Andrea Dematteis

Marco Giovo

Rostagno Fabrizio

Omar Giordano

David Fina

Arianna Menzano
email: arianna.menzano@unito.it

Paolo Tizzani

Giorgio Ficetto

Luca Rossi

Giuseppe Meneguz

F Rostagno

: O Giordano

: A Menzano

Ge S Fa

P G Meneguz

Radio-controlled up-net enclosure to capture free-ranging Alpine chamois Rupicapra rupicapra

Keywords: Mechanical capture, Mountain ungulates, Alpine chamois, Radio-controlled up-net, Rupicapra rupicapra

We used an enclosure trap with a lifting net to capture Alpine chamois (Rupicapra rupicapra). The trap was activated by remote radio-controlled electromagnets powered by photovoltaic modules. The up-net trap had considerable advantages over mechanical methods described in the literature for the capture of chamois. During 36 capture sessions, we captured 50 chamois, or 1.39 animals per session. Capture success was 96.2% of the average of 1.4 animals that entered the trap during a capture session. Mortality was 2%, and another 2% of the captured chamois was injured. There were no known postrelease capture-induced pathologies, and the capture effort was 1.7 man-days per chamois. The trap allowed to select specific target animals and to capture sex-age classes (particularly kids and their mothers) that are normally difficult or impossible to capture. It could be set off from a distance; it only required about 4 h to assemble and could be operated by as few as two people.

Introduction

Live captures of Alpine chamois (Rupicapra rupicapra) are challenging because of its steep habitat and the long flight distance, which rarely allow use of dart guns, especially in hunted populations [START_REF] Hamr | Disturbance behaviour of chamois in an alpine tourist area of Austria[END_REF]. Consequently, many capture programs rely on mechanical methods, including box traps (Berducou 1993;[START_REF] Delmas | Comparaison de deux methodes de capture de chamois Rupicapra rupicapra en milieu ouvert dans le Parc National de la Vanoise[END_REF], foot snares [START_REF] Struch | Experiences of catching chamois (Rupicapra rupicapra) in a wooded mountain area in Switzerland[END_REF], drop nets [START_REF] Jullien | La cham'arche, un filet pour la capture des ongulés de montagne[END_REF], descending nets [START_REF] Hansen | Mise au point d'une methode de captures multiples d'isards Rupicapra pyrenaica par enclos-piege[END_REF], and drive nets (Berducou 1993;[START_REF] Meneguz | Esperienze di cattura di caprioli (Capreolus capreolus) e di camosci (Rupicapra rupicapra) con reti verticali. Nota preliminare[END_REF]. Most of these methods, however, have severe limitations in efficacy, selectivity, risk of injury for captured chamois, capture of nontarget species, and substantial manpower needs [START_REF] Schemnitz | Capturing and handling wild animals[END_REF]. None of these methods allow the regular capture of kids, which has relied on hand-capture of newborns with the aid of dogs [START_REF] Jullien | Marquage de jeunes chamois à l'aide de chiens de berger dressés[END_REF]). To our knowledge, no study has been able to capture a substantial number of mother-kid pairs.

Here, we present a new mechanical capture technique called "up-net" that allows capture of all chamois sex-age classes. We also compare the new method with other methods used to capture this species.

Materials and methods

Study area

We captured chamois in two locations on the Italian Western Alps, the Pellice valley (44°82′N, 7°23′E), and the Varaita valley (44°58′N, 7°19′E), at elevations ranging from 2,205 to 2,420 m above sea level. Both sites had open habitats with interspersed alpine pastures and rockslides, with slopes of 15 to 25°and a predominant south and southwest aspect. During summer, they were frequently visited by chamois, mainly groups of females, kids and yearlings, and occasionally males. Based on block counts carried out on a yearly basis, the estimated density of chamois was 8-9/km 2 in Pellice valley and 7-8/km 2 in Varaita valley. Both traps were also visited by roe deer (Capreolus capreolus), and the one in the Pellice valley by Alpine ibex (Capra ibex) and European mouflon (Ovis aries).

Methods

Captures were conducted between July and September 2006 and 2007. The up-net enclosure is a square (perimeter of 100-150 m; Fig. 1) made of aluminum/iron poles (3.5 m high) connected together by a steel cable (2.8-3 m high), an electrical circuit, and nets (3×50 m; 10-cm mesh, 4-mmdiameter nylon rope; Ziboni Ornitecnica, Bergamo, Italy). Nets were folded in a small trench along the perimeter of the frame. The bottom of the nets was pegged down so that animals could not escape after the nets were raised. The top side was connected with a nylon rope to a counterweight that was tied to an electromagnet on the top of each pole. When the electromagnet was activated, the counterweight raised the net using a pulley mechanism (Fig. 1). The separation of electromagnets required a 24-V voltage pulse supplied by a battery powered by two photovoltaic modules (12 V/10 W). Due to the limited power of the solar panels, we used electromagnets that required no electricity while on stand-by (Compact electromagnetic release unit®-Cooper Csa Srl, Corsico (MI), Italy). A remote control supplied by alkaline cells (type AAA LR03/1.5 V) was used to activate the electric impulse generated by the battery. The working range of the remote control was reported up to 1 km.

Salt blocks in the enclosures were used as baits (Mattfeld et al. 1972;[START_REF] Pedersen | Summer elk trapping with salt[END_REF]. Traps were operated from inside a cabin about 500 m from the up-net. Observations and captures were limited to two 4-h periods, at dusk and dawn. The capture team included two to four operators.

Captured chamois were blindfolded and hog-tied. Each animal was measured, weighed, and marked with plastic ear tags. Lactating females and their kids were fitted with a radio collar with mortality sensor (Televilt-TVP Positioning, Lindesberg, Sweden). Finally, animals were released.

Each day when we attempted to capture chamois was considered as "capture session." We defined "exposure time" as the number of days from when the up-net was installed to when chamois first visited it; "efficacy" as the number of animals captured per capture session; "relative efficacy" as the ratio between efficacy and chamois density in the study area; "success" as the number of animals captured of those that entered the trap; "effort" as the number of man-days taken to capture an animal; "handling time" as the interval between physical restraint and release of a single animal; and "trapping time" as the interval between trap activation and the release of a single animal. We monitored released animals for a month to check for possible capture-related pathologies or mortality [START_REF] Peracino | Bilan de 30 annee d'experiences de capture des ongules sauvages, bouquetin des Alpes (Capra ibex ibex) et chamois (Rupicapra rupicapra rupicapra), dans le Parc National du Grand Paradis (Italie)[END_REF].

Results

The up-net enclosure can be assembled in about 4 h by three experienced operators. During 36 capture sessions, 52 chamois (20 lactating females, 5 unlactating females, 15 kids, 8 yearlings, and 4 males) entered the trap: 50 were caught and 2 kids (3.8% of entered chamois) escaped. With the exception of kids, chamois usually entangled their hooked horns in the net and were then easily restrained. Kids were chased into the net. We captured eight motherkid pairs. Exposure time averaged 8.3±3.3 days and ranged from 4 to 12 days. We caught on average 1.39 chamois per capture session (range 1-6), or 96.2% of those that entered the trap. The effort required was 1.7 man-days per animal; handling time averaged 7.2±2.6 min (range 5-9 min) while trapping time was 28±5.3 min (range 9-62 min). One adult female (2% of captured chamois) asphyxiated after becoming entangled into the net, and a male suffered a cutaneous wound after hitting a pole; this animal was treated with a single dose of long-acting antibiotic and released. No capture-related pathologies were observed.

One female was captured twice in the same year, and two chamois were recaptured the following year. In addition, 28 mouflon, 7 roe deer, and 72 ibex entered the traps, but they were not activated. No handlers were injured. The total cost of materials for a single trap, net excluded, is approximately 3,500.00 € (VAT included).

Discussion

Our trap differs from drop nets [START_REF] Jullien | La cham'arche, un filet pour la capture des ongulés de montagne[END_REF]) and from the descending-net trap described by [START_REF] Hansen | Mise au point d'une methode de captures multiples d'isards Rupicapra pyrenaica par enclos-piege[END_REF] and [START_REF] Montané | Valoraciò de l'estrés de captura i maneig en el cabirol (Capreolus capreolus). Efecte de l'acepromazina sobre la resposta d'estrés agut[END_REF] because up-nets are laid down and then lifted, with the bottom preanchored to the ground. Two of 15 kids escaped by squeezing under the net where we had forgotten to anchor it. None of the captured chamois could jump over the 2.5-m net.

The radio control allowed us to trigger the trap from more than 500 m, which minimizes disturbance to the animals as they approach the trap. The self-sufficient method for supplying energy means that the enclosure can be used in remote areas.

Fig. 1 Radio-controlled up-net enclosure. On standby: nets are folded on the ground; the two parts of the electromagnets are in attractive position; the counterweights are hanged on the top of the pole. At the electromagnets activation (power supplied by the photovoltaic panels): nets are raised by ropes connected to the counterweights through a pulley mechanism. In the enlarged box: the self-sufficient device for supplying energy (on the left); the electromechanical system to activate the raising of the net (on the right) Very few animals were killed or injured during captures. We observed no clinical signs of capture myopathy [START_REF] Peracino | Bilan de 30 annee d'experiences de capture des ongules sauvages, bouquetin des Alpes (Capra ibex ibex) et chamois (Rupicapra rupicapra rupicapra), dans le Parc National du Grand Paradis (Italie)[END_REF], and no mortality was recorded in the first month postcapture.

Roe deer, ibex, and mouflon regularly entered the traps. Therefore, considering the high capture success for chamois, we suggest that the up-net holds promise to capture other species of small to medium-sized wild ungulates.

In addition to the mechanical methods listed in Table 1, free-ranging chamois have been captured with foot snares (Berducou 1993;[START_REF] Delmas | Comparaison de deux methodes de capture de chamois Rupicapra rupicapra en milieu ouvert dans le Parc National de la Vanoise[END_REF], dog-assisted hand capture of newborns [START_REF] Jullien | Marquage de jeunes chamois à l'aide de chiens de berger dressés[END_REF], and chemical immobilization [START_REF] Gauthier | Pratiques francaises en matiere d'immobilisation par voie chimique: synthese des questionnaires et experience du Parc National de la Vanoise[END_REF][START_REF] Peracino | Bilan de 30 annee d'experiences de capture des ongules sauvages, bouquetin des Alpes (Capra ibex ibex) et chamois (Rupicapra rupicapra rupicapra), dans le Parc National du Grand Paradis (Italie)[END_REF][START_REF] Bassano | Chamois et isards: bilan des captures par filets, pieges et engins drivers realisees en France au cours des trente dernieres annees (1958-1989)[END_REF][START_REF] Dematteis | Immobilising free-ranging Alpine chamois with xylazine, reversed with atipamezole[END_REF]). Because few of these studies reported complete data on the efficacy, success, effort required, mortality, and injuries, direct comparisons of methods are difficult.

Capture efficacy varies according to the employed method, but it may also depend on the chamois abundance in the study area (Berducou 1993). Comparing therefore the relative efficacy in the situations where chamois density is known (Berducou 1993;[START_REF] Hansen | Mise au point d'une methode de captures multiples d'isards Rupicapra pyrenaica par enclos-piege[END_REF], we note that the up-net presents the higher index (Table 1).

The capture success of the up-net (96.2%) is clearly more favorable than the one (39.8%) obtained by [START_REF] Hansen | Mise au point d'une methode de captures multiples d'isards Rupicapra pyrenaica par enclos-piege[END_REF] using a descending-net trap. It could depend on the way the bottom of the net lies on the ground, respectively pegged down and flitting.

Drive-nets require substantially more manpower than the up-net and often lead to higher capture-related pathology and mortality [START_REF] Meneguz | Esperienze di cattura di caprioli (Capreolus capreolus) e di camosci (Rupicapra rupicapra) con reti verticali. Nota preliminare[END_REF][START_REF] Kock | Capture methods in five subspecies of free-ranging bighorn sheep: an evaluation of drop-net, drive-net, chemical immobilization and the net-gun[END_REF]). Drive nets are not selective, and their use is generally not indicated above the tree line [START_REF] Cressonier | Reprises de chevreuils dans le forets domaniales de Biscarosse et Saint-Eulalie en Born[END_REF][START_REF] Kattel | Capturing and handling of the Himalayan musk deer[END_REF][START_REF] Meneguz | Esperienze di cattura di caprioli (Capreolus capreolus) e di camosci (Rupicapra rupicapra) con reti verticali. Nota preliminare[END_REF].

Although newborn chamois have previously been captured by hand [START_REF] Jullien | Marquage de jeunes chamois à l'aide de chiens de berger dressés[END_REF], the up-net trap allows the capture of mother-kid pairs. Knowledge of mother-kid links has several potential applications in fundamental and management studies [START_REF] Powell | Trapping and marking terrestrial mammals for research: integrating ethics, performance criteria, techniques, and common sense[END_REF].

A mortality of 2% was recorded using the radiocontrolled up-net trap, on the low end of the range reported for other chamois capture methods (0-6%; Table 1). The short handling time of trapped chamois minimized the risk of injury [START_REF] Schemnitz | Capturing and handling wild animals[END_REF][START_REF] Powell | Trapping and marking terrestrial mammals for research: integrating ethics, performance criteria, techniques, and common sense[END_REF]. The use of chemical immobilization was not deemed necessary, limiting costs, permit requirements, and the need for veterinary assistance [START_REF] Plumb | Veterinary drug handbook[END_REF][START_REF] Kreeger | Salt versus browseseasonal baits for deer trapping[END_REF].

Management implications

Information gathered from wild animals is required for wildlife research, conservation, and management. Although much can be learned by indirect techniques, some informa-tion is collected only by capturing animals, for example, age determination, morphometric measurements, marking, or serum biochemistry. Capture of wild animals has potential to cause injury and to change normal behavior and physiology [START_REF] Kreeger | Chemical immobilization of red foxes[END_REF][START_REF] Proulx | Review of current mammal trap technology in North America[END_REF]. Consequently, researchers are challenged to design research and use methods that have minimal impact on study animals and remain safe for field personnel. Procedures that affect study animals adversely not only raise important ethical and animal welfare issues but also are likely to influence the animals' behavior or physiology in ways that affect research results [START_REF] Powell | Trapping and marking terrestrial mammals for research: integrating ethics, performance criteria, techniques, and common sense[END_REF]. The capture method we proposed has produced considerable advantages compared with other techniques described in literature for the capture of chamois.

Table 1

 1 Efficacy and safety of selected methods used to capture free-ranging chamois, Rupicapra spp

	Method	N. chamois	Chamois	Capture session Efficacy Relative	Success % chamois	Mortality Reference
		captured	density			efficacy		injured
			(N/km 2 )
	Drop-net	99/101 a		86	1.15		98%		0%	Jullien et al. 2001
	Box-trap	164/188 a		486	0.34		87.2%		4%	Jullien et al. 2001
	Box-trap	1,043		3,066	0.34					Berducou 1993
	Box-trap	45		770	0.06			4.4%	6%	Delmas 1993
	Box-trap	355		570	0.62					Boillot 1993
	Box-trap	268		2,154	0.12				4%	Houssin 1993
	Drive-net	237	12-13	159	1.49	0.11				Berducou 1993
	Drive-net	57		21	2.71				3.5% Meneguz et al. 1997
	Drive-net	10		4	2.5					Boillot 1993
	Drive-net	114		171	0.67					Geraud and Nebel 1993
	Descending-net trap 41/103 a	30	14	2.93	0.10	39.8%		4.9% Hansen et al. 1993
	Up-net	50/52 a	7-9	36	1.39	0.17	96.2%	2%	2%	Current study

Capture session, each day dedicated to capture; efficacy, number of animals captured per capture session; relative efficacy, ratio efficacy/chamois density in the study area; success, number of animals captured of those that entered the trap; a Chamois that entered in the traps (captured, escaped, or released without handling)

Eur J Wildl Res (2010) 56:535-539

Acknowledgments This study was supported by "Comprensorio Alpino TO1-Valle Pellice, Chisone e Germanasca." In particular, we thank the president of the CATO1, E. Armand-Pilon, for supporting this study despite initial setbacks, and the Comunità Montana Valle Pellice, and P. C. Roggiero for logistic support. Thanks to P. Bottini, M. Bessone, P. Bonagura, R. Brignone, C. Demarco, F. Muttoni, N. Pellissier, N. Perotto, and A. Vignetta for their help on the field. A special thanks to Marco Festa-Bianchet for his encouragement in developing the up-net method and for comments on an earlier draft.

Declaration The experiments in this study comply with the current Italian laws.


PhD. Valérie Delague
email: valerie.delague@univmed.fr

Elsa Nicolas

Yannick Poitelon

Eliane Chouery

Nabiha Salem

Nicolas Lévy

André Mégarbané

Nicolas Levy

CAMOS, a non-progressive, autosomal recessive, congenital cerebellar ataxia, is caused by a mutant Zinc-Finger protein, ZNF592

Keywords: CAMOS, missense mutation, ZNF592, C2H2 zinc finger domain, cerebellar ataxia, nonprogressive

Introduction

Non Progressive Congenital ataxias (NPCA) are a small group of disorders, accounting for about 10% of non-progressive infantile encephalopathies [START_REF] Steinlin | Non-progressive congenital ataxias[END_REF] . Clinically, NPCA manifests in infancy with abnormal motor development, hypotonia, and delayed ability to sit and stand, followed by the appearance of ataxia [START_REF] Steinlin | Non-progressive congenital ataxias[END_REF] . Dysarthria, mental retardation, and spasticity are also often present [START_REF] Harding | Hereditary ataxias and related disorders[END_REF] .

Pathologically, most of the congenital ataxias are characterized by hypoplasia or atrophy of parts of the cerebellum and brain stem [START_REF] Harding | Clinical features and classification of inherited ataxias[END_REF] . It has been estimated that 50% of cases of congenital ataxia and mental retardation are genetically determined, most being of autosomal recessive inheritance [START_REF] Gustavson | Identical syndromes of cerebral palsy in the same family[END_REF] . To date, about seventeen loci responsible for NPCA are known, of which fourteen are of autosomal recessive transmission. When excluding the nine loci responsible for Joubert syndrome, five loci are assigned to autosomal recessive NPCA: Cayman ataxia (MIM 601238) at chromosome 19p13.3 [START_REF] Nystuen | A cerebellar ataxia locus identified by DNA pooling to search for linkage disequilibrium in an isolated population from the Cayman Island[END_REF] , due to mutations in ATCAY (MIM 608179) [START_REF] Bomar | Mutations in a novel gene encoding a CRAL-TRIO domain cause human Cayman ataxia and ataxia/dystonia in the jittery mouse[END_REF] , Cerebellar ataxia 3 (SCAR6) at chromosome 20q11-q13 (MIM 608029) [START_REF] Kvistad | Autosomal recessive non-progressive ataxia with an early childhood debut[END_REF] , disequilibrium syndrome at chromosome 9p24 (MIM 224050) [START_REF] Boycott | Homozygous deletion of the very low density lipoprotein receptor gene causes autosomal recessive cerebellar hypoplasia with cerebral gyral simplification[END_REF] , "Norman type" ataxia (SCAR2 or CLA1) at chromosome 9q34-9qter (MIM 213200) [START_REF] Delague | A non-progressive autosomal recessive ataxia maps to chromosome 9q34-9qter in a large consanguineous Lebanese family[END_REF] , and CAMOS (SCAR5) at chromosome 15q24-q26 [START_REF] Delague | A new autosomal recessive non-progressive congenital cerebellar ataxia, associated with optic atrophy and mental retardation, maps to chromosome 15q24-q26 in a large consanguineous Lebanese Druze family[END_REF] .

ZNF592 is a 1267-aa zinc finger protein, predicted to contain thirteen classical C2H2-type zinc finger domains. C2H2 Zinc fingers (ZnF) were first discovered in transcription factor IIIA from Xenopus laevis [START_REF] Miller | Repetitive zinc-binding domains in the protein transcription factor IIIA from Xenopus oocytes[END_REF] and constitute one of the most common DNA-binding motifs found in eukaryotes [START_REF] Bouhouche | The origin of prokaryotic C2H2 zinc finger regulators[END_REF] . C2H2-ZnF proteins usually play a crucial role as transcriptional regulators by mediating interactions between DNAs and proteins [START_REF] Miller | Repetitive zinc-binding domains in the protein transcription factor IIIA from Xenopus oocytes[END_REF] and perform various functions in cellular processes, such as transcription, translation, metabolism and signalling by binding to nucleic acids or proteins [START_REF] Gamsjaeger | Sticky fingers: zinc-fingers as protein-recognition motifs[END_REF][START_REF] Pabo | Design and selection of novel Cys2His2 zinc finger proteins[END_REF] .

In this study, we report the identification of a missense mutation in ZNF592, encoding a novel, highly conserved, zinc finger transcription factor, as the pathogenic mutation causing CAMOS, a rare NPCA syndrome, where Cerebellar Ataxia is associated with Mental Retardation, Optic Atrophy and Skin abnormalities [START_REF] Mégarbané | A new autosomal recessive cerebellar ataxia disorder in a large inbred Lebanese Family[END_REF] .

Material and Methods

Patients

We previously published the localization of CAMOS to chromosome 15q24-q26 in a large consanguineous Lebanese family (Fig 1) [START_REF] Delague | A new autosomal recessive non-progressive congenital cerebellar ataxia, associated with optic atrophy and mental retardation, maps to chromosome 15q24-q26 in a large consanguineous Lebanese Druze family[END_REF] . Briefly, all patients share the following clinical features: severely delayed developmental milestones, severe psychomotor retardation, proportionate short stature, cerebellar spastic ataxia, microcephaly, optic atrophy, speech defect, ultrastructural skin abnormalities, and cerebellar atrophy, most probably of prenatal onset. For a fully detailed clinical description of the patients, see the work of Mégarbané et al. [START_REF] Mégarbané | A new autosomal recessive cerebellar ataxia disorder in a large inbred Lebanese Family[END_REF] .

After informed consent was obtained from all individuals and parents of children included in this study, EDTA blood samples were collected and genomic DNA was extracted from lymphocytes using standard methods. All together, fifteen DNA samples were collected for the study, including 5 affected individuals (Fig1). All protocols performed in this study complied with the ethic guidelines of the institutions involved.

Mutation analysis

Of the twenty-four candidate genes present in the 3.6 cM homozygous interval, as described in the databases (Ensembl Genome Browser, UCSC Human Genome Browser), the following ten were selected, based on their function and tissue-specific expression; and tested for the presence of a pathogenic mutation: AP3B2, SH3GL3, BTBD1, HMG20A, HOMER2, RKHD3, EFTUD1, ZSCAN2, SCAND2 and ZNF592 (Fig 2A). Exploration of the entire coding sequence, as well as of exon-intron boundaries and 5' and 3' untranslated regions (UTRs), was performed for each candidate gene (Fig 2A). Intronic primers were designed using the Primer3 and OLIGOS v.9.3 softwares. Primer sequences and annealing temperatures used for PCRs are available as supplementary material (Table 1). DNA sequences were obtained from the UCSC Human Genome Browser (UCSC, March 2006 freeze), by comparing genomic DNA with cDNA sequences.

Genomic DNA from Patient VI.14 and a control were amplified under standard PCR conditions.

All PCR amplified fragments were analyzed by dHPLC/WAVE (Transgenomic, Omaha, NE, USA) and fluorescently sequenced in both directions, using an ABI 310 or ABI 3130 automated sequencer (Applied Biosystems, Foster City, USA), for those presenting abnormal elution profiles (conditions for dHPLC analysis are available upon request). Chromatograms were compared to reference sequences using Sequencher v4.2 (Gene Codes Corporation, Michigan, USA) and ChromasPro v1.33 (Technelysium, Tewantin, Australy).

Segregation in the pedigree, of the identified c.3136G>A nucleotide change, as well as its presence in 444 Lebanese control chromosomes, were assessed by PstI restriction endonuclease digestion (Boehringner Mannheim) or dHPLC.

Transcriptional analysis

Total RNA was extracted from freshly isolated lymphocytes or immortalized lymphocytes, using standard protocols as described before [START_REF] Delague | Mutations in FGD4 encoding the Rho GDP/GTP exchange factor FRABIN cause autosomal recessive Charcot-Marie-Tooth type 4H[END_REF] . cDNAs were obtained from total RNA with use of Superscript I Reverse Transcriptase (Invitrogen Life Technologies) and random primers (InvitrogenLife Technologies), in accordance with the recommendations of the supplier. cDNAs were then PCR amplified as described above. Primers and annealing temperatures for amplification of the whole ZNF592 cDNA are available as supplementary material (Table 1).

Primers corresponding to fragment 6 have been used for verification of the effect of the variation on ZNF592's splicing.

Semi-quantitative RT-PCR

In human adult tissues, ZNF592's expression profile was characterized, using Rapid Scan Gene Expression Panels from ORIGENE (Rockville, USA). These panels consist of cDNAs synthesized from poly(A+) RNA and immobilized at four cDNAs concentrations (100X and 1000X) on a 96well PCR plate. Human panels include 24 different human adult tissues and 12 brain tissues (Supp. fig. 1A-B). Expression of ZNF592 during development was assessed in 6 human foetal tissues by semi-quantitative RT-PCR using Multiple Choice cDNAs from ORIGENE (Rockville, USA), and, in mouse, using mRNAs extracted from whole embryo, at different developmental stages (Supp. fig. 1D-E).

Primers used for amplification are listed in Table 1 (Supplementary Material). In all experiments, ß-Actin was used for normalisation and amplified using primers included in the kit (ORIGENE, Rockville, USA).

Northern-Blot

Quantitative Northern-Blot analysis of ZNF592 expression in different human tissues was realized using commercially available synthetic polyA+ membranes from Ambion (Foster City, USA) and Clontech (Moutain View, USA), that were hybridized with a 972 bp radioactively labelled ([ 32 P]-dATP) cDNA probe, covering ZNF592 exons 3 to 8. A Human ß-Actin cDNA probe provided by the manufacturer (ORIGENE, Rockville, USA) was used as a normalizing control.

For patients' Northern-Blot, we immobilized polyA+ mRNAs, extracted from homozygous patient VI.1 's, heterozygous father V.2's and Lebanese control's lymphoblastoid cells, using the µMacs mRNA isolation kit from Myltenyibiotech (Bergisch Gladbach, Germany); and the obtained synthetic membrane was hybridized to the 972 bp ZNF592 cDNA probe cited above. All steps were realized using the NorthernMax-Gly kit (Ambion, Foster City, USA), following the manufacturer's recommendations.

Real-Time RT-PCR (QRT-PCR)

SYBR Green real-time PCRs (QRT-PCRs) were realized according to standard protocols in a 20-µl amplification mixture containing 10 μl of SYBR® Green PCR Master Mix buffer (Applied Biosystems, Foster City, CA, USA), 0.25 μM of each primer and 20 ng of RNAse H treated (Invitrogen Life Technologies) cDNAs obtained from reverse transcription of 5µg of DNAse Itreated total RNA extracted from homozygous patient VI.1, heterozygous father V.2 and controls blood lymphocytes by use of the High Capacity cDNA Archive Kit (Applied Biosystems).

Reactions were performed and data collected on the ABI PRISM 7500 Sequence Detection System (Applied Biosystems, Foster City, CA, USA) using conditions recommended by the manufacturer. Each assay included non-template controls and the unknown samples in triplicates: i.e patient VI.1, heterozygous father V.2. For ZNF592, five different calibrators (Lebanese controls) were used. All experiments have been repeated twice, with a freshly extracted mRNA from patient VI.1 and father V.2. The expression values of ZNF592 were normalized to that of GUS and GAPDH, while CCDN1 and CCDN2 expression values were normalized to that of TBP and GUS. For each gene, the expression ratio for a sample was calculated as the ratio between the average mRNA signal in the patient and the signal from calibrators. After the reaction, the data were analyzed using the comparative CT relative quantification method with ABI PRISM 7500 system SDS software version 1.2.3 (Applied Biosystems, Foster City, CA, USA). Primers for QRT-PCR were designed using Primer Express software version 2 (Applied Biosystems, FosterCity, CA, USA). All primer sequences are listed in

Protein homology modelling studies

Wild-type and mutant eleventh ZNF592's C2H2 Zinc Finger (ZnF) were modelized using freely available Swiss-Pdb Viewer software. As no PDB structure was available for ZNF592 in the Protein Data Bank (PDB), we used the structure of the C2H2 zinc-binding domain from ZFP64/ZNF338 (PDB ID : 1X5W), another human zinc finger protein, presenting sequence homologies with ZNF592's zinc fingers. Using Swiss-Pdb Viewer, we changed all amino acids (aa) to ZNF592 aa. In the mutant ZnF, the glycine at position 41 was replaced by an arginine, as observed in patients affected with CAMOS, who harbour the p.Gly1046Arg missense mutation.

In the mutant C2H2 zinc-finger domain 3D structure (B), mutation of Gly41 to Arg41 results in the formation of a new hydrogen bond interaction between Arg41 and the adjacent tyrosine Tyr42.

Web resources

GenBank Accession numbers:

Results

Using DNA pooling and homozygosity mapping, we had previously assigned CAMOS to a 3.6 cM (5.7 Mb) homozygous region at chromosome 15q24-q26 between markers D15S206 and D15S199, in a large consanguineous Lebanese family, with five affected individuals [START_REF] Delague | A new autosomal recessive non-progressive congenital cerebellar ataxia, associated with optic atrophy and mental retardation, maps to chromosome 15q24-q26 in a large consanguineous Lebanese Druze family[END_REF] (Fig 1).

Screening of the coding sequence of genes lying in the candidate interval, by direct sequencing, allowed us to identify a c.3136G>A homozygous transition in exon 6 of ZNF592, a gene encoding a 1267-aa zinc finger protein, and predicted to contain thirteen classical C2H2-type zinc finger domains (Fig 2). The c.3136G>A nucleotide change identified in our patients was not reported in the NCBI dbSNP database, segregated perfectly with the phenotype in the pedigree and was not found in the 444 tested Lebanese control chromosomes, excluding the possibility that it might be a rare polymorphism and indicating that this variant was likely to be pathogenic. As the variation is affecting the second last nucleotide of exon 6, just upstream the 5' consensus donor splice site, we tested whether it might affect splicing of ZNF592 transcript. RT-PCR studies using total RNAs extracted from patients and Lebanese control's blood lymphocytes, and primers located in exons surrounding ZNF592 exon 6, allowed us to rule out this hypothesis, at least in the tested tissue (Fig 2C). Occurrence of small deletions/insertions was excluded by sequencing of the obtained RT-PCR fragment in patients and control. Other complex splicing defects were excluded by amplification and sequencing of the entire cDNA. At the protein level, the ZNF592 c.3136G>A mutation is likely to be a missense mutation, leading to the replacement of a glycine by an arginine at residue 1046 (p.Gly1046Arg; GGG>AGG). It targets a highly conserved amino acid residue among eutherian mammals, located in the eleventh C2H2 zinc-finger domain, at the base of the loop between the two conserved cysteines (Fig 3).

Protein homology modelling using wild-type and mutant predicted C2H2 zinc-finger domain 3D structure showed that mutation of glycine to arginine results in the formation of a new hydrogen bond interaction between Arg41 and the adjacent tyrosine Tyr42 in the mutant C2H2 zinc-finger (Fig 4).

Considering the specificity of tissues involved in our pathology (CNS and skin), we characterized ZNF592's expression profile, in both human and mouse tissues (Supp. fig. 1). Both semiquantitative RT-PCR experiments, using Rapid Scan Gene Expression Panels from ORIGENE (Rockville, USA), and Northern Blot experiments demonstrated ubiquitous expression of ZNF592 in all studied human adult tissues, notably in brain and skin, with higher expression in skeletal muscle (Supp. fig 1A-C). In the Central Nervous System (CNS), ZNF592 is expressed widely, including in cerebellum and cerebellar vermis, with higher expression in Substantia Nigra (Supp. In patients affected with CAMOS, we analysed ZNF592's mRNA levels using Northern Blot and Quantitative Real-Time RT-PCR (QRT-PCR). Both experiments evidenced higher levels of ZNF592 transcript levels in both the patient, and heterozygous father, as compared to control (data not shown for Northern Blot and Supplementary figure 2 for QRT-PCR), with a mean 3-fold increase in patient VI.1. Surprisingly, ZNF592 transcripts levels were even higher in the heterozygous father. No statistical analysis could be performed due to the small size of the sample (only one patient), however all experiments have been performed in triplicates and have been repeated twice, with freshly extracted total RNA samples in the second experiment. Unfortunately, we were not able to confirm these results at the protein level, as a polyclonal antibody against ZNF592 generated in rabbit failed to detect ZNF592 in control tissues (data not shown).

We studied the expression of cyclin-D1 (CCND1) and -D2 (CCND2) in CAMOS patient VI.1 's lymphocytes using QRT-PCR. Interestingly, we found an increase in CCND1 and CCND2 mRNA levels; again, both in the patient and in the heterozygous father as compared to control, with a mean 43-fold and 3-fold increase in CCND1 and CCND2 patient's transcripts levels respectively.

As for ZNF592, no statistical analysis could be performed, but all experiments have been performed in triplicates and have been repeated twice.

Discussion

CAMO is a rare non progressive cerebellar ataxia syndrome, where Cerebellar Ataxia is associated with Mental Retardation, Optic Atrophy and Skin abnormalities [START_REF] Mégarbané | A new autosomal recessive cerebellar ataxia disorder in a large inbred Lebanese Family[END_REF] . Since the first report and localization of the gene at chromosome 15q24-q26 in a large consanguineous Lebanese family [START_REF] Delague | A new autosomal recessive non-progressive congenital cerebellar ataxia, associated with optic atrophy and mental retardation, maps to chromosome 15q24-q26 in a large consanguineous Lebanese Druze family[END_REF][START_REF] Mégarbané | A new autosomal recessive cerebellar ataxia disorder in a large inbred Lebanese Family[END_REF] , no additional patients have been reported, pointing out the very low prevalence of this disease. In this study, we report the identification of a c.3136G>A missense mutation (p.Gly1046Arg) in ZNF592, in patients from this family. ZNF592 is a novel, highly conserved, 1267-aa zinc finger protein, predicted to contain thirteen classical C2H2-type zinc finger domains (ZnF) (Fig 2A and3A), which constitute one of the most common DNA-binding motifs found in eukaryotes [START_REF] Bouhouche | The origin of prokaryotic C2H2 zinc finger regulators[END_REF] . Several genes encoding zinc-finger proteins have been implicated in human pathologies, such as ZNF215 in Beckwith-Wiedemann syndrome 17 (MIM 130650); ZNF41 (MIM 314995) [START_REF] Shoichet | Mutations in the ZNF41 gene are associated with cognitive deficits: identification of a new candidate for X-linked mental retardation[END_REF] , ZNF81 [START_REF] Kleefstra | Zinc finger 81 (ZNF81) mutations associated with X-linked mental retardation[END_REF] (MIM 314998) and ZNF674 [START_REF] Lugtenberg | ZNF674: a new kruppel-associated boxcontaining zinc-finger gene involved in nonsyndromic X-linked mental retardation[END_REF] (MIM 300573) in non syndromic, X-linked mental retardation or ZNF750 in Seborrhea-like dermatitis with psoriasiform elements [START_REF] Birnbaum | Seborrhea-like dermatitis with psoriasiform elements caused by a mutation in ZNF750, encoding a putative C2H2 zinc finger protein[END_REF] . ZNF592 is the first gene of this family found to be mutated in a cerebellar syndrome, although mutations have been described in APTX (MIM 606350), the gene mutated in oculomotor-apraxia (AOA1) and encoding aprataxin, a nuclear protein with a role in DNA repair and containing one C2H2 ZnF [START_REF] Moreira | The gene mutated in ataxia-ocular apraxia 1 encodes the new HIT/Zn-finger protein aprataxin[END_REF][START_REF] Date | Early-onset ataxia with ocular motor apraxia and hypoalbuminemia is caused by mutations in a new HIT superfamily gene[END_REF] .

The p.Gly1046Arg mutation identified here targets a highly conserved amino acid and is located within the eleventh zinc finger of ZNF592. In silico protein homology modelling studies predict a destabilizing effect for the mutation, via the formation of a new hydrogen bond interaction between the mutated arginine and the adjacent Tyrosine (Fig 4), thereby leading to the disruption of the ZnF, as described for other transcription factors [START_REF] Smith | Structural elements in the N-terminal half of transcription factor IIIA required for factor binding to the 5S RNA gene internal control region[END_REF][START_REF] Necela | A single amino acid change in the first zinc finger of the DNA binding domain of the glucocorticoid receptor regulates differential promoter selectivity[END_REF][START_REF] Aarnisalo | Transcription activating and repressing functions of the androgen receptor are differentially influenced by mutations in the deoxyribonucleic acid-binding domain[END_REF] . By affecting ZNF592's DNA binding properties or interactions with other TFs, the p.Gly1046Arg mutation in ZNF592 might also regulate ZNF592's own expression, as evidenced by the higher levels of ZNF592 transcripts observed in the studied patient homozygous for the p.Gly1046Arg mutation. Thus, the ratio of wild-type versus mutant ZNF592 might be crucial, explaining the peculiar pattern of expression observed in heterozygote father versus homozygote patient.

The multiplicity of tissues/organs involved, as well as the non-progressive nature of CAMOS, is characteristic of a developmental disease, with abnormal development of the cerebellum as a hallmark. Several genes for congenital human cerebellar malformations have been identified to date, including members of the Zic family of C2H2 zinc finger TFs [START_REF] Grinberg | Heterozygous deletion of the linked genes ZIC1 and ZIC4 is involved in Dandy-Walker malformation[END_REF] . Indeed, heterozygous deletions of the adjacent ZIC1 (MIM 600470) and ZIC4 (MIM 608948) genes cause Dandy-Walker malformation (MIM 220200), the most common human congenital cerebellar malformation [START_REF] Grinberg | Heterozygous deletion of the linked genes ZIC1 and ZIC4 is involved in Dandy-Walker malformation[END_REF] , and deletion of Zic1 in mouse results in cerebellar malformations and axial skeletal abnormalities [START_REF] Merzdorf | Emerging roles for zic genes in early development[END_REF] . Zic genes play critical roles in a variety of developmental processes and are regulated by a number of pathways/TFs. We postulate that ZNF592 might be a downstream or upstream element in the Zic regulated pathways. By disrupting the interactions between ZNF592 and its target consensus sequence, or between ZNF592 TF and another TF (as described for Zic with members of the Gli family of C2H2 TFs [START_REF] Millen | Cerebellar development and disease[END_REF][START_REF] Koyabu | Physical and functional interactions between Zic and Gli proteins[END_REF] ), the p.Gly1046Arg mutation identified here is likely to affect the pathways regulated by Zic genes. This hypothesis is supported by the early expression of ZNF592, as early as E10 (Supp. fig 1E), the non progressive nature of CAMOS, and the presence of a dilated fourth ventricle in CAMOS patients as observed in patients affected with Dandy-Walker malformation. Cyclin D1 (MIM 168461), a downstream effector of Zic proteins [START_REF] Aruga | The role of Zic genes in neural development[END_REF] , shows reduced transcript expression levels in the cerebella of Zic mutants [START_REF] Aruga | Zic2 controls cerebellar development in cooperation with Zic1[END_REF] , and mice lacking cyclin D1 and cyclin D2 (MIM 123833) (cyclin D3-only mice) lacked normally developed cerebella [START_REF] Ciemerych | Development of mice expressing a single Dtype cyclin[END_REF] . In our patient's lymphocytes, we observe an increase in cyclin-D1 (CCND1) and -D2 (CCND2) mRNA levels, especially important for CCND1 (43 fold increase).

Although preliminary, these results of altered expression patterns are extremely interesting and bring further support to the hypothesis of ZNF592, as a TF implicated in a complex developmental pathway. Indeed, D1-cyclin has been shown to be upregulated by Notch signalling [START_REF] Ronchini | Induction of cyclin D1 transcription and CDK2 activity by Notch(ic): implication for cell cycle disruption in transformation by Notch(ic)[END_REF] , known to inhibit differentiation of cerebellar granule neuron precursors by maintaining proliferation [START_REF] Solecki | Activated Notch2 signaling inhibits differentiation of cerebellar granule neuron precursors by maintaining proliferation[END_REF] . Abnormally elevated levels of cyclin D1 in cerebellar granule neuron precursors, by disrupting proliferation/differentiation processes in these cells, might have impaired cerebellar development in our patients. In this context, the surprisingly elevated levels of ZNF592, cyclin D1 and D2 transcripts in the heterozygous father (Supp. fig. 2), are difficult to interpretate, but might be explained by the fact that the regulation of the described pathways is highly orchestrated in time, and that the amount of each TF might change rapidly in time, with a combination of tightly regulated levels of expression.

In conclusion, this study describes the identification of ZNF592 as the gene responsible for CAMOS, a rare, non progressive, cerebellar ataxia syndrome previously identified in a Lebanese family. Further studies have to be performed in order to elucidate the pathophysiological mechanisms underlying CAMOS. However, our results allow us to formulate the hypothesis that ZNF592 might be implicated in a complex developmental pathway, affecting several tissues, such as the "Zic/Cyclin/Notch" pathway. A major argument in favour of the involvement of ZNF592 in this pathway is the presence, in our patients, of an inversion of the usual osmiophilic pattern of the vessels in skin biopsies: the endothelial cells in patients are osmiophilic, compared to normal endothelium, which is electrolucent [START_REF] Mégarbané | A new autosomal recessive cerebellar ataxia disorder in a large inbred Lebanese Family[END_REF] . Indeed, neural and vascular precursors use common signals and pathway, such as Notch, Sonic Hedgehog (Shh) or BMP, to specify their fate; and neural and vascular cells influence the cell-fate decision making of one another [START_REF] Carmeliet | Blood vessels and nerves: common signals, pathways and diseases[END_REF] . The Notch pathway, in particular, has a crucial role in arterial Endothelial Cell (EC) specification, by inducing arterial fate at the expense of venous EC fate [START_REF] Carmeliet | Blood vessels and nerves: common signals, pathways and diseases[END_REF] . Implication of ZNF592 in a pathway common to neural and vascular progenitors would explain the affection of both tissues in CAMOS.

The identification of ZNF592 as the defective protein in CAMOS constitutes a first step in the comprehension of the pathophysiological mechanisms underlying this syndrome. Further experiments will be conducted in order to better define which pathways are involved. Primers sequences and annealing temperatures used for the analysis of ZNF592 coding sequence at the genomic and transcriptional level. Specific primers for real time RT-PCR are also mentioned. All human primers for genomic screening of mutations have been selected based on comparison of genomic DNA sequence with Genbank cDNA sequence BC094688.

Legends to figures and tables

Homo Sapiens

--DTVKKFYTCGYCTEDSPSFPRPSLLESHISLMHGIRNPDLS--

Macaca Mulatta

--DTVKKVYTCGYCTEDSPSFPRPSLLESHISLMHGIRNPDLS--

Mus musculus

--DTVKKVYTCGYCTEDSPSFPRPSLLESHISLMHGIRNPDLS--

RaƩus Norvegicus

--DTVKKVYTCGYCSEDSPSFPRPSLLESHISLMHGIRNPDLS--

Canis familiaris

--DTVKKVYTCGYCTEDSPSFPRPSLLESHISLMHGIRNPDLS--

Equus Caballus

--DTVKKVYTCGYCTEDSPSFPRPSLLESHISLMHGIRNPDLS--

Bos Taurus

--DTVKKVYTCGYCTEDSPSFPRPSLLESHISLMHGIRNPDLS--

Monodelphis domesƟca

--DTAKKVYTCWYCTEDKPSFPQLSLLENHVSLMHGIKNLDLS--

Danio Rerio

--NGKKKVYTCWYCTSERMSFTEHSLLKNHISLMHGRPKKRRA--

Xenopus Tropicalis

--DTKKD-YTCCYCT-DKPTFVKPSMLANHIILMHGIKNPELP--p.Gly1046Arg

A B

  SCAND2 : NM_033634 (the sequence was suppressed afterwards as the transcript is in fact a NMD transcript) ZNF592: BC094688, NM_014630, NC_000015, ENST00000299927, ENSG00000166716In the databases, discrepancies exist between GenBank (NM_014630 and NC_000015), the UCSC Genome Browser, and the Ensembl browser (ENST00000299927, ENSG00000166716) concerning the length of the transcript (but not the CDS), the number of exons, the length of the UTRs and the region covered by ZNF592. Based on results of Northern blot experiments (see Suppl. Fig 1C), we used the sequence with Acc. Number BC094688, as a reference in our study. ZFP64/ZNF388: NP_060667 PDB ID for ZFP64/ZNF338: 1X5W ZNF592 proteins: NP_055445 (Homo sapiens), NP_848822 (Mus musculus), XP_001084237 (Macaca Mulatta), NP_001099742 (Rattus norvegicus), XP_545869 (Canis familiaris), XP_001916274 (Equus Caballus), NP_001095506 (Bos Taurus), XP_001364673 (Monodelphis domestica), NP_001072160 (Xenopus Tropicalis), NP_001038678 (Danio Rerio). URLs: Online Mendelian Inheritance in Man (OMIM): http://www.

  fig 1B). Very low levels of ZNF592 mRNA were detected in ovary, uterus and salivary glands

Figure 1 .

 1 Figure 1. Pedigree of the Lebanese family

Figure 2 .

 2 Figure 2. Candidate genes in the homozygous region identified in CAMOS with, identification

Figure 3 .

 3 Figure 3. Schematic representation of the zinc fingers (ZnF) and conservation between species

Figure 4 .

 4 Figure 4. 3D structures of wild-type and mutant ZNF592 C2H2 Zinc finger

Table 1 (

 1 Supplementary Material). Results are presented as average values for experiments withGUS as a normalizing gene.

  ncbi.nlm.nih.gov/Omim Design of primers available at http://frodo.wi.mit.edu/ The UCSC Genome Browser is available at http://genome.ucsc.edu/cgi-bin/hgGateway.

	Ensembl Server: http://www.ensembl.org/
	NCBI dbSNP database: http://www.ncbi.nlm.nih.gov/SNP/
	RCSB Protein Databank: http://www.rcsb.org/pdb/home/home.do
	Swiss-Pdb Viewer: http://spdbv.vital-it.ch/
	DEPP (Disorder Enhanced Phosphorylation predictor):
	http://www.pondr.com/Phosphorylation_PONDR

Acknowledgments

We express our deepest gratitude and sympathy to the families for their full cooperation throughout the study. The authors wish to thank Pr. Gérard Lefranc for constant support and logistics. This work was financially supported by the Saint-Joseph University (USJ) and the Institut National de la Santé et de la Recherche Médicale (Inserm). Elsa Nicolas was supported by a grant from the Agence Universitaire de la Francophonie (AUF).

Supplementary information is available at the European Journal of Human Genetics' website

Legends to supplementary tables and figures

Supplementary Figure 1. Expression Analysis

(A) Semi quantitative expression of ZNF592 in 24 different human adult tissues. cDNAs synthesized from poly(A+) RNA and immobilized at four cDNAs concentrations (1X, 10X, 100X and 1000X) on a 96-well PCR plate, were amplified using primers located in ZNF592 exons 1 and 2 (see Supp. table 1).

(B) Semi quantitative expression of ZNF592 in 12 different parts of the central nervous system, using immobilized cDNAs at two concentrations as in (A). ZNF592 is expressed widely, including in cerebellum and cerebellar vermis, with higher expression in Substantia Nigra.

Supplementary Table 1.


A Pashkevich
email: anatol.pashkevich@emn.fr

A Klimchik

D Chablat
email: damien.chablat@irccyn.ec-nantes.fr

Stiffness Analysis of Parallel Manipulators with Preloaded Passive Joints

Keywords: modeling, parallel manipulators, external loading, internal preloading, passive joints

The paper presents a methodology for the enhanced stiffness analysis of parallel manipulators with internal preloading in passive joints. It also takes into account influence of the external loading and allows computing both the non-linear "load-deflection" relation and the stiffness matrices for any given location of the end-platform or actuating drives. Using this methodology, it is proposed the kinetostatic control algorithm that allows to improve accuracy of the classical kinematic control and to compensate position errors caused by elastic deformations in links/joints due to the external/internal loading. The results are illustrated by an example that deals with a parallel manipulator of the Orthoglide family where the internal preloading allows to eliminate the undesired buckling phenomena and to improve the stiffness in the neighborhood of its kinematic singularities.

Introduction

Parallel manipulators have become very popular in many industrial applications due to their inherent advantages of providing better accuracy, lower mass/inertia properties, and higher structural rigidity compared to their serial counterparts [START_REF] Merlet | Parallel Robots[END_REF]. These features are induced by the specific kinematic structure, which eliminates the cantilever-type loading and allows to minimize deflections caused by external torques and forces. One recent development in this area, which is targeted at highprecision manipulation, is a replacing the standard passive joints by preloaded ones, which contain internal passive springs eliminating the backlash or ensure some degree of static balancing [START_REF] Arsenault | Kinematic and static analysis of a 3-PUPS spatial tensegrity mechanism[END_REF][START_REF] Griffis | Preloading compliant couplings and the applicability of superposition[END_REF]. This modification obviously improves the manipulator performances but requires some revision of existing stiffness analysis techniques that are in the focus of this paper.

In most of previous works, the manipulator stiffness analysis was based on the linear modeling assumptions which ignore influence of the external or internal forces [START_REF] Ceccarelli | A stiffness analysis for CaPaMan (Cassino Parallel Manipulator)[END_REF][START_REF] Company | Modelling and preliminary design issues of a 4-axis parallel machine for heavy parts handling[END_REF][START_REF] Kao | Conservative Congruence Transformation for Joint and Cartesian Stiffness Matrices of Robotic Hands and Fingers[END_REF][START_REF] Alici | The stiffness matrix in elastically articulated rigid-body systems[END_REF][START_REF] Ciblak | Synthesis of Cartesian Stiffness for Robotic Applications[END_REF]. Consequently, relevant techniques are targeted at linearization of the "force-deflection" relation in the neighborhood of the non-loaded equilibrium, which is perfectly described by the stiffness matrix [START_REF] Kovecses | The stiffness matrix in elastically articulated rigid-body systems[END_REF][START_REF] Quennouelle | Stiffness Matrix of Compliant Parallel Mechanisms[END_REF]. However, in the case of non-negligible internal and/or external loading, the manipulator may demonstrate essentially non-linear behaviour, which is not exposed in the unloaded case [START_REF] Timoshenko | Theory of elasticity[END_REF]. In particular, the loading may potentially lead to multiple equilibriums, to bifurcations of the equilibriums or to static instability of certain manipulator configurations [START_REF] Su | A polynomial homotopy formulation of the inverse static analysis of planar compliant mechanisms[END_REF][START_REF] Carricato | Catastrophe analysis of a planar system with flexural pivots[END_REF].

This paper presents an extension of our previous results [START_REF] Pashkevich | Stiffness analysis of overconstrained parallel manipulators[END_REF] devoted to the stiffness analysis of parallel manipulators by generalizing them for case of internal preloading [START_REF] Crane | Kinematic analysis of a planar tensegrity mechanism with pre-stressed springs[END_REF] in the passive joints. It implements the virtual joint method (VJM) of Salisbary [START_REF] Salisbury | Active Stiffness Control of a Manipulator in Cartesian Coordinates[END_REF] and Gosselin [START_REF] Gosselin | Stiffness mapping for parallel manipulators[END_REF] that describes the compliance of the manipulator elements by a set of localized multi-dimensional springs separated by rigid links and perfect joints. The proposed technique allows computing the loaded equilibrium, finding the full-scale "load-deflection" relation and evaluating the corresponding stiffness matrices for any given location of the end-platform or actuating drives [START_REF] Pashkevich | Stiffness analysis of multichain parallel robotic systems with loading[END_REF]. It is also developed a kinetostatic control algorithm that allows to improve accuracy of the classical kinematic control and to compensate position errors caused by elastic deformations in links/joints due to the external/internal loading.

The remainder of this paper is organized as follows. Section 2 defines the research problem and basic assumptions. Section 3 deals with computing of the loaded static equilibrium and corresponding "load-deflection" relation. Section 4 focuses on its linearization and evaluation of the stiffness matrix. Section 5 presents the kinetostatic control algorithm. Section 6 contains an illustrative example. And finally, Section 7 summarizes the main results and contributions.

Manipulator model

Let us consider a general parallel manipulator that is composed of n serial kinematic chains connecting a fixed base and a moving platform Figure 1. It is assumed, that the chain architecture ensures kinematic control of the manipulator but may introduce some redundant constraints that improve the rigidity. Following the VJMconcept [START_REF] Gosselin | Stiffness mapping for parallel manipulators[END_REF], let us presents the manipulator chains as sequences of pseudo-rigid links separated by rotational or translational joints of one of the following types: (i) perfect passive joints ; (ii) preloaded passive joints that include auxiliary flexible elements; (iii) virtual flexible joints that describe compliance of the actuators and manipulator links; (iv) actuating joints. Using this notation the geometrical model of the chain may be written as

t = g(ρ, q, ϑ , θ ), (1)
where the vector t = (p, ϕ) T includes the Cartesian position p = (x, y, z) T and orientation ϕ = (ϕ x , ϕ y , ϕ z ) T of the end-platform, ρ is the vector of actuated coordinates (they are constant for static analysis), the vector q contains coordinates of all perfect passive joints, the vector ϑ includes coordinates of the preloaded pas- sive joints, and the vector θ collects coordinates of all virtual springs describing elasticity of the links and joints.

The above mentioned elements of the kinematic chain differ in their static characteristics. In particular, the joints (i) and (iii) are described by the standard expressions [START_REF] Pashkevich | Stiffness analysis of overconstrained parallel manipulators[END_REF] τ q = 0 and τ

θ = K θ • θ (2)
where τ q and τ θ are the generalized force/torque reactions corresponding to the aggregated vectors of the passive joint coordinates q and virtual joint coordinates θ ; K θ is the generalized stiffness matrix of all virtual springs. However, the preloaded passive joints (ii) may include both linear and non-linear auxiliary springs, some examples of which are shown in Figure 2. In this paper, we will describe statics of the preloaded joints by a general expression

τ ϑ = K ϑ • h(ϑ -ϑ 0 ) (3)
where τ ϑ is the generalized force/torque reactions corresponding to the aggregated vectors of the preloaded joint coordinates ϑ ; ϑ 0 defines the preloading value; K ϑ is the generalized stiffness matrix of preloaded joints, and the vector function h(...) is assumed to be piecewise-linear, such that each of its scalar components h i (...) can be expresses either as the difference (ϑ i -ϑ i0 ), or its positive or negative part 2 for details). Using these assumptions, let us derive the stiffness model of the considered manipulator and sequentially consider the following sub-problems: (i) computing the loaded static equilibrium and obtaining the "load-deflection" relation; (ii) lineariza-tion of this relations in the neighborhood of this equilibrium and computing the stiffness matrix; (iii) developing the kinetostatic control algorithm, which allows to compensate position errors caused by the elastic deformations and preloading.

[ϑ i -ϑ i0 ] + , [ϑ i -ϑ i0 ] -(see Figure

Static equilibrium

Let us obtain first the configuration of each kinematic chain (q, θ , ϑ ) and external force F that correspond to the static equilibrium with the end-point location t. Obviously, it is a dual problem compared to the classical static analysis but it is more reasonable here because of strictly parallel structure of the considered manipulator (see Figure 1). The latter allows applying the same technique to all kinematic chains (with the same end-point location) and to compute the total external loading as the sum of the partial loadings.

Taking into account the assumption on the piecewise-linear property of the function h(.), let us perform regrouping of the variables. In particular, for each current configuration of the chain, the coordinates of the preloaded passive joints described by the vector ϑ may be separated into two parts ϑ θ and ϑ q , where the first one corresponds to the active state of the auxiliary springs and the second part describes non-active springs (see Figure 2 for geometrical interpretation). This allows replacing the original set of the configuration variables (q, θ , ϑ ) by a set of two vectors ( q, θ ), where q aggregates the joint coordinates (q, ϑ q ) that currently are passive and the vector θ collects all spring coordinates (θ , ϑ θ ) (both virtual and passive).

Using these notations and applying the virtual work technique, the static equilibrium equation of the kinematic chain may be written as

JT θ • F = Kθ • ( θ -θ0 ); JT q • F = 0 ( 4
)
where F is the external force applied at the end-point of the chain, the vector θ T 0 = [0 T , ρ T 0 ] aggregates the spring preloadings (which is obviously zero for the virtual springs), Kθ = diag(K θ , K ϑ ), and Jθ , Jq are the kinematic Jacobians derived from (1) by differentiating it with respect to θ , q. This system of equation ( 4) combined with the geometrical model (1), which must be rewritten in terms of the redefined variables t = g( q, θ ).

(

) 5
This yields the desired joint coordinates of the static equilibrium for a separate kinematic chain with given end-point location. Since the derived system is highly nonlinear, in general case a desired solution can be obtained only numerically. In this paper, it is proposed to use the following iterative scheme

F i+1 qi+1 = Jθ ( qi , θi ) • K-1 θ • JT θ ( qi , θi ) Jq ( qi , θi ) JT q ( qi , θi ) 0 -1 ε i 0 θi+1 = K-1 θ • JT θ ( qi , θi ) • F i+1 + θ0 ε i = t -g( qi , θi ) + Jq ( qi , θi ) • qi + Jθ ( qi , θi ) • ( θi + θ0 ) (6)
where the starting point ( θ0 , q0 ) is also computed iteratively, started from a nearest unloaded configuration where the joint coordinates are easily obtained from the inverse kinematic model. On the following iterations, to improve convergence, the system variables are slightly randomly disturbed. As follows from computational experiments, the proposed iterative algorithm possesses rather good convergence (3-5 iterations are usually enough).

Stiffness matrix

To compute the desired stiffness matrix, let us consider the neighborhood of the equilibrium configuration and assume that the external force and the end-effector location are incremented by some small values δ F, δ t. Besides, let us assume that a new configuration also satisfies the equilibrium conditions. Hence, it is necessary to consider simultaneously two equilibriums corresponding to the manipulator state variables (F, q, θ , t) and (F + δ F, q + δ q, θ + δ θ , t + δ t). Relevant equations of statics may be written as

JT θ F = Kθ ( θ -θ0 ); JT q F = 0; Jθ + δ Jθ T (F + δ F) = Kθ θ -θ0 + δ θ ; Jq + δ Jq T (F + δ F) = 0 (7)
where δ Jq ( q, θ ) and δ Jθ ( q, θ ) are the differentials of the Jacobians due to changes in ( q, θ ). Besides, in the neighborhood of ( q, θ ), the kinematic equation ( 5) may be also presented in the linearized form:

δ t = Jθ ( q, θ ) • δ θ + Jq ( q, θ ) • δ q, (8)
Hence, after neglecting the high-order small terms and expanding the differentials via the Hessians of the function Ψ = g( q, θ )

T F HF qq = ∂ 2 Ψ /∂ q2 ; HF θ θ = ∂ 2 Ψ /∂ θ 2 ; HF qθ = ( HF θ q ) T = ∂ 2 Ψ /∂ q ∂ θ , (9)
equations ( 7) may be rewritten as

JT θ ( q, θ ) • δ F + HF θ q ( q, θ ) • δ q + HF θ θ ( q, θ ) • δ θ = Kθ • δ θ JT q ( q, θ ) • δ F + HF qq ( q, θ ) • δ q + HF qθ ( q, θ ) • δ θ = 0 (10) qθ • kF θ • JT θ HF qq + HF qθ • kF θ • HF θ q -1 (12)
Finally, when the stiffness matrices for all kinematic chains are computed, the stiffness of the entire multi-chain manipulator can be found by simple summation

K Σ = ∑ n i=1 K ci .
It should be noted that, because of presence of the passive joints, the stiffness matrix of a separate serial kinematic chain is always singular, but aggregation of all the manipulator chains of a parallel manipulator produce a non-singular stiffness matrix.

Kinetostatic control

In robotics, the manipulator motions are usually generated using the inverse kinematic model that allows computing the input (reference) signals for actuators ρ corresponding to the desired end-effector location t. However, for manipulators with preloaded passive joints, the kinematic control becomes non-applicable because of changes in the end-platform location due to the internal loading. Hence, in this case, the control must be based on the inverse kinetostatic model that takes into account both the manipulator geometry and elastic properties of its links and joints [START_REF] Su | A polynomial homotopy formulation of the inverse static analysis of planar compliant mechanisms[END_REF].

Using results from the previous sections, the desired inverse kinetostatic transformation can be performed iteratively, in the following way:

Step#1. For given target location of the end-platform t, compute initial values of the actuated coordinates ρ 0 by applying the inverse kinematic transformation.

Step#2. For current values of the actuated coordinates ρ i and target location of the end-platform t, find the equilibrium configuration for each kinematic chain and compute the corresponding total external loading F i Σ required to achieve the target location.

Step#3. If the computed external loading is less than the prescribed error, i.e. F i Σ < ε F , stop the algorithm, otherwise continue the next step Step#4. Repeat Step#2 several times in the neighborhood of the current solution ρ i and evaluate numerically the matrix S i Fρ = ∂ F i Σ /∂ ρ i describing the sensitivity of F with respect to ρ. As follows from simulation results, this algorithm demonstrates good convergence and can be used both for on-line and off-line trajectory planning. It was successfully applied to the case-study presented in the following Section.

Application example

Let us apply the proposed techniques to the stiffness analysis of the planar manipulator of the Orthoglide family (Figure 3). For illustration purposes, let us assume that the only source of the manipulator elasticity is concentrated in actuated drives, while the passive joints may be preloaded by (i) standard linear springs, or (ii) nonlinear springs with mechanical stop-limit (see Figure 2 for details).

For this manipulator, the kinematic model includes a single parameter L (the leg length) and the dexterous workspace was defined as the maximum square area that provides the velocity (and force) transmission factors in the range [0.5, 2.0]. Using the critical point technique developed for this type of manipulators [START_REF] Chablat | Architecture Optimization of a 3-DOF Parallel Mechanism for Machining Applications, the Orthoglide[END_REF], it was proved that the desired square vertices are located in the points Q 1 (-p, -p) and Q 2 (p, p), where p = 0.45 L. Besides, the square centre Q 0 (0, 0) is isotropic with respect to the velocity and force transmission. The parameters of the actuating drives are also assumed identical and their linear stiffness is denoted as K θ . The auxiliary springs incorporated in the passive joints adjacent to the actuators are described by two parameters: the angular stiffness coefficient K ϑ and the activation angle ϑ 0 that defines the preloading activation point. During simulation, the manipulator endpoint was displaced by value ∆ in the direction Q 0 Q 1 or Q 0 Q 2 , and it was computed corresponding magnitude for external force F.

The stiffness analysis results are summarized in Figures 4,5 and in Table 1. As follows from them, the original manipulator (without preloading in passive joints) demonstrates rather low stiffness in the neighborhood of the point Q 2 , which is roughly 4 times lower than in the isotropic point Q 0 . In contrast, the linear stiffness in the point Q 1 is twice higher than in the point Q 0 . Besides, in the point Q 2 , the external loading may provoke the buckling phenomenon that is caused by a local minimum of the force-deflection relation. In this case, the distance-to-singularity is essentially lower that it is estimated from the kinematical model and the manipulator may easily loose its structural stability.

To improve the manipulator stiffness and to avoid the buckling in the neighborhood of Q 2 , the passive joints were first preloaded by linear springs with activation angle ϑ 0 = 0. As follows from Figure 4, the preloading with parameter K ϑ = 0.1 K θ L 2 allows completely eliminate buckling and improves the stiffness by the factor of 2.3. On the other hand, the stiffness in the points Q 0 and Q 1 changes non-essentially, by 10% and 5% respectively. Hence, with respect to the stiffness, such preloading has positive impact.

The only negative consequence of such preloading is related to changes of the actuator control strategy. In fact, instead of standard kinematic control, it is necessary to apply the kinetostatic control algorithm presented in Section 5. It allows The most efficient solution that eliminates this problem is using of non-linear springs with mechanical stop-limits that are activated while approaching to Q 2 . For instance, as follows from dedicated study, the preloading with the parameters K ϑ = 0.5 K θ L 2 , ϑ 0 = π/12 provides almost the same improvements in Q 2 as the linear spring while preserving usual control strategies if the preloading is not activated. The efficiency of this approach is illustrated by the compliance maps presented in Figure 5.

Stiffness in preloaded joints

K ϑ = 0 0.01 K θ L 2 0.05 K θ L 2 0.1 K θ L 2 Point Q 0 (isotropic point) Actuating joint coordinates ρ L L L L Manipulator stiffness K c K θ 1.01 K θ 1.05 K θ 1.10 K θ Point Q 1 (

Conclusions

Recent advances in mechanical design of robotic manipulators lead to new parallel architectures that incorporates internal preloading in passive joints allowing to improve accuracy but leading to revision of existing stiffness analysis techniques. This paper presents new results in this area that allow simultaneously evaluate influence of internal and external loading and compute both the non-linear "load-deflection" relation and the stiffness matrices for any given location of the end-platform or actuating drives. Using this methodology, it is proposed the kinetostatic control algorithm that allows to improve accuracy of the classical kinematic control and to compensate position errors caused by elastic deformations in links/joints due to the external/internal loading. The efficiency of this technique is confirmed by an application example that deals with a parallel manipulator of the Orthoglide family where the internal preloading allows to eliminate the undesired buckling phenomena and to improve the stiffness in the neighborhood of its kinematic singularities.

In future, these results will be generalized to other types of preloading that may be generated by external gravity-compensation mechanisms and also applied to micromanipulators with flexure joints.

Fig. 1 Fig. 2

 12 Fig. 1 Typical parallel manipulator and VJM-model of its kinematic chain. (Ac -actuator; Ps -Passive joint)

Fig. 3 Step# 5 . 1 •

 351 Fig. 3 Architecture of the Orthoglide manipulator and its planar version.

Fig. 4

 4 Fig.[START_REF] Ceccarelli | A stiffness analysis for CaPaMan (Cassino Parallel Manipulator)[END_REF] Force-deflection relations F = f (∆ /L) in critical points:(1)K ϑ = 0; (2) K ϑ = 0.01 K θ L 2 ; (3) K ϑ = 0.1 K θ L 2(case of preloading with linear springs).

Fig. 5

 5 Fig. 5 Compliance maps for cases of: (a) manipulator without preloading; (b) manipulator with preloading non-linear springs with K ϑ = 0.5 K θ L 2 and ϑ 0 = π/12 (b).

Table 1

 1 Manipulator stiffness for different linear preloading.

  errors caused by elastic deformations due to the internal preloading and to achieve the target end-point location with modified values of the actuated joint coordinates. As follows from Table1, corresponding adjustments of the joint coordinates may reach 0.1 L and are not negligible for most of applications.

		neighborhood of "bar" singularity)
	Actuating joint coordinates ρ 0.437 L	0.433 L	0.419 L	0.402 L
	Manipulator stiffness K c	2.276 K θ	2.286 K θ	2.329 K θ	2.382 K θ
	Point Q 2 (neighborhood of "flat" singularity)
	Actuating joint coordinates ρ 1.345 L	1.356 L	1.399 L	1.453 L
	Manipulator stiffness K c	0.24 K θ	0.27 K θ	0.39 K θ	0.55 K θ
	Critical force F cr	0.020 K θ L	0.027 K θ L	-	-
	compensating the position

Acknowledgements

The work presented in this paper was partially funded by the Region "Pays de la Loire" (project RoboComposite).