| Popis: |
From enzyme binding to robot grasping, the function of many mechanical systems depends upon large, coordinated motions of their components. Such motions arise from a network of physical interactions in the form of links (edges) that transmit forces between constituent elements (nodes) and have been fruitfully modeled in known networks. However, the principled design of precise motions in novel networks is made difficult by the number and nonlinearity of interactions. Here, we formulate a simple but powerful framework for designing fully nonlinear motions using concepts from dynamical systems theory. We demonstrate that a small network unit acts as a one-dimensional map between the distances across pairs of nodes, and we represent the act of combining units as an iteration of this map. By tying the map’s attractors and their stability to the shape and folding sequence in a network of combined units, we program the precise coordinated motion between arbitrarily complex macroscopic shapes, the exact folding sequence between the shapes, and exotic network behaviors such as a mechanical and gate and a period-doubling route to chaos. Further, we construct a unit with a 3-cycle that combines to form a lattice with any positive integer period as a result of Sharkovskii’s theorem. Finally, we construct physical networks and analyze the effect of bond elasticity to demonstrate the framework’s potential and versatility. The precise design of shape change and folding sequence makes this framework ideal as a starting minimal model for many applications, such as robotics, providing a promising direction for future work in metamaterials. |
