Reconciling Enumeration Contradictions: Complete List of Baranov Chains With Up to 15 Links With Mathematical ProofSource: Journal of Mechanical Design:;2021:;volume( 143 ):;issue: 008::page 083304-1DOI: 10.1115/1.4048964Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: The identification of Baranov chains is associated with the rigid subchain identification problem, which is a crucial step in several methods of structural synthesis of kinematic chains. In this article, a systematic approach for the detection of rigid subchains, based on matroid theory, is presented and proved. Based on this approach, a novel method for the enumeration of Baranov chains is proposed. A novel algorithm is applied to a database of nonisomorphic graphs of nonfractionated zero-mobility kinematic chains. By means of the proposed algorithm, the previous results for Baranov chains presented in the literature with up to 11 links are compared and validated. Furthermore, discrepancies in the number of Baranov chains with up to 13 links, presented in the literature, are pointed out, discussed, and the proven results are presented. Finally, the complete family of Baranov chains with up to 15 links is obtained. Examples of application of the proposed method are provided.
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| contributor author | Morlin, Fernando Vinícius | |
| contributor author | Carboni, Andrea Piga | |
| contributor author | Martins, Daniel | |
| date accessioned | 2022-02-06T05:46:04Z | |
| date available | 2022-02-06T05:46:04Z | |
| date copyright | 2/9/2021 12:00:00 AM | |
| date issued | 2021 | |
| identifier issn | 1050-0472 | |
| identifier other | md_143_8_083304.pdf | |
| identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4278716 | |
| description abstract | The identification of Baranov chains is associated with the rigid subchain identification problem, which is a crucial step in several methods of structural synthesis of kinematic chains. In this article, a systematic approach for the detection of rigid subchains, based on matroid theory, is presented and proved. Based on this approach, a novel method for the enumeration of Baranov chains is proposed. A novel algorithm is applied to a database of nonisomorphic graphs of nonfractionated zero-mobility kinematic chains. By means of the proposed algorithm, the previous results for Baranov chains presented in the literature with up to 11 links are compared and validated. Furthermore, discrepancies in the number of Baranov chains with up to 13 links, presented in the literature, are pointed out, discussed, and the proven results are presented. Finally, the complete family of Baranov chains with up to 15 links is obtained. Examples of application of the proposed method are provided. | |
| publisher | The American Society of Mechanical Engineers (ASME) | |
| title | Reconciling Enumeration Contradictions: Complete List of Baranov Chains With Up to 15 Links With Mathematical Proof | |
| type | Journal Paper | |
| journal volume | 143 | |
| journal issue | 8 | |
| journal title | Journal of Mechanical Design | |
| identifier doi | 10.1115/1.4048964 | |
| journal fristpage | 083304-1 | |
| journal lastpage | 083304-10 | |
| page | 10 | |
| tree | Journal of Mechanical Design:;2021:;volume( 143 ):;issue: 008 | |
| contenttype | Fulltext |