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A methodology for static stiffness mapping in lower mobility parallel manipulators with decoupled motions

Published online by Cambridge University Press:  24 September 2009

Charles Pinto ,
Javier Corral ,
Oscar Altuzarra  and
Alfonso Hernández
Charles Pinto*
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, 48013 Bilbao, Spain
Javier Corral
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, 48013 Bilbao, Spain
Oscar Altuzarra
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, 48013 Bilbao, Spain
Alfonso Hernández
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, 48013 Bilbao, Spain
*
*Corresponding author. E-mail: charles.pinto@ehu.es
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Summary

In this paper a general methodology for obtaining static stiffness maps in lower mobility parallel manipulators is proposed. The main objective is to define a set of guidelines, which allow the experimental work to be optimized and computational time to be reduced. First, a two-degree-of-freedom (DOF) mechanism will be used for methodology validation, since it is the stiffness of the basic kinematic chain of the manipulator that is to be analysed. Two mathematical models of this mechanism and an experimental prototype will be considered for the validation. After that, the methodology will be applied to a lower mobility (4-DOF) parallel manipulator. In this paper, the experimental prototype and its set-up is highly important because some particular features of the experimental analysis will be defined. This paper introduces a key experimental tool: the preload, which allows the clearances and possible assembling errors to be considered. The added value from the application of this procedure is the obtaining of graphs that describe, in an intuitive and useful way, the behaviour of the manipulator's stiffness inside its workspace as a function of the mobile platform position and orientation.

Keywords

Parallel manipulatorStiffness mapsFinite element methodAnalytical modelExperimental set-up
Type
Article
Information
Robotica , Volume 28 , Issue 5 , September 2010 , pp. 719 - 735
Copyright
Copyright © Cambridge University Press 2009

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References

1.Gosselin, C., “Stiffness mapping for parallel manipulators,” IEEE Trans. Robot. Autom. 6, 377–382 (1990).CrossRefGoogle Scholar
2.El-Khasawneh, B. S. and Ferreira, P. M., “Computation of stiffness and stiffness bounds for parallel link manipulators,” Int. J. Mach. Tools Manuf. 39, 321–342 (1999).CrossRefGoogle Scholar
3.Gosselin, C. and Zhang, D., “Stiffness analysis of parallel mechanisms using a lumped model,” Int. J. Robot. Autom. 17, 17–27 (2002).Google Scholar
4.Zhang, D., Xi, F., Mechefske, C. M. and Lang, S. Y., “Analysis of parallel kinematic machine with kinetostatic modelling method,” Robot. Comput.-Integr. Manuf. 20, 151–165 (2004).CrossRefGoogle Scholar
5.Li, Y. and Xu, Q., “Kinematics and Stiffness Analysis for a General 3-PRS Spatial Parallel Mechanism,” Fifteenth CISM-IFToMM Symposium on Robot Design, Dynamics and Control, Montreal, Canada (2004).Google Scholar
6.Company, O., Pierrot, F. and Fauroux, J., “A Method for Modeling Analytical Stiffness of a Lower Mobility Parallel Manipulator,” Proceedings of the 2005 IEEE International Conference on Robotics and Automation, Barcelona, Spain (2005), pp. 3243–3248.Google Scholar
7.Majou, F., Gosselin, C., Wenger, P. and Chablat, D., “Parametric stiffness analysis of the Orthoglide,” Mech. Mach. Theory 42, 296–311 (2006).CrossRefGoogle Scholar
8.Wu, J., Wang, J-J., Wang, L-P. and Li, T-M., “Dexterity and stiffness analysis of a three-degree-of-freedom planar parallel manipulator with actuation redundancy,” J. Mech. Eng. Sci., Proc. IMECH, Part C 221, 961–969 (2007).CrossRefGoogle Scholar
9.Wang, Y., Liu, H., Huang, T. and Chetwynd, D.G., “Stiffness modeling of the Tricept robot using the overall Jacobian matrix,” J. Mech. Robot. 1 (2), 021002–1-021002–8 (2009).CrossRefGoogle Scholar
10.Clinton, C., Zhang, G. and Wavering, A., “Stiffness modeling of a Stewart-platform-based milling machine,” Transaction of NAMRI/SME, Technical Report, Institute for Systems Research (1997).Google Scholar
11.Deblaise, D., Hernot, X. and Maurine, P., “A Systematic Analytical Method for PKM Stiffness Matrix Calculation,” Proceedings of the 2006 IEEE International Conference on Robotics and Automation, Orlando, FL (2006) pp. 4213–4219.Google Scholar
12.Li, Y. and Xu, Q., “Stiffness analysis for a 3-PUU parallel kinematic machine,” Mech. Mach. Theory 43, 186–200 (2008).CrossRefGoogle Scholar
13.Huang, T., Zhao, X. and Withehouse, D. J., “Stiffness estimation of a tripod-based parallel kinematic machine,” IEEE Trans. Robot. Autom. 18, 50–58 (2002).CrossRefGoogle Scholar
14.Deblaise, D. and Maurine, P., “Analytical Modeling of Redundant PKM Stiffness Using Matrix Structural Analysis,” Proceedings of the 5th Chemnitz Parallel Kinematics Seminar, Chemnitz (2006) pp. 155–174.Google Scholar
15.Sales, R. and Mendes, J. C., “Stiffness Analysis of a Parallel Manipulator Using Matrix Structural Analysis,” Proceedings of the EUCOMES 08 (2008) pp. 255–262.Google Scholar
16.Corradini, C., Fauroux, J., Krut, S. and Company, O., “Evaluation of a 4 Degree of Freedom Parallel Manipulator Stiffness,” Proceedings of the 11th IFToMM World Congress on the Theory of Machines and Mechanisms, Tianjin, China (2003).Google Scholar
17.Li, Y-W., Wang, J-S. and Wang, L-P., “Stiffness Analysis of a Stewart Platform-Based Parallel Kinematic Machine,” Proceedings of the 2002 IEEE International Conference on Robotics and Automation 4, Washington, DC (2002) pp. 3672–3677.Google Scholar
18.Ceccarelli, M. and Carbone, G., “Numerical and experimental analysis of the stiffness performances of parallel manipulators,” Second International Colloquium “Collaborative Research Centre 562”, Braunschweig, Gerany (2005) pp. 21–35.Google Scholar
19.ANSI/RIA R15.05-1-1990 (R1999), “Evaluation of point-to-point and static performance characteristics of industrial robots and robot systems” (1999).Google Scholar
20.ISO 9283:1998, “Manipulating industrial robots-performance criteria and related test methods” (2003).Google Scholar
21.B5.54, “Methods for performance evaluation of computer numerically controlled machining centers” (2005).Google Scholar
22.Ray, P., “Design of New High Speed Machining Machines,” InProduct Engineering, Eco-Design, Technologies and Green Energy Part 4 (Springer, The Netherlands, 2006) pp. 379–396.Google Scholar
23.Kuehl, R. O., Diseño de experimentos: principios estadísticos para el diseño y análisis de investigaciones, 2nd ed. (Paraninfo, Mexico, 2000).Google Scholar
24.Macho, E., Altuzarra, O., Pinto, Ch. and Hernández, A., “Workspaces associated to assembly modes of the 5R planar parallel manipulator,” Robotica 26, 395–403 (2008).CrossRefGoogle Scholar
25.Timoshenko, S. P. and Goodier, J. N., Theory of elasticity (URMO, S.A. de Ediciones, New York, 1987).Google Scholar
26.Salgado, O., Altuzarra, O., Petuya, V. and Hernández, A., “Type Synthesis of 3T1R Fully-Parallel Manipulators Using a Group-Theoretic Approach,” Proceedings of the 12th IFToMM World Congress, Besançon, France (2007).Google Scholar
27.ISO 463:2006, “Geometrical Product Specifications (GPS) – Dimensional measuring equipment – Design and metrological characteristics of mechanical dial gauges,” ICS: 17.040.30, Stage: 60.60 (2006-02-28), TC/SC: TC 213.Google Scholar