Designing novel structures with hierarchically synchronized deformations

In this paper, we propose a general mechanism to realize a uniform global motion of an n-level hierarchical structure constructed by base components of various shapes, which has only n degrees of freedom. The uniform global motion of the components at the same level of hierarchy is synchronized and independent of movements at other levels. The significantly reduced number of degrees of freedom is achieved by introducing a parallelogram linkage loop to the structure while the hierarchy is obtained from the similarity between the structure and its representative components at different levels. Theoretical analysis reveals the kinematic equations that govern the expansion and retraction of the deployable devices. Numerical simulation and physical prototyping verify the theoretical prediction. This study paves a way towards designing deployable and easily controllable devices and structures for many applications in aeronautics, electronics, optics, and MEMS.