Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators
To address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The S...
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MDPI AG
2025-03-01
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| author | Nijia Ye Zhengwei Geng |
| author_facet | Nijia Ye Zhengwei Geng |
| author_sort | Nijia Ye |
| collection | DOAJ |
| description | To address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The SCG achieves a deeper level of simplification by omitting the consideration of ternary links on the basis of traditional contracted graphs. Firstly, this paper defines the application of characteristic strings to express the construction rules of SCG, thereby transforming the construction process into an automated generation problem of characteristic strings. Building on this, to mitigate the interference of link arrangement in the construction of conventional SCGs, this paper further proposes the concept of a simplified SCG and investigates its isomorphism properties. A program is designed based on the criteria for generating characteristic strings and isomorphism judgment, successfully generating several special SCGs. Finally, this paper introduces the edge-adding method, which enables the reconstruction of special SCGs into ordinary SCGs and contracted graphs, providing an effective tool for the topological synthesis of parallel mechanisms. |
| format | Article |
| id | doaj-art-926f6294707f45aa946f7cd4d11f2001 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-926f6294707f45aa946f7cd4d11f20012025-08-20T02:09:11ZengMDPI AGMathematics2227-73902025-03-01137107610.3390/math13071076Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel ManipulatorsNijia Ye0Zhengwei Geng1Key Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao 066004, ChinaKey Laboratory of Advanced Forging & Stamping Technology and Science of Ministry of National Education, Yanshan University, Qinhuangdao 066004, ChinaTo address the complexity of constructing traditional topological contracted graphs due to the significant increase in the types and quantities of basic links during the synthesis of complex parallel mechanisms, this paper introduces a novel concept termed “Simplified Contraction Graph (SCG)”. The SCG achieves a deeper level of simplification by omitting the consideration of ternary links on the basis of traditional contracted graphs. Firstly, this paper defines the application of characteristic strings to express the construction rules of SCG, thereby transforming the construction process into an automated generation problem of characteristic strings. Building on this, to mitigate the interference of link arrangement in the construction of conventional SCGs, this paper further proposes the concept of a simplified SCG and investigates its isomorphism properties. A program is designed based on the criteria for generating characteristic strings and isomorphism judgment, successfully generating several special SCGs. Finally, this paper introduces the edge-adding method, which enables the reconstruction of special SCGs into ordinary SCGs and contracted graphs, providing an effective tool for the topological synthesis of parallel mechanisms.https://www.mdpi.com/2227-7390/13/7/1076contracted graphcharacteristic arraytopology synthesisparallel manipulator |
| spellingShingle | Nijia Ye Zhengwei Geng Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators Mathematics contracted graph characteristic array topology synthesis parallel manipulator |
| title | Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators |
| title_full | Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators |
| title_fullStr | Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators |
| title_full_unstemmed | Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators |
| title_short | Auto-Derivation of Simplified Contracted Graphs with Quaternary Links and Re-Construction Contracted Graphs for Topology Synthesis of Parallel Manipulators |
| title_sort | auto derivation of simplified contracted graphs with quaternary links and re construction contracted graphs for topology synthesis of parallel manipulators |
| topic | contracted graph characteristic array topology synthesis parallel manipulator |
| url | https://www.mdpi.com/2227-7390/13/7/1076 |
| work_keys_str_mv | AT nijiaye autoderivationofsimplifiedcontractedgraphswithquaternarylinksandreconstructioncontractedgraphsfortopologysynthesisofparallelmanipulators AT zhengweigeng autoderivationofsimplifiedcontractedgraphswithquaternarylinksandreconstructioncontractedgraphsfortopologysynthesisofparallelmanipulators |