Architected Mechanologics and Design Rules for Integrated Mechanical Computing

Mechanical computing is an unconventional domain of computation where computational operations are made solely by mechanical components and mechanisms. Recent studies in this direction harness built-in material responsiveness and structural intelligence to achieve seamless, monolithic integration between the computing process and input/output agents that can be directly coupled to surrounding environments. Specifically, digital abstractions of mechanical information (i.e., mechanical bits) have been realized by multistable configurations of mechanical elements that are able to change their shapes along with origami kinematics and/or nonlinear buckling dynamics of thin soft beams or shells. Pioneering studies have further demonstrated that architected design and engineered assembly of the multistable elements can accomplish stable transmission of elastic waves, mathematical computations, programmable metamaterials, and robotic mechanisms, all of which form the basis of mechanical computing. Despite these achievements, however, an understanding of mechanical computing has still been limited to the implementation of standalone computing units or mechanical transition waves lacking the rational design for deterministic computational functions.<br/> In this work, we introduce a basic design principle of soft bistable beams with engineered potential energy profiles, and show how the strategic topological assembly of these engineered bistable elements can form into a monolithic computational platform in which nondispersive elastic solitary waves autonomously propagate with deterministic computational functions. Drawing inspiration from a mature design architecture of conventional electrical computing systems, we first postulate the design and functional requirements for integrated mechanical computing as follows: (i) stable transmission of mechanical signals without loss of information, (ii) a complete set of functional computing units with form factors matched with the transmission line, and (iii) lossless, computational cascades of mechanical signals through multiple computing units. The designs of transmission line units and mechanologics are physically implemented by topological assemblies of bistable building blocks into a unit square lattice frame. The resulting lattice-unit connection between fundamental mechanical components (i.e., transmission line units and mechanologics) allows us to investigate propagation behaviors of mechanical signals not only through a homogeneous elastic medium (transmission line), but also through a medium containing a computing unit with structural heterogeneity. Based on an extensive set of experimental and numerical studies on the proposed mechanical system, we generalize a design rule for computational propagation of mechanical signals through networked computing units, and implement this decisive principle in realizing integrated mechanical computing. Proof-of-concept demonstrations of Mimosa plant-inspired soft machines show how the developed integrated mechanical computing can direct mechanical instructions across environmental inputs, computational operations and actuator modules in a seamless and monolithic form.<br/> J.B. and A.P. thank the Alexander von Humboldt Foundation for financial support. This work was supported by the Max Planck Soiety and European Research Council (ERC) Advanced Grant SoMMoR project with grant No. 834531, and by the Korea Institute of Science and Technology (KIST) Future Resource Research Program.