBCOM acceleration. The counter-rotating mechanism significantly contributed to WBCOM acceleration during small amounts of time, that may come from variability, however, this remains to be confirmed in future studies. It does, however, make a contribution toward the stance lower-limb at the end of the anticipatory period (Fig. 3, right panel). This contribution was in the opposite direction to the desired direction, probably to avoid a fall toward the stance lower-limb side (Mickelborough et al., 2004). This may explain why the CoP movement toward the swing lower-limb was quickly stopped, namely, to avoid excessive WBCOM acceleration toward the stance lower-limb side. To resolve this conflict, mediolateral WBCOM acceleration appeared to be almost exclusively modulated by the moving CoP mechanism (similar experimental and moving CoP curves in Fig. 3, right panel). Thus, our results suggest that the moving CoP mechanism in the frontal plane is critical and must be trained in populations with balance deficits, because it cannot be completed by the
counter-rotating mechanism to fulfil its balancing role.

### 4.3. The role of the counter-rotating mechanism in movement initiation

In earlier work, anteroposterior WBCOM acceleration was only characterised with respect to the moving CoP mechanism (Brenière et al., 1987). However, the backward CoP movement is constrained by the length of the base of support. Thus, other mechanisms can be used to accelerate the WBCOM, as demonstrated during toe-raising gait initiation, where the backward CoP displacement is even more constrained (Nolan and Kerrigan, 2003). Our findings suggest that the increase in $H_{ML}$ made a significant contribution to forward WBCOM acceleration, and complemented the moving CoP mechanism (Fig. 3). WBCOM velocity and acceleration at the end of the anticipatory period may determine the placement of the next foot (Bancroft and Day, 2016), and WBCOM velocity at the end of the first step (Brenière et al., 1987), which represents approximately 90% of the steady-state velocity (Jian et al., 1993). Thus, the contribution of the counter-rotating mechanism to WBCOM acceleration appears to help the transition from a postural state to steady-state gait.

While the counter-rotating mechanism appeared to only make a small contribution, it seemed to fine-tune WBCOM acceleration, depending on the task. Studies have found that individuals with balance deficits make smaller first steps, and require more steps to reach steady-state velocity (Roemmich et al., 2012; Muir et al., 2014; Massot et al., 2019). Although the backward CoP movement is clearly reduced (Halliday et al., 1998), it is also possible that the counter-rotating mechanism is less effective (Begue et al., 2019), limiting WBCOM acceleration. However, the contribution of the counter-
357 rotation mechanism remains to be quantified in these populations.

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4.4. Limitations

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We quantified the two mechanisms using a linearised inverted pendulum model (Hof, 2007). This model assumes a unique rotation around the CoP. During gait initiation, the counter rotating mechanism partly results from trunk movements (Thorstensson et al., 1984; Bechet et al., 2025a), violating inverted pendulum model assumptions. As a result, we observed non-negligible differences between modelled and experimental WBCOM acceleration in the sagittal plane. However, we found a very good correlation when comparing the experimental and modelled accelerations (r = 0.996 ± 0.002, Appendix A), suggesting that the offset may come from the normalisation of the model, and that it does not compromise our interpretations. More precise quantification of the acceleration coming from each mechanism would require more detailed biomechanical models to precisely account for the inertia of a current posture. Additionally, our results came from a homogeneous and a small number of participants, preventing us to generalise to broader populations. However, our results may serve as foundation for future clinical research to compare how individuals with balance deficits use the counter-rotating mechanism compared to young healthy people. The parameters may also serve to identify and detect possible deficits and help identify rare disease as suggested by Trabassi et al. (2024), and to adapt existing exoskeleton to different populations (Molinaro et al., 2024).
379 **5. Conclusion**

380 Our findings *showed* that the counter-rotating mechanism plays a sub-
381 stantial role in balance-movement coordination during the anticipatory pe-
382 riod of gait initiation in the sagittal plane. The counter-rotating mechanism
383 *supported* the maintenance of balance before foot lift to prepare for unipedal
384 support, and *made* a major contribution to forward WBCOM acceleration.
385 Moreover, our characterisation of the counter-rotating mechanism clarifies
386 the period of mechanical instability, which cannot be determined by simply
387 characterising the moving CoP mechanism. Therefore, we suggest that fu-
388 ture research in populations with balance deficits should characterise both
389 mechanisms, as this would provide insight into how these individuals manage
390 the period of mechanical instability, and use segment rotations for balance-
391 movement coordination during the anticipatory period of motor transitions.
392 References

393 Bancroft, M.J., Day, B.L., 2016. The Throw-and-Catch Model of Human Gait: Evidence from Coupling of Pre-Step Postural Activity and Step Location. Frontiers in Human Neuroscience 10. doi:10.3389/fnhum.2016.00635.

397 Bechet, R., Tisserand, R., Bart, A., Fradet, L., Colloud, F., 2025a. Two different roles of the trunk segment during the anticipatory phase of gait initiation. Multidisciplinary Biomechanics Journal 49th congress of the Société de Biomécanique. doi:10.46298/mbj.14472.

401 Bechet, R., Tisserand, R., Fradet, L., Colloud, F., 2025b. Anticipatory muscle activations to coordinate balance and movement during motor transitions: A narrative review. Gait & Posture 118, 130–140. doi:10.1016/j.gaitpost.2025.02.009.

405 Begue, J., Peyrot, N., Dalleau, G., Caderby, T., 2019. Age-related changes in the control of whole-body angular momentum during stepping. Experimental Gerontology 127, 110714. doi:10.1016/j.exger.2019.110714.

408 Bennett, B.C., Russell, S.D., Sheth, P., Abel, M.F., 2010. Angular momentum of walking at different speeds. Human Movement Science 29, 114–124. doi:10.1016/j.humov.2009.07.011.

411 Brenière, Y., Cuong Do, M., Bouisset, S., 1987. Are Dynamic Phenomena Prior to Stepping Essential to Walking? Journal of Motor Behavior 19, 62–76. doi:10.1080/00222895.1987.10735400.
Crenna, P., Carpinella, I., Rabuffetti, M., Rizzone, M., Lopiano, L., Lanotte, M., Ferrarin, M., 2006. Impact of subthalamic nucleus stimulation on the initiation of gait in Parkinson's disease. Experimental Brain Research 172, 519-532. doi:10.1007/s00221-006-0360-7.

Dumas, R., Chèze, L., Verriest, J.P., 2007. Adjustments to McConville et al. and Young et al. body segment inertial parameters. Journal of Biomechanics 40, 543-553. doi:10.1016/j.jbiomech.2006.02.013.

Ehrig, R.M., Taylor, W.R., Duda, G.N., Heller, M.O., 2006. A survey of formal methods for determining the centre of rotation of ball joints. Journal of Biomechanics 39, 2798-2809. doi:10.1016/j.jbiomech.2005.10.002.

Ehrig, R.M., Taylor, W.R., Duda, G.N., Heller, M.O., 2007. A survey of formal methods for determining functional joint axes. Journal of Biomechanics 40, 2150-2157. doi:10.1016/j.jbiomech.2006.10.026.

Halliday, S.E., Winter, D.A., Frank, J.S., Patla, A.E., Prince, F., 1998. The initiation of gait in young, elderly, and Parkinson's disease subjects. Gait & Posture 8, 8-14. doi:10.1016/S0966-6362(98)00020-4.

Halvorsen, K., 2003. Bias compensated least squares estimate of the center of rotation. Journal of Biomechanics 36, 999-1008. doi:10.1016/S0021-9290(03)00070-8.

Herr, H., Popovic, M., 2008. Angular momentum in human walking. Journal of Experimental Biology 211, 467-481. doi:10.1242/jeb.008573.

Hof, A.L., 2007. The equations of motion for a standing human reveal
three mechanisms for balance. Journal of Biomechanics 40, 451–457.
doi:10.1016/j.jbiomech.2005.12.016.

Hof, A.L., van Bockel, R.M., Schoppen, T., Postema, K., 2007. Control of lateral balance in walking: Experimental findings in normal subjects and above-knee amputees. Gait & Posture 25, 250–258.
doi:10.1016/j.gaitpost.2006.04.013.

Jian, Y., Winter, DA., Ishac, MG., Gilchrist, L., 1993. Trajectory of the body COG and COP during initiation and termination of gait. Gait & Posture 1, 9–22. doi:10.1016/0966-6362(93)90038-3.

Lyon, I.N., Day, B.L., 2005. Predictive control of body mass trajectory in a two-step sequence. Experimental Brain Research 161, 193–200.
doi:10.1007/s00221-004-2058-z.

Massot, C., Simoneau-Buessinger, E., Agnani, O., Donze, C., Leteneur, S., 2019. Anticipatory postural adjustment during gait initiation in multiple sclerosis patients: A systematic review. Gait & Posture 73, 180–188.
doi:10.1016/j.gaitpost.2019.07.253.

Mickelborough, J., van der Linden, M.L., Tallis, R.C., Ennos, A.R., 2004. Muscle activity during gait initiation in normal elderly people. Gait & Posture 19, 50–57. doi:10.1016/S0966-6362(03)00016-X.

Molinaro, D.D., Scherpereel, K.L., Schonhaut, E.B., Evangelopoulos, G., Shepherd, M.K., Young, A.J., 2024. Task-agnostic exoskeleton control via biological joint moment estimation. Nature 635, 337–344.
doi:10.1038/s41586-024-08157-7.
Muir, B.C., Rietdyk, S., Haddad, J.M., 2014. Gait initiation: The first four steps in adults aged 20–25 years, 65–79 years, and 80–91 years. Gait & Posture 39, 490–494. doi:10.1016/j.gaitpost.2013.08.037.

Neptune, R.R., Vistamehr, A., 2019. Dynamic Balance During Human Movement: Measurement and Control Mechanisms. Journal of Biomechanical Engineering 141. doi:10.1115/1.4042170.

Nolan, L., Kerrigan, D.C., 2003. Keep on your toes: Gait initiation from toe-standing. Journal of Biomechanics 36, 393–401. doi:10.1016/S0021-9290(02)00429-3.

Nott, C.R., Neptune, R.R., Kautz, S.A., 2014. Relationships between frontal-plane angular momentum and clinical balance measures during post-stroke hemiparetic walking. Gait & Posture 39, 129–134. doi:10.1016/j.gaitpost.2013.06.008.

Orendurff, M.S., Schoen, J.A., Bernatz, G.C., Segal, A.D., Klute, G.K., 2008. How humans walk: Bout duration, steps per bout, and rest duration. Journal of Rehabilitation Research and Development 45, 1077–1089. doi:10.1682/jrrd.2007.11.0197.

Pataky, T., 2010. Generalized n-dimensional biomechanical field analysis using statistical parametric mapping. Journal of biomechanics 43, 1976–82. doi:10.1016/j.jbiomech.2010.03.008.

Polcyn, A.F., Lipsitz, L.A., Kerrigan, D.C., Collins, J.J., 1998. Age-related changes in the initiation of gait: Degradation of central mechanisms for
momentum generation. Archives of Physical Medicine and Rehabilitation 481 79, 1582-1589. doi:10.1016/S0003-9993(98)90425-7.

Pruszynski, J.A., Scott, S.H., 2012. Optimal feedback control and the long-latency stretch response. Experimental Brain Research 218, 341-359. doi:10.1007/s00221-012-3041-8.

Robertson, D.G.E., Dowling, J.J., 2003. Design and responses of Butterworth and critically damped digital filters. Journal of Electromyography and Kinesiology 13, 569-573. doi:10.1016/S1050-6411(03)00080-4.

Robinovitch, S.N., Feldman, F., Yang, Y., Schonnop, R., Lueng, P.M., Sarraf, T., Sims-Gould, J., Loughin, M., 2013. Video capture of the circumstances of falls in elderly people residing in long-term care: An observational study. Lancet (London, England) 381, 47-54. doi:10.1016/S0140-6736(12)61263-X.

Roemmich, R.T., Nocera, J.R., Vallabhajosula, S., Amano, S., Naugle, K.M., Stegemöller, E.L., Hass, C.J., 2012. Spatiotemporal variability during gait initiation in Parkinson's disease. Gait & Posture 36, 340-343. doi:10.1016/j.gaitpost.2012.01.018.

Sadeghi, H., Allard, P., Shafie, K., Mathieu, P.A., Sadeghi, S., Prince, F., Ramsay, J., 2000. Reduction of gait data variability using curve registration. Gait & Posture 12, 257-264. doi:10.1016/S0966-6362(00)00085-0.

Schoene, D., Heller, C., Aung, Y.N., Sieber, C.C., Kemmler, W., Freiberger, E., 2019. A systematic review on the influence of fear of falling on quality
503

of life in older people: Is there a role for falls? Clinical Interventions in Aging 14, 701–719. doi:10.2147/CIA.S197857.

504

505

Selikson, S., Damus, K., Hamerman, D., 1988. Risk Factors Associated with Immobility. Journal of the American Geriatrics Society 36, 707–712. doi:10.1111/j.1532-5415.1988.tb07172.x.

506

507

508

Thorstensson, A., Nilsson, J., Carlson, H., Zomlefer, M.R., 1984. Trunk movements in human locomotion. Acta Physiologica Scandinavica 121, 9–22. doi:10.1111/j.1748-1716.1984.tb10452.x.

509

510

511

Trabassi, D., Castiglia, S.F., Bini, F., Marinozzi, F., Ajoudani, A., Lorenzini, M., Chini, G., Varrecchia, T., Ranavolo, A., De Icco, R., Casali, C., Ser-rao, M., 2024. Optimizing Rare Disease Gait Classification through Data Balancing and Generative AI: Insights from Hereditary Cerebellar Ataxia. Sensors 24, 3613. doi:10.3390/s24113613.

512

513

514

515

516

Winter, D.A., 2009. Anthropometry, in: Biomechanics and Motor Control of Human Movement. John Wiley & Sons, Ltd. chapter 4, pp. 82–106. doi:10.1002/9780470549148.ch4.

517

518

519

Yiou, E., Caderby, T., Delafontaine, A., Fourcade, P., Honeine, J.L., 2017. Balance control during gait initiation: State-of-the-art and research perspectives. World Journal of Orthopedics 8, 815–828. doi:10.5312/wjo.v8.i11.815.

520

521

522
<table><caption>Table 1: Nomenclature used in equations (all variables are expressed in the global reference frame). *nFrames* represents the number of points for a given trial.</caption><thead><tr><th>Term</th><th>Dimension</th><th>Description</th></tr></thead><tbody><tr><td>a<sub>M</sub><sup>H<sub>M</sub></sup></td><td>(3, nFrames)</td><td>Whole-body centre of mass acceleration due to the counter-rotating mechanism</td></tr><tr><td>a<sub>M</sub><sup>CoP</sup></td><td>(3, nFrames)</td><td>Whole-body centre of mass acceleration due to the moving CoP mechanism</td></tr><tr><td>F<sub>G</sub></td><td>(3, nFrames)</td><td>Ground reaction force</td></tr><tr><td>H<sub>M</sub></td><td>(3, nFrames)</td><td>Internal whole-body angular momentum about the whole-body centre of mass (M)</td></tr><tr><td>H<sub>M</sub><sup>i</sup></td><td>(3, nFrames)</td><td>Contribution of the i<sup>th</sup> segment to internal whole-body angular momentum about the whole-body centre of mass</td></tr><tr><td>I<sub>i</sub></td><td>(3, 3)</td><td>Inertia tensor of the i<sup>th</sup> segment with respect to its centre of mass</td></tr><tr><td>κ<sub>j</sub></td><td>(1, nFrames)</td><td>Coefficient of cancellation of internal whole-body angular momentum about the whole-body centre of mass around the j<sup>th</sup> axis</td></tr><tr><td>l</td><td>(1)</td><td>Effective pendulum length</td></tr><tr><td>m</td><td>(1)</td><td>Mass of the whole-body</td></tr><tr><td>m<sub>i</sub></td><td>(1)</td><td>Mass of the i<sup>th</sup> segment</td></tr><tr><td>n</td><td>(1)</td><td>Number of segments of the multi-body model</td></tr></tbody></table>
<table><thead><tr><th>Term</th><th>Dimension</th><th>Description</th></tr></thead><tbody><tr><td>OM'</td><td>(3, nFrames)</td><td>Position of the whole-body centre of mass in the transverse plane on the ground</td></tr><tr><td>OM<sub>i</sub></td><td>(3, nFrames)</td><td>Position of the centre of mass of the <i>i</i><sup>th</sup> segment</td></tr><tr><td>OP</td><td>(3, nFrames)</td><td>Position of the centre of pressure</td></tr><tr><td>v<sub>M</sub></td><td>(3, nFrames)</td><td>Linear velocity of the whole-body centre of mass</td></tr><tr><td>v<sub>M<sub>i</sub></sub></td><td>(3, nFrames)</td><td>Linear velocity of the whole-body centre of mass of the <i>i</i><sup>th</sup> segment</td></tr><tr><td>ω<sub>i</sub></td><td>(3, nFrames)</td><td>Angular velocity of the <i>i</i><sup>th</sup> segment</td></tr><tr><td>×</td><td></td><td>Cross product between two vectors</td></tr></tbody></table>
<figure><img src="image_2.png" /><figcaption>Figure 1: a. Anterior and posterior view of marker placements (red dots). Markers were placed on the pelvis (4), thigh (2 × 5), shank (2 × 5), foot (2 × 4), torso (5), head (5), arm (3 × 2), and forearm (3 × 2). b. Details of the task. Participants began by maintaining five seconds of quiet standing (initial state), and then initiated walking with their preferred lower-limb for five meters. The anticipatory period begins when the whole-body centre of mass is accelerated forward (0%, symbolised by the red arrow, see D. for details), and ends at first foot-off (100%). c. Representative trial showing the centre of pressure (CoP) trajectory (light blue) for one participant, normalised by the length and width of the base of support, defined as the distance between the calcaneus and the second toe tip markers, and the distance between the left and right metatarsal, respectively, both measured during the first second of quiet standing. The red point represents the max CoP event (i.e., when the CoP is the most backward and toward the swing lower-limb side). d. Determination of the onset of the anticipatory period. The threshold for anteroposterior whole-body centre of mass acceleration ($a_{MAP}$) was determined using a sliding one second window, which identified the second with the smallest standard deviation of $a_{MAP}$ during the initial state. The threshold was then defined as the average plus three standard deviations during this second, and the anticipatory period started when $a_{Mx}$ exceeded this threshold. e. Determination of the momentum reversal event, defined as the first instant when the time derivative of internal whole-body angular momentum around the mediolateral axis ($\dot{H}_{ML}$) was positive, and related to the maximal value of $\dot{H}_{ML}$.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>Figure 2: Average (continuous lines) and one standard deviation (dotted lines) time evolution of the centre of pressure (CoP), internal whole-body angular momentum ($H_M$) and the coefficient of cancellation ($\kappa$) (from top to bottom) during the anticipatory period of gait initiation, in the sagittal (left) and frontal (right) planes. Time is measured from 0% (the onset of the anticipatory period) to 100% (first foot-off). Black vertical lines represent the averaged *max CoP* event. Red vertical lines represent the averaged *momentum reversal* event. The large variability in $\kappa_{ML}$ at the beginning of the anticipatory period (left panel) is due to the very small amplitude of $H_{MML}$.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 3: Average (continuous lines) and standard deviation (dotted lines) time evolution of whole-body centre of mass acceleration computed with experimental data ($a_M$, dark blue), moving CoP ($a_M^{CoP}$, light blue), and counter-rotating ($a_M^{H_M}$, dark red) mechanisms during the anticipatory period of gait initiation in the sagittal (left) and frontal (right) planes. Time is measured from 0% (the onset of the anticipatory period) to 100% (first foot-off). Dark red rectangles represent the statistical significance between the contribution of the counter-rotating mechanism and null acceleration using non-parametric Statistical Parametric Mapping. In the frontal plane, the contribution of the counter-rotating mechanism was significantly different from zero during the following intervals of the anticipatory period: 24–26%, 33–39%, 43–45%, 51–52%, 55–61%, and 96–100%. Black vertical lines represent the averaged *max CoP* event. Red vertical lines represent the averages *momentum reversal* event.</figcaption></figure>
Appendix A. Supplementary Figure
<figure><img src="image_5.png" /></figure>

Figure A.4: Average (continuous lines) and standard deviation (dotted lines) of the time evolution of whole-body centre of mass acceleration computed with experimental data ($a_{MAP}$, dark blue), and summing the contribution of the two mechanisms ($a_{MAP}^{CoP} + a_{MAP}^{HM}$, orange) during the anticipatory period of gait initiation in the sagittal plane. Time is measured from 0% (the onset of the anticipatory period) to 100% (first foot-off). The Pearson correlation coefficient ($r$) between the two curves was computed for each participant, to assess the ability of the model to reproduce the whole-body centre of mass acceleration. The overall coefficient was $r = 0.996 \pm 0.002$, representing an almost perfect correlation between the two curves (i.e., they evolve similarly) and indicating that there is only an offset between the experimental and the modelled whole-body centre of mass acceleration.