Abstract
Cable-driven robots (CDRs) are a special class of parallel mechanisms in which the end-effector is actuated by cables, instead of rigid-linked actuators. They are characterized by lightweight structures with low moving inertia and large workspace, due to the location of the cable winching actuators at the fixed base of the structure, and thereby reducing the mass and inertia of the moving platform. CDRs also possess an intrinsically safe feature due to the cables’ flexibility, which allows CDRs to provide safe manipulation in close proximity to their human counterparts. This chapter will highlight the various research endeavors in the performance analysis of CDRs such as force-closure analysis, stiffness analysis, workspace analysis, and cable tension planning. Several case studies will also be presented to serve as illustrations on the application of the proposed performance analysis tools.
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References
Agrawal SK (1990) A study of in-parallel manipulator systems. Ph.D. thesis, Department of Mechanical Engineering, Stanford University
Agrawal SK, Roth B (1992) Statics of in-parallel manipulators. ASME J Mech Design 114(4):564–568
Albus J, Bostelman R, Dagalakis N (1993) The nist robocrane. J Robot Syst 10(5):709–724
Alp AB, Agrawal SK (2002) Cable-suspended robots: design, planning and control. In: Proceedings of IEEE international conference on robotics and automation, Washington, DC, May 2002, pp 4275–4280
Ball RS (1900) A treatise on the theory of screws. Cambridge University Press, Cambridge
Bauchau OA, Craig JI (2009) Structural analysis: with applications to aerospace structures. Springer, Dordrecht
Behzadipour S (2009) Kinematics and dynamics of a self-stressed cartesian cable-driven mechanism. ASME J Mech Design 131(6):061005
Behzadipour S, Khajepour A (2006) Stiffness of a cable-based parallel manipulators with application to stability analysis. J Mech Design 128:303–310
Bonev IA, Gosselin CM (2005) Singularity loci of spherical parallel mechanisms. In: Proceedings IEEE international conference Robotics and Automation, Barcelona, April 2005, pp 2968–2973
Bonev IA, Ryu J (2001) A new approach to orientation workspace analysis of 6-dof parallel manipulators. Mech Mach Theory 36:15–28
Borgstrom PH, Jordan BL, Sukhatme GS, Batalin MA, Kaiser WJ (2009) Rapid computation of optimally safe tension distributions for parallel cable-driven robots. IEEE Trans Robot 25:1271–1281
Bosscher P, Ebert-Uphoff I (2004a) Wrench-based analysis of cable-driven robots. In: Proceedings of IEEE international conference robotics and automation, New Orleans, 26 Apr–01 May 2004, pp 4950–4955
Bosscher P, Ebert-Uphoff I (2004b) A stability measure for underconstrained cable-driven robots. In: Proceedings of IEEE international conference robotic automation, New Orleans, 26 April–01 May 2004, pp 4943–4949
Buckingham R et al (2007) Snake-arm robots: a new approach to aircraft assembly. In: Proceedings of SAE Aerotech congress, vol 1, Los Angeles, Sept 2007
Ceccarelli M (2004) Fundamentals of mechanics of robotic manipulation. Kluwer Academic Publishers, Dordrecht
Ceccarelli M, Carbone G (2002) A stiffness analysis for capaman (cassinoparallel manipulator). Mech Mach Theory 37:427–439
Chen Q, Chen W, Yang G, Liu R (2013) An integrated two-level self-calibration method for a cable-driven humanoid arm. IEEE Trans Autom Sci Eng 10(2):380–391
Chirikjian GS, Kyatkin AB (2000) Engineering applications of noncommutative harmonic analysis with emphasis on rotation and motion groups. CRC Press, Boca Raton
Choe W, Kino H, Katsuta K, Kawamura S (1996) A design of parallel wire driven robots for ultrahigh speed motion based on stiffness analysis. In: Proceedings of Japan-USA symposium flexible automation, vol 1. Ann Arbor, pp 159–166
Dai JS, Jones JR (2002) Null-space construction using cofactors from a screw-algebra context. Proc Math Physical Eng Sci 458(2024):1845–1866
Dallej T et al (2011) Towards vision-based control of cable-driven parallel robots. In: Proceedings of IEEE international conference on intel-legent robotics systems, pp 2855–2860
Diao X, Ma O (2008) Workspace determination of general 6-d.o.f. cable manipulators. J Adv Robot 22:261–278
El-Khasawneh BS, Ferreira PM (1999) Computation of stiffness and stiffness bounds for parallel link manipulators. Int J Mach Tool Manuf 39:321–342
Fang S, Franitza D, Torlo M, Bekes F, Hiller M (2004) Motion control of a tendon-based parallel manipulator using optimal tension distribution. IEEE/ASME Trans Mechatron 9:561–568
Fattah A, Agrawal SK (2002) Design of cable-suspended planar parallel robots for an optimal workspace. In: Proceedings workshop fundamental issues future research directions parallel mechanism manipulators, Quebec City, 3–4 October 2002, pp 195–202
Ferraresi C, Paoloni M, Pescarmona F (2007) A new methodology for the determination of the workspace of six-dof redundant parallel structures actuated by nine wires. Robotica 25:113–120
Gosselin CM, Angeles J (1991) A global performance index for the kinematic optimization of robotic manipulators. J Mech Design 113:220–225
Gosselin CM, Wang J (2004) Kinematic analysis and design of cable-driven spherical parallel mechanisms. In: Proceedings of 15th CISM-IFToMM symposium on robot design, dynamics and control, Montreal, 14–18 June 2004
Gouttefarde M (2008) Characterizations of fully constrained poses of parallel cable-driven robots: a review. In: Proceedings of ASME international design engineering technical conference, Brooklyn, pp 21–30
Gouttefarde M, Merlet JP, Daney D (2006) Determination of the wrench-closure workspace of 6-dof parallel cable-driven mechanisms. In: Lenarcic J, Roth B (eds) Advanced robotics kinematics. Springer, Dordrecht, pp 315–322
Hamilton N, Luttgens K (2002) Kinesiology: scientific basis of human motion. Mc-Graw Hill, New York
Hassan M, Khajepour A (2011) Analysis of bounded cable tensions in cable-actuated parallel manipulators. IEEE Trans Robot 27:891–900
Homma K, Fukuda O, Sugawara J, Nagata Y, Usuba M (2003) A wire-driven leg rehabilitation system: development of a 4-dof experimental system. In: Proceedings of IEEE/ASME international conference on advanced intelligent mechatronics, pp 908–913
http://www.skycam.tv. Accessed 06 Jan 2014
Hunt KH (1978) Kinematic geometry of mechanisms. Oxford Science, New York
Jeong JW, Kim SH, Kwak YK, Smith CC (1998) Development of a parallel wire mechanism for measuring position and orientation of a robot end-effector. J Mechatron 8:845–861
John Blair (2006) Nist robocrane cuts aircraft maintenance costs. http://www.nist.gov/el/isd/robo-070606.cfm. Accessed 06 Jan 2014
Karger A, Novák J (1985) Space kinematics and Lie groups. Gorden and Beach Science Publishers, New York
Kawamura S, Choe W, Tanaka S, Pandian SR (1995) Development of an ultrahigh speed robot falcon using wire drive system. In: Proceedings of IEEE conference on robotics and automation, vol 1. Aichi, pp 215–220
Kim D, Chung WK (2003) Analytical formulation of reciprocal screws and its application to nonredundant robot manipulators. ASME J Mech Design 125:158–164
Korein JU (1984) A geometrical investigation of reach. MIT Press, Philadelphia
Lafourcade P, Llibre M (2002) Design of a parallel wire-driven manipulator for wind tunnels. In: Proceedings workshop on fundamental issues and future research directions for parallel mechanisms and manipulators, Quebec City, pp 187–194
Lim WB, Yang G, Yeo SH, Mustafa SK (2011) A generic force-closure analysis algorithm for cable-driven parallel manipulators. Mechanism Mach Theory 46(9):1265–1275
Lim WB, Yeo SH, Yang G (2013) Optimization of tension distribution for cable-driven manipulators using tension-level index. IEEE/ASME Trans Mechatron 99:1–8
Lipkin H, Duffy J (1985) The elliptical polarity of screws. ASME J Mech Trans Autom Design 107:377–387
Liu H, Gosselin C (2011) A spatial spring-loaded cable-loop-driven parallel mechanism. In: Proceedings of ASME international design engineering technical conference
Liu X, Qiu Y, Duan X (2011) Stiffness enhancement and motion control of a 6-DOF wire-driven parallel manipulator with redundant actuations for wind tunnels. In: Okamoto S (ed) Wind tunnels. InTech, doi:10.5772/14974
MacCarthy JM (1990) Introduction to theoretical kinematics. MIT Press, Cambridge
Mao Y, Agrawal SK (2012) Design of a cable driven arm exoskeleton (carex) for neural rehabilitation. IEEE Trans Robot 28(4):922–931
Merlet J-P (2000) Parallel robots, vol 74. Kluwer Academic Publishers, Dordrecht
Mikelsons L, Bruckmann T, Hiller M, Schramm D (2008) A real time capable force calculation algorithm for redundant tendon-based parallel manipulators. In: Proceedings of IEEE international conference on robotics and automation, Pasadena, pp 3869–3874
Ming A, Higuchi T (1994) Study on multiple degree-of-freedom positioning mechanism using wires (part 1) – concept, design and control. Int J Jpn Soc Precis Eng 28(2):131–138
Morizono T, Kurahashi K, Kawamura S (1997) Realization of a virtual sports training system with parallel wire mechanism. In: Proceedings of international conference on robotics automation, Alberquerque, pp 3025–3030
Morizono T, Kurahashi K, Kawamura S (1998) Analysis and control of a force display system driven by parallel wire mechanism. Robotica 16:551–563
Murray RC, Li Z, Sastry SS (1994) A mathematical introduction to robotic manipulation. CRC Press, Boca Raton
Mustafa SK, Agrawal SK (2012a) Force-closure of spring-loaded cable-driven open chains: minimum number of cables required & influence of spring placements. In: Proceedings of IEEE international conference on robotics automation, Saint Paul, pp 1482–1487
Mustafa SK, Agrawal SK (2012b) On the force-closure analysis of n-dof cable-driven open chains based on reciprocal screw theory. IEEE Trans Robot 28(1):22–31
Mustafa SK, Yang G, Yeo SH, Lin W (2006) Optimal design of a bio-inspired anthropocentric shoulder rehabilitator. Appl Bionics Biomech 3(3):199–208
Oh S-R, Agrawal SK (2005) Cable suspended planar robots with redundant cables: controllers with positive tensions. IEEE Trans Robot 21(3):457–465
Oh S-R, Agrawal SK (2006a) Generation of feasible set points and control of a cable robot. IEEE Trans Robot 22(3):551–558
Oh S-R, Agrawal SK (2006b) The feasible workspace analysis of a set point control for a cable-suspended robot with input constraints and disturbance. IEEE Trans Control Syst Tech 14(4):735–742
Park FC, Ravani B (1997) Smooth invariant interpolation of rotations. ACM Trans Graph 16(3):277–295
Pham CB, Yeo SH, Yang G (2005) Tension analysis of cable-driven parallel mechanisms In: Proceedings of IEEE/RSJ international conference on intelligent robots system, Edmonton, 2–6 Aug 2005, pp 2601–2606
Pham CB, Yeo SH, Yang G, Mustafa SK, Chen I-M (2006a) Force-closure workspace analysis of cable-driven parallel mechanisms. Mech Mach Theory 41:53–69
Pham CB, Yeo SH, Yang G, Kurbanhusen MS, Chen IM (2006b) Force-closure workspace analysis of cable-driven parallel mechanisms. J Mech Mach Theory 41:53–69
Pham CB, Yeo SH, Yang G, Chen I-M (2009) Workspace analysis of fully restrained cable-driven manipulators. Robot Auton Syst 57:901–912
Pott A, Bruckmann T, Mikelsons L (2009) Closed-form force distribution for parallel wire robots. In: Computational kinematics: proceedings of 5th international workshop computational kine, Springer, Duisburg, pp 25–34
Pusey J, Fattah A, Agrawal SK, Messina E, Jacoff A (2003) Design and workspace analysis of a 6-6 cable-suspended parallel robot. In: Proceedings IEEE/RSJ international conference intellegent on robotics systems, Las Vegas, 27–31 Oct 2003, pp 2090–2095
Pusey J, Fattah A, Agrawal SK, Messina E (2004) Design and workspace analysis of a 6-6 cable-suspended parallel robot. Mech Mach Theory 39(7):761–778
Rosati G, Zanotto D, Secoli R, Rossi A (2009) Design and control of two planar cable-driven robots for upper-limb neurorehabilitation. In: Proceedings of IEEE international conference on rehabilitation robotics, Kyoto, pp 560–565
Roth B (1984) Screws, motors, and wrenches that cannot be bought in a hardware store. In: Robotics research: the first international symposium, Cambridge, MA, pp 679–693
Rudich S, Wigderson A (2004) Computational complexity theory. American Mathematical Society, Providence
Salisbury JK, Craig JJ (1982) Articulated hands: force control and kinematic issues. Int J Robot Res 1(1):4–7
Stoer J, Witzgall C (1970) Convexity and optimization in finite dimensions I. Springer, New York
Strang G (1976) Linear algebra and its applications. Academic, New York
Stump E, Kumar RV (2004) Workspace delineation of cable-actuated parallel manipulators. In: Proceedings of ASME international design engineering technical conference, Salt Lake City, Sept 2004, vol 2B, pp 1303–1310
Stump E, Kumar V (2006) Workspaces of cable-actuated parallel manipulators. J Mech Design 128:159–167
Sugimoto K, Duffy J (1982) Application of linear algebra to screw systems. Mech Mach Theory 17(1):73–83
Svinin MM, Ueda K, Uchiyama M (2000) On the stability conditions for a class of parallel manipulators. In: Proceedings of IEEE International Conference on Robotics Automation, San Francisco, April 2000, pp 2386–2391
Svinin MM, Hosoe S, Uchiyama M (2001) On the stiffness and stability of gough-stewart platforms. In: Proceedings of. IEEE International of Conference Robotics and Automation, Seoul, 21–26 May 2001, pp 3268–3273
Thomas F, Ottaviano E, Ceccarelli M (2005) Performance analysis of a 3-2-1 pose estimation device. IEEE Trans Robot 21(3):288–297
Tsai LW (1998) The jacobian analysis of a parallel manipulator using reciprocal screws. Technical Research Report T.R. 98-34, Institute of Systems Research, University of Maryland
Tsai LW (1999) Robot analysis – the mechanics of serial and parallel manipulators. Wiley, New York
Tsai L-W, Joshi S (2002) Kinematic analysis of 3-dof position mechanisms for use in hybrid kinematic machines. J Mech Design 124:245–253
Verhoeven R, Hiller M (2000) Estimating the controllable workspace of tendon-based stewart platforms. In: Proceedings of international symposium advance robotic kinematics, Portoroz, pp 277–284
Verhoeven R, Hiller M (2002) Tension distribution in tendon-based stewart platforms. In: Proceedings of international symposium on advance robotic kine, Caldes de Malavella
Verhoeven R, Hiller M, Tadokoro S (1998) Workspace, stiffness, singularities and classification of tendon-driven stewart platforms, In: International symposium on advances on robot and kinematics, Strobl, pp 105–114
Williams RL II (1998) Cable-suspended haptic interface. J Virtual Real 3(3):13–21
Woo L, Freudenstein F (1970) Application of line geometry to theoretical kinematics and the kinematic analysis of mechanisms. J Mech 5:417–460
Yang G, Ho HL, Wei L, Chen I-M (2003) A differential geometry approach for the workspace analysis of spherical parallel manipulators. In: Proceedings of 11th world congress in mechanism machine science, Tianjin, 1–4 April 2003, vol 4, pp 2060–2065
Yang G, Lin W, Mustafa SK, Chen I-M, Yeo SH (2006) Numerical orientation workspace analysis with different parameterization methods. In: Proceedings IEEE conference robotics automation mechatronics, Bangkok, 07 July–09 2006, pp 720–725
Yang G, Mustafa SK, Yeo SH, Lin W, Lim WB (2011) Kinematic design of an anthropomimetic 7-dof cable-driven robotic arm. Front Mech Eng 6(1):45–60
Yi B-J, Freeman RA, Tesar D (1989) Open-loop stiffness control of overconstrained mechanisms/robotic linkage systems. In: Proceedings of IEEE international conference robotics and automation, Scottsdale, pp 1350–1355
Yi B-J, Cho W, Freeman RA (1990) Open-loop stability of overconstrained parallel robotic systems. In: Proceedings of IEEE international conference robotics and automation, Cincinnati, pp 1350–1355
Yu K, Lee L-F, Tang CP, Krovi VN (2010) Enhanced trajectory tracking control with active lower bounded stiffness control for cable robot. In: Proceedings of IEEE international conference robotics and automation, Anchorage, pp 669–674
Zhang D (2009) Global stiffness modeling and optimization of a 5-dof parallel mechanism. In: Proceedings of International Conference Mechatronics Automation, Changchun, pp 3551–3556
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The authors would like to acknowledge the Agency for Science, Technology and Research for the support in this research endeavor.
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Appendices
Appendix 1: Formulation of the Jacobian and Integration Measure Associated with 2-DOF CDR’s Parameterized Rotations
Jacobian Associated with 2-DOF CDR’s Parameterized Rotations
For the 2-DOF CDR, the time-varying rotation matrix is parameterized as
Using chain rule from calculus, Eq. 63 becomes
Right multiply Eq. 64 by R T and extracting the dual vectors yields
where \( {\omega}^s=\mathrm{vect}\left(\dot{\mathbf{R}}{\mathbf{R}}^T\right) \) is the angular velocity with respect to the spatial reference frame and \( \mathbf{Q}\left(\mathbf{H}\left(\mathbf{h}\right)\right)=\left[\mathrm{vect}\left(\frac{\partial \mathbf{H}}{\partial {h}_1}\right){\mathbf{H}}^T,\mathrm{vect}\left(\frac{\partial \mathbf{H}}{\partial {h}_2}\right){\mathbf{H}}^T\kern0.24em \right] \) is the Jacobian associated with 2-DOF CDR’s parameterized rotations.
For the 2-DOF CDR, H(θ 1, θ 2) = R X(θ 1)R Y(θ 2). Hence,
Since vect(R ′ i R T i ) = e i regardless of the value of the parameter and vect(R i XR T i ) = Rvect(X), the Jacobian is given as
Integration Measure Associated with 2-DOF CDR’s Parameterized Rotations
Using the XYZ Euler angles parameterization, the rotation matrix is given as
Employing the same approach the Jacobian matrix is derived as
The determinant of Q(H(θ 1, θ 2, θ 3)) is:
Therefore, the integration measure is determined as follows:
Appendix 2: Formulation of the Integration Measure for SO(3) Representation in Cylindrical Coordinates
It has been addressed in (Bonev and Gosselin 2005) that the entire rigid body group SO(3) can be visualized as a solid cylinder when the cylindrical coordinates are employed to represent the Tilt-&-Torsion angles, as shown in Fig. 22. However, integration measures need to be introduced when computing the volume of the orientation workspace of rigid body rotations from the T&T angles domain. It can be verified that if Cartesian coordinates are used to represent the T&T angles, the integration measure will be same as that of the Euler angle representation, which is given by sin θ. In this case, the volume of the entire rigid body rotation group is given as
Equation 71 has the same form as when the T&T angles are represented with Cartesian coordinates, i.e., x ≡ ϕ, y ≡ θ, and z ≡ σ. However, since the T&T angles are normally represented with cylindrical coordinates, i.e., x ≡ θ cos ϕ, y ≡ θ sin ϕ, and z ≡ σ, an additional integration measure needs to be included for the change of the coordinate representation. Geometrically, such a transformation of the coordinate representations maps the parametric domains of the T&T angles from a rectangular parallelepiped to a solid cylinder. It can be further verified that determinant of the Jacobian (i.e., the additional integration measure) for the transformation of the coordinate representations is given by \( \frac{1}{\theta } \). The resultant integration measure becomes \( \left|\frac{ \sin \theta }{\theta}\right| \). It follows that the volume of the entire SO(3) under cylindrical coordinate representation of the T&T angles is given by
where \( {\mathcal{D}}^2\times \mathcal{R} \) represents a solid cylinder. If the integration is computed using cylindrical coordinates, Eq. 72 can be rewritten as
Although Eqs. 71 and 73 are equivalent for the volume computation of SO(3), they possess different geometrical meanings. Equation 71 is associated with the Cartesian coordinate representation of the T&T angles, while Eq. 73 is associated with the cylindrical coordinate representation of the T&T angles. In Eq. 73, the terms \( \left|\frac{ \sin \theta }{\theta}\right| \) and θdϕdθdσ represent the integration measure and the differential volume element, respectively.
Equations 72 and 73 also indicate that the integration measure becomes singular when θ approaches 0 or π. However, with strategic selection of the cylindrical coordinate representation for T&T angles, singularity point at θ = 0 can be avoided. This is a significant feature for the numerical volume computation of SO(3) through its parametric domains.
With the equivalent integration measure derived for the cylindrical coordinate representation of T-&-T angles, the integration or convolution of a rotation-dependent function f (R) over a set of rotations S ∈ SO(3) in the T&T angles domain is given by
where Q t denotes the parameter space of the T&T angles (with cylindrical coordinate representation), i.e., a subset of the solid cylinder.
After the finite partition of the solid cylinder, the orientation workspace for a set of rotations S ∈ SO(3) can be numerically computed as
where v t is the unit volume of the equi-volumetric partition scheme in the cylindrical coordinate representation of the T&T angles. Consequently, Eq. 74 can be written as
where (ϕ i jk , θ i jk , σ i jk ) ∈ Q t .
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Mustafa, S.K., Lim, W.B., Yang, G., Yeo, S.H., Lin, W., Agrawal, S.K. (2014). Cable-Driven Robots. In: Nee, A. (eds) Handbook of Manufacturing Engineering and Technology. Springer, London. https://doi.org/10.1007/978-1-4471-4976-7_101-1
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