[{"file_date_updated":"2023-07-04T08:11:28Z","issue":"5","publication":"ACM Transactions on Graphics","type":"journal_article","day":"20","status":"public","intvolume":"        42","department":[{"_id":"BeBi"}],"has_accepted_license":"1","file":[{"date_updated":"2023-07-04T08:11:28Z","access_level":"open_access","file_name":"kirchhoff-rods.pdf","file_size":19635168,"date_created":"2023-07-04T08:11:28Z","checksum":"4954c1cfa487725bc156dcfec872478a","content_type":"application/pdf","relation":"main_file","creator":"chafner","file_id":"13194","success":1},{"date_updated":"2023-07-04T07:46:28Z","access_level":"open_access","file_name":"supp-main.pdf","file_size":420909,"date_created":"2023-07-04T07:46:28Z","checksum":"79c9975fbc82ff71f1767331d2204cca","content_type":"application/pdf","relation":"supplementary_material","file_id":"13190","creator":"chafner","title":"Supplemental Material with Proofs"},{"title":"Cheat Sheet for Notation","file_id":"13191","creator":"chafner","content_type":"application/pdf","relation":"supplementary_material","date_created":"2023-07-04T07:46:30Z","checksum":"4ab647e4f03c711e1e6a5fc1eb8684db","file_name":"supp-cheat.pdf","file_size":430086,"date_updated":"2023-07-04T07:46:30Z","access_level":"open_access"},{"file_size":268088064,"file_name":"kirchhoff-video-final.mp4","checksum":"c0fd9a57d012046de90c185ffa904b76","date_created":"2023-07-04T07:46:39Z","access_level":"open_access","date_updated":"2023-07-04T07:46:39Z","title":"Supplemental Video","relation":"supplementary_material","content_type":"video/mp4","creator":"chafner","file_id":"13192"},{"file_name":"matlab-submission.zip","file_size":25790,"date_created":"2023-07-04T07:47:10Z","checksum":"71b00712b489ada2cd9815910ee180a9","date_updated":"2023-07-04T07:47:10Z","access_level":"open_access","title":"Matlab Source Code with Example","content_type":"application/x-zip-compressed","relation":"supplementary_material","creator":"chafner","file_id":"13193"}],"date_created":"2023-07-04T07:41:30Z","article_type":"original","date_published":"2023-09-20T00:00:00Z","month":"09","language":[{"iso":"eng"}],"publisher":"Association for Computing Machinery","date_updated":"2024-03-25T23:30:26Z","oa":1,"volume":42,"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"We thank the anonymous reviewers for their generous feedback, and Julian Fischer for his help in proving Proposition 1. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 715767).","quality_controlled":"1","oa_version":"Submitted Version","project":[{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","_id":"24F9549A-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"715767"}],"_id":"13188","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"publication_status":"published","citation":{"chicago":"Hafner, Christian, and Bernd Bickel. “The Design Space of Kirchhoff Rods.” <i>ACM Transactions on Graphics</i>. Association for Computing Machinery, 2023. <a href=\"https://doi.org/10.1145/3606033\">https://doi.org/10.1145/3606033</a>.","ieee":"C. Hafner and B. Bickel, “The design space of Kirchhoff rods,” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5. Association for Computing Machinery, 2023.","apa":"Hafner, C., &#38; Bickel, B. (2023). The design space of Kirchhoff rods. <i>ACM Transactions on Graphics</i>. Association for Computing Machinery. <a href=\"https://doi.org/10.1145/3606033\">https://doi.org/10.1145/3606033</a>","short":"C. Hafner, B. Bickel, ACM Transactions on Graphics 42 (2023).","ista":"Hafner C, Bickel B. 2023. The design space of Kirchhoff rods. ACM Transactions on Graphics. 42(5), 171.","mla":"Hafner, Christian, and Bernd Bickel. “The Design Space of Kirchhoff Rods.” <i>ACM Transactions on Graphics</i>, vol. 42, no. 5, 171, Association for Computing Machinery, 2023, doi:<a href=\"https://doi.org/10.1145/3606033\">10.1145/3606033</a>.","ama":"Hafner C, Bickel B. The design space of Kirchhoff rods. <i>ACM Transactions on Graphics</i>. 2023;42(5). doi:<a href=\"https://doi.org/10.1145/3606033\">10.1145/3606033</a>"},"author":[{"last_name":"Hafner","full_name":"Hafner, Christian","first_name":"Christian","id":"400429CC-F248-11E8-B48F-1D18A9856A87"},{"id":"49876194-F248-11E8-B48F-1D18A9856A87","first_name":"Bernd","last_name":"Bickel","full_name":"Bickel, Bernd","orcid":"0000-0001-6511-9385"}],"keyword":["Computer Graphics","Computational Design","Computational Geometry","Shape Modeling"],"abstract":[{"lang":"eng","text":"The Kirchhoff rod model describes the bending and twisting of slender elastic rods in three dimensions, and has been widely studied to enable the prediction of how a rod will deform, given its geometry and boundary conditions. In this work, we study a number of inverse problems with the goal of computing the geometry of a straight rod that will automatically deform to match a curved target shape after attaching its endpoints to a support structure. Our solution lets us finely control the static equilibrium state of a rod by varying the cross-sectional profiles along its length.\r\nWe also show that the set of physically realizable equilibrium states admits a concise geometric description in terms of linear line complexes, which leads to very efficient computational design algorithms. Implemented in an interactive software tool, they allow us to convert three-dimensional hand-drawn spline curves to elastic rods, and give feedback about the feasibility and practicality of a design in real time. We demonstrate the efficacy of our method by designing and manufacturing several physical prototypes with applications to interior design and soft robotics."}],"article_number":"171","isi":1,"ddc":["516"],"related_material":{"record":[{"status":"public","relation":"part_of_dissertation","id":"12897"}]},"ec_funded":1,"acknowledged_ssus":[{"_id":"M-Shop"}],"year":"2023","doi":"10.1145/3606033","title":"The design space of Kirchhoff rods","external_id":{"isi":["001086833300010"]}},{"issue":"5","publication":"ACM Transactions on Graphics","file_date_updated":"2021-12-17T08:13:51Z","day":"08","type":"journal_article","intvolume":"        40","status":"public","has_accepted_license":"1","department":[{"_id":"BeBi"}],"date_created":"2021-05-08T17:37:08Z","file":[{"content_type":"application/pdf","relation":"main_file","file_id":"9377","creator":"bbickel","date_updated":"2021-05-08T17:36:59Z","access_level":"open_access","file_name":"Multistable-authorversion.pdf","file_size":18926557,"date_created":"2021-05-08T17:36:59Z","checksum":"8564b3118457d4c8939a8ef2b1a2f16c"},{"date_updated":"2021-05-08T17:38:22Z","access_level":"open_access","date_created":"2021-05-08T17:38:22Z","checksum":"3b6e874e30bfa1bfc3ad3498710145a1","file_name":"multistable-video.mp4","file_size":76542901,"creator":"bbickel","file_id":"9378","content_type":"video/mp4","relation":"main_file","success":1},{"date_created":"2021-12-17T08:13:51Z","checksum":"20dc3bc42e1a912a5b0247c116772098","file_name":"multistable-supplementary material.pdf","file_size":3367072,"date_updated":"2021-12-17T08:13:51Z","access_level":"open_access","title":"Supplementary Material for “Computational Design of Planar Multistable Compliant Structures”","creator":"bbickel","file_id":"10562","content_type":"application/pdf","description":"This document provides additional results and analyzes the robustness and limitations of our approach.","relation":"supplementary_material"}],"month":"10","article_type":"original","date_published":"2021-10-08T00:00:00Z","publisher":"Association for Computing Machinery","language":[{"iso":"eng"}],"date_updated":"2023-08-08T13:31:38Z","volume":40,"oa":1,"article_processing_charge":"No","_id":"9376","publication_identifier":{"eissn":["1557-7368"],"issn":["0730-0301"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","acknowledgement":"We would like to thank everyone who contributed to this paper, the authors of artworks for all the examples, including @macrovec-tor_official and Wikimedia for the FLAG semaphore, and @pikisuper-star for the FIGURINE. The photos of iconic poses in the teaser were supplied by (from left to right): Mike Hewitt/Olympics Day 8 - Athletics/Gettty Images, Oneinchpunch/Basketball player training on acourt in New york city/Shutterstock, and Andrew Redington/TigerWoods/Getty Images. We also want to express our gratitude to Christian Hafner for insightful discussions, the IST Austria machine shop SSU, all proof-readers, and anonymous reviewers. This project has received funding from the European Union’s Horizon 2020 research and innovation programme, under the Marie Skłodowska-Curie grant agreement No 642841 (DISTRO), and under the European Research Council grant agreement No 715767 (MATERIALIZABLE).","quality_controlled":"1","project":[{"_id":"2508E324-B435-11E9-9278-68D0E5697425","name":"Distributed 3D Object Design","call_identifier":"H2020","grant_number":"642841"},{"name":"MATERIALIZABLE: Intelligent fabrication-oriented Computational Design and Modeling","_id":"24F9549A-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"715767"}],"oa_version":"Published Version","publication_status":"published","citation":{"short":"R. Zhang, T. Auzinger, B. Bickel, ACM Transactions on Graphics 40 (2021).","ista":"Zhang R, Auzinger T, Bickel B. 2021. Computational design of planar multistable compliant structures. ACM Transactions on Graphics. 40(5), 186.","mla":"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>.","ama":"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>","chicago":"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>.","ieee":"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.","apa":"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>"},"abstract":[{"lang":"eng","text":"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."}],"author":[{"first_name":"Ran","orcid":"0000-0002-3808-281X","last_name":"Zhang","full_name":"Zhang, Ran","id":"4DDBCEB0-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Auzinger","full_name":"Auzinger, Thomas","orcid":"0000-0002-1546-3265","first_name":"Thomas","id":"4718F954-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Bernd","orcid":"0000-0001-6511-9385","full_name":"Bickel, Bernd","last_name":"Bickel","id":"49876194-F248-11E8-B48F-1D18A9856A87"}],"keyword":["multistability","mechanism","computational design","rigidity"],"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"isi":1,"article_number":"186","ddc":["000"],"acknowledged_ssus":[{"_id":"M-Shop"}],"year":"2021","doi":"10.1145/3453477","ec_funded":1,"external_id":{"isi":["000752079300003"]},"title":"Computational design of planar multistable compliant structures"}]