Hostname: page-component-7479d7b7d-k7p5g Total loading time: 0 Render date: 2024-07-12T03:37:45.687Z Has data issue: false hasContentIssue false
  • English
  • Français

Position-singularity analysis of a special class of the Stewart parallel mechanisms with two dissimilar semi-symmetrical hexagons

Published online by Cambridge University Press:  20 April 2012

Baokun Li ,
Yi Cao ,
Qiuju Zhang  and
Zhen Huang
Baokun Li
Affiliation:
School of Mechanical Engineering, Jiangnan University, Wuxi, Jiangsu 214122, China School of Mechanical Engineering, Anhui University of Science and Technology, Huainan, Anhui 232001, China
Yi Cao*
Affiliation:
School of Mechanical Engineering, Jiangnan University, Wuxi, Jiangsu 214122, China The State Key Laboratory of Fluid Power and Mechatronic Systems, Hangzhou, Zhejiang 310027, China
Qiuju Zhang
Affiliation:
School of Mechanical Engineering, Jiangnan University, Wuxi, Jiangsu 214122, China
Zhen Huang
Affiliation:
Robotics Research Center, Yanshan University, Qinhuangdao, Heibei 066004, China
*
*Corresponding author. Email: caoyi@jiangnan.edu.cn
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, for a special class of the Stewart parallel mechanism, whose moving platform and base one are two dissimilar semi-symmetrical hexagons, the position-singularity of the mechanism for a constant-orientation is analyzed systematically. The force Jacobian matrix [J]T is constructed based on the principle of static equilibrium and the screw theory. After expanding the determinant of the simplified matrix [D], whose rank is the same as the rank of the matrix [J]T, a cubic symbolic expression that represents the 3D position-singularity locus of the mechanism for a constant-orientation is derived and graphically represented. Further research shows that the 3D position-singularity surface is extremely complicated, and the geometric characteristics of the position-singularity locus lying in a general oblique plane are very difficult to be identified. However, the position-singularity locus lying in the series of characteristic planes, where the moving platform coincides, are all quadratic curves compromised of infinite many sets of hyperbolas, four pairs of intersecting lines and a parabola. For some special orientations, the quadratic curve can degenerate into two lines or even one line, all of which are parallel to the ridgeline. Two theorems are presented and proved for the first time when the geometric characteristics of the position-singularity curves in the characteristic plane are analyzed. Moreover, the kinematic property of the position-singularity curves is obtained using the Grassmann line geometry and the screw theory. The theoretical results are demonstrated with several numeric examples.

Keywords

Parallel mechanismPosition-singularityGeometric characteristicsKinematic property
Type
Articles
Information
Robotica , Volume 31 , Issue 1 , January 2013 , pp. 123 - 136
Copyright
Copyright © Cambridge University Press 2012

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,” Proc. Inst. Mech. Eng. 180 (5), 371–378 (1965).CrossRefGoogle Scholar
2.Huang, Z., Zhao, Y. S. and Zhao, T. S., Advanced Spatial Mechanism (Higher Education Press, Beijing, China, 2005).Google Scholar
3.Hunt, K. H., “Structural kinematics of in-parallel-actuated-robot-arms,” ASME, J. Mech. Transm. Autom. Des. 105 (4), 705–712 (1983).CrossRefGoogle Scholar
4.Fichter, E. F., “A Stewart platform-based manipulator: General theory and practical construction,” Int. J. Robot. Res. 5 (2), 157–182 (1986).CrossRefGoogle Scholar
5.Merlet, J. P., “Parallel Manipulator Part 2: Singular Configurations and Grassmann Geometry,” Technical Report No.791 (INRIA, Centre de Sophia Antipolis, Valbonne, France, 1988) 194–212.Google Scholar
6.Merlet, J. P., “Singular configurations of parallel manipulators and Grassmann geometry,” Int. J. Robot. Res. 8 (5), 45–56 (1989).CrossRefGoogle Scholar
7.Merlet, J. P., “Singular Configuration and Direct Kinematics of a New Parallel Manipulator,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Nice, France (1992) pp. 338–343.Google Scholar
8.Gosselin, C. M. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
9.Zlatanov, D., Fenton, R. G. and Benhabib, B., “Singularity Analysis of Mechanisms and Robots via a Motion-Space Model of the Instantaneous Kinematics,” In: Proceedings of the IEEE International Conference on Robobics and Automation, San Diego, USA (1994) 980–991.Google Scholar
10.Ma, O. and Angeles, J., “Architecture Singularity of Platform Manipulators,” In: Proceedings of the IEEE International Conference on Robotics and Automation, Sacramento, USA (1991) 1542–1547.Google Scholar
11.Huang, Z., Zhao, Y. S., Wang, J.et al., “Kinematic principle and geometrical condition of general-linear-complex special configuration of parallel manipulators,” Mech. Mach. Theory 34 (8), 1171–1186 (1999).CrossRefGoogle Scholar
12.Huang, Z. and Du, X., “General-linear-complex special configuration analysis of 3/6-SPS Stewart parallel manipulator,” China Mech. Eng. 10 (9), 997–1000 (1999).Google Scholar
13.Huang, Z., Chen, L. and Li, Y. W., “The singularity principle and property of Stewart parallel manipulator,” J. Robot. Syst. 20 (4), 163–176 (2003).CrossRefGoogle Scholar
14.Saglia, J., Dai, J. S and Caldwell, D. G., “Geometry and kinematic analysis of a redundantly actuated parallel mechanism that eliminates singularity and improves dexterity,” ASME, J. Mech. Des. 130 (12), 124501_1–5 (2008).CrossRefGoogle Scholar
15.Pendar, H., Mahnama, M. and Zohoor, H., “Singularity analysis of parallel manipulators using constraint plane method,” Mech. Mach. Theory 1 (46), 33–43 (2011).CrossRefGoogle Scholar
16.Zhu, S. J., Huang, Z. and Zhao, M. Y., “Singularity analysis for six practicable 5-DoF fully symmetrical parallel manipulators,” Mech. Mach. Theory 4 (44), 710–725 (2009).CrossRefGoogle Scholar
17.Ben-Horin, P. and Shoham, M., “Singularity analysis of a class of parallel robots based on Grassmann–Cayley algebra,” Mech. Mach. Theory 8 (41), 958–970 (2006).CrossRefGoogle Scholar
18.Li, H., Gosselin, C. M., Richard, M. J. and Mayer St-Onge, B., “Analytic form of the six-dimensional singularity locus of the general Gough–Stewart platform,” ASME, J. Mech. Des. 1 (128), 279–287 (2006).CrossRefGoogle Scholar
19.Sefrioui, J. and Gosselin, C. M., “Study and representation of the singularities of spheric parallel manipulators with prismatic actuators, with three degrees of freedom,” Mech. Mach. Theory 29 (4), 559–579 (1994).CrossRefGoogle Scholar
20.Sefrioui, J. and Gosselin, C. M., “On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators,” Mech. Mach. Theory 30 (4), 533–551 (1995).CrossRefGoogle Scholar
21.Wang, J. and Gosselin, C. M., “Kinematic analysis and singularity loci of spatial four-degree-of-freedom parallel manipulators using a vector formulation,” ASME, J. Mech. Des. 120 (4), 555–558 (1998).CrossRefGoogle Scholar
22.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
23.Huang, Z., Cao, Y., Li, Y. W. and Chen, L. H., “Structure and property of the singularity loci of the 3/6-Stewart–Gough platform for general orientations,” Robotica 1 (24), 75–84 (2006).CrossRefGoogle Scholar
24.Huang, Z. and Cao, Y. “Property identification of singularity loci of a class of the Gough–Stewart manipulators,” Int. J. Robot. Res. 24 (8), 675–685 (2005).CrossRefGoogle Scholar
25.Bandyopadhyay, S. and Ghosal, A., “Geometric characterization and parametric representation of the singularity manifold of a 6–6 Stewart platform manipulator,” Mech. Mach. Theory 11 (41), 1377–1400 (2006).CrossRefGoogle Scholar
26.Cheng, S., Wu, H. and Wang, C.et al., “A novel method for singularity analysis of the 6-SPS parallel mechanisms,” Sci. China:Technol. Sci. 54 (5), 1220–1227 (2011).CrossRefGoogle Scholar
27.Nawratil, G., “Stewart–Gough platforms with non-cubic singularity surface,” Mech. Mach. Theory 12 (45), 1851–1863 (2009).Google Scholar