Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-25T04:22:24.112Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimization of a redundantly actuated 5R symmetrical parallel mechanism based on structural stiffness

Published online by Cambridge University Press:  15 May 2014

Sangrok Jin ,
Jongwon Kim  and
TaeWon Seo
Sangrok Jin
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul Nat'l University, Seoul 151-019, Republic of Korea
Jongwon Kim*
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul Nat'l University, Seoul 151-019, Republic of Korea
TaeWon Seo*
Affiliation:
School of Mechanical Engineering, Yeungnam University, Gyeongsan 712-749, Republic of Korea
*
*Corresponding author. E-mail: [email protected], [email protected]
*Corresponding author. E-mail: [email protected], [email protected]
Get access Rights & Permissions [Opens in a new window]

Summary

A redundantly actuated parallel kinematic machine (PKM) can be used to avoid singularities, normalize manipulability, and increase the stiffness of anon-redundant mechanism. In this study, a redundantly actuated symmetrical PKM with five revolute (5R) joints is optimized for isotropic stiffness in the workspace. The stiffness of the 5R symmetrical PKM is calculated by the superposition of the actuator stiffness and the structural stiffness. We compared the stiffness of anon-redundant PKM and a redundant PKM. Compliance ellipses of the actuator stiffness and the structural stiffness of the non-redundant PKM resulted in the same configurations in the workspace, while those of the redundant PKM resulted in very different configurations. Optimization was performed by determining the optimal actuator torques that are needed to maximize the conditioning index. Optimal results considering structural stiffness can provide a more uniform directional stiffness than optimal results considering the index. When the strength of the linkages in a PKM is weak, the structural stiffness affects the actual stiffness considerably. We believe that the results of this study can be used to help design and control redundant PKMs.

Keywords

Parallel mechanismRedundant actuationOptimizationStiffness analysisStructural stiffness
Type
Articles
Information
Robotica , Volume 33 , Issue 9 , November 2015 , pp. 1973 - 1983
Copyright
Copyright © Cambridge University Press 2014 

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, 2nd ed. (Springer, Dordrecht, the Netherlands, 2006).Google Scholar
2. H.-S. Shim, Seo, T. and Lee, J. W., “Optimal torque distribution method for a redundant 3-RRR parallel robot using a geometrical analysis,” Robotica 31 (4), 549–554 (2013).Google Scholar
3. Ahn, C., Seo, T., Kim, J. and Kim, T., “High-tilt parallel positioning mechanism development and cutter path simulation for laser micro-machining,” Comput.-Aided Des. 39 (3), 218–28 (2007).Google Scholar
4. Kim, J., Park, F. C., Ryu, S. J., Kim, J., Hwang, J., Park, C. and Iurascu, C., “Design and analysis of a redundantly actuated parallel mechanism for rapid machining,” IEEE Trans. Robot. Autom. 17 (4), 423–434 (2001).Google Scholar
5. Zhang, D., “On stiffness improvement of the Tricept machine tool,” Robotica 23 (3), 377–286 (2005).Google Scholar
6. Wu, J., Wang, J., Li, T. and Wang, L., “Performance analysis and application of a redundantly actuated parallel manipulator for milling,” J. Intell. Robot. Syst. 50 (2), 163–180 (2007).Google Scholar
7. Chakarov, D., “Study of the antagonistic stiffness of parallel manipulators with actuation redundancy,” Mech. Mach. Theory 39 (6), 583–601 (2004).Google Scholar
8. Lee, S., Kim, S., In, W., Kim, M., Jeong, J. I. and Kim, J., “Experimental verification of antagonistic stiffness planning for a planar parallel mechanism with 2-DOF force redundancy,” Robotica 29 (4), 547–554 (2011).Google Scholar
9. Xu, Y., Yao, J. and Zhao, Y., “Inverse dynamics and internal forces of the redundantly actuated parallel manipulators,” Mech. Mach. Theory 51, 172–184 (2012).Google Scholar
10. Limaye, P., Ramu, G., Pamulapati, S. and Ananthasuresh, G. K., “A compliant mechanism kit with flexible beams and connectors along with analysis and optimal synthesis procedures,” Mech. Mach. Theory 49, 21–39 (2012).Google Scholar
11. 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).Google Scholar
12. Shin, H., Lee, S., In, W., Jeong, J. I. and Kim, J., “Kinematic optimization of a redundantly actuated parallel mechanism for maximizing stiffness and workspace using Taguchi method,” J. Comput. Nonlinear Dyn. 6 (1) (2011).Google Scholar
13. 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
14. Liu, X.-J., Wang, J. and Pritschow, G., “Kinematics, singularity and workspace of planar 5R symmetrical parallel mechanisms,” Mech. Mach. Theory 41 (2), 145–169 (2006).Google Scholar
15. Goncalves, R. S., Carvalho, J. C. M., Carbone, G. and Ceccarelli, M., “Indices for stiffness and singularity evaluation for designing 5R parallel manipulator,” Open Mech. Eng. J. 4, 61–68 (2010).Google Scholar