Superposition Design Of Adjacency Matrix And Topological Chain Expression Of Planar Mechanism And Isomorphism Discriminant Method

Based on planar mechanism as the main research object,based on the study of the planar mechanism of Assur rod group,this paper proposes a using rod group element adjacency matrix and rod set of elements to represent the topological chain bar set combination superposition process,and realize the structure type synthesis of planar mechanism motion chain,at the same time to isomorphism discriminant problem in mechanism type synthesis was studied,This paper mainly has the following aspects of work and achievements:Firstly,the adjacent matrix and topological chain representation method of bar group elements based on basic kinematic chain and basic bar group were proposed.The characteristic symbol expression of bar group was established according to the type of bar group,and the numbering rules of members,motion pairs and extension nodes on members were established.The kinematic chain of the mechanism was separated based on the Assur bar group of planar mechanism,and the topology representation of the kinematic chain of the mechanism was realized by the adjacency matrix of the bar group elements and the kinematic chain of the bar group elements.On this basis,a synthesis method is proposed to generate new kinematic chain types by superposing the basic Assur bar group on the basic kinematic chain,and the configuration synthesis design is carried out by taking the multi-bar single free single hinge kinematic chain as an example.By using this method,not only the single hinge kinematic chain with any degree of freedom can be synthesized,The structure type synthesis can also be carried out for complex hinge kinematic chains with specified degrees of freedom and complex hinge factors.Then,an isomorphism discriminant method of weighted mixed graph is proposed to discriminate the graph and the kinematic chain of mechanism.The isomorphism discriminant method can be used to discriminate undirected graph and directed graph.In this method by defining the vertex degree of prime Numbers,tectonic boundary direction of the prime elements of empowerment matrix as well as the prime element matrix,based on the prime elements of empowerment matrix multiplication way such as empowerment and direction matrix elements to the edge and empowerment multiple mixed side to the edge of a single undirected,using adjacency matrix dynamic modification method can improve the figure of isomorphism identification,The isomorphism discrimination of weights and kinematic linkage of mechanisms is carried out,and the effectiveness of the discriminant example is demonstrated.Finally,the 11-bar 2-DOF motion chain of a loader was synthesized by using the proposed Assur bar group combination superposition method.In the synthesis process,the bar group and the bar group were first superposed to generate the multi-bar group opening chain containing the corresponding external pair,and then the multi-bar group opening chain and the basic motion chain were superimposed to generate the target mechanism.Finally,according to the comprehensive results,28 kinds of mechanism motion chain were selected to draw the mechanism diagram,and the loader mechanism diagram was selected to complete the comprehensive study of the mechanism structure type of the loader,and the comprehensive example shows that the method proposed in this paper is effective.