Theoretical Analyses on Actuator Stiffness and Structural Stiffness of Non-redundant and Redundant Symmetric 5R Parallel Mechanisms

비과구동, 과구동 대칭형 5R 병렬기구의 구동 및 구조 강성의 이론적 해석

  • Jin, Sang-Rok (School of Mechanical and Aerospace Engineering, Seoul National Univ.) ;
  • Kim, Jong-Won (School of Mechanical and Aerospace Engineering, Seoul National Univ.) ;
  • Seo, Tae-Won (School of Mechanical Engineering, Yeungnam Univ.)
  • 진상록 (서울대학교 기계항공공학부) ;
  • 김종원 (서울대학교 기계항공공학부) ;
  • 서태원 (영남대학교 기계공학부)
  • Received : 2011.09.28
  • Accepted : 2012.02.21
  • Published : 2012.09.01


Redundant actuated parallel kinematic machines (PKMs) have been widely researched to increase stiffness of PKMs. This paper presents theoretical analyses on the stiffness of non-redundant and redundant actuated PKM. Stiffness of each mechanism is defined by summation of actuator and structural stiffness; the actuator stiffness is determined from displacements of actuators, and the structural stiffness is determined from deformations of links by external forces. Calculated actuator and structural stiffness of non-redundant PKM show same distribution in entire workspace. On the contrary, the actuator and the structural stiffness of a redundant PKM has very different distribution in the workspace; so, we conclude the structural stiffness of redundant PKM should be considered to design the redundant PKM. The results can be used to design and analyze non-redundant and redundant PKMs.


Supported by : 한국연구재단


  1. Merlet, J. P., "Parallel Robots, 2nd ed.," Springer, 2006.
  2. Lee, S. H., Lee, J. H., Kim, W. K., and Yi, B. J., "Analysis on Kinematic Characteristics for Spatial 3- DOF Parallel Mechanisms Employing Stewart Platform Structure," J. of the KSPE, Vol. 22, No. 8, pp. 118-127, 2005.
  3. Kim, H. S. and Choi, Y. J., "The Forward/Inverse Force Transmission Analyses of the Stewart Platform," J. of the KSPE, Vol. 16, No. 5, pp. 200- 208, 1999.
  4. Kim, S. H., Jeon, D., Shin, H. P., In, W., and Kim, J., "Design and Analysis of Decoupled Parallel Mechanism with Redundant Actuator," Int. J. Precis. Eng. Manuf., Vol. 10, No. 4, pp. 93-99, 2009.
  5. Kang, D. S., Seo, T., Kim, J., Liu, X.-J., Ahn, C. S., and Kang, Y. J., "A Parallel Mechanism Micro- Positioning Platform with a 100-degree Tilting Capability," Asian Symposium for Precision Engineering and Nanotechnology, 2005.
  6. Seo, T., In, W., and Kim, J., "A New Planar 3-DOF Parallel Mechanism with Continuous 360-degree Rotational Capability," Journal of Mechanical Science and Technology, Vol. 23, No. 11, pp. 3088-3094, 2009.
  7. Zhang, D., "On Stiffness Improvement of the Tricept Machine Tool," Robotica, Vol. 23, pp. 377-386, 2005.
  8. Wu, J., Wang, J., Li, T., and Wang, L., "Dynamic analysis of the 2-DOF planar parallel manipulator of heavy duty hybrid machine tool," International Journal of Advanced Manufacturing Technology, Vol. 34, No. 3-4, pp. 413-420, 2007.
  9. Yi, B. J. and Freeman, R. A., "Simultaneous stiffness generation and internal load distribution in redundantly actuated mechanisms," International Conference on Advanced Robotics, Vol. 1, pp. 802-807, 1991.
  10. Chakarov, D., "Study of the Antagonistic Stiffness of Parallel Manipulators with Actuation Redundancy," Mechanism and Machine Theory, Vol. 39, pp. 583-601, 2004.
  11. Lee, S. H., Lee, J. H., Yi, B. J., Kim, S. H., and Kwak, Y. K., "Optimization and Experimental Verification for the Antagonistic Stiffness in Redundantly Actuated Mechanisms: A Five-Bar Example," Mechatronics, Vol. 15, pp. 213-238, 2005.
  12. 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, Vol. 29, pp. 547-554, 2011.
  13. Goncalves, R. S., Carvalho, J. C. M., Carbone, G., and Ceccarelli, M., "Indices for Stiffness and Singularity Evaluation for Designing 5R Parallel Manipulator," The Open Mechanical Engineering Journal, Vol. 4, pp. 61-68, 2010.
  14. Liu, X.-J., Wang, J., and Pritschow, G., "Kinematics, Singularity and Workspace of Planar 5R Symmetrical Parallel Mechanisms," Mechanism and Machine Theory, Vol. 41, pp. 145-169, 2006.

Cited by

  1. Stiffness optimization of 5-axis machine tool for improving surface roughness of 3D printed products vol.31, pp.7, 2017,