Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-25T10:07:13.912Z Has data issue: false hasContentIssue false
  • English
  • Français

Stiffness analysis of multibody systems using matrix structural analysis—MSA

Published online by Cambridge University Press:  10 February 2015

G. D. L. Soares Júnior ,
J. C. M. Carvalho  and
R. S. Gonçalves
G. D. L. Soares Júnior
Affiliation:
Federal University of Uberlandia School of Mechanical Engineering Uberlandia, MG, Brazil. E-mails:[email protected], [email protected]
J. C. M. Carvalho
Affiliation:
Federal University of Uberlandia School of Mechanical Engineering Uberlandia, MG, Brazil. E-mails:[email protected], [email protected]
R. S. Gonçalves*
Affiliation:
Federal University of Uberlandia School of Mechanical Engineering Uberlandia, MG, Brazil. E-mails:[email protected], [email protected]
*
*Corresponding author. E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

This paper deals with the stiffness analysis of multibody systems using the Matrix Structural Analysis—MSA. This methodology allows us to obtain the stiffness matrix of the structure from the stiffness properties of each element. First the MSA method is described and its application is detailed using an L-structure in order to make easy its understanding. Numerical and experimental results obtained for the L-structure and a 6-RSS parallel manipulator, follow to prove the validity of the methodology.

Keywords

Parallel manipulatorMultibody systemsStiffness analysisMatrix structural analysis
Type
Articles
Information
Robotica , Volume 34 , Issue 10 , October 2016 , pp. 2368 - 2385
Copyright
Copyright © Cambridge University Press 2015 

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. Dimarogonas, A. D., Machine Design: A CAD Approach (John Wiley and Sons, Inc. N.Y., 2001).Google Scholar
2. Hartenberg, R. S. and Denavit, J., Kinematic Systhesis of Linkages (Mc Graw-Hill, New York, 1964).Google Scholar
3. Chondros, T. G., “Archimedes life works and machines,'' J. Mech. Mach. Theory 45, 1766–1775 (2010).CrossRefGoogle Scholar
4. Merlet, J. P., Parallel Robots, 2nd ed. (Kluwer, Dordrecht, 2005).Google Scholar
5. Macho, E., Altuzarra, O., Pinto, C. and Hernandez, A., “Workspaces associated to assembly modes of the 5R planar parallel manipulator,'' Robotica 26 (3), 395–403 (May 2008).Google Scholar
6. Figielski, A., Bonev, I. A. and Bigras, P., “Towards development of a 2-DOF planar parallel robot with optimal workspace use,” 2007 IEEE International Conference on Systems, Man, and Cybernetics, Montréal, QC, Canada, (2007) pp. 7–10.Google Scholar
7. Stewart, D., “A Platform Whit Six Degrees of Freedom,” Proceedings of the Institution of Mechanical Engineers, (1965) Vol. 180, Pt. 1, n. 15, pp. 371–386.CrossRefGoogle Scholar
8. Ceccarelli, M., “A new 3 dof spatial parallel mechanism,” Mech. Mach. Theory 32 (8), 895–902 (1997).Google Scholar
9. Nava Rodriguez, N. E., Carbone, G. and Ceccarelli, M., “CaPaMan2bis as Trunk Module in CALUMA (CAssino Low-Cost hUMAnoid Robot),” Proceedings of the 2nd IEEE International Conference on Robotics, Automation and Mechatronics RAM 2006, Bangkok, (2006) pp. 347–352.Google Scholar
10. Ottaviano, E. and Ceccarelli, M., “An application of a 3-DOF parallel manipulator for earthquake simulations,” IEEE Trans. Mechatronics 11 (2), 240–146 (2006).Google Scholar
11. Martines, E. E. H., Conghui, L., Carbone, G., Ceccarelli, M. and Cajun, C. S. L., “Experimental and numerical characterization of CaPaMan 2bis operation,” J. Appl. Res. Technol. 8 (1), 101–119 (2010).Google Scholar
12. Hess-Coelho, T. A., Batalha, G. F., Moraes, D. T. B. and Boczko, M., “A Prototype of a Contour Milling Machine Based on a Parallel Kinematic Mechanism,” Proceedings of the 32nd Int. Symposium on Robotics, Seoul, Korea, (2001).Google Scholar
13. Gosselin, C. M. and Angeles, J., “Singularity analysis of closed loop kinematic chains,” IEEE Trans. Robot. Autom. 6 (3), 281–290 (1990).Google Scholar
14. Castelli, G., Ottaviano, E. and Ceccarelli, M., “A fairly general algorithm to evaluate workspace characteristics of serial and parallel manipulators,” Int. J. Mech. Based Design Struct. Mach. 36, 14–33 (2008).Google Scholar
15. Gonçalves, R. S., Santos, R. R. and Carvalho, J. C. M., “On The Performance of Strategies for the Path Planning of a 5R Symmetrical Parallel Manipulator,” Proceedings of the DINCON 2008, 7th Brazilian Conference on Dynamics, Control and Applications, Unesp at Presidente Prudente, SP, Brazil, (2008).Google Scholar
16. Tsai, L.W., Robot Analysis: The Mechanics of Serial and Parallel Manipulators (John Wiley & Sons, New York, 1999).Google Scholar
17. Rivin, E. I., Stiffness and Damping in Mechanical Design (Marcel Dekker Inc., New York, 1999).Google Scholar
18. Dimarogonas, A. D. and Paipetis, S. A., Analytical Methods in Rotor Dynamics (Appl. Sci. Publishers, London, 1983).Google Scholar
19. Dimarogonas, A. D., Vibration for Engineers, 2nd ed. (Prentice-Hall International Editions, Upper Saddle River, New Jersey, 1996).Google Scholar
20. Chondros, T. G. and Dimarogonas, A. D., “Identification of cracks in welded joints of complex structures,” J. Sound Vib. 69 (4), 531–538 (1980).Google Scholar
21. Carbone, G. and Ceccarelli, M., “A comparison of indices for stiffness performance evaluation,” Proceedings of the 12th IFToMM World Congress, Besançon, France (2007) pp. n.A831.Google Scholar
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).Google Scholar
23. Simaan, N. and Shoham, M., “Stiffness Synthesis of a Variable Geometry Planar Robot,” In: 8th International Symposium on Advances in Robot Kinematics ARK 2002 (Lenarcic, J. and Thomas, F., eds.) (Kluwer Academic Publishers, Caldes de Malavella, 2002) pp. 463–472.Google Scholar
24. Carbone, G., Lim, H. O., Takanishi, A. and Ceccarelli, M., “Optimum Design of a New Humanoid Leg by Using Stiffness Analysis,” Proceedings of the 12th International Workshop on Robotics in Alpe-Andria-Danube Region RAAD 2003, Cassino, (2003), paper 045RAAD03.Google Scholar
25. Lim, B. and Park, F., “Minimum vibration mechanism design via convex programming,” J. Mech. Design 131 (1), 110091–110099 (2009).Google Scholar
26. Menon, C., Vertechy, R., Markot, M. and Parenti-Castelli, V., “Geometrical optimization of parallel mechanism based in natural frequency evaluation: Application to a spherical mechanism for future space applications,” IEEE Trans. Robot. 25 (1), 12–24 (2009).CrossRefGoogle Scholar
27. Ceccarelli, M., Fundamentals of Mechanics of Robotic Manipulation (Kluwer, Dordrecht, 2004).Google Scholar
28. Yoon, W. K., Suehiro, T., Tsumaki, Y. and Uchiyama, M., “Stiffness analysis and design of a compact modified delta parallel mechanism,” Robotica 22, 463–475 (2004).Google Scholar
29. Deblaise, D., Hernot, X. and Maurine, P., “A Systematic Analytical Method for PKM Stiffness Matrix Calculation,” Proceedings of the IEEE International Conference on Robotics and Automation, (2006).Google Scholar
30. Gonçalves, R. S. and Carvalho, J. C. M., “Stiffness Analysis of Parallel Manipulator Using Matrix Structural Analysis,” Proceedings of the EUCOMES 2008, 2nd European Conference on Mechanism Science, Cassino, Italy, (2008) pp. 255–262.Google Scholar
31. Zhang, D., Xi, F., Mechefske, C. M. and Lang, S. Y. T., “Analysis of parallel kinematic machine with kinetostatic modeling method,” Robot. Comput.-Integr. Manuf. 20 (2), 151–165 (2004).Google Scholar
32. Majou, F., Gosselin, C. M., Wenger, P. and Chablat, D., “Parametric Stiffness Analysis of the Orthoglide,” Proceedings of the 35th International Symposium on Robotics, Paris, France, (2004).Google Scholar
33. Bouzgarrou, B. C., Fauroux, J. C., Gogu, G. and Heerah, Y., “Rigidity Analysis of T3R1 Parallel Robot with Uncoupled Kinematics,” Proceedings of the 35th International Symposium on Robotics, Paris, France, (2004).Google Scholar
34. Corradini, C., Fauroux, J. C., Krut, S. and Company, O., “Evaluation of a 4 Degree of Freedom Parallel Manipulator Stiffness,” Proceedings of the 11th World Cong. in Mechanism & Machine Science, IFTOMM'2004, Tianjin, China, (2004).Google Scholar
35. Enferadi, J. and Tootoonchi, A. A., “Accuracy and stiffness analysis of a 3-RRP spherical parallel manipulator,” Robotica 1–17 (2010).Google Scholar
36. Pashkevich, A., Chablat, D. and Wenger, P., “Stiffness analysis of overconstrained parallel manipulators,” Mech. Mach. Theory, 44, 966–982 (2009).Google Scholar
37. Li, B., Yu, H., Deng, Z., Yang, X. and Hu, H., “Stiffness modeling of a family of 6-DoF parallel mechanisms with three limbs based on screw theory,” J. Mech. Sci. Technol. 24, 373–382 (2010).Google Scholar
38. Pinto, C., Corral, J., Oscar, A. and Hernández, A., “A methodology for static stiffness mapping in lower mobility parallel manipulators with decoupled motions,” Robotica, 28, 719–735 (2009).Google Scholar
39. Przemieniecki, J. S., Theory of Matrix Structural Analysis (Dover Publications, Inc., New York, 1985).Google Scholar
40. Dong, W., Du, Z. and Sun, L., “Stiffness Influence Atlases of a Novel Flexure Hinge-Based Parallel Mechanism with Large Workspace,” Proceedings of IEEE ICRA: Int. Conf. On Robotics and Automation, Barcelona, Spain, (2005).Google Scholar
41. Gonçalves, R. S. and Carvalho, J. C. M., “Singularities of Parallel Robots Using Matrix Structural Analysis,” Proceedings of the XIII International Symposium on Dynamic Problems of Mechanics – DINAME, Angra dos Reis, RJ, Brazil, (2009).Google Scholar
42. Gonçalves, R. S., Estudo de Rigidez de Cadeias Cinemáticas Fechadas Thesis, (Uberlândia, Brazil: Universidade Federal de Uberlândia (in Portuguese), 2009. <repositorio.ufu.br/bitstream/123456789/51/1/EstudoRigidezCadeias.pdf>>Google Scholar
43. Gonçalves, R. S. and Carvalho, J. C. M., “A Multi-Objective Optimization Design for Parallel Structures,” Proceedings of the 20th International Congress of Mechanical Engineering COBEM2009, Gramado, Brazil, (2009).Google Scholar
44. Gonçalves, R. S., Carvalho, J. C. M., Carbone, G. and Ceccarelli, M., “A General Approach for Accuracy Analysis of Parallel Manipulator with Joint Clearance,” Proceedings of the 20th International Congress of Mechanical Engineering COBEM2009, Gramado, Brazil, (2009).Google Scholar
45. Gonçalves, R. S., Carvalho, J. C. M., Carbone, G. and Ceccarelli, M., “Indices for stiffness and singularity evaluation for designing 5R parallel manipulators,” Open Mech. Eng. J. 4, (2010).Google Scholar
46. El-Khasawneh, B. S. and Ferreira, P. M., “Computation of stiffness and stiffness bounds for parallel link manipulator,” Int. J. Mach. Tools Manuf. 39 (2), 321–342 (1999).Google Scholar
47. Zhang, D., Kinetostatic Analysis and Optimization of Parallel and Hybrid Architecture for Machines Tolos Ph.D Thesis (Laval University Quebec, Canada, 2000).Google Scholar
48. Ceccarelli, M. and Carbone, G., “Numerical and Experimental Analysis of the Stiffness Performance of Parallel Manipulators,” Proceedings of the 2nd International Colloquium Collaborative Research Centre 562, Braunschweig, (2005) pp. 21–35.Google Scholar
49. Huang, T., Zhao, X. and Whitehouse, D. J., “Stiffness estimation of a tripod-based parallel kinematic machine,” IEEE Trans. Robot. Autom. 18 (1), (2002).Google Scholar
50. Clinton, C. M., Zhang, G. and Wavering, A. L., “Stiffness Modeling of a Stewart-Platform-Based Milling Machine,” Proceedings of the Trans. of the North America Manufacturing Research Institution of SME, Vol. XXV, Lincoln, (1997) pp. 335–340.Google Scholar
51. Logan, D. L., A First Course in the Finite Element Method, 5 ed. (Cengage Learning, Stamford, CT, 2011).Google Scholar
52. Shabana, A. A., Dynamics of Multibody Systems (John Wiley & Sons, New York, 1989).Google Scholar
53. Berthouex, P. M. and Brown, L. C., Statistics for Environmental Engineers (Lewis Publishers, Boca Raton, FL, 2002) p. 463.CrossRefGoogle Scholar
54. Bezerra, C. A. D., Modelagem Geométrica da Estrutura Cartesiana Totalmente Paralela (In Portuguese) MSc Thesis (Brazil: Federal University of Uberlândia, 1996).Google Scholar
55. Carvalho, J. C. M., Duarte, M. A. V. and Ribeiro, C. R., “Forward and Inverse Kinematic Model of a Parallel Cartesian Structure Using Neural Network,” Proceedings of the Dynamic Problems of Mechanics (IX DINAME), (pp. 207–211. 2001)Google Scholar
56. Sudhakar, U. and Srinvas, J., “A stiffness index prediction approach for 3-RPR planar parallel linkage,” Int. J. Eng. Res. Tecnol. 2 (9), 2747–2751 (2013).Google Scholar
57. Guohua, C., Bin, W., Nan, W. and Yanwei, Z., “Stiffness, workspace analysis and optimization for 3UPU parallel robot mechanism,” TELKOMNIKA 11 (9), 5252–5261 (2013).Google Scholar
58. Aginaga, J., Zabalza, I., Altuzarra, O. and Nájera, J., “Improving static stiffness of the 6-RUS parallel manipulator using inverse singularities,” Robot. Comput.-Integr. Manuf. 28, (2012).Google Scholar
59. Rezaei, A., Akbarzadeh, A. and Akbarzadeh, M., “An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form,” Mech. Mach. Theory 51, (2012).CrossRefGoogle Scholar