Geometry Modeling and Simulation of the Wire-Driven Bending Section of a Flexible Ureteroscope

Transcription

1 Poceedings of the Wod Congess on Engineeing and Compute Science 2011 Vo II Geomety Modeing and Simuation of the Wie-Diven Bending Section of a Fexibe Ueteoscope Man-Cheong Lei, Ruxu Du Abstact Reseach and deveopment of biomedica engineeing boost in ecent yeas. In which the inceasing empoyment of endoscopy poves itsef a tustwothy sugica technoogy to epace the taditiona opeations. It is mainy because it owes the sugica isk as we as the patient s heaing time by pefoming non- o minimay invasive sugey. A fexibe endoscope is abe to adopt the totuous channes within a human body. It enabes sugeon to not ony obseve but aso cay out theapy within the patient s body. It can thank to the tiny bending section embedded in the font of it. Athough many poducts have been binging to the maket fo decades, thee is no systematic study about the design o specification of the endoscopes. The pupose of this eseach is to configue the infomation on designing the bending section of a fexibe ueteoscope which is paticuay used in uoogica sugey. Geomety modeing of the bending section consisting of one and two sub-sections wi be given. A pogam is composed fo simuating the defection of the bending section with diffeent vaues of the paametes. Index Tems bending section, ueteoscope, wie-diven mechanism, continuum obot, constant cuvatue I. INTRODUCTION U RETEROSCOPE is one type of endoscopes which is speciay design fo the use in the uinay system. By diffeent configuations, it can be cassified as igid, semi-igid and fexibe [1]. In this study, the focus is put on the fexibe ueteoscope. Fig. 1 shows the popua modes used nowadays. The majo chaacteistic of a fexibe Gyus ACMI DUR-8 Eite Oympus URF-P5 Fig. 1. Popua modes using in the cuent ueteoscopy. Manuscipt eceived Juy 16, 2011; evised August 05, This wok was suppoted in pat by the MedSev Intenationa unde Gant TM (sponso and financia suppot acknowedgment goes hee. M. C. Lei is with Depatment of Mechanica and Automation Engineeing, The Chinese Univesity of Hong Kong, Shatin, NT, Hong Kong (phone: ; e-mai: mcei@mae.cuhk.edu.hk). R. Du is with Depatment of Mechanica and Automation Engineeing, The Chinese Univesity of Hong Kong, Shatin, NT, Hong Kong (phone: ; e-mai: du@mae.cuhk.edu.hk). ueteoscope is the embedment of the defection mechanism. This defection mechanism mainy consists of the conto body and the bending section as shown in Fig. 2. Conto wies Conto body Bending section Fig. 2. Defection Mechanism of a fexibe ueteoscope The defection mechanism is a snake-ike mechanism which distinguishes itsef fom the popua snake obots fom the diven method. Basicay, the snake obots have motos assembed at a the joints of the bending section and by contoing a the motos, the snake obots ae abe to move ike a snake. Howeve, fo the defection mechanism of a fexibe ueteoscope, the bending section can defect by contoing the wies passing though it. Thus this kind of actuation is caed wie-diven. The conto pant can aso be emoved fom the moving pat. Indeed, thee ae many industia obot ams o manipuatos adopting the simia mechanisms. They can be cassified as discete, sepentine and continuum. Among which, the continuum obots attact the most eseaches to study. Wok done by Robinson, e. [2] and Webste, e. [3] on continuum obots ae compete and thoough. But the bending section is moe simia to the sepentine obot am. It has highe igidity than continuum obots and is moe fexibe than discete obots. Fo the simpicity, peope woud athe teat it as a continuum obot am [4]. In this study, the compaison between these two types is given. Othe than the wie-diven method, thee ae some existing actuation methods such as using Shape Memoy Aoy [5], Eecto Active Poyme [6][7], and Piezoeectic Ceamic [8] intoduced by othe eseaches and schoas. This pape continues ou pevious study [9]. The geomety modeing of the bending section wi fisty be intoduced. In which the eationship between the dimensions of the pats and the adius of defection wi be gone though. It foows by the vaidation of constant cuvatue assumption. Based on the geomety modeing and constant cuvatue assumption, simuations of the defection fo diffeent configuations of bending sections wi be demonstated. It consides a bending section composed of one o two sub-sections as we as using one o two pais of conto wies. The ast section is concusion that summaizes the wok pesent in this pape and aises some possibe futue wok.

2 II. GEOMETRY MODELING OF THE BENDING SECTION A. Desciption of fomuation In this study, the defection of the bending section is assumed to be a pana motion. In othe wods, the ocations of the pats composing the bending section can be defined in a goba x-y coodinate fame. The fomuation is easonabe because the ueteoscope is abe to pefom a pana motion ony. If the uoogist wishes to change the oientation of the ueteoscope, he has to otate the entie ueteoscope to the desied ange and it is totay ieevant to the defection mechanism within the ueteoscope. B. Assumption A bending section can be fomed by sevea sub-sections. In the foowing geomety anaysis, the pats foming a singe sub-section ae assumed to be identica. The cuvatue aong one sub-section is assumed to emain constant simutaneousy whie the bending section is unde defection. Fo simpicity, the anaysis of the defection can be educed to conside a sma section foming by two pats as shown in Fig. 3. Such assumptions ae effective since most existing modes in the maket use this design fo the ease of manufactuing. R N R out β d γ Fig. 3. Schematic diagam of the 2-pat sma section. C. Notations To study the bending, it is vey impotant to caify the key paametes in advance. The best way is to state some significant notations fist: adius of the bending section (), pat ength of the bending section (), haf the distance of the gap between 2 pats when they ae in eaxed state (g), bending ange of a pat (β), neuta adius of the bending (R N ), inne bending adius (R in ) and oute bending adius (R out ). D. Deivation Fig. 3 aso demonstates the countecockwise defection of the bending section at a cetain moment. The geomety of the sub-section whie defecting can be concuded by equations (1) to (6). 2 (1) 2/2 (2) Then the neuta adius of the sub-section is /2 (3) h R in g Let /2, then /2 (4) The inne bending adius of the whoe bending section is (5) The oute bending adius of the whoe bending section is 2 (6) In most of the cases, peope ae moe inteested in the minimum adii as we as the ange of defection of the bending section. Hence, R in is the most concened item by the doctos and the manufactues of the endoscopes. Fig. 4 iustates this case and the minimum vaue of R in can be found by: 0 2 (7) (8) R in R N Equation (7) aso tes that the ange of defection of a pat is constained by the atio of the gap distance and the adius of the bending section. At this moment, eaches its maximum vaue and it can be denoted as. Fig. 5 iustates the dimension of of a bending section composes of identica pats. Connecting wie Conto wies Fig. 5. Fu defection of bending section composed by identica pats III. CONSTANT CURVATURE ASSUMPTION Aftewads, it is impotant to vaidate the assumption that the cuvatue aong each sub-section of the bending section emains constant simutaneousy whie the bending section is unde defection. It heps to eate the ange of defection of Fig. 4. Fu defection of the sub-section g

3 the pats within one sub-section. Not mentioning devices as specific as ueteoscope, thee ae a few studies about the continuum obots which ae simia to the configuation of the bending section in this eseach. Most of them intend to teat the configuation of the bending section as a cicua cuve, thus the study woud become much easie because of the simpification. It may be acceptabe to teat it as an ac if pecision equiement is not that seious. Howeve, fo the bending section of a ueteoscope, it is necessay to adopt the most eaistic geometic featues and dimensiona vaues in ode to obtain the most accuate outcome of cacuations. Then the ange of tota defection ange is: The cuvatue is the invese of the neuta adius, i.e. 1 2 (9) Accoding this assumption, fo any two sets of adjunct pats within a sub-section, they shoud have the same cuvatue. Suppose a, b denote any two sets of adjunct two pats within a sub-section of a bending section, then Besides, fo the sub-section consists of n pats, 1 Thus it is easy to obtain the tota ange of defection of one sub-section, (10) If the bending section consists of N sub-sections, the tota ange of defection of the entie bending section is Fig. 6. Compaison of and with espect to. Fom Fig. 6, both adii ae vey age when the defection ange is vey sma. It is because the bending section is neay staight which means the cuvatue of it is amost zeo. In othe wods, the adius of defection appoaches to infinity. Meanwhie, it is vey difficut to obseve the diffeence between and, theefoe a paamete is intoduced to be the atio between these two adii. It can be simpified in the foowing expession: / (13) (11) whee denotes the numbe of pats in the i-th sub-section. As a esut, given the dimensions of the bending section, N and can be detemined by the equied maximum ange of defection. Othe than the numbe of sub-sections, the numbe of pais of conto wies detemines the defection abiity of the bending section. Each pai of conto wies indeed epesents one degee of feedom (DOF). In the foowing simuation, cases associate with both one pai and two pais of conto wies wi be gone though. Howeve, if the bending section foming by identica pats is consideed as a continuum obot am, it can be teated as a cicua cuve as a whoe. Since the neuta axis of the bending section does not extend o shoten no matte how it defects, the ength of it emains constant. In othe wods, the cicua cuve shoud be a constant and can be expessed by: whee 2 2 (12) In ode to compae in equation (3) and, Fig. 6 shows both adii with espect to. Hee the bending section compises 6 identica pats and the dimensions ae: 1.163, 0.139, Fig. 7. Vaiation of atio with espect to diffeent. The cuve in Fig. 7 epesents the vaiation of the atio when diffeent tota defection anges of the bending section occu. It can be easiy obseved that when the tota defection ange is vey sma, the adius about the neuta axis is most ikey equa to the adius of the cicua cuve. It can be anayzed mathematicay fom equation (13). Fo vey sma /2, In othe wods, the defected bending section can be egaded as a continuum obot am when the bending ange of one inkage is sufficienty sma. Fo a desied esut of defection, inceasing the numbe of inkages can aso

4 enhance the simiaity of the two pattens povided that the pat ength is shot enough. IV. SIMULATION OF THE MOTION OF THE DEFLECTION MECHANISM With the infomation fom the pevious section, a pogam is made fo simuating the defection of a bending section with adjustabe dimensions. Accoding to the given vaues of the paametes, simuations ae possiby geneated to povide a bette obsevation o an easie way to study the motion of the defection of the bending section. Because the uoogist contos the ueteoscope to defect vey sowy, it can be assumed to be a static system. Aso fo simpicity, the defecting anges between the pats ae the same at any instant at this stage of study unde the constant cuvatue assumption. A. Constuction of the simuation The simuation mainy consists of two stages. The fist one is initiaization. In which some constant paametes wi be defined and be cacuated by the given dimensions of the bending section. Except the paametes mentioned in section II, the numbe of the pais of conto wies as we as thei ocations mounted on the bending section ae necessay to povide too. The second stage is endeing the configuation of the bending section with espect to the pat defection ange. To configue the bending section, it is impotant to know whee each pat is ocated at that instant. By cacuating the defecting anges between two adjacent pats at an instant, it is possibe to figue out the ocation of a the pats. Then it foows to oient the pats at thei own positions. Since pana motion is consideed at this moment, the pats ae epesented in the simuation by the contou of its coss section. As is cacuated in the initiaization stage, the bending section in the simuation is abe to stop at the maximum defection. B. Contoed by a singe pai of wies As shown in the pevious study [9], the wies mounted at diffeent ocations within a bending section woud esut in diffeent extent of defection. The pats without the wies sting up woud not invove in the defection whie a wie is being pued except fo the case that the wies ae mounted at the dista end of a bending section. Hee the case shown in Fig. 8 simuates a bending section composing of two sub-sections and is geneated by the simuation pogam. It demonstates the pocess of fu defection contoed by a pai of wies. Distinguished fom the one shown in Fig. 3, this design contains two cuvatues with espect to the two sub-sections. It is because the cuvatue eates to not ony the gap distance and adius of a pat, but aso the ength of it. It can be tod fom equation (8). Hee the pat ength of the 1 st sub-section and the 2 nd sub-section ae 3.048mm and 1.881mm espectivey. Thus the coesponding inne adii ae mm and mm. C. Contoed by two pais of wies In Fig. 9, two pais of wies ae used to conto the bending section. Such configuation enabes the bending section to pefom two stages of active defections. Refeing to Fig.9, the 1 st pai of wies is mounted at the 12 th pat of the bending section, thus it can conto the fist tweve pats to defect to 180 cockwise. Meanwhie, the 2 nd pai of wies is mounted at the 18 th pat of the bending section. It enabes one to pu the ight wie to make the est of the bending section defect to the exta 90. On the contay, in Fig. 9, the eft wie of the 1 st pai is initiay pued to conto the fist six pats defecting to 90 countecockwise and then the eft wie of the 2 nd pai contos the est to defect to the exta 180 countecockwise as we. Tajectoy of the defection (d) (c) (c) (d) Defecting (c) 140 (d) 275 Fig. 8. Simuation of a bending section composed by two sub-sections 1st pai of wies O 2nd pai of wies Fig. 9. Simuations of a bending section contoed by two pais of conto wies defecting in the same diection

5 Thanks to this simuation, anothe case of motion pefomed by this mechanism can be obseved too. By adopting the configuation as shown on Fig. 9, the owe sub-section of the bending section can fisty defect to 90 cockwise by puing the ight wie of the 1 st pai. The eft wie of the 2 nd pai is then pued unti the est of the bending section defects to 180 countecockwise. Fig. 10 demonstates the case that the bending section eaches its maximum defection. With this simuation pogam, it is possibe to change the paametes o dimensions of the bending section so that the coesponding pefomance can be obseved. It is aso compatibe fo an input function of bending ange β(t) soved fom the dynamic equations in futue study. VI. FUTURE WORK In the futue, the wok about the defection mechanism of endoscopic devices shoud be focused on the foce anaysis. A successfu foce anaysis can be a soid foundation fo the deveopment of automatic endoscopic sugey. The appoach can be using the Lagagian method and the pincipe of east action by consideing the minimum potentia enegy unde some constaints such as the conto wies must be fixed on cetain pats. Heein a the bending anges ae teated as geneaized coodinates. It is expected that soving a set of Lagange s equations wi give the soutions of defection anges and the input foce which can be the appied moment to the whee mechanism. By pugging in the anges in the simuation, the motion of the defection mechanism can be obseved. Hence, the deivation of the mathematica mode can be veified. Of couse, the pototypes of the designs wi be made to cay out some expeiments. It is aways the best way to veify the theoetica wok. 1st pai of wies O 2nd pai of wies Othe than appication ike ueteoscope, thee ae othe possibe appications fo this wie-diven mechanism. Instead of a singe system, two o moe systems may be combined to fom an integated system. The integated system maybe use in the bioogica inspied obots such as octopus obot. Besides, thee is an innovative design of continuum obot which is caed concentic tube continuum obot o aso known as active cannuas is invented fo the potentia medica appications [3]. The specia featue of it attibutes to the bending actuation method. This opeation is done by contoing the pe-cuved eastic tubes at the backbone of the design to twist in ode to tansmit the otation and tansation to one anothe. Moe wok shoud be caied out on the optimization of this design and it is expected a evoution of the defection mechanism. Fig. 10. Simuation of a bending section contoed by two pais of conto wies defecting in the opposite diection: the ight wie of the 1st pai is pued initiay and then the eft wie of the 2nd is pued unti the bending section fuy defects. V. CONCLUSION As the bending section is vey sma in tems of the ength and the adius of each pat, it is necessay to conside the manufactuabiity duing the design. In addition, accoding to some suveys, duabiity of the ueteoscope seems to be had to impove [1]. It is because the mateia and the size of the bending section ae constained and sometimes the sugica devices damage the bending section inevitaby. So fa it is bette to focus on impoving the maintenance which can be achieved by oweing the cost and time. Hence, the abiity of assemby shoud be consideed. The pupose of this eseach is to state the citica issues fo designing the bending section of a fexibe ueteoscope. Meanwhie a simuation pogam is made to faciitate the designes to obseve the feasibiity as we as the motion of thei poposed designs. Futhemoe, a feasibe and good design may ead to saving the time and money in the manufactuing pocess. REFERENCES [1] Conin MJ, Mabege M, Bagey DH: Ueteoscopy. Deveopment and instumentation. Uoogic Cinics of Noth Ameica 1997; 24: [2] G. Robinson and J. B. C. Davies, Continuum Robots a State of the At, Poceedings of the 1999 IEEE Intenationa Confeence on Robotics and Automation, pp , May, [3] R. J. Webste Ⅲ and B. A. Jones. Design and Kinematic Modeing of Constant Continuum Robots: A Review, Int.J.of Robotics Reseach, vo.29, pp , [4] D.B. Camaio, C.F. Mine, C.R. Cason, M. Zinn, and J.K. Saisbuy, "Mechanics Modeing of Tendon-Diven Continuum Manipuatos", IEEE Tansactions on Robotics, 2008, pp [5] V.D. Sas, S. Hyiyo and J. Szewczyk. A pactica appoach to the design and conto of active endoscopes, Mechatonics. vo. 20, pp , [6] C. Laschi, B. Mazzoai, V. Mattoi, etc. Design of a biomimetic obotic octopus am, Bioinspiation & Biomimetic, doi: / /4/1/015006, [7] C. Laschi, B. Mazzoai, V. Mattoi, etc. Design and Deveopment of A Soft Actuato fo a Robot Inspied By the Octopus Am Expei. Robotics: The 11 th Inten. Sympo. STAR 54, pp 25-33, [8] Takahau Idogaki, Takayuki Tominaga, Kouji Senda, etc. Bending and expanding motion actuatos, Sensos and Actuatos A: Phys, 54, pp , [9] MC. Lei, R. Du, A Study on the Bending Mechanism of the Fexibe Ueteoscope, ICCAS 2010, pp , Oct. 2010, Gyeonggi-do, Koea.