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From the complex motions of robots to the oxygen binding of hemoglobin, thefunction of many mechanical systems depends on large, coordinated movements oftheir components. Such movements arise from a network of physical interactionsin the form of links that transmit forces between constituent elements.However, the principled design of specific movements is made difficult by thenumber and nonlinearity of interactions. Here, we model mechanical systems aslinkages of rigid bonds (edges) connected by joints (nodes), and formulate asimple but powerful framework for designing full nonlinear coordinated motionsusing concepts from dynamical systems theory. We begin with principles fordesigning finite and infinitesimal motions in small modules, and show that eachmodule is a one-dimensional map between distances across pairs of nodes. Next,we represent the act of combining modules as an iteration of this map, anddesign networks whose geometries reflect the map's fixed points, limit cycles,and chaos. We use this representation to design different folding sequencesfrom a deployable network and a soliton, to a branched network acting as amechanical AND gate. Finally, we design large changes in curvature of theentire network, and construct physical networks from laser-cut acrylic,origami, and 3D printed material to demonstrate the framework's potential andversatility for designing the full conformational trajectory of morphingmetamaterials and structures.

Design of Large Sequential Conformational Change in Mechanical Networks