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JRM Vol.19 No.2 pp. 141-147
doi: 10.20965/jrm.2007.p0141
(2007)

Paper:

Integrated Multi-Step Design Method for Practical and Sophisticated Compliant Mechanisms Combining Topology and Shape Optimizations

Masakazu Kobayashi*, Shinji Nishiwaki**, and Hiroshi Yamakawa***

*Department of Information-aided Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tempaku-ku, Nagoya 468-8511, Japan

**Department of Aeronautics and Astronautics, Kyoto University, Yoshida Hon-machi, Sakyo-Ku, Kyoto 606-8501, Japan

***Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo 169-8555, Japan

Received:
October 23, 2006
Accepted:
December 21, 2006
Published:
April 20, 2007
Keywords:
optimal design, compliant mechanism, topology optimization, shape optimization, nonlinear analysis
Abstract

Compliant mechanisms designed by traditional topology optimization have a linear output response, and it is difficult for traditional methods to implement mechanisms having nonlinear output responses, such as nonlinear deformation or path. To design a compliant mechanism having a specified nonlinear output path, we propose a two-stage design method based on topology and shape optimizations. In the first stage, topology optimization generates an initial conceptual compliant mechanism based on ordinary design conditions, with “additional” constraints used to control the output path in the second stage. In the second stage, an initial model for the shape optimization is created, based on the result of the topology optimization, and additional constraints are replaced by spring elements. The shape optimization is then executed, to generate the detailed shape of the compliant mechanism having the desired output path. At this stage, parameters that represent the outer shape of the compliant mechanism and of spring element properties are used as design variables in the shape optimization. In addition to configuring the specified output path, executing the shape optimization after the topology optimization also makes it possible to consider the stress concentration and large displacement effects. This is an advantage offered by the proposed method, because it is difficult for traditional methods to consider these aspects, due to inherent limitations of topology optimization.

Cite this article as:
Masakazu Kobayashi, Shinji Nishiwaki, and Hiroshi Yamakawa, “Integrated Multi-Step Design Method for Practical and Sophisticated Compliant Mechanisms Combining Topology and Shape Optimizations,” J. Robot. Mechatron., Vol.19, No.2, pp. 141-147, 2007.
Data files:
References
  1. [1] L. L. Howell, “Compliant Mechanisms,” John Wiley & Sons, Inc., New York, N. Y., 1, 2001.
  2. [2] G. K. Ananthasuresh and S. Kota, “Designing compliant mechanisms,” ASME Mechanical Engineering, pp. 93-96, 1995.
  3. [3] U. D. Larsen, O. Sigmund, and S. Bouswstra, “Design and fabrication of compliant mechanisms and material structures with negative Poisson’s ratio,” Journal of Microelectromechanical Systems, San Diego, California, 6, pp. 99-106, 1997.
  4. [4] I. Her and A. Midah, “A compliance number concept for compliant mechanisms, and type synthesis,” Journal of Mechanisms, Transmissions, and Automation in Design, 109, 3, pp. 348-355, 1987.
  5. [5] L. L. Howell and A. Midha, “Method for the Design of Compliant Mechanisms with Small-Length Flexural Pivots,” Journal of Mechanical Design, 116, pp. 280-289, 1994.
  6. [6] M. P. Bendsφe and N. Kikuchi, “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Computer Methods in Applied Mechanics and Engineering, 71, 2, pp. 197-224, 1988.
  7. [7] O. Sigmund “On the Design of Compliant Mechanisms Using Topology Optimization,” Mechanics of Structures and Machines, 25, 4, pp. 495-526, 1997.
  8. [8] S. Nishiwaki, S. Min, J. Yoo, and N. Kikuchi, “Optimal Structural Design Considering Flexibility,” Computer Methods in Applied Mechanics and Engineering, 190, 34, pp. 4457-4504, 2001.
  9. [9] O. Sigmund and J. Petersson, “Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima,” Structural Optimization, 16, pp. 68-75, 1998.
  10. [10] D. Fujii and N. Kikuchi, “Improvement of numerical instabilities in topology optimization using the SLP method,” Structural Optimization, 19, pp. 113-121, 2000.
  11. [11] B. Bourdin, “Filters in topology optimization,” International Journal for Numerical Methods in Engineering, 50, pp. 2143-2158, 2001.
  12. [12] K. Matsui and K. Terada “Continuous approximation of material distribution for topology optimization,” International Journal for Numerical Methods in Engineering, 59, pp. 1925-1944, 2004.
  13. [13] T. A. Poulsen, “A new Scheme for Imposing a Minimum Length Scale in Topology Optimization,” International Journal for Numerical Methods in Engineering, 57, pp. 741-760, 2003.
  14. [14] G. H. Yoon, Y. Y. Kim, M. P. Bendsφe, and O. Sigmund, “Hingefree topology optimization with embedded translation-invariant differentiable wavelet shinkage,” Structural and Multidisciplinary Optimization, 27, pp. 139-150, 2004.
  15. [15] J. T. Pereira, E. A. Fancello, and C. S. Barcellos, “Topology Optimization of Continuum Structures with Material Failure Constraints,” Structural and Multidisciplinary Optimization, 26, pp. 50-66, 2004.
  16. [16] P. Duysinx and M. P. Bendsφe, “Topology Optimization of Continuum Structures with Local Stress Constraints,” International Journal for Numerical Methods in Engineering, 43, pp. 1453-1478, 1998.
  17. [17] C. B. Pedersen, Y. Buhl, and O. Sigmund, “Topology synthesis of large-displacement compliant mechanisms,” International Journal for Numerical Methods in Engineering, 50, pp. 2683-2705, 2001.
  18. [18] T. E. Bruns and D. A. Tortorelli, “Topology Optimization of Nonlinear Structures and Compliant Mechanisms,” Computer Methods in Applied Mechanics and Engineering, 190, 26-27, pp. 3443-3459, 2001.
  19. [19] A. Midha, Y. Annamalai, and S. K. Kolachalam, “A Compliant Mechanism Design Methodology for Coupled and Uncoupled Systems, and Governing Free Choice Selection Considerations,” Proceedings of DETC/CIE 2004, DETC2004-57579, 2004.
  20. [20] B. D. Jensen and L. L. Howell, “Bistable Configurations of Compliant Mechanisms Modeled Using Four Links and Translational Joints,” Journal of Mechanical Design, 126, pp. 657-666, 2004.
  21. [21] C. C. Swan and S. F. Rahmatalla, “Design and Control of Path Following Compliant mechanisms,” Proceedings of DETC/CIE 2004, DETC2004-57441, 2004.
  22. [22] T. Sekimoto and H. Noguchi, “Homologous Topology Optimization in Large Displacement and Buckling Problems,” JSME International Journal, Series A, 44, pp. 610-615, 2001.
  23. [23] T. E. Bruns, O. Sigmund, and D. A. Tortorelli, “Numerical Methods for the Topology Optimization of Structures that Exhibit Snapthrough,” International Journal for Numerical Methods in Engineering, 55, pp. 1215-1237, 2002.
  24. [24] T. E. Bruns and O. Sigmund, “Toward the topology design of mechanisms that exhibit snap-through behavior,” Computer Methods in Applied Mechanics and Engineering, 193, pp. 3973-4000, 2004.
  25. [25] A. Hosoyama, S. Nishiwaki, K. Izui, M. Yoshimura, K. Matsui, and K. Terada, “Structural Topology Optimization of Compliant Mechanisms: In cases Where the Ratio of the Displacement at the Input Location to the Displacement at the Output Location is Included in an Objective Function,” Transactions of the Japan Society of Mechanical Engineers, Series C, Vol.70, No.696, pp. 2384-2391, 2004.
  26. [26] MSC Marc,
    http://www.mscsoftware.com/.
  27. [27] modeFrontier,
    http://www.esteco.com/.

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