Mechanical metamaterials are architected structures designed to exhibit unconventional mechanical responses. Their engineered properties make them especially valuable for realizing precise motion and load-bearing functions, with broad applications in machines, robotics, and related technologies. Straight-line mechanisms, typically based on compliant or rigid designs, offer compactness and accuracy but are often limited by parasitic motion, restricted range of motion, and load-capacity constraints. In this work, we introduce the concept of shear cell, develop a suitable embodiment, and demonstrate how a planar straight-line metamaterial mechanism approximates its behavior. Both series and parallel tessellations of a rectangular shear cell are investigated, considering full and partial scaling strategies. Through analytical modeling, finite element simulations, and experimental validation, we examine how tessellation influences key performance parameters, including range of motion, stiffness, and crosstalk. Finally, the concept is extended to demonstrate the design of planar multi-degrees-of-freedom mechanisms and spatial straight-line metamaterial motion systems.

Poisson’s ratio metamaterials exhibit unconventional deformation behaviors enabled by architected internal geometries. While numerous planar auxetic and related designs have been reported, the systematic generation and classification of spatial Poisson’s ratio metamaterials remains limited. In this work, we introduce the Spatial Poisson’s Ratio Design Method (SPRDM), a unified geometric framework that extends a previously established planar design approach to three-dimensional architectures. The SPRDM is built on two minimal kinematic bases, a planar and a spatial chiral structure and eight symmetry-based topological transformations that enable controlled manipulation of dimensionality and chirality. The method systematically generates 1.5D, 2D, 2.5D, and 3D metamaterial families, reproducing known auxetic, anepirretic, and meiotic architectures as well as enabling the design of previously unreported spatial and superchiral structures. A consistent classification scheme and naming protocol are introduced to organize the resulting design space, together with a unit-cell construction strategy supporting planar tessellations and three-dimensional honeycombs. Representative examples demonstrate the versatility of the method, including spatial auxetic and anepirretic architectures with tunable deformation mechanisms. Volume strain is employed as a general metric to characterize compressibility beyond directional Poisson’s ratios. The SPRDM provides a systematic foundation for the design of spatial Poisson’s ratio metamaterials with broad relevance to architected materials research.

Conventional fingered grippers often struggle in confined spaces because limited lateral access prevents finger insertion and inward closing. This letter presents the DBCF-EM gripper, whose fingers combine a base-driven curved flexure, prescribing a tangential object-following trajectory, with a dual-belt eversion system that creates near-stationary contact surfaces and reduces sliding at the contact interfaces. This enables a low-disturbance caging grasp strategy in which the fingers propagate along the object surface rather than closing perpendicularly toward it. A prototype gripper was built for robotic tomato-removal experiments from a crate. Experiments showed contour following with a maximum deviation of 3 mm, negligible normal disturbance of at most 0.1 N, and a 91–97% reduction in tangential disturbance forces. In robotic trials, the gripper achieved 100% pick-up success and a 91% damage-free success rate, demonstrating its effectiveness for confined-space grasping.

In this study, a promising design for a compact compliant torsion-reinforced Sarrus mechanism (CORS) capable of achieving ultralinear motion is presented. The CORS prototype, made entirely of aluminum, is produced monolithically using electric discharge machining (EDM). The design incorporates four torsion-reinforced folded leaf springs that together function as a flexural mechanism. This design effectively reduces parasitic motion while improving support stiffness. To meet the specified requirements, a design optimization process is undertaken, carefully considering constraints, to attain an optimal CORS configuration. Integration of the CORS with a voice coil actuator and confocal chromatic sensors is carried out to detect parasitic motion. Experimental validation demonstrates that the CORS outperforms existing designs in terms of build volume, manufacturability, and scalability, and has parasitic translations of around 10 nm and parasitic rotations of around 5 μrad over the critical region of the range of motion.

Multistable metamaterials are architected structures capable of adopting multiple stable geometrical configurations. This unique characteristic makes them highly valuable for stiffness control, energy harvesting, and morphing technologies. As a result, multistable structures hold great potential for diverse applications across various fields. The development of multistable metamaterials primarily relies on buckled beam technology, enabling the creation of a wide range of structures. However, only a few rotational multistable designs have been explored. Additionally, the geometry of buckled beams imposes constraints on the range of motion. To overcome these limitations, our work introduces a novel design method for magnet-based rotational multistable stages. This approach, grounded in the electrostatic ideal dipole assumption, enables precise control over the angle of multistability and the stiffness of the stable states.

Meiotic metamaterials are intricately designed structures characterized by a positive Poisson's ratio, surpassing the conventional limit of 0.5 observed in natural materials. This exceptional attribute allows them to contract or expand perpendicularly to the applied stretch or compression, respectively. Structures featuring a high positive Poisson's ratio exhibit a counter-intuitive negative compressibility behavior, holding significant promise for diverse applications spanning various domains. Despite the potential of Poisson's ratio metamaterials, including auxetic, anepirretic, and meiotic structures, their recent development has been hindered by the lack of efficient design methods. This paper aims to address this limitation, concentrating on the meiotic variant of a minimal 2D auxetic structure recently proposed. We employ a design method incorporating two topological transformations, not only enabling the creation of known meiotic structures but also facilitating the generation of new ones while understanding the impact of chirality. Additionally, the proposed method enables the categorization of these structures into three achiral families that present meiotic behavior and can exhibit negative linear compressibility and three chiral families that possess an auxetic behavior. Only the base chiral structure was found to exhibit a meiotic behavior while being chiral. In an effort to enhance comprehension and standardization, we introduce a naming protocol and define the associated unit cell for these structures. We also delve into the potential of tessellations within this framework. Finally, our study examines meiotic structures from the perspective of surface strain, a more general metrics, linked to the compressibility, providing further insights into their unique mechanical properties.

Auxetic metamaterials are architected structures that possess a unique property known as a negative Poisson's ratio. This remarkable characteristic enables them to expand or contract in a direction perpendicular to stretch or compression. Due to their exceptional attributes such as energy absorption and fracture resistance, these auxetic metamaterials hold great promise for various applications across multiple domains. However, the widespread development of these materials has been hindered by the absence of an efficient design method. Addressing this limitation, our work introduces a minimal 2D auxetic structure and a corresponding design approach that comprises two geometric transformations. This design method not only allows for the replication of existing auxetic structures but also facilitates the creation of novel structures. Additionally, it enables the classification of these structures into six distinct categories. To enhance the understanding and standardization of these structures, we propose a naming protocol and define their associated unit cell. Furthermore, we explore the possibilities of tessellations within this framework. Finally, we examine the auxetic structures from the perspective of surface strain, which is closely linked to the Poisson's ratio, the Bulk modulus and compressibility.

Compliant mechanisms have the potential to be utilized in numerous applications where the use of conventional mechanisms is unfeasible. These mechanisms have inherent stiffness in their range of motion as they gain their mobility from elastic deformations of elements. In most systems, however, complete control over the elasticity is desired. Therefore, compliant mechanisms with variable, including zero, stiffness can have a great advantage. We present a novel concept based on the prestressing of open thin-walled multi-symmetric beams. It is demonstrated that by changing the prestress on the center-axis of these beams, a range of variable torsional stiffness can be achieved. For beams with a large warping constant, the stiffness changes from positive to zero and negative as the prestress increases, while for beams with a near-zero warping constant, the range of neutrally stable twisting motion increases. A planar equivalent is shown in this work to elucidate the notion, and numerical and experimental analyses are performed to validate the prestress-related behavior.

Compliant mechanisms (CMs), along with soft robotics devices formed therewith, may be defined as engineering systems achieving force and motion transmission via the deflection of flexible members. CMs have increasingly gained a strong foothold in the scientific arena owing to their hinge-less nature, shock resistance, potential single-piece manufacturability, safety in human–machine interaction, minimal maintenance requirements, and adaptability to work in unstructured environments. In parallel, current advances in the production of inherently compliant sensory-motor apparatus, as well as progresses in the development of robust control methods, are paving the way to practical CM adoption in a large variety of engineering fields, here including healthcare, manufacturing, inspection/maintenance, and agrifood.

Current design methods for flexure (or compliant) mechanisms regard stress as a secondary, limiting factor. This is remarkable because stress is also known as a useful design parameter. In this paper we propose the Stress And Geometry (STAGE) method, to design the geometry of a flexure mechanism together with a desired stress field. From this design, the stress-free to-be-fabricated geometry is computed using the inverse finite element method. To demonstrate the potential of the method, the geometry of the well-known crossed-flexure pivot is taken as example. We first show how this mechanism can be redesigned for the same functional geometry with various internal stresses. This results for a specific choice of stress field in a design of a crossed-flexure pivot with 23% lower peak stresses during motion as compared to the known designs, for a ±45° rotation. We then present a second example, of a Folded Leaf Spring (FLS). With a parameter sweep the optimal stress field is calculated, showing a peak stress reduction of 28% during motion. This result was validated with an experiment, showing a normalized mean absolute error of 5.5% between experiment and theory. With a second experiment it was verified that the functional geometry of the FLS with internal stresses was equal to the one without internal stresses, with geometric deviations smaller than half the thickness of the flexures.

A cantilevered rod's endpoint has a symmetric stiffness profile throughout its range of motion. Generally, this is not the case for spatially curved compliant beams, particularly if they are asymmetric, i.e., their fixation is not in the symmetry plane of their endpoint operating field. This paper discusses a technique for obtaining symmetric kinetostatic behavior from this type of asymmetric compliant beam over a relatively large range of motion. To accomplish this, a parametrization scheme was used to base the geometry of the beam on a limited number of control parameters. These parameters were then used as inputs for optimization in order to create beams with symmetric endpoint behavior. This process was further investigated using different sets of parameters. To validate the method's performance, experiments on prototypes were conducted. The results demonstrated a high degree of congruence with simulations of the anticipated behavior. Comparing to the non-optimized benchmark beam, the experimental performance of the resulting shapes demonstrated up to a 68% improvement in the desired symmetric behavior.

The ability to convert reciprocating, i.e., alternating, actuation into rotary motion using linkages is hindered fundamentally by their poor torque transmission capability around kinematic singularity configurations. Here, we harness the elastic potential energy of a linear spring attached to the coupler link of four-bar mechanisms to manipulate force transmission around the kinematic singularities. We developed a theoretical model to explore the parameter space for proper force transmission in slider-crank and rocker-crank four-bar kinematics. Finally, we verified the proposed model and methodology by building and testing a macro-scale prototype of a slider-crank mechanism. We expect this approach to enable the development of small-scale rotary engines and robotic devices with closed kinematic chains dealing with serial kinematic singularities, such as linkages and parallel manipulators.

Continuously Variable Transmissions (CVT) can serve as subsystems for a variety of machineries and robotic systems. A compliant CVT mechanism based on the warping of twisting beams is presented here. The design works based on the demonstrated fact that the twist on one side of a beam can be transferred via sectional warping and propagate across a rotational constraint in the middle of the beam to create a reverse twist on the opposite side. In the proposed compliant CVT the transmission ratio is dependent on the position of the middle rotational constraint which can vary in a continuous range. We have demonstrated this concept and its relation to the twisting beam's warping constant, as well as its functionality for different transmission ratios of 1:4 to 4:1. An analytical model as well as a Finite Element Analysis (FEA) and experiments are employed to characterize and verify the concept and its relation to the warping constant.

The usually high eigenfrequencies of miniaturized oscillators can be significantly lowered by reducing the stiffness through stiffness compensation. In this work, a mechanical design for a compliant ortho-planar mechanism is proposed in which the stiffness is compensated to such a degree that it can be identified as statically balanced. The mechanism was fabricated using laser micro-machining and subsequently preloaded through packaging. The statically balanced property of the mechanism was experimentally validated by a measurement of the force-deflection relation. A piezoelectric version of the design was fabricated for the purpose of energy harvesting from low-frequency motion. For a sub 1 Hz excitation, the device demonstrated an average power output of 21.7 μW and an efficiency that compares favorably to piezoelectric energy harvesters reported in the literature. Therefore, it was found that stiffness compensation is a promising method for the design of piezoelectric energy harvesters for low-frequency motions.

Compliant mechanisms (CM) with adaptive stiffness have been widely used in robotics and machine design applications. This paper proposes adapting the endpoint stiffness of a spatially curved compliant beam using a movable torsional stiffener and a new graphical characterization method for the resulting anisotropic stiffness of the endpoint for large deflections. A slender clamped-free cruciform beam with a predetermined spatial shape was utilized as the main compliant part, and a shorter sliding bellow was served as the torsional stiffener. The beam's endpoint displacements are mainly determined by its bending and torsional deformations. Therefore, the relocation of a bellow stiffener with high torsion and low bending stiffness along the described beam with relatively low torsion and high bending stiffness led to notable changes in the kinetostatic behavior at the endpoint. The share of bending and torsional stiffness of elements along the beam to endpoint stiffness varies depending on the direction. Experiments with arbitrarily chosen parameters of the current design reveal an anisotropically adaptive stiffness with 21.5 times more stiffness variations in one direction compared to the other. Effective characteristics for this behavior, such as the length and position of the bellow, were explored in an effort to improve it. To capture the effect of these parameters, the Isoforce Displacement Closed Surface (IDCS) was introduced as a new characterization method to visualize the nonlinear kinetostatic behavior of a CM throughout its three-dimensional range of motion. The IDCS was further used to elucidate how individual components of the current mechanism contribute to the system's overall kinetostatic behavior. Experiments were done on prototypes to confirm the changes in endpoint stiffness that were predicted by simulations.

In this study, a flexure-based (compliant) linear guide with a motion range comparable to its footprint is presented. The design consists of two-folded leaf springs on which torsion reinforcement structures are added. Due to these structures, only two-folded leaf springs are needed instead of a minimum of five as in preexisting designs. The new design is compared to such a preexisting design, after optimizing both on a support stiffness metric. The new design scores over twice as high on the support stiffness metric, while occupying a smaller (-33%) and a less obstructive build volume. Stress, build volume, and manufacturing limitations are taken into account. In addition, a variation on the new design using three torsion reinforced folded leaf springs is presented and optimized. This design occupies a build volume similar to the preexisting design, but scores four times higher on the support stiffness metric. A prototype of the new design is built and its parasitic eigenfrequencies are measured, validating the theoretical models (normalized mean absolute error of 4.3%).

Passive shoulder supports show large potential for a wide range of applications, such as assisting activities of daily living and supporting work-related tasks. The rigid-link architecture used in currently available devices, however, may pose an obstacle to finding designs that offer low protrusion and close-to-body alignment. This study explores the use of mechanisms that employ a flexible element which connects the supported arm to an attachment at the back and acts as energy storage, transmission and part of the load bearing structure. Based on the synthesis method explained in this paper, a large scope investigation into possible flexure-based mechanism topologies is conducted. Thereby, many potential designs are discovered, which are presented, categorized and compared. Two promising designs are developed into prototypes, and are built and tested on a dedicated test bench. These two mechanisms reduce the necessary moment to lift the arm by more than 80 % throughout 85 % of the range of motion, while staying within 18 cm and 10 cm distance from the body, respectively. The study indicates that, due to its lower protrusion and interface loads, a design with a tapered flexure connecting the upper arm via a hinge to a spring-loaded slider at the back offers the most promising solution.