Explicit kinematic equations for degree-4 rigid origami vertices, Euclidean and non-Euclidean

We derive algebraic equations for the folding angle relationships in completely general degree-4 rigid-foldable origami vertices, including both Euclidean (developable) and non-Euclidean cases. These equations in turn lead to elegant equations for the general developable degree-4 case. We compare our equations to previous results in the literature and provide two examples of how the equations can be used: in analyzing a family of square twist pouches with discrete configuration spaces, and for proving that a folding table design made with hyperbolic vertices has a single folding mode

A Review of Cooperative Actuator and Sensor Systems Based on Dielectric Elastomer Transducers

This paper presents an overview of cooperative actuator and sensor systems based on dielectric elastomer (DE) transducers. A DE consists of a flexible capacitor made of a thin layer of soft dielectric material (e.g., acrylic, silicone) surrounded with a compliant electrode, which is able to work as an actuator or as a sensor. Features such as large deformation, high compliance, flexibility, energy efficiency, lightweight, self-sensing, and low cost make DE technology particularly attractive for the realization of mechatronic systems that are capable of performance not achievable with alternative technologies. If several DEs are arranged in an array-like configuration, new concepts of cooperative actuator/sensor systems can be enabled, in which novel applications and features are made possible by the synergistic operations among nearby elements. The goal of this paper is to review recent advances in the area of cooperative DE systems technology. After summarizing the basic operating principle of DE transducers, several applications of cooperative DE actuators and sensors from the recent literature are discussed, ranging from haptic interfaces and bio-inspired robots to micro-scale devices and tactile sensors. Finally, challenges and perspectives for the future development of cooperative DE systems are discussed

The grammar of developable double corrugations (for formal architectural applications)

This paper investigates the geometrical basis of regular corrugations, with specific emphasis on Developable Double Corrugations (DDCs), which form a unique sub-branch of Origami Folding and Creasing Algorithms. The aim of the exercise is three fold – (1) To define and isolate a ‘single smallest starting block’ for a given set of distinct and divergent DDC patterns, such that this starting block becomes the generator of all DDCs when different generative rules are applied to it. (2) To delineate those generic parameters and generative rules which would apply to the starting block, such that different DDCs are created as a result (3) To use the knowledge from points (1) and (2) to create a complete family of architectural forms and shapes using DDCs. For this purpose, a matrix of 12 underlying geometry types are identified and used as archetypes. The objective is to mathematically explore DDCs for architectural form finding, using physical folding as a primary algorithmic tool. Some DDCs have more degrees of freedom than others and can fit varied geometries, while others cannot. The discussion and conclusions involve - (a) identifying why certain DDCs are ideal for certain forms and not others, when all of them are generated using the same/or similar starting block(s), (b) discussing the critical significance of flat-foldability in this specific context and (c) what we can do with this knowledge of DDCs in the field of architectural research and practice in the future

Transformers for Lunar Extreme Environments: Ensuring Long-Term Operations in Regions of Darkness and Low Temperatures

This report shows how solar power could enable robotic operations in permanently shaded regions at lunar poles, to extract water ice and further produce liquid hydrogen and oxygen (LH2/LO2) propellant. The power needs are derived from an Architecture for Human Exploration of Mars based entirely on lunar propellant. The extraction of 10 metric tons of water per day (at 10% water in regolith) requires approx. 0.6 MW thermal power. Additional approx. 2 MW electric power are required to produce 7.5 metric tons of LH2/LO2 propellant per day, as needed by the architecture. To provide power to processing equipment inside Shackleton Crater, optimal locations are determined on the crater rim, from which several reflecting TransFormers (TFs) would redirect sunlight, achieving a combined period of illumination of approx. 99% of the year. A single 40-m diameter reflector could provide up to 1 MW solar power. Inflatable rigidizable tower support structures raise reflectors above ground for better solar exposure. There are trade-offs: e.g., two reflectors at ground level would provide the same combined total illumination as a single tower approx. 100-m tall. Such a TF based on a 100-m tower made with inflatable 2-m beams and 40-m diameter reflectors would be of similar dimensions as an MSL-class rover (approx. 1000 kg, 10 m(exp 3)). A TF-prospector rover combo could be designed and deployed in a Discovery-class mission searching for water. The TransFormers would be nodes of a Lunar Utilities Infrastructure that provides solar power year-round in the proximity of the pole, as well as local data transmission andintermittent direct to earth communications. This infrastructure would be instrumental infacilitating the development of a lunar economy

Structural Systems Inspired by the Architecture of Skeletal Muscle

Modern engineering applications call for structural and material systems that exhibit advanced performance. To achieve this performance, researchers often look to nature for inspiration. Skeletal muscle is a multifunctional system with remarkable versatility and robustness, offering a great example on how to effectively store, convert, and release energy for force generation and shape change. To date, most efforts seeking to emulate muscle have focused on its bulk characteristics. However, it has recently been shown that many of muscle’s advantageous properties arise from the assembly and geometry of its microscale constituents. This dissertation will aim to develop new concepts for structural and material systems inspired by a fundamental understanding of the assembly of muscle’s constituent elements into contractile units. This is achieved by exploiting two key ingredients expressed by these constituents: metastability, which is the existence of multiple stable conformations for a prescribed global geometry, and ¬¬local conformation changes to switch between these stable topologies. Rather than faithfully emulating or seeking to explain the complex chemo-mechanical processes that govern muscle contraction, the major contributions of this thesis arise from the exploitation of the aforementioned key features within the context of engineered structures and materials systems. First, a fundamental metastable unit is studied under harmonic excitation. Experimental, numerical, and analytical investigations uncover the coexistence of multiple response regimes with significantly different amplitudes. These distinct regimes are exploited to achieve highly adaptable energy dissipation characteristics that vary by up to two orders of magnitude among them, even as excitation parameters are held constant. On the other hand, introducing asymmetry by varying a static bias parameter allows for smooth, finer variation of energy dissipation performance. Then, inspired by the ability of the myofibril lattice in skeletal muscle to trap strain energy that can be released on-demand, this thesis explores structural systems that leverage asymmetric multistability for energy capture and storage. The initial kinetic energy from impulsive excitation is shown to trigger state transitions that result in the capture of recoverable strain energy in higher-potential states. Reverse transitions to lower-energy states exploit this stored energy to facilitate efficient deployment and length change in the structure. Lastly, the effect of myofibril lattice spacing in skeletal muscle, and shear-like motions of adjacent filaments during contraction, serves as inspiration for the development of an architected modular material system that uses transverse confinements in conjunction with oblique, shear-like motions to give rise to sudden state transitions. Numerical results provide insight into the experimentally-observed behaviors, revealing that these energy-releasing transitions correspond to discrete changes in reaction force magnitude and direction Mechanical response properties can be tailored by strategic variation of transverse confinement and system geometry. Analytical tools using relatively simple models are developed to offer meaningful prediction of the above features. The overall outcomes of this thesis reveal great potential to develop high-performance, versatile, and adaptable structural and material systems by exploiting fundamental features of skeletal muscle architecture.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/145893/1/kidambi_1.pd

Folding Photopolymerized Origami Sheets by Post-Curing

Origami,which is generally fabricated from one single sheet of paper by sequential folding, has enjoyed a high popularity during the past centuries. Because of the deployability and ability to reconfigure its shape, it is a promising structural design technique that is utilized in biomedical and aerospace engineering. The purpose of this paper is to present a novel manufacturing approach to fabricate origami based on 3D printing utilizing digital light processing. Specifically, it is proposed to leave part of the model uncured during the printing step, and then cure it in the post-processing shape-setting step in the folded configuration. While the cured regions in the first step try to regain their unfolded shape, the regions cured in the second step try to keep their folded shape. As a result, the final shape will be obtained when both regions stresses reach equilibrium. Finite element Analysis is performed in ANSYS to obtain the stress distribution on common hinge designs. This proves that the square-hinge has a lower maximum principal stress compared with elliptical and triangle hinges. Based on the square-hinge and rectangular cavity two variables, the width of the hinge and height of the cavity, are selected as principal variables to construct relationships between the two parameters and final folding angle. In the end, experimental verification show that the developed method is valid and reliable to realize the proposed deformation and 3D development of 2D hinges

Applied Mathematics to Mechanisms and Machines

This book brings together all 16 articles published in the Special Issue "Applied Mathematics to Mechanisms and Machines" of the MDPI Mathematics journal, in the section “Engineering Mathematics”. The subject matter covered by these works is varied, but they all have mechanisms as the object of study and mathematics as the basis of the methodology used. In fact, the synthesis, design and optimization of mechanisms, robotics, automotives, maintenance 4.0, machine vibrations, control, biomechanics and medical devices are among the topics covered in this book. This volume may be of interest to all who work in the field of mechanism and machine science and we hope that it will contribute to the development of both mechanical engineering and applied mathematics

Folding Photopolymerized Origami Sheets by Post-Curing

Origami,which is generally fabricated from one single sheet of paper by sequential folding, has enjoyed a high popularity during the past centuries. Because of the deployability and ability to reconfigure its shape, it is a promising structural design technique that is utilized in biomedical and aerospace engineering. The purpose of this paper is to present a novel manufacturing approach to fabricate origami based on 3D printing utilizing digital light processing. Specifically, it is proposed to leave part of the model uncured during the printing step, and then cure it in the post-processing shape-setting step in the folded configuration. While the cured regions in the first step try to regain their unfolded shape, the regions cured in the second step try to keep their folded shape. As a result, the final shape will be obtained when both regions stresses reach equilibrium. Finite element Analysis is performed in ANSYS to obtain the stress distribution on common hinge designs. This proves that the square-hinge has a lower maximum principal stress compared with elliptical and triangle hinges. Based on the square-hinge and rectangular cavity two variables, the width of the hinge and height of the cavity, are selected as principal variables to construct relationships between the two parameters and final folding angle. In the end, experimental verification show that the developed method is valid and reliable to realize the proposed deformation and 3D development of 2D hinges