Four-cable-driven parallel robot

2013 13th Internatonal Conference on Control, Automaton and Systems (ICCAS 2013) Oct. 20-23, 2013 n Kmdaejung Conventon Center, Gwangju, Korea Four-cable-drven parallel robot XueJun Jn 1, Dae Ik Jun 1, Andreas Pott 2, Sukho Park 1, Jong-Oh Park 1* and Seong Young Ko 1* 1 School of Mechancal Engneerng, Chonnam Natonal Unversty, Gwangju, 500-757, Korea (Tel : +82-062-530-1679; E-mal: {jop, sko}@jnu.ac.kr ) * Correspondng author 2 Fraunhofer Insttut für Produktonstechnk und Automatserung (IPA), Stuttgart, Germany Abstract: Ths paper presents desgn and knematc analyss for a cable-drven parallel robotc (CDPR) manpulator wth four cables, The CDPR manpulator produces a planar moton ncludng two translatonal and one rotatonal degrees of freedom. To move the end-effector of CDPR, ts knematc structure s analyzed and the nverse knematcs s formulated n the closed-form soluton. The expermental tests usng an mplemented prototype have shown the feasblty of the system desgn and ts operaton. Keywords: Wnches, Forward knematcs, Parallel manpulators, Cable-drven manpulator. 1. INTRODUCTION Parallel robots are defned as robots that have closed knematc chans. It means several actuators meet at one end-effector or jont. Cable-drven parallel robots (CDPR) are a type of parallel manpulators wheren the end-effector s supported n parallel by multple cables that are controlled by multple tensonng actuators. As for classcal parallel robots, moton of an end-effector may be generated ether by changng lengths of cables or modfyng the locatons of attachment ponts when the actuators lengths are fxed. In ths paper, cable lengths are controlled by usng colng wnches that act as lnear actuators wth long stroke. CDPRs are structurally smlar to parallel robots, but they have addtonal merts, such as large workspace, f compared wth the workspace of classcal parallel manpulators. Moreover, ther actuators are fxed on the frame, thus they have a few movng parts, resultng n small nertal propertes, hgh payload-weght rato, transportablty, and economcal constructon. In the last decade, a lot of research has been carred out to study the related theory [2, 3, 4] and/or mplementaton of these robots [1, 5]. Cable-drven parallel manpulators can be classfed nto fully constraned and under constraned based on the extent to whch the end-effector s constraned by the cables. Fgure 1 shows an example of the two types of cable robots. Ths paper concerns about cable robots of the fully constraned type. We present desgn and knematc analyss of a four-cable-drven parallel manpulator. A prototype has been bult and expermental tests show the feasblty of the cable system desgn and ts operaton for planar tasks. Fg.1 Example of the two types of parallel cable robots. (a) Fully-constraned cable robot, (b) Under-constraned cable robot 2. MECHANICAL DESIGN OF A FOUR-CABLE-DRIVEN PARALLEL ROBOT In ths paper, we explan a four-cable-drven planar parallel robot, whose specfcatons are gven as n Table 1. The prototype presented n ths work s used to verfy the algorthms such as nverse/forward knematcs, workspace analyss, tenson control and so forth. Table 1 Specfcaton of a four-cable-drven planar parallel robot Sze of Frame Speed Payload DOF Settlng Tme 2.1 System Confguraton 2 m x 2 m x 2 m 2.5 m/s 5 kg 3 DOF 1 sec The four-cable-drven parallel manpulator s composed of a rgd frame, four wnches that control the cable lengths, a low-level poston controller, a PC for a hgh-level control, an end-effector that contans a laser scanner, as shown n Fg. 2. 879

n the wnch should be sgnfcantly smaller than the mnmum curvature of the cables themselves. Secondly, the drecton of the cables changes contnuously durng operaton of the cable robot. Therefore, t s necessary to nclude an omndrectonal gudance mechansm nto the wnch. The manufactured cable-drven parallel robot and ts wnches are shown n Fg. 4. Fg.2 System confguraton of the developed CDPR 2.2 Desgn of Wnches Fg. 4 (a) The manufactured CDPR and (b) ts wnches 2.3 Choce of the Motors and Cables A statc analyss has been carred out n order to decde properly the sze of actuators and cables of the proposed manpulator. In partcular, two cables are connected to one pont at the end-effector, as shown n the smplfed scheme of Fg. 5, where m s the mass of the end-effector plus the payload. The smplfcaton s done snce the upper cables support most of load n the statc stuaton. Fg. 3 Assembly of the wnch Fgure 3 shows assembly of the wnch, whose basc concept s same as the wnch explaned n [10]. A man shaft s supported by two bearngs at both ends for reducng lateral deflecton. The dscrepancy between the ptch of the ball screw and that of the drum was corrected by usng the ptch of the ball screw and the reducton rato of tmng pulleys. The reducton rato between two tmng pulleys s thus chosen as 1: 2. Due to equal ptch of the drum and the spndle the relatve drecton of the coled cable s constant allowng for relable colng and uncolng of the cable. Ths s especally mportant snce the veloctes and acceleratons of the cables are very hgh for cable robots. The tenson of each wre s measured by a load cell. The mechancal desgn of the wnches s derved from crane wnches where some addtonal requrements have to be taken nto account to control and operate cable-drven parallel robots as n [11]. A frst requrement for lastng operaton of cable robots wthout excessve wear of the cables s that the maxmum curvature of the cable route Fg. 5 Two-dmensonal free body dagram For these condtons, each cable s loaded by a tenson F whose drecton s nclned by an angle αwth respect to the horzontal plane. Thus, one can wrte 2 F sn mg ma. (1) A maxmum requred force F req can be calculated as n (2) to satsfy the specfcaton n Table 1. The requred torque for the actuator can be calculated as n (3), consderng the drum radus and the gear reducton. mg ( a sn 2 max F req (2) mn ) 880

req F req r (3) G The maxmum acceleraton a max and the maxmum payload are assumed to be 2.5m/s 2, and 5kg, respectvely. The drum radus and gear reducton rato are selected to r=0.004m and G=5, respectvely. It s worth notng that f αbecomes 0 the actuaton torque becomes nfnte. In fact, the confguraton where all cables are horzontal s sngular, n whch all the tensons of the cables are orthogonal wth respect to the force gven by gravty (mg). Assumng α mn = 20 degrees, we can get F req = 90N and τ req =0.072Nm. Thus, for the above-mentoned consderatons each cable should yeld a force hgher than about 90 N and each actuator has a nomnal torque of about 0.1 Nm. These propertes can be acheved, for example, by usng commercal cables and motors PANASONIC MSMD012S1T001 wth 5:1 reducton rato. 2.3 2-D Laser Scanner Fg. 6 LMS400, SICK The LMS400 manufactured from SICK provdes a measurement soluton wth hgh scannng rates, comprehensve process relablty and mproved measurement resoluton for close range applcatons. The laser scanner can measure up to 3 m, wth hgh angular and dstance resoluton whch satsfy wth our applcaton. The LMS400 wll be ntegrated wth our cable robotc system. 3.1 Inverse Knematcs 3. Knematcs Fgure 7 shows the knematc structure of our four-cable-drven parallel robot. Black dotted arrows ndcate poston vectors from the attachment ponts, where the cables are connected to the end-effector, to anchor ponts of the rgd frame. A vector descrbng th sngle cable s shown usng a red sold arrow. The world coordnate system K w and the end-effector coordnate system K p are assgned as shown n Fg. 7. Fg. 7 Geometry and knematcs The pose of the end-effector s defned by ts Cartesan poston x, y and orentaton θ relatve to the world coordnate system. Varable vectors l denote the lengths of cables, postonng vectors a denote the center poston of the end-effector from the proxmal anchor ponts on the frame, the vectors b are the relatve postons of the dstal attachment ponts on the movable end-effector. Then, gven vector r and rotaton matrx R the closed-form soluton for any pose can be obtaned as n (4). a r Rb l (4) where x cos sn r and R y sn cos 3.2 Forward Knematcs Fndng the Cartesan poston of the end-effector when jont varables are gven s called forward knematcs. The problem of forward knematcs of CDPR s one of hghly complcated ssues and cannot be solved n a closed form. It s also an area of consstent research for parallel manpulators n general. In fact, for the general case wth 6 degrees of freedom up to 40 solutons may exst for the forward knematc problem [6]. Husty proposed a method usng a unvarate polynomal of degree 40 fndng all these solutons [7]. Ths would be very mpractcal to mplement. In ths research, the cables tenson forces s used as an extra sensory data n the soluton of forward knematcs. Snce only the nverse knematcs s needed for a poston control, the forward one s not performed n ths work. 4. SIMULATION 4.1 Interpolaton We desgn a smooth curve usng cubc-splne nterpolaton to gude CDPR along a vertcal cycle assumng that the end-effector leaves the home locaton, moves the object to a release locaton, and returns to the home locaton. We use the nverse algorsm to calculate 881

the cable lengths to control CDPR usng MATLAB. Fgures 8 and 9 show the smulaton results of the cable lengths to produces the crcular moton. Fg. 8 Generated crcular path wth 100mm of radus Fg. 9 Generated cable lengths for crcular moton 4.2 Workspace The wrench feasble workspace for CDPR s governed by the fundamental requrement that all cables must be under tenson. Ths means, that for a gven wrench (forces and moments actng on the end-effector) there must exst such a dstrbuton of forces n the cables, where all cables are under suffcent tenson. For planar cable robots there exsts a closed form method llustrated n [8]. The unt vector along the tenson becomes 100 80 60 40 20 0-20 -40-60 -80-100 u -100-50 0 50 100 l 1 l. For force equlbrum t holds that [5, 9] f1 f x u1 u4 f y 0 p1 u1 p4 u4 f 4 T Af w 0 (5) It s constructed through the unt vectors u of each cable and the dstal attachment ponts on the end-effector p, whch are descrbed wth respect to the world coordnate system. The relaton between the structure matrx A and the vector of cable forces f and the external wrench w appled on the end-effector. For a gven pose we now check whether there exsts a vector f wth only postve values so that Eq. (5) holds true. If ths s not the case, the pose s consdered to be outsde of the workspace. 5. FURTHERWORK Increasng the accuracy through a better structural knematc model s one of mportant ssues of nvestgaton. Ths may nclude modelng of cable sag, cable tenson, or the geometrc effects of wnch pulleys. Another very mportant ssue s the lack of constrant normal to the plane. Thus any actng force n ths drecton wll result n vbratons and naccuraces n poston and control due to deflectons on ths normal. It was observed that ncreasng cable tenson mproved ths behavor. A detaled expermental and theoretcal examnaton s needed n order to generalze these observatons and add valdty to ths clam. Ths s an mportant area of research whch can be expermentally verfed usng the laser scanner to calbraton. 6. CONCLUSION A sutable knematcs analyss of four-cable-drven parallel archtecture has gven the possblty to conceve an easy-operaton desgn of a cable manpulator. Basc performances have been smulated for desgn purposes and they have been experenced n successful tests for valdaton purposes. The proposed four-cable drven parallel manpulator has been used n laboratory tests both for under constraned and fully constraned applcatons that have outlned the possblty to extend, and also can combne wth laser scanner applcaton n the future, the desgn concepts for a general 8-cable parallel manpulator. ACKNOWLEDGEMENT Ths work s supported by the Natonal Strategc R&D Program for Industral Technology (10041605) funded by the Mnstry of Trade, Industry and Energy (MOTIE) and by Leadng Foregn Research Insttute Recrutment Program (No. 2012-026740) through the Natonal Research Foundaton of Korea (NRF) funded by the Mnstry of Educaton, Scence and Technology (MEST). REFERENCES [1] Bruckmann, T., Pott, A. and Hller, M., Calculatng force dstrbutons for redundantly actuated tendon-based Stewart platforms. In Advances n Robot Knematcs, Ljubljana, Slovena, pp. 403 412, Sprnger (2006). [2] Gouttefarde, M., Merlet, J.-P. and Daney, D., Wrench-feasble workspace of parallel cable drven mechansms. In Proceedngs IEEE Internatonal Conference on Robotcs and Automaton, Roma, Italy, pp. 1492 1497 (2007). [3] Hller, M., Fang, S., Melczarek, S., Verhoeven, R. and Frantza, D., Desgn, analyss and realzaton of tendon-based parallel manpulators. Mechansm and Machne Theory 40(4), 429 445 (2005). [4] Merlet, J.-P. and Daney, D., A new desgn for 882

wre-drven parallel robot. In Proceedngs 2nd Internatonal Congress, Desgn and Modellng of Mechancal Systems (2007). [5] Verhoeven, R., Analyss of the Workspace of Tendon-Based Stewart Platforms. PhD Thess, Unversty of Dusburg-Essen (2004). [6] Detmaer, P.: The stewart-gough platform of general geometry can have 40 real postures. In: Advances n Robot Knematcs, pp. 7 16. Kluwer Academc Publshers, Salzburg and Austra (1998) [7] Husty, M.L.: An algorthm for solvng the drect knematc of stewart-gough-type platforms. In: Mechansm and Machne Theory, vol. 31, pp. 365 380 (1996) [8] Chablat, D., Ottavano, E., Moroz, G.: A comparatve study of 4-cable planar manpulators based on cylndrcal algebrac decomposton. In: Internatonal Desgn Engneerng Techncal Conferences & Computers and Informaton n Engneerng Conference, pp. 1 10 (2011) [9] Mng, A. and Hguch, T., Study on multple degree-of-freedom postonng mechansm usng wres (Part 1) Concept, desgn and control. Internatonal Journal of the Japanese Socety for Precson Engneerng 28(2), 131 138 (1994). [10] Pott, A., C. Meyer, and A. Verl. Large-scale assembly of solar power plants wth parallel cable robots. n Robotcs (ISR), 2010 41st Internatonal Symposum on and 2010 6th German Conference on Robotcs (ROBOTIK). 2010. VDE. [11] Kraus, W., et al. Investgaton on a Planar Cable-Drven Parallel Robot. n Robotcs; Proceedngs of ROBOTIK 2012; 7th German Conference on. 2012. VDE. 883