Hostname: page-component-7dd5485656-tbj44 Total loading time: 0 Render date: 2025-10-31T05:16:25.532Z Has data issue: false hasContentIssue false
  • English
  • Français

Determining the maximal singularity-free circle or sphere of parallel mechanisms using interval analysis

Published online by Cambridge University Press:  13 June 2014

Mohammad Hadi Farzaneh Kaloorazi ,
Mehdi Tale Masouleh  and
Stéphane Caro
Mohammad Hadi Farzaneh Kaloorazi*
Affiliation:
Human-Robot Interaction Lab (TaarLab), Faculty of New Sciences and Technologies, University of Tehran, North Kargar, Tehran, Iran
Mehdi Tale Masouleh
Affiliation:
Human-Robot Interaction Lab (TaarLab), Faculty of New Sciences and Technologies, University of Tehran, North Kargar, Tehran, Iran
Stéphane Caro
Affiliation:
IRCCyN/CNRS, UMR 6597, 1 rue de la Noë, 44321 Nantes, France
*
*Corresponding author. E-mail: mhfarzane@ut.ac.ir
Get access Rights & Permissions [Opens in a new window]

Summary

This paper proposes a systematic algorithm based on the concept of interval analysis to obtain the maximal singularity-free circle or sphere within the workspace of parallel mechanisms. As case studies the 3-RPR planar and 6-UPS parallel mechanisms are considered to illustrate the relevance of the algorithm for 2D and 3D workspaces. To this end, the main algorithm is divided into four sub-algorithms, which eases the understanding of the main approach and leads to a more effective and robust algorithm to solve the problem. The first step is introduced to obtain the constant-orientation workspace and then the singularity locus. The main purpose is to obtain the maximal singularity-free workspace for an initial guess. Eventually, the general maximal singularity-free workspace is obtained. The main contribution of the paper is the proposition of a systematic algorithm to obtain the maximal singularity-free circle/sphere in the workspace of parallel mechanisms. The combination of a maximal singularity-free circle or sphere with the workspace analysis by taking into account the stroke of actuators, as additional constraint to the latter problem, is considered. Moreover, the center point of the circle/sphere is not restrained to a prescribed point.

Keywords

Parallel manipulatorsSingularity analysisWorkspace analysisKinematicsInterval analysis

Information

Type
Articles
Information
Robotica , Volume 34 , Issue 1 , January 2016 , pp. 135 - 149
Copyright
Copyright © Cambridge University Press 2014 

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.)

Article purchase

Temporarily unavailable

References

1.Kong, X. and Gosselin, C., Type Synthesis of Parallel Mechanisms, vol. 33 (Springer, Heidelberg, Germany, 2007).Google Scholar
2.Li, B., Cao, Y., Zhang, Q. and Huang, Z., “Position-singularity analysis of a special class of the stewart parallel mechanisms with two dissimilar semi-symmetrical hexagons,” Robotica 31 (1), 123–136 (2013).CrossRefGoogle Scholar
3.Liu, X.-J., Wang, J., Gao, F. and Wang, L.-P., “Mechanism design of a simplified 6-dof 6-rus parallel manipulator,” Robotica 20 (1), 81–91 (2002).CrossRefGoogle Scholar
4.Li, T. and Payandeh, S., “Design of spherical parallel mechanisms for application to laparoscopic surgery,” Robotica 20 (3), 133–138 (2002).CrossRefGoogle Scholar
5.Bhutani, G. and Dwarakanath, T. A., “Practical feasibility of a high-precision 3-upu parallel mechanism,” Robotica 1 (8)1–15 (2013).Google Scholar
6. “Parallelmic,” available at: http://www.parallemic.org/Reviews/Review007.html (accessed January 24, 2003).Google Scholar
7.Gosselin, C. and Angeles, J., “Singularity analysis of closed-loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).CrossRefGoogle Scholar
8.Masouleh, M. Tale and Gosselin, C., “Determination of singularity-free zones in the workspace of planar 3-PRR parallel mechanisms,” J. Mech. Des. 129, 649 (2007).CrossRefGoogle Scholar
9.Bhattacharya, S., Hatwal, H. and Ghosh, A., “On the optimum design of stewart platform type parallel manipulators,” Robotica 13 (3), 133–140 (1995).CrossRefGoogle Scholar
10.Merlet, J. P., Parallel Robots (Springer, Heidelberg, Germany, 2006).Google Scholar
11.Voglewede, P. and Ebert-Uphoff, I., “Overarching framework for measuring closeness to singularities of parallel manipulators,” IEEE Trans. Robot. 21 (6), 1037–1045 (2005).CrossRefGoogle Scholar
12.Merlet, J. P. and Donelan, P., “On the regularity of the inverse Jacobian of parallel robots,” In: Advances in Robot Kinematics (Jadran, L. and Roth, B., eds.) (Springer, Heidelberg, Germany, 2006) pp. 41–48.CrossRefGoogle Scholar
13.Conconi, M. and Carricato, M., “A new assessment of singularities of parallel kinematic chains,” IEEE Trans. Robot. 25 (4), 757–770 (2009).CrossRefGoogle Scholar
14.Bonev, I. A., Zlatanov, D. and Gosselin, C. M., “Singularity analysis of 3-DOF planar parallel mechanisms via screw theory,” J. Mech. Des. 125, 573 (2003).CrossRefGoogle Scholar
15.Yang, Y. and O'Brien, J., “A Case Study of Planar 3-RPR Parallel Robot Singularity Free Workspace Design,” Proceedings of the International Conference on Mechatronics and Automation (ICMA) (IEEE, New York, NY, 2007) pp. 1834–1838.Google Scholar
16.Li, H., Gosselin, C. and Richard, M., “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
17.Jiang, Q. and Gosselin, C., “Geometric synthesis of planar 3-RPR parallel mechanisms for singularity-free workspace,” Trans. Can. Soc. Mech. Eng. 33 (4), 667–678 (2009).CrossRefGoogle Scholar
18.Jiang, Q. and Gosselin, C., “The Maximal Singularity-Free Workspace of Planar 3-RPR Parallel Mechanisms,” Proceedings of the 2006 International Conference on Mechatronics and Automation (IEEE, New York, NY, 2006) pp. 142–146.CrossRefGoogle Scholar
19.Jiang, Q. and Gosselin, C. M., “Geometric optimization of planar 3-RPR parallel mechanisms,” Trans. Can. Soc. Mech. Eng. 31 (4), 457–468 (2007).CrossRefGoogle Scholar
20.Abbasnejad, G., Daniali, H. and Kazemi, S., “A new approach to determine the maximal singularity-free zone of 3-RPR planar parallel manipulator,” Robotica 1 (1), 1–8.Google Scholar
21.Jiang, Q., “Singularity-Free Workspace Analysis and Geometric Optimization of Parallel Mechanisms,” PhD Dissertation, Université Laval, Canada (2008).Google Scholar
22.Merlet, J.-P. and Daney, D., “A Formal-Numerical Approach to Determine the Presence of Singularity within the Workspace of a Parallel Robot.” Proceedings of the 2nd Workshop on Computational Kinematics (2001) pp. 167–176.Google Scholar
23.Gallant, M. and Boudreau, R., “The synthesis of planar parallel manipulators with prismatic joints for an optimal, singularity-free workspace,” J. Robot. Syst. 19 (1), 13–24 (2002).CrossRefGoogle Scholar
24.Li, H., Gosselin, C. and Richard, M., “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
25.Moore, R. E. and Bierbaum, F., Methods and Applications of Interval Analysis, vol. 2 (Society for Industrial Mathematics, Philadelphia, PA, 1979).CrossRefGoogle Scholar
26.Abdallah, F., Gning, A. and Bonnifait, P., “Box particle filtering for nonlinear state estimation using interval analysis,” Automatica 44 (3), 807–815 (2008).CrossRefGoogle Scholar
27.Dwyer, P., “Computation with approximate numbers,” In: Linear Computations (Wiley, New York, NY, 1951) pp. 11–34.Google Scholar
28.Sungana, T., “Theory of interval algebra and application to numerical analysis,” Res. Assoc. Appl. Geom. Mem. 2, 29–46 (1958).Google Scholar
29.Warmus, M., “Calculus of approximations,” Bull. Acad. Pol. Sci. 4 (5), 253–257 (1956).Google Scholar
30.Wilkinson, J., “Turings Work at the National Physical Laboratory and the Construction of Pilot Ace, Deuce, and Ace,” In: A History of Computing in the Twentieth Century (Metropolis, et al., eds.) (Academic Press, New York, NY, 1980), pp. 101–114 [MHR80].Google Scholar
31.Moore, R. E., Interval Analysis. Series in Automatic Computation (Prentice-Hall, Englewood Cliff, NJ, 1966).Google Scholar
32.Hansen, E. and Walster, G., Global Optimization Using Interval Analysis: Revised and Expanded, vol. 264 (Boca Raton, FL, 2003).CrossRefGoogle Scholar
33.Merlet, J. P., “Solving the forward kinematics of a Gough-type parallel manipulator with interval analysis,” Int. J. Robot. Res. 23 (3), 221–235 (2004).CrossRefGoogle Scholar
34.Hao, F. and Merlet, J. P., “Multi-criteria optimal design of parallel manipulators based on interval analysis,” Mech. Mach. Theory 40 (2), 157–171 (2005).CrossRefGoogle Scholar
35.Merlet, J. P., “Interval analysis and robotics,” Robot. Res. (Springer, 2011) pp. 147–156.Google Scholar
36.Chablat, D., Wenger, P., Majou, F. and Merlet, J. P., “An interval analysis based study for the design and the comparison of three-degrees-of-freedom parallel kinematic machines,” Int. J. Robot. Res. 23 (6), 615–624 (2004).CrossRefGoogle Scholar
37.Oetomo, D., Daney, D., Shirinzadeh, B. and Merlet, J. P., “Certified Workspace Analysis of 3RRR Planar Parallel Flexure Mechanism,” Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) (IEEE, New York, NY, 2008) pp. 3838–3843.Google Scholar
38.Gosselin, C., “Determination of the workspace of 6-DOF parallel manipulators,” ASME J. Mech. Des. 112 (3), 331–336 (1990).CrossRefGoogle Scholar
39.Saadatzi, M., Tale Masouleh, M. and Taghirad, H., “Workspace analysis of 5-PRUR parallel mechanisms (3T2R),” Robot. Comput.-Integr. Manuf. 28 (3), 437–448 (2012).CrossRefGoogle Scholar
40.Laboratoire de Robotique de L'Université Laval. Available at: http://www.robot.gmc.ulaval.ca (online)Google Scholar
41.Bonev, I. A., “Geometric Analysis of Parallel Mechanisms,” Ph.D. dissertation, Laval University, Quebec, QC, Canada (Oct. 2002).Google Scholar
42.Sefrioui, J. and Gosselin, C., “On the quadratic nature of the singularity curves of planar three-degree-of-freedom parallel manipulators,” Mech. Mach. Theory 30 (4), 553–551 (1995).CrossRefGoogle Scholar