Abstract: The general adjacent matrix only provides the links connecting information of the mechanism, so that neither Assur group nor theirs connecting ships, which to be used in the mechanism synthesis based on Assur structure theory, are not described directly by the matrix. Assur group are treated as an element instead of the link element of the adjacent matrix, and a new kind of structural topological matrix so called group adjacent matrix is proposed. The diagonal elements of group adjacent matrix are composed of driver link, frame and Assur group and/or augmented Assur group, which clearly shows the topological structure of planar mechanisms based on Assur structure theory, and non-diagonal elements describe the connection ships and the types of the connecting joints of the diagonal elements. The Assur group element is for the structural study of general planar mechanisms, and augmented Assur group element is for the structural study of planar metamorphic mechanisms. The group adjacent matrix provides a new systematic way of structural synthesis of planar mechanisms, especially for the computer-aided structure synthesis based on Assur structure theory. Examples show that the matrix is efficient and practical.

Key words: Assur group element, Group adjacent matrix, Structural synthesis, Topological representation