A constraint graph representation of metamorphic linkages

A metamorphic linkage has the property that the effective number of links and joints can change during the movement of the device. This means the kinematic structural representation of a metamorphic linkage has different forms in which vertices and edges combine depending on the configuration of the device. In this paper, we use the constraint graph of computational geometry rather than the traditional topological graph to characterize a metamorphic linkage in order to simplify the representation of its configuration changes. A constraint graph has geometric elements as vertices and their relationships as edges. We find that the adjacency sub matrix of the constraint graph provides a convenient description of changes in the topology of links and joints in the operation of the metamorphic linkage. Operations on the adjacency submatrix capture topological changes in a metamorphic linkage. We illustrate our results with several examples.