Identifying the largest sphere inscribed in the constant orientation wrench-closure workspace of a spatial parallel manipulator driven by seven cables
This paper presents a methodology to find the largest sphere inside the constant orientation wrench-closure workspace of spatial cable-driven parallel robots driven by seven cables. The sphere is centred at a prescribed point of interest and is obtained for a given orientation of the moving platform. The method builds upon the analytical description of the boundary of the constant orientation wrench-closure workspace to obtain the desired spheres. The problem has been reduced to solving seven systems, each consisting of three cubic polynomial equations in three unknowns. A computer algebra system (CAS) has been used to solve these systems of equations, using a formulation based on Sylvester’s dialytic elimination and generalised eigenproblem, which has been illustrated through an example.
KeywordsCable-driven parallel robots wrench-closure workspace singularity-free sphere parallel robots cable robots
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- 1.Gouttefarde, M., Gosselin, C. M.: On the Properties and the Determination of the Wrench-Closure Workspace of Planar Parallel Cable-Driven Mechanisms. In: Proceedings of DETC’04, ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Salt Lake City, Utah, USA, pp. 337–346. American Society of Mechanical Engineers (2004)Google Scholar
- 2.Sheng, Z., Park, J.-H., Stegall, P., Agrawal, S. K.: Analytic Determination of Wrench Closure Workspace of Spatial Cable Driven Parallel Mechanisms. In: Proceedings of the ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Boston, Massachusetts, USA, p. V05CT08A048; 10 pages. American Society of Mechanical Engineers (2015)Google Scholar
- 3.Nag, A., Reddy, V., Agarwal, S., Bandyopadhyay, S.: Identifying Singularity-Free Spheres in the Position Workspace of Semi-regular Stewart Platform Manipulators. In: J. Lenarčič, J.P. Merlet (eds.) Advances in Robot Kinematics 2016, pp. 421–430. Springer International Publishing, Cham, Switzerland (2018). DOI https://doi.org/10.1007/978-3-319-56802-7zbMATHGoogle Scholar
- 5.Bayani, H., Masouleh, M. T., Karimi, A., Cardou, P., Ebrahimi, M.: On the determination of the maximal inscribed ellipsoid in the Wrench-Feasible Workspace of the cable-driven parallel robots. In: Proceedings of the 2nd RSI/ISM International Conference on Robotics and Mechatronics (ICRoM), Tehran, Iran, pp. 422–427. IEEE (2014)Google Scholar
- 6.Gouttefarde, M., Merlet, J.-P., Daney, D.: Wrench-Feasible Workspace of Parallel Cable-Driven Mechanisms. In: 2007 IEEE International Conference on Robotics and Automation, Roma, Italy, pp. 1492–1497. IEEE (2007)Google Scholar
- 7.Salmon, G.: Lessons Introductory to the Modern Higher Algebra (4th Ed.). Hodges, Figgis, and Co., Grafton Street, Dublin, Ireland (1885)Google Scholar
- 8.Golub, G. H., Van Loan, C. F.: Matrix Computations. Johns Hopkins Studies in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, Maryland, USA (2013)Google Scholar
- 11.Verhoeven, R.: Analysis of the Workspace of Tendon-based Stewart Platforms. PhD thesis, Germany: University of Duisburg-Essen (2004)Google Scholar
- 13.Wolfram Research, Inc.: Mathematica, Version 11.1.1. Champaign, IL (2018)Google Scholar
- 14.Pott, A., Kraus, W.: Determination of the Wrench-Closure Translational Workspace in Closed-Form for Cable-Driven Parallel Robots. In: 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden, pp. 882–887 (2016). DOI https://doi.org/10.1109/ICRA.2016.7487218
- 15.Kilaru, J., Karnam, M.K., Agarwal, S., Bandyopadhyay, S.: Optimal design of parallel manipulators based on their dynamic performance. In: Proceedings of the 14th IFToMM World Congress, pp. 406–412. Tapei, Taiwan (25-30, October, 2015)Google Scholar