Judit Marigó
email: judit.marigo@icp.cat

Nicole Verrière

Marc Godinot

Systematic and locomotor diversification of the Adapis group (Primates, Adapiformes) in the late Eocene of the Quercy (Southwest France) revealed by humeral remains

Keywords: Adapis, humeri, Quercy, locomotion, active arboreal quadrupedalism, climbing adaptations

Twenty humeral specimens from the old and new Quercy collections attributed to the fossil primates Adapis and Palaeolemur are described and analysed together. We 2 provide a qualitative and quantitative analysis of the different humeri, revealing that high variability is present within the "Adapis group" sample. Six different morphotypes are identified, confirming that what has often been called "Adapis parisiensis" is a mix of different species that present different locomotor adaptations. Such a relatively high level of locomotor diversity is unique in the Paleogene primate fossil record.

The humeral proportions of Adapis overlap with different groups of extant strepsirrhines and platyrrhines depending on the specimen, so the popular view of Adapis as a lorislike slow climbing primate does not apply to the whole sample presented here.

Moreover, different humeral features traditionally associated with "Adapis parisiensis", such as the absence of a zona conoidea and a reduced brachioradialis flange, are variable depending on the sample studied. In addition, results of our analyses show that adapine and omomyid humeral morphology overlap extensively, leading us to question the accuracy of taxonomic attributions based on morphology of isolated humeri at localities where omomyids and adapines of similar size coexist.

Finally, assuming our different morphotypes represent different species within two genera, we propose a phylogenetic hypothesis relating these morphotypes, which inhabited a small geographic area.

Introduction

Dental, cranial, and postcranial remains of the Eocene European primate Adapis were found at the end of the nineteenth century, during the exploitation of phosphatic deposits in the Quercy region, south-west France. It was evident to early researchers that several species were represented in these "old Quercy collections", represented by material found in hundreds of fissure-fillings spread in the region (now dated from the Middle Eocene to the late Oligocene). The old Quercy collections lack the information of provenance of the fossils, and they represent numerous faunas coming from hundreds of fissures [START_REF] Legendre | Les phosphorites du Quercy: 30 ans de recherche. Bilan et perspectives[END_REF]. However, since 1965, different teams from Paris, Poitiers and Montpellier have organized field campaigns in the area and discovered new fossils in well-identified karstic fillings, which are called "new Quercy collections".

Among them are the localities of Rosières 2 and Escamps, which have yielded Adapis material. The numerous new faunas accumulated in the Quercy have allowed many systematic revisions of vertebrates. Among them, micromammals, especially the abundant rodents, led researchers to propose a series of evolving specific lineages which contributed to the elaboration of a regional biochronological scale. This work was used for the elaboration of the European biochronological scale based on mammals, in which Escamps is the reference fauna of the reference level MP 19. The distinction of several levels in what were earlier considered Ludian faunas (Ludian is the latest Eocene stage in the Paris Basin regional stratigraphy) was adopted following earlier work on Palaeotherium lineages and the new studies of micromammals [START_REF] Legendre | International Symposium on Mammalian Biostratigraphy and Paleoecology of the European Paleogene[END_REF]. Reference faunas were chosen for their richness in both large and micromammals. Complete faunal lists of all known Quercy localities were given in [START_REF] Rémy | Biochronologie des phosphorites du Quercy: Mise à jour des listes fauniques et nouveaux gisements de mammifères fossiles[END_REF]. Rosières 1 to 4 were associated with four other localities as being close to Escamps. Continuous work on Quercy faunas led to the introduction of a new reference level MP 17b between the former MP 17a and MP 18 (BiochroM'97, 1997).

The use of numerical techniques underlined the proximity of MP 19 and MP 20, the last Eocene level preceding the Grande Coupure (Terminal Eocene Event or TEE), and suggested a probable small difference in age between Escamps and the slightly older Rosières 2 [START_REF] Escarguel | Sur l'âge numérique des faunes de mammifères du Paléogène d'Europe occidentale, en particulier celles de l'Eocène inférieur et moyen[END_REF]. Since then, the revision of Quercy bats added to the arguments differentiating MP 18 and MP 19 (likely lineage Cuvierimops parisiensis intermedius -C. p. parisiensis), and also confirmed the identity of bats of several loci within Escamps, which is a large fissure [START_REF] Maitre | Western European middle Eocene to early Oligocene Chiroptera: systematics, phylogeny and palaeoecology based on new material from the Quercy (France)[END_REF]. Updated faunal lists for micromammals, with detailed references to all the original studies, are given by [START_REF] Sigé | Les micromammifères des gisements à phosphate du Quercy (SW France)[END_REF], comments on large mammals are given by [START_REF] Rémy | L'apport des faunes du Quercy à la connaissance des grands mammifères[END_REF], and analyses of community structure and dynamics are given by [START_REF] Escarguel | New methods for analysing deep-time metacommunity dynamics and their application to the Paleogene mammals from the Quercy and Limagne area (Massif Central, France)[END_REF]. The progressive addition of new faunas, new systematic studies, and technical advances, means that Rosières 2 now appears close in age to Escamps, possibly slightly older, and both are placed in the latest Eocene, not far from the TEE.

Adapis species, too often considered as one species "Adapis parisiensis", are adapiform primates known from both cranial and postcranial remains (e.g., [START_REF] Delfortrie | Un Singe de la famille des Lémuriens dans les phosphates de chaux quaternaires du département du Lot[END_REF][START_REF] Filhol | Mémoires sur quelques mammifères fossiles des phosphorites du Quercy[END_REF][START_REF] Filhol | Observations relatives au mémoire de M. Cope intitulé : relation des horizons renfermant des débris d'animaux vertébrés fossiles en Europe et en Amérique[END_REF][START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF][START_REF] Gingerich | Cranial morphology and adaptations in Eocene Adapidae. I. Sexual dimorphism in Adapis magnus and Adapis parisiensis[END_REF][START_REF] Gingerich | Cranial morphology and adaptations in Eocene Adapidae. II. The Cambridge skull of Adapis parisiensis[END_REF][START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF][START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF][START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF][START_REF] Godinot | Morphological diversity in the skulls of large adapines (Primates, Adapiformes) and its systematic implications[END_REF]. [START_REF] Stehlin | Die Säugetiere des schweizerischen Eocäens: critischer Catalog der Materialen. Part 7, first half[END_REF] added two species to the earlier named A. parisiensis and Palaeolemur betillei, as a result of his study of well-preserved crania. Large-sized adapines have been recently revised [START_REF] Godinot | Morphological diversity in the skulls of large adapines (Primates, Adapiformes) and its systematic implications[END_REF], however the systematics of smaller-sized adapines still needs clarification. At least four species can be distinguished among this group [START_REF] Lanèque | Variation in the shape of the palate in Adapis (Eocene, Adapiformes) compared with living primates[END_REF][START_REF] Lanèque | Variation of orbital features in adapine skulls[END_REF][START_REF] Godinot | A summary of adapiform systematics and phylogeny[END_REF] based on cranio-dental remains from the old Quercy collections. It has proven difficult until now to integrate this systematic arrangement with the discoveries made more recently in well-identified localities because the latter are represented by fragmentary remains (no crania found so far) and adapine dentitions are quite uniform in morphology (Godinot, 1998, pers. obs.).

In the work that follows, the group of species of close size and morphology will be referred to informally as the "Adapis group". Postcranials have been ascribed to the Adapis group since [START_REF] Filhol | Observations relatives au mémoire de M. Cope intitulé : relation des horizons renfermant des débris d'animaux vertébrés fossiles en Europe et en Amérique[END_REF] and [START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF]. More material coming from the old collections was studied by [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] and [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF]. This material is often referred to "A. parisiensis", however such a referral is misleading, because there are many species represented in the Adapis group [START_REF] Lanèque | Variation in the shape of the palate in Adapis (Eocene, Adapiformes) compared with living primates[END_REF][START_REF] Lanèque | Variation of orbital features in adapine skulls[END_REF][START_REF] Godinot | A summary of adapiform systematics and phylogeny[END_REF] and no one knows if the species A. parisiensis, described in the Paris Basin, was really present in the Quercy or not. Adapis has traditionally been interpreted as an arboreal quadruped with slow climbing adaptations and not a frequent leaper, based on noted postcranial similarities to lorises. This loris-like slow climbing mode of locomotion for Adapis was proposed by [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF] due to several features of the humerus such as the rounded humeral head that faces posteriorly, projecting proximal to the tuberosities, the broad and shallow bicipital groove, the thick deltopectoral crest, the well-marked and distally extensive tuberosity of teres major, the very large brachioradialis flange extending proximally on the shaft, the absence of a distinct ridge on the lateral side of the trochlea and the absence of a distinct groove between the trochlea and the capitulum. Some of these features were also noted by [START_REF] Filhol | Mémoires sur quelques mammifères fossiles des phosphorites du Quercy[END_REF][START_REF] Filhol | Observations relatives au mémoire de M. Cope intitulé : relation des horizons renfermant des débris d'animaux vertébrés fossiles en Europe et en Amérique[END_REF] as well as by [START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF]. However, some authors have suggested a more "monkey-like" (i.e., pronograde arboreal quadruped) mode of locomotion for it [START_REF] Godinot | La main d'Adapis (Primate, Adapide)[END_REF][START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF][START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF].

Postcranials from both old and new Quercy collections have been attributed to Adapis.

When the new collections were recovered, researchers preserved information on the local fissure for each bone. Furthermore, they processed sediments using screenwashing techniques, yielding more small postcranials than in the nineteenth century collections. Thanks to this, [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF] could compare closely the morphology of two Adapis species coming from two distinct localities. One species from Rosières 2 appeared more quadrupedal and fast-moving, and the species from Escamps had traits that suggested adaptations to climbing. A later study of femora and tibiae from both old and new Quercy collections revealed that five different morphotypes could be distinguished among the Adapis group femora, two of them being present at Rosières 2, suggesting that an episode of locomotor diversification probably occurred in the Adapis group [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF]. Field work in the Quercy continues, as well as identification of specimens in the old collections, which are present in many institutions.

Further study of the dental material from Rosières 2 indicated that at least two species of Adapis were present in that locality, confirming the interpretation of the femora, and providing a new perspective on the high morphological variability found earlier, especially of the cuboid facet of Adapis calcanei of Rosières 2 and Escamps [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF]. It also explained the variability in the humeri found in the same locality.

Here we present the study of several already-known and as yet undescribed humeral specimens attributed to Adapis from old Quercy collections stored in several museums, as well as specimens from new Quercy collections with a precise locality of origin. As stated above, some Adapis humeri have been previously described and figured by Filhol (1883), [START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF], [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF], [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF] and [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF], but the whole sample has never been studied together. Only three complete humeri, one proximal end and seven distal ends were available to [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF], five more distal ends were added by [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF], whereas now the total sample is up to 20 fossil remains.

Prosimian humeri of similar age are not very common in the fossil record. Concerning adapiforms, the only humeri known besides those of Adapis are those of Notharctus [START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF], Leptadapis [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF], Europolemur [START_REF] Franzen | Ein neuer Primate aus dem Mitteleozän der Grube Messel (Deutschland, S-Hessen)[END_REF], Protoadapis [START_REF] Godinot | Early North African primates and their significance for the origin of Simiiformes (= Anthropoidea)[END_REF], Pronycticebus [START_REF] Thalmann | Die Primaten aus dem eozäen Geiseltal bei Halle/Saale (Deutschland)[END_REF], Cantius [START_REF] Gebo | Humeral morphology of Cantius, an early Eocene adapid[END_REF], Adapoides [START_REF] Gebo | New primate hind limb elements from the middle Eocene of China[END_REF], Smilodectes [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF], Darwinius [START_REF] Franzen | Complete primate skeleton from the Middle Eocene of Messel in Germany: Morphology and Paleobiology[END_REF], and asiadapids [START_REF] Rose | Early Eocene primates from Gujarat, India[END_REF][START_REF] Dunn | New euprimate postcrania from the early Eocene of Gujarat, India, and the strepsirrhinehaplorhine divergence[END_REF].

Regarding omomyiforms, those of Shoshonius [START_REF] Dagosto | Revision of the Wind River faunas, early Eocene of central Wyoming. Part 14. Postcranium of Shoshonius cooperi (Mammalia: Primates)[END_REF], Necrolemur and Microchoerus [START_REF] Dagosto | Postcranial anatomy and locomotor behavior in Eocene primates[END_REF], Omomys [START_REF] Anemone | New skeletal remains of Omomys (Primates, Omomyidae): functional morphology of the hindlimb and locomotor behavior of a Middle Eocene primate[END_REF], Hemiacodon [START_REF] Dagosto | Postcranial anatomy and locomotor behavior in Eocene primates[END_REF] and Absarokius [START_REF] Covert | Description of the new skeletal remains of the early Eocene anaptomorphine primate Absarokius (Omomyidae) and a discussion about its adaptive profile[END_REF] are known. Moreover, early anthropoids of late Eocene age are also known from Egypt [START_REF] Seiffert | Anthropoid humeri from the late Eocene of Egypt[END_REF].

The primate humeri attributed to Adapis in the Quercy collections show a great morphological and probably also taxonomic diversity. We hypothesize that these primate humeri display morphological variability that is too great for a single species.

Even though it is not yet possible to make clear systematic attributions, we describe them here as if they belonged to a series of morphotypes and discuss their possible phylogenetic relationships. Regardless of the number of species, we test the hypothesis that a loris-like slow-climbing morphology best fits these bones by analyzing measurements of features known to provide information on locomotor behavior. Such analysis could decipher the locomotor signal present in these humeri and tangentially support the suggestion of multiple species if variation in the fossil sample overlaps that of more than one locomotor group.

Material and methods

Studied sample

A total of 20 primate humeri have been identified from the old (10 specimens) and new (another 10 specimens) Quercy collections. The latter set comes from the localities of Rosières 2 and Escamps (Figs. 123456). Three are complete. Six are almost complete, only lacking the humeral head and/or a small part of the distal epiphysis. Three are proximal parts. Eight of them are distal parts. A complete list of all the specimens included in this paper can be found in Table 1. Vidalenc (Vi, presently loaned to the MNHN in Paris, this collection will remain available for study).

3D surface reconstructions

Most of the specimens studied herein were scanned from the original fossil using a Breuckmann 3D surface scanner available at the "Plateau de morphométrie Outils et Méthodes de la Systématique Intégrative, OMSI -UMS 2700 CNRS MNHN" of the Muséum national d'Histoire naturelle (MNHN, Paris) with a medium lens. This surface scanner allows the acquisition of the 3D surface of the bone at high resolution using white light fringes (StereoSCAN 3D model with a camera resolution of five megapixels).

The specimens Ma-PhQ-330, Ma-PhQ-332, NMB-QW-1481 and AMNH-FM-10018 were scanned with the same scanner but this time using high quality casts instead of the originals. Ma-PhQ-331 and Ma-PhQ-333 were not scanned but measured and photographed at the MNHN in Paris.

All 3D surface reconstructions are available in the online repositories MorphoSource (www.morphosource.org) and/or MorphoMuseuM (www.morphomuseum.com;[START_REF] Marigó | 3D models related to the publication: Systematic and locomotor diversification of the Adapis group (Primates, Adapiformes) in the late Eocene of the Quercy (Southwest France), revealed by humeral remains[END_REF]. See Table 2 for information about 3D surface reconstructions, accessibility and citation instructions.

Nomenclature and measurements

The anatomical terms used in the descriptions are illustrated in Figure 7. The measurements taken are illustrated in Figure 8. Measurements were taken on the actual bone when possible, using a digital caliper Electro DH (model 60.205), with a resolution of 0.01 mm. When not possible, they were taken on the 3D reconstruction using the 2D and 3D tools of the program Avizo (Visualization Sciences Group, 2009).

All measurements and indices taken can be found in Table 3. Measurements follow [START_REF] Ford | Postcranial adaptations of the earliest platyrrhine[END_REF], [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] and [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF]. Indices of the proximal ends follow [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF], and those of the distal ends follow [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] and [START_REF] Boyer | New postcrania of Deccanolestes from the Late Cretaceous of India and their bearing on the evolutionary and biogeographic history of euarchontan mammals[END_REF].

Statistical analyses and descriptive indices and plots

Univariate plots of proximal articular surfaces of humeri of extant and extinct primates have been performed and are presented in Figure 9 (following [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF]. [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF] calculated different indices that reflect locomotor behavior among living strepsirrhines taking into account different measurements of the humeral head, and found two that help distinguish between arboreal quadrupeds (AQ) and vertical clingers and leapers (VCL): (1) the index of distal mediolateral width divided by central proximodistal length of the humeral head (Fig. 8, 9A), and (2) the index of the height of the humeral head derived from the distal mediolateral width divided by the distal mediolateral width (Fig. 8,9B).

The Adapis group sample is quite homogeneous regarding humeral head measurements, but it presents a high variation in some measurements of the distal articulation (see Table 3), which suggests that we may be dealing with more than one species in our sample. In order to refute the hypothesis that our entire fossil sample can be treated as a single population, we have performed a series of Levene's tests [START_REF] Levene | Robust tests for equality of variances[END_REF] on all measurements of distal articulations in order to compare variances of two samples at a time. In fact, we have compared the variance present in the Adapis group to the variance in different species of living primates of similar size (Saimiri sciureus, Hapalemur griseus and Perodicticus potto) as well as fossil primate specimens belonging to different genera present in the Indian fossil site of Vastan Mine, the adapiform Marcgodinotius indicus, the omomyiforms Vastanomys gracilis and V. major, as well as at least one other unidentified euprimate from the same site. We collected data on seven S. sciureus, 11 H. griseus, five P. potto, two M. indicus, one V. gracilis, one V. major and four unidentified Vastan euprimate remains (see below for information on comparative sample specimens). All Levene's tests have been performed using Excel, calculating the mean of each of the groups (the Adapis group and the comparison group), and then calculating the absolute value of the difference between each of the original values and the mean value for the group. After these data transformations, a one-way ANOVA has been performed, since its result is equivalent to the result of a Levene's test.

Regarding the distal end of the humerus, [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] found the following two indices to be most informative in distinguishing locomotor behavior: the trochlear articular index (TAI) and trochlear height-width index (THWI). These indices (see results for Adapis in Table 3) have been traditionally used to distinguish between AQ and VCL. We have calculated them for all Adapis specimens and compared them to other primate taxa (see below for information on comparative sample specimens).

Because distal articulation indices were also found to be not very informative (see Results section), we have performed principal components analyses (PCA) of four distal humeral measurements: trochlear width (TW), maximum trochlear height (TH), capitulum width (CW) and entepicondylar width (EEC). These results are presented in Figure 10. See Figure 8 for information on how measurements were taken. Following [START_REF] Boyer | New postcrania of Deccanolestes from the Late Cretaceous of India and their bearing on the evolutionary and biogeographic history of euarchontan mammals[END_REF], measurements were size-standardized using geometric means, then transformed into natural logarithms, and compared among taxa using PCA of the Euclidean distance matrix relating the specimens using the software PAST [START_REF] Hammer | PAST: Paleontological statistics software package for education and data analysis[END_REF].

For a complete list of taxa used as comparative samples for all statistical analyses, indices and plots see Table 4.

Results

Analyses of variance (Levene's tests)

The Adapis group sample is quite homogeneous regarding humeral head measurements (see Table 3), but it shows a significantly higher variance than any of the extant and fossil species to which it has been compared in many measurements of the distal articulation. Indeed, the presence and width of the zona conoidea shows significant (pvalue < 0.05) results when compared to S. sciureus, H. griseus and P. potto. Concerning trochlear height, its variance in the Adapis group is also statistically different from that of S. sciureus and H. griseus, and the total length of the humerus measured from below the humeral head also significantly varies from that of H. griseus (see Table 5).

Moreover, indices concerning the distal articulation also show significantly greater variance than in extant species. For instance, the TAI is significantly greater than in S. sciureus, and the THWI index is significantly greater than in H. griseus. Indeed, the extant specimens employed for the Levene's tests come from different institutions (see Table 4), were collected in different locations and years, and they probably represent different populations of the same species. Thus, significant results provide even stronger support to the conclusion that the Adapis group specimens studied herein represent multiple species.When the same data were compared to the fossil primates recovered from Vastan Mine (India), belonging to at least two different genera and at least four different species, and attributed to adapiforms and omomyids, the results are also striking. We found that trochlear height and width of the zona conoidea were significantly more variable in the Adapis group specimens than in the Vastan primates.

Summary of the main features of each morphotype

Due to the different morphological features found, we grouped the different specimens into six morphotypes. A list of the different morphotypes and specimens included in each one is given in Table 1. A complete table listing all features and specimens can be found in SOM 1. Complete descriptions and comparisons of all the Adapis group humeri studied in this paper arranged depending on morphotype attribution can be found in SOM 2. For anatomical terms used see Figure 7.

Morphotype 1 specimens are characterized by being large and gracile, with a small tubercle of teres major and a shallow bicipital groove, a laterally flaring brachioradialis flange (except for specimen NMB-QW-1481, which has a straight brachioradialis flange). Moreover, morphotype 1 specimens present a deep radial fossa and lack a zona conoidea. Size and morphological differences between the complete humerus ISE-M-ROS-2-95 and NMB-QW-1481 suggest that we place NMB-QW-1481 as aff. sp. 1.

Morphotype 2 specimens are medium to large with a medium robustness. They mainly have, as all other specimens in this study do, a greater tuberosity below the level of the humeral head, except for specimen Ma-PhQ-332 (Adapis cf. sp. 2), which has a greater tuberosity that surpasses the humeral head slightly. They present a small tubercle of teres major and a shallow bicipital groove, a straight or slightly concave brachioradialis flange, a deep radial fossa (except for specimen Ma-PhQ-332, which is allocated to Adapis cf. sp. 2), and present a zona conoidea.

Morphotype 3 specimens are medium to large in size and medium in robustness, and do not have a prominent tubercle of teres major. They present a continuous crest between the latter and the lesser tuberosity, and a deep bicipital groove. At the distal end, morphotype 3 specimens present a straight brachioradialis flange and a deep radial fossa (except for specimen FSM-PQ-1744, attributed to Adapis aff. sp. 3), and no zona conoidea. Moreover, specimen MNHN-Qu-16583 presents the most rounded capitulum and is attributed to Adapis cf. sp. 3).

The only morphotype 4 specimen is characterized by being small and robust, with a prominent tubercle of teres major and a continuous crest present between the latter tubercle and the lesser tuberosity, as well as a deep bicipital groove. At the distal end, it presents a laterally flaring brachioradialis flange.

The only morphotype 5 specimen is very small and medium in robustness, with a prominent tubercle of teres major but no crest connecting it with the lesser tuberosity, and the shallowest bicipital groove of the whole sample studied herein. It is also characterized by a straight (or even slightly concave) brachioradialis flange, a shallow radial fossa and the lack of a zona conoidea.

Morphotype 6 specimens are large or medium-large in size and medium to gracile in robustness. The prominence of their tubercle of teres major varies, but they all present a continuous crest between that tubercle and the lesser tuberosity. Their bicipital grooves are all medium to deep. Their distal ends present a laterally flaring brachioradialis flange, a shallow radial fossa and the presence of a zona conoidea or at least a lateral lip marking the lateral end of the trochlea. [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF] to reflect locomotor behavior among living strepsirrhines, taking into account different measurements of the humeral head, have been calculated for those Adapis specimens that preserve their proximal epiphyses (Table 3, Fig. 9). See discussion of Figure 9 below with reference to abbreviations for behavioral categories. We can see that in both graphs (Fig. 9) Adapis specimens overlap with different species of arboreal quadrupeds (AQ) and vertical clingers and leapers (VCL), although we can see some variation in the different specimens. The mean of all Adapis specimens for the index of distal mediolateral width divided by central proximodistal length of the humeral head (Fig. 9A) is equal to that of the specimen MNHN-Qu-16584. However, the mean of all Adapis specimens for the index of height of the humeral head derived from the distal mediolateral width divided by the distal mediolateral width (Fig. 9B) does not overlap with any of the specimens available. Figure 9A shows how VCLs have a narrower articular surface on the distal third of the humeral head than AQs. Some Adapis specimens are closer to the VCL means in this plot, suggesting a narrowing on the distal third of the humeral head in these specimens. However, the specimen ISE-M-ROS-2-80 is closer to the AQ, suggesting a wider distal third of the humeral head in this specimen. The range of Adapis in this case is similar to those of Notharctus and Smilodectes, and mean and standard deviation in the Adapis sample are below those of Notharctus and Smilodectes, and further below those of Cantius. If we were interpreting these numbers in comparison with the living strepsirrhine AQs and VCLs, we would have to conclude that species of the Adapis group were more specialized leapers than notharctines, in complete opposition with limb proportions or distal femur morphology, which clearly show the absence of leaping specialization in the Adapis group [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF]. To increase our understanding of these ratios, we calculated them in platyrrhines showing different kinds of locomotor adaptations, and also in some lorisids (Fig. 9). Few differences appear among the platyrrhines, and in fact the most contrasted results are between Adapis species and lorisids. It seems that this ratio conveys a strong phylogenetic signal, and is difficult to simply interpret in terms of locomotion. In fact, the range of Adapis specimens overlaps with all locomotor categories in Figure 9A.

Proximal articulation indices The indices found by

This strengthens the assertion that this index (ML/PD values) is minimally useful in distinguishing between locomotor groups.

The other ratio quantified by [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF] among living strepsirrhines (Fig. 9B) shows that VCLs present a higher distal third of the humeral head compared to AQs.

Adapis in this case falls in between AQ and VCL, and its mean is very close to that of Hapalemur griseus. The most "quadrupedal" specimens of Adapis are ISE-M-ROS-2-80 and ISE-M-ROS-2-95, which present a lower distal third of the humeral articular surface than the rest of the specimens. If we compared this index directly between Adapis and notharctines, it would suggest that Adapis species had less leaping tendencies than Notharctus and most Smilodectes, but still clearly more leaping propensities than Cantius species, which is likely not the case. Taking into account our broader sample of living taxa, we can see that all platyrrhines present a quite high distal third of the humeral head (higher than in most VCLs), and much higher than strepsirrhine AQs. We see more variation in this index within platyrrhines, with Ateles, Pithecia, Aotus and Saimiri presenting higher distal thirds of the humeral head than Cebus and particularly Alouatta. Adapis mainly overlaps with Alouatta in this regard, and this might be a real functional signal, as Adapis has been interpreted as a relatively slow moving primate [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF]. It might well have had a deliberate kind of quadrupedalism, as is typical of Alouatta. Here again, a noticeable fact is that Adapis species appear far away from living lorisids, suggesting that the interpretation of them as slow climbers [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF] has to be corrected in favor of a less specialized kind of quadrupedalism [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF]. However, these conclusions have to be considered provisional, as it is again clear that this ratio also includes a strong phylogenetic signal.

It is in fact remarkable how different strepsirrhine AQs are from platyrrhine AQs, suggesting that platyrrhines do not share the same adaptations as strepsirrhines concerning humeral head shape associated with locomotor behavior, or that it is inappropriate (from a mechanical and behavioral perspective) to consider strepsirrhine AQs as equivalent to platyrrhines. That is, they inhabit very different environments that likely put different locomotor pressures on them. This same pattern has also been seen in other bones such as the calcaneus and the femur [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF].

Distal articulation indices

The trochlear articular index (TAI) is generally high in arboreal quadrupeds (AQs) and low in vertical clingers and leapers (VCLs). Contrarily, the trochlear height-width index (THWI) is usually high in VCLs and low in AQs [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF]. The results for different Adapis humeri when these indices are calculated for each of them are listed in Table 3, together with the definition of these indices. The values that represent the different specimens are strikingly different (see Table 3 andSOM 3).

The TAI indicates the relative portion of the articular width occupied by the trochlea in anterior view. Most of the Adapis specimens studied here are close to the 40% that [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] calculated for adapiforms. However, the specimen FSM-PQ-1744 falls far above the 40%, indicating the presence of a proportionally wider trochlea, which makes it fall closer to microchoerine omomyids, and also close to Eulemur mongoz and Lemur catta. We must note that the indices provided by [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] are not exactly the same as the ones we obtained for the same specimens, NMB-QW-1481 and AMNH-FM-10018 (specimen that the former authors mistakenly called AMNH-FM-81001). [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] mentioned in their work the difficulty of replicating accurately some of these measurements.

The THWI indicates the relationship between the height and width of the anterior side of the trochlea. In extant quadrupedal primates, the trochlea is wider than high as in most Adapis specimens (index less than 100). Hovewer, extant VCL taxa present an index higher than 100 because of the secondarily shortened trochlea and/or the increase of joint surface area on the anterior side of the humerus [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF].

Only one of the specimens studied presents an index much higher than the other specimens and closer to 100 (Vi-Esc--839). This specimen presents an anterior side of the trochlea that is closer in height to the capitulum, whereas for the rest of the Adapis group sample studied here the trochlea is always much lower than the capitulum in height. The only other specimen from the same site (ISE-M-ECA-1364) is missing the capitulum, but the trochlea, even if not as high as in Vi-Esc--839, still appears higher than in other Adapis group specimens. The variability found in the Adapis group for this index clearly surpasses that found in extant Hapalemur griseus (see Table 5). Moreover, taking into account that trochlear height is one of the variables for which we also obtained significant results of extremely high variance in the Adapis group, this supports the idea that these specimens probably represent a different species (our morphotype 3).

In addition, if we look at the values obtained for the different morphotypes, they vary within each morphotype. Within morphotype 3, FSM-PQ-1744 has peculiar values.

Principal componentsaAnalysis

The results of the PCA of some distal humeral measurements can be found in Figure 10.

There is no overlap of the Adapis fossils with Plesiadapidae, Lorisidae and Tarsiidae (Fig. 10A). In Figure 10B we show the results of the same analysis only including fossil forms as well as extant strepsirrhines and tarsiers. However, we can see that the results from both analyses are not very different in terms of overlapping morphospace.

PC1 is mainly driven by increasing entepicondylar width (EEC), and PC2 is mainly driven by increasing trochlear height (TH) and decreasing trochlear width (TW). In both plots, a number of Adapis group specimens overlap with omomyids and especially microchoerines, and, depending on the specimen, overlap with extant strepsirrhines and/or platyrrhines. The large area covered by the Adapis group is again a testimony of its unusual morphological diversity when compared to extant groups.

Of the 15 Adapis group specimens available, seven clearly overlap with proportions circumscribed by omomyids and none of them overlaps with plesiadapiforms.

Moreover, there is no overlap between Adapis group specimens and lorisids whatsoever regarding distal humeral morphospace (Figure 10A Regarding Vastan primates, at least four different species have been identified (see [START_REF] Rose | Early Eocene primates from Gujarat, India[END_REF][START_REF] Dunn | New euprimate postcrania from the early Eocene of Gujarat, India, and the strepsirrhinehaplorhine divergence[END_REF]. One form, attributed to an unknown euprimate, is represented here by specimens GU 713, GU 765 andGU The former overlaps with Galagidae in morphospace, and the latter overlaps with Atelinae and falls in between the morphospace occupied by Plesiadapidae and Tarsiidae. On the other hand, the specimens attributed to the omomyid Vastanomys (GU 764 and GU 1692) overlap with Omomyidae, but both fall very close to the morphospace occupied by the Adapis group, the former also falling very close to Lepilemur mustelinus, and the latter specimen (V. major) also falling very close to the Adapis group specimen MNHN-Qu-16583 (morphotype 3).

To summarize, Adapis group specimens show a great variability concerning distal epiphyseal measurements, overlapping with many primate groups, including platyrrhines. Some specimens overlap mostly with omomyids, again suggesting that differences between adapiforms and omomyiforms are not so clear regarding distal humeral proportions.

Discussion

Number of species

From the morphological variation present in the Adapis humeri studied in this work, we have concluded that sixdifferent morphotypes, probably corresponding to at least six different species, are present. A summary of the different morphotypes observed and the specimens attributed to each one is presented in Table 1. In SOM 1, we provide a summary of the different features observed in every specimen studied, while complete descriptions can be found in SOM 2.

As seen in the statistical analyses used, some features of the distal articulations of the Adapis group present higher variance than in extant species of similar size, as well as the same variance as adapiforms and omomyids found in the same fossil site (Vastan Mine) in India (Table 5). The differences in length and overall proportions of the different humeri, the width (presence or absence) of the zona conoidea and trochlear height in the sample studied confirm that more than one species (and probably more than one genus) is present in our sample.

Functional morphology and locomotor behavior

The humeral shafts of all the Adapis group humeri are retroflexed, with the humeral heads more posterior than the shaft and the humeral heads are flattened posteriorly, as happens in generalized arboreal quadrupedal primates [START_REF] Gebo | Primate Comparative Anatomy[END_REF]. The greater tubercle is generally slightly lower than the humeral head except for one specimen (Ma-PhQ-332), which presents a greater tubercle slightly above the humeral head, which happens in lemurs, most platyrrhines and some colobines [START_REF] Gebo | Primate Comparative Anatomy[END_REF]. In this regard, the Adapis group humeri appear similar to living active arboreal quadrupeds, which present humeral tuberosities of roughly the same height as the humeral head [START_REF] Jolly | The evolution of the baboons[END_REF][START_REF] Gebo | A hominoid proximal humerus from the Early Miocene of Rusinga Island, Kenya[END_REF][START_REF] Rose | Another look at the anthropoid elbow[END_REF][START_REF] Harrison | New postcranial remains of Victoriapithecus from the middle Miocene of Kenya[END_REF][START_REF] Kay | A synopsis of the phylogeny and paleobiology of Amphipithecidae, South Asian middle and late Eocene primates[END_REF].

As previously discussed, all the humeral heads in the sample present similar proportions of the whole head and the articular surface area, with all specimens having similar length and width measurements of the head, and all specimens presenting a slightly longer than wide humeral head. Ma-PhQ-332 (the specimen with the highest greater tuberosity) is also the specimen with the longest humeral head relative to width. Even though no significant features are found regarding the proximal articulation that could indicate important differences in locomotor behavior, our measurements indicate a generalized type of locomotion, with no specific specialization for vertical clinging or leaping or slow climbing (Figures 6A and6B). In fact, the humeral heads of the Adapis group specimens do not present the strikingly rounded humeral head of lorisids (see Figure 11).

On the contrary, the distal ends of the humeri of the Adapis group specimens studied herein present significant differences depending on the different morphotypes discussed, especially in some features such as the development of the brachioradialis flange, the height of the trochlea, and the presence of a zona conoidea.

The striking variability we find in the development of the brachioradialis flange of the different Adapis specimens could indicate differences in locomotor behavior [START_REF] Fabre | Functional associations between support use and forelimb shape in strepsirrhines and their relevance to inferring locomotor behavior in early primates[END_REF]. Adapiforms usually present an extensive development of the brachioradialis flange [START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF][START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF][START_REF] Gebo | Primate Comparative Anatomy[END_REF], which has been interpreted as being an indicator of better-developed arm muscles when compared to those of extant strepsirrhines. The rounded brachioradialis flange offers a large attachment surface for the muscles brachioradialis, brachialis and triceps brachii [START_REF] Jouffroy | La musculature des membres chez les lémuriens de Madagascar. Étude descriptive et comparative[END_REF]. Thus, we could hypothesize that those Adapis presenting more laterally expanded brachioradialis flanges must possess larger flexion and extension muscles in the elbow joint, resulting in more powerful flexion and extension of the forearm. The triceps muscle (extensor of the elbow joint) is essential for climbing on highly inclined supports, and brachialis and brachioradialis muscles are the main flexors of the forearm and used in fast flexions of the forearm, as well as slow flexions against resistance, no matter the position of the hand [START_REF] Basmajian | Integrated actions and functions of the chief flexors of the elbow[END_REF]. This could indicate that those specimens presenting larger brachioradialis flanges (especially morphotypes 4 and 6) present some vertical climbing component in their locomotion. to Varecia or Lemur. The effects of having larger, smaller, straighter or more curved brachioradialis flanges are not clear and should be further explored. A well developed brachioradialis flange, however, is also present in plesiadapiforms, omomyids (see Figure 11) and microchoerids [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF]. This broad distribution has led to the idea that a large crest is primitive for primates. Since a flexed position of the forelimb is primitive for mammals [START_REF] Jenkins | Limb posture and locomotion in the Virginia opossum (Didelphis marsupialis) and in other non-cursorial mammals[END_REF], this flange tends to decrease in development in many primates as the forelimb becomes less habitually flexed. A long brachioradialis flange is no doubt linked to a position with flexed limbs during locomotion.

The Adapis specimens described in this work have different degrees of development of the brachioradialis flange. However, they never reach the exceptional development observed in Leptadapis [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF]; see Figure 11). A proximally extensive brachioradialis flange has been discussed to be more typical of adapoids than omomyids [START_REF] Gregory | On the structure and relations of Notharctus, an American Eocene primate[END_REF][START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF]. However, some microchoerines present highly developed flanges [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF].

Traditionally, the humerus of Adapis has been considered to present a quite reduced brachioradialis flange and no zona conoidea on its distal end, based on a single specimen attributed to A. parisiensis [START_REF] Gebo | Primate humeral remains from the middle Eocene of China[END_REF]. [START_REF] Szalay | Evolutionary History of the Primates[END_REF] suggested that the development of the brachioradialis flange in Adapis was quite small and that it approached the reduced condition seen in most platyrrhines. However, we see in the sample analyzed here that this is not always the case. We see several specimens with relatively large brachioradialis flanges (ISE-M-ROS-2-95, MNHN-ACQ-262, MNHN-Qu-16584, Ma-PhQ-331, Ma-PhQ-333, ISE-M-ROS-2-534: morphotypes 1, 2, 4 and 6), and we also see specimens that present a clear separation between the trochlea and the capitulum (Ma-PhQ-332, Ma-PhQ-330, ISE-M-ROS-2-79, Vi-Ros-640: morphotypes 2 and 6). All these specimens do not fall in the "traditional" Adapis morphotype and in fact show a remarkable diversity of morphologies within the Adapis group.

The entepicondylar foramen is a primitive feature found in primitive mammals that serves as a passage for the median nerve and the brachial artery when it is present [START_REF] Landry | The function of the entepicondylar foramen in mammals[END_REF]. It can be found in many fossil primates as well as most living prosimians, some platyrrhines, and is exceptionally present in Homo [START_REF] Ankel-Simons | Primate Anatomy: An Introduction[END_REF]. Variation in the size and shape of this foramen within the same species is sometimes observed [START_REF] Landry | The function of the entepicondylar foramen in mammals[END_REF], however the differences found among Adapis specimens are quite large and could well convey a phylogenetic signal: the very large entepicondylar foramen of AMNH-FM-10018 could indicate that our morphotype 5 is more primitive than the others; and conversely, the very small entepicondylar foramen of MNHN-ACQ-262, which is in a state of advanced reduction, may well indicate an advanced evolutionary stage for our morphotype 4. ISE-M-ECA-1364 also has a small entepicondylar foramen possibly indicating an ongoing reduction of the foramen in the Escamps species (morphotype 3).

Our morphotype 3 specimens also present the tallest trochleas (relative to width). Moreover, our Levene's test results support the idea that such differences in trochlear height in the different Adapis group specimens is higher than in extant species of similar size and higher than those seen in Vastan Mine primates attributed to different genera.

The same is true in some cases for the THWI index. Specifically, specimen Vi-Esc-839 presents an anterior side of the trochlea that is closer in height to the capitulum, whereas for the rest of the Adapis sample studied here the trochlea is always much lower than the capitulum in height. The only other specimen from the same site (ISE-M-ECA-1364) is missing the capitulum, but the trochlea, even if not as high as in Esc 839, still appears higher than in the other Adapis specimens. We interpret the high trochlea as a derived trait that must have appeared in one Adapis lineage. Smilodectes (an adapiform inferred as a VCL) and other VCLs also present particularly high THWI indices, however VCL seems extremely unlikely in the Escamps species. Among the tarsals of the Escamps Adapis described by [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF], the astragali with a very flat trochlea clearly indicate a mobile upper ankle joint, and one tibia and several femora from Escamps studied by [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF] also reflect a high mobility at the level of hip, knee and ankle joints. In this context, the high THWI index of these specimens is to be compared to the high index of lorisids, indicating the frequent use of highly flexed forearms in the context of a climbing adaptation.

Our results for distal articulation indices present values for Adapis group specimens that are closer to those obtained for omomyids than for lorises. This suggests that these values are indicating a generalized quadrupedalism behavior, which contrasts not only with VCL but also with the locomotion of living lorisids. Moreover, no specimens of the Adapis group present the relative increase in size of the capitulum typical of lorisids [START_REF] Gebo | Primate humeral remains from the middle Eocene of China[END_REF]Figure 11).

The high variability shown in these indices in the different Adapis group specimens present within the sample studied here strongly agree with the idea that several species must be represented within this sample, or even several genera, if we take into account that no differences in variance were found between the specimens attributed to the Adapis group and Vastan Mine primates which belong to at least four species of both adapiforms and omomyids. From the study of femora and tibiae, [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF] distinguished five locomotor types probably reflecting at least five species, and suggested that probably two genera (Adapis and Palaeolemur) were present. From the humeri, we can see even more diversity, with six morphotypes, and our morphotype 6 being quite heterogeneous and probably representing more than one species. Despite this variability, the relatively low THWI found for most of the Adapis group specimens makes them similar to living arboreal quadrupeds routinely using moderately flexed forearms, and emphatically different from VCL and slow climbers which frequently strongly flex their forearms.

The three specimens that have both the proximal articular surface and the distal articular surface preserved (MNHN-Qu-16584, ISE-M-ROS-2-95 and Ma-PhQ-332), present similar proportions of the humeral head, presenting a similar width of the distal third of the humeral head (Figure 9A). The heights of the distal third of the humeral head are different, but all are within the range of Hapalemur griseus (Figure 9B), ISE-M-ROS-2-95 being the specimen with the lowest distal third of the humeral head, and MNHN-Qu-16584 one of the Adapis specimens with the highest distal third of the humeral head.

Ma-PhQ-332 is very close to the mean for Adapis. These results could indicate that MNHN-Qu-16584 is a little more leaping specialized than the rest of the specimens represented by proximal articular surfaces, since a higher head has been associated with a stronger leaping component [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF]. However, VCLs also present a narrow head and this specimen does not have the narrowest humeral head of the whole Adapis sample (see Figure 9).

Regarding distal articulation proportions, our PCA results show that two out of these three specimens (MNHN-Qu-16584 and Ma-PhQ-332) overlap with omomyids (Fig. 10), suggesting that omomyids and adapiforms were not very different in distal humeral proportions. Moreover, our results of the Levene's tests comparing the Adapis group with Vastan Mine primates also confirm this hypothesis. On the other hand, Ma-PhQ-332 falls very close to Otolemur crassicaudatus. The morphospace occupied by the Callitrichinae regarding distal humeral proportions falls right in the middle of the Adapis morphospace. This could suggest that some galagids as well as some platyrrhines might be a better model for understanding distal humeral morphology of the extinct Adapis rather than lorisids.

In summary, our PCA results again make it evident that distal humeral proportions of strepsirrhines and haplorhines had many things in common in early forms, and that telling them apart is not as easy as previously thought. In any case our study has two clear conclusions. First it confirms the extraordinary morphological diversity found within the Adapis group. Second, despite the partial overlap of the group with many strepsirrhines and omomyids, the absence of overlap with lorisids is important, suggesting that species of the Adapis group may not have shared the specializations of living lorisids.

Hypotheses of phylogenetic relationships and functional interpretations

Before exploring the possible phylogenetic relationships of the different morphotypes, it is important to recall what the general "Adapis pattern" may be. Earlier studies found that these species have no characters recalling living VCLs [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF][START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF][START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF]. They have no lengthening of the hindlimb, no leaping characters on the distal femur or on the tarsals. This is confirmed by the general appearance of their humeri. Placed side to side with a humerus of Smilodectes (a Paleogene adapiform inferred to be a VCL; see Figure 11) with a similar shaft size, the latter appears to have a proportionally smaller, narrower and more anteroposteriorly elongated articular head, and also a more proximally salient articular head as in living indriids. The general appearance of these Adapis humeri confirms that VCL is not possible for them. On the other hand, since Dagosta's (1983) study Adapis has often been compared with lorisids, however all indices, proportions, qualitative characters and, especially, multivariate analyses of these humeri have shown that they are distinctly different from our sample of lorisids. The latter have, for example, a strongly proximally salient articular head, linked to their high shoulder mobility, which is not ever present in the Adapis group. Species of Adapis pertain to a broad category of arboreal quadrupeds, some of which may have had relatively deliberate kinds of locomotion, but none of which shared the articular specializations linked to the cryptic adaptation of living slow climbers [START_REF] Godinot | La main d'Adapis (Primate, Adapide)[END_REF][START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF]; in partial accordance with [START_REF] Dagosto | Postcranium of Adapis parisiensis and Leptadapis magnus (Adapiformes, Primates)[END_REF]).

If we try to make sense of the differences found between the different morphotypes, one group is clearly separated from all the others, the group uniting morphotypes 3 and 5.

The humeri of this group differ by a shorter proximal part: whereas in all the others, the deltopectoral crest extends around half way distally along the shaft, MNHN-Qu-16583 and AMNH-FM-10018 have a much shorter deltopectoral crest, giving them a very different profile (Figs. 3 and 5 respectively). Associated with this is a straighter shaft, less anteroposteriorly narrow, and the proximal surface for the unfused articular head suggests that the latter was less posteriorly directed than in the other morphotypes.

Distally, the brachioradialis flange is straight, the medial epicondyle is much less salient both medially and distally than in the other morphotypes, and they possess the most spherical and salient capitulum. Such marked differences suggest that these two morphotypes had a general increased agility in comparison with all the others. Morphotype 3 includes the two Escamps specimens, with Vi-Esc-839 which appeared quite specialized on the PCA diagram. Morphotype 3 was found to present the most features associated with climbing among the five morphotypes, which from the morphology of femora and tibiae were delineated in a spectrum from more quadrupedal to more climbing forms [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF]. Concerning tarsals, the astragali and calcanei from Escamps also indicated a much more mobile foot than in the species from Rosières 2, again suggesting a great agility in climbing in this species [START_REF] Godinot | Toward the locomotion of two contemporaneous Adapis species[END_REF]. The two localities Rosières 2 and Escamps are considered to be latest Eocene, just prior to adapid extinction in Europe, and their different species indicate a diversity of at least three subcontemporaneous species. The species from Escamps, morphotype 3, appears to be the most specialized in terms of agility and climbing among the whole Adapis group. The species from Escamps may be close to Palaeolemur betillei from the old Quercy collections [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF], however this attribution must await confirmation from further dental studies. Given the biochronological context, morphotype 5 is very probably older, and in fact it appears as a likely ancestral form for morphotype 3, with its smaller size and larger entepicondylar foramen. Other small differences between them are less easy to interpret, AMNH-FM-10018 having a more proximally located teres major tubercle, distally a deeper trochlear concavity (ulna better stabilized on the humerus). The shallower olecranon fossa in AMNH-FM-10018, reflecting less forearm extension in this ancestral form, would fit with the hypothesis of an increase in the capacity of forearm extension in the lineage, consistent with the extremes of hindlimb mobility found in the Escamps species.

The other four morphotypes generally show more anteroposteriorly compressed shafts, more posteriorly inclined proximal articular heads, and a combination of more extensive muscular insertions (longer deltopectoral crests and often more salient brachioradialis flanges), more salient medial epicondyles and somewhat less mobile elbows. They would indicate more generalist and powerful active arboreal quadrupeds. Among them, morphotypes 1 and 2, present at Rosières 2 and sharing several characters, may represent the most quadrupedal end of the spectrum, as was found by [START_REF] Bacon | Analyse morphofonctionelle des fémurs et des tibias des "Adapis" du Quercy: mise en évidence de cinq types morphologiques[END_REF] when studying hindlimb bones, which are easier to interpret functionally. Their brachioradialis flanges are less extended than in morphotype 6. The capitulum is slightly keeled anteroposteriorly on Vi-Ros-640 and ISE-M-ROS-2-79, which may reflect predominantly anteroposterior movements. Several of these humeri show the best developed dorsoepitrochlear fossae, indicating that the elbows were not only less mobile in pronation-supination (less spherical capitulum) but also tightly maintained by strong ligaments. These morphotypes seem to be interpretable as active, possibly rapidly moving, arboreal quadrupeds. They seem to indicate a lineage (with two species at Rosières 2) with increased quadrupedal specialization at the end of the Eocene. Were they walking and running, maybe more horizontally jumping, on branches? A specimen like Ma-PhQ-332 also has a greater tuberosity higher than the articular head and distally the largest dorsoepitrochlear fossa: could a restricted shoulder mobility associated with a ligamentous reinforcement of the elbow suggest a first degree of semi-terrestriality? Interpreting differences between them, probably between different closely related species, would need more abundant and better preserved specimens. In any case, these latest Eocene morphotypes together strongly suggest a second line of specialization in the Adapis group, toward more specialized quadrupedalism.

Morphotype 6 is a heterogeneous group, representing between two and four different species, that we consider probably primitive for the second group (morphotypes 1, 2, 4 and 6), especially because they have more extended brachioradialis flanges. Ma-PhQ-333 is the most gracile and has a very large entepicondylar foramen. It could well be the most primitive in this group. Its slightly less distally extended deltopectoral crest recalls the other group (morphotypes 3 and 5) and might suggest either closeness to their common origin or an early convergence. It is difficult to comment more on these bones because they are incomplete. Only MNHN-Qu-15584 is complete and seems to belong to a powerful arboreal quadruped. Morphotype 4 is a special case, represented by one specimen, MNHN-ACQ-262. It belongs to the same large group, however it presents some characters shared with morphotypes 1 and 2, and several autapomorphic characters, like the prominent deltopectoral crest, the deep olecranon fossa and the presence of a crest between the lesser tuberosity and the tubercle of teres major. This suggests that it represents a "side-specialization" branched off from the broad line of evolution going from the primitive group (morphotype 6) to morphotypes 1 and 2. On the whole, we propose a schema of four evolutionary lines, one represented by morphotypes 5 to 3, the others branched off from the primitive morphotype 6 and having evolved toward morphotype 4 and toward morphotypes 1 and 2.

The great diversity present in the Adapis group poses a problem for the performance of phylogenetic analyses of primates containing Adapis parisiensis from now on, since what has been traditionally called A. parisiensis is most probably constituted of different species. Common character matrices used for phylogenetic analyses [START_REF] Seiffert | Basal anthropoids from Egypt and the antiquity of the Africa's higher primate radiation[END_REF][START_REF] Seiffert | Convergent evolution of anthropoid-like adaptations in Eocene adapiform primates[END_REF][START_REF] Marigó | New Anchomomys (Adapoidea, Primates) from the Robiacian (Middle Eocene) of northeastern Spain. Taxonomic and evolutionary implications[END_REF][START_REF] Marigó | Nievesia sossisensis, a new anchomomyin (Adapiformes, Primates) from the early Late Eocene of the southern Pyrenees (Catalonia, Spain)[END_REF][START_REF] Marigó | Astragalar and calcaneal morphology of the middle Eocene primate Anchomomys frontanyensis (Anchomomyini): implications for early primate evolution[END_REF]Femenias-Gual et al., 2017a,b) contain codifications of humeral features such as the brachioradialis flange (usually coded as moderate to large for A. parisiensis), the trochlear-capitular junction (usually coded as confluent), and the relative width of the capitulum, which may need to be recoded in future analyses in order to include all the character states present in the Adapis group sample. Indeed, exchanging "Adapis parisiensis" for "Adapis group" would be better in future phylogenetic analyses using postcranial characters in order to illustrate that A. parisiensis is most probably in this case a compilation of different closely related species or even closely related genera. In fact, that several species of Adapis are recongnized through cranial characters has been known for a long time [START_REF] Stehlin | Die Säugetiere des schweizerischen Eocäens: critischer Catalog der Materialen. Part 7, first half[END_REF][START_REF] Lanèque | Variation in the shape of the palate in Adapis (Eocene, Adapiformes) compared with living primates[END_REF][START_REF] Lanèque | Variation of orbital features in adapine skulls[END_REF].

Conclusions

The primate humeri attributed to Adapis parisiensis in the Quercy collections show a great morphological diversity, with variance in some features of the distal articulation exceeding that found in living species, confirming the hypothesis that several species must be represented within the sample, as has been proposed in previous studies of the femora and tibiae. Even though it is not yet possible to make clear systematic attributions, six different morphotypes are described, probably corresponding to at least six different species.

Humeral features previously thought to be not present in Adapis, such as the zona conoidea, are shown to be variable, since they are present in some specimens attributed to the Adapis group. Moreover, this is one of the features that has been shown to have much less variance in extant species. This high morphological variability suggests that locomotor diversification occurred among this group and that different locomotor repertoires were used by different species (or morphotypes).

Two clear groups can be distinguished in the sample, one including morphotypes 3 and 5, and a second one including morphotypes 1, 2, 4 and 6. Regarding the former, morphotype 5 is probably older and it is probably ancestral to morphotype 3, which appears specialized towards agility and climbing adaptations, and may include specimens of the genus Palaeolemur. In the latter group, we find more generalist active arboreal quadrupeds.The idea that modern lorisids are analogous to fossil adapines finds no support from examination of the humerus. Adapis group specimens do not overlap with living lorisids regarding humeral head and distal articulation proportions. Instead, even though some ratios of the humeral head seem to present a strong phylogenetic signal, our analyses favor the interpretation of a less specialized kind of quadrupedalism. Proportions of the distal epiphyses overlap with many primate groups including omomyids, as well as extant strepsirrhines and platyrrhines. This suggests that telling apart distal humeral remains of strepsirrhines and haplorhines in early forms can be problematic. It is possible that the humeral specializations lag behind other regions of the skeleton during locomotor differentiation. If so, the slow-climbing hypothesis could still potentially be correct. However, this would have to be tested by studies comparing the behavioral signal in multiple elements for the same species. [START_REF] Ford | Postcranial adaptations of the earliest platyrrhine[END_REF]; H derived from ML distal, PD central and ML distal following [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF]; TL, CL, TH, TW, CW and AW following [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF]; EEC following [START_REF] Boyer | New postcrania of Deccanolestes from the Late Cretaceous of India and their bearing on the evolutionary and biogeographic history of euarchontan mammals[END_REF]. Humerus used is MNHN-Qu-16584, reversed. Figure 10. Principal components analysis results of four distal humeral measurements following [START_REF] Boyer | New postcrania of Deccanolestes from the Late Cretaceous of India and their bearing on the evolutionary and biogeographic history of euarchontan mammals[END_REF]. Data taken from Szalay andDagosto (1980), Senturia (1995), [START_REF] Rose | Early Eocene primates from Gujarat, India[END_REF], [START_REF] Boyer | New postcrania of Deccanolestes from the Late Cretaceous of India and their bearing on the evolutionary and biogeographic history of euarchontan mammals[END_REF][START_REF] Dunn | New euprimate postcrania from the early Eocene of Gujarat, India, and the strepsirrhinehaplorhine divergence[END_REF] and this paper. A, PCA results obtained with several groups of living platyrrhines and catarrhines. B, PCA results obtained after the removal of the living anthropoid groups. For more information on specimens used see Table 4. All scales represent 1 cm.

Figure and table legends

  These bones are housed in different institutions: American Museum of Natural History (AMNH, New York, United Stated of America), Muséum d'Histoire Naturelle Victor Brun (MHNVB, Montauban, France) , Muséum national d'Histoire naturelle (MNHN, Paris, France), Université de Montpellier, Institut des Sciences de l'Évolution-Montpellier (ISE-M, Montpellier, France), Aix-Marseille Université, Faculté des Sciences Saint-Charles (FSM, Marseille, France), and the private collection of D.

  However the other two, Vi-Esc-839 and MNHN-Qu-16583 have values similar to those of other morphotypes. Ma-PhQ-330 is peculiar in the other direction, however the other specimen from morphotype 6, MNHN-Qu-16584, again has values similar to those of other morphotypes. The group from Rosières 2 + NMB-QW-1481 (morphotypes 1 and 2) might seem more homogeneous, however in fact Ma-PhQ-332, placed with the morphotype 2 from Rosières 2, again has different values. It appears that the variation within morphotypes is relatively large, and that the values from the different morphotypes largely overlap with each other. In sum, the numbers found for the indices TAI and RTWI (Relative trochlear width index, see Table3) do not allow the differentiation, morphological or functional, of morphotypes. However, the generally low THWI indices in the Adapis group are opposite to the high values of VCLs and especially slow climbers (see values in SOM 3), very probably giving them a real functional signal of broadly arboreal quadruped types of locomotion.

  and 10B) Esc 839 overlaps with the morphospace of Pitheciinae, but it does not overlap with any extant strepsirrhine group, FSM-PQ-1744 overlaps with Galagidae, NMB-QW-1481 overlaps with Callitrichinae and Galagidae, and Ma-PhQ-330, MNHN-Qu-16584, ISE-M-ROS-2-95 and MNHN-Qu-16583 overlap with Omomyidae. Specimen Vi-Ros-640 and Ma-PhQ-332 do not overlap with any other group but they fall very close to Omomyidae, Galagidae and Callitrichinae. Vastan primates have also been included in the PCA, as well as the fossils Smilodectes and Notharctus (Figure 10A and 10B). Smilodectes overlaps only with Atelinae, and also falls close to some Indriidae. Notharctus specimens, on the other hand, fall closer in morphospace to Plesiadapidae than to the Adapis group. Specimen AMNH-FM-127167 does not overlap with any fossil or extant group, and specimen USNM 21864 overlaps with both Omomyidae and Plesiadapidae (Figure 10A and 10B).

  9005. The first specimen falls very close to the morphospace occupied by Lorisidae, and very close to Hapalemur simus as well, far from the Adapis morphospace, the second one overlaps with the common morphospace of omomyids and Plesiadapis (overlapping with microchoerine omomyid number 4 [M4 in Figure 10B]), and the latter falls in between the morphospace occupied by Notharctus and Smilodectes but closer to the latter, and also closer to Plesiadapidae and Tarsiidae than to Lorisidae. Another form, attributed to the adapiform Marcgodinotius indicus, is represented by specimens GU 763 and GU 812.

  However, even though having those more powerful muscles should indicate changes in locomotion, we find massive brachioradialis flanges in extant taxa that have very different locomotor repertoires such as Daubentonia, Microcebus and Lepilemur, and narrow and straight flanges in indriids as well as Loris and Nycticebus, though lorisids such as Perodicticus present an intermediate flange development (see Figure 11) closer

Figure 1 .

 1 Figure 1. Adapis humeri attributed to morphotype 1. Complete specimen: ISE-M-ROS-

Figure 2 .

 2 Figure 2. Adapis humeri attributed to morphotype 2. Complete specimen: Ma-PhQ-332;

Figure 3 .

 3 Figure 3. Adapis humeri attributed to morphotype 3. Specimen missing humeral head:

Figure 4 .

 4 Figure 4. Adapis humerus attributed to morphotype 4. Single specimen missing

Figure 5 .

 5 Figure 5. Adapis humerus attributed to morphotype 5. Single specimen missing humeral

Figure 6 .

 6 Figure 6. Adapis humeri attributed to morphotype 6. Complete specimen: MNHN-Qu-

Figure 7 .

 7 Figure 7. Anatomical terms used in the descriptions. 1: greater tuberosity; 2: lesser

Figure 8 .

 8 Figure 8. Measurements taken on Adapis humeri as well as some other primates used

Figure 9 .

 9 Figure 9. Plot of humeral head indices comparing fossil and extant taxa, following

Figure 11 .

 11 Figure 11. Comparison of humeri of different extinct and extant primates. Adapis group

Table 1 .

 1 Complete list of all Adapis group humeri included in this paper with information on morphotype (MT) attribution, species attribution, preservation, locality and institution. (R) right humerus; (L) left humerus; (AMNH) American Museum of Natural History, New York, USA; (MNHN) Muséum National d'Histoire Naturelle, Paris, France; (MHNVB) Muséum d'Histoire Naturelle Victor Brun, Montauban, France; (NMB) Naturhistorisches Museum Basel, Basel, Switzerland. See Table 2 for availability of specimens through online repositories MorphoSource and /or MorphoMuseuM.

Acknowledgements

We are deeply indebted to the following institutions for letting us study material under their care (original or high-quality casts): American Museum of Natural History (AMNH, New York, United Stated of America), Naturhistorisches Museum Basel (Basel, Switzerland), Muséum d'Histoire Naturelle Victor Brun (MHNVB, Montauban, France), Muséum National d'Histoire Naturelle (MNHN, Paris, France), Institut des Sciences de l'Évolution-Montpellier, Université de Montpellier (ISE-M, Montpellier, France) and the private collection of D. Vidalenc (Vi, presently loaned at the MNHN in Paris, France). We thank J. Cuisin and C. Bens for access to extant primate specimens from the collections "Anatomie Comparée" (MNHN). We are also really grateful to Raphaël Cornette, Amandine Blin, Alexandra Houssaye and Damien Germain of the "Plateau de morphométrie Outils et Méthodes de la Systématique Intégrative, OMSI -UMS 2700 CNRS MNHN" of the Muséum National d'Histoire Naturelle (MNHN, Paris) for access to the surface scanner. We thank Florent Goussard for access to the "Salle d'imagerie 3D" of the CR2P (MNHN, Paris) and B. Senut for a helpful discussion concerning humeral morphology and function in living primates. Judit Marigó thanks Josep Fortuny This study has been supported by the projects CGL2014-54373-P and CGL2017-82654-P (MINECO/FEDER, UE) and by Generalitat de Catalunya (project 2014/100604, research groups 2014 SGR 416 GRC and 2017 SGR 86) and the CERCA Programme. J. Marigó also wants to thank the Fondation Fyssen for funding, as well as the Spanish Ministerio de Economía y Competitividad (MINECO) for the "Juan de la Ciervaincorporación" fellowship (IJCI-2015-26392), and the Catalan Government (Generalitat de Catalunya) for the fellowship included in the "Programa postdoctoral Beatriu de Pinós de la Secretaria d'Universitats i Recerca del Departament d'Empresa i Coneixement de la Generalitat de Catalunya" (2017 BP 00003).

for sharing his caliper during their long stay at the MNHN in Paris, as well as Anne-Claire Fabre for help and advice during surface scanning and fruitful discussions about primate functional morphology.

Our most sincere thanks also to Doug M. Boyer, Gabriel S. Yapuncich, Kenneth D.

Rose and Rachel H. Dunn for providing access to many specimens in Morphosource. Doug M. Boyer provided access to data originally appearing in Boyer et al. (2013) We thank Doug M. Boyer for assistance during the upload of Adapis group specimens to MorphoSource, as well as Renaud Lebrun and Maeva Orliac for help when uploading specimens to MorphoMuseuM.

We also enormously thank the reviewers Erik R. Seiffert, Doug M. Boyer, Rachel H.

Dunn, and the Editor J. Michael Plavcan for their help, their never-ending patience, as well as their helpful comments that enormously improved the manuscript.

Table 2. Humeri attributed to the Adapis group and used in this study with information about the 3D surface reconstruction of each specimen and where to get it (online repositories MorphoSource and /or MorphoMuseuM), as well as citation instructions.

Table 3. Measurements and indices performed on Adapis specimens. Measurements follow [START_REF] Ford | Postcranial adaptations of the earliest platyrrhine[END_REF], [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF] and [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF]. Indices of the proximal ends follow [START_REF] Schmitt | Humeral head shape as an indicator of locomotor behavior in extant strepsirhines and Eocene adapids[END_REF], and those of the distal ends follow [START_REF] Szalay | Locomotor adaptations as reflected on the humerus of Paleogene primates[END_REF]. Copyright Holder: USNM. All files with media number and/or doi number were downloaded from www.MorphoSource.org, Duke University.


Atal Anil Kumar

Jean-François Antoine

Patrick Zattarin

Gabriel Abba

Workspace Analysis of a 4 Cable-Driven Spatial Parallel Robot

Keywords: Static equilibrium workspace, under-constrained cable robot, collaborative cable-driven robot

This paper presents the static equilibrium workspace of an under-constrained cable-driven robot with four cables taking into account the forces and the moments due to the forces acting on the moving platform. The problem is formulated as a non-linear optimization problem with maintaining static equilibrium as the objective function. The simulations are done using MATLAB. The maximum force on the cables and tilting angle of the platform are used to define the feasible static equilibrium workspace and the results obtained are used to finalize the design of the collaborative cable-driven robot to be installed in existing production lines for the agile handling of parts in a manufacturing industry.

Introduction

A new class of parallel robots emerged in the late 1980s and early 1990s from the works of [START_REF] Landsberger | A new design for parallel link manipulators[END_REF], [START_REF] Higuchi | Application of multi-dimensional wire crane in construction[END_REF] and [START_REF] Albus | The NIST robocrane[END_REF] with a major modification in the structure of the traditional parallel robot. This class of manipulators is commonly referred to as the Cable-Driven Parallel Robots (CDPRs) in which a platform is driven by a set of cables whose length is adjusted by a winch consisting of a tensioning motor and spool or a linear actuator moving a pulley system [START_REF] Merlet | A portable, modular parallel wire crane for rescue operations[END_REF]. Coordinated retraction and extension of cable control the position and orientation of the platform.

CDPRs possesses a number of desirable features, such as simple structure, large load capacity, high payload-to-weight ratio, and low inertia, compared to serial-link and other parallel type robots. Moreover, its simple design makes CDPRs low cost, portable, and reconfigurable [START_REF] Verhoeven | Analysis of the workspace of tendon-based Stewart platforms[END_REF]. CDPRs are well suited for a variety of applications [START_REF] Gosselin | Cable-driven parallel mechanisms: state of the art and perspectives[END_REF] such as large-scale material handling and manufacturing process, building construction, rescue operations, aerial cameras, high-speed assembly and pick and place operations, large-scale radio telescopes, medical rehabilitation of people.

One of the earliest classifications of CDPRs was proposed by [START_REF] Cone | Skycam-an aerial robotic camera system[END_REF] and has been extended by [START_REF] Verhoeven | Analysis of the workspace of tendon-based Stewart platforms[END_REF]. A cable robot with m-cables and ndegrees of freedom is said to be completely restrained or fully-constrained if it has one cable more than the number of degrees of freedom, i.e. 𝑚=𝑛+1. In such a type of arrangement, all degrees of freedom can be controlled through the cables. An incompletely restrained or under-constrained cable robot is one in which the number of cables is less than or equal to the number of degrees of freedom, i.e. 𝑚 ≤𝑛. Such systems have one feasible solution for cable tensions and mostly rely on gravity for keeping the cables taut.

Though under-constrained CDPRs have received little attention in the literature [START_REF] Fattah | On the design of cable-suspended planar parallel robots[END_REF][START_REF] Jiang | The direct kinematics of objects suspended from cables[END_REF][START_REF] Merlet | Wire-driven parallel robot: Open issues[END_REF], it is favorable to use CDPRs with a limited number of cables in several applications in which the task to be performed requires a limited number of controlled freedoms or a limitation of dexterity is acceptable in order to decrease complexity, cost, setup time, likelihood of cable interference etc. (Abbasnejad and Carricato, 2015). For example, CALOWI, a 4 cable-driven parallel robot designed at the LARM laboratory was intended to be used in a hospital environment (Ottaviano, 2007). Some important results on the stability analysis and kinematics of underconstrained parallel robots have been discussed by [START_REF] Merlet | Wire-driven parallel robot: Open issues[END_REF]Daney (2009), Carricato and[START_REF] Merlet | Wire-driven parallel robot: Open issues[END_REF].

The major objective of the project is to design a collaborative cable-driven parallel robot for agile handling of parts in the manufacturing industry. Collaborative robots are a recent trend to allow the interaction of the workers and robot in a safe way making use of the worker's experience. The CDPR is planned to be installed in the existing lines of the industry where available space is reduced by already installed machines. In such a scenario, there is a severe space constraint to install new serial robots and would cost a lot to the company. Installing the robots on the ceiling would require reinforcement of the structure, again making the task costlier. Hence, a cable driven parallel robot with 4 cables is proposed as a solution. The number of cables is restricted to 4 for the ease of installation with simple anchor points in the environment and also to reduce the complexity of cable collision with the equipment installed on the shop floor. It is desired to have the actuators on the moving platform, unlike other designs in which the motors are placed in the base or fixed structure. This paper presents the preliminary studies done to calculate the static equilibrium workspace of a 4 cable-driven parallel robot. Earlier works with such CDPRs take into account only the forces acting on the moving platform (pointmass). However, this work takes into account both the forces and the moments due to the forces acting on the moving platform with a given dimension. The results obtained from this study indicate that it is possible to achieve satisfactory results with 4 cables and the values of tensions obtained can be used in finalizing the parameters for the design of the CDPR.

The paper is organized as follows: section 2 presents the kinematic and geometric modelling equations used in the study of CDPRs followed by section 3 which gives a brief about the workspace to be studied and non-linear solver used for solving the tension equation. The results are presented in section 4 followed by the conclusion and future work in section 5.

Kinematic and Geometric Modelling

The equations used in the modeling of CDPR is presented in this section. The modeling and analysis methods developed for conventional rigid link manipulators cannot be directly applied to the cable-driven robots because of the unilateral constraints where the tensions in the cables must be considered [START_REF] Gosselin | Cable-driven parallel mechanisms: state of the art and perspectives[END_REF]. A general cable-driven parallel robot with m-cables is shown in figure1. As seen in the figure above, a fixed reference frame (O, x, y, z) is attached to the base of a CDPR and is referred to as the base frame. A moving reference frame (P, x', y', z') is attached to the mobile platform where P is the reference point of the platform to be positioned by the mechanism. The rotation matrix Q gives the orientation of the moving frame with respect to the base frame.

From the figure 2, ai and bi are respectively defined as the vector connecting point O to point Ai and the vector connecting point P of the platform to the point Bi, both vectors being expressed in the base frame. The position p of the mobile platform is given by 𝑂𝑃 ⃗⃗⃗⃗⃗ .

Few assumptions are made in the modeling procedure to reduce the complexity of computation [START_REF] Gosselin | Cable-driven parallel mechanisms: state of the art and perspectives[END_REF] 1) The mass of the cables is negligible and the cables are non-elastic.

2) The i th cable is assumed to be taut between points and is therefore considered a straight segment and is denoted by 𝜌 𝑖 .

3) The moving platform is assumed to be a rigid body, defined by its mass and inertia matrix. To identify the kinematic relationship between the cable space and body space for a CDPR, the loop closure equations are first developed for each chain of the CDPR. The length of the cable can be calculated by using the vector loop equation given by

𝑑 𝑖 ⃗⃗⃗ = 𝑎 𝑖 ⃗⃗⃗ -𝑏 𝑖 ⃗⃗⃗ -𝑝 (1)
where, d i ⃗⃗⃗ is the vector along cable i pointing from Bi to Ai and (i=1,2…m). The length of the cable is calculated using

𝜌 𝑖 = ‖𝑑 𝑖 ⃗⃗⃗ ‖ 2
(2) Also using the above equation, the unit vector can be calculated by

𝑑 𝑖 ̂= (𝑎 𝑖 ⃗⃗⃗ -𝑏 𝑖 ⃗⃗⃗ -𝑝 )/𝜌 𝑖 (3)
This basic model has been established in the early works on CDPRs and is purely based on the geometric analysis. This equation, however, does not take into account the ability of the mechanism to maintain the tensions in the cables. In order to address this issue, the concept of wrench matrix was introduced where statics of CDPR is considered.

When a tension ti is applied, the cable i exerts at point Bi, a pure force 𝑡 𝑖 𝑑 𝑖 ̂ on the mobile platform. This pure force generates a moment 𝑏 𝑖 ⃗⃗⃗ × 𝑡 𝑖 𝑑 𝑖 ̂ at the reference point P of the mobile platform and the wrench (force/moment pair) applied at P by the i th cable is tiwi with the wrench wi defined as

𝑤 𝑖 = [ 𝑑 ̂𝑖 𝑏 𝑖 ⃗⃗⃗ × 𝑑 ̂𝑖] (4)
If wp is the total wrench applied at point P by the m-cables then the relationship between the tensions in the cables and the wrench is written in matrix form as

𝑊𝑡 = 𝑤 𝑝 (5)
where, t ⃗ is the vector of cable tensions and W is the 6 × m pose dependent wrench matrix.

Most of the analytical results proposed in the literature are based on this equation. By properly defining the vector wp, different solutions can be obtained to understand the workspace of CDPRs.

Workspace Analysis

Because of the unilateral constraint on the cables, the workspace analysis cannot be based solely on the change in cable lengths but must also take into account the statics of the manipulator [START_REF] Gosselin | Cable-driven parallel mechanisms: state of the art and perspectives[END_REF].

The workspace of a CDPR is the set of position and orientation in which [START_REF] Tavolieri | A workspace analysis of a overconstrained cable-based parallel manipulator by using the interval analysis[END_REF] 1) The end-effector is controllable, 2) The tensions in the cables are positive, 3) The force values lie between a minimum and a maximum in order to avoid the cables break or become slack, 4) The end-effector is far from singularities, and 5) Cable wrapping is avoided.

Based on the conditions given above several different types of workspaces have been addressed in the literature, including (a) static equilibrium workspace [START_REF] Pusey | Design and workspace analysis of a 6-6 cable-suspended parallel robot[END_REF], (b) wrench closure workspace (WCW) [START_REF] Gouttefarde | Determination of the wrench-closure workspace of 6-DOF parallel cable-driven mechanisms[END_REF], (c) wrench feasible workspace (WFW) (Ruiz et al., 2014), (d) dynamic workspace [START_REF] Gagliardini | Determination of a dynamic feasible workspace for cable-driven parallel robots[END_REF], and (e) collision-free workspace (Ruiz et al., 2014).

The current work presents the static equilibrium workspace of the cable robot to be designed. The static equilibrium workspace (SEW) is the set of postures (position and orientation of the end-effector) that the end-effector can attain statically (only taking gravity into account). SEW is a subset of workplace for cable robots as all postures of the cable-driven robot are not statically attainable. It is not possible to calculate the WCW and WFW for the robot considered as they require the robot to be fully constrained or over-constrained. Hence it is important to have a good knowledge about SEW as it will help in the appropriate determination of the design parameters (motor speed, platform dimensions etc.).

In order to calculate the SEW of the CDPR, the static equilibrium condition of the cable robot is used to find the force on each cable. In other words, the equations given below which indicate the sum of forces (∑ 𝐹 𝑖 , 𝑖 = 𝑥, 𝑦, 𝑧) acting on the moving platform along the x, y, z direction and the sum of moments ((∑ 𝑀 𝑖 , 𝑖 = 𝑥, 𝑦, 𝑧) acting on the moving platform along the x, y, z direction respectively, needs to be satisfied to achieve static equilibrium ∑ 𝐹 𝑥 = 0, ∑ 𝐹 𝑦 = 0, ∑ 𝐹 𝑧 = 0, ∑ 𝑀 𝑥 = 0, ∑ 𝑀 𝑦 = 0, ∑ 𝑀 𝑧 = 0

The only external force acting on the platform is the gravitational force (along with the mass of the platform and payload acting at the center of mass of the moving platform) and all other external forces and moments will not be discussed in this paper. The equations described above are formulated as a nonlinear optimization problem and is solved using fsolve in MATLAB with static equilibrium condition as the objective function.

Results and Discussion

The results of the simulation carried out in MATLAB are presented in this section. The SEW of the CDPR inside a room of dimension 5m*5m*3m with a moving platform of size 0.5m*0.5m and a total payload of 30kg is shown in figure 3. The constraints on the angle of inclination of the moving platform about x-axis and y-axis are ±30˚. The maximum and minimum allowed tensions in the cables were 500N and 1N respectively. The center of mass (CoM) of the moving platform was considered to be at a height of 0.2m below the cable attachment points while the CoM of the payload was considered at a height of 0.4m below the CoM of the platform. The step size was fixed along x and y axis to 0.05 while it was kept at 0.1 along the z-axis. The search for possible workspace value was fixed to the region of (0.3<x<4.7, 0.3<y<4.7, 0.5<z<2.3). The points were checked to see if they can be included in the SEW and it was found that 77% of the points from the selected region were satisfying the constraints considered during the simulation.

The dimensions of the platform were varied and the corresponding percentage of SEW is presented in the table given below. Since the final design includes the actuating motors on the moving platform, a dimension of 0.5m*0.5m is considered to be a good compromise. Since a 4 cable-driven spatial parallel robot has 4 degrees of freedom (the position x, y, z and one angle) that can be controlled by the cables, it is important to have an idea about how the platform orientation behaves as the simulation is done for static equilibrium condition.

Figures below show the variation of cable tensions and the corresponding changes in the value of the angles about x-axis and y-axis when the moving platform is moving in a plane at the center of the room (z=1.5m) considered. It can be seen that the change in angles about x-axis and y-axis is symmetrical under the consideration that the moving platform has equal length and width. The plot of cable tensions also exhibits symmetrical behavior with respect to x and y axis.

Conclusion

The work presents the preliminary studies carried out in the design of a 4 cabledriven parallel robot. The static equilibrium workspace of the robot is calculated and the corresponding tensions for the cables are presented. It can be seen that it is possible to have a sufficiently large workspace for such robots by limiting the orientation of the platform within a certain range. Future work will include the calculation of dynamic feasible workspace taking into account the platform accelerations along with the performance evaluation of the workspace. The end product of the current work is to have a prototype of the robot considered, in the agile handling of parts in a manufacturing environment.

Figure 1 .

 1 Figure 1. A simple arrangement of a CDPR.

Figure 2 .

 2 Figure 2. Kinematic model of a CDPR.

Figure 3 .

 3 SEW of the CDPR for a payload of 30kg (10kg platform+ 20kg payload) acting on the platform (a) 3-D representation and (b) 2-D representation.

Figure 4 .

 4 Figure 4. Tension distribution (N) in 4 cables for z=1.5m.

Figure 5 .

 5 Figure 5. SEW for z=1.5m.

Figure 6 .

 6 Figure 6. Variation of angle (in degrees) about x-axis for z=1.5m.

Figure 7 .

 7 Figure 7. Variation of angle (in degrees) about y-axis for z=1.5m.

Table 1 .

 1 % of SEW for platform with different dimensions

	Platform dimensions(m) 0.5*0.5	0.75*0.75	0.6*0.4	0.8*0.6
	SEW %	68	56	68	58

We would like to thank the Robotix Academy for funding this work as a part of the project funded by INTERREG V-A Grand Region program.