RESEARCH REGARDING FRICTION INFLUENCE OF WIRES TO JOINTS INTERIOR ON PRECISION POSITIONING OF A ROBOTIC ARM

Transcription

1 Internatonal Journal of Modern Manufacturng Technologes ISSN , Vol. VIII, No. 1 / 2016 RESEARCH REGARDING FRICTION INFLUENCE OF WIRES TO JOINTS INTERIOR ON PRECISION POSITIONING OF A ROBOTIC ARM Catalna Cofu 1, Gheorghe Stan 2 1, 2 Vasle Alecsandr Unversty of Bacau, Department of Industral Engneerng Calea Marasest, No. 157, , Bacau, Romana Abstract: Robotc structures are used ncreasngly often n operatons from ndustral feld. By now, desgners came wth nnovatve robotc structures that mmc the movements nspred from nature (snake, octopus arm, elephant s trunk) to acheve flexble postonng. The specfc actuaton of elephant s trunk robotc arms wth wre-drven jonts through nner structure has several mportant advantages such as mnaturzaton possblty of the robotc arm dameter, flexble postonng through narrows spaces and a large workspace wth respect to robot sze. Inner actuaton causes elastc deformaton because of wres frcton to jonts nteror, whch contrbutes to the decreasng of jonts precson postonng. Elastc deformatons of drvng wres vary from jont to jont dependng upon the wnded surfaces number and wres length. In the analyss, we obtan varaton dagrams of postonng precson for each wre drven jont on Y and Z axes. The analytcal method s necessary for postonng precson optmzaton of the partcular robotc arm. Key words: actuatng wres frcton, nner actuaton, seral robotc structure, precson postonng, elastc deformaton. 1. INTRODUCTION The structure of elephant s trunk robotc arms conssts of serally connected jonts that enable flexble spatal postonng. Jonts of smlar structures are commonly drven by wres or cables to actuate them from dstance wth actuators dsposed at the base arm. Ths partcularty assures a low weght of the robotc arm. The actuaton of jonts wth pulley systems and drvng wres placed through structure arm nteror has the advantage of enablng small arm dameters along wth flexble postonng n narrow spaces. However, manpulaton n narrow spaces requres precson postonng that has dfferent sources of postonng errors. Ths paper hghlghts the nfluence of frcton between drvng wres and nner surfaces of robotc arm on postonng precson. Wre actuaton of jonts s commonly used at robotc hands for fngers drvng as t s a demand for mnmum dameters of fngers Correspondng author: Catalna Cofu, blgcatalna@yahoo.com 24 and, consequently for nner actuaton wth wres [1]. Robotc arms wth the structure smlar to elephant s trunk and a smaller number of actuators than the number of jonts have moton control ssues that are solved by an elastc tube mounted to arm s structure nteror [2, 3, 4]. Another robotc arm smlar to elephant s trunk structure has a PID devce for postonng errors compensaton of whch sources cannot be dentfed, [6]. More and more researchers are developng dfferent optmzaton methods of closed loop command systems and moton control usng PID devces to acheve accuracy and trajectory precson of elephant s trunk robotc arms, [5, 8]. The elastcty of drvng wres and ther frcton to jonts nteror surfaces ental the optmzaton ssue of precson postonng by errors compensaton of whch source s elastc deformaton of drvng wre,s [7]. Pulley system wth wres s commonly used as moton transmsson mechansm of elephant s trunk robotc arms. However, wre drven jonts presume postonng errors because of jonts backlashes and elastc deformatons of drvng wres. Determnaton of systematc errors caused by pulley system frctons s emphaszed n ths paper for a partcular desgn of elephant s trunk robotc arm wth 5 degrees of freedom. 2. TRANSMISSION MECHANISM AND ACTUATION SYSTEM OF SPECIFIC JOINTS STRUCTURE Structure desgn of jonts C from the partcular elephant s trunk robotc arm allows 1 degree of freedom and a rotaton of angle θ wthn drvng wres fxed to cylnder wth of radus R c wth opposte dametrcally bolts from structure nteror as descrbed n fg. 1. Each jont (=1...5) of the robotc arm conssts of a gudng element G through whch are crossng the drvng wres of next jont +1. The partcular jont s structure employs a specfc automatc command system, fg. 2, and the crossng of

2 Fg. 1. The crossng of drvng wres through nner jonts structure of robotc arm drvng wres through robotc arm s specfc to each jonts. Actuatng wres of jonts are wndng, one by one, the surfaces of radus R 2 and R 3 to whch corresponds frcton coeffcents μ 1 and μ 2 respectvely, before crossng the grooved wheel R c. Drvng mechansm of jonts C s a tangental transmsson mechansm of moton through wres and a pulley system wth drvng propertes. Each reducer shaft r s lnked to a grooved wheel R c whch transfers the rotaton to knematc jont through two wres fxed to grooved wheel at the bottom end and to cylnder of jont (C ) at the upper end, fg. 2. Actuaton system of each degree of freedom from the elephant s trunk robotc arm conssts of servomotors wth varable number of revolutons (M ), whch are responsble to move a correspondng weght by a rotaton moton and enable closed loop actuaton. Each degree of freedom employs the rotaton of dfferent weghts and a correspondng moment of nerta. The generated moments of nerta are C 5 C 4 G 4 C 3 G 3 G 3 C 2 G 2 G 2 G 2 C 1 R 3 R 2 R c1 R c2 R c3 R c4 R c5 r 1 r 2 r 3 r 4 r 5 ω T p1 1 ω T p2 2 ω T p3 3 ω T p4 4 ω T p5 5 M 1 M 2 M 3 M 4 M 5 FC 1 T v1 FC 2 T v2 FC 3 T v3 FC 4 T v4 FC 5 T v5 + - e 1v + - e 2v + - e 3v + - e 4v + - e 5v + - e 1p + - e 2p + - e 3p + - e 4p + - e 5p e 1 e 2 e 3 e 4 e 5 Control Assembly Fg. 2. The command structure of each degree of freedom 25

3 drectly proportonal wth masses correspondng to each degree of freedom. Thus, for hgh masses of jonts the performances of elephant s trunk robotc arm decrease. The servo drves answer to amplfer outputs and, thus, ther output s a proportonal command sgnal gven by a rotatonal moton ω and measured by a velocty transducer T v n the closed loop system. The poston of dstal end robotc arm s defned by rotaton θ of each jont and t s controlled by the poston loop wth a transducer T p whch s mounted on the gearbox output shaft of jont. Transmsson of moton mechansm between gearbox shaft and unversal jont shaft consst of wres and a pulley system wth transmsson rato R s Rc. Parameters R s and R c defne the radus of grooved wheel (R c ) and the radus of jont cylnder (C ) respectvely. Servo drves receve output sgnals from amplfers FC (frequency converter) and gve the requred moton of actuaton system, a rotatonal moton respectvely. Poston transducers dentfy output parameters and convert them n sgnals accepted by the servomechansms. Input sgnal of servomechansm s summed wth feedback sgnal ( e e ) and produce the proper command sgnal for drvng components of the system. Control assembly computes the reference parameters of servomotors M at each samplng perod. Each jont poston s controlled by the velocty loop and a dgtal poston transducer (T p ) mounted to the shaft of gearbox output, and the controlled sgnal s read by the assembly unt through poston loop. Feedback loops enable automatc error correcton of grooved wheel R c knematc parameters (poston, velocty and acceleraton). 3. DETERMINATION OF PULLEY FRICTION INFLUENCE ON JOINTS POSITIONING PRECISION The elephant s trunk robotc arm wth 5 degrees of freedom and wre drven jonts brngs on the ssue of wres frcton to nner structure surfaces of jonts. Frcton of wres to jonts nteror s a sldng frcton to wnded crcular surfaces. Drvng wres are made of stanless steel wth PTFE (Polytetrafluoroethylene) coatng and are sldng on metallc surfaces (duralumn, steel) of robotc arm components. Frcton of drvng wres to crcular surfaces of gudng component G made of PTFE, fg. 2, s gnorable because of the angle of wndng about radans and the small coeffcent of frcton about 0.04 [9]. The drvng wres of jonts subjected to frcton on crcular surfaces from nner structure of robotc arm presume angles of wndng α 1, α 2 and coeffcents of frcton μ 1, μ 2 gven for crcular metallc surfaces wth radus R 2 and R 3 respectvely, fg. 3. p 26 The effect of frcton between drvng wres and nner structure of robotc arm s an addtonal elastc deformaton of drvng wres on sectons between angles of wndng α 1 ș α 2, fg. 3. Usng Euler s frcton equaton related to wre frcton we obtan equatons for forces that stress addtonally the drvng wres, equatons (1-2). A T 1 T T T e 1 1 (1) T T e 2 2 (2) l 1 Fg. 3. Wnded angles of jont drvng wre We note the pull-force appled at bottom end of drvng wre wth T 1 and the actuatng force of jont wtht 1. From the bottom to the top end of drvng wre, we note the hold-forces wtht, T andt, fg. 3. Therefore, wth gven forces and consderng frcton only, let us consder the followng equvalences T 1=T and T = T 1. We obtan the relaton between pull-force from bottom end of drvng wre and drvng force of jont usng equatons (1-2), equaton (3). l T T1 e (3) Thus, actuatng force of jont s smaller than the pullforce from bottom end of drvng wre as gven n equaton (4) where we note the amount of dvsor wth k, equaton (5). 1 T 1 T C T B α 2 α 1

4 T T k (4) k e (5) Parameter k gven n percentage defnes the coeffcent of effcency for transmsson mechansm of jont. Elastc deformaton of the wre l1 that actuates jont s the sum of elastc deformatons l 1 and l gven for each sectons length of drvng wre l and l respectvely, equaton (6), whch defne the length between tangent ponts of wnded surfaces accordng to fg. 3. l1 l1 l1 T l1 T l E A s (6) 1 l e1 1 l l T E A e s (7) Usng equatons (1-2) and (6), we obtan equaton (7) that defnes elastc deformaton of drvng wre as a consequence of frcton to jonts nteror whch depends on the value of pull-force T appled at wre end fxed to groove wheel R c. Length l defnes the secton length of drvng wre between grp pont A on grooved wheel and tangent pont B after wndng crcular surface wth angle α 1. Length l defnes the secton of drvng wre between tangent pont B and tangent pont C after wndng crcular surface wth angle α 2. Elastc deformatons of drvng wres ental postonng precson of jonts ssue and, thus, angular devatons, equaton (8). 180 l R (8) Angular devatons of jonts affect postonng precson of dstal end robotc arm and ental postonng errors because the pulley system s not part of closed loop command system. If we substtute the known structural and knematc parameters nto equaton (8) we obtan the nfluence of frcton between drvng wres and nteror structure of robotc arm on precson postonng of jonts. Frcton coeffcents depend on the surface qualty between PTFE coated stanless steel wre and nteror of jonts structure, the surfaces roughness of matng metals respectvely. The elephant s trunk robotc arm consst of metal components wth specfc roughness R a =1.6 of crcular surfaces from structure nteror that are wnded by drvng wres upon radus R 2 and R 3, fg. 2. Therefore, for the specfc structure of elephant s trunk robotc arm we have frcton coeffcents gven n table 1. The lengths of drvng wres before elastc c 27 deformaton, l, the lengths of drvng wres sectons subjected to frcton, l and l, the angles of frcton to nner crcular surfaces of robotc arm structure, α 1 and α 2, are also constructve gven. In real case each drvng wre of jonts from elephant s trunk robotc arm wth 5 degrees of freedom are subjected to dfferent pull-forces T. μ 1 μ 2 Table 1. Structural parameters C 1 C 2 C 3 C 4 C α [rad] α l [mm] l l [mm] In the analyss, we use the same value T = 1 N for all pull-forces appled n order to acheve the amount of jonts postonng errors proceeded from frcton between drvng wres and structure nteror of robotc arm. The radus of cylnder jont and the radus of grooved wheel are also constructve gven, R c =16 mm and R s =10 mm respectvely. Maxmum rotaton on X axs of unversal jonts s θ =±23 n both drectons. In calculus we consder that jonts are rotatng n left drecton by pullng the actve wre as shown n fg. 3, and, thus, the angle of jonts rotaton s θ =23. We also know: cross sectonal area of drvng wres A s =0.113 mm 2 and Young modulus E= MPa. Thus, we determne the ratos T / T gven by parameters k n table 2. Usng equatons (7) and (8) we obtan elastc deformatons of the 5 drvng wres and rotaton devatons of jonts respectvely, as a consequence of frcton to crcular surfaces from nner structure of elephant s trunk robotc arm, table 2. Table 2. Elastc deformatons and resulted postonng devatons C 1 C 2 C 3 C 4 C 5 k 100 [%] l [μm] [ ] From table 2 we fnd that frcton of drvng wres to nner structure of jont 1 and of subsequent jonts reduce the effcency of transmsson mechansm wth maxmum 3.93 % and 3.70 % respectvely. The dfference of 0.23 % between last mentoned effcences comes from the value of angle α 2 dfferent at jont 1. Elastc deformatons of drvng wres are about mcrometers and do not exceed 10.7

5 μm at the wre that actuates jont 5. The varaton of postonng errors for each jont depends on angular devatons and results from the postonng equatons obtaned wth homogeneous transformaton matrces. Let us consder the world coordnate system O X Y Z of jont, fg. 4, wth poston coordnates x, y and z, whch defne nomnal poston of jont, equaton (9), towards base coordnate system O 0 X 0 Y 0 Z 0, x 0, y0, z0 0, 0, 0 respectvely. For the analyss, let us assume the poston of prevous jonts n the zero poston reference n order to acheve devatons of jonts that arse only from frcton between drvng wres and nners surfaces of robotc structure, equatons (16-17). Y 0 Z 0 X cos sn 0 0 sn cos x 0 y l z 1 1 l l l l l O 0 O 1 O 2 O 3 O 4 O 5 θ 1 θ 2 θ 3 θ 4 θ 5 (9) postons on Y and Z axes defne absolute postonng errors, equaton (16) and (17) respectvely. y y y (16) z z z (17) Fg. 5 and fg. 6 hghlght the varaton of postonng errors on Y and Z axes respectvely. Postonng errors of jonts reach varable values about mcrometers that are due to frcton between drvng wres and nner surfaces of robotc arm. Δy [μm] Δy 5 Δy 4 Δy 3 Δy 2 Δy θ [ ] Fg. 5. Dagram of postonng errors on Y axs Fg. 4. Elephant s trunk robotc arm knematcs We note the dstance between jonts wth l, fg. 4. From equaton (9) we obtan nomnal poston x, y and z of jont gven by equatons (10-12) towards the base coordnate system of robotc arm dependng upon rotaton angle. x 0 (10) y l sn (11) z l cos (12) The rotaton of jonts on X axs ental that poston coordnate x equals wth zero at each jont. We obtan vrtually poston of jonts on Y and Z axes by addng angular devatons nto postonng equatons of each jont, equatons (13) and (14) respectvely. y l sn (13) z l cos (14) The absolute dfference between vrtual and nomnal 28 Δz [μm] Fg. 6. Dagram of postonng errors on Z axs The maxmum postonng errors are obtaned at drvng wre of jont 5 that are about 50μm and 20μm on Y and Z axes respectvely. From varaton dagrams of postonng precson, we fnd that postonng errors from Y axs decrease as the angle of rotaton ncrease because of cosne functon. 4. CONCLUSION θ [ ] The elephant s trunk robotc arm wth 5 degrees of freedom, wre drven unversal jonts through nner structure and wre-pulley system presume frcton of Δz 5 Δz 4 Δz 3 Δz 2 Δz 1

6 drvng wres to jonts nteror ssue. The rotaton of jonts on X axs only mples postonng errors about mcrometers on Y and Z axes, y and z respectvely. In the analyss, we obtan that frcton between drvng wres and nner surfaces of robotc arm affects also the effcency of pulley system and goes to mnmum 96%. Drvng mechansm of the elephant s trunk robotc arm nclude AC servomotors that actuate the wres n a closed loop system. Thus, elephant s trunk robotc arms may reach mnmzed dameters and adequate precson of spatal postonng. However, postonng errors resulted from elastc deformaton of drvng wres due frcton to nner structure of robotc arm are found outsde the closed loop system and presume the use of compensaton methods. The obtaned elastc deformatons reach about 5μm at drvng wre of jont 1 and 10μm at drvng wre of jont 5. These deformatons affect precson postonng of jonts and mply maxmum rotaton devaton about mnutes of sexagesmal degrees, at jont 1 and at jont 5. The rotatonal devatons cause postonng errors that reach maxmum 50μm at the zero poston of jont 5 on Y axs. We obtaned postonng errors of jonts wthout takng nto consderaton the postonng devaton of prevous jonts and, thus, we assumed n the analyss that prevously jonts to the analyzed jont are n zero poston. We recommend the obtaned results for further research of maxmum postonng errors at end-effector usng the postonng equaton from drect knematcs when all prevously jonts reach maxmum rotaton. Elastc deformatons consdered as an effect of drvng wres frcton to nner structure surfaces of jonts are a part of total elastc deformatons supported by the drvng wres of jonts from consdered elephant s trunk robotc arm. Addtonally to the analyzed deformatons, there are elastc deformatons from resstance moments of each jont. Therefore, for a complete analyss on precson postonng of robotc arm we have to take nto consderaton both mentoned sources that affect elastc deformatons of drvng wres. Postonng errors obtaned n ths paper are systematc errors that are generally adjusted by adequate correcton appled n the programmng algorthm of robotc arm to elmnate postonng devatons obtaned n analytcal and expermental research. (1999), Ed. Frank Kreth, pp. 29, CRC Press LLC, Boca Raton. 2. L, J., Xu, C., Yao, Y., Dng, J., Fang, H., (2015), Predctng synchronous accuracy of the wre sheave drves, Precson Engneerng, 39, L, Z., Du, R., (2013), Desgn and Analyss of a Bo-Inspred Wre-Drven Mult-Secton Flexble Robot, Int J of Advanced Robotc Systems, 10, Lao, B., L, Z., Du, R., (2012), Robot Tadpole wth a Novel Bommetc Wre-drven Propulsor, Proceedngs of the 2012 IEEE Int Conf on Robotcs and Bommetcs, , Guangzhou, Chna 5. Hedar, S., Pltan, F., Shamsodn, M., Hedar, K., Zahmatkesh, S., (2013), Desgn New Nonlnear Controller wth Parallel Fuzzy Inference System Compensator to Control of Contnuum Robot Manpulator, Int J of Control and Automaton, 6 (4), Sadrna, O. R., Pltan, F., Jafar, M, Eram, M., Shamsodn, M., (2013), Desgn PID Estmator Fuzzy Plus Backsteppng to Control of Uncertan Contnuum Robot, Internatonal Journal of Hybrd Informaton Technology, 6 (4), Song. S., L, Z., Yu, H., Ren, H., (2015), Shape reconstructon for wre-drven flexble robots based on Bézer curve and electromagnetc postonng, Mechatroncs, 29, Xong, Y., L, Y., (2015), Modfed Internal Model Control Scheme for the Drve Part wth Elastc Jonts n Robotc System, J Intell Robot Syst, 79, Avalable from: box.com/frcton-coeffcents-d_778.html, Accesed: 15/04/ REFERENCES 1. Lews, F. L., et. al., End effectors and Toolng, Robotcs Mechancal Engneerng Handbook, 29 Receved: December 10, 2015 / Accepted: June 10, 2016 / Paper avalable onlne: June 20, 2016 Internatonal Journal of Modern Manufacturng Technologes.