KINEMATIC BIFURCATIONS IN THE SIMULATION OF DEPLOYABLE STRUCTURES

Abstract. This paper deals with the kinematic simulation of deployable structures that go through bifurcation points as they move. A series of algorithms are developed for structures that can be modelled using pin-jointed bars and that admit a single-parameter motion. These algorithms are able to detect and locate any bifurcation points that exist along the path of the structure and, at each bifurcation point, can determine all possible motions of the structure. The theory behind the various algorithms is explained and the analysis of a simple example is discussed in detail. Then, a simplified version of the particular problem that had motivated this work, the simulation of the folding and deployment of a thin membrane structure forming a solar sail, is analysed. For the particular cases that are considered it is found that the deployment process is inextensional, but a detailed study of the simulation results show that in more general cases it is likely that stretching or wrinkling will occur. Praveen Kumar and Sergio Pellegrino 1 Background and introduction The work described in this paper originates from a series of difficulties that had been encountered in using standard algorithms to simulate the motion of deployable structures. A particular proble