Computation of kinematic paths and bifurcation points

This article deals with the kinematic simulation of movable structures that go through special configurations of kinematic bifurcation, 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 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 entire process is inextensional, but a detailed study of the simulation results shows that in more general cases, it is likely that stretching or wrinkling will occur.