Interval Analysis of Controllable Workspace for Cable Robots

Document Type : Research Article


1 Assistant Professor, Department of Electrical Engineering, Pardis Branch, Islamic Azad University, Pardis, Tehran, Iran

2 Professor, Department of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran

3 M.Sc. Student, Department of Computer Engineering, Arak Branch, Islamic Azad University, Arak, Iran


Workspace analysis is one of the most important issues in the robotic parallel manipulator design.
‎However, ‎the unidirectional constraint imposed by cables causes this analysis more challenging in the cable
driven redundant parallel manipulators. Controllable workspace is one of the general workspace in the cable
driven redundant parallel manipulators due to the dependency on geometry parameters in the cable driven
redundant parallel manipulators. In this paper, a novel tool is presented based on interval analysis for
determination of ‎the boundaries and proper assessment of the enclosed region of controllable workspace of
cable-driven redundant parallel manipulators. This algorithm utilizes the fundamental wrench interpretation
to analyze the controllable workspace of cable driven redundant parallel manipulators. Fundamental wrench
is the newly definitions that opens new horizons for physical interpretation of controllable workspace of
general cable driven redundant parallel manipulators. ‎Finally, ‎the proposed method is implemented on a
spatial cable driven redundant manipulator of interest.


Y. X. Su, B. Y. Duan, R. D. Nan, B. Peng, “Development of a large parallel-cable manipulator for the feed-supporting system of a next-generation large radio telescope”, Journal of Robotic Systems, vol.18, No. 11, pp. 633– 643, 2001.
M. Rajh, S. Glodez, J. Flasker, K. Gotlih, et al., “Design and analysis of an fMRI compatible haptic robot”, Robotics and Computer-Integrated Manufacturing, vol.27, No. 2, pp. 267– 275, 2011.
R. L. Williams, J. S. Albus, R. V. Bostelman, “3D cable-based cartesian metrology system”, Journal of Robotic Systems, vol.21, No. 5, pp. 237– 257, 2004.
G. Rosati, P. Gallina, S. Masiero, Design, “implementation and clinical tests of a wire-based robot for neuron rehabilitation”, IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 15, No. 4, pp. 560– 569, 2007.
A. Alikhani, S. Behzadipour, A. Alasty, S. A. Sadough Vanini, “Design of a large-scale cable-driven robot with translational motion”, Robotics and Computer-Integrated Manufacturing, vol. 27, No. 2, pp. 357– 366, 2011.
R. G. Roberts, T. Graham, T. Lippitt, “On the inverse kinematics, statics, and fault tolerance of cable-suspended robots”, Journal of Robotic Systems, vol. 15, No. 10, pp. 581– 597, 1998.
P. Bosscher, A. Riechel, I. Ebert-Uphoff, “Wrench-Feasible Workspace Generation for Cable-Driven Robots”, IEEE Transaction on Robotics, vol. 22, No. 5, pp. 890- 902, 2006.
G. Barrette, and C.M. Gosselin, “Determination of the dynamic workspace of cable-driven planar parallel mechanisms”, Journal ASME Journal of Mechanical Design, vol. 127, No. 2, pp. 242- 248, 2005.
A. Fattah, and S. Agrawal, “On the design of cable-suspended planar parallel robots”, ASME Journal of Mechanical Design, vol. 127, No. 5, pp. 1021- 1028, 2005.
R. Verhoeven, M. Hiller, “Estimating the controllable workspace of tendon-based stewart platforms”, Advances in Robot Kinematics, pp. 277– 284, 2000.
M. Gouttefarde, and C.M. Gosselin, “Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms”, IEEE Transactions on Robotics, vol. 22, No. 3, pp. 434- 445, 2006.
C.B. Pham, S.H. Yeo, G. Yang, M.S. Kurbanhusen, I-M. Chen, “Force-closure workspace analysis of cable-driven parallel mechanisms”, Mechanism and Machine Theory, vol. 41, No.1, pp. 53- 69, 2006.
X. Diao and O. Ma, “force-closure analysis of general 6-DOF cable manipulators with seven or more Cables”, Robotica, vol. 27, No. 2, pp.209- 215, 2009.
C. Ferraresi,M. Paoloni, and F. Pescarmona, “A new methodology for the Determination of the workspace of six-DOF redundant parallel structures actuated by nine wires”, Robotica, vol. 25, No. 1, pp. 113– 120, 2007
A. Zarif Loloei, H. D. Taghirad, “Controllable workspace of cable driven redundant parallel manipulator by fundamental wrench analysis”, Transactions of the Canadian Society for Mechanical Engineering, vol. 36, No. 3, pp. 297- 314, 2012.
M. Gouttefarde, D. Daney, and J.P. Merlet, “Interval-Analysis-Based Determination of the Wrench-Feasible Workspace of Parallel Cable-Driven Robots”, IEEE Transactions on Robotics, vol. 27, No.1, pp. 1- 13, 2011.
S. A. Khalilpour, A. Zarif Loloei, H. D. Taghirad, and M. Tale Masouleh. “Feasible kinematic sensitivity in cable robots based on Interval analysis”, T. Bruckmann and A. Pott (eds.), Cable-Driven Parallel Robots, Mechanisms and Machine Science, Springer-Verlag Berlin Heidelberg, pp. 233- 249, 2013.
R.G. Roberts, T. Graham, T. Lippitt, “On the Inverse Kinematics, Statics, and Fault Tolerance of Cable-Suspended Robots”, Journal of Robotic Systems, vol. 15, No.10, pp. 581- 597, 1998.
S. Fang, D. Franitza, M. Torlo, F. Bekes, and M. Hiller, “Motion control of a tendon- based parallel manipulator using optimal tension distribution”, IEEE/ASME Transactions on Mechatronics, vol. 9, No. 3, pp. 561- 568, 2004.
A.Z. Loloei, and H.D. Taghirad, , “Controllable Workspace of General Cable Driven Redundant Parallel Manipulator Based on Fundamental wrench”, CCToMM Symposium on Mechanisms, Machines, and Mechatronics, Montreal, Canada, July, 2011.
L. Jaulin, M. Kieffer, O. Didrit, and E. Walter, Applied Interval Analysis. New York: Springer-Verlag, 2001.
R. E. Moore, R. B. Kearfott, M. J. Cloud, Introduction to interval analysis, Society for Industrial Mathematics, 2009.
L. Jaulin, Applied interval analysis: with examples in parameter and state estimation, robust control and robotics, vol. 1, Springer Verlag, 2001.
B.M. St.-Onge, and C.M. Gosselin, , “Singularity analysis and representation of the general Gough-Stewart platform”, International Journal of Roboic. Research, vol. 19, No. 3, pp. 271– 288, 2000.
M.M. Aref, , H.D. Taghirad, and S.Barissi, “Optimal Design of Dexterous Cable Driven Parallel Manipulators”, International Journal of Robotics, vol. 1, No. 1, pp. 29- 47, 2009.