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

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.

*J. Robot. Mechatron.*, Vol.19, No.2, pp. 141-147, 2007.

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