Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T16:46:08.741Z Has data issue: false hasContentIssue false
  • English
  • Français

Force-closure analysis of 6-DOF cable manipulators with seven or more cables

Published online by Cambridge University Press:  01 March 2009

Xiumin Diao  and
Ou Ma
Xiumin Diao
Affiliation:
Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA
Ou Ma*
Affiliation:
Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003, USA
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

A cable manipulator controls its end-effector by a number of cables. If the cables can balance any external and inertia wrenches at a certain pose of the end-effector, the cable manipulator is said to have a force-closure at this pose. Since a cable can work only in tension, the force-closure at a specific pose may not exist. Thus, how to check the existence of force-closure at a given pose is an important issue for design and control of cable manipulators. This paper describes a systematic method of verifying the existence of force-closure at a specific pose of a general 6-DOF cable manipulator with seven or more cables. By examining the Jacobian matrix of the manipulator, the method can determine whether a force-closure exists at the pose corresponding to the Jacobian matrix. The necessity and sufficiency of the proposed method are mathematically proven. Moreover, a convex-analysis-based simplification of the method for manipulators with more than seven cables is also discussed.

Keywords

Cable manipulatorCable robotWire robotTendon robotForce-closure
Type
Article
Information
Robotica , Volume 27 , Issue 2 , March 2009 , pp. 209 - 215
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cone, L. L., “Skycam: An aerial robotic camera system,” Byte 122–132 (1985).Google Scholar
2.Dagalakis, N. G. et al. , “Stiffness study of a parallel link robot crane for shipbuilding applications,” J. Offshore Mech. Arctic Eng. 111, 183–193 (1989).CrossRefGoogle Scholar
3.Kawamura, S., Kino, H. and Won, C., “High-speed manipulation by using a parallel wire-driven manipulators,” Robotica 18, 13–21 (2000).CrossRefGoogle Scholar
4.Merlet, J.-P., “Analysis of the influence of wires interference on the workspace of wire robots,” In: Advances in Robot Kinematics (Sestri-Levante, Italy, 2004) pp. 211–218.CrossRefGoogle Scholar
5.Williams, R. L. II, Albus, J. S. and Bostelman, R. V., “3D cable-based Cartesian metrology system,” J. Rob. Syst. 21 (5), 237–257 (2004).CrossRefGoogle Scholar
6.Oh, S., Ryu, J. and Agrawal, K., “Dynamics and control of helicopters with a six-cables suspended robot,” J. Mech. Des. 128, 1113–1121 (2006).CrossRefGoogle Scholar
7.Ming, A. and Higuchi, T., “Study on multiple degree-of-freedom positioning mechanism using wires (part 1),” Int. J. Jpn. Soc. Precision Eng. 28 (2), 131–138 (1994).Google Scholar
8.Ebert-Uphoff, I. and Voglewede, P. A., “On the Connections Between Cable-Driven Manipulators, Parallel Manipulators and Grasping”, Proc. of IEEE Int. Conf. on Robotics & Automation, New Orleans, LA (2004) 4521–4526.CrossRefGoogle Scholar
9.Nguyen, V.-D., “Constructing force-closure grasps,” Int. J. Rob. Res. 7 (3), 3–16 (1988).CrossRefGoogle Scholar
10.Cutkosky, M. R., “On grasp, choice, grasp model, and the design of hands for manufacturing tasks,” IEEE Trans. Rob. Automat. 5 (3), 269–279 (1989).CrossRefGoogle Scholar
11.Pham, C. B. et al. , “Force-closure workspace analysis of cable-driven parallel mechanisms,” Mech. Mach. Theory 41 (1), 53–69 (2006).CrossRefGoogle Scholar
12.Rockafellar, R. T., Convex Analysis (Princeton University Press, Princeton, NJ, 1970).CrossRefGoogle Scholar
13.Gallina, P. and Rosati, G., “Manipulability of a planar wire driven haptic device,” Mech. Mach. Theory 37 (2), 215–228 (2002).CrossRefGoogle Scholar
14.Gouttefarde, M. and Gosselin, C., “On the properties and the determination of the wrench-closure workspace of planar parallel cable-driven mechanisms,” ASME Des. Eng. Tech. Conf. Computer Inf. Eng. Conf. Salt Lake City, UT, 337–346 (2004).CrossRefGoogle Scholar
15.Diao, X. and Ma, O., “A method of verifying the force-closure condition for general cable manipulators with seven cables,” Mech. Mach. Theory 42 (12), 1563–1576, (2007).CrossRefGoogle Scholar
16.Yin, X. and Bowling, A. P., “Dynamic performance limitations due to yielding in cable-driven robotic manipulators,” J. Mech. Des. 128 (1), 311–318 (2006).CrossRefGoogle Scholar
17.Murray, R., Li, Z. and Sastry, S. S., A Mathematical Introduction to Robotic Manipulation (Boca Raton, FL, CRC Press, 1994).Google Scholar
18.Roberts, R. G., Graham, T. and Lippitt, T., “On the inverse kinematics, statics, and fault tolerance of cable-suspended manipulators,” J. Rob. Syst. 15 (10), 581–597 (1998).3.0.CO;2-P>CrossRefGoogle Scholar
19.Stump, E. and Kumar, V., “Workspace delineation of cable-actuated parallel manipulators,” ASME Des. Eng. Tech. Conf. Computer Inf. Eng. Conf., Salt Lake City, UT (2004).CrossRefGoogle Scholar
20.Yang, G. et al. , “Kinematic Design of a 7-DOF Cable-Driven Humanoid Arm: A Solution-in-Nature Approach,” Proceedings of IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Monterey, CA (2005) pp. 444–449.Google Scholar
21.Diao, X. and Ma, O., “Workspace Analysis of a 6-DOF Cable Robot for Hardware-in-the-Loop Dynamic Simulation,” Proceedings of the IEEE International Conference on Intelligent Robots and Systems, Beijing, China (2006) pp. 4103–4108.Google Scholar
22.Bosscher, P. M., Disturbance Robustness Measures and Wrench-Feasible Workspace Generation Techniques for Cable-Driven Manipulators Ph.D. Thesis (Georgia Institute of Technology, 2004).Google Scholar
23.Barrette, G. and Gosselin, C., “Determination of the dynamic workspace of cable-driven planar parallel mechanisms,” ASME J. Mech. Des. 127 (2), 242–248 (2005).CrossRefGoogle Scholar
24.O'Rourke, J., Computational Geometry in C (Cambridge University Press, Cambridge, UK, 1994).Google Scholar
25.Barber, C., Dobkin, D. and Huhdanpaa, H., “The quickhull algorithm for convex hulls,” ACM Trans. Math. Software 22 (4), 469–483 (1996).CrossRefGoogle Scholar