Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T03:14:56.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators

Published online by Cambridge University Press:  15 January 2010

Yi Cao ,
Zhen Huang ,
Hui Zhou  and
Weixi Ji
Yi Cao*
Affiliation:
School of Mechanical Engineering, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, P.R. China
Zhen Huang
Affiliation:
Robotics Research Center, Yanshan University, Qinghuangdao, Hebei 066004, P.R. China.
Hui Zhou
Affiliation:
School of Mechanical Engineering, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, P.R. China
Weixi Ji
Affiliation:
School of Mechanical Engineering, Jiangnan University, 1800 Lihu Avenue, Wuxi, Jiangsu 214122, P.R. China
*
*Corresponding author. E-mails: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

The workspace of a robotic manipulator is a very important issue and design criteria in the context of optimum design of robots, especially for parallel manipulators. Though, considerable research has been paid to the investigations of the three-dimensional (3D) constant orientation workspace or position workspace of parallel manipulators, very few works exist on the topic of the 3D orientation workspace, especially the nonsingular orientation workspace and practical orientation workspace. This paper addresses the orientation workspace analysis of a special class of the Stewart–Gough parallel manipulators in which the moving and base platforms are two similar semisymmetrical hexagons. Based on the half-angle transformation, a polynomial expression of 13 degree that represents the orientation singularity locus of this special class of the Stewart–Gough parallel manipulators at a fixed position is derived and graphical representations of the orientation singularity locus of this special class of the Stewart–Gough manipulators are illustrated with examples to demonstrate the result. Exploiting this half-angle transformation and the inverse kinematics solution of this special class of the Stewart–Gough parallel manipulators, a discretization method is proposed for computing the orientation workspace of this special class of the Stewart–Gough parallel manipulators taking limitations of active and passive joints and the link interference all into consideration. Based on this algorithm, this paper also presents a new discretization method for computing the nonsingular orientation workspace of this class of the manipulators, which not only can satisfy all the kinematics demand of this class of the manipulators but also can guarantee the manipulator is nonsingular in the whole orientation workspace, and the practical orientation workspace of this class of the manipulators, which not only can guarantee the manipulator is nonsingular and will never encounter any kinematic interference but also can satisfy the demand of the orientation workspace with a regular shape in practical application, respectively. Examples of a 6/6-SPS Stewart–Gough parallel manipulator of this special class are given to demonstrate these theoretical results.

Keywords

Stewart–Gough parallel manipulatorOrientation singularityOrientation workspaceNonsingular orientation workspacePractical orientation workspace
Type
Article
Information
Robotica , Volume 28 , Issue 7 , December 2010 , pp. 989 - 1000
Copyright
Copyright © Cambridge University Press 2010

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.Stewart, D., “A Platform with Six Degrees of Freedom,” Proceedings of the Institution of Mechanical Engineers (1965) 180 (5) pp. 371–378.CrossRefGoogle Scholar
2.Gough, V. E., “Contribution to Discussion to Papers on Research in Automobile Stability and Control and in Type Performance,” Proceedings of the Automobile Division Institution of mechanical Engineers (1957) pp. 392–395.Google Scholar
3.Gosselin, C. M. and Angeles, J., “The optimum kinematic design of a spherical three-DOF parallel manipulator,” J. Mech. Transm. Autom. Des. 111, 202–207 (1989).CrossRefGoogle Scholar
4.Gosselin, C. M., “Determination of the workspace of six-DOF parallel manipulator,” J. Mech. Des. 112, 331–336 (1990).CrossRefGoogle Scholar
5.Tahmasebi, F. and Tsai, L.-W., “Workspace and singularity analysis of a novel six-DOF parallel manipulator,” J. Appl. Mech. Robot. 1 (2), 31–40 (1994).Google Scholar
6.Masory, O. and Wang, J., “Workspace evaluation of Stewart platform,” Adv. Robot. 9 (4), 443–461 (1995).CrossRefGoogle Scholar
7.Bulca, F., Angeles, J. and Zsombor-Murray, P. J., “On the workspace determination of spherical serial and platform mechanisms,” Mech. Mach. Theory 34 (4), 497–512 (1999).CrossRefGoogle Scholar
8.Majid, M. Z. A., Huang, Z. and Yao, Y. L., “Workspace analysis of a six-degree of freedom, three-prismatic-spheroid- revolute parallel manipulator,” Int. J Adv. Manuf. Technol. 16, 441–449 (2000).CrossRefGoogle Scholar
9.Bonev, I. A. and Ryu, J., “A geometrical method for computing the constant-orientation workspace of 6-PRRS parallel manipulators,” Mech. Mach. Theory 36 (1), 1–13 (2001).CrossRefGoogle Scholar
10.Koteswara Rao, A. B., Rao, P. V. M. and Saha, S. K., “Workspace and Dexterity Analyses of Hexaslide Machine Tools,” Proceedings of the 2003 IEEE International Conference on Robotics & Automation, Taipei, Taiwan (2003) pp. 4104–4109.Google Scholar
11.Gregorio, R. D. and Zanforlin, R., “Workspace analytic determination of two similar translational parallel manipulators,” Robotica 21, 555–566 (2003).CrossRefGoogle Scholar
12.Pusey, J., Fattah, A., Agrawal, S. and Messina, E., “Design and workspace analysis of a 6–6 cable-suspended parallel robot,” Mech. Mach. Theory 39 (5), 761–778 (2004).CrossRefGoogle Scholar
13.Zhao, J. S., Feng, Z. J. and Zhou, K., “On the workspace of spatial parallel manipulator with multi-translational degrees of freedom,” Int. J. Adv. Manuf. Technol. 27, 112–118 (2005).CrossRefGoogle Scholar
14.Pernkopf, F. and Husty, M. L., “Workspace analysis of Stewart–Gough-type parallel manipulators,” Proc. IMECHE C: J. Mech. Eng. Sci. 220 (7), 1019–1032 (2006).Google Scholar
15.Li, H. D., Gosselin, C. M. and Richard, M. J., “Determination of maximal singularity-free zones in the workspace of planar three-degree-of-freedom parallel mechanisms,” Mech. Mach. Theory 41 (10), 1157–1167 (2006).CrossRefGoogle Scholar
16.Li, H. D., Gosselin, C. M. and Richard, M. J., “Determination of the maximal singularity-free zones in the six- dimensional workspace of the general Gough–Stewart platform,” Mech. Mach. Theory 42 (4), 497–511 (2007).CrossRefGoogle Scholar
17.Merlet, J. P., Parallel Robots (Kluwer Academic Publishers, Dordrecht, The Netherlands, 2000).CrossRefGoogle Scholar
18.Bonev, I. A. and Ryu, J., “A new approach to orientation workspace analysis of 6-DOF parallel manipulators,” Mech. Mach. Theory 36 (1), 15–28 (2001).CrossRefGoogle Scholar
19.Pernkopf, F. and Husty, M. L., “Workspace Analysis of Stewart–Gough Manipulators using Orientation Plots,” Proceedings of MUSME 2002, the International Symposium on Multibody Systems and Mechatronics/M33, Mexico City (2002) pp. 315–330.Google Scholar
20.Yang, G. L. and Chen, I. M., “Equivolumetric partition of solid spheres with applications to orientation workspace analysis of robot manipulators,” IEEE Trans. Robot. Autom. 22 (5), 869–879 (2006).CrossRefGoogle Scholar
21.Hwang, Y. K., Yoon, J. W. and Ryu, J. H., “The Optimum Design of a 6-DOF Parallel Manipulator with Large Orientation Workspace,” Proceedings IEEE International Conference on Robotics and Automation, Roma, Italy (2007) pp. 163–168.CrossRefGoogle Scholar
22.Jiang, Q. M. and Gosselin, C. M., “Determination of the maximal singularity-free orientation workspace for the Gough–Stewart platform,” Mech. Mach. Theory 44 (6), 1281–1293 (2009).CrossRefGoogle Scholar
23.Huang, Z., Kong, L. F. and Fang, Y. F., Theory and control of parallel robotic mechanisms manipulator (Publisher of Mechanical Industry, Beijing, China, 1997).Google Scholar
24.Huang, Z., Zhao, Y. S., Wang, J. and Yu, J. J., “Kinematic principle and geometrical condition of general-linear-complex-special-configuration of parallel manipulators,” Mech. Mach. Theory 34 (8), 1171–1186 (1999).CrossRefGoogle Scholar
25.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
26.St-Onge, B. M. and Gosselin, C. M., “Singularity analysis and representation of the general Gough–Stewart platform,” Int. J. Robot. Res. 19 (3), 271–288 (2000).CrossRefGoogle Scholar
27.Cao, Y. and Huang, Z., “Property Identification of the Singularity Loci of the Stewart Manipulator,” The Tenth IASTED on Robotics and Application 2004/RA 447-017, Honolulu, HI (2004) pp. 5–9.Google Scholar
28.Cao, Y. and Huang, Z., “Property identification of the singularity loci of a class of Gough–Stewart manipulators,” Int. J. Robot. Res. 24 (8), 675–685 (2005).Google Scholar
29.Pernkopf, F. and Husty, M. L., “Singularity-analysis of spatial Stewart–Gough platforms with planar base and platform,” ASME DETC 2002/MECH-34267, Montreal, Canada (2002) pp. 593–600.Google Scholar
30.Cao, Y., Huang, Z. and Ge, Q. J., “Orientation-singularity and orientation capability analyses of the Stewart–Gough manipulator,” Proceedings of ASME DETC 2005/MECH-84556, California, CA (2005) pp. 1009–1015.Google Scholar