Anne Tournillon

Isabelle A Siegler

Voluntary control of pelvic frontal rotations in oriental dance experts

Keywords: Oriental dance, belly dance, rhythmic coordination, voluntary pelvic movement, motor performance, continuous relative phase Highlights

The present study investigated how oriental dance experts perform the "hip shimmy", a complex rhythmic dance movement consisting in a voluntary oscillation of the pelvis exclusively in the frontal plane with maximised amplitude, with no movement of the upper trunk. The aims of this study were to 1) assess whether the amplitude and stability of the pelvic movement can be maximised in certain postural and frequency conditions; and 2) investigate in a 1 to 3 Hz range whether it is indeed possible to oscillate the pelvis only in the frontal plane and to dissociate this one-axis pelvic rotation from potential spontaneous upper-trunk oscillations. Nineteen oriental dance experts performed this task in three frequencies and three knee bending postures. Eight joint angles were calculated using the kinematic data of 20 markers over the entire body collected with a motion capture system. Mean amplitude, frequency, and spatial and temporal variability of frontal pelvic oscillations were analysed to characterise motor performance and movement stability. Five Continuous Relative Phases (CRP) were computed to identify the modes and stability of coordination patterns. The results showed that a low posture enhances amplitude performance and that the pelvic oscillation amplitude tended to decrease at 3 Hz, although between-condition differences remained small. Temporal stability was highest at 2 Hz and significant inter-individual differences emerged at 3 Hz. CRP analysis revealed an unpreventable coupling between pelvis and upper-trunk oscillations in the frontal and transversal planes. A consistent antiphase coordination between transversal pelvis and upper-trunk may have been caused by anatomical and counter-balancing constraints. In the frontal plane, multiple stable pelvisupper trunk patterns including inphase, out-of-phase and antiphase evolved to antiphase predominance and inphase disappearance upon reaching 3 Hz. In sum, increasing frequency highlighted the concomitance of two control phenomenon: the inter-individual differentiation in performance and standardisation of the possible pelvis-upper-trunk patterns.

Introduction

According to the non-linear dynamical system approach, coordination can be defined as a selforganised intersegmental coupling spontaneously converging towards a consistent stable pattern, also called state attractor. Several state attractors can coexist, resulting in a multistable system. Pioneering work used the bimanual index finger oscillation rhythmic task to highlight the existence of two state attractors, antiphase and inphase coordination patterns, whose transition from the first to the second occurs abruptly along with increased variability when movement frequency is increased [START_REF] Haken | A Theoretical Model of Phase Transitions in Human Hand Movements[END_REF]. The Continuous Relative Phase (CRP) between two body segments, which is the difference between their phase angles at each moment of the movement, has been efficiently used as an order parameter to assess such intersegmental coordination, with mean value and standarddeviation of the CRP associated to the coordination mode and its stability, respectively [START_REF] Burgess-Limerick | Relative phase quantifies interjoint coordination[END_REF][START_REF] Haken | A Theoretical Model of Phase Transitions in Human Hand Movements[END_REF][START_REF] Kelso | Nonequilibrium phase transitions in coordinated biological motion: Critical fluctuations[END_REF][START_REF] Van Emmerik | Effects of walking velocity on relative phase dynamics in the trunk in human walking[END_REF]. Previous research used the CRP to examine the spontaneous coordination patterns between pelvic and upper-trunk rotations during healthy and pathological human gait. Several studies showed that with increasing gait velocity, a healthy coordination pattern between the pelvis and the upper trunk in the transverse plane changed from a more inphase pattern to a more antiphase pattern, accompanied by an increasing variability of the CRP during a "gradual" transition [START_REF] Lamoth | Pelvis-thorax coordination in the transverse plane during gait[END_REF][START_REF] Van Emmerik | Effects of walking velocity on relative phase dynamics in the trunk in human walking[END_REF], while Low Back Pain or Parkinson subjects experienced more difficulty achieving the antiphase pattern [START_REF] Seay | Low back pain status affects pelvis-trunk coordination and variability during walking and running[END_REF]. The authors suggest that this coupling provides dynamic stability and balance, and prevents injury: as velocity increases, pelvic swing in axial rotation increases to help lengthen the stride, forcing the trunk to counterbalance the pelvis in an antiphasic pattern. Similarly, the literature often emphasises the lumbo-pelvic-hip complex in stabilizing the centre of mass and the spine in order to prevent injury and maintain postural balance [START_REF] Chang | Muscle activation patterns of the lumbo-pelvic-hip complex during walking gait before and after exercise[END_REF][START_REF] Tojima | Three-dimensional motion analysis of lumbopelvic rhythm during lateral trunk bending[END_REF]. However, very few studies investigate the control and coordination mechanisms in voluntary pelvic movements, such as those performed in dance.

Oriental dance is an artistic and physical activity that requires complex, expert coordination. Its main features can be characterised by wide and isolated movements of different parts of the trunk (pelvis, chest, belly and shoulders) at different controllable speeds and amplitudes, possibly resulting from underlying control mechanisms that are not observable in more common pedestrian tasks. In oriental dance, the voluntary, rhythmic and isolated (dissociated from the rest of the body) pelvic rotation in the frontal plane is called "hip lift", or "pelvis side bending" when performed at slow or moderate speed, and "hip shimmy" when performed at high speed. It is a rotation of the pelvis around the anterioposterior axis alternating the clockwise and counter-clockwise directions, together with the antiphase coordination of the lower limbs, i.e., alternating knee flexion and extension. This movement is said to be expert when the speed and amplitude of the pelvis are controlled and when the three following task constraints are respected: an almost immobile upper trunk (from the rib cage to the shoulder line), continuous contact between the soles of the feet and the ground and exclusively frontal pelvic rotation with equal amplitude on both sides. In oriental dance performance, efficient hip shimmy execution is defined by the artistic relevance of the pelvis speed and amplitude choice, in order to perfectly synchronise the movement with the rhythm and intensity of the music, in accordance with the aforementioned constraints that define the task. Therefore, stability in controlling the movement's amplitude and frequency is a key feature of expert performance. A recent study emphasised the existence of several coordination patterns of the lumbar erector spinae muscles in the control of this hip shimmy movement, depending on the movement frequency and the level of expertise (Nugent & Milner, 2017). The authors identified three different erector spinae (ES) muscle coordination patterns from the fourth lumbar vertebral (L4) to the tenth thoracic vertebral level (T10) during the hip shimmy. An ipsilateral simultaneous pattern (S) of ES activation, causing an antiphasic relation between the first thoracic level (TH1) and the pelvic segment (PELV), was mainly observed in novices. A diagonal synergy pattern (D) characterized by an antiphasic muscle activation of the ipsilateral ES between T10 and L4, resulting in the absence of a clear phase relationship between TH1 and PELV with a small amplitude of TH1, dominated in experts in 2 Hz and 3 Hz frequencies. An asynchronous pattern (A) emerged in novices and experts from 3 Hz and above, and represented a continuous phase shift of the ipsilateral ES activation and between the rotations of the different trunk segments, in a travelling wave along the rostral-caudal direction, analogous to the EMG pattern recorded in the swimming salamander. However, coordination and control mechanisms involved in the maximisation of pelvis amplitude in the frontal plane have yet to be examined.

The aim of the present study was to use the hip shimmy movement performed by oriental dance experts to investigate voluntary pelvic rotations and trunk coordination features that would not be observable in more common gait gestures. We particularly aimed to 1) assess whether pelvic movement amplitude and stability could be maximised in some postural and frequency conditions, and 2) characterise how the expected independent control of frontal pelvic from other trunk motions was frequency dependent, using CRP analysis.

Methods

Participants

Nineteen female oriental dance experts volunteered to take part in this study (age: 30.3 ±6.9 years, height: 165.0 ±0.1 cm, weight: 59.5 ±7.0 kg, body mass index: 21.9 ±2.3, experience: 11.1 ±5.1 years). They were recruited via social media and by e-mail exchanges over a one-month period. The inclusion criteria were a minimum of three years of experience in oriental dance and a body mass index less than or equal to 25. The participants read an information notice carefully and completed an informed consent form approved by the Ethic Committee for Research (CER) of the University of Paris-Saclay.

Experimental setup

The body movements were recorded by the QUALISYS optoelectronic system, using eight infrared cameras with a sampling frequency of 179 Hz. Twenty reflective markers were placed on the participants with double-sided tape according to the Plug-in Gait Full Body model as follows: over the second metatarsal head (LTOE, RTOE); on the lateral malleolus (LANK, RANK); on the calcaneus of each foot (LHEE, RHEE); over the upper lateral third of the right shank (RTIB); over the lower lateral third of the left shank (LTIB); on the flexion/extension axis of the lateral side of both knees (LKNE, RKNE); over the upper lateral third of the right thigh (RTHI); over the lower lateral third of the left thigh (LTHI); over the left and right anterior superior iliac spine (LASI, RASI); over the left and right posterior superior iliac spine (LPSI, RPSI); on the spinous process of the tenth thoracic vertebra (T10); on the spinous process of the seventh cervical vertebra (C7); and on the left and right acromioclavicular joints (LSHO, RSHO).

The participants stood in front of a pole on which three visual markers were taped to help the dancers adopt a standing posture with their knees flexed at an indicative angle. For each participant, the visual markers were positioned at eye level for the three postures studied: a knee angle of 160 deg for High These values were chosen in order to guarantee task feasibility for all participants: no less than 130 deg to prevent the heels from leaving the floor and balance loss, and no greater than 160 deg to prevent the participants from locking their knees. The knee bending angle was measured with a medical goniometer on the lateral side of the right knee, while the participants bent both knees equally.

Nevertheless, the achievement of the accurate instruction value was not required: no feedback on the postural angle was given to the participants during the experiment.

Experimental procedure

The participants performed a three-minute standardised dance warm-up at the beginning of the experiment. A 15-second static trial was recorded for each participant. In three posture (HP, IP, LP) and three frequency (1 Hz, 2 Hz, 3 Hz) conditions, they were asked to perform a hip shimmy with the greatest possible amplitude of pelvic rotation in the frontal plane, with equal pelvic inclination on both sides. The three frequency conditions consisted of three frequencies led by a metronome (120 bpm, 240 bpm, 360 bpm) to which the participants were required to synchronise their pelvic motion. Two 15-second trials were performed in each condition. Conditions were organised in a pseudo-random order by frequency: for each randomly-ordered frequency, the participants had to perform the movement in each posture condition in a randomised order. Each trial was separated by a 10-second break.

Data processing

One participant was removed from data analysis due to missing data during the experiment. The first two seconds of each trial were discarded from data analysis. With the use of Visual3D (C-Motion, Inc., Rockville, MD), the time series of six joint angles were calculated: rotation of the pelvis in the frontal plane (FronPel), in the transverse plane (TranPel) and in the sagittal plane (SagiPel), and rotation of the upper-trunk in the frontal plane (FronSho), in the transverse plane (TranSho) and in the sagittal plane (SagiSho). For each participant, a kinematic model based on the static trial was constructed with two rigid segments: pelvis and upper trunk. Both segments were associated with a local segment coordinate system consistent with the global coordinate system (X as the medio-lateral axis, Y as the antero-posterior axis, Z as the axial up axis). CODA Pelvis was used to construct the pelvis segment and calculate the hip joint centres, from the LASI, RASI, LPSI and RPSI markers [START_REF] Bell | Prediction of hip joint centre location from external landmarks[END_REF][START_REF] Bell | A comparison of the accuracy of several hip center location prediction methods[END_REF]. The local coordinate system of the pelvis (respectively upper trunk) segment was defined with the X-axis passing through LASI and RASI (respectively LSHO and RSHO) markers, Yaxis orthogonal to X-axis and included in the plane formed by the LASI, RASI and middle of LPSI and RPSI (respectively LSHO, RSHO and C7) markers, and the Z-axis perpendicular to Y and X.

Using this kinematic model, we calculated the six pelvic and upper-trunk variables according to the Visual3D default Cardan sequence X-Y-Z [START_REF] Cole | Application of the Joint Coordinate System to Three-Dimensional Joint Attitude and Movement Representation: A Standardisation Proposal[END_REF]. Rotations of the local pelvis (respectively upper-trunk) coordinate system in relation to the X, Y, Z-axis of the global coordinate system corresponds to the sagittal, frontal and transversal pelvis (respectively upper-trunk) angles. We chose to calculate the flexion angle of both knees (LeftKne, RighKne) as the convex 3D angle between LTIB, LKNE and LTHI (respectively RTIB, RKNE and RTHI), where LKNE (respectively RKNE) is the vertex of the angle. The angle-time series were filtered using a fourth order Butterworth low-pass filter with a 12 Hz cut-off frequency.

The first ten cycles of each trial were used to perform the following analyses. For each cycle in a trial, a custom-made MATLAB program (MATLAB r2014a, The MathWorks, USA) was used to identify the minimum and maximum peak values of FronPel, subtracting each minimum value from the following maximum value to obtain the amplitude of FronPel. The mean of the cycle amplitudes was computed for each trial, as well as the standard deviation as an indicator of spatial stability. The mean and standard deviation of the frontal pelvic oscillation frequency were computed using the time stamps of maximum peak values of FronPel. The coefficient of variation of frequency, defined as the ratio of standard deviation over mean frequency, was computed and used to evaluate the temporal stability of the pelvic movement.

The mean range of motion of FronSho, TranSho, SagiSho, TranPel and SagiPel angles was computed to assess the quasi-immobility of the upper-trunk and the predominance of frontal rotation of the pelvis over its transversal and sagittal components in each trial. It was defined as the mean difference between the maximum and minimum value of the angle across the ten shimmy cycles, defined between two maximum peak values of FronPel.

A pelvic asymmetry index was computed to assess the participants' ability to rotate the pelvis with the same amplitude to the left and right side during the trials. For both LASI and RASI markers, the mean distances in the 3D space between their positions when the frontal pelvis rotation angle reached its maximum and minimum peak values (meanLASI and meanRASI) were calculated for each trial and used to calculate (meanLASI -meanRASI)/(meanLASI + meanRASI). It varies between -1 and 1. The closer it is to 0, the more symmetrical the pelvic rotation is on the left and right side.

In order to identify how the coordination patterns of the trunk were affected by frequency, we calculated the continuous relative phase (CRP) between the following joint angles in each trial:

FronPel and TranPel (∆𝝋 𝑭𝒓𝒐𝒏𝑷𝒆𝒍-𝑻𝒓𝒂𝒏𝑷𝒆𝒍 ), FronPel and SagiPel (∆𝝋 𝑭𝒓𝒐𝒏𝑷𝒆𝒍-𝑺𝒂𝒈𝒊𝑷𝒆𝒍 ), FronPel and FronSho (∆𝝋 𝑭𝒓𝒐𝒏𝑷𝒆𝒍-𝑭𝒓𝒐𝒏𝑺𝒉𝒐 ), FronPel and TranSho (∆𝝋 𝑭𝒓𝒐𝒏𝑷𝒆𝒍-𝑻𝒓𝒂𝒏𝑺𝒉𝒐 ), and FronPel and SagiSho (∆𝝋 𝑭𝒓𝒐𝒏𝑷𝒆𝒍-𝑺𝒂𝒈𝒊𝑺𝒉𝒐 ). We calculated the angular velocity of each joint by differentiating each joint angle. Then, the angular velocities and joint angles were normalised in order to range between -1 and 1 by rescaling to their respective minimum and maximum. The phase angle of each joint variable was calculated as the inverse tangent of the division of the normalised velocity over the normalised joint angle. The phase angle was calculated in the range from -180 to 180 deg. Finally, the CRP between two variables is the result of subtracting the phase angles of these two variables. In order to restrain CRP to the [-180; 180 deg] range, 360 deg were added or subtracted to the CRP values if needed.

For each trial, relative frequency histograms (proportions) of CRP values were computed to identify different distribution patterns depending on the number of peaks: unimodal, multimodal or uniform (no peak). When the histogram presented a clear unimodal distribution, the CRP was considered to be relatively constant over the trial, so mean and standard deviation of the CRP were performed to assess the mode and the stability of the coordination, using directional statistics [START_REF] Burgess-Limerick | Note: A Statistical Problem in Testing Invariance of Movement Using the Phase Plane Model[END_REF][START_REF] Lamoth | Pelvis-thorax coordination in the transverse plane during gait[END_REF][START_REF] Mello | Statistiques circulaires et utilisations en psychologie[END_REF]. We defined the coordination to follow an antiphase pattern if the mean CRP within a trial ranged from ±140 deg to ±180 deg, out-of-phase pattern from ±40 deg to ±140 deg, and inphase pattern from 0 deg to ±40 deg.

Statistical analysis

The following analyses were performed using Matlab, Statistica 7.1 package (Statsoft, 2005) and JASP (JASP Team, 2020). Only the data from the second trial in each condition were analysed, as the first trial was considered a practice trial. The level of significance was set to p = 0.05. Normality was verified with the Shapiro-Wilk test. BoxCox transformations were performed on a dataset when normality was not met [START_REF] Osborne | Improving your data transformations: Applying the Box-Cox transformation[END_REF][START_REF] Sakia | The Box-Cox Transformation Technique: A Review[END_REF]. Paired sample t-tests performed on the mean of RighKne and LeftKne were used to verify whether RighKne in the three posture conditions differed.

Repeated-measures ANOVAs were conducted to study the combined influence of the frequency (1 Hz, 2 Hz, 3 Hz) and the posture (LP, IP, HP) conditions on the dependent variables characterizing mean performance and its variability, with a Bonferroni correction [START_REF] Cramer | Hidden multiplicity in exploratory multiway ANOVA: Prevalence and remedies[END_REF]. K-means clustering and Mixed ANOVAs were also performed to test inter-individual differences [START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF].

Results

Figure 1 shows typical behaviour of joint angles during 12 cycles (five seconds) of a hip shimmy trial: FronSho 2.61±1.47 2.61±1.43 2.38±1.18 2.02±1.36 1.84±1.18 2.75±2.32 2.03±1.36 1.55±0.8 1.71±0.9

TranSho 4.58±2.41 4.78±2.79 4.26±2.17 3.64±2.42 3.16±2.06 4.39±2.90 3.26±1.97 2.95±2.56 3.36±2.37

SagiSho 2.67±0.88 2.79±1.06 2.75±1.07 1.93±0.60 1.84±0.54 2.44±0.85 2.07±0.70 1.66±0.49 1.83±0.52

TranPel 8.92±4.02 9.35±4.74 9.02±3.84 9.65±3.75 10.51±3.95 10.46±4.65 10.08±4.22 8.64±3.52 7.98±3.59

SagiPel 4.61±1.59 4.56±1.57 4.69±2.01 4.01±1.12 4.63±1.55 3.76±1.45 3.94±1.50 3.26±1.16 3.14±1.27

Finally, in all of the recorded trials, the absolute value of the asymmetry index ranged between 0.0006 and 0.2, and the mean value was 0.07 ±0.05, showing good symmetry in pelvic oscillations. A repeated-measures ANOVA (3 frequencies × 3 postures) showed no significant influence of frequency and posture on the asymmetry index.

Pelvic oscillations in the frontal plane: Mean performance and variability

Frequency

The mean frequency of frontal pelvic oscillation was 1.02 ±0.003 Hz, 2.02 ±0.03 and 3.07 ±0.14 Hz in the 1, 2 and 3 Hz conditions, respectively, showing that the imposed frequency was respected.

However, observations of large inter-individual differences in the 3 Hz condition led us to use Kmeans clustering in order to divide the participants into three different groups (Figure 2). Four participants performed a lower than expected frequency (F3-group), five participants a higher one (F3+ group) and nine participants performed the actual 3 Hz frequency (F3 group). One-sample t-tests showed that F3-(t(11)=-19.94; p<0.001) and F3+ (t(14)=-9.24; p<0.001) differed significantly from the instructed 3 Hz frequency, while F3 was not different from 3 Hz. Independent samples t-test showed that in the 3 Hz condition, the three groups were significantly different from one another: F3differed from F3+ (t(25)=-13.94; p<0.001), F3-differed from F3 (t(37)=-7.41; p<0.001) and F3+ differed from F3 (t(40)=9.22; p<0.001).

****** Insert Figure 2 approximately here *****

The following three ANOVAs were performed with an additional between-subject factor, resulting from this clustering.

The mixed ANOVA (3 frequencies × 3 postures × 3 groups) performed on the coefficient of variation of pelvic frequency yielded a significant effect of frequency condition (F(2,30) = 24.68; p < 0.001; η² = 0.20). Post-hoc comparisons with the Bonferroni correction revealed that the coefficient of variation was significantly smaller at 2 Hz than at 1 Hz (p<0.001) and 3 Hz (p<0.001) (Figure 3).

Amplitude

Mean amplitude (over a trial) of pelvic oscillation in the frontal plane ranged from 3.14 deg to 31.80 deg across participants (Table 2) order to better understand these relatively complex distributions, mean and standard deviation of ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝐹𝑟𝑜𝑛𝑆ℎ𝑜 were calculated for each trial, as 93.8% of all individual trial distributions were unimodal. Figure 6 shows the mean individual relative phase values for the three frequencies, revealing the prevalence of the three coordination types as a function of frequency. At 1 Hz, 37% of the trials exhibited an inphase pattern, 29.6% and out-of-phase pattern and 33% an antiphase pattern.

At 2 Hz, the figures were 22.2%, 35.2% and 42.6%, respectively. At 3 Hz, more than half of the trials exhibited antiphase patterns (64.8%) and a very small proportion exhibited an inphase pattern (5.5%), while 29.6% exhibited an out-of-phase pattern. An inphase pattern means that FronSho rotates with the right shoulder downwards when FronPel rotates with the right hip downwards, while it rotates with the left hip downwards in an antiphase pattern. An out-of-phase pattern means that FronSho and

FronPel minimum or maximum peak rotations do not coincide in time but are phase-shifted (Figure 7).

Discussion

In the present study, we investigated the extent to which it is possible to intentionally oscillate the pelvis in the frontal plane independently from rotations in the two other pelvic planes (i.e. transverse and sagittal planes) while the upper trunk remains still, as expected in an oriental dance movement called the "hip-shimmy". More specifically, the first aim was to assess whether pelvic movement amplitude and stability could be maximised in certain postural and frequency conditions in order to contribute to performance optimisation in this well-known dance movement, whose kinematic properties have rarely been documented. The second and more fundamental aim was to characterise how the expected phase unlocking (or potential phaselocking) of 3D pelvis and upper-trunk rotations was frequency dependent. The ability of the oriental dance experts to independently control the different rotations of the pelvis, as well as the pelvis from upper-trunk movements was analysed with continuous relative phases.

Performance features.

The mean amplitude of frontal pelvis rotation among experts oriental dancers ranged from 15 to 20 deg depending on the condition, which is higher than in gait: approximately 10 deg when walking at preferential speed [START_REF] Taylor | The effect of walking faster on people with acute low back pain[END_REF] and 7 deg in racewalking [START_REF] Majed | Learning an energy-demanding and biomechanically constrained motor skill, racewalking: Movement reorganization and contribution of metabolic efficiency and sensory information[END_REF]. A main significant effect of the role of posture was observed, with a low posture enhancing performance.

However, the size of this effect was small with a difference of less than 2 deg between the movement amplitude in high and low postures. The anatomical constitution of the hips might explain this postural effect. As posture lowers, the knees and hips are more flexed and the anterior ligaments of the hips are looser. This increases the abduction and adduction amplitude ability of the hips, both of which occur when the pelvis is rotated in the frontal plane (Calais-Germain, 2013).

Concerning the significant effect of movement frequency, mean performance was similar and highest in the 1 and 2 Hz conditions. A drop of approximately 3-4 deg was observed at 3 Hz. In cyclical movements, it is often observed that the amplitude of cycle drops inversely as frequency is increased and that amplitude and frequency cannot necessarily be controlled independently (B. A. Kay, J. A.

Kelso, E. L. Saltzman, G Schöner, 1987). Finally, the absence of a significant interaction between posture and frequency effects, as well as parallel curves in Figure 4.a, show that the frequency effect was not posture dependent.

Is there independent control of pelvic motion in the frontal plane?

The analysis of mean joint motion amplitudes showed that expert oriental dancers are able to minimise pelvic sagittal and upper-trunk motions which were much smaller (although not completely absent) than pelvic motion in the frontal plane. It was less the case for the pelvic rotation in the transverse plane, which reached approximately 11 deg in some conditions. These results appear to show that, at least to some extent, expert oriental dancers are able to dissociate the pelvic motion from the uppertrunk motion, as well as the pelvic motions around the three pelvic rotation axes. Yet, the analysis of produced when it is too slow [START_REF] Park | Moving slowly is hard for humans : limitations of dynamic primitives[END_REF]. Regarding 3 Hz, more inter-individual differences arose. The 3 Hz condition seemed more difficult to maintain for half of our participants, who naturally converged into either a higher or a lower frequency, and exhibited larger temporal variability. This result is in accordance with Nugent et al. ( 2017) who mention that 3 Hz is the threshold frequency where tempo would be difficult to maintain, leading to a either lower or higher frequency than expected. In the non-linear dynamical systems view, we could interpret this frequency as being located in an instability area between two stable attractors, yielding critical fluctuations in movement. Nugent et al. ( 2017) found that a new pattern of erector spinae muscle activation emerges from 3 Hz and could not be performed at lower frequencies (the "A" pattern). We believe that our expert participants who performed at a higher frequency than the imposed 3 Hz may have switched to this A pattern. This group also performed smaller pelvic oscillations at 3 Hz than the other participants.

The frequency threshold, above which dancers spontaneously shift to this A pattern, could be related to the level of expertise and thus be used to characterise oriental dancers' performance level. In future studies, a between-group design experiment with groups of different levels of expertise and higher frequencies tested (up to 6 Hz as suggested by Nugent et al ( 2017)) could provide more insight into this issue of inter-individual differences and frequency-related variability.

Although not directly studied in the present paper, there were also some inter-individual differences in the knee bending posture adopted by the participants. We contend that this is a factor of interindividual variability in mean performance (maximal pelvic frontal motion) since posture was shown to have a significant (but small) main effect. Still, this effect did not interact significantly with the frequency-dependent effects on performance that were observed and discussed.

Conclusion

Oriental dance provides an innovative approach for the study of human motor control and coordination to provide insight into complex control mechanisms of pelvic motion. Although dancers were able to maintain a wide, stable, voluntary pelvic rotation in the frontal plane while minimizing the other pelvis and upper-trunk rotations, frontal pelvis control could not be kept perfectly independent because of anatomical/mechanical constraints, yielding some unpreventable coordination in the trunk. Moreover, frequency could most probably be a differentiating factor of the expertise level between individuals, and a control parameter of the different pelvic coordination pattern occurrences. The ability to voluntarily control the pelvic motion in a hip shimmy through changing and high frequencies among dancers of different levels of expertise and novices should be explored in further studies.

Legends

  Posture (HP); 145 deg for Intermediate Posture (IP), and 130 deg for Low Posture (LP), respectively.

  FronPel, RighKne, LeftKne and TranPel trace a clear oscillatory movement whereas FronSho, TranSho, SagiSho, SagiPel show very small oscillations. ****** Insert Figure 1 approximately here ***** 3.1 Motor performance 3.1.1 Compliance with task instructions In all trials of each participant, the mean knee angle respected an increasing order between LP, IP, and HP conditions. Averaged across all participants, it reached 151.00 ±5.19 deg in the HP condition, 147.49 ±5.86 deg in the IP condition, and 141.54 ±6.83 deg in the LP condition. The non-significant Shapiro-Wilk test confirmed the normality assumption prior to performing t-tests on this postural angle. Paired sample t-tests showed that the performed angles differed from each other, with a significant difference between LP and IP (t(53)=-13.75; p<0.001), IP and HP (t(53)=-8.47; p<0.001), LP and HP (t(53)=-16.74; p<0.001).The mean range of motion of the upper trunk in the three planes(FronSho, TranSho, SagiSho) and pelvic motion in the transversal and sagittal planes (TranPel, SagiPel) were always very small (< 5 deg for all these variables except TranPel < 11 deg), as required in the task instructions (see

*

  . A mixed ANOVA (3 frequencies × 3 postures × 3 groups) performed on this variable yielded a significant main effect of posture (F(2,30) = 5.60; p = 0.01; η² = 0.01), of frequency (F(2, 30) = 3.58; p = 0.04; η² = 0.05), as well as a marginally significant interaction between frequency and group (F(4, 30) =2.57; p = 0.06; η² = 0.08) (Figure4.a). Post-hoc comparisons with the Bonferroni correction revealed that mean amplitude was significantly smaller in the high posture than in the low posture (mean difference = 1.44 deg; p = 0.007). Concerning the marginal interaction between frequency and group, Figure 4.b shows that the F3+ group exhibits the lowest amplitude in the 3 Hz condition. A mixed ANOVA (3 frequencies × 3 postures × 3 groups) performed on the standard deviation of the within-trial frontal pelvic amplitudes showed no significant influence of any of the three factors, nor any significant interactions between them, suggesting a relatively constant spatial variability across groups and conditions. ****** Insert Figures 4.a and 4.b approximately here *****3.2 Trunk coordination mode and stability: CRP analysisThe individual CRP proportion distributions were averaged for each frequency condition (Figure5). Three types of distribution were identified depending on the number of peaks. A unimodal distribution reflected either a "more" inphase coordination mode with a peak around 0 deg, or antiphase coordination mode with two peaks around ±180 deg. A bimodal distribution reflected the coexistence of two coordination modes among participants, inphase and antiphase with three peaks around ±180 deg and 0 deg. However, in both cases, non-null values between peaks show that some out-ofphase patterns could be observed and analysed thereafter. Finally, a uniform distribution with no peak reflected the absence of stable coordination. ****** Insert Figure 5 approximately here ***** ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝐹𝑟𝑜𝑛𝑆ℎ𝑜 displays a bimodal distribution with three peaks around 0 deg and ±180 deg at 1 Hz and 2 Hz, whereas it shows a unimodal distribution with two peaks around ±180 deg at 3 Hz. In

*

  ***** Insert Figure 6 approximately here ***** ****** Insert Figure 7 approximately here ***** In order to see if the variability increases in out-of-phase patterns, standard deviation was plotted for each trial (Figure 8). Standard deviation of each trial seemed more or less constant through the patterns. The mean standard deviation was 55.72 ±11.79 deg in the inphase trials, 63.41 ±8.97 deg in the out-of-phase trials, and 52.55 ±12.63 deg in the antiphase trials. ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝑇𝑟𝑎𝑛𝑆ℎ𝑜 displays a clear unimodal distribution around 0 deg regardless of the frequency condition (Figure 5). More than 94% of all individual histograms showed this same unimodal distribution pattern around 0 deg. Averaged between participants, the mean value of ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝑇𝑟𝑎𝑛𝑆ℎ𝑜 was 24.43 ±30.94 deg, and the mean standard deviation was 47 ±13.73 deg. This inphase pattern means that when FronPel rotates downward with the right hip, the TranSho rotates forward with the right shoulder. Both ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝑆𝑎𝑔𝑖𝑃𝑒𝑙 and ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝑆𝑎𝑔𝑖𝑆ℎ𝑜 display a diffuse bimodal distribution around 0 deg and ±180 deg at 1 Hz and an uniform distribution at 2 Hz and 3 Hz. However, the individual histogram displays no coordination pattern consistency between subjects, and none of them displayed a clear unimodal distribution. ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝑇𝑟𝑎𝑛𝑃𝑒𝑙 depicts a clear antiphasic pattern in all frequency conditions (Figure 5), which is observed in more than 96% of all individual histograms. This antiphase pattern means that when FronPel rotates downward with the right hip, TranPel rotates backward with the right hip. Averaged between participants, the absolute mean value of ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝑇𝑟𝑎𝑛𝑃𝑒𝑙 reached 156.99 ±30.72 deg, and mean standard deviation reached 33.39 ±16.07 deg.

Figure 1 .

 1 Figure 1. Joint angles in five seconds of a hip shimmy trial of one participant in the 2 Hz and Low Posture condition.

Figure 2 .

 2 Figure 2. Mean frequencies (± standard error) of frontal pelvic oscillation (FronPel) as a function of experimental conditions in three groups of participants (white circle: F3-group, grey square: F3, black diamond: F3-).

Figure 3 .

 3 Figure 3. Mean (± standard error) coefficient of variation of frontal pelvic frequency as a function of metronome frequency in the F3-group (circle), F3 group (square), F3+ group (diamond) (prior to BoxCox transformation).

Figure 4

 4 Figure 4.a) Mean amplitude of pelvic motion in the frontal plane (FronPel) in all conditions as a function of metronome frequency (white square: Low Posture; grey square: Out-of-phase Posture; black square: High Posture). b) Mean amplitude of pelvic motion in the frontal plane for the three groups as a function of metronome frequency.

Figure 5 .

 5 Figure 5. Proportion (y-axis) distributions of CRP values in the [-180 ; 180] deg range (x-axis), across frequency trials, averaged in all participants.

Figure 6 .

 6 Figure 6. Mean ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝐹𝑟𝑜𝑛𝑆ℎ𝑜 of each individual trial as a function of frequency condition (in each frequency graph, from left to right, successive means of LP, IP, HP of each participant).

Figure 7 .

 7 Figure 7. Example of Out-of-phase pattern coordination between FronPel and FronSho in participant no. 2, in the 2 Hz and HP condition. Mean CRP: 103.73 ±57.74 deg. Top: unimodal histogram of CRP. Bottom: FronPel (black line) and FronSho (grey line).

Figure 8 .

 8 Figure 8. Mean (circles) and standard deviation (error bars) of ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝐹𝑟𝑜𝑛𝑆ℎ𝑜 of each trial, sorted along the x-axis according to the increasing order of mean ∆𝜑 𝐹𝑟𝑜𝑛𝑃𝑒𝑙-𝐹𝑟𝑜𝑛𝑆ℎ𝑜 . Inphase pattern trials (white circles), out-of-phase pattern trials (grey circles) and antiphase pattern trials (black circles).

Table 1

 1

	).
	****** Insert Table 1 approximately here *****

Table 1 .

 1 Mean range of motion and standard deviation (degrees) of FronSho, TranSho, SagiSho, TranPel and, SagiPel in the nine experimental conditions, averaged between all participants.

		1 Hz			2 Hz			3 Hz
	LP	IP	HP	LP	IP	HP	LP	IP	HP

the continuous relative phases enables us to be more specific and moderate about this latter assertion. Indeed, while the upper-trunk motion remained very small in all the conditions, the results showed some clear inphase phase locking between the pelvic motion in the frontal plane and the shoulder motion in the transverse plane, in all three frequency conditions. There was also a clear antiphase phase locking between the pelvic motion in the frontal plane and the transverse planes for all participants in all frequency conditions. By deduction, the transversal pelvis and upper trunk are systematically coordinated in antiphase. These very consistent observations tend to show that uppertrunk and pelvic motion in the transverse plane may be due to either mechanical, anatomical or both factors that would be impossible to suppress even after more than three years of training. The antiphase relationship between the pelvis and shoulders in the transverse plane could reflect the counter-balancing mechanism often suggested in gait analysis [START_REF] Lamoth | Pelvis-thorax coordination in the transverse plane during gait[END_REF][START_REF] Van Emmerik | Effects of walking velocity on relative phase dynamics in the trunk in human walking[END_REF] and/or that large voluntary pelvic movements induce small but systematic mechanical upper-trunk vibrations.

Conversely, other relative phases exhibit frequency-dependent distributions. At 1 Hz, three distributions demonstrate that more or less inphase, antiphase or even out-of-phase coordination modes are possible, namely between the frontal pelvic motion and respectively sagittal pelvic motion, frontal and sagittal upper-trunk motion. Unlike bimanual rhythmic tasks which present only two stable states, either inphase or antiphase (J.A. [START_REF] Kelso | Phase transitions and critical behavior in human bimanual coordination[END_REF], we found that coordination between the frontal pelvis and the upper trunk can reach multiple stable levels. This finding is consistent with Van Emmerik et al (1996) who showed that multiple stable coordination patterns exist in trunk motion during gait when velocity is increased.

In our study, a reduction in the number of coordination modes or even no phase locking was observed when frequency was increased. At 2 and 3 Hz, there was no stable phase relationship between frontal pelvic oscillation and sagittal pelvic or shoulder oscillations. Thus, high frequency enhances some dissociation between joint rotations expected in the hip-shimmy movement, whereas, as mentioned above, other phase-locked coordination patterns seem impossible to prevent.

Frequency-dependent variability in motor performance and inter-individual differences

Frequency also has an influence on movement variability. The temporal variation of oscillations was significantly smaller in 2 Hz than in 1 Hz and 3 Hz, which can be interpreted as greater stability at 2 Hz than at the other two studied frequencies. Two main interpretations are possible. The 2 Hz frequency may be close to the natural frequency of the hip shimmy movement since it is known that movement natural frequencies enhances stability [START_REF] Jordan | Walking speed influences on gait cycle variability[END_REF][START_REF] Rosenblum | Maintenance tendency in co-ordinated rhythmic movements : Relative fluctuations and phase[END_REF]. It could also be that this frequency is the one most often practiced by our participants when moving in rhythm with music. It could well be that pelvic movements performed at 1 Hz are more a succession of discrete movements than a true rhythmic movement. It is known that rhythmic movement cannot be


domain: spi chim phys

text:
Yann Le Bouar

Louise Toualbi

Frederic Fossard

Jean-Sébastien Mérot

Pauline Stricot

Simon Fritz

Agnes Bachelier-Locq

Nicolas Horezan

Quentin Barres

Maria Tsoutsouva

Jean-Sébastien Mérot

J.-S Mérot

; P Stricot

; N Horezan

M Fèvre

C Davoine

M Thomas

Microstructure and mechanical properties of a laser powder bed fused Al-Fe alloy

est destinée au dépôt

Introduction

In recent years, the advent of additive manufacturing techniques has allowed a considerable gain in terms of manufacturing costs, especially for parts with complex geometries. The L-PBF process studied here allows the elaboration, by a succession of lasering passes on a powder bed, of metal parts, which can present geometries difficult to achieve with conventional manufacturing techniques. However, the microstructure of the as-built parts depends not only on the parameters of the FA process used, but also on the thermal specificities of this process. In the case of the L-PBF process, which is characterized by particularly short laser-material interaction times, the as-manufactured microstructures are generally far from equilibrium, and characterized by a high dislocation density [START_REF] Sames | The metallurgy and processing science of metal additive manufacturing[END_REF]. Up to now, industrialists have been trying to obtain microstructural and mechanical properties for the parts obtained by FA that are comparable to those obtained by conventional manufacturing and shaping processes. It is therefore necessary to find a suitable heat treatment to apply to the post manufacturing parts [START_REF] Zhao | Microstructure and mechanical properties of laser additive repaired Ti17 titanium alloy[END_REF][START_REF] Lin | Microstructure and mechanical properties of laser forming repaired 17-4PH stainless steel[END_REF][START_REF] Rokni | The effects of heat treatment on 7075 Al cold spray deposits[END_REF][START_REF] Fang | Microstructure evolution of wire-arc additively manufactured 2319 aluminum alloy with interlayer hammering[END_REF][START_REF] Guevenoux | Influence of interlayer dwell time on the microstructure of Inconel 718 Laser Cladded components[END_REF][START_REF] Uzan | High-temperature mechanical properties of AlSi10Mg specimens fabricated by additive manufacturing using selective laser melting technologies (AMSLM)[END_REF][START_REF] Takata | Anomalous strengthening by supersaturated solid solutions of selectively laser melted Al-Si-based alloys[END_REF]. However, an increasing number of studies are tending to propose grades specially designed to meet the specificities of additive manufacturing processes [START_REF] Chehab | A new aluminium alloy for PBF-LB[END_REF][START_REF] Buttard | Multi-scale microstuctural investigation of a new Al-Mn-Ni-Cu-Zr aluminium alloy processed by laser powder bed fusion[END_REF][START_REF] Wang | High-temperature strength sustained by nano-sized eutectic structure of Al-Fe alloy manufactured by laser powder bed fusion[END_REF]. For example, in the case of the families of metal alloys with structural hardening, the nanometric precipitation of hardening phases takes place concomitantly with a pinning of dislocations resulting from the thermal process on these same precipitates [START_REF] Vilaro | Microstructural and mechanical approaches of the selective laser melting process applied to a nickel-base superalloy[END_REF][START_REF] Zhang | Effect of standard heat treatment on the microstructure and mechanical properties of selective laser melting manufactured Inconel 718 superalloy[END_REF][START_REF] Wang | Formation of multiple intermetallic phases in a hypereutectic Al-Fe binary alloy additively manufactured by laser powder bed fusion[END_REF]. The resulting hardening, linked to both thermal hardening and alloy chemistry, can be of great benefit, especially if it avoids the need for a post manufacturing heat treatment. In the framework of this study, the case of aluminium alloys with structural hardening is considered. The aim is to study a model alloy, the binary alloy Al-Fe, and of being interested in the interactions between the dislocations resulting from the thermal processing and the nanoprecipitates present from the first stages of the solidification, and which are found in the as-built microstructures.

Experimental procedure

The material of this study is a binary aluminum alloy with a nominal composition of Al-4Fe (wt%). The rapid solidification in the L-PBF process enables the formation of very fine precipitates which are known to improve both strength and ductility of these alloys [START_REF] Wang | Formation of multiple intermetallic phases in a hypereutectic Al-Fe binary alloy additively manufactured by laser powder bed fusion[END_REF][START_REF] Qi | Managing both high strength and thermal conductivity of a laser powder bed fused Al-2.5Fe binary alloy: Effect of annealing on microstructure[END_REF]. Therefore, this model system enables the study of the correlated apparition of high dislocation densities resulting from the thermal work hardening of the L-PBF process and the hardening nanoprecipitates specific to this family of alloys. This characteristic is particularly interesting for the definition of a process/material couple allowing to avoid the implementation of a post-production thermal treatment. It has also been found that by limiting the number of alloying elements, a good compromise between mechanical and thermal properties can be achieved, hence the interest in using binary or ternary alloys in the case of aluminum parts made by Additive Manufacturing [START_REF] Chehab | A new aluminium alloy for PBF-LB[END_REF]. The studied samples were manufactured by L-PBF using different parameters. Without being able to give the details of the parameters used, the main modifications concerned the plateau heating temperature, the vector gap and the feed rate, with the aim of inducing a modification of the thermal phenomena undergone by the material.

The study of the microstructure organization requires the use of complementary characterization techniques, at different scales of interest. Thus, optical microscopy is used to visualize the trace of the melt pool. Scanning electron microscopy characterizations allow imaging the largest precipitates. Electron BackScatter Diffraction analysis gives access to the morphology of the grains and their crystallographic orientation. Finally, the fine characterization carried out by transmission electron microscopy allows highlighting the solidification substructures, as well as the finest precipitates, which appeared at the first stages of solidification. The evaluation of thermal hardening is a particularly delicate subject, which remains open [START_REF] Kamaya | Assessment of local deformation using EBSD: Quantification of accuracy of measurement and definition of local gradient[END_REF]. We propose to couple fine and localized measurements of Vickers micro-hardness to a local analysis of intragranular disorientations, obtained from EBSD maps. In perspectives of the work presented in this paper, we propose to use transmission electron microscopy to visualize the dislocations, and in particular, their interactions with precipitates, in order to propose hypotheses about the hardening mechanisms involved. The evolution of this non-equilibrium microstructure will also be studied following the implementation of different post manufacturing thermal treatments. The aim is not only to study the stability of the thermal hardening resulting from the L-PBF process, but also the precipitation and growth kinetics of the phases present in the as-built microstructure. Thus, a matrix of thermal treatments has been proposed and carried out.

Microstructure characterization

The optical micrographs made in the building direction give a good visualization of the melt pools and of the different layers (Figure 1-left). The transverse direction features discontinuous beads, , due to the three-dimensional morphology of the beads and to a partial melting of the previous layer during the passage of the laser of the current layer (Figure 1-right). It also reveals the 67° rotation of the scan directions between the successive layers, used to prevent the development of single-crystalline-like texture [START_REF] Sun | Effect of scanning strategy on texture formation in Ni-25 at.%Mo alloys fabricated by selective laser melting[END_REF]. Scanning electron microscopy characterization also shows an epitaxial growth of columnar grains through the melt pools (Error! Reference source not found.-left). EBSD characterization permits a better visualization of the grain shape. We may note the presence of finer grains at the border of the melt pool. We observe that the epitaxial growth of columnar grains can pass through several melt pools (Figure 2-right). These EBSD measurements also give access to an average estimation of the grain size. Given their elongated morphology, this average value is only indicative. Thus, we estimate that in their smallest dimension, the elongated grains have an average width of 50 µm. Figure 3 reveals that the border of the melt pools is decorated by a micrometric precipitation, which appears in white on the images. These precipitates probably play the role of nucleant, inducing the presence of the finer grains at the border of the melt pool as described above. With further analysis by scanning electron microscopy, we detect the presence of three different zones, in terms of size of microstructure (Figure 4). The first one, which corresponds to a remelted zone, is a zone with a coarse microstructure, located at the bottom of the melt pool, where the cooling rate is the lowest. We can note the presence of micrometric precipitates visible in this coarse zone.

The second one, which corresponds to a heat-affected zone, is a zone where the temperature increases but not to the melting point, inducing slight evolutions of the microstructure, in this case a slight coarsening of the cell-like structure. The third one, which was melted only once, is a zone with a very fine microcellular structure. Many authors classically point out the presence of these different zones in L-PBF as-built Al-Fe samples [START_REF] Wang | High-temperature strength sustained by nano-sized eutectic structure of Al-Fe alloy manufactured by laser powder bed fusion[END_REF][START_REF] Wang | Formation of multiple intermetallic phases in a hypereutectic Al-Fe binary alloy additively manufactured by laser powder bed fusion[END_REF][START_REF] Qi | Laser powder bed fusion of a near-eutectic Al-Fe binary alloy: Processing and microstructure[END_REF]. Some prefer to differentiate only two of them, the remelted zone and the fine zone, and then mention a gradual refinement of the cell-like structure.

Other authors identify a third intermediate zone, thermally affected, which presents distinct microstructural characteristics [START_REF] Sun | Selective Laser Melting of an Al-Fe-V-Si Alloy: Microstructural Evolution and Thermal Stability[END_REF][START_REF] Michi | Towards high-temperature applications of aluminium alloys enabled by additive manufacturing[END_REF]. The fine characterization of the microstructure by transmission electron microscopy reveals a solidification in cell-like structure. EDS chemical analyses in HAADF (High Angle Annular Dark Field) mode show that the iron segregates at the border of the sub-cells (Figure 5). Furthermore, we can see that the thermal cycling induced by the L-PBF process results in different subcell sizes. We can see the presence of precipitates of different shapes and sizes whose distribution in the microstructure is not homogeneous. In the bottom of the melt pool, we have already seen that we have some coarse precipitates, visible in scanning electron microscopy (Figure 3). Within the heataffected zones, we find some fine precipitates, of a few hundred nanometers (Figure 6). At least, in the so-called fine microstructure zone, which seemed to be without precipitates, we can detect at high magnification, precipitates of a few nanometers (Figure 6). It has to be noted that these characteristics are found on all the samples, independently of the manufacturing parameters used. The nanoprecipitates that have been highlighted in the ultrafine microstructure zones are those that are likely to interact with the dislocations resulting from the thermal cycling of the L-PBF process to induce an interesting hardening. Figure 6 shows two types of precipitates, whose interactions with dislocations depend on their size. Concerning the different L-PBF parameters used to manufacture the samples of this work, the main result is that, despite the presence of columnar grains highlighted by the EBSD maps, none of our samples show any cracks along the High Angle Grain Boundaries. This can be explained by the absence of segregation at the grain boundaries at the end of solidification.

Thermal treatment post-fabrication

Different post manufacturing heat treatments are being investigated. The objective of this work is to evaluate the stability of the microstructure, in terms of grain size, precipitate coarsening and thermal hardening. The treatment temperatures are between 250°C and 600°C, for durations ranging from 2h up to 20h. For the time being, only a few first samples could be characterized. It can be seen that a treatment at 600°C for 6h induces a significant coarsening of the precipitates (Figure 7-upper left). On the counterpart, the heat treatments carried out at 250°C show a remarkable stability of the microstructure, and this for all the durations, in particular 20h of holding at temperature (Figure 7upper right and bottom). As pointed out by Qi et al. in an Al-2.5Fe alloy, even after 1000h of thermal exposure at 300°C, a considerable number of nanosized precipitates remain. No significant grain growth occurs, which can be explained by the pinning effect of these fine precipitates on the grain boundary, preventing their migration [START_REF] Qi | Change in microstructural characteristics of laser powder bed fused Al-Fe binary alloy at elevated temperature[END_REF].

Estimation of the thermal hardening

Vickers micro-hardness measurement is one of the techniques used to evaluate the level of hardening of the as-built samples. The microstructural analysis having shown a strong heterogeneity, it appears important to carry out hardness measurements in similar zones of the microstructure. Thus, measurements were made in the center of the melting baths and other measurements at the border.

The tests are performed with an applied load equal to 100 g which leads to a footprint of several tens of micrometers, as shown in the Figure 8. The area impacted by the indentation is therefore of the same order of magnitude as the average grain width (about 50 µm,) but smaller than the size of the melt pool. In average, the Vickers micro-hardness measurements at the center of the melt are 20 points higher than those obtained at the border. Indeed, as shown in the Error! Reference source not found., the border of the melt pool is the area with the highest density of micrometric precipitates. By contrast, in the center of the melt, we find nanometric precipitates that seem to participate more effectively in the hardening process, particularly by pinning dislocations. The effect of the presence of iron in solid solution can also be considered to explain these differences in hardness, but the solubility of iron in the crystalline lattice of aluminum is so limited that this hypothesis seems not very robust. Even taking into account the microstructure variations due to the specific organization induced by the L-PBF process, the hardness values show a relatively large standard deviation. On the other hand, we note that considering this standard deviation, the variation in hardness between the three manufacturing conditions is low, all samples featuring a Vickers micro-hardness value around 120. This shows the good robustness of this alloy with respect to the manufacturing conditions. The second technique used to estimate the thermal hardening induced by the L-PBF process is the analysis of intragranular misorientations from the EBSD maps [START_REF] Jiang | Measurement of geometrically necessary dislocation density with high resolution electron backscatter diffraction: Effects of detector binning and step size[END_REF]. Thus, maps processed in Kernel Average Misorientation mode were obtained with a step size of 300 nm to estimate the residual thermal hardening of the as-built samples. Figure 9 shows the maps obtained for three different processing conditions: the KAM values calculated are globally low, meaning that the residual thermal hardening is not as high as we thought, probably because of the pre-heating of the plate. Futhermore, it seems that the measurement noise is too large to obtain a reliable quantitative analysis [START_REF] Moussa | About quantitative EBSD analysis of deformation and recovery substructures in pure Tantalum[END_REF]. New analyses, with a refined step size, could allow a better estimation of the thermal hardening on these as-built samples [START_REF] Wright | Post processing effects on GND calculations from EBSDbased orientation measurements[END_REF]. These EBSD characterizations will also be coupled with TEM and ECCI observations, which will allow a better quantification [START_REF] Moussa | Statistical analysis of dislocations and islocation boundaries from EBSD data[END_REF][START_REF] Wang | Characterization of the microstructure and deformation substructure evolution in a hierarchal high-entropy alloy by correlative EBSD and ECCI[END_REF][START_REF] Zhang | Geometrically necessary dislocations distribution in face-centred cubic alloy with varied grain size[END_REF]. Here again, the variation in residual thermal hardening between the three manufacturing conditions is very small, proving the robustness of the alloy at the intragranular scale.

Conclusion

This preliminary study shows the interest of a complete control of the relationships between thermal, metallurgical and mechanical phenomena. Indeed, the gain in terms of mechanical strength that can be obtained by defining an aluminum alloy grade dedicated to Additive Manufacturing is significant. It allows benefiting from the double advantage of an anchoring of dislocations resulting from the thermal cycling of L-PBF process on nanoprecipitates themselves hardening. The manufacturing without cracking phenomena, the possibility to use simplified post processing thermal treatments and the stability of the microstructure with respect to the processing parameters are all elements of major interest for the industrials. The next step in this study will be to compare samples with higher levels of work hardening, in order to validate the interest of using the KAM method of analysis from the EBSD maps. One of the ambitions of this work is also to study the interactions between dislocations and nanoprecipitates present in the early stages of solidification. We will be interested in comparing the dislocations resulting from a thermal phenomenon via the comparison of specimens presenting different levels of thermal hardening due to a modification of the manufacturing parameters L-PBF, and the dislocations of strain hardening resulting from a mechanical solicitation, in this case via the application of compressive stresses on the studied samples.

Figure 1 .

 1 Figure 1. Optical micrographs of Al-4Fe L-PBF samples in parallel i.e. building (left) and transverse (right) directions.

Figure 2 .

 2 Figure 2. SEM image in BSE mode of one melt pool (left) and EBSD IPF maps of several melt pools of Al-4Fe L-PBF samples in building direction.

Figure 3 .

 3 Figure 3. SEM image in BSE mode of micrometric precipitation at the border of a melt pool of an Al-4Fe L-PBF sample in building direction.

Figure 4 .

 4 Figure 4. SEM images in BSE mode of the three different zones of an Al-4Fe L-PBF sample.

Figure 5 .

 5 Figure 5. STEM images in HAADF mode (left) showing EDS Al and Fe chemical maps of the cell-like structure in an Al-4Fe L-PBF sample.

Figure 6 .

 6 Figure 6. TEM images in Bright Field mode showing the interaction between dislocations and precipitates in an Al-4Fe L-PBF sample.

Figure 7 .

 7 Figure 7. SEM images in BSE mode of micrometric precipitation at the border of a melt pool of four heat-treated Al-4Fe L-PBF samples in building direction.

Figure 8 .

 8 Figure 8. Vickers micro-hardness measurements on as-built Al-4Fe L-PBF samples obtained with three different manufacturing parameters.

Figure 9 .

 9 Figure 9. EBSD KAM maps on as-built Al-4Fe L-PBF samples obtained with three different manufacturing parameters.


Anne Tournillon

Isabelle Siegler

 Expert belly dancers performed a higher pelvis amplitude than in gait in the frontal plane [1][2]. Anatomical constraints could explain the posture effect on pelvis amplitude.

 Dancers are able to separately control amplitudes of pelvic and upper-trunk oscillations, as the upper-trunk rotations amplitude (< 5 deg) were much smaller than the pelvis (≈ 18 deg).

 Unpreventable coupling between trunk segments occured in all frequency conditions: frontal pelvic rotation induced transverse pelvic rotation, and there was a consistent antiphase pattern between transverse rotations of the pelvis and upper-trunk. These consistent patterns may be due to mechanical and/or anatomical factors, and could reflect the counter-balancing mechanism often described in gait analysis [3][4].

 Coordination patterns between the pelvis and upper-trunk frontal rotations are frequency dependent: three stable patterns, inphase, out-of-phase, antiphase were equally distributed among participants at 1 Hz, while the antiphase pattern was predominant at 3 Hz.

 Less temporal variation of pelvic oscillations was observed at 2 Hz than 1 Hz and 3 Hz; thus, 2 Hz could be close to a stable attractor according to the non-linear dynamical systems view. It could well be that pelvic movements performed at 2 Hz resemble a rhythmic movement, but still slow enough for a cycle-by-cycle control, while those performed at 1 Hz are more a succession of discrete movements.

.

Introduction Results

Method Discussion

The "hip shimmy" belly dance movement is a rotation of the pelvis around the anteroposterior axis alternating the clockwise and counter-clockwise directions, together with the antiphase coordination of the lower limbs, i.e., alternating knee flexion and extension. Its main features can be characterised by wide and isolated movement of the pelvis in the frontal plane, at different controllable speeds and amplitudes, possibly resulting from underlying control mechanisms that are not observable in more common pedestrian tasks. Kinematic properties of the hip shimmy have been rarely documented in the literature.

Participants

Figure 1 .

 1 Figure 1. Joint angles in a hip shimmy trial of one participant (2 Hz, Low Posture)

  2. characterise how the expected independent control of frontal pelvic from other trunk motions is frequency dependent.