Contracted Graph Theory And Application Of Closed And Parallel Mechanism

Determining the mechanism topology is the key issue of mechanical innovation and mechanical conceptual design to be resolved, the main task of modern mechanisms is to provide theoretical, practical and effective way for the creation of new mechanisms of modern mechanical systems and create new mechanisms to meet the specific requirements. Extensive use of parallel mechanism promotes the continuous development of innovative research. As the primary means of mechanism design, mechanism topology type synthesis, has become a very important research topic and direction in recent years.The type synthesis of parallel mechanism is studied using feature arrays. On the basis of the reasonable associated linkages, the solution of contracted graphs type synthesis and contracted graphs isomorphism identification is proposed. With advanced CAD software, the procedure that can achieve number, graph, type synthesis process automatically.The relations among the associated linkages, redundant constraints, degrees of freedom and passive degrees of freedom of the closed mechanisms are studied. Firstly, the formula that can calculate the degree of freedom, the number of joints and the number of effective basic link is deduced. Secondly, the intrinsic relations among the associated linkages, redundant constraints, degrees of freedom and passive degrees of freedom are analyzed. Thirdly, several topology graphs are derived and the relevant closed mechanisms containing redundant constraints and passive degrees of freedom are synthesized. Finally, the numbers of redundant constraint and passive degree of freedom of the closed mechanisms including redundant constraints and passive degrees of freedom are determined.This paper focuses on the derivation of valid contracted graphs from simpler contracted graphs by adding edge and the identification of their isomorphism. The concepts of contracted graphs are explained, and the numbers of vertices and edges in contracted graphs are determined. First, many different contracted graphs are constructed from associated linkages. Second, based on the numbers of different edges, many contracted graphs corresponding to the same associated linkage are grouped and the isomorphic and invalid contracted graphs are identified and deleted. Finally, many complex valid contracted graphs are derived from simpler valid contracted graphs or virtual contracted graphs by adding edge.The derivation of the valid contracted graphs with pentagonal links, quaternary links and ternary links is studied for the type synthesis of closed mechanisms. By means of the arrays, the relations between the number of points and edges in the contracted graphs are indicated. At the same time, the relevant standards used to identify isomorphic and invalid contracted graphs are determined. Some simple contracted graphs containing pentagonal links are described, and the isomorphic contracted graphs are identified. This paper focuses on the derivation of the valid contracted graphs with hexagonal links plus other links using the characteristic strings. First, the concepts on the contracted graphs and characteristic strings are explained, and the numbers of vertices and edges in the contracted graphs are solved. Second, the relative criterion is determined for representing/deriving contracted graphs and identifying isomorphic/invalid contracted graphs by characteristic strings. Third, some simple contracted graphs are derived from some associated linkages with hexagonal links plus more other links, are represented by characteristic strings, and the isomorphic/invalid contracted graphs are identified using the characteristic strings and the isomorphic queues of the links. Finally, some examples are given for illustrating their applications.A characteristic string approach is presented for derivation and isomorphism identification of valid topological graphs for some 1, 2 degree of freedom planar closed mechanisms from the contracted graphs. The equivalent conditions between the characteristic string and the topology graph with digits are determined and verified by some created simulation mechanisms of valid topology graphs.