DETC2002/MECH A FINGER MECHANISM FOR ADAPTIVE END EFFECTORS

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1 Poceedings of DETC ASME Design Engineeing Technical Confeence and Computes and Infomation in Engineeing Confeence Monteal, Canada, Septembe 9-Octobe, DETC/MECH A FINGER MECHANISM FOR ADAPTIVE END EFFECTORS Venketesh N Dubey School of Design Engineeing and Computing Bounemouth Univesity 1 Chistchuch Road, Studland House Bounemouth, BH1 3NA, UK Tel Fax [email protected] Richad M Cowde Intelligence Agents Multimedia Goup Depatment of Electonics and Compute Science Univesity of Southampton Southampton, SO17 1BJ, UK Tel Fax [email protected] ABSTRACT This pape pesents design and analysis of a igid link finge, which may be suitable fo a numbe of adaptive end effectos. The design has evolved fom an industial need fo a tele-opeated system to be used in nuclea envionments. The end effecto is designed to assist epai wok in nuclea eactos duing etieval opeation, paticulaly fo the pupose of gasping objects of vaious shape, size and mass. The wok is based on the Univesity of Southampton s Whole Am Manipulato, which has a special design consideation fo safety and flexibility. The pape discusses kinematic issues associated with the finge design, and to the end of the pape specifies the limits of finge opeating paametes fo implementing contol laws. Keywods: End Effectos, Finge Design, Robotic Hand, Adaptive Finge, Mechanism Analysis INTRODUCTION Dexteous manipulation is an aea of obotics whee an end effecto with co-opeating multiple finges is capable of gasping and manipulating an object. One of the main chaacteistics of the dexteous manipulation concept is that it is object centeed. As dexteous manipulation is quintessentially a human activity, majoity of the dexteous obotic end effectos developed to date has consideable anthopomophic chaacteistics. In view of the impotance of the eseach aea, a consideable body of eseach liteatue is available on the analysis of gasp quality and contol of the end effectos. Review by Okamua et al povides an excellent intoduction to the field [1]. Howeve, vey few papes addess the issues associated with end effecto design and its evolution fo specific application needs, paticulaly computation of loading condition of the finge components fo a known fingetip inteaction to ensue obust mechanical design. Futhe to achieve a specific gip, study of the finge motion is impotant to validate design as well as fo implementing position contol algoithms. The finge mechanism pesented in this pape oiginated with the design developed fo the Univesity of Southampton Whole Am Manipulato (WAM) []. This manipulato was developed fo insetion into the human sized hypelon 1 glove fo use in a conventional glove box. Due to the design equiement, this manipulato has an anthopomophic end effecto with fou adaptive finges and a pehensile thumb, the gasp being contolled by thee moto-geaboxes assembles located within the palm, with connections to the finge segments via solids mechanical linkages. The WAM design 1 Hypelon is the tade name of a high pefomance ubbe used in specialist applications. 1 Copyight by ASME

2 ational was dictated by the tight size constaint of the hand, its enclosing glove and the opeating envionment. The WAM s hand is capable of foming a ange of gasps, which allowed it to pefom a wide ange of handling opeations. Howeve due to the design of the finge mechanism, the movement of its finges cannot be pecisely contolled duing gasping opeation, as this is detemined by the compliance of the glove. Subsequent to the WAM design, a thee-fingeed end effecto has been developed [3] based on a modified finge design; it is this design that is analyzed in this pape. The gippe design pocess stats with a eview of gasp taxonomy, elating the equied task to the available gasps. It is clea that the hand kinematics and foces ae closely elated to the gip postues. As detailed by Cutkosky [4], two main gip classifications can be identified, eithe as a pecision o powe gip. In a pecision gip, contact is made at the tip of the finge, while in the powe gip the finges enclose the object and fully constain it. In a powe gip the gasped object is constained by multiple contacts between the object and the finges [5] with no foces being tansmitted via the top finge segment. In a pe-gasp situation fo known shape and size of the object, finges ae equied to move to pecise locations in a coodinated manne to fom a secue gasp. This equies an accuate knowledge of the finge kinematics. Also fo design pupose, toque tansmission though the finge linkages and estimation of the loading condition of finge components ae of impotant consideation fo safety and eliability, if it has to opeate in a nuclea envionment. Thus kinematic and static analyses of the finge mechanism ae consideed in this pape fo design of the multi-fingeed end effectos with aticulated links. FINGER DESIGN Ove the last thity yeas a consideable numbe of dexteous end effectos have been developed. The most notably being the Stanfod/JPL [6] and Utah/MIT hands [7], that wee developed to eseach object manipulation. These designs ae based on the finges being actuated via tendons fom an extenal actuato pack. The Belgade/USC hand [8] was developed with posthetic application in mind, and has a moe compact actuating mechanism. Okada [9] designed a theefingeed hand with 11 degees of feedom using pulley/tendon system to pefom assembly opeations. Anothe thee-fingeed hand developed at the Univesity of Pennsylvania [1] and late maketed as BaettHand has a compact design, howeve, the hand uses fou actuatos on a wom dive with cable and beakaway clutch to povide finge motions. Othe notable hands include the Kalsuhe hand [11], NTU hand [1] and Delft Univesity of Technology hand [13]. The design of the hand and finge ae to a lage extent dictated by the appoach taken to tansmit the actuato foces to the finge joint. If special pupose localized actuatos, such as atificial muscles ae excluded, only two ealistic appoaches fo powe tansmission within the hand between the finge-joints and actuatos need to be consideed; tendons o a igid link kinematic chain. Tendon vs. Solid Dives Many dexteous hand designs ae tendon based, whee each finge joint is connected to a emote actuato by a flexible cod o tendon. To achieve full joint motion a minimum of two tendons ae equied pe joint. The advantage of this appoach is that the actuatos ae emote fom the hand and hence educing the oveall inetia by emoving mass fom the end of the manipulato. If size is not a limitation, the actuatos can be mounted extenal to the hand, with the powe tansmission to the hand via tendons. While satisfactoy fo expeimental systems, this appoach is not suitable fo industial applications. The space estiction imposed by cetain industial applications esult in the extenal actuatos togethe with tendons not being a pactical design poposition. In addition, the use of hand mounted pneumatic and hydaulic actuatos in many applications ae consideed to be impactical, due to leakage poblems. In a numbe of applications fo a fully dexteous hand to opeate satisfactoily, electic actuatos need to be located within the pofile of the end effecto. As physical size of the system limits the numbe of actuatos, the design solution pesented equies the motion of the finges to be contolled by solid mechanical linkages. An advantage of this design is the high eliability of electic motos; this was an impotant consideation as the manipulato is intended fo continuous industial opeation. Finge Mechanism The finge mechanism consists of thee sections (lowe, middle and tip) pivoted togethe as shown in Fig. 1, with the maximum elative movements of 9 o between each section. Bell cank K A B Lowe section I J Link 1 D C Middle section E Link Fig. 1. Basic Finge Mechanism (bell cank displaced) The uppe two finge sections ae used to poduce a coodinated culing motion. The tip is linked to the lowe section by link, so that any motion of the middle section by link 1 will cause the tip to move, poducing culing motion to the finge. The lowe and middle sections ae individually connected to the actuating mechanism at points B and K. The mechanism is gounded at joints A and J. The finge mechanism can be consideed to have two degees of feedom: Bending, whee displacement of joint B bends all the thee finge segments about joint A. Culing, whee displacement of joint K esults in the culing of the two uppe finge segments about joint C. Thus the finge discussed above equies two dive inputs. This can be poduced in a numbe of ways, depending on the application equiements. Thee appoaches can be consideed to achieve this: G F Tip Copyight by ASME

3 Equalizing mechanism. Single moto, and diffeential gea box Fully independent dives. Leadscew Lowe section Link Middle section Equalizing Mechanism The equalizing ba mechanism used in the end effecto of the Whole Am Manipulato is shown in Fig.. In the est position the finge is consideed to be in the fully extended position. To close the finge the equalize ba is diven to the left, by a cank and slide mechanism. Due to the built-in diffeence in the mechanical advantages between links A and B and thei espective sections, the finge is designed to pefeentially otate aound pivot A of the lowe section. The design of the mechanism is such that the finge will emain staight while it otates aound this pivot. The otation of the complete finge will continue until such time as the lowe section is stopped eithe at its mechanical limit o by an extenal object. Link B Link 1 M Link A Fig. 3. Lead scew diven finge Lowe segment Link1 Joint B Tip Lowe section Middle section Joint A Link A LinkB Dive output Slide Equilise ba Link A A Link Bake Bell c ank Joint J Bake 1 Tip Link 1 Geabox Link B Fig.. Equalizing ba mechanism Moto Rotating fame Fixed fam As the lowe section and link A cannot move, foce is tansfeed to the middle section, via link B, thus causing the uppe two sections of the finge to cul ove and complete the gip aound the object. The esultant finge motion is simila to that of a human finge and is descibed as being "tip diven", as the fingetip effectively leads the motion. The position of the equalizing ba is contolled by the loads applied to the finge section thus is consideed to be indeteminate. While compact, the design elies on extenal foces povided in the WAM s application by the hypelon glove, which is used to stabilize the finge position. Diffeential Geabox To satisfactoily contol the finge fo an adaptive end effecto without the equiements of a compliant glove o simila systems, both input links need to be individually and positively contolled. This equiement led to the development of a mechanism capable of independently contolling the two input links. Due to application constaints imposed, only a single moto could be used to contol all the equied motions. The design of complete finge module can be consideed in two pats; the finge, Fig. 3 and its actuating mechanism, Fig. 4. The actuating mechanism has a cental diffeential geabox unit diving two lead scews suppoted on a otay fame. The moto connected to the diffeential geabox can be used to dive the two lead scews as well as the mechanism fame, poviding thee diffeent components of a motion. These motions ae detemined by the use of thee electomagnetic bakes. Bake 3 Fig. 4. Finge dive mechanism with diffeential geabox As shown in Fig. 4, bakes 1 and contol the two lead scews, while bake 3 contols the finge oientation elative to the end effecto fame. Thus this mechanism povides thee degees of feedom to the finge. The stuctue of the finge offes independent cul motion while the bend motion is only patially independent as it esults in a slight culing effect to the finge. By contolling the thee bakes as shown in Table 1 (R signifies the bake elease), the thee components of motions can be contolled individually o in combination, thus opeating the finge eithe in adaptive o pecise contol mode with concentic o opposing-thumb configuation. Table 1. Finge motion contolled by the actuato bakes Bake 1 Bake Bake 3 Motion R Cul R Bend R Rotate As shown in Fig. 5, a pototype mechanism has been built and used to veify the pefomance of the tansmission system. 3 Copyight by ASME

4 FINGER KINEMATICS While homogenous matix tansfomation has geneally been used to epesent the kinematic elation of the aticulated links [15] and static foce analysis fo multi-fingeed gasping [6], the pesent analysis is based on the vectoial method of link epesentation fo developing static foce and kinematic elationships. The kinematic chain of the finge is shown in Fig. 7 with fames fixed to the finge joints. The fingetip position is given by, AH = a cosα + bcosβ + g cos ρ (1) x AH = a sin α + bsin β + gsin ρ () z Fig. 5. Pototype finge dive mechanism Fully Contolled Mechanism This appoach is the logical extension of the pevious design, whee all thee motions ae independently poweed and contolled. This equies thee motos within the end effecto envelope fo each finge. This appoach does allow fully contolled independent motion to be achieved, howeve at the cost of additional cabling and possible size estictions. Finge and End Effecto Constuction The basic constuction of the finge is based on an open stuctue using side plates and coss pivots joining them. This mode of constuction gives the maximum clea space within the pofile of finge fo accommodating the mechanical linkages and fo incopoating any sensos within. In the end-effecto design thee individual finges as shown in Fig. 6 ae symmetically placed, this gives a high degee of flexibility in gipping objects. As nine-degees of feedom esult fom the design, a lage numbe of pecision and powe gips can be poduced. The flexibility of the hand is enhanced by the capability of the finges to otate about its own axis allowing geneation of eithe two o thee fingeed paallel gips, o thee fingeed pinch gips [14]. Fig. 6. Plan view of the thee-fingeed end effecto Z A η α a R C X b H g Fig. 7. Kinematic chain of the finge The solution fo these angles develops into complex nonlinea elations with many invese tigonometic functions [14]. These elationships descibe a closed fom kinematic elation between two lead scew inputs (defined as d1, d) and the fingetip position. Fom these elations fingetip wokspace with efeence to the finge s datum ove the displacement ange of lead scew can be plotted as is shown in Fig. 8. Invese Kinematics Solution Futhe to move the fingetip to a specified location, displacement of the lead scews needs to be known in advance. The invese solution fo such a mechanism should have fast convegence, and must opeate satisfactoily thoughout the finge wokspace. Existing end effectos have eithe adaptable finges [,8], which do not equie exact invese kinematics, o the finge movement is detemined by the intepolation of the joint positions between two successive locations [6,7,9]. The movement of finge to a pecise point in case of adaptable configuations has poved to be difficult wheeas the exact tacking of a finge tajectoy in est cases may pove to be time consuming due to the intepolating natue of the implementation. The numeical invese kinematic solution E G F β β ρ 4 Copyight by ASME

5 pesented in this pape is consideed to be fast enough to be tenable to eal-time applications. Finge Z axis (mm) Finge X axis (mm) Fig. 8. Loci of the fingetip ove lead scew tavel limits Solution Stategy The numeical solution is based on the calculation of the two finges angles, α and β, fo a given fingetip location H, as shown in Fig. 7. These ae selected since angles α and β detemine the bend and cul motion of the finge. In ode to bing point H to a taget point P, the finge is fist assumed to be diven in cul until the adius AH equaled the distance fom A to the taget point, then the finge is bent to bing point H to the taget point. This technique helps in sepaating cul and bend angles, which allows an easy deivation of the displacement components. Once these angles ae known, lead scew displacements d1 and d can be back calculated. An independent cul vaiable β (β elative to α) is defined which equals (β-α), and the angle α is set to zeo. The fingetip location can now be epesented in pola fom using R and η as shown in Fig. 7. Unde this situation all the finge vaiables can be solely epesented as a function of the single vaiable β theefoe, R = f + (3) 1(β ) = AH x AH z 1 AH z η = f (β ) = tan (4) AH x Whee AH x and AH z ae the x and z components of the vecto AH. Fo a given taget point P with espect to the joint A, the pola fom of position vecto can be witten as, AP x + z = (AP AP ) (5) 1 APz AP = tan (6) APx At the taget point, the magnitude of the position vecto in Eq. (3) and (5) ae equal, hence x z x AH + AH = AP + AP (7) Since the taget point is known, Eq. (7) can be witten as, AH x z = z + AH K (8) Whee K is a constant, hence Eq. (8) can be solely expessed as function of β f (β )= (9) Eq. (9) can now be solved fo β. Once this is known, angle η can be detemined since this is a function of β. The value of angle α can be defined as: α = AP-η (1) β =β + α (11) Eq. (9) can be optimized fo fast numeical solutions using the Newton-Raphson method, f ( β1) β = β1 (1) f ( β ) 1 Whee β 1 is the fist appoximation, β is a bette appoximation and f ( β ) 1 is the deivative of the function β1. Although the fist appoximation can be taken abitaily between β _min to β _max values, howeve, fo fast convegence the fist appoximation based on the following polynomial fitted to f(β ) is used. AH = a β + b β + c (13) 1 1 Whee coefficient a 1, b 1 and c 1 ae constant fo a specified finge linkages dimensions and can be detemined using thee known finge locations fo known values of β in the opeating ange. Once these coefficients ae known, fo any taget point the fist appoximation can be found by solving the following equation, a β 1 + b β + (c AP ) (14) = Afte the equied pecision in the value of β is attained, the othe dependent angles can be calculated which in tun povide the lead scew displacements d1 and d allowing a solution to the invese kinematics. In most cases of fingetip position, the implementation is found to convege to the desied accuacy (less than a mm) in just thee iteations. By Fichte s theoem [16] the finge should have at least twelve solutions to the invese kinematics; howeve, many of these ae not eal due imaginay values of invese tigonometic functions within the kinematic equations. Of the fou possible eal solutions, only one povides the valid configuation to the finge linkages as shown in Fig. 9. Allowing only a limited displacement of the lead scews, as shown in fist case, ensues that a unique linkage configuation is obtained fo a given fingetip position. The displacement ange fo such 5 Copyight by ASME

6 configuation is found to be 6 mm to 3mm, ove which the finge has a unique solution to invese kinematics. This is used to ensue non-singula configuations of the finge mechanism within its opeational wokspace fo implementation of contol algoithms. of the applied fingetip foce espectively. The foces on these components ae, howeve, maximum at d1 min, d min, which is the fully extended finge situation, making appoximately 9 o angle with the vetical (lead scew) axis. This is clealy not the situation when a finge would nomally be loaded hence in pactical cases the applied load would be smalle than this. Resultant foce at joint A Resultant foce at joint J 6 foce, N 15 1 foce, N d, metes..1 d1, metes.3.4. d, metes..1 d1, metes.3 Resultant foce at joint C Resultant foce at joint F 6.5 foce, N 5 4 foce, N d, metes..1 d1, metes d, metes..1 d1, metes.3 Fig. 1. Foce in finge links fo a pecision gip Fig. 9. Linkages configuation analysis FORCE ANALYSIS In ode to design components of the finge, foce analysis of the finge has been caied out. Equilibium equations ae deived fom the fee body diagam of each link. The fou links, the thee main finge sections and the bell cank, povide a total of twelve equations in twelve unknown foces, thus the equations ae soluble. In actual design, howeve, each finge section has been loaded by vaiable foces at diffeent inclinations to identify the citical condition of finge loading, also fiction within the system has been accounted at vaious stages of the design [14]. The analysis of the finge gives, [A][B]=[C] (15) Whee [A] is the matix of geometical coefficients, [B] is the column vecto of the unknown foces, and [C] is the column vecto of known foces with geometical coefficients. Inveting the above elation gives the unknown foces. These foces have been used to detemine the loading conditions of vaious finge components. Fig. 1 shows the computed nomalized foce on the joint pins when a nomal foce is applied to the fingetip. The plots ae shown in lead scews displacement ange of.6 m to.3 m. This displacement ensues unifom foce vaiations as well as continuous fingetip motions without any singulaity fo the stuctue of the finge linkages. Beyond this ange, the finge configuation is unattainable due to the dimensional constaints of the linkages, and the foce vaiation becomes non-unifom with vey high foces on the finge components. Within this opeating ange, the maximum foce on any component is found to be within twenty times the fingetip foce. The citical components identified ae joint A and link A whee the maximum esultant foces acting ae twenty and sixteen times CONCLUSIONS AND DISCUSSION This pape has pesented design of an aticulated finge mechanism suitable fo adaptive end effectos. The mechanism emoves a numbe of significant poblems expeienced with tendon-based designs. The finge actuation mechanism foms a compact and positive dive unit within the end effecto s body with the use of solid mechanical linkage and the tansmission though the toothed belts, thus offeing a stong and eliable system fo use in nuclea/hazadous envionments whee safety is an impotant consideation. The contol of the finge is easie with one moto and thee bakes as compaed to individually actuated finge joints, since only one moto needs to be contolled with bakes opeating in just ON/OFF situation. Futhe the finges can be diven in adaptive as well as pecise contol mode which can be otated about its own axis allowing it to fom eithe concentic o two finges and opposing thumb gasps. Thus the finge design offes a pactical solution to the specific tasks of gasping objects of specified shape and size secuely within the stuctue of the end effecto. The ange of the fingetip loci deived fom the kinematic analysis povides the size of the object that can be gasped by the end effecto using the finge. The continuity of the finge wokspace poves the mechanical integity of the system, which means any point in this egion can be attained by the finge. The developed invese kinematic solution fo the complex geomety of the aticulated finge allows the finge to be moved to a known location to gasp o to fom a gasp-postue fo the known shape and size of the object. The solution shows that fo specified displacement of the lead scews, the finge has a unique solution to the invese kinematics, thus thee is no mathematical ambiguity in locating the fingetip. The numeic solution to the invese kinematics conveges fast which means eal-time opeation of the end effecto is possible. 6 Copyight by ASME

7 The static analysis identifies the citical loading conditions of finge components based on which they can be designed. Futhe the analysis helps in sizing vaious end effecto components like motos and electomagnetic bakes used in the design. ACKNOWLEDGMENTS The Faculty of Engineeing & Applied Science, Depatment of Electical Engineeing of Univesity of Southampton, and the Oveseas Reseach Student awad fom the UK Committee of Vice-Chancellos and Pincipals have suppoted this eseach. The authos acknowledge the contibution of the Cental Design Sevice, in paticula Dave Whatley fo the ealization of the design, and the constuction of the pototype actuato mechanism. REFERENCES [1] Okamua, A. M., Smaby, N. and Cutkosky, M. R.,, An oveview of dexteous manipulation Poceedings IEEE Intenational confeence on Robotics and Automation, San Fancisco, pp [] Cowde, R. M., 1991, An anthopomophic obotic end effecto Robotics and Autonomous Systems, Vol. 7, pp [3] Cowde, R. M., Dubey, V. N., Chappell, P. H. and Whatley, D. R., 1999, A multi-fingeed end effecto fo unstuctued envionments Poceedings of the IEEE Intl. Conf. on Robotics and Automation, Detoit, Michigan, Vol. 4, pp [4] Cutkosky, M R., 1989, On gasp choice gasp models and the design of hands fo manufactuing tasks, IEEE Tansactions on Robotics and Automation, Vol. 5. No 3, pp [5] Omata, T. and Nagata, K.,, Rigid body analysis of the indeteminate gasp foce in powe gasps, IEEE Tansactions on Robotics and Automation, Vol. 16, No. 1, pp [6] Salisbuy, J. K. 1985, Design and contol of an aticulated hand, In M. T. Mason and J. K. Salisbuy edited, Robot hands and mechanics of manipulation, MIT Pess, Cambidge, MA, pp [7] Jacobsen, S. C., Wood, J. E., Knutti, D. F. and Bigges, K. B., 1986, The Utah/MIT dextous hand: wok in pogess, In D.T. Pham and W.B. Heginbotham edited Robot Gippes, pp [8] Bekey, G. A., Tomovic, R. and Zeljkovic, I. 199, Contol achitectue fo the Belgade/UCS hand, In S.T. Venketaaman edited Dextous Robot Hands.: Spige-Velag New Yok pp [9] Okada, T., 1986, Compute contol of multijointed finge system fo pecise object handling, In D.T. Pham and W.B. Heginbotham edited Robot Gippes, pp [1] Ulich, N., Paul, R. and Bajcsy R., 1988, A mediumcomplexity compliant end effecto Poc. IEEE Intl. Conf. on Robotics and Automation, pp [11] Doll, T. J. and Schneebeli, H. J. 1988, The Kalsuhe hand Poc. on IFAC obot contol, Kalsuhe, pp [1] Lin, L. R. and Huang, H. P., 1996, Integating fuzzy contol of the dexteous National Taiwan Univesity (NTU) hand, IEEE/ASME Tansactions on Mechatonics, Vol. 1, No. 3, pp [13] Jongkind, W., 1993, Dextous gipping in a hazadous envionment guidelines, fault toleance and contol Poc. IEEE Intl. Conf. on Systems Man and Cybenetics, Vol. 1, pp [14] Dubey, V. N., 1997, Sensing and contol within a obotic end effecto, PhD Thesis, Univesity of Southampton, UK. [15] Asada, H. and Slotine, J. J. E., 1986, Robot analysis and contol, John Wiley, New Yok. [16] Hunt, K.H., 1978, Kinematic Geomety of Mechanisms, Claendon Pess, Oxfod. 7 Copyight by ASME