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.

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.

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.

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.

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.