Skip to main content
SpringerLink
Log in

Motion and stress analysis of direct-driven compliant mechanisms with general-purpose finite element software

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

Compliant mechanisms with embedded direct-driven actuators are gaining a wide interest in manufacturing systems as well as structural systems. In this paper, we present a procedure for motion analysis of a compliant mechanism which is driven by three embedded piezoelectric actuators with a general-purpose finite element system, in particular, ANSYS. This includes finite element modeling of the piezoelectric actuator and finite element modeling of the compliant mechanism. An experimental validation was conducted, which shows that the model is highly accurate. The contribution of this paper is a novel application of finite element methods with multidisciplinary elements to motion and stress analysis of compliant mechanisms with embedded piezoelectric actuators. In the current literature, for a complaint mechanism, either the piezoelectric actuator is modeled with absence of piezoelectric effects or a pseudo rigid body approach is applied with poor accuracy. Another contribution lies in the use of a general-purpose finite element software system, which will greatly increase the generalization of finite element modeling applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdalla MM, Frecker M, Gurdal Z, Johnson T, Lindner DK (2003) Maximum energy-efficiency compliant mechanism design for piezoelectric stack actuators. Am Soc Mech Eng Aerosp Div (Publ) AD 68:53–61

    Google Scholar 

  2. Alik H, Hughes TJR (1970) Finite element method for piezoelectric vibration. Int J Numer Methods Eng 2:151–157

    Article  Google Scholar 

  3. Angelino MR, Washington GN (2002) Design and construction of a piezoelectric point actuated active aperture antenna. J Intell Mater Syst Struct 13:125–136

    Article  Google Scholar 

  4. ANSYS (2004) ANSYS Release 8.1 documentation preview, Swanson Analysis System, Inc., Houston

  5. Bharti S, Frecker MI (2004) “Optimal design and experimental characterization of a compliant mechanism piezoelectric actuator for inertially stabilized rifle’. J Intell Mater Syst Struct 15:93–106

    Article  Google Scholar 

  6. Cattafesta,L., Mathew,J., and Kurdila,A, 2000. “Modeling and design of piezoelectric actuators for fluid flow control (online posting)’, SAE International and AIAA, Inc. http://www.img.ufl.edu/publications/Modeling%20and%20Design%20of%20Piezoelectric%20Actuators%20for%20Fluid%20Control_Conference_October2000.pdf

  7. Chen W, Lin W (2003) A miniature gripper system for optical fiber handling. Proc SPIE Int Soc Opt Eng 4902:436–443

    Article  Google Scholar 

  8. Handley DC, Zhao W, Zhang W J, Li Q and Lu Tien-Fu (2002) “An experimental observation of uncoupling of multi-DOF PZT actuators in a compliant mechanism”, Proceedings of the 7th International Conference on Control, Automation, Robotics and Vision, ICARCV 2002, 1, pp. 1354-1358

  9. Hara A, Sugimoto K (1989) Synthesis of parallel micromanipulators. ASME Trans J Mech Transm Autom Des 111:34–39

    Article  Google Scholar 

  10. Her I, Chang JC (1994) A linear scheme for the displacement analysis of micropositioning stages with flexure hinges. ASME Trans J Mech Des 116:770–776

    Article  Google Scholar 

  11. Kim J, Ko B, Lee J-K, Cheong C-C (1999) Finite element modeling of a piezoelectric smart structure for the cabin noise problem. Smart Mater Struct 8:380–389

    Article  Google Scholar 

  12. Lee KM, Arjunan S (1989) A three-degrees-of-freedom micromotion in-parallel actuated manipulator. IEEE Trans Robot Autom 7(5):634–641

    Article  Google Scholar 

  13. Li Q, Zhang WJ and Chen L, (2001) Design for control (DFC): a concurrent engineering approach for mechatronic system design, IEEE/ASME Trans on Mechatronics, June, 6(2), pp. 161-169. (cited by 29, 2009 by GS)

  14. Peelamedu SM, Dukkipati RV, Naganathan NG (2001) “Finite element approach to model and analyze piezoelectric actuators”. JSME Int J, Series C: Mech Syst Mach Elem Manuf 44(2):476–485

    Article  Google Scholar 

  15. Piefort V and Preumont A, (2001) “Finite element modeling of piezoelectric structures (on-line posting)”, Active Structure Laboratory, Belgium. <http://www.ulb.ac.be/scmero/documents/piezo/js2001_ulb_vp.pdf>

  16. Ouyang P, Clement R, Zhang WJ and Yang GS (2008) Micro motion devices technology: the state of arts review. J Advanced Manuf Technol (Online: 17 July 2007; http://www.springerlink.com/content/j01055248rgm151t/), 38

  17. Ouyang PR, Zhang WJ, Gupta MM, Zhao W (2007) Overview of the development of a visual based automated bio-micromanipulation system. Mechatronics 17(10):578–588

    Article  Google Scholar 

  18. Von Preissig FJ and Kim ES (2000) “Topics in finite element modeling of piezoelectric MEMS (on-line posting)”, University of Hawaii and University of South Carolina, USA, 2000. <http://www.comppub.com/publications/MSM/2000/pdf/T45.09.pdf>

  19. Tjiptoprodjo RC (2005) On a finite element approach to modeling of piezoelectric element driven compliant mechanism. University of Saskatchewan, Saskatoon

    Google Scholar 

  20. Zettl B (2003) Effective finite element modeling of micro-positioning systems. University of Saskatchewan, Saskatoon

    Google Scholar 

  21. Zhang WJ, Li Q, Guo SL (1999) Integrated design of mechanical structure and control algorithm for a programmable four-bar linkage. IEEE/ASME Trans on Mechatronics 4(4):354–362

    Article  MathSciNet  Google Scholar 

  22. Zhang WJ, Zou J, Watson G, Zhao W, Zong GH, Bi SS (2002) Constant-Jacobian method for kinematics of a 3-DOF planar micro-motion stage. J of Robotic Systems 19(2):63–79, April

    Article  Google Scholar 

  23. Zou J (2000) Kinematics, dynamics, and control of a particular micro-motion system. University of Saskatchewan, Saskatoon

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Donghua University, Shanghai, China

    Ranier Clement, Z. H. Sun & W. J. Zhang

  2. Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, SK, Canada

    Ranier Clement, J. L. Huang, J. Z. Wang & W. J. Zhang

Authors
  1. Ranier Clement
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. L. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Z. H. Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. Z. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W. J. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. J. Zhang.

Appendix

Appendix

Data of the piezoelectric actuators used in the RRR mechanism

For the matrices in the main body of text, i.e., Eqs. 10, 11, 12, 13, 14, and 15, the data of the particular piezoelectric actuators used in the RRR mechanism populated these matrices as follows (respectively):

$$ \left[ {{s^E}} \right] = \left[ {\matrix{ {1.48e - 11} & 0 & 0 & 0 & 0 & 0 \\ {} & 0 & 0 & 0 & 0 & 0 \\ {} &{} &{3.2942e - 9} & 0 & 0 & 0 \\ {} &{} &{} & 0 & 0 & 0 \\ {} &{} &{} &{} & 0 & 0 \\ {} &{} &{} &{} &{} & 0 \\ }<!end array> } \right] $$
$$ \left[ {{\varepsilon^T}} \right] = \left[ {\matrix{ {2356} & 0 & 0 \\ 0 &{2356} & 0 \\ 0 & 0 &{5.1246e5} \\ }<!end array> } \right] $$
$$ \left[ d \right] = \left[ {\matrix{ 0 & 0 & 0 & 0 &{9.3e - 10} & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 \\ { - 2.87e - 10} & 0 &{1.1557e - 7} & 0 & 0 & 0 \\ }<!end array> } \right] $$
$$ \begin{array}{*{20}{c}} {\quad {\text{X}}\quad \quad {\text{Y}}\quad \quad \,\,{\text{Z}}\quad \quad \quad \quad \quad \quad \quad {\text{X}}\quad \quad \quad {\text{Y}}} \\ {\left[ {{{\varepsilon }^{T}}} \right] = \left[ {\begin{array}{*{20}{c}} {2536}00 \\ 0{2536}0 \\ 00{5.1236e5} \\ \end{array} } \right]\begin{array}{*{20}{c}} {\text{X}} \\ {\text{Y}} \\ {\text{Z}} \\ \end{array} \to \left[ {\begin{array}{*{20}{c}} {5.1236e5}0 \\ 0{2536} \\ \end{array} } \right]\begin{array}{*{20}{c}} {\text{X}} \hfill \\ {\text{Y}} \hfill \\ \end{array} } \\ \end{array} $$
$$ \begin{array}{*{20}{c}} {\quad \quad \quad \quad {\text{X}}\quad \quad {\text{Y}}\quad \quad \quad {\text{Z}}\quad \quad \quad \quad \quad \quad \quad {\text{X}}\quad \quad \quad \quad \;{\text{Y}}} \hfill \\ {\left[ {\text{e}} \right] = \left[ {\begin{array}{*{20}{c}} 0 & 0 &{ - 2.87e - 10} \\ 0 & 0 & 0 \\ 0 & 0 &{1.1557e - 7} \\ 0 & 0 & 0 \\ {9.3e - 10} & 0 & 0 \\ 0 & 0 & 0 \\ \end{array} } \right]\begin{array}{*{20}{c}} {\text{X}} \hfill \\ {\text{Y}} \hfill \\ {\text{Z}} \hfill \\ {\text{X}} \hfill \\ {\text{Y}} \hfill \\ {\text{Z}} \hfill \\ \end{array} \to \left[ {\begin{array}{*{20}{c}} {1.1557e7} & 0 \\ { - 2.87e - 10} & 0 \\ 0 & 0 \\ 0 &{9.3e - 10} \\ \end{array} } \right]\begin{array}{*{20}{c}} {\text{X}} \hfill \\ {\text{Y}} \hfill \\ {{\text{XY}}} \hfill \\ {{\text{XZ}}} \hfill \\ \end{array} } \hfill \\ \end{array} $$
$$ \begin{array}{*{20}{c}} {\quad \quad \quad \quad \quad {\text{X}}\quad \quad \;{\text{Y}}\quad \quad \quad {\text{Z}}\quad \quad \;\,{\text{XY}}\,{\text{YZ}}\,{\text{XZ}}\quad \quad \quad \quad \;\;{\text{X}}\quad \quad \quad \quad \;{\text{Y}}\quad \quad \,{\text{XY}}\,{\text{XZ}}} \hfill \\ {\left[ {{{S}^{E}}} \right] = \left[ {\begin{array}{*{20}{c}} {1.48e - 11} & 0 & 0 & 0 & 0 & 0 \\ {} & 0 & 0 & 0 & 0 & 0 \\ {} &{} &{3.2942e - 9} & 0 & 0 & 0 \\ {} &{} &{} & 0 & 0 & 0 \\ {} &{} &{} &{} & 0 & 0 \\ {} &{} &{} &{} &{} & 0 \\ \end{array} } \right]\begin{array}{*{20}{c}} {\text{X}} \hfill \\ {\text{Y}} \hfill \\ {\text{Z}} \hfill \\ {\text{X}} \hfill \\ {\text{Y}} \hfill \\ {\text{Z}} \hfill \\ \end{array} \to \left[ {\begin{array}{*{20}{c}} {3.2942e - 9} & 0 & 0 & 0 \\ {} &{1.48e - 11} & 0 & 0 \\ {} &{} & 0 & 0 \\ {} &{} &{} & 0 \\ \end{array} } \right]\begin{array}{*{20}{c}} {\text{X}} \hfill \\ {\text{Y}} \hfill \\ {{\text{XY}}} \hfill \\ {{\text{XZ}}} \hfill \\ \end{array} } \hfill \\ \end{array} $$

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clement, R., Huang, J.L., Sun, Z.H. et al. Motion and stress analysis of direct-driven compliant mechanisms with general-purpose finite element software. Int J Adv Manuf Technol 65, 1409–1421 (2013). https://doi.org/10.1007/s00170-012-4266-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-012-4266-1

Keywords

Search

Navigation