Abstract
This paper studies the direct geometrico-static analysis of under- constrained cable-driven parallel robots with 3 cables. The task consists in finding all equilibrium configurations of the end-effector when the cable lengths are assigned. An interval-analysis-based procedure is proposed to numerically find the real solutions of the problem for a robot of generic geometry. Three equation sets obtained by different approaches are implemented in the problem-solving algorithm and a comparison between the main merits and drawbacks of each one of them is reported.
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- 1.
The notation \({\mathbf M}_{hij,klm}(O)\) denotes the block matrix obtained from rows \(h\), \(i\) and \(j\), and columns \(k\), \(l\) and \(m\), of \({\mathbf M}(O)\).
References
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
Carricato, M., Merlet, J.P.: Geometrico-static analysis of under-constrained cable-driven parallel robots. In: Lenarčič, J., Stanišić, M.M. (eds.) Advances in Robot Kinematics: Motion in Man and Machine, pp. 309–319. Springer, Dordrecht (2010)
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, China (2011)
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, Mexico (2011)
Collard, J.F., Cardou, P.: Computing the lowest equilibrium pose of a cable-suspended rigid body. Optim. Eng. (2012). doi:10.1007/s11081-012-9191-5
Fattah, A., Agrawal, S.K.: On the design of cable-suspended planar parallel robots. ASME J. Mech. Des. 127(5), 1021–1028 (2006)
Heyden, T., Woernle, C.: Dynamics and flatness-based control of a kinematically undetermined cable suspension manipulator. Multibody Syst. Dyn. 16(2), 155–177 (2006)
Jansson, C., Rohn, J.: An algorithm for checking regularity of interval matrices. SIAM J. Matrix Anal. Appl. 20(3), 756–776 (1999)
Jaulin, L.: Applied Interval Analysis: with Examples in Parameter and State Estimation, Robust Control and Robotics, vol. 1. Springer, Berlin (2001)
Jiang, Q., Kumar, V.: The direct kinematics of objects suspended from cables. In: Proceedings of the ASME 2010 International Design Engineering Technical Conferences, vol. 2A, pp. 193–202, Paper no. DETC2010-28036. Montreal, Canada (2010)
McCarthy, J.M.: 21st century kinematics: synthesis, compliance, and tensegrity. ASME J. Mech. Robot. 3(2), 020201/1–020201/3 (2011)
Merlet, J.P.: Solving the forward kinematics of a Gough-Type parallel manipulator with interval analysis. Int. J. Robot. Res. 23(3), 221–235 (2004)
Merlet, J.P.: ALIAS-C++. http://www-sop.inria.fr/coprin/logiciels/ALIAS/ALIAS-C++/ALIAS-C++.html (2007)
Merlet, J.P., Daney, D.: A portable, modular parallel wire crane for rescue operations. In: Proceedings of the 2010 IEEE International Conference on Robotics and Automation, pp. 2834–2839. Anchorage, USA (2010)
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 Conferences, vol. 7A, pp. 83–91, paper no. DETC2009-87677. San Diego, USA (2009)
Ming, A., Higuchi, T.: Study on multiple degree-of-freedom positioning mechanism using wires—Part 1: concept, design and control. Int. J. Japan Soc. Precis. Eng. 28(2), 131–138 (1994)
Moore, R., Bierbaum, F.: Methods and Applications of Interval Analysis, vol. 2. Society for Industrial Mathematics (1979)
Rosati, G., Gallina, P., Masiero, S.: Design, implementation and clinical tests of a wire-based robot for neurorehabilitation. IEEE Trans. Neural Syst. Rehabi. Eng. 15(4), 560–569 (2007)
Surdilovic, D., Zhang, J., Bernhardt, R.: STRING-MAN: wire-robot technology for safe, flexible and human-friendly gait rehabilitation. In: Proceedings of the 2007 IEEE International Conference on Rehabilitation Robotics, pp. 446–453. Noordwijk, The Netherlands (2007)
Tapia, R.: The Kantorovitch theorem for Newton’s method. Am. Math. Monthly 78(1.ea), 389–392 (1971)
Yamamoto, M., Yanai, N., Mohri, A.: Trajectory control of incompletely restrained parallel-wire-suspended mechanism based on inverse dynamics. IEEE Trans. Robot. 20(5), 840–850 (2004)
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Berti, A., Merlet, JP., Carricato, M. (2013). Solving the Direct Geometrico-Static Problem of 3-3 Cable-Driven Parallel Robots by Interval Analysis: Preliminary Results. In: Bruckmann, T., Pott, A. (eds) Cable-Driven Parallel Robots. Mechanisms and Machine Science, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31988-4_16
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DOI: https://doi.org/10.1007/978-3-642-31988-4_16
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