Based On Vertex Symmetry Detection To Synthesis Planar3and5-dof Fractionated Kinematic Chains

Structural synthesis plays a basis role of all kinds of mechanism structuresoptimization and mechanism innovation, which is the most creative phase of themechanical innovative design process. For a long time, the subject has been a focus anddifficult to the international mechanism scientists. But at first the mechanism synthesismethod is mainly relying on the experience and institution. Until into the1960s, theknowledge of graph theory was introduced into research of mechanisms, From then on itprovided a powerful mathematical theory for enumeration methods, which make scholarsobtained numerous effective planar mechanism enumeration methods that largely promotethe planar structural synthesis development, but mostly has been studied aboutnon-fractionated kinematic chain little about fractionated.Currently simple structures have far unable to meet in the field of fractionatedstructures of areospace deployable structure and large engineering machinery designing.In response to this situation, this paper presents a new method which based on the vertexsymmetry discrimination to achieve exclusive planar3and5degree of freedom (DOF)fractionated kinematic chains enumeration. It’s vital to provide an important mechanismoptimization during the mechanical innovation design phase.Firstly, the paper briefly introduces the relevant basic knowledge of graph theory andmechanisms, as well as the basic theory of fractionated kinematic chain includingtopology graph, adjacency matrix. Meanwhile, Put forward solving model and determinethe corresponding kinematic chain fractionated type according to planar3and5-DOFkinematic chains fractionated characteristics, also sketch Visual C++6.0programmingsoftware to realize the enumeration. These laid a theoretical foundation for synthesizeplanar3and5-DOF fractionated kinematic chains computerization and mechanismcreative design automatically.Secondly, this context proposes symmetry discriminant algorithm via traversaling thedepth search vertex of the path chain. Then determine the kinematic chain topology graphvertex asymmetric set by vertex symmetry discrimination method from the kinematic chain’s vertex adjacency matrix. Meanwhile, it needs to obtain the effective vertexasymmetric set according to the characteristics of the planar3and5-DOF fractionatedkinematic chains and their topology graph’s adjacency matrix. At last planar3and5-DOFfractionated kinematic chains could be synthesized via the effective vertex asymmetric setwithout any isomorphic kinematic chains.Finally, the method of enumeration of planar3and5-DOF fractionated kinematicchain presented here could be accomplished by Visual C++programming language on theWindows platform. Also, new results of planar3and5-DOF fractionated kinematic chainwithin18link are obtained for the first time and presented in a table.