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Erschienen in:
Global Planning of Dynamically Feasible Trajectories for Three-DOF Spatial Cable-Suspended Parallel Robots Kapitel lesen Erstes Kapitel lesen

2013 | OriginalPaper | Buchkapitel

Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with 4 Cables

verfasst von : Marco Carricato, Ghasem Abbasnejad

Erschienen in: Cable-Driven Parallel Robots

Verlag: Springer Berlin Heidelberg

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Abstract

This paper studies the direct geometrico-static problem of under- constrained parallel robots suspended by \(4\) cables. The task consists in determining the end-effector pose and the cable tensions when the cable lengths are assigned. The problem is challenging, because kinematics and statics are coupled and they must be solved simultaneously. An effective elimination procedure is presented that provides the complete solution set, thus proving that, when all cables are in tension, 216 potential solutions exists in the complex field. A least-degree univariate polynomial free of spurious factors is obtained in the ideal governing the problem and solutions are numerically computed via both an eigenvalue formulation and homotopy continuation. Equilibrium configurations with slack cables are also considered.

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Vorheriges Kapitel Solving the Direct Geometrico-Static Problem of 3-3 Cable-Driven Parallel Robots by Interval Analysis: Preliminary Results
Nächstes Kapitel Implementing Extended Kinematics of a Cable-Driven Parallel Robot in Real-Time
Fußnoten
1
The notation \({\mathbf M}_{hijkl}\left(P\right)\) denotes the block matrix obtained from rows \(h\), \(i\), \(j\), \(k\) and \(l\) of \({\mathbf M}\left(P\right)\).
 
2
The \(216\)th-degree characteristic polynomial associated to the eigenvalue problem (14) provides a theoretical way to compute the resultant in \(w\). However, under a practical viewpoint, expanding a \(216\times 216\) matrix is even less effectual than applying Dhingra et al.’s method to \(G[J]\).
 
3
The partition \([\{x,y,z\},\{e_1,e_2,e_3\}]\) also provides the fastest computation of \(\langle {J}\rangle \cap \mathbb Q [e_3]\) by the hybrid elimination approach proposed in Sect. 3.2. This observation confirms the heuristic advanced in [10] to determine which variables may be most conveniently eliminated by the FGLM procedure before attempting the final dialytic step.
 
Literatur
1.
Abbasnejad, G., Carricato, M.: Real solutions of the direct geometrico-static problem of under-constrained cable-driven parallel robots with 3 cables: a numerical investigation. Meccanica (2012). doi:10.​1007/​s11012-012-9552-3
2.
Alikhani, A., Behzadipour, S., Vanini, S.A.S., Alasty, A.: Workspace analysis of a three DOF cable-driven mechanism. ASME J. Mech. Robotics 1(4), 041005/1–7 (2009)
3.
4.
Behzadipour, S., Khajepour, A.: Stiffness of cable-based parallel manipulators with application to stability analysis. ASME J. Mech. Des. 128(1), 303–310 (2006)CrossRef
5.
Berti, A., Merlet, J.P., Carricato, M.: Solving the direct geometrico-static problem of 3–3 cable-driven parallel robots by interval analysis: preliminary results. In: Proceedings of the 1st International Conference on Cable-Driven Parallel Robots. Stuttgart, (2012)
6.
Bosscher, P., Riechel, A.T., Ebert-Uphoff, I.: Wrench-feasible workspace generation for cable-driven robots. IEEE Trans. Robotics 22(5), 890–902 (2006)CrossRef
7.
Bouchard, S., Gosselin, C., Moore, B.: On the ability of a cable-driven robot to generate a prescribed set of wrenches. ASME J. Mech. Robotics 2(1), 011010/1–10 (2010)
8.
Carricato, M., Abbasnejad, G., Walter, D.: Inverse geometrico-static analysis of under-constrained cable-driven parallel robots with four cables. In: Lenarčič, J., Husty, M. (eds.) Advances in Robot Kinematics. Springer, Dordrecht (2012)
9.
Carricato, M., Merlet, J.P.: Geometrico-static analysis of under-constrained cable-driven parallel robots. In: Lenarčič, J., Stanišic, M.M. (eds.) Advances in Robot Kinematics: Motion in Man and Machine, pp. 309–319. Springer, Dordrecht (2010)
10.
Carricato, M., Merlet, J.P.: Direct geometrico-static problem of under-constrained cable-driven parallel robots with three cables. In: Proceedings of the 2011 IEEE International Conference on Robotics and Automation, pp. 3011–3017. Shanghai, (2011)
11.
Carricato, M., Merlet, J.P.: Inverse geometrico-static problem of under-constrained cable-driven parallel robots with three cables. In: Proceedings of the 13th World Congress in Mechanism and Machine Science, pp. 1–10, Paper No. A7_283. Guanajuato, (2011)
12.
13.
14.
Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms. Springer, New York (2007)MATHCrossRef
15.
Dhingra, A.K., Almadi, A.N., Kohli, D.: A Gröbner-Sylvester hybrid method for closed-form displacement analysis of mechanisms. ASME J. Mech. Des. 122(4), 431–438 (2000)CrossRef
16.
Diao, X., Ma, O.: Force-closure analysis of 6-dof cable manipulators with seven or more cables. Robotica 27(2), 209–215 (2009)CrossRef
17.
Dietmaier, P.: The Stewart–Gough platform of general geometry can have \(40\) real postures. In: Lenarčič, J., Husty, M.L. (eds.) Advances in Robot Kinematics: Analysis and Control, p. 16. Kluwer Academic Publishers, Dordrecht (1998)
18.
Fattah, A., Agrawal, S.K.: On the design of cable-suspended planar parallel robots. ASME J. Mech. Des. 127(5), 1021–1028 (2006)CrossRef
19.
Faugère, J.C., Gianni, P., Lazard, D., Mora, T.: Efficient computation of zero-dimensional Gröbner bases by change of ordering. J. Symb. Comput. 16(4), 329–344 (1993)MATHCrossRef
20.
Ghasemi, A., Eghtesad, M., Farid, M.: Workspace analysis for planar and spatial redundant cable robots. ASME J. Mech. Robotics 1(4), 044502/1–6 (2009)
21.
Gouttefarde, M., Daney, D., Merlet, J.P.: Interval-analysis-based determination of the wrench-feasible workspace of parallel cable-driven robots. IEEE Trans. Robotics 27(1), 1–13 (2011)CrossRef
22.
Heyden, T., Woernle, C.: Dynamics and flatness-based control of a kinematically undetermined cable suspension manipulator. Multibody Syst. Dyn. 16(2), 155–177 (2006)MathSciNetMATHCrossRef
23.
Hiller, M., Fang, S., Mielczarek, S., Verhoeven, R., Franitza, D.: Design, analysis and realization of tendon-based parallel manipulators. Mech. Mach. Theory 40(4), 429–445 (2005)MATHCrossRef
24.
Jiang, Q., Kumar, V.: The direct kinematics of objects suspended from cables. In: Proceedings of the ASME 2010 International Design Engineering Technical Conferences, vol. 2, pp. 193–202, Paper No. DETC2010-28036. Montreal, (2010)
25.
Kawamura, S., Kino, H., Won, C.: High-speed manipulation by using parallel wire-driven robots. Robotica 18(1), 13–21 (2000)CrossRef
26.
Lau, D., Oetomo, D., Halgamuge, S.: Wrench-closure workspace generation for cable driven parallel manipulators using a hybrid analytical-numerical approach. ASME J. Mech. Des. 133(7), 071004/1–10 (2011)
27.
McCarthy, J.M.: 21st century kinematics: synthesis, compliance, and tensegrity. ASME J. Mech. Robotics 3(2), 020201/1–3 (2011)
28.
Merlet, J.P.: Parallel Robots. Springer, Dordrecht (2006)MATH
29.
Merlet, J.P.: Interval analysis for certified numerical solution of problems in robotics. Int. J. Appl. Math. Comput. Sci. 19(3), 399–412 (2009)CrossRef
30.
Michael, N., Kim, S., Fink, J., Kumar, V.: Kinematics and statics of cooperative multi-robot aerial manipulation with cables. In: Proceedings of the ASME 2009 International Design Engineering Technical Conference, vol. 7, pp. 83–91, Paper No. DETC2009-87677. San Diego, (2009)
31.
Ming, A., Higuchi, T.: 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 (1994)
32.
Möller, H.M.: Gröbner bases and numerical analysis. In: Buchberger, B., Winkler, F. (eds.) Gröbner Bases and Applications, London Mathematical Society Lecture Note Series, vol. 251, pp. 159–178. Cambridge University Press, Cambridge (1998)
33.
Perreault, S., Gosselin, C.M.: Cable-driven parallel mechanisms: application to a locomotion interface. ASME J. Mech. Des. 130(10), 102301/1–8 (2008)
34.
Pusey, J., Fattah, A., Agrawal, S., Messina, E.: Design and workspace analysis of a 6–6 cable-suspended parallel robot. Mech. Mach. Theory 39(7), 761–778 (2004)MATHCrossRef
35.
Raghavan, M., Roth, B.: Solving polynomial systems for the kinematic analysis and synthesis of mechanisms and robot manipulators. ASME J. Mech. Des. 117(2B), 71–79 (1995)
36.
Rosati, G., Zanotto, D., Agrawal, S.K.: On the design of adaptive cable-driven systems. ASME J. Mech. Robotics 3(2), 021004/1–13 (2011)
37.
Sommese, A.J., Wampler, C.W.: The Numerical Solution of Systems of Polynomials Arising in Engineering and Science. World Scientific Publishing, Singapore (2005)MATHCrossRef
38.
Stump, E., Kumar, V.: Workspaces of cable-actuated parallel manipulators. ASME J. Mech. Des. 128(1), 159–167 (2006)CrossRef
39.
Su, Y.X., Duan, B.Y., Nan, R.D., Peng, B.: Development of a large parallel-cable manipulator for the feed-supporting system of a next-generation large radio telescope. J. Robotic Syst. 18(11), 633–643 (2001)MATHCrossRef
40.
Wampler, C.W.: Bezout number calculations for multi-homogeneous polynomial systems. Appl. Math. Comput. 51(2–3), 143–157 (1992)
41.
Yamamoto, M., Yanai, N., Mohri, A.: Trajectory control of incompletely restrained parallel-wire-suspended mechanism based on inverse dynamics. IEEE Trans. Robotics 20(5), 840–850 (2004)CrossRef
Metadaten
Titel
Direct Geometrico-Static Analysis of Under-Constrained Cable-Driven Parallel Robots with 4 Cables
verfasst von
Marco Carricato
Ghasem Abbasnejad
Copyright-Jahr
2013
Verlag
Springer Berlin Heidelberg
Buch
Cable-Driven Parallel Robots

Print ISBN: 978-3-642-31987-7

Electronic ISBN: 978-3-642-31988-4

Copyright-Jahr: 2013

DOI
https://doi.org/10.1007/978-3-642-31988-4_17

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