Abstract: Planar multi-angulated beams are commonly used in retractable structures. They are generated based on planar beam. The inner degree-of-freedoms (DOFs) of these macro-elements are packaged, and the equilibrium matrices are deduced by matrix reduction theory. The global equilibrium matrix is assembled by element equilibrium matrix. The characteristics of structural and kinematic properties, e.g. modes of independent states of self-stress and inextensional mechanisms, minimum non-zero singular values, etc., are achieved by equilibrium matrix SVD(Singular Value Decomposition). The kinematic properties and mobility condition of retractable structures are analyzed. Then the geometrically nonlinear force method is introduced, and two kinds of trajectory tracking simulation methods, i.e. active and positive control, are proposed and the corresponding algorithm procedures are listed. Based on the equilibrium matrix analysis method this paper discussed, the topology of two types of circular radially retractable structure is found numerically. The trajectory tracking simulations of retractable structures are also illustrated.