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A Novel Perspective in the Design of Cable-Driven Systems

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A Novel Perspective in the Design of Cable-Driven Systems
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  Proceedings of IMECE 20082008 ASME International Mechanical Engineering Congress and ExpositionOctober 31 - November 6, 2008, Boston, Massachusetts, USA IMECE2008-67272 A NOVEL PERSPECTIVE IN THE DESIGN OF CABLE-DRIVEN SYSTEMS Giulio Rosati ∗ , Damiano Zanotto Dept. of Innovation in Mechanics and Management (DIMEG)University of Padua - Faculty of Engineeringvia Venezia 1, 35131 Padova, Italygiulio.rosati@unipd.it ABSTRACT This paper deals with a novel approach to the design of cable-driven systems. This kind of robots possesses several de-sirable features that distinguish them from common manipula-tors, such as: low-inertia, cost-effectiveness, safety, easy recon- figuration and transportability. One key-issue that arises fromthe unilateral actuation is the design for workspace optimiza-tion. Most previous researches on cable-driven systems design focused their attention on workspace analysis for existing de-vices. Conversely, we introduce a new approach for improvingworkspace by design, introducing movable pulley-blocks rather than increasing the number of cables. By properly moving the pulley-blocks, the end-effector can be always maintained in thebest part of the working space, thus enhancing robot capabilitieswithout the need for additional cables. Furthermore, the eventu-ality of cable interference is strongly reduced. In this paper, thenovel design concept is applied to different planar point-masscable-driven robots, with one or more translating pulley-blocks.The maximum feasible isotropic force, along with the power dis-sipation and the effective mass at the end-effector are employed to compare the performances of different configurations. INTRODUCTION Cable-based robots are a type of parallel manipulatorwherein the end-effector is supported in-parallel by cables thatare actuated by tensioning motors. A main difference betweencable-based systems and common parallel robots is that cablescan only carry tension forces [1,2]. Usually, each cable is reeled ∗ Address all correspondence related to this paper to this author. on a pulley that is keyed on the shaft of an electric motor, andhas the other extremity fixed to an attaching point on the endeffector. By properly adjusting cable lengths and tensions, therequired poses and wrenches are attained.Several advantages distinguish cable-based systems fromcommon manipulators: first of all, the mechanical architectureis rather simple and cost-effective, even in the case of multi-ple DOFs spatial systems. Furthermore, since cables are low-weight components, inertia forces are usually limited or, alterna-tively, very high accelerations can be obtained at the end effec-tor. As a further consequence, these robots often present veryhigh payload-to-weight ratios. In addition, a low mechanicalimpedance is felt at the end-effector, so that cable-based robotscan be conveniently utilized as haptic displays. Moreover, unilat-eral actuation can be used to improve the system safety, which isessentialfordevicesthatmustinteractwithhumanoperators(e.g.medical applications [3]). Finally, these manipulators are verysuitable for modular designs that allow rearrangeable configura-tions and easy transportability, and cables can be long enough tocover quite large workspaces.On the other hand, several issues have to be considered fora proper design of a cable-based device. Cable interference is aproblem to cope with in parallel structures, furthermore, becauseof cable-stretching, high levels of accuracy are hardly obtained atthe end-effector. Despite of the simple mechanical design, ma- jor issues may arise in control system implementation: in fact,due to the unilateral actuation (i.e., cables can only pull), atten-tion must be paid to always keep positive tensions in the cables.The controllable workspace is often extended through actuationredundancy (over-actuated and fully-actuated parallel configura-1 Copyrightc  2008 by ASME  tions) or, alternatively, by using gravity as an additional virtualcable with a constant, downward-directed tension (underactuatedcrane-type systems). Elaborated control algorithms must be im-plemented to assure positive cable tension and to obtain optimumdistribution of tension among cables. Related work Wire-driven robots have attracted the attention of many re-searchers in the last decade, so that there is an extensive pub-lished research on this topic.Y. Shen, H. Osumi et al. studied necessary and sufficientconditions for manipulability of wire-driven robots, and pro-posed the use of the velocity ellipsoid  and the volume of the set of manipulating forces as performance evaluation indexes forwire-driven systems [4].R. L. Williams II and P. Gallina [1] defined the staticsworkspace  as the space wherein all possible Cartesian forces andmoments may be exerted with only positive cable tensions, andinvestigated several layouts of planar translational cable-drivenrobots, with three and four cables.P. Lafourcade, M. Llibre et al. defined the theoretical workspace  W  Th as the set of poses of the end-effector, whereall forces and moments can be exerted, with tensions in wiresgreater than an arbitrarily chosen value [5,6]. They introduceda geometrical method, based on planar reasoning, as a tool for afirst design of spatial cable-driven manipulators (SACSO-7 andSACSO-9): from cable number and attachment point disposi-tion, an approximated idea of the corresponding workspace canbe obtained easily. This can help designers in the early choice of the robot layout, whereas more reliable data can be obtained ina next step via numerical algorithms. Nonetheless, the geomet-rical, sketch-based approach is a proper method for workspaceestimation in the case of planar manipulators.Barrette and Gosselin introduced the definition of  dynamic workspace  , as the set of all configurations and accelerations forwhich cables are in tension [7]. An analytical method is de-scribed to derive a subset of the dynamic workspace, when theorientation and the set of accelerations are fixed.R. Verhoeven and M. Hiller coped with the problem of workspace estimation and cable tension distribution in tendon-based 6-DoF Stewart platforms [8]. The controllable workspace  (CWS) was defined as the space wherein a given wrench canbe exerted by the end-effector with acceptable cable tensions(i.e.within a given interval). The authors illustrate how the prob-lem of deriving a set of acceptable solutions can be reduced totwo appropriate nonlinear optimization problems. Furthermore,a modification to the algorithm is proposed to account for thecontinuity of the force path as the trajectory evolves in time.An extensive study on cable-based systems can be found inthe papers of S.K. Agrawal et al. Both design optimization andcontrol strategies to maintain positive cable tensions have beenhandled for different types of cable manipulators: 3-DoF planarsystems, 6-DoF tendon-based Stewart platforms, and dual-stagecable robots. As to planar systems, A. Fattah and S.K. Agrawaldeveloped an algorithm to optimize design parameters, based onthe workspace area and the global condition index of the struc-ture matrix [2]. For a given orientation of the end-effector, theworkspace is defined as the set of points where the end-effectorcan reach static equilibrium, assuming that no external forces butgravity are acting. Results showed that larger workspaces mustbeexpected whencablenumberincreasesand, inthecaseofnon-pointmasssystems, whenthedimensionsofthemovingplatformare reduced. Another work by S.R. Oh and S.K. Agrawal [9] pre-sented some approaches for control system design, with the aimof following prescribed trajectories while keeping all tensionspositive during motion.Diao et al. [10] developed a systematic numerical methodto calculate the workspace of any 6-dof completely restrainedcable-based robot. The introduced force-closure workspace  co-incides with the first definition given in [11], thus it is a purelygeometrical definition and does not account for any upper con-straint on cable tensions. By following this approach, however,the workspace of a manipulator can be easily computed for dif-ferent positions and orientations of the end-effector, and its vol-ume can be used as a parameter for robot design.D. Surdilovic et al. developed a cable-based robot prototypefor gait rehabilitation, called the STRING-MAN [12]. In thiswork, the number of cables and the location of their attachmentpoints are tested through a dedicated software that integrates akinematic and dynamic model of the patient. The condition num-ber of the structure matrix and the homogeneity of the kernelcomponents are used as optimization parameters inside a costfunction. As the design process progressed, the authors reducedthe number of cables in order to simplify the control system andreduce cable interference [13].P. Bosscher, I. Uphoff et al. presented an analytical methodto calculate the boundaries of the workspace for cable drivenrobots [14]. The Wrench-Feasible Workspace ( WFW  ) was de-fined as the set of end-effector poses where a Required NetWrench Set (  NW  req ) is contained inside the Avaible Net WrenchSet (  NW  avail ). The former is a set of wrenches that the end-effector must  apply to its surroundings, and depends on the spe-cific application. The latter is the set of wrenches that the end-effector is able  to apply, taking into consideration cable tensionconstraints. Workspace boundaries are derived by imposing thecondition of contact between NW  req and the faces of  NW  avail .Examples are presented for point-mass, planar, and spatial ca-ble robots. The main advantage of this approach is to overcomethe usual numerical algorithms. On the other hand, the formu-lation grows in complexity as the number of DOFs increases.Secondly, no information is given about the effective capabilitiesof the robot within the WFW  . Lastly, the reported procedures toconstruct WFW  do not suit to non-underconstrained cable ma-2 Copyrightc  2008 by ASME
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