--- res: bibo_abstract: - We study structural rigidity for assemblies with mechanical joints. Existing methods identify whether an assembly is structurally rigid by assuming parts are perfectly rigid. Yet, an assembly identified as rigid may not be that “rigid” in practice, and existing methods cannot quantify how rigid an assembly is. We address this limitation by developing a new measure, worst-case rigidity, to quantify the rigidity of an assembly as the largest possible deformation that the assembly undergoes for arbitrary external loads of fixed magnitude. Computing worst-case rigidity is non-trivial due to non-rigid parts and different joint types. We thus formulate a new computational approach by encoding parts and their connections into a stiffness matrix, in which parts are modeled as deformable objects and joints as soft constraints. Based on this, we formulate worst-case rigidity analysis as an optimization that seeks the worst-case deformation of an assembly for arbitrary external loads, and solve the optimization problem via an eigenanalysis. Furthermore, we present methods to optimize the geometry and topology of various assemblies to enhance their rigidity, as guided by our rigidity measure. In the end, we validate our method on a variety of assembly structures with physical experiments and demonstrate its effectiveness by designing and fabricating several structurally rigid assemblies.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Zhenyuan foaf_name: Liu, Zhenyuan foaf_surname: Liu foaf_workInfoHomepage: http://www.librecat.org/personId=70f0d7cf-ae65-11ec-a14f-89dfc5505b19 orcid: 0000-0001-9200-5690 - foaf_Person: foaf_givenName: Jingyu foaf_name: Hu, Jingyu foaf_surname: Hu - foaf_Person: foaf_givenName: Hao foaf_name: Xu, Hao foaf_surname: Xu - foaf_Person: foaf_givenName: Peng foaf_name: Song, Peng foaf_surname: Song - foaf_Person: foaf_givenName: Ran foaf_name: Zhang, Ran foaf_surname: Zhang - foaf_Person: foaf_givenName: Bernd foaf_name: Bickel, Bernd foaf_surname: Bickel foaf_workInfoHomepage: http://www.librecat.org/personId=49876194-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0001-6511-9385 - foaf_Person: foaf_givenName: Chi-Wing foaf_name: Fu, Chi-Wing foaf_surname: Fu bibo_doi: 10.1111/cgf.14490 bibo_issue: '2' bibo_volume: 41 dct_date: 2022^xs_gYear dct_identifier: - UT:000802723900039 dct_isPartOf: - http://id.crossref.org/issn/0167-7055 - http://id.crossref.org/issn/1467-8659 dct_language: eng dct_publisher: Wiley@ dct_title: Worst-case rigidity analysis and optimization for assemblies with mechanical joints@ ...