Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-05T21:46:04.666Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical Procedure Based on the Matrix Structural Method for the Analysis of the Stiffness of the 2PRU–1PRS Parallel Manipulator

Published online by Cambridge University Press:  31 January 2019

Saioa Herrero ,
Charles Pinto ,
Mikel Diez Open the ORCID record for Mikel Diez [Opens in a new window]  and
Javier Corral
Saioa Herrero*
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, Bilbao, Spain. E-mails: [email protected], [email protected], [email protected]
Charles Pinto
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, Bilbao, Spain. E-mails: [email protected], [email protected], [email protected]
Mikel Diez
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, Bilbao, Spain. E-mails: [email protected], [email protected], [email protected]
Javier Corral
Affiliation:
Department of Mechanical Engineering, University of the Basque Country, Bilbao, Spain. E-mails: [email protected], [email protected], [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

Parallel manipulators, especially those with outputs as one translation and two rotations (1T2R), are being increasingly studied. The kinematic chains of parallel manipulators share the loads and make the stiffness higher than the stiffness of serial manipulators with equivalent limbs. This high stiffness ensures a minimal deformation of the limbs, allowing a high positioning accuracy of the endeffector. Thus, it is very important to be able to measure the stiffness in parallel manipulators. In this work, we present a novel 1T2R multi-axial shaking table (MAST) for automobile pieces testing purposes—the 2PRU–1PRS parallel manipulator—and focus on the analysis of its stiffness all over the useful workspace. Analysis methods based on matrix structural method need to be validated for every parallel manipulator, and we present these steps along with a comparison between experimental and analytical methods.

Keywords

Parallel manipulatorsStiffnessMatrix structural methodRobotics
Type
Articles
Information
Robotica , Volume 37 , Issue 8 , August 2019 , pp. 1401 - 1414
Copyright
© Cambridge University Press 2019 

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

Uchiyama, U., Iimura, K., Pierrot, F., Dauchez, P., Unno, K. and Toyama, O., “A new design of a very fast 6-DOF parallel robot,” Int. Symp. Ind. Robots 2, 771–776 (1992).Google Scholar
Wu, J., Chen, X. and Wang, L., “Design and dynamics of a novel solar tracker with parallel mechanism,” IEEE/ASME Trans. Mechatron. 21(1), 88–97 (2016).Google Scholar
Herrero, S., Pinto, Ch., Altuzarra, O. and Diez, M., “Analysis of the 2PRU–1PRS 3DOF parallel manipulator: Kinematics, singularities and dynamics,” Robot. Comput.-integr. Manuf. 51, 63–72 (2018).CrossRefGoogle Scholar
Avilés, R., Métodos de análisis para diseño mecánico, Vol II: elementos finitos en estática. Escuela de Ingeniería de Bilbao, (2002).Google Scholar
Bouzgarrou, B., Faurroux, J., Gogu, G. and Heerah, Y., “Rigidity Analysis of T3R1 Parallel Robot with Uncoupled Kinematics,” In: Proceedings of the 35th International Symposium of Robotics, Paris, France, (2004).Google Scholar
Kozyrev, A. and Glazunov, V., “Finite element modeling and analysis of an Isoglide-type parallel manipulator to determine its rigidity/stiffness,” In: New trends in Mechanim and Machine Science, vol. 24 (Springer International Publishing, Switzerland, 2015) pp. 203–210.CrossRefGoogle Scholar
Martin, H., Introduction to Matrix Methods of Structural Analysis (McGraw-Hill Book Company, New York, 1966).Google Scholar
Clinton, C., Zhang, G. and Wavering, A., “Stiffness modeling of a Stewart-platform-based miling machine,” Trans. North Am. Manif. Res. Inst. SME XXV, 335–340 (1997).Google Scholar
Deblaise, D., Hernot, X. and Maurine, P., “A Systematic Analytical Method for PKM Stiffness Matrix Calculation,” In: Proceeding IEEE International of the Conference on Robotics and Automation (2006) pp. 4213–4219.Google Scholar
Gonçalves, R. S. and Carvalho, J. C. M., “Stiffness Analysis of Parallel Manipulator Using Matrix Structural Analysis,” In: Proceedings of EUCOMES08 (Springer, 2008).Google Scholar
Corral, J., Caracterización del comportamiento estructural de manipuladores de cinemática paralela Ph.D. Thesis (University of the Basque Country, Spain, 2011).Google Scholar
Salisbury, K., “Active Stiffness Control of a Manipulator in Cartesian Coordinates,” In: 19th IEEE Conference on Decision and Control including the Symposium on Adaptative Processes (1980) pp. 95–100.CrossRefGoogle Scholar
Gosselin, C., “Stiffness mapping for parallel manipulators,” IEEE Trans. Robot. Autom. 6, 377–382 (1990).CrossRefGoogle Scholar
Zhang, D., Kinetostatic Analysis and Optimization of Parallel and Hybrid Architecture for Machine Tools Ph.D. Thesis (Laval University, Quebec, Canada, 2000).Google Scholar
Chen, S.-F. and Kao, I., “Conservative congruence transformation for joint and cartesian stiffness matrices of robotic hands and fingers,” Int. J. Robot. Res. 19(9), 835–847 (2000).CrossRefGoogle Scholar
Chen, S.-F. and Kao, I., “Geometrical Approach to the Conservative Congruence Transformation (CCT) for Robotic Stiffness Control,” In: Proceedings of the 2002 IEEE International Conference on Robotics and Automation (2002).Google Scholar
Alici, G. and Shirinzadeh, B., “Enhanced stiffness modeling, identification and characterization for robot manipulators,” IEEE Trans. Robot. 21(4), 554–564 (2005).CrossRefGoogle Scholar
Rezaei, A., Akbarzadeh, A. and Akbarzadeh-T, M. R., “An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form,” Mech. Mach. Theory 51, 195–216 (2012).CrossRefGoogle Scholar
Klimchik, A., Chablat, D. and Pashkevich, A., “Stiffness model for perfect and non-perfect parallel manipulators under internal and external loadings,” Mech. Mach. Theory 79, 1–28 (2014).CrossRefGoogle Scholar
Wu, J., Wang, J., Wang, L., Li, T. and You, Z., “Study on the stiffness of a 5-DOF hybrid machine tool with actuation redundancy,” Mech. Mach. Theory. 44, 289–305 (2009).CrossRefGoogle Scholar
Yang, C., Li, Q., Chen, Q. and Xu, L., “Elastostatic stiffness modeling of overconstrained parallel manipulators,” Mech. Mach. Theory 122, 58–74 (2018).CrossRefGoogle Scholar
ANSI/ASME, “B5.54-1992 Methods for Performance Evaluation of Computer Control Machining Centers,” In: ASME (1993).Google Scholar
Aginaga, J., Zabala, I., Altuzarra, O. and Nájera, J., “Improving static stiffness of the 6RUS parallel manipulator using inverse singularities,” Robot. Comput.-Integr. Manuf. 28, 458–471 (2012).CrossRefGoogle Scholar
Company, O., Pierrot, F. and Faroux, J., “A Method for Modeling Analytical Stiffness of a Lower Mobility Parallel Manipulator,” In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation (2005) pp. 3232–3237.CrossRefGoogle Scholar
Ceccarelli, M. and Carbone, G., “Numerical and Experimental Analysis of the Stiffness Performance of Parallel Manipulators,” In: Second international colloquium. Collaborative Research Centre, vol. 562 (2005).Google Scholar
Pinto, Ch., Corral, J., Altuzarra, O. and Hernández, A., “A methodology for static stiffness mapping in lower mobility manipulators with decoupled motions,” Robotica 28(5), 719–735 (2010).CrossRefGoogle Scholar
Carretero, J., Podhorodeski, R., Nahon, M. and Gosselin, C., “Kinematic analysis and optimization of a new three degree-of-freedom spatial parallel manipulator,” J. Mech. Des. 122, 17–24 (2000).CrossRefGoogle Scholar
Herrero, S., Pinto, Ch., Altuzarra, O. and Roldan-Paraponiaris, C., “Analysis and Design of the 2PRU–1PRS Manipulator for Vibration Testing,” In: Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition (2014).Google Scholar
Herrero, S., Pinto, Ch., Altuzarra, O. and Diez, M., “Workspace Study of the 2PRU–1PRS Parallel Manipulator,” In: 14th World Congress in Mechanism and Machine Science. IFToMM (2015).Google Scholar