Mobility of symmetric block-and-hole polyhedra
| dc.contributor.author | Guest, SD | |
| dc.contributor.author | Fowler, PW | |
| dc.contributor.author | Schulze, B | |
| dc.contributor.orcid | Schulze, B [0000-0002-6272-4296] | |
| dc.date.accessioned | 2018-10-10T17:30:25Z | |
| dc.date.available | 2018-10-10T17:30:25Z | |
| dc.date.issued | 2018 | |
| dc.description.abstract | Block-and-hole polyhedra can be derived from a bar-joint triangulation of a polyhedron by a stepwise construction: select a set of non-overlapping disks defined by edge-cycles of the triangulation of length at least 4; then modify the interior of each disk by an addition or deletion operation on vertices and edges so that it becomes either a rigid block or a hole. The construction has a body-hinge analogue. Models of many classical objects such as the Sarrus linkage can be modelled by block-and-hole polyhedra. Symmetry extensions of counting rules for mobility (the balance of mechanisms and states of self-stress) are obtained for the bar-joint and body-hinge models. The extended rules detect mechanisms in many cases where pure counting would predict an isostatic framework. Relations between structures where blocks and holes are swapped have a simple form. Examples illustrate the finer classification of isostatic and near-isostatic block-and-hole polyhedra achievable by using symmetry. The present approach also explains a puzzle in standard models of mobility. In the bar-joint model, a fully triangulated polyhedron is isostatic, but in a body-hinge version it is heavily overconstrained. When the bodies are panels with hinge lines intersecting at vertices, the overconstraints can be explained in local mechanical terms, with a direct symmetry description. A generalisation of the symmetry formula explains the extra states of self-stress in panel-hinge models of block-and-hole polyhedra. | |
| dc.identifier.doi | 10.17863/CAM.30932 | |
| dc.identifier.eissn | 1879-2146 | |
| dc.identifier.issn | 0020-7683 | |
| dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/283570 | |
| dc.language.iso | eng | |
| dc.publisher | Elsevier BV | |
| dc.publisher.url | http://dx.doi.org/10.1016/j.ijsolstr.2018.05.029 | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Symmetry | |
| dc.subject | Rigidity | |
| dc.subject | Mechanisms | |
| dc.subject | Block-and-hole polyhedra | |
| dc.subject | Bar-joint frameworks | |
| dc.subject | Panel-hinge structures | |
| dc.title | Mobility of symmetric block-and-hole polyhedra | |
| dc.type | Article | |
| dcterms.dateAccepted | 2018-05-31 | |
| prism.endingPage | 51 | |
| prism.publicationDate | 2018 | |
| prism.publicationName | International Journal of Solids and Structures | |
| prism.startingPage | 40 | |
| prism.volume | 150 | |
| rioxxterms.licenseref.startdate | 2018-10-01 | |
| rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
| rioxxterms.type | Journal Article/Review | |
| rioxxterms.versionofrecord | 10.1016/j.ijsolstr.2018.05.029 |
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