Designing mechanical metamaterials is overwhelming for most computational approaches because of the staggering number and complexity of flexible elements that constitute their architecture—particularly if these elements don’t repeat in periodic patterns or collectively occupy irregular bulk shapes. We introduce an approach, inspired by the freedom and constraint topologies (FACT) methodology, that leverages simplified assumptions to enable the design of such materials with ~6 orders of magnitude greater computational efficiency than other approaches (e.g., topology optimization). Metamaterials designed using this approach are called directionally compliant metamaterials (DCMs) because they manifest prescribed compliant directions while possessing high stiffness in all other directions. Since their compliant directions are governed by both macroscale shape and microscale architecture, DCMs can be engineered with the necessary design freedom to facilitate arbitrary form and unprecedented anisotropy. Thus, DCMs show promise as irregularly shaped flexure bearings, compliant prosthetics, morphing structures, and soft robots.

With the implementation of just one mechanism, variable topology mechanisms can serve the functions of many mechanisms by changing their topology. These types of mechanisms have raised interest and attracted numerous studies in recent years, yet few of these studies have focused discussing of these mechanisms in light of their operation space. As the change of a variable topology mechanism is induced by either intrinsic constraints or constraints due to the change of joint geometry profile, the operation space of kinematic joints and kinematic chains in various working stages is changed in accordance. A theoretic framework based on the concept of the operation space of variable topology mechanisms is presented here. A number of characteristics with regard to the motion compatibility among joints and loops in different working stages are derived, laying a foundation for systematical synthesis of variable topology mechanisms. Design of a novel latch mechanism for the standardized mechanical interface system is given as an illustrative example for the synthesis of a variable topology mechanism.

This paper introduces a general method for analyzing flexure systems of any configuration, including those that cannot be broken into parallel and serial subsystems. Such flexure systems are called interconnected hybrid flexure systems because they possess limbs with intermediate bodies that are connected by flexure systems or elements. Specifically, the method introduced utilizes screw algebra and graph theory to help designers determine the freedom spaces (i.e., the geometric shapes that represent all the ways a body is permitted to move) for all the bodies joined together by compliant flexure elements within interconnected hybrid flexure systems (i.e., perform mobility analysis of general flexure systems). This method also allows designers to determine (i) whether such systems are under-constrained or not and (ii) whether such systems are over-constrained or exactly constrained (i.e., perform constraint analysis of general flexure systems). Although many flexure-based precision motion stages, compliant mechanisms, and microarchitectured materials possess topologies that are highly interconnected, the theory for performing the mobility and constraint analysis of such interconnected flexure systems using traditional screw theory does not currently exist. The theory introduced here lays the foundation for an automated tool that can rapidly generate the freedom spaces of every rigid body within a general flexure system without having to perform traditional computationally expensive finite element analysis. Case studies are provided to demonstrate the utility of the proposed theory.

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Unconventional computing, such as mechanical1 and microfluidic logic circuits2, quantum gates3, and mechanical metamaterials4 create opportunities for embedded computation, which overcome the power5, package size, and environmental limitations of conventional electronics. Emerging micro-manufacturing capabilities6 with environmentally robust materials enable mechanical logic circuits miniaturization. Kinematically, bistable logic propagates binary signals through cascading gate displacement transitions. Energetically, the inter- and intra- node compliances are tuned for re-programmable signal propagation. Applications need computational architectures which integrate resettable signal propagation7–10, logical operation11–16, and signal storage17–19. While many researchers explore aspects of these elements1, 20–23, none consider energetic limits and propagation dynamics to evaluate and advance the field. Here, we show a generalized model and metrics, validated by experimental results, that enables the design of scale-independent, resettable, mechanical logic circuits. By studying propagation energy flows, we identified non-dimensional operating regimes in which signals propagate and resettable logic is possible. We provide deterministic design methods to evaluate future divergent topologies for displacement-based mechanical logic structures. Our results demonstrate the framework for designing densely integrated mechanical computation systems which harvest available ambient energy to propagate computational cascades. This logic responds to multi-dimensional environmental inputs and thus enables re-programmable, powerless, and embedded computation.