Pauline Provini
email: pauline.provini@mnhn.fr

Anick Abourachid

E L Brainerd

S M Gatesy

Whole-body 3D kinematics of bird take-off: key role of the legs to propel the trunk

Keywords: 3D kinematics, X-ray Reconstruction Of Moving Morphology, trunk, hindlimbs, Zebra Finch, Diamond Dove

Previous studies showed that birds primarily use their hindlimbs to propel themselves into the air in order to take-off. Yet, it remains unclear how the different parts of their musculoskeletal system move to produce the necessary acceleration. To quantify the relative motions of the bones during the terrestrial phase of take-off, we used biplanar fluoroscopy in two species of birds, Diamond Dove (Geopelia cuneata) and Zebra Finch (Taeniopygia guttata). We obtained a detailed 3D kinematics analysis of the head, the trunk, and the three long bones of the left leg. We found that the entire body assisted the production of the needed forces to takeoff, during two distinct but complementary phases. The first one, a relatively slow preparatory phase, started with a movement of the head and an alignment of the different groups of bones with the future take-off direction. It was associated with a pitch down of the trunk and a flexion of the ankle, of the hip and to a lesser extent of the knee. This crouching movement could contribute to the loading of the leg muscles and store elastic energy that could be released in the propulsive phase of take-off, during the extension of the leg joints. Combined with the fact that the head, together with the trunk, produced a forward momentum, the entire body assisted the production of the needed forces to take-off. The second phase was faster with mostly horizontal forward and vertical upward translation motions, synchronous to an extension of the entire lower articulated musculo-skeletal system. It led to the propulsion of the bird in the air with a fundamental role of the hip and ankle joints to move the trunk upward and forward. Take-off kinematics were similar in both studied species, with a more pronounced crouching movement in Diamond Dove, which can be related to a large body mass compared to Zebra Finch.

Introduction

Take-off is a challenging phase of flight as it allows the transition between two environments with different physical constraints. The animal must move from a standing position with a very low speed, to an efficient flying posture with enough velocity to stay inflight. Therefore, take-off involves significant transitional motions of the articulated system between two locomotor positions, combined with the production of enough acceleration to propel itself into the air. In small animals, such as insects or small birds, take-off generally starts with a jump [START_REF] Alexander | Leg design and jumping technique for humans, other vertebrates and insects Philosophical Transactions of the Royal Society of London B[END_REF][START_REF] Dudley | The biomechanics of insect flight: form, function, evolution[END_REF][START_REF] Manzanera | Flight in nature I: Take-off in animal flyers The[END_REF], consisting in a crouching movement followed by a rapid extension of the legs. It has been observed that the first wing downstroke starts after lift-off [START_REF] Brackenbury | Insects in flight[END_REF][START_REF] Card | Performance trade-offs in the flight initiation of Drosophila[END_REF][START_REF] Earls | Kinematics and mechanics of ground take-off in the starling Sturnis Sturnus vulgaris and the quail Coturnix coturnix[END_REF][START_REF] Manzanera | Flight in nature I: Take-off in animal flyers The[END_REF]Provini et al. 2012b;[START_REF] Zumstein | Distance and force production during jumping in wild-type and mutant Drosophila melanogaster[END_REF], suggesting that the legs produce most of the acceleration needed to become airborne. In birds, ground reaction force measurements during take-off [START_REF] Bonser | Measuring leg thrust forces in the common starling[END_REF][START_REF] Earls | Kinematics and mechanics of ground take-off in the starling Sturnis Sturnus vulgaris and the quail Coturnix coturnix[END_REF][START_REF] Heppner | Leg thrust important in flight take-off in Pigeon[END_REF][START_REF] Tobalske | Take-off mechanics in hummingbirds (Trochilidae)[END_REF]) and a quantification of wings' and legs' contribution in the small columbid Diamond Dove (Geopelia cuneata) and the passerine Zebra Finch (Taeniopygia guttata) (Provini et al. 2012b) confirmed this hypothesis. Interestingly, despite large discrepancies between the different studied species in terms of body size, terrestrial locomotion strategy, wing morphology, and slow-flight kinematics, the most important differences were not observed in the production of aerodynamic forces during the first wingbeats, but in the ground reaction forces, when the bird is still in contact with the perch. Indeed, both the magnitude and the timing of the forces generated by the two species of birds were different (see SM1 and Provini et al. (2012b)). Here, we aim to understand how the different parts of the avian musculoskeletal system moved in relation to each other to produce the necessary force to take-off and what in the kinematics could explain the differences observed in the ground reaction forces between Diamond Dove and Zebra Finch.

In spite of the obvious importance of take-off to flight only few studies have investigated bird take-off kinematics [START_REF] Berg | Wing and body kinematics of takeoff and landing flight in the pigeon (Columba livia)[END_REF][START_REF] Earls | Kinematics and mechanics of ground take-off in the starling Sturnis Sturnus vulgaris and the quail Coturnix coturnix[END_REF]Provini et al. 2012b;[START_REF] Tobalske | Take-off mechanics in hummingbirds (Trochilidae)[END_REF]). On the one hand, the fact that take-off is a non-cyclic transitional motion makes it relatively difficult to study. Contrary to walking, running, hopping, swimming or flying, for which a high number of cycles can be recorded, it is more challenging to obtain a great number of take-off trials. Moreover, the lack of data could be explained by several technical factors. First, the rapidity of take-off requires high-speed video cameras to capture the movement of the animal. Furthermore, as feathers hide most of the body in birds, it is impossible to infer accurately the skeleton motions of the proximal parts of the limbs solely with the use of light cameras; thus, X-ray imaging has to be included in the data acquisition.

Third, motions of the head, the trunk, and the hindlimbs are not truly planar. Recent studies in birds have demonstrated the importance of long-axis rotations in hindlimbs kinematics [START_REF] Kambic | Long-axis rotation: a missing degree of freedom in avian bipedal locomotion[END_REF]) which can only be quantified with an accurate 3D analysis of the bones motions. Until recently, it was nearly impossible to acquire high-speed 3D X-ray data, but thanks to the combination of X-ray imaging and computational process (X-ray Reconstruction of Moving Morphology, XROMM), we are now able to record precise and accurate 3D skeletal movement [START_REF] Blandford | X-Ray Reconstruction of Moving Morphology (XROMM)[END_REF][START_REF] Gatesy | Scientific Rotoscoping: A Morphology-Based Method of 3-D Motion Analysis and Visualization[END_REF] and have access to relatively concealed motions. The present study took advantage of these technical advances and used XROMM methods to carry out a 3D kinematics analysis during the terrestrial phase of takeoff, finishing when the bird loses contact with the perch at lift-off.

We chose Zebra Finch (Taeniopygia guttata) and Diamond Dove (Geopelia cuneata) for their compatibility in terms of size and behaviour with our experimental protocol and because of the ground reaction forces data previously obtained from a similar experiment (Provini et al. 2012b), allowing us to draw a biomechanical comparison between these two species.

We carried out a kinematic analysis of the lower appendicular skeleton, i.e. the legs' three long bones (femur, tibiotarsus, and tarsometatarsus) and the pelvis. Including the pelvic girdle in our kinematics analysis, in addition to the leg bones, was motivated by the fact that the trunk participates in the crouching movement of the first phase of take-off and also because the trunk is known to play an important role to guide the entire body trajectory in bird locomotion [START_REF] Abourachid | Bird terrestrial locomotion as revealed by 3D kinematics[END_REF][START_REF] Berg | Wing and body kinematics of takeoff and landing flight in the pigeon (Columba livia)[END_REF][START_REF] Gatesy | Guineafowl hind limb function. I: Cineradiographic analysis and speed effects[END_REF]Provini et al. 2012a). Finally, we included the head kinematics in our study as its position differs from a standing to a flying posture [START_REF] Maurice | Influence of the behavioural context on the optocollic reflex (OCR) in pigeons (Columba livia)[END_REF]) and to investigate its potential role in takeoff kinematics. Because the role of the wings is not determinant to propel the centre of mass during this phase (Provini et al. 2012b) we did not include the wing motions in our study, however, the two light cameras allowed us to follow their general motions.

Materials and methods

Animals

Two Taeniopygia guttata (mean+s.d mass: 15.4±1.2g) and two Geopelia cuneata (mean+s.d mass: 52.0±3.2g) were purchased from commercial dealers, housed in flight cages, and provided with food and water ad libitum at the Concord Field Station in Bedford, MA, USA.

They were trained to take-off from a wood perch in the scope of two C-arms and two visiblelight video cameras (Fig. 1).

Surgical and experimental protocols

Prior to videographic recording, birds were implanted with 0.5 mm diameter tantalum beads.

For this purpose, birds were anesthetized with isoflurane in O2. Anaesthesia was induced using a custom constructed facemask and maintained for the duration of the surgery through an endotracheal tube. Then, feathers overlying the implantation sites were removed and a small cutaneous incision was made. Connective tissue and muscle were incised and 0.5 mm diameter tantalum beads were implanted on the head, the pelvis and left hindlimb bones (femur, tibiotarsus, and tarsometatarsus). We implanted one to three markers per bones: one marker on the beak, one on the pelvis, two on the left femur, two on the left tibiotarsus, and three on the left tarsometatarsus (SM2). When two or three markers were implanted on the same bone, we spaced them as far apart as possible to maximise the accuracy of bone 3D reconstruction [START_REF] Blandford | X-Ray Reconstruction of Moving Morphology (XROMM)[END_REF]. Finally, after all tissues were sutured closed, birds were allowed to recover until a normal locomotion behaviour had resumed. All experiments were conducted in accordance with international and institutional guidelines for the care and use of the animals.

Birds were recorded while taking-off at a resolution of 1080 x 1024 pixels and a speed of 1000 frames per second (fps) using two X-ray videography systems, each composed of a Photron 1024 PCI camera (Photron USA Inc., San Diego, CA, USA) coupled to an X-ray Carm system (Model 9400, OEC-Diasonics Inc., remanufactured by Radiological Imaging Services). The two X-ray C-arms were set in a lateral and a dorsoventral positions and set to emit at 60 kVp and 100 mA (Fig. 1). Two visible-light video cameras were added to the experimental setup: a Photron 1024 PCI (Photron, Inc., San Diego, CA, USA) recording at a resolution of 1024 x 1024 pixels and 1000 fps a Phantom MiroEx4 (Vision Research Inc., Wayne, NJ, USA) recording at 800 x 600 pixels and 1000 fps (Fig. 1). We followed recommendations regarding distortion correction and calibration of the space during the experiment [START_REF] Blandford | X-Ray Reconstruction of Moving Morphology (XROMM)[END_REF][START_REF] Gatesy | Scientific Rotoscoping: A Morphology-Based Method of 3-D Motion Analysis and Visualization[END_REF]. We use both a perforated steel sheet with precise hole size and spacing for distortion correction and a calibration object for accurate camera 3D placement for each video. We selected trials where birds kept a relatively straight trajectory during take-off.

Bone models and XROMM analysis

To obtain the bones models, needed for the XROMM analysis, animals were sacrificed via an overdose of isoflurane inhalant and scanned in a micro computed tomography (μCT) system (XRA-002 X-tek microCT scan available at the Center for Nanoscale Systems at Harvard University; 66kV, 130mA and a resolution of 0.04mm on each axis). We used Avizo (version 6.3; FEI Visualization Sciences Group) to reconstruct bones models from the µCT scans.

Then, models were imported in obj file format into Maya (version 2013; Autodesk). For bones with less than three markers, we used rotoscoping methods [START_REF] Gatesy | Scientific Rotoscoping: A Morphology-Based Method of 3-D Motion Analysis and Visualization[END_REF] or a combination of rotoscoping and marker-based methods [START_REF] Blandford | X-Ray Reconstruction of Moving Morphology (XROMM)[END_REF], with marker positions digitized and reconstructed in 3D, using the program XrayProject 2.2.4 in MATLAB (Brainerd et al. 2010) (www.xromm.org). We obtained a 3D animation of the head, the trunk, and the three long bones of the left hindlimb (femur, tibiotarsus, and tarsometatarsus) for two take-off trials in two Zebra Finches and two Diamond Doves (Figs 2a,2b,SM3).

Kinematics analysis a. Three-dimensional coordinate systems

The XROMM analysis provided the 3D motion of five rigid bodies: head, trunk (pelvis, keel and rib cage considered as one rigid body), femur, tibiotarsus (tibia and fibula considered as one rigid body), and tarsometatarsus. To quantify the 3D motion of joints and bones, we used a combination of two sets of coordinate systems: Anatomical Coordinate Systems (ACSs) and Joint Coordinate System (JCS) [START_REF] Grood | A joint coordinate system for the clinical description of threedimensional motions: application to the knee[END_REF]) that were previously proposed as a common framework, established for guineafowl hindlimbs, to facilitate comparisons among individuals and different avian species [START_REF] Kambic | Long-axis rotation: a missing degree of freedom in avian bipedal locomotion[END_REF].

The relative motions between a bone and a global coordinate system can be measured with one ACS and one global coordinate system. The construction of the ACSs was exclusively based on skeletal anatomy. We defined a global coordinate system to quantify the 3D motions of both the trunk and the head. Its origin was defined as the point on the perch intersecting with the sagittal plane of the trunk at the beginning of the take-off trial, with a horizontal Xaxis in the direction of the trunk motion pointing backwards, a vertical Z-axis pointing up, and a horizontal Y-axis perpendicular to the two previous axes pointing to the right. For the trunk, we used the pelvis ACS previously described [START_REF] Kambic | Long-axis rotation: a missing degree of freedom in avian bipedal locomotion[END_REF]) (SM4), for the head, we built a specific ACS, following a similar rationale. To establish the head ACS origin, we isolated the two orbits in the head 3D model and fitted them with spheres in Geomagic Studio 2013 (3D Systems, Morrisville, NC, USA). The midway between sphere centroids was used as the origin, the Y-axis ran through the right and left orbit centres, positive to the right, the X-axis ran orthogonally down the midline, intersecting the middle of the beak tip and the occipital region, positive pointing caudally, the Z-axis was set orthogonal to both Y-axis and X-axis, positive dorsally (SM4a).

Moreover, the relative motions between two adjacent bones can be measured with a combination of two ACSs, one on each bone, enabling the definition of a JCS for the corresponding joint. The characteristics of the ACSs (origin and orientations) were previously defined for the trunk, femur, tibiotarsus and tarsometatarsus [START_REF] Kambic | Long-axis rotation: a missing degree of freedom in avian bipedal locomotion[END_REF], allowing us to build the JCSs corresponding to the hip, knee, and ankle. We built a specific JCS for the head. Z-axis rotations (Yaw and flexion-extension) measured rotation of the head ACS about a fixed, global vertical Z-axis, positive to the left. X-axis rotation (roll and long-axis rotation) designated rotation about the local head X-axis, raising to the right orbit relative to the left being positive. Y-axis rotations (pitch and abduction-adduction) quantified rotation about a floating JCS Y-axis (always orthogonal to the yaw and roll axes), head up being positive (SM4).

A reference pose (SM4) was also built following [START_REF] Kambic | Long-axis rotation: a missing degree of freedom in avian bipedal locomotion[END_REF] recommendations. All translations and rotations were set to zero, each pair of ACS contributing to the JCS was perfectly aligned. The head JCS was aligned on the pelvis JCS, head and pelvis interpenetrating (SM4g).

Thereby, for each trial of each species of birds, we obtained a dataset of 6 variables, corresponding to the six degrees of freedom motions, of the left hip, left knee, and left ankle, as well as of the trunk and the head, relative to a global coordinate system. Translations along the X-axis (tx), the Y-axis axis (ty), and the Z-axis (tz) were measured for the head, trunk, left hip, left knee and left ankle. Roll (rx), pitch (ry) and yaw (rz) were obtained for the head and the trunk. Long-axis rotation (rx), abduction/adduction (ry), and flexion/extension (rz) angles for the left hip, left knee and left ankle (Figs 3, 4) were also calculated. We followed previous similar analysis for notations [START_REF] Gidmark | Flexibility in starting posture drives flexibility in kinematic behavior of the kinethmoid-mediated premaxillary protrusion mechanism in a cyprinid fish[END_REF]. We defined letters to refer to each rigid body or joint: head (H), trunk (Tr), hip (Hip), knee (Kn), ankle (Ank). These letters were followed by either "t" for translation along or "r" for rotation about, and "x", "y", or "z" to denote the specific axis. Therefore, translation about the x-axis of the head would be Htx.

b. Trials synchronisation and space adjustment

As birds did not perform take-off exactly at the same rate, trials lengths differed. To be able to compare and average trials among a given species, we synchronized our data in both space and time. Our observations of all the take-off trials revealed that the minimum of head vertical translation (Htz) corresponded to a repeatable event, thus we used it to set a synchronization time. The timing of each degree of freedom motions of rigid bodies or joints was synchronized to this instant. Then, trials were cropped to start at the beginning of take-off (t0), when the bird initiates the crouching movement and the alignment of the head with the rest of the body, and to end at lift-off (LO), when the bird loses contact with the perch. We calculated a sequence percentage with 0% corresponding to t0 and 100% corresponding to lift off (LO).

Moreover, as the initial point of each take-off was slightly different among trials, we shifted the data to an arbitrary point. For each degree of freedom motions of rigid bodies or joints, we recorded the magnitude at synchronized time equals zero and subtracted this value to the corresponding data set (for example, if the magnitude of Trtx at synchronized time equals zero was equal to 2.1 for a given trial, we subtracted 2.1 to the Trtx data of the entire trial).

Therefore, further of translations and rotations values were not absolute. The synchronized data adjusted in space allowed us to calculate an average of each degree of freedom motions of rigid bodies or joints within each species.

c. Take-off sequence

We observed three key events during takeoff (SM3): 1) take-off start (t0), when the bird initiates the crouching movement and the alignment of the head with the rest of the body, 2) beginning of leg extension, also corresponding to the end of the crouching movement, 3) lift off, LO, when the bird loses contact with the perch (Fig. 2). These three events defined two distinct phases, previously named "phase 1" and "phase 2" (Provini et al. 2012b).

The beginning of the leg extension phase corresponded to a modification of rigid bodies trajectories. To extract the instant it occurred, we used the trunk trajectory (Trtx, and Trtz), because the motions of the trunk, being the heaviest part of the body, was considered as a proxy for the motions of the center of mass. We performed a segmented linear regression, using the R package segmented (version 0.5-1.4) (R Development Core Team 2010). It provided a breakpoint for Trtx, and Trtz for each trial of each species of birds. We averaged the results and obtained an objective measure to divide the take-off sequence between the "crouching movement phase" and the "legs extension phase" for each species (SM5). Note that the timing of the breakpoint was not necessarily similar to the synchronization time.

d. Bones and joints motion quantification

Using the R package stats (version 3.3.0) (R Development Core Team 2010) and with the previously synchronized and space adjusted data (tx, ty, tz, rx, ry, and rz for the head, trunk, left femur, left tibiotarsus and left tarsometatarsus), we averaged and calculated standard deviation at each time step for the four trials of Diamond Dove and the four trials of Zebra Finch. We calculated a magnitude, corresponding to the difference between the maximum value and the minimum value of each variable. We calculated the mean and standard deviation associated to the magnitude of each previous variable, during phase 1 and during phase 2 (Table 1).

To quantify the change in velocity between the two phases of take-off, we derived Trtx and Trtz on each trial (SM6). We calculated the mean and standard deviation associated to trunk velocity on the X and Z axes for phase 1 and phase 2 in each species of birds.

The head aligned with the trunk before the beginning of legs extension (Fig. 2,SM3). To quantify this alignment, we measured the angle formed between the head and the trunk. To do so, we used the 3D animation obtained from Maya (Autodesk, version 2013) and added virtual markers (VM), corresponding to small icons on the Maya scene that mark a point in space. We added one VM at the most caudal part of the sagittal plane of the trunk, at the level of the first caudal vertebrae (VMT1), and another one on the most cranial part of the sagittal plane of the trunk at the level of first thoracic vertebrae (VMT2)(SM2). We measured the angle formed by these two virtual markers and the marker located on the beak during each trial. We named this variable angle_neck and calculated mean and standard deviation for this variable for each species of birds at each time step.

In order to capture the neck flexion/extension, we measured the distance between the head and the trunk, between a virtual marker located at the level of the supraoccipital bone on the sagittal plane of the head (VMH1) and VMH2. We named this variable dist_neck and calculated the mean and the associated standard deviation for each species of bird at each time step (Fig. 5a). Following the same rationale, to capture the entire limb flexion/extension effect, we used VMT2 and placed another virtual marker on the most distal part of the tarsometatarsus at the third digit trochlea level (VMTmt1) (SM2). We named this variable dist_limb and calculated the mean and the associated standard deviation for each species of bird at each time step (Fig. 5b).

Considering the small number of trials and specimens, inter-species comparisons were only performed qualitatively for each variable, with the help of the figures (Figs 2,3,4,5).

Results

Take-off sequence

Take-off was divided into two phases, phase 1 and phase 2, corresponding to a downward motion of the trunk followed by an upward motion of the trunk. The segmented linear regressions of the trajectory of the trunk showed that two linear regressions could fit the data for Trtx and Trtz as a function of the sequence percentage for both species of birds (SM5).

For Diamond dove, we found a breakpoint at 63.6±2.2% of take-off sequence for Trtx and 65.5±3.0% for Trtz. We thus considered that the beginning of phase 2 occurred at 64.5±2.7 % of take-off sequence. For Zebra finch, the breakpoint occurred at 59.1±4.3% of take-off sequence for Trtx and 64.6±7.9% for Trtz. Therefore, we considered that the beginning of phase 2 was at 61.8±6.6 % of take-off sequence.

3D motions analysis a. Head motions

During phase 1, the head aligned with the sagittal plane of trunk. This is visible on the dorsoventral view of Fig. 2a for Diamond dove and in Fig. 2b for Zebra Finch. In Diamond Doves, angle_neck went from 140.5±2.8 deg at the beginning of phase 1 to 178.6±3.4 deg at the beginning of phase 2. In Zebra Finch, angle_neck went from 144.58±4.6 deg at the beginning of phase 1 to 178.01±2.6 deg at the beginning of phase 2. Thus in both species, the head was in very close alignment to the trunk at the beginning of phase 2. This alignment was linked to a rotation of the trunk or of the head along the vertical axis (Figs 2,3). As the magnitude of Hrz (the difference between the maximum and the minimum of Hrz), during phase 1 was lower than Trtz for Diamond Dove, it suggested that the alignment was mostly due to a trunk rotation. In contrast, because the magnitude of Hrz was higher than of Trrz for Zebra Finch, the alignment was mostly due to the head rotation. At the same time, dist_neck slightly decreased in Zebra Finch, equivalent to a flexion of the neck (Fig. 5a), whereas it was not the case in Diamond Dove. The magnitude of Htz was higher compared to the magnitude of Trtz in both species, suggesting that the flexion was due to the vertical upward translation of the head downwards. The head also translated forward in both species during phase 1.

During phase 2, the head remained aligned with the sagittal plane of the trunk with a consistent value of angle_neck of 181±3.6 deg in Diamond Dove and of 179±2.5 deg in Zebra Finch (Fig. 2). The head followed a linear trajectory in the direction of take-off with a similar shape of Htx, Hty, and Htz as Trtx, Trty, and Trtz respectively. The increase of dist_neck during phase 2 corresponded to an extension of the neck.

b. Trunk motions

During phase 1, the velocity of Trtz was of 4.2±3.8 mm/s in Diamond Dove, and of 3.1±2.9 cm/s in Zebra Finch. Translations of the trunk were mostly caudocranial with a magnitude of Trtx (10.3±1.0 cm in Diamond Dove and 4.1±2.6 in Zebra) relatively higher than the magnitude of Trtz (2.4±1.7 in Diamond Dove and 1.3±1.3 cm in Zebra Finch) or of Trty (0.8±1.0 in Diamond Dove and 1.4±0.3 cm in Zebra Finch). This indicated a propulsion of the trunk in the forward direction during this phase. Trunk rotations predominantly corresponded to a downward pitch (Table 1 and Fig. 3). Trunk pitch was relatively higher in Diamond Dove compared to Zebra Finch (magnitude of 17.5±3.8 deg and 7.43 deg respectively). In Diamond Dove, roll and yaw motions were still substantial during phase 1, (magnitude of Trrx = 7.1±2.8 deg and Trrz =7.6±2.7 deg), which was not the case in Zebra Finch (magnitude inferior to 2.5 deg) (Table 1).

During phase 2, the velocity of Trtz increased to reach 39.5±10.7 mm/s in Diamond Dove, and 28.2±8.8 cm/s in Zebra Finch. In both species, caudocranial translations of the trunk remained important (magnitude of 21.7±2.9 cm in Diamond Dove and 11.9±7.2 cm in Zebra Finch) but went with an increase of trunk vertical upward translations (magnitude of 13.0±2.7 cm in Diamond Dove and 8.2±2.0 cm in Zebra Finch). Upward pitch of the trunk was high in Diamond Dove (magnitude of 14.5±1.1 deg), which was not the case in Zebra Finch (magnitude of 2.5±3.6 deg).

c. Hip motions

During phase 1, flexion of the hip was predominant in both species (magnitude of 11.6±2.9 deg in Diamond Dove and 4.5±9.9 deg in Zebra Finch) (Fig. 4), whereas abduction-adduction and long-axis rotations of the femur were low in both species (lower than 3 deg magnitude of, (Table 1).

During phase 2, extension of the hip was dominant (magnitude of 36.3±3.0 deg in Diamond Dove and 20.4±7.9 deg in Zebra Finch) (Fig. 4). In Diamond Dove, abduction increased (magnitude of 5.2±2.8 deg), whereas adduction increased in Zebra Finch (magnitude of 6.5±3.3 deg). Long axis rotation became higher in Zebra Finch (magnitude of 10.7±6.2 deg), which was less noteworthy in Diamond Dove (magnitude of 4.4±5.6 deg).

d. Knee motions

During phase 1, flexion-extension motions were low (less than 2 deg in both species) (Table 1). In Diamond Dove, we observed a relatively high adduction magnitude (magnitude of 8.4±10.1 deg), which was not true in Zebra Finch where the tibiotarsus remained static during this phase of take-off (magnitude lower than 4 deg) (Fig. 4).

During phase 2, we observed an increase of knee extension in both species (magnitude of 31.9±11.9 deg in Diamond Dove and 15.8±8.4 deg in Zebra Finch). This went with a rise of the tibiotarsus long axis rotation (magnitude of 13.7±6.7 deg in Diamond Dove and 7.0±2.7 deg in Zebra Finch). In Diamond Dove, adduction stopped during phase 2, whereas abduction increased in Zebra Finch (magnitude of 3.4±4.8 deg in Diamond Dove and 6.6±4.4 deg in Zebra Finch).

e. Ankle motions

During phase 1, flexion of the ankle was predominant in Diamond Dove (magnitude of 8.9±4.8 deg), which was not the case in Zebra Finch, with a relatively low rotation magnitudes in all three directions (Fig. 4).

During phase 2, the ankle extension became dominant (magnitude of 72.4±16.0 deg in Diamond Dove and 39.8±16.6 deg in Zebra Finch) compared to adduction-abduction (magnitude inferior to 3 deg in both species). We can note that long axis rotation was relatively important in both species (magnitude of 11.0±8.3 deg in Diamond Dove and 11.1±7.1 deg in Zebra Finch).

f. Timing of joint flexion-extension

In both species, dist_limb mostly increased during the take-off sequence, although in Diamond Dove, this augmentation was preceded by a reduction of dist_limb during phase 1 (Fig. 5).

In Diamond Dove, we observed a clear sequence of joint extension. First, the hip extension began at around 45% of the take-off sequence, followed by the ankle extension at around 60% of the take-off sequence, and finally the knee extension at around 75% of the take-off sequence. In Zebra Finch, the sequence was not as obvious, with a synchronous extension of the hip, knee and ankle at 50% of the take-off sequence.

Discussion

Our 3D kinematics analysis revealed a stereotyped behaviour during perch take-off in two species of birds, Taeniopygia guttata and Geopelia cuneata. Indeed, considering the small number of recorded sequences, the relatively low standard deviations of translation and rotation motions in both species (Table 1) demonstrates a consistency of motions among takeoff trials. Overall, the kinematics is similar in the two studied species, although we observed differences in motion magnitudes that could be linked to differences in size and long bone proportions between the two species. In both species, take-off could be divided into two phases. Phase 1 corresponds to a preparatory phase, including both an alignment of the different parts of the skeleton into the direction of the future motion and a crouching motion.

Phase 2 was described as a propulsive phase, with an extension of the lower appendicular skeleton, propelling the entire body into the air.

During phase 1, we observed relatively slow motions, with a trunk vertical velocity corresponding to only 8.3% and 6.5% of the velocity at Lift off in Diamond Dove and Zebra Finch, respectively. The head is aligning with the sagittal plane of the trunk, which is demonstrated by angle_neck, reaching 180 deg at the end of phase 1. This alignment is produced by both latero-medial translation and rotation of the head along the vertical axis (Fig. 3). In this respect, the high variability of Hrz in Zebra Finch (Table 1) is linked to the fact that some animals were looking to the right and others to the left at the beginning of the sequence. By aligning with the future direction of take-off, the head anticipates the global motion of the animal. This can be compared to what is observed in human locomotion where the eyes and the head anticipate the change in trajectory during turning, with a delay of the trunk [START_REF] Imai | Interaction of the body, head, and eyes during walking and turning Experimental brain[END_REF]. This alignment phase could contribute to reduce the aerodynamic drag, one of the forces resisting the forward motion. Although drag dominates at higher speeds than those observed during the terrestrial part of take-off, the frontal area remains an important factor in the drag coefficient calculation [START_REF] Pennycuick | Mechanics of flight[END_REF]) and a streamlined profile contributes to reduce drag. Simultaneously with the head alignment, roll and yaw motions of the trunk are relatively important in Diamond Dove, also suggesting a reorientation of the trunk to align with the future motion of the animal. This motion could also help to reach take-off velocity by aligning the joints in the take-off direction.

The crouching motion observed in phase 1 goes with a trunk pitch down, as well as with flexions of the hip, knee and ankle (Fig. 4, Table 1). This leads to a decrease of dist_limb in both species (Fig. 5) and contributes to lowering down the entire body. Previous studies in a variety of birds [START_REF] Earls | Kinematics and mechanics of ground take-off in the starling Sturnis Sturnus vulgaris and the quail Coturnix coturnix[END_REF][START_REF] Heppner | Leg thrust important in flight take-off in Pigeon[END_REF][START_REF] Tobalske | Take-off mechanics in hummingbirds (Trochilidae)[END_REF]) suggested that a continuum exists in the take-off strategies, where tiny birds (3-5 g) show a crouching movement less exaggerated than the one displayed in small birds (15-90 g), which is itself less pronounced than in medium birds (100 g to 1.5 kg) who exhibit a motion similar to a squat [START_REF] Manzanera | Flight in nature I: Take-off in animal flyers The[END_REF]. Zebra Finch and Diamond Dove fall at the two sides of the small bird category, with a less pronounced pitching movement in Zebra Finch compared to Diamond Dove. This classification suggests that the size of the bird is correlated to the intensity of the crouching movement. A heavier bird needs more force output to take-off, per unit time compared to a smaller bird. However, because muscular force is proportional to muscular cross-section (a squared measurement), whereas weight is proportional to a volume (a cubed measurement), the potential muscular force generated by a heavy bird is lower than in a lighter bird. A higher flexion of the ankle and the hip in a heavier bird, such as in Diamond Dove compared to Zebra Finch (Fig. 4, Table 1), contributes to a more pronounced crouching movement. Because stretched muscle tendon units could store elastic energy, a more pronounced flexion of the ankle and the hip could lead to the loading of the associated muscles and tendons, and generate more force than if they simply shortened [START_REF] Henry | Performance of guinea fowl Numida meleagris during jumping requires storage and release of elastic energy[END_REF][START_REF] Roberts | Contribution of elastic tissues to the mechanics and energetics of muscle function during movement[END_REF]). Then, this elastic energy could be released during phase 2, the propulsive phase of take-off. The heavier the bird is, the more efficient this phenomenon could be and the more pronounced crouching movement it should display. Ground reaction forces, recorded with a similar protocol in the same two species (Provini et al. 2012b) (SM1) revealed a higher maximum vertical force magnitude in Diamond Dove, compared to Zebra Finch. If we standardize this value, taking the bird's body weight into account, maximal hindlimbs force produced by Diamond Dove corresponds to 3 times body weight compared to around 5 times body weight in Zebra Finch (Provini et al. 2012b). This means that a Diamond Dove, with a more pronounced crouching movement needs proportionally less forces to accomplish the same task as a Zebra Finch. This is coherent with the previous hypothesis and the potential use of elastic energy in Diamond Dove.

In addition to the crouching motion, we observed an importance of the forward motions, i.e.

antero-posterior translations of the head and trunk. Therefore, the global motion of the skeleton tends to move the animal downwards and forwards. Given that in birds, the centre of mass is located in the trunk [START_REF] Abourachid | Mechanics of standing in birds -Functional explanation of lameless problems in giant turkeys[END_REF][START_REF] Allen | Variation in center of mass estimates for extant sauropsids and its importance for reconstructing inertial properties of extinct archosaurs The[END_REF]), a forward translation of the head and trunk can generate a forward momentum. This momentum could also contribute to the initial acceleration in the forward movement and could assist take-off.

The second part of the terrestrial phase of take-off allows the propulsion of the entire body in the direction of flight. The alignment of the different body parts persists during this phase.

The yaw, pitch and roll of the head are low (Fig. 4, Table 1) and the head rotations are close to zero at lift-off, corresponding to a stabilisation of the head, previously documented during flight [START_REF] Warrick | Bird maneuvering flight: blurred bodies[END_REF]. We also observed a low and stable abduction-adduction of the hip, knee and ankle in both species (Table 1) with symmetrical and synchronous latero-medial motions of the limb joints that allow an adjustment of the limb position. It is interesting to note that long-axis rotations are higher than abduction-adduction (Table 1). This result confirms the importance of 6 degrees of freedom kinematics analysis and justify the use of XROMM to quantify such motions, especially because long-axis rotations of a proximal bone have effect on distal bones [START_REF] Hutchinson | Adductors, abductors, and the evolution of archosaur locomotion[END_REF][START_REF] Kambic | Long-axis rotation: a missing degree of freedom in avian bipedal locomotion[END_REF]; a small motion of the femur can have drastic consequences on the motions of the foot [START_REF] Fischer | Basic limb kinematics of small therian mammals[END_REF].

Phase 2 of take-off is associated with a dominance of antero-posterior (tx) and ventro-dorsal translations (tz). The head is protracted as demonstrated by the increase of dist_neck (Fig. 5b).

An extended neck is typical during flight and has been related to vestibular and optical reflexes [START_REF] Bilo | Neck flexion related activity of flight control muscles in the flowstimulated pigeon[END_REF][START_REF] Maurice | Influence of the behavioural context on the optocollic reflex (OCR) in pigeons (Columba livia)[END_REF]. As the head hold the sensory organs, especially the eyes and the vestibular system, we can hypothesis that its position at the beginning of the take-off triggers the beginning of the propulsive phase. Therefore, even if it does not participate to propulsion, its kinematics is essential for a successful take-off.

Because the foot is immobile on the perch, upward and forward translations of the trunk are the result of the flexion-extension of the leg joints: the trunk is pitching upwards as the hip extends. More generally, the entire lower limb is extended, mainly due to the extension of the ankle, hip, and to a lesser extent of the knee (Table 1). It is true for both species of birds, although the timing of motions slightly differs. In Diamond Dove, the beginning of hindlimb joint extension is not synchronous, starting with the hip, followed by the ankle and finally by the knee, whereas in Zebra Finch, the extension of the three joints is synchronous. Only tendinous parts of muscles cross the ankle in birds [START_REF] Baumel | Handbook of avian anatomy: nomina anatomica avium Publications of the Nuttall Ornithological Club (USA)[END_REF] which are known to contribute to mechanical energy storage and recovery. This has been demonstrated during running [START_REF] Alexander | Elastic Mechanisms in Animal Movement[END_REF][START_REF] Alexander | Elastic energy stores in running vertebrates[END_REF][START_REF] Cavagna | Mechanical work in running[END_REF]) and can easily be applied to take-off, especially given the previous assertions regarding crouching movement and the probable loading of muscles in Diamond Dove. Such a system is energetically efficient, as this passive mechanism contributes to decrease both muscular work and metabolic cost [START_REF] Roberts | The integrated function of muscles and tendons during locomotion Comparative Biochemistry and Physiology Part A[END_REF][START_REF] Roberts | Contribution of elastic tissues to the mechanics and energetics of muscle function during movement[END_REF]. Overall, during this first phase of take-off, the trunk and the hindlimb segments can be seen as a spring [START_REF] Henry | Performance of guinea fowl Numida meleagris during jumping requires storage and release of elastic energy[END_REF]. Incidentally, bioinspired jumping robots often use a spring to copy a biological leg structure, because it produces good jumping performances [START_REF] Zhang | A Survey of Bioinspired Jumping Robot: Takeoff, Air Posture Adjustment, and Landing Buffer Applied Bionics and Biomechanics[END_REF] as it is a simple structure with a strong energy storage capacity and a potential of fast energy release. Take-off is a transition between a static state to a dynamic state, and in contrast to terrestrial locomotion, inertial forces do not contribute to the propulsion. All the motions of the centre of mass are generated by the leg muscles, especially the thigh muscles, which are the main part of the leg musculature [START_REF] Baumel | Myology In: Handbook of avian anatomy: nomina anatomica avium[END_REF]. The first leg joint extended during take-off is the hip, demonstrating that thigh muscles primarily move the trunk. During take-off from a perch, all of the leg joints are flexing during crouching and then, all the joints are extending during the propulsion. These similar and successive motions of all the leg joints contribute to the propulsion of the centre of mass because the feet are immobile on the perch. This situation is different in other locomotor conditions, which are cyclic, with dissimilar joint motions within the legs, and highly mobile feet. During bird bipedal locomotion, depending on the propulsion mechanics, the thigh musculature can have different functions. During take-off, the thighs mainly move the trunk, participating to the propulsion of the centre of mass. During walking, they move the trunk to guide the centre of mass path [START_REF] Abourachid | Bird terrestrial locomotion as revealed by 3D kinematics[END_REF]. During paddling, the thighs stabilize the hip (Provini et al. 2012a). During running, which is a bouncing mechanics [START_REF] Hancock | Whole-body mechanics and kinematics of terrestrial locomotion in the Elegant-crested Tinamou Eudromia elegans[END_REF]) the thighs participate to the increase of the stride length [START_REF] Gatesy | Guineafowl hind limb function. I: Cineradiographic analysis and speed effects[END_REF]). If we consider the leg joints participation, during take-off, knee extension is the lowest among leg joints whereas during the propulsive phase of terrestrial locomotion, knee extension is high at low as well as high speeds [START_REF] Gatesy | Guineafowl hind limb function. I: Cineradiographic analysis and speed effects[END_REF]. During takeoff, the ankle extension magnitude is twice as high as the hip and knee extensions. The ankle is supporting the animal forward motion, similarly to what is observed in semi-aquatic birds, during paddling, where the tarsometatarsus associated with the webbed-foot displays a high amplitude of motions and plays the role of the paddle, responsible for most of the propulsion (Provini et al. 2012a). Therefore, depending on the locomotion mode, the function of the joints changes, participating to the versatility of the avian body plan.

Our 3D kinematics analysis revealed the importance of studying the entire body and not only the limbs of the animal while studying locomotion. In that sense, a detailed kinematics analysis of the forelimbs motion would be helpful to understand take-off completely. Another key moment in bird flight is landing, where forces are also transmitted between the substrate and the rest of the body through the hindlimbs, it would be interesting to compare the kinematics of take-off with the one of landing in the same species of birds, also with a whole body approach.

Figure legends

Fig. 1 Fig. 2

 12 Fig. 1 Experimental protocol sketch, showing the orientation of the two X-ray sources and the two light cameras. Examples of the pictures recorded, with rotoscoped 3D model of a Diamond Dove are shown for each source of data

Fig. 3

 3 Fig. 3 Plots of translations (a, c) along the antero-posterior (red), left-right (green), and ventro-dorsal (blue) axes, and roll (red), pitch (green), and yaw (blue) rotations (b, d) of the head and trunk in Diamond Dove and Zebra Finch. In each plot, means calculated at each time step are represented with a solid line, the envelop represents standard deviation, for

Concord field station, especially A Biewener for accommodation and equipment access as well as his remarks on the draft of the manuscript. Thanks to Ivo Ross for his help with the CT-scans acquisition at the Harvard facilities. This research was supported by grants from the UMR 7179, l'Action Transversale du Muséum National d'Histoire Naturelle formes possibles, formes réalisées and from Ecole Doctorale Frontières du Vivant and Bettencourt-Schueller foundation fellowships. Travels were paid by the UMR 7179.

Diamond Dove (n=4) on the left and Zebra Finch (n=4) on the right. Note that the values are not absolute as the data have been adjusted to in each trial in order to be averaged (see Material and Methods section for further details). The orientation and direction of the motions are represented on the drawings of the head and trunk, with a coloured arrow for translations and a black arrow for rotations. In each plot, means calculated at each time step are represented with a solid line, the envelop represents standard deviation, for Diamond Dove (n=4) on the left and Zebra Finch (n=4) on the right. Note that the values are not absolute as the data have been adjusted to in each trial in order to be averaged (see Material and Methods section for further details). The orientation and direction of the motions are represented with a black arrow on the drawings of the axes located on the femur, tibiotarsus and tarsometatarsus, the proximal bone of the joint is represented with a semi-transparent model whereas the distal bone is represented with an opaque model.