Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-17T20:18:31.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator

Published online by Cambridge University Press:  04 March 2010

Javad Enferadi  and
Alireza Akbarzadeh Tootoonchi
Javad Enferadi*
Affiliation:
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Alireza Akbarzadeh Tootoonchi
Affiliation:
Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

In this paper, accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator (SPM) (Enferadi and Tootoonchi, A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design, Robotica, vol. 27, 2009, pp. 663–676) with symmetrical geometry is investigated. At first, the 3-RRP SPM is introduced and its inverse kinematics analysis is performed. Isotropic design, because of its design superiority, is selected and workspace of the manipulator is obtained. The kinematics conditioning index (KCI) is evaluated on the workspace. Global conditioning index (GCI) of the manipulator is calculated and compared with another SPM. Unlike traditional stiffness analysis, the moving platform is assumed to be flexible. A continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano's theorem. The mathematical model is verified by finite element model. Finally, using mathematical model, kinematics stiffness index (KSI), and global stiffness index (GSI) are evaluated.

Keywords

Spherical parallel manipulatorInverse kinematicsAccuracy analysisStiffness analysisFinite element method
Type
Article
Information
Robotica , Volume 29 , Issue 2 , March 2011 , pp. 193 - 209
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.Enferadi, J. and Tootoonchi, A. A., “A novel spherical parallel manipulator: Forward position problem, singularity analysis and isotropy design,” Robotica 27, 663–676 (2009).CrossRefGoogle Scholar
2.Di Gregorio, R., “The 3-RRS wrist: A new, simple and non-overconstrained spherical parallel manipulator,” J. Mech. Des. 126, 850–855 (2004).CrossRefGoogle Scholar
3.Chablat, D. and Angeles, J., “The Computation of all 4R serial spherical wrists with an isotropic architecture,” J. Mech. Des. 125 (2), 275–280 (2003).CrossRefGoogle Scholar
4.Wiitala, J. M. and Stanisic, M. M., “Design of an overconstrained and dexterous spherical wrist,” J. Mech. Des. 122 (3), 347–353 (2000).CrossRefGoogle Scholar
5.Di Gregorio, R., “A new family of spherical parallel manipulators,” Robotica (20), 353–358 (2002).CrossRefGoogle Scholar
6.Gupta, K. C., “On the nature of robot workspace,” Int. J. Robot. Res. 5 (2), 112–121 (1985).CrossRefGoogle Scholar
7.Gosselin, C. M. and Jean, M., “Determination of the workspace of planar parallel manipulators with joint limits,” Robot. Auton. Syst. 17, 129–138 (1996).CrossRefGoogle Scholar
8.Klein, C. A. and Blaho, B. E., “Dexterity measures for the design and control of kinematically redundant manipulators,” Int. J. Robot. Res. 6, 72–82 (1987).CrossRefGoogle Scholar
9.Gosselin, C. M., “The optimum design of robotic manipulators using dexterity indices,” Robot. Auton. Syst. 9, 213–226 (1992).CrossRefGoogle Scholar
10.Gao, F., Guy, F. and Gruver, W. A., “Criteria Based Analysis and Design of Three Degree-of-Freedom Planar Robotic Manipulators,” IEEE International Conference on Robotics and Automation, New Mexico (1997) pp. 468–473.Google Scholar
11.Gao, F., Liu, X. J. and Gruver, W. A., “The Global Conditioning Index in the Solution Space of Two Degree-of-Freedom Planar Parallel Manipulators,” IEEE SMC'95, Vancouver, BC, Canada (1995) pp. 4055–4058.Google Scholar
12.Gao, F., Liu, X. J. and Gruver, W. A., “Performance evaluation of two degrees-of-freedom planar parallel robots,” Mech. Mach. Theory 33 (2), 661–668 (1998).CrossRefGoogle Scholar
13.Gosselin, C. M., Kinematic Analysis, Optimization and Programming of Parallel Robotic Manipulators Ph.D. thesis (Montreal, Quebec, Canada: McGill University, 1988).Google Scholar
14.Gosselin, C. M., “Stiffness map for parallel manipulators,” IEEE Trans. Robot. Autom. 6 (3), 377–382 (1990).CrossRefGoogle Scholar
15.Arsenault, M. and Boudreau, R., “Synthesis of planar parallel mechanisms while considering workspace, dexterity, stiffness and singularity avoidance,” J. Mech. Des. 128 (1), 69–78 (2006).CrossRefGoogle Scholar
16.Merlet, J. P., “Jacobian, manipulability, condition number, and accuracy of parallel robots,” J. Mech. Des. 128 (1), 199–205 (2006).CrossRefGoogle Scholar
17.Gosselin, C. M. and Angeles, J., “A global performance index for the kinematic optimization of robotic manipulators,” J. Mech. Des. 113 (3), 220–226 (1991).CrossRefGoogle Scholar
18.Merlet, J. P., Les Robots Parallèles, 2nd ed. (Hermès, Paris, France, 1997).Google Scholar
19.Ceccarelli, M. and Carbone, G., “A stiffness analysis for CaPaMan (CassinoParallel Manipulator),” Mech. Mach. Theory 37 (5), 427–439 (2002).CrossRefGoogle Scholar
20.Huang, T., Zhao, X. and Whitehouse, D. J., “Stiffness estimation of a tripod-based parallel kinematic machine,” IEEE Trans. Robot. Autom. 18 (1), 50–58 (2002).CrossRefGoogle Scholar
21.Bhattacharyya, S., Hatwal, H. and Ghosh, A., “On the optimum design of Stewart platform type parallel manipulators,” Robotica 13 (2), 133–140 (1995).CrossRefGoogle Scholar
22.El-Khasawneh, B. S. and Ferreira, P. M., “Computation of stiffness and stiffness bounds for parallel link manipulators,” Int. J. Mach. Tools Manuf. 39 (2), 321–342 (1999).CrossRefGoogle Scholar
23.Tsai, L. W. and Joshi, S., “Kinematics analysis of 3-DOF position mechanisms for use in hybrid kinematic machines,” J. Mech. Des. 124 (2), 245–253 (2002).CrossRefGoogle Scholar
24.Liu, X. J., Jin, Z. L. and Gao, F., “Optimum design of 3-DOF spherical parallel manipulators with respect to the conditioning and stiffness indices,” Mech. Mach. Theory 35 (9), 1257–1267 (2000).CrossRefGoogle Scholar
25.Gosselin, C. M. and Zhang, D., “Stiffness analysis of parallel mechanisms using a lumped model,” Int. J. Rob. Autom. 17 (1), 17–27 (2002).Google Scholar
26.Majou, F., Gosselin, C. M., Wenger, P. and Chablat, D., “Parametric stiffness analysis of the Orthoglide,” Mech. and Mach. Theory 42, 296–311 (2007).CrossRefGoogle Scholar
27. [Online]. Available http://www.rollonbearings.com/linearalrails.htmlGoogle Scholar
28.Craig, J., Introduction to Robotics: Mechanics and Control (Addison-Wesley, 1989).Google Scholar
29.Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithms, 2nd ed. (Springer, 2002).Google Scholar
30.Wampler, C. W., “On a rigid body subject to point-plane constraints,” J. Mech. Des. 128, 151–158 (2006).CrossRefGoogle Scholar
31.Kumar, V., “Characterization of workspaces of parallel manipulators,” J. Mech. Des. 114 (3), 368–375 (1992).CrossRefGoogle Scholar
32.Merlet, J. P., Gosselin, C. M. and Mouly, N., “Workspaces of planar parallel manipulators,” Mech. Mach. Theory 33, 7–20 (1998).CrossRefGoogle Scholar
33.Strang, G., Linear Algebra and its Application (Academic Press, New York, 1976).Google Scholar
34.Salisbury, J. K. and Graig, J., “Articulated hands: Force control and kinematic issues,” Int. J. Robot. Res. 1 (1), 4–17 (1982).CrossRefGoogle Scholar
35.Yu, A., Bonev, I. A. and Zsombor-Murray, P., “Geometric approach to the accuracy analysis of a class of 3-DOF planar parallel robots,” Mech. Mach. Theory 43, 364–375 (2008).CrossRefGoogle Scholar
36.Beer, F. P. and Johnston, E. R., Mechanics of Materials (McGraw-Hill, 1988).Google Scholar
37.Xu, Q. and Li, Y., “An investigation on mobility and stiffness of a 3-DOF translational parallel manipulator via screw theory,” Robot. Comput. Integr. Manuf. 24, 402–414 (2008).CrossRefGoogle Scholar
38.Li, Y. and Xu, Q., “Stiffness analysis for a 3-PUU parallel kinematic machine,” Mech. Mach. Theory 43, 186–200 (2008).CrossRefGoogle Scholar
39.Jung, H. K., Crane, C. D. and Roberts, R. G., “Stiffness mapping of compliant parallel mechanisms in a serial arrangement,” Mech. and Mach. Theory 43, 271–284 (2008).CrossRefGoogle Scholar
40.Liu, X-J., Tang, X. and Wang, J., “A Novel 2-DOF Parallel Mechanism based Design of a New 5-Axis Hybrid Machine Tool,” IEEE International Conference on Robotics and Automation, Taipei, Taiwan (2003), pp. 3990–3995.Google Scholar