Design and Control of Finite Conformational Changes in Mechanical Networks*

Conformational changes in physical networks play a crucial role in many systems, enabling error correction in DNA replication, cooperativity in hemoglobin, and mechanical capacities in metamaterials. Important work has begun to delineate the relationship between network structure and instantaneous conformational change. However, these efforts have failed to address finite conformations, which are critical for the successful function of most physical networks. Here we establish a simple framework for the design and control of mechanical spring networks in 2 and 3 dimensions. Specifically, for a set of nodes with arbitrarily specified initial and final positions, we characterize all bipartite networks with zero energy at these positions, demonstrate transitions between these positions, and design multi-stable networks for information storage. Finally, we use hysteresis and bi-stability to design networks demonstrating cooperativity.