Identification of Rigid Subchains in Graphs of Mechanisms obtained from Contracted Graphs

Abstract

The enumeration of graphs of kinematic chains of mechanisms is of outmost importance in the design of new mechanical devices. A database of graphs of kinematic chains of mechanisms can be used in the conceptual design stage to search, by using a computer, mechanisms with given structural properties: number of degrees of freedom, loops, joints and links, as well as particular characteristics of links and joints of the mechanisms, such as the input joints, the ground and the output links, among others. Any state-of-the-art database of graphs of mechanisms contains millions of mechanisms. Each graph must not be and must not contain a rigid subgraph as a substructure. The correctness of the algorithm to identify degenerated graphs is critical to define the correctness of the database of mechanism. This work firstly reviews several approaches to identify degenerated mechanisms. Secondly, a rigid-chain identification procedure for graphs of kinematic chains obtained from contracted graphs by the assignment of binary chains is described. The results are validated with those found in the literature.