A Dexterous System for Laryngeal Surgery

Transcription

1 A Dxrous Sysm for aryngal Surgry Mul-Backbon Bndng Snak-lk Slavs for Tloprad Dxrous Surgcal Tool Manpulaon Nabl Smaan, Russll Taylor Johns Hopkns Unvrsy-ERC-CISST Balmor, MD, 8, USA {nsmaan, Paul Fln Johns Hopkns School of Mdcn Balmor, MD, 87, USA Absrac Ths papr prsns a dsgn ovrvw of a novl hgh DoF (Dgrs-of-Frdom) sysm bng dvlopd for mnmally nvasv surgry of h hroa. Th sysm s dsgnd o allow rmo opraon of - ools wh hgh p dxry o nabl suurng and sof-ssu manpulaon whl usng h pan s mouh as h only nry por. Th slav s a 4 DoF un quppd wh hr snak-lk dsal dxry uns for surgcal ool manpulaon. Each of hs uns s a mul-backbon snaklk mchansm quppd wh a dachabl mll paralll manpulaor allowng nrchangabl ools o b usd. Th papr prsns h ouln of h knmac analyss of h snak-lk uns and proposs on possbl acuaon rdundancy rsoluon o allow furhr downsz scalably whl rducng h rsk of bucklng of h prmary backbon of h snak-lk uns. Fnally, h papr prsns a frs arly xprmn wh a prooyp of h snak-lk un. Kywords- NT, muly backbon robo, snak robos, surgcal asssan, masr-slav mod. I. INTRODUCTION Ths papr rpors our work o dvlop a hgh-dxry roboc sysm for mnmally nvasv surgry (MIS) of h hroa an organ unusually challngng bcaus of s shap, lngh, and complxy. Throa surgry s characrzd by nsron of ndoscops and mulpl long ools hrough a narrow ub (h laryngoscop) nsrd no h pan s mouh. Currn manual nsrumnaon s awkward, hard o manpula prcsly, and lacks suffcn dxry o prm common surgcal subasks such as suurng vocal fold ssu. Our goal s a hr-armd loprad robo wh hgh dsal dxry capabl of suurng and smlar ssu manpulaon asks hrough h laryngoscop. Our approach mphaszs Dsal Dxry Uns (DDU) wh a novl dsgn mound on h nd of prcsly manpulad, hn robo arms. Th DDU dsgn s asly scalabl o small szs, smpl o manufacur, and can b usd wh mulpl dachabl surgcal ools. Prvous work on lroboc sysms for MIS has focusd on ndoscopc surgry of h chs and abdomn. Th slav robos usd n hs sysms us dffrn mchancal archcurs, ncludng rmo-cnr-of-moon mchansms (.g., [], []), sral-lnk robos wh passv jons [], and mn-paralll robos (.g., [4], [5]). Furhr xampls may b found n [6]. A fundamnal challng for all of hs robos s h knmac consran mposd by h passag of surgcal ools hrough fxd nry pors no h pan s body. If mor han four dgrs-of-frdom (DoF) ar rqurd n manpulang a surgcal nsrumn, hn som form of dsal dxry mchansm s rqurd. Svral approachs o dsal ool dxry nhancmn hav bn rpord. Many sysms (.g., [7] []) usd wr acuad arculad wrss. Ohr sysms usd snak-lk acv bndng dvcs. For xampl, [8] usd bndng SMA (Shap Mmory Alloy) forcps for laparoscopc surgry. Daro al [9] prsnd a DoF SMA acuad a planar bndng snak-lk dvc for kn arhroscopy and [0] dsgnd a hypr-rdundan SMA acuad snak for gasro-nsnal nrvnon. Rcnly, [] prsnd a wo DoF 5 mm damr wr-drvn snak-lk ool usng supr-lasc NT. Th auhors of [7] analyzd alrnav dsgns of a DoF wrs for MIS suurng. Thy proposd a mhod o drmn h workspac and o opmz h poson of h nry por n h pan s body o provd opmal dxry. Mor rcnly, [] proposd an algorhm for nry por poson opmzaon basd on dxry consdraons. In hroa surgry h nry por s prdrmnd (h pan s mouh) and mulpl ools hav o opra hrough a long and narrow laryngoscop. Hnc, h nd for xra dxry and sz rducon n MIS hroa surgry s wofold. In h currn papr, w dscuss our ovrall sysm dsgn approach, bu focus on our dsgn for h DDU. Th DDU dffrs from prvous work n rms of applcaon, sz, downsz scalably, acuaon, and knmac archcur. In oal, h DDU s quppd wh svn acuad jons and has sx ndpndn DoF. Th whol sysm prsnd n scon III has 4 conrolld DoF allowng h manpulaon of up o hr ools nsd h hroa. Th followng scon prsns h clncal rlvanc of h chosn applcaon of hs sysm. Thn, scon III prsns h ovrall sysm archcur. Scon IV prsns h workspac and forc rqurmns from h dsgnd sysm. Scon V prsns h dsal dxry uns. Scon VIII prsns a knmac analyss of h snak-lk uns. Scon VII proposs a mhodology for anagonsc acuaon h downsz scalably of hs snak-lk uns o vn smallr damrs han 4 mm. VIII prsns a frs prooyp of h snak-lk un of h DDU. II. CINICA REEVANCE Th human larynx, or voc box, s rsponsbl for brahng, arway procon durng swallowng, and voc

2 producon. As wh any organ sysm n h body, h larynx s subjc o a vary of bngn and malgnan dsass rqurng surgcal procdurs for xcson and/or rconsrucon. Ths procdurs may b prformd usng opn surgcal chnqus, or mnmally nvasv ndoscopc procdurs. Opn procdurs provd adqua xposur for xcson and rconsrucon a h xpns of dsrupng h framwork supporng laryngal carlag, muscl and conncv ssu val o normal funcon. Endoscopc procdurs prsrv h laryngal framwork and provd a mans for rmoval of ssu, howvr, funconal rconsrucon s no possbl du o lmd accssbly. Rgardlss of h approach undrakn, prsrvaon of h basc funcons s paramoun o mananng qualy of lf. To manan h voc characrscs, s of prm mporanc o rconsruc h vocal fold srucurs as accuraly as possbl. Approachng hs rgons by usng mnmally nvasv approach rqurs h us of an array of long MIS ools and a laryngoscop ha s nsrd no h pan s mouh and srvs as a vsualzaon ool and a gud for surgcal nsrumnaon, Fg.. Ths surgcal sup rqurs h surgon o manpula svral long ools (for xampl on ool for sucon and anohr for ssu manpulaon) hrough a laryngoscop havng an oval cross-scon usually rangng bwn 6-0 mm n wdh. Th currn array of MIS ools avalabl for hs surgrs dos no provd h surgons wh h rqurd p dxry o allow ssu flap roaon or swng acons. Th sysm prsnd n h followng scon s bng dsgnd and consrucd o ovrcom hs shorcomngs. Fg. ndoscop Surgcal ool (ssu shavr) aryngoscop A ypcal surgcal sup of mnmally nvasv laryngal surgry. III. OVERA SYSTEM ARCHITECTURE monor Fg. llusras our hroa surgry sysm. I ncluds a laryngoscop, a bas lnk, wo smlar DDUs for ool/ssu manpulaon, and anohr DDU for sucon. Each DDU s mound on a corrspondng DDU holdr, whch s manpulad by a corrspondng 4 DoF ool manpulaon un (TMU) ha conrols h angl of approach, h roaon abou and h poson along h axs of h DDU holdr. Th TMUs ar mound on a roang bas un (RBU) prmng h sysm o b ornd whn h hroa so as o mnmz collsons bwn DDU holdrs. Th DDU holdrs ar hn ubs (abou 4 mm n ousd damr) provdng an acuaon pahway for h DDU and possbly a lgh-sourc or a sucon channl. Each TMU s quppd wh a fas clampng dvc allowng h surgon o adjus h axal locaon of h DDU. Th acuaon un of ach DDU s locad a h uppr xrmy of ach ool and h acuaon s by supr-lasc ubs oprad n push-pull mod as dscrbd n scon V. Excludng h dgrs of frdom assocad wh h dsal dxry uns, hs sysm has hrn conrolld dgrs of frdom. Each DDU adds svn conrolld acuaors o produc 6 DoF moon, as prsnd n scon V. Hnc, h oal slav sysm of Fg. has hry four conrolld acuaors IV. Fg laryngoscop bas lnk Dsal dxry un 4 sucon snak 5 DDU holdr 6 4 DoF ool manpulaon un (TMU) 7 roang bas 8 fas clampng dvc 9 DDU acuaon un 0 lcrcal supply /daa Ovrvw of h hroa surgcal asssanc slav. CINICA WORKSPACE AND FORCE REQUIREMENTS Th clncal applcaon dfns h rqurd workspac and forc applcaon capably of h sysm. Th goal rachabl workspac for l-oprad suurng pas and n h vcny of h vocal folds rqurs a cylndrcal work volum 40 mm n damr and 50 mm n hgh. Ths dfns a consrvav rqurd workspac for h TMUs manpulang h DDU holdr. Also, h lngh of h DDU holdr s nough o rach mm no h hroa. Th rqurmn from h DDU s o b abl o bnd 90 sdways n any drcon and o ransm roaon of h DDU holdr abou s axs no roaon abou h axs of h grppr. Ths faur wll b usd for h suurng applcaon. Th rqurd forc applcaon capably s nwon a h p of h grppr for ssu manpulaon. V. THE DISTA DEXTERITY UNITS Fg. prsns h dsal dxry un composd of a bndng snak-lk un and a dachabl mll-paralll wrs. Th dsal dxry uns provd h ncssary flxbly for bypassng obsacls and dlvrng orqu abou hr backbon hus ransformng h roaon of h snak holdr abou s axs no roaon of h snak-lk un abou s backbon axs. Ths s a valuabl propry for suurng and ssu manpulaon n a confnd spac. Ths scon prsns hs uns n dal. A. Th mul-backbon snak-lk un Snak-lk robos can b classfd basd on hr backbon characrscs and accordng o hr acuaon. TABE I. prsns hs classfcaon and summarzs som of

3 h works n hs fld. As n h abl, snak lk robos can b classfd no dscr or connuous backbon robos and no xnsbl or non-xnsbl backbon robos. Also, hy can b classfd accordng o hr acuaon no connuous acuaon or bnary acuaon robos. Robos wh dscr backbons us a sral chan backbon mad of rgd bods and jons whl connuous backbon robos us a flxbl maral (such as an lasomr, a sprng, bllows, or a flxbl hn rod) as a backbon. Robos wh xnsbl backbons can chang h ovrall lngh of hr backbon. Th snak-lk un prsnd hr s a connuous non-xnsbl mul-backbon un. Th snak-lk un s composd from a bas dsk, an nd dsk, svral spacr dsks, and four supr-lasc ubs arrangd as n Fg.. Ths ubs ar calld h backbon ubs of hs snak-lk un. Th cnral ub s h prmary backbon whl h rmanng hr ubs ar h scondary backbons. Th scondary backbons ar qudsan from h cnral backbon and from on anohr. Th cnral backbon s aachd o boh h bas and nd dsks and o all spacr dsks whl h scondary backbons ar aachd only o h nd dsk and ar fr o sld and bnd hrough proprly dmnsond hols n h bas and spacr dsks. Ths scondary backbons ar usd for acuang hs snak-lk dvc and hy pass hrough gudng channls n h DDU holdr o allow hr acuaon n boh push and pull mods. Th spacr dsks ar dsancd from on anohr o prvn bucklng of h cnral and scondary backbons and o manan an qual dsanc bwn h scondary backbons and h cnral backbon. Ths dsgn s nsprd by h works of [9] and [6], who suggsd and analyzd h knmacs and nrnal sacs of wr-acuad flxbl backbon (connuum) robos. Usng h rmnology of [9] and [6], h snak-lk un of Fg. rprsns on bndng scon n a snak robo. Usng addonal supr-lasc ubs passng hrough h scondary backbons of a frs scon, allows sral sackng of a scond scon. Ths opns h possbly of mul-scon snak ha can b usd for xploraon and surgcal nrvnon n dpr rgons hrough h lung arways. Th ky dffrnc bwn hs dsgn and hs works ( [9], [6]) s n h sz and n h us of scondary backbons ha hav h sam sz as h prmary backbon and hrfor hr bndng proprs ar sgnfcan (.. hy can no b rad as wrs). Ths s mporan whn dsgnng small damr snak-lk robos whl mananng srucural rgdy and smplcy of acuaon. By usng hr push-pull lmns for h acuaon of h snak-lk un of Fg. s possbl o sasfy h sacs of h srucur whl prvnng bucklng of h backbons an mporan faur for h succssful rducon of damr for mdcal applcaons rqurng smallr damr han 4 mm. On archcur-nhrn advanag of h snak-lk un of Fg. sms from usng flxbl backbons, hus rmovng h dpndncy on small unvrsal jons and wrs. Ths rducs h manufacurng coss of h un and conrbus o h possbl rducon n s sz du o h small numbr of movng pars and h absnc of sandard mnaur jons. Anohr advanag coms from h us of ubs for h backbons, hus provdng a scondary applcaon for hs backbons. Ths backbons can srv also as sucon channls, acuaon channl for h ool mound on s dsal nd or as a sourc of lgh for magng. Fg TABE I. Sampl works 4 grppr movng plaform paralll sag wrs 4 grppr wr 5 nd dsk 6 spacr dsk 7 cnral backbon ub 8 bas dsk 9 DDU holdr Th DDU (Dsal Dxry Un) usng a mul-backbon snak-lk robo wh dachabl paralll p. ARCHITECTURE PROPERTIES OF SNAKE IKE ROBOTS IN PREVIOUS WORKS. Classfcaon crra Backbon Backbon Acuaon archcur xnsbly dscr connuous B. Th dachabl mll-paralll un Th snak-lk un dscrbd n h prcdng scon s capabl for provdng wo DoF for h dsal p of h MIS ool. Ths DoF ar assocad wh bndng sdways n any drcon. Howvr, hs un s of rducd applcably f s quppd only wh on ool (.., grpprs) snc h surgcal applcaons rqurs dffrn grppr gomrs and dffrn ools. Hnc, an ffcn way o aach dffrn ools o h snak-lk un s rqurd. To achv hs, a mll-paralll un s bng consrucd. Ths un wll no only answr h nd for ool dachably, bu wll also provd addonal hr DoF for dlca and accura moons n a vry confnd spac; hus ulzng h archcur-nhrn rgdy of paralll robos and supporng furhr downsz scalably of h DDU whl mananng usful srucural rgdy. Th dachabl mll-paralll un s consrucd from supr-lasc acuaon wrs passng hrough h scondary backbons, sphrcal jons, and a movng plaform o whch a grppr of a ool s affxd, Fg. 4. Th movng plaform s machnd wh machng grovs such ha h balls aachd o h nd of h acuaon wrs mach s damr and a flxbl lockng rng s placd around h crcumfrnc of h movng plaform o manan hs balls nsd hr groovs. To dach h ool on nds o rmov h rng and rmov h movng plaform oghr wh s grppr/ool. xnsbl Non xnsbl [], [4], [5], [6] [7], [8] [9], [0] [] [], [] connuous dscr

4 Thr ar wo possbl opraon mods usng h dachabl mll-paralll un. In h frs mod of opraon, h acuaon wrs ar usd only o xnd ouwards n ordr o aach a nw movng plaform quppd wh anohr ool. Onc h ool s aachd hn h acuaon wrs ar rrvd unl h movng plaform s scurd on h nd plaform of h snak-lk un. In h ohr mod, for opraons rqurng small workspac and fn moons, h acuaon wrs ar usd o acua h movng plaform as a hr DoF paralll plaform wh xnsbl lnks. Th flxbly of h wrs allows h moon of h movng plaform vn hough h acuaon wrs manan prpndculary o h nd dsk of h snak-lk un hrough hr passag pors. Th acuaon wr for h grppr/ool s also quppd wh a fas conncon o h grppr and s xndd accordng o h knmacs of h DDU o manan h opraon of h ool. Ths wr can also b usd for mcro-drll applcaons whr s also acuad n roaon. ockng rng scondary backbon Inrnal wr VI. Fg. 4 nd dsk ball jon Th dachabl paralll p. suurng ndl movng plaform KINEMATICS OF THE SNAKE-IKE UNIT Ths scon prsns h nsananous knmacs of h snak-lk un. By conrollng h lnghs of h scondary backbons, h nd dsk s movd n wo DoF n spac. Th snak-lk un assums a shap ha mnmzs s ponal nrgy. Ths shap s gvn by shap funcons ha ar a soluon of a sysm of non-lnar paral dffrnal quaons [0] [9]. A gnral closd-form soluon has no bn oband and som smplfyng assumpons ar ncssary o oban h approxma shap of h backbons. Th followng ls summarzs h smplfyng assumpons mad n hs papr.. Th wgh of h dsks of h snak-lk un s nglgbl. Hnc, h snak un bnds n a plan prpndcular o h bas dsk onc h scondary backbons ar acuad. Ths s no ru for larg snak-lk robos [9] snc gravy can chang h mnmum ponal nrgy soluon.. Th xrnal forcs acng on h DDU ar small nough no o consdrably chang h ovrall ponal nrgy of h sysm,.., h forcs ar small nough o caus small dflcons from h nomnal knmac soluon.. Th spacr dsks ar placd clos nough o ach ohr so ha h shaps of h prmary and scondary backbons ar consrand o l a prscrbd fxd dsanc apar. 4. Th shap of h cnral backbon s assumd o b a connuous smooh funcon paramrzd by h radus of curvaur (s). Ths s ru only f h spacr dsks ar dsgnd and fxd on h prmary backbon such ha hy do no prvn from bndng whl provdng nglgbl frcon. A. Knmac nomnclaur Fg. 5 shows h snak-lk un n a bn confguraon wh only h prmary and on scondary backbon llusrad. Thr coordna sysms ar also shown. Ths coordna sysms ar h Bas Dsk coordna Sysm (BDS) { ˆx b ŷ b ẑ b }, h Snak Plan coordna Sysm (SPS) { ˆx ŷ ẑ }, and h End Dsk coordna Sysm (EDS) { ˆx ŷ ẑ }. BDS s aachd o h bas dsk such ha ˆx b pons from h cnr o h frs scondary backbon and ẑb s normal o h dsk as n Fg. 5. ẑ s prpndcular o h bas dsk and ˆx ls along h nrscon of h snak plan (h plan n whch h snak un bnds) and h bas dsk. EDS s oband from SPS by a smpl roaon abou ŷ such ha ẑ bcoms h backbon angn a h nd dsk. Th followng symbols ar dfnd: - ndx of h scondary backbons =,,. s - arc-lngh paramr of h prmary backbon. s=0 a h bas dsk and s= a h nd dsk. - lngh of h h backbon from h bas o h nd dsk. r - radus of h bas, spacr, and nd dsks. (s) - radus of curvaur dfnd as ds d (s). (s) - h angl of h prmary backbon angn n h ˆx ẑ plan. (s=) and (s=0) ar dsgnad by and 0, rspcvly. - h rgh-handd roaon angl from ˆx abou ẑ o a ln passng hrough h prmary backbon and h h scondary backbon a s=0. - h snak plan angl. I s dfnd as. - dvson angl ( / n whr n s h numbr of scondary backbons). x - m drvav of varabl x. J xy - Jacoban marx such ha x J y. Th only xcpon for hs nomnclaur s J x, whch rprsns h mappng J x whr s an angular vlocy. x B. Knamc rlaons bwn h backbons Th poson and ornaon of h nd dsk rlav o h bas dsk s characrzd by wo angls and. Th angls =,,, ar rlad o accordng o Eq. (), Fg. 5.,,, () Th projcon of h h scondary backbon on h snak plan s a curv whch s offs by [r, r] from h prmary backbon. Th radus of curvaur and arc-lngh of hs curv ar rspcvly ndcad by s and (s ) and ar rlad o h paramrs of h prmary backbon accordng o Eq. (). (s) (s), whr r cos( ) 0, (), 0

5 Th lngh of h prmary backbon and h lngh of h h backbon ar rlad accordng o: 0 () ds ds dsds (s) (s) d 0, 0 Usng Eq. (), ylds h nrsng rsul of Eq. (4). Th lngh of h h backbon dpnds on h angl of h nd dsk rlav o h bas dsk. I dos no dpnd on h shap of h backbon (s also [9]). ( ) 0 (4) 0, C. Drc knmacs Gvn h lnghs of h prmary backbon and of wo scondary backbons, on sks h lngh of h hrd scondary backbon and h confguraon of h nd dsk. Assum ha and ar gvn, hn Eq. (4) rsuls n h nd dsk angl as a funcon of an unknown offs. (5) 0 Usng Eqs. (,, 4) and som rgonomrc manpulaon, on can wr a knmac compably condon on and : c c s s 0 (6) A whr cx and s x sand for h cosn and sn of angl x. Solvng for = rsuls n wo soluons of Eq. (7) for whom h corrspondng soluons for wr gvn n Eq. (5). Ths wo soluons rprsn h sam on possbl confguraon of h snak, bu for wo opposng drcons of ˆx of Fg. 5. Aan A B or Aan A B (7) Th rqurd lngh of h hrd backbon s found by usng Eq. (5) for h valu of gvn by Eq. (7). Th poson, p, and h ornaon, b R, of h nd dsk ar found by ngrang along h angn of h backbon and by a succssv roaon squnc as n Eq. (8). Th marx b R s a roaon marx of (-) abou ẑ b and R s a roaon marx of ( 0 ) abou ŷ, Fg. 5. p b R cos, 0 0 b b (s) ds,0, sn(s) ds R R R (8) D. Insananous knmacs Ths scon prsns h mappng bwn h acuaon spds q, and h gnralzd ws of h nd dsk, l x. Th gnralzd ws s dnod by a 6 vcor x p, whr p and dsgna h lnar and angular vlocy of h nd dsk. In hs scon, w would lk o fnd h Jacoban J xq. Th scon procds whou gvng all h xplc xprssons for spac lmaons. Ths scon follows smlar mhods as n [4], [9]. x J q (9) xq B 0 Fg. 5 Th snak-lk un n a bn confguraon (a) op v w of h bas dsk (b) If h snak un s acuad by hr scondary backbons, hn s assumd ha h hrd backbon fulflls h knmac consran of Eq. (6) a all ms. Th angular vlocy of h nd dsk s gvn by / b : zˆ yˆ (0) /b By dfnng, and akng h m drvav of Eq. (6), on fnds h Jacoban rlang h jon spds wh h lmns of h nd dsk angular vlocy: Jq Jq qjqq, Jq J q Jq () whr J J rprsn h mappngs J q, J zˆ z ˆ b q ˆx b q, q q. By usng Eq. () on obans h angular vlocy. J J J q J q () ŷ (a) / b q Th shap of h backbon s a funcon of and s f,s. By akng h m drvav of hs funcon on obans a dsrbuon of bndng spd along h backbon as a funcon of h bndng spd of h p. Ths dsrbuon s dsgnad by g(,s), Eq. (). q q f f s s g(,s) () s Th lnar vlocy of h nd dsk n SPS s gvn by: p sn (s) g(,s) ds, 0, cos (s) g(,s) ds 0 0 (4) Th lnar vlocy of h nd dsk rlav o h bas s: b p R p p (5) ŷ b 0 / bas Snak plan whr /bas ˆ zb s h angular vlocy of SPS n BDS. Ths rsuls lad o h followng Jacoban mappng: p J p J pjqq J pqq (6) Hnc, h Jacoban of h snak un s gvn by: J pq J pq x q J q, J xq (7) J q J q ˆx ŷ ẑ ˆx ˆx b ˆx (b) ŷ ŷ b

6 Ths rsuls dpnd on h shap funcon, s, mnmzng h ponal nrgy of h sysm. For dal unloadd snaklk un s wll b a crcular scon of lngh [9]. Ohrws, numrcal or drc varaonal mhods can b usd o fnd an approxmaon for s. VII. ANTAGONISTIC ACTUATION Th snak-lk un of Fg. has on rdundan scondary backbon. Ths backbon can b acuad o rduc h amoun of forc acng on h prmary backbon and by dong so, rducng h rsk of s bucklng. Ths scon prsns a rdundancy rsoluon ha achvs hs goal. Ths faur s mporan o allow ffcv downsz scalably whl prvnng h hn prmary backbon from bucklng. Th analyss s basd on a lnarzd vrual work modl n whch h ffcs of acuaon forcs on h oal dformaon nrgy of h backbons s nglgbl compard o h oal dformaon nrgy du o h bndng of h backbons. Undr hs assumpon, h nrgy of h sysm of backbons s a funcon of h bndng of h backbons. Snc h shap s f,s and, h nrgy may b s characrzd by prsnd as a funcon of s f,s and. E E(, ) (8) Assum an xrnal wrnch w f, m s acng on h nd dsk whr f ndcas h forc and m h momn. Th vrual work prncpl s usd by assumng a chang n h posur of h nd dsk, x, an xrnal wrnch, w, acng on h nd-dsk, a corrspondng chang n h scondary backbons lnghs, l,, acuaon forcs,,, l, and an assocad, and a chang n h ponal nrgy of h backbon sysm E, Eq. (9). w x E 0 (9) Th vrual dsplacmn of h snak un s characrzd by,. Th ns x and ar rlad o accordng o Eqs. (0). J x Jx (0) whr Jx s gvn by Eq. () and J s found by akng h m drvav of Eq. (4) for, =,,. Jp Jx () J Nx, h vrual work prncpl s rwrn as n Eq. (). Th qulbrum condon rqurs h rms assocad wh ach ndpndn DoF o vansh. Ths rsuls n a sysm of wo quaons n hr unknowns,, l. Th marx for of hs sysm of quaons s gvn n Eq. () whr E rprsns h gradn of h ponal lasc nrgy. w J J E () x 0 x J E J w () Eq. () s a sysm of wo quaons n hr unknowns. An addonal rqurmn s ncssary o choos among h nfn numbr of soluons. Ths rqurmn s mnmzng h oal forc on h prmary backbon such ha h rsulan forc on s zro, Eq. (4). Ths mans ha h acuaon forcs balanc h xrnal forc and ha hr ar only momns acng on h prmary backbon. In a smplfd approach, h scondary backbons wll assum h sam drcon gvn by ẑ ( Fg. 5). Z f, whr Z zˆ, zˆ, zˆ (4) Th soluon o Eq. () wh Eq. (4) as a scondary ask, [4], s gvn by Eq. (5) whr h (+) suprscrp ndcas h gnralzd nvrs. For brvy l J b ndcad by A and l E J x w b ndcad by b. Th vcor s chosn so ha sasfs Eq. (4). A b I A A (5) Z I A A f Z A b (6) Ths rdundancy rsoluon prsns on possbl way o conrol h load sharng bwn h backbons whl rducng h rsk of bucklng of h prmary backbon. Howvr, dos no ncssarly consu an opmal soluon n whch h load sharng among all h backbons (scondary and prmary) s fulflld. An acuaon un s bng dsgnd o acua h snak-lk un usng hs soluon or ohr opmal soluons ha ar sough as par of our fuur work. VIII. PROTOTYPE EXPERIMENT A frs prooyp of h snak un s shown n Fg. 6. Th lngh of h snak un s 8 mm and s damr s 4. mm. I s dsgnd o bnd 90 n any drcon. Th prmary and scondary backbons ar mad of supr lasc NT ubs havng 0.66 and 0.5 mm xrnal and nrnal damrs. All h dsks hav a damr of 4. mm and.6 mm hcknss. Th un of Fg. 6 was manually acuad by wo ou of hr xsng scondary backbons and was abl o apply mor han nwon a s p. In h dsgn w followd a dsgn goal such ha h sran n h ubs dos no xcd 4%. Ths sran lm s usd o prvn dgradaon of h suprlasc proprs of h ubs ovr connuous opraon. Onc h acuaon un s bul, wll b acuad usng h hr scondary backbons and by dong so wll dmonsra br load sharng among h backbons and hus w wll b abl o bnd furhr whou volang h sran lm. Ths prooyp srvs as an xprmnal sup for drmnng fagu rslnc and addonal dsgn paramrs such as h maxmal dsanc bwn h spacr dsks o prvn bucklng. Th un of Fg. 6 dmonsrad som bndng nonlnary whch can b sn n Fg. 6-b. W suspc sms from xra loos olrancs of h passags n h bas dsk. Ths passags allow h scondary backbons o pass hrough h

7 bas and ar supposd o provd only axal moon capably, bu n h xsng modl hy allow small angular moon capably du o h olrancs. Anohr possbl xplanaon for hs bhavor s h fac ha w ar usng only wo backbons ou of hr and by dong so w ar loadng h ubs such ha hr xnson bcoms non-nglgbl. Ths hypohss rman o b vrfd n our fuur work. (a) (b) Fg. 6 Th 4. mm damr prooyp n wo bn confguraons wh only wo of h avalabl hr scondary backbons acuad manually. IX. CONCOSION Ths papr prsnd our up-o-da work on dsgnng a hgh dxry, hgh accuracy slav for l-oprad mnmally nvasv surgry of h hroa. Th slav s a 4 DoF un capabl of smulanously manpulang up o hr surgcal ools. Ths sysm s dsgnd o allow ssu rconsrucon of h vocal folds and suurng asks - currnly xrmly dffcul o prform n a mnmally nvasv approach. Th man un of hs slav s an lvn DoF dsal dxry un composd from a snak-lk un and a dachabl paralll wrs ha provds surgcal ool xchangably. Th dsgn of h snak-lk un was prsnd. Ths un uss mulpl suprlasc ubs as flxbl backbons acuad n push-pull mods. Ths dsgn provds fuur downsz scalably and manufacurng smplcy. Fnally, h papr oulnd h knmac analyss gudng our dsgn. Th papr suggsd usng h avalabl acuaon rdundancy n h snak-lk un o mnmz h rsk of bucklng of h prmary backbon. On possbl rdundancy rsoluon achvng hs goal was prsnd. Fnally, an arly xprmn wh a frs bul prooyp was shown. ACKNOWEDGEMENTS Ths work was parally fundd by h Naonal Scnc Foundaon (NSF) undr Engnrng Rsarch Cnr gran #EEC97478, NSF gran #IIS980684, and by h Johns Hopkns Unvrsy nrnal funds. REFERENCES [] R. Taylor, J. Funda, B. Eldrdg, S. Gomory, K. Gurbn, D. aros, M. Talamn,. Kavouss, J. Andrson, A Tlrobocs Asssan for aproscopc Surgry, IEEE Engnrng n Mdcn and Bology Magazn, 4(), pp , 995. [] G.S. Guhar, J.K. Salsbury, Th Inuv TM Tlsurgry Sysm: Ovrvw and Applcaon, ICRA 000, pp. 68-6, 000. [] J. M. Sackr and Y. Wang, Robocally asssd laprascopc surgry from concp o dvlopmn, Surgcal Endoscopy, Vol. 8, pp. 6-66, 994. [4] M. Shoham, M. Burman, E. Zhav,. Joskowcz, E. Bakln, Y. Kunchr, Bon-Mound Mnaur Robo for Surgcal Procdurs: Concp and Clncal Applcaons, IEEE Trans. Robo. Auoma., Vol. 9, No. 5, pp , 00. [5] N. Smaan, M. Shoham, "Robo Consrucon for Surgcal Applcaons." Th Frs IFAC Confrnc on Mcharonc Sysms, Darmsad, Grmany, Spmbr 8-0, 000. [6] R.H. Taylor, D. Sanovc, Mdcal Robocs n Compur-Ingrad Surgry, IEEE Trans. Robo. Auoma., Vol. 9, No. 5, pp , 00. [7] M. Cavusoglu, I. Vllanuva, F. Tndck, 00, Workspac Analyss of Robocs Manpulaors for a Tloprad Suurng Task, IEEE/RSJ Inrnaonal Confrnc on Inllgn Robos and Sysms (IROS00), Mau, HI. [8] Y. Nakamura, A. Masu, T. Sao, K. Yoshmoo, Shap-Mmory- Alloy Acv Forcps for aparoscopc Surgry, ICRA 95, pp. 0-7, 995. [9] P. Daro, C. Pagg, N. Trosfonan, E. Papa, T. Cucc, M.C. Carrozza, M. Marcacc, A Mnaur Srabl End-Effcor for Applcaon n an Ingrad Sysm for Compur-Asssd Arhroscopy, ICRA 97, pp , 997. [0] D. Rynars, J. Prs, H. Van Brussl, Shap mmory mcro-acuaon for a gasro-nsnal nrvnon sysm, Snsors and Acuaors, Vol. 77, pp , 999. [] J. Prs, D. Rynars, H. Van Brussl, G. D Grsm, H.T. Tang, Dsgn of an Advancd Tool Gudng Sysm for Roboc Surgry, ICRA 00, pp , 00. []. Adham, E.C. Manr, Opmal Plannng for Mnmally Invasv Surgcal Robos, IEEE Trans. Robo. Auoma., Vol. 9, No. 5, pp , 00. [] S. Hros, S. Ma, Coupld Tndon-Drvn Muljon Manpulaor, Proc. ICRA 9, pp.68-75, 99. [4] G., Chrkjan, J. Burdck, Dsgn and Exprmns wh a 0 DOF Robo, ICRA 9, pp. -9, 99. [5] E. Paljug, T. Ohm, S. Haya, Th JP Srpnn Robo: a DOF Sysm for Inspcon, ICRA 95, pp. 4-48, 995. [6] I. Walkr, M. Hannan, A Novl "Elphan's Trunk" Robo. Procdngs of h 999 IEEE/ASME Inrnaonal Confrnc on Advancd Inllgn Mcharoncs, pp , 999. [7] I. Ebr-Uphoff, G. Chrkjan, Invrs Knmacs of Dscrly Acuad Hypr-Rdundan Manpulaors Usng Workspac Dnss, ICRA 96,pp. 9-45, 996. [8] J. Suhakorn, G.S. Chrkjan, A Nw Invrs Knmacs Algorhm for Bnary Manpulaors wh Many Acuaors Advancd Robocs, pp 5-44, Vol. 5, No., 00. [9] I.A. Gravang, I.D. Wlakr, Knmac Transformaons for Rmoly- Acuad Planar Connuum Robos, ICRA 000, pp. 9-6, 000. [0] C., C. Rhan, Dsgn of Connuous Backbon, Cabl-Drvn Robos, ASME J. of Mchancal Dsgn, Vol. 4, pp., 65-7, 00. [] P. Brdvld, Inrnaonal Pan applcaon, Inrnaonal Publcaon Numbr WO 0/09 A, Applcan: Dlf Unvrsy of Tchnology, Prory da 06/08/999, 000. [] S. Hros, Bologcally Insprd Robos, Snak-k ocomoors and Manpulaors, Oxford Unvrsy Prss, scon 0., pp , 99. [] G. Immga, K. Anonll, Th KSI Tnacl Manpulaor, ICRA 95, pp , 995. [4] T. Yoshkawa, Foundaons of Roboc Analyss and conol, Th MIT Prss, 990.