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 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.