On the Self-Mobility of Point-Symmetric Hexapods
In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally...
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| Format: | Article |
| Language: | English |
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MDPI AG
2014-11-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/6/4/954 |
| _version_ | 1811187062830792704 |
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| author | Georg Nawratil |
| author_facet | Georg Nawratil |
| author_sort | Georg Nawratil |
| collection | DOAJ |
| description | In this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries. |
| first_indexed | 2024-04-11T13:56:56Z |
| format | Article |
| id | doaj.art-3adc3852ea334206a78502dcd7dc091b |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:56:56Z |
| publishDate | 2014-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3adc3852ea334206a78502dcd7dc091b2022-12-22T04:20:14ZengMDPI AGSymmetry2073-89942014-11-016495497410.3390/sym6040954sym6040954On the Self-Mobility of Point-Symmetric HexapodsGeorg Nawratil0Institute of Discrete Mathematics and Geometry, Vienna University of Technology, Wiedner Hauptstrasse 8-10/104, Vienna 1040, AustriaIn this article, we study necessary and sufficient conditions for the self-mobility of point symmetric hexapods (PSHs). Specifically, we investigate orthogonal PSHs and equiform PSHs. For the latter ones, we can show that they can have non-translational self-motions only if they are architecturally singular or congruent. In the case of congruency, we are even able to classify all types of existing self-motions. Finally, we determine a new set of PSHs, which have so-called generalized Dietmaier self-motions. We close the paper with some comments on the self-mobility of hexapods with global/local symmetries.http://www.mdpi.com/2073-8994/6/4/954hexapodself-motionbond theoryBorel–Bricard problem |
| spellingShingle | Georg Nawratil On the Self-Mobility of Point-Symmetric Hexapods Symmetry hexapod self-motion bond theory Borel–Bricard problem |
| title | On the Self-Mobility of Point-Symmetric Hexapods |
| title_full | On the Self-Mobility of Point-Symmetric Hexapods |
| title_fullStr | On the Self-Mobility of Point-Symmetric Hexapods |
| title_full_unstemmed | On the Self-Mobility of Point-Symmetric Hexapods |
| title_short | On the Self-Mobility of Point-Symmetric Hexapods |
| title_sort | on the self mobility of point symmetric hexapods |
| topic | hexapod self-motion bond theory Borel–Bricard problem |
| url | http://www.mdpi.com/2073-8994/6/4/954 |
| work_keys_str_mv | AT georgnawratil ontheselfmobilityofpointsymmetrichexapods |