Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T15:03:53.015Z Has data issue: false hasContentIssue false

Stiffness analysis and comparison of a Biglide parallel grinder with alternative spatial modular parallelograms

Published online by Cambridge University Press:  08 February 2016

Guanglei Wu*
Affiliation:
Department of Mechanical and Manufacturing Engineering, Aalborg University, 9220 Aalborg, Denmark
Ping Zou
Affiliation:
School of Mechanical Engineering and Automation, Northeastern University, 110819 Shenyang, P. R. China. E-mail: pzou@mail.neu.edu.cn
*
*Corresponding author. E-mail: gwu@m-tech.aau.dk

Summary

This paper deals with the stiffness modeling, analysis and comparison of a Biglide parallel grinder with two alternative modular parallelograms. It turns out that the Cartesian stiffness matrix of the manipulator has the property that it can be decoupled into two homogeneous matrices, corresponding to the translational and rotational aspects, through which the principal stiffnesses and the associated directions are identified by means of the eigenvalue problem, allowing the evaluation of the translational and rotational stiffness of the manipulator either at a given pose or the overall workspace. The stiffness comparison of the two alternative Biglide machines reveals the (dis)advantages of the two different spatial modular parallelograms.

Type
Articles
Copyright
Copyright © Cambridge University Press 2016 

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. Merlet, J.-P., Parallel Robots (Kluwer Academic Publishers, Norwell, MA, USA, 2000).CrossRefGoogle Scholar
2. Gosselin, C., “Stiffness mapping for parallel manipulators,” IEEE Trans. Robot. Autom. 6 (3), 377382 (1990).CrossRefGoogle Scholar
3. 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, 835847 (2000).Google Scholar
4. Alici, G. and Shirinzadeh, B., “Enhanced stiffness modeling, identification and characterization for robot manipulators,” IEEE Trans. Robot. 21 (4), 554564 (2005).Google Scholar
5. Quennouelle, C. and Gosselin, C., “Stiffness Mtrix of Compliant Parallel Mechanisms,” Advances in Robot Kinematics: Analysis and Design (Springer, Netherlands, 2008) pp. 331341.CrossRefGoogle Scholar
6. Gosselin, C. and Zhang, D., “Stiffness analysis of parallel mechanisms using a lumped model,” Int. J. Robot. Autom. 17 (1), 1727 (2002).Google Scholar
7. Zhang, D. and Gosselin, C., “Parallel kinematic machine design with kinetostatic model,” Robotica 4 (7), 429438 (2002).CrossRefGoogle Scholar
8. Majou, F., Gosselin, C., Wenger, P. and Chablat, D., “Parametric stiffness analysis of the Orthoglide,” Mech. Mach. Theory 42 (3), 296311 (2007).CrossRefGoogle Scholar
9. Pashkevich, A., Chablat, D. and Wenger, P., “Stiffness analysis of overconstrained parallel manipulators,” Mech. Mach. Theory 44 (5), 966982 (2009).CrossRefGoogle Scholar
10. Pashkevich, A., Klimchik, A. and Chablat, D., “Enhanced stiffness modeling of manipulators with passive joints,” Mech. Mach. Theory 46 (5), 662679 (2011).CrossRefGoogle Scholar
11. Ciblak, N. and Lipkin, H., “Synthesis of Cartesian stiffness for robotic applications,” Proc. IEEE Int. Conf. Robot. Autom. 3, 21472152 (1999).Google Scholar
12. Huang, S. and Schimmels, J. M., “The eigenscrew decomposition of spatial stiffness matrices,” IEEE Trans. Robot. Autom. 16 (2), 146156 (2000).CrossRefGoogle Scholar
13. Ding, X. and Selig, J. M., “On the compliance of coiled springs,” Int. J. Mech. Sci. 46 (5), 703727 (2004).Google Scholar
14. Dai, J. and Ding, X., “Compliance analysis of a three-legged rigidly-connected platform device,” ASME J. Mech. Des. 128 (4), 755764 (2006).Google Scholar
15. Chen, G., Wang, H., Lin, Z. and Lai, X., “The principal axes decomposition of spatial stiffness matrices,” IEEE Trans. Robot. 31 (1), 191207 (2015).CrossRefGoogle Scholar
16. Kövecses, J. and Ebrahimi, S., “Parameter analysis and normalization for the dynamics and design of multibody systems,” ASME J. Comput. Nonlin. Dyn. 4 (3), 031008 (2009).CrossRefGoogle Scholar
17. Taghvaeipour, A., Angeles, J. and Lessard, L., “On the elastostatic analysis of mechanical systems,” Mech. Mach. Theory 58, 202216 (2012).CrossRefGoogle Scholar
18. Angeles, J., “On the nature of the Cartesian stiffness matrix,” Ingeniería Mecánica 3 (5), 163170 (2010).Google Scholar
19. Zou, P., “Kinematic analysis of a Biglide parallel grinder,” J. Mater. Process. Technol. 138 (1–3), 461463 (2003).CrossRefGoogle Scholar
20. Germain, C., Caro, S., Briot, S. and Wenger, P., “Singularity-free design of the translational parallel manipulator IRSBot-2,” Mech. Mach. Theory 64, 262285 (2013).Google Scholar
21. Nagai, K. and Liu, Z., “A Systematic Approach to Stiffness Analysis of Parallel Mechanisms,” Proc. IEEE Int. Conf. Robot. Autom., Pasadena, California, USA (2008) pp. 15431548.Google Scholar
22. Wu, G., Bai, S. and Kepler, J., “Mobile platform center shift in spherical parallel manipulators with flexible limbs,” Mech. Mach. Theory 75, 1226 (2014).Google Scholar
23. Wang, D., Fan, R. and Chen, W., “Stiffness analysis of a hexaglide parallel loading mechanism,” Mech. Mach. Theory 70, 454473 (2013).CrossRefGoogle Scholar
24. Shigley, J. E., Mischke, C. R. and Brown, T. H., Standard Handbook of Machine Design (McGraw-Hill, New York, USA, 2004).Google Scholar
25. Roberts, R. G., “On the Normal Form of a Spatial Stiffness Matrix,” Proc. IEEE Int. Conf. Robot. Autom., Washington, DC, USA, vol. 1 (2002) pp. 556561.Google Scholar
26. Angeles, J., Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms (Springer, New York, 2007).Google Scholar
27. Strang, G., Linear Algebra and Its Applications, 4th ed. (Cengage Learning, Boston, MA, USA, 2005).Google Scholar
28. Briot, S., Pashkevich, A. and Chablat, D., “Optimal Technology-Oriented Design of Parallel Robots for High-Speed Machining Applications,” Proc. IEEE Int. Conf. Robot. Autom., Anchorage, Alaska (2010) pp. 11551161.Google Scholar
29. Klimchik, A., Furet, B., Caro, S. and Pashkevich, A., “Identification of the manipulator stiffness model parameters in industrial environment,” Mech. Mach. Theory 90, 122 (2015).Google Scholar