article published yes Ran Zhang author 4DDBCEB0-F248-11E8-B48F-1D18A9856A870000-0002-3808-281X Thomas Auzinger author 4718F954-F248-11E8-B48F-1D18A9856A870000-0002-1546-3265 Bernd Bickel author 49876194-F248-11E8-B48F-1D18A9856A870000-0001-6511-9385 BeBi department Distributed 3D Object Design project MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling project This paper presents a method for designing planar multistable compliant structures. Given a sequence of desired stable states and the corresponding poses of the structure, we identify the topology and geometric realization of a mechanism—consisting of bars and joints—that is able to physically reproduce the desired multistable behavior. In order to solve this problem efficiently, we build on insights from minimally rigid graph theory to identify simple but effective topologies for the mechanism. We then optimize its geometric parameters, such as joint positions and bar lengths, to obtain correct transitions between the given poses. Simultaneously, we ensure adequate stability of each pose based on an effective approximate error metric related to the elastic energy Hessian of the bars in the mechanism. As demonstrated by our results, we obtain functional multistable mechanisms of manageable complexity that can be fabricated using 3D printing. Further, we evaluated the effectiveness of our method on a large number of examples in the simulation and fabricated several physical prototypes. https://research-explorer.ista.ac.at/download/9376/9377/Multistable-authorversion.pdf application/pdfno https://research-explorer.ista.ac.at/download/9376/9378/multistable-video.mp4 video/mp4no https://research-explorer.ista.ac.at/download/9376/10562/multistable-supplementary material.pdf application/pdfno Association for Computing Machinery2021 eng multistabilitymechanismcomputational designrigidity 0730-0301 1557-7368 00075207930000310.1145/3453477 405 Zhang, Ran, et al. “Computational Design of Planar Multistable Compliant Structures.” <i>ACM Transactions on Graphics</i>, vol. 40, no. 5, 186, Association for Computing Machinery, 2021, doi:<a href="https://doi.org/10.1145/3453477">10.1145/3453477</a>. Zhang, R., Auzinger, T., &#38; Bickel, B. (2021). Computational design of planar multistable compliant structures. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href="https://doi.org/10.1145/3453477">https://doi.org/10.1145/3453477</a> R. Zhang, T. Auzinger, and B. Bickel, “Computational design of planar multistable compliant structures,” <i>ACM Transactions on Graphics</i>, vol. 40, no. 5. Association for Computing Machinery, 2021. Zhang R, Auzinger T, Bickel B. Computational design of planar multistable compliant structures. <i>ACM Transactions on Graphics</i>. 2021;40(5). doi:<a href="https://doi.org/10.1145/3453477">10.1145/3453477</a> Zhang, Ran, Thomas Auzinger, and Bernd Bickel. “Computational Design of Planar Multistable Compliant Structures.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2021. <a href="https://doi.org/10.1145/3453477">https://doi.org/10.1145/3453477</a>. R. Zhang, T. Auzinger, B. Bickel, ACM Transactions on Graphics 40 (2021). Zhang R, Auzinger T, Bickel B. 2021. Computational design of planar multistable compliant structures. ACM Transactions on Graphics. 40(5), 186. 93762021-05-08T17:37:08Z2025-03-31T15:58:16Z