Research Papers: Design of Mechanisms and Robotic Systems

Conditions on the Cable-Routing Matrix for Wrench Closure of Multilink Cable-Driven Manipulators

[+] Author and Article Information
Darwin Lau

Department of Mechanical and
Automation Engineering,
The Chinese University of Hong Kong,
Hong Kong
e-mail: darwinlau@mae.cuhk.edu.hk

Denny Oetomo

Department of Mechanical Engineering,
The University of Melbourne,
Victoria 3010, Australia
e-mail: doetomo@unimelb.edu.au

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 19, 2015; final manuscript received November 2, 2015; published online January 27, 2016. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 138(3), 032303 (Jan 27, 2016) (7 pages) Paper No: MD-15-1432; doi: 10.1115/1.4032402 History: Received June 19, 2015; Revised November 02, 2015

Wrench-closure is an important property of cable-driven parallel manipulators (CDPMs), representing the ability to generate wrench in any direction by positive cable forces. For single link CDPMs, it is well known that m ≥ n + 1 cables are necessary for an n degrees-of-freedom CDPM to achieve wrench-closure. However, for multilink cable-driven manipulators (MCDMs), this condition is too relaxed and the cable routing should also be considered. In this paper, necessary conditions to achieve wrench-closure for MCDMs are mathematically derived based on the cable routing arrangements. Since the approach is independent on the exact attachment locations, the proposed necessary conditions can be efficiently validated during the design and synthesis of MCDMs. Analysis is performed on a range of different MCDM structures to identify cable arrangements that do not satisfy wrench-closure for an MCDM.

Copyright © 2016 by ASME
Topics: Cables , Manipulators
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Wittmeier, S. , Alessandro, C. , Bascarevic, N. , Dalamagkidis, K. , Devereux, D. , Diamond, A. , Jäntsch, M. , Jovanovic, K. , Knight, R. , Marques, H. G. , Milosavljevic, P. , Mitra, B. , Svetozarevic, B. , Potkonjak, V. , Pfeifer, R. , Knoll, A. , and Holland, O. , 2013, “ Toward Anthropomimetic Robotics: Development, Simulation, and Control of a Musculoskeletal Torso,” J. Artif. Life, 19(1), pp. 171–193. [CrossRef]
Kozuki, T. , Mizoguchi, H. , Asano, Y. , Osada, M. , Shirai, T. , Urata, J. , Nakanishi, Y. , Okada, K. , and Inaba, M. , 2012, “ Design Methodology for Thorax and Shoulder of Human Mimetic Musculoskeletal Humanoid Kenshiro—A Thorax With Rib Like Surface,” IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Vilamoura, Portugal, Oct. 7–12, pp. 3687–3692.
Yang, G. , Mustafa, S. K. , Yeo, S. H. , Lin, W. , and Lim, W. B. , 2011, “ Kinematic Design of an Anthropomimetic 7-DOF Cable-Driven Robotic Arm,” Front. Mech. Eng., 6(1), pp. 45–60.
Lau, D. , Oetomo, D. , and Halgamuge, S. K. , 2013, “ Generalized Modeling of Multilink Cable-Driven Manipulators With Arbitrary Routing Using the Cable-Routing Matrix,” IEEE Trans. Rob., 29(5), pp. 1102–1113. [CrossRef]
Rezazadeh, S. , and Behzadipour, S. , 2011, “ Workspace Analysis of Multibody Cable-Driven Mechanisms,” ASME J. Mech. Rob., 3(2), p. 021005. [CrossRef]
Mustafa, S. K. , and Agrawal, S. K. , 2012, “ On the Force-Closure Analysis of n-DOF Cable-Driven Open Chains Based on Reciprocal Screw Theory,” IEEE Trans. Rob., 28(1), pp. 22–31. [CrossRef]
Fang, S. , Franitza, D. , Torlo, M. , Bekes, F. , and Hiller, M. , 2004, “ Motion Control of a Tendon-Based Parallel Manipulator Using Optimal Tension Distribution,” IEEE Trans. Mechatronics, 9(3), pp. 561–568. [CrossRef]
Oh, S.-R. , and Agrawal, S. K. , 2005, “ Cable Suspended Planar Robots With Redundant Cables: Controllers With Positive Tensions,” IEEE Trans. Rob., 21(3), pp. 457–465. [CrossRef]
Lau, D. , Oetomo, D. , and Halgamuge, S. K. , 2015, “ Inverse Dynamics of Multilink Cable-Driven Manipulators With the Consideration of Joint Interaction Forces and Moments,” IEEE Trans. Rob., 31(2), pp. 479–488. [CrossRef]
Lau, D. , Bhalerao, K. , Oetomo, D. , and Halgamuge, S. K. , 2012, “ On the Task Specific Evaluation and Optimisation of Cable-Driven Manipulators,” Advances in Reconfigurable Mechanisms and Robots I, J. S. Dai , M. Zoppi , and X. Kong , eds. Springer, London, UK, pp. 707–716.
Gouttefarde, M. , Collard, J. F. , Riehl, N. , and Baradat, C. , 2015, “ Geometry Selection of a Redundantly Actuated Cable-Suspended Parallel Robot,” IEEE Trans. Rob., 31(2), pp. 501–510. [CrossRef]
Perreault, S. , Cardou, P. , Gosselin, C. M. , and M. J.-D. Otis , 2010, “ Geometric Determination of the Interference-Free Constant-Orientation Workspace of Parallel Cable-Driven Mechanisms,” ASME J. Mech. Rob., 2(3), p. 031016. [CrossRef]
Lau, D. , Eden, J. , Oetomo, D. , and Halgamuge, S. K. , 2015, “ Musculoskeletal Static Workspace of the Human Shoulder as a Cable-Driven Robot,” IEEE Trans. Mechatronics, 20(2), pp. 978–984. [CrossRef]
Gouttefarde, M. , Daney, D. , and Merlet, J.-P. , 2011, “ Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots,” IEEE Trans. Rob., 27(1), pp. 1–13. [CrossRef]
Lau, D. , Oetomo, D. , and Halgamuge, S. K. , 2011, “ Wrench-Closure Workspace Generation for Cable Driven Parallel Manipulators Using a Hybrid Analytical-Numerical Approach,” ASME J. Mech. Des., 133(7), p. 071004. [CrossRef]
Lim, W. B. , Yang, G. , Yeo, S. H. , and Mustafa, S. K. , 2011, “ A Generic Force-Closure Analysis Algorithm for Cable-Driven Parallel Manipulators,” Mech. Mach. Theory, 46(9), pp. 1265–1275. [CrossRef]
Hassan, M. , and Khajepour, A. , 2011, “ Analysis of Bounded Cable Tensions in Cable-Actuated Parallel Manipulators,” IEEE Trans. Rob., 27(5), pp. 891–900. [CrossRef]
Lau, D. , Eden, J. , Halgamuge, S. , and Oetomo, D. , 2014, “ Cable Function Analysis for the Musculoskeletal Static Workspace of a Human Shoulder,” Cable-Driven Parallel Robots, Vol. 32 (Mechanisms and Machine Science), A. Pott and T. Bruckmann , eds. Springer International Publishing, Berlin, pp. 263–274.
Ming, A. , and Higuchi, T. , 1994, “ Study on Multiple Degrees-of-Freedom Positioning Mechanism Using Wires (Part 1)—Concept, Design and Control,” Int. J. Jpn. Soc. Eng., 28(2), pp. 131–138.
Voglewede, P. A. , and Ebert-Uphoff, I. , 2005, “ Application of the Antipodal Grasp Theorem to Cable-Driven Robots,” IEEE Trans. Rob., 21(4), pp. 713–718. [CrossRef]
Mustafa, S. K. , and Agrawal, S. K. , 2011, “ Reciprocal Screw-Based Force-Closure of an n-DOF Open Chain: Minimum Number of Cables Required to Fully Constrain It,” IEEE International Conference on Robotics and Automation (ICRA), Shanghai, May 9–13, pp. 3029–3034.
Rezazadeh, S. , and Behzadipour, S. , 2007, “ Tensionability Conditions of a Multi-Body System Driven by Cables,” ASME Paper No. IMECE2007-42433.


Grahic Jump Location
Fig. 1

Examples of cable arrangement for the two link SR MCDM that do not satisfy WCV. (a) and (b) are examples where link 2 and link 1 do not satisfy the WCC, respectively. (a) Example 1: m2*=1≱2 and (b) Example 2: m1*=3≱4.

Grahic Jump Location
Fig. 2

Cable arrangement for the two link SR MCDM that satisfy the necessary conditions of WCV. (a) Example 3: valid and (b) Example 4: invalid due to cable attachments.

Grahic Jump Location
Fig. 3

Examples of cable arrangement for the three link 3R MCDM. (a) and (b) are examples where link 3 and link 2 do not satisfy the WCC, respectively. (c) An example of a valid arrangement. (a) Example 1: m3*≱2, (b) Example 2: m2*≱2, and (c) Example 3: valid.




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