Abstract
The force/moment capability of cable driven parallel mechanisms is characterized by force/moment polytopes resulting from a linear transformation between the space of cable tension and the space of the force/moment of the moving platform. Conventional method developed in computational geometry has been used to identify the vertices and faces of the polytopes. In this paper, we explored the relationship between the polytopes and the structure of a cable driven parallel mechanism and proposed a new method to identify the vertices and the faces of the polytopes. We analyzed the characteristics of the hyper cuboid defined by the minimum and maximum cable tensions and took into account inherent relationships between all vertices and faces of the polytopes. By utilizing the inherent relationships, we were able to show the relationships between the force/moment polytopes and the cable directions. These relationships are potentially useful for the design of cable driven parallel mechanisms. As an example, the polytopes of a 9-cable driven 6-DOF parallel mechanism are presented.
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References
Kokkinis, T., Paden, B.: Kinetostatic performance limits of cooperating robot manipulators using force–velocity polytopes. In: Proceedings of the ASME Winter Annual Meeting-Robotics Research, vol. 3, pp. 151–156. San Francisco, CA (1989)
Nokleby, S.B., Fisher, R., Podhorodeski, R.P., Firmani, F.: Force capabilities of redundantly-actuated parallel manipulators. Mech. Mach. Theory 40, 578–599 (2005)
Zibil, A., Firmani, F., Nokleby, S.B., Podhorodeski, R.P.: An explicit method for determining the force-moment capabilities of redundantly actuated planar parallel manipulators. J. Mech. Des. 129, 1046–1055 (2007)
Garg, V., Nokleby, S.B., Carretero, J.A.: Wrench capability analysis of redundantly actuated spatial parallel manipulators. Mech. Mach. Theory 44, 1070–1081 (2009)
Grünbaum, B.: Convex Polytopes. Springer, New York (2003)
Hwang, Y.-S., Leet, J., Hsia, T.C.: A recursive dimension-growing method for computing robotic manipulability polytope. In: Proceedings of the 2000 IEEE International Conference on Robotics and Automation, vol. 3, pp. 2569–2574. San Francisco, CA, 24–28 April 2000
Firmani, F., Zibil, A., Nokleby, S.B., Podhorodeski, R.P.: Wrench capabilities of planar parallel manipulators—part I: wrench polytopes and performance indices. Robotica 26, 791–802 (2008)
Firmani, F., Zibil, A., Nokleby, S.B., Podhorodeski, R.P.: Wrench capabilities of planar parallel manipulators part II: redundancy and wrench workspace analysis. Robotica 26, 803–815 (2008)
Carretero, J.A., Nokleby, S.B., Firmani, F.: Wrench capabilities of redundantly-actuated spatial parallel manipulators using wrench polytopes. In: Proceedings of the Second International Workshop on Fundamental Issues and Future Research Directions for Parallel Mechanisms and Manipulators, Montpellier, France, 21–22 Sep 2008
Bouchard, B., Gosselin, C., Moore, B.: On the ability of a cable-driven robot to generate a prescribed set of wrenches. J. Mech. Robot. 2, 1–10 (2010)
Zhang, Y., Zhang, Y., Wang, D., Li, C., et al.: Workspace analysis of a novel 6-dof cabal-driven parallel robot. In: Proceeding of the 2009 IEEE International Conference on Robotics and Biomimetics, pp. 2403–2408. Guilin, China (2009)
Barber, C.B., Huhdanpaa, H.: The Quickhull Algorithm for Convex Hulls. ACM Trans. Math. Softw. 22(4), 469–483 (1996)
Acknowledgements
This work is supported by National Hi-tech Research and Development Program of China under the grant No. 2008AA04Z206 and 2009AA012105.
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Dai, X., Zhang, Y., Wang, D., Song, J. (2016). Structural Characteristics of Force/Moment Polytopes of Cable Driven Parallel Mechanisms. In: Ding, X., Kong, X., Dai, J. (eds) Advances in Reconfigurable Mechanisms and Robots II. Mechanisms and Machine Science, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-319-23327-7_33
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DOI: https://doi.org/10.1007/978-3-319-23327-7_33
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