Configuration transformations of mechanisms with variable topologies

A mechanism with multiple topological structures during the operation process is called a mechanism with variable topologies (MVT). The kinematic joints whose types and/or motion orientations are changeable during the operation process of an MVT are called the variable joints. The MVTs are usually designed for achieving multiple design requirements. Hence, the variability configurations of an MVT at each stage should be determined to meet the design requirements. This paper proposes a mapping function method to describe the topology changes of mechanisms and to determine the relationships of mechanism configurations between different stages. Firstly, the operation and its principles are defined. Then, a variable joint subject to the input motion is modeled for its topology changes, and the concept of mapping functions is proposed. Furthermore, the configurations of an MVT are represented by the matrix forms of colored graphs by edges. A sawing mechanism and a mechanical lock with variable passwords are exemplified to analyze the topological characteristics and the configuration transformations in MVTs.