Kinematic Analysis of Planar Deployable Structures with Angulated Beams Based on Equilibrium Matrix

摘要

This paper mainly deals with the kinematics of those widely used planar deployable structures, which are formed by angulated beams connected at with pivots. The equilibrium matrix method, which is quite different from displacement based methods, has been used to study their kinematic properties and as the basis for numerical simulations of the deployment movements. Two typical angulated beams, i.e. the depth multi-angulated beam (DMAB) and the breadth multi-angulated beam (BMAB), are explained and the corresponding equilibrium matrices deduced using matrix reduction theory, in addition, for these macro elements, the nature of the relationships between the equilibrium matrix and the stiffness matrix is discussed. Kinematic properties, e.g. infinitesimal movements and self-stress modes etc., have been studied and interpreted based on the orthogonal subspace of the equilibrium matrix. In this paper, an algorithm based on the equilibrium matrix SVD adopting an incremental procedure is described and applied to the motion analysis of deployable structures. Some typical numerical examples are illustrated to demonstrate the validity and efficiency of the proposed method.