Geometry and design of origami bellows with tunable response

Untethered bistable origami crawler for confined applications

Magnetically actuated miniature origami crawlers are capable of robust locomotion in confined environments but are limited to passive functionalities. Here, we propose a bistable origami crawler that can shape-morph to access two separate regimes of folding degrees of freedom that are separated by an energy barrier. Using the modified bistable V-fold origami crease pattern as the fundamental unit of the crawler, we incorporated internal permanent magnets to enable untethered shape-morphing. By modulating the orientation of the external magnetic field, the crawler can reconfigure between an undeployed locomotion state and a deployed load-bearing state. In the undeployed state, the crawler can deform to enable out-of-plane crawling for robust bi-directional locomotion and navigation in confined environments based on friction anisotropy. In the deployed state, the crawler can execute microneedle insertion in confined environments. Through this work, we demonstrated the advantage of incorporating bistability into origami mechanisms to expand their capabilities in space-constraint applications.

4D printed origami-inspired accordion, Kresling and Yoshimura tubes

Applying tessellated origami patterns to the design of mechanical materials can enhance properties such as strength-to-weight ratio and impact absorption ability. Another advantage is the predictability of the deformation mechanics since origami materials typically deform through the folding and unfolding of their creases. This work focuses on creating 4D printed flexible tubular origami based on three different origami patterns: the accordion, the Kresling and the Yoshimura origami patterns, fabricated with a flexible polylactic acid (PLA) filament with heat-activated shape memory effect. The shape memory characteristics of the self-unfolding structures were then harnessed at 60°C, 75°C and 90°C. Due to differences in the folding patterns of each origami design, significant differences in behaviour were observed during shape programming and actuation. Among the three patterns, the accordion proved to be the most effective for actuation as the overall structure can be compressed following the folding crease lines. In comparison, the Kresling pattern exhibited cracking at crease locations during deformation, while the Yoshimura pattern buckled and did not fold as expected at the crease lines. To demonstrate a potential application, an accordion-patterned origami 4D printed tube for use in hand rehabilitation devices was designed and tested as a proof-of-concept prototype incorporating self-unfolding origami.

Elastic Snap-Through Instabilities Are Governed by Geometric Symmetries

Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside out. This snap through is a general motif for the storage and rapid release of elastic energy, and it is exploited by many biological and engineered systems from the Venus flytrap to mechanical metamaterials. Shape transitions are known to be related to the type of bifurcation the system undergoes, however, to date, there is no general understanding of the mechanisms that select these bifurcations. Here we analyze numerically and analytically two systems proposed in recent literature in which an elastic strip, initially in a buckled state, is driven through shape transitions by either rotating or translating its boundaries. We show that the two systems are mathematically equivalent, and identify three cases that illustrate the entire range of transitions described by previous authors. Importantly, using reduction order methods, we establish the nature of the underlying bifurcations and explain how these bifurcations can be predicted from geometric symmetries and symmetry-breaking mechanisms, thus providing universal design rules for elastic shape transitions.

Multistability, symmetry and geometric conservation in eightfold waterbomb origami

The nonlinearities inherent in the mechanics of origami make it a rich design space for multistable structures and mechanical metamaterials. Here, we investigate the multistability of a classic origami base: the symmetric eightfold waterbomb. We prove that the waterbomb is bistable for certain crease properties, and derive bounds on, and closed-form approximations of, its stable states. We introduce a simplified form of the waterbomb kinematics and present a design procedure for tuning the depth and the symmetry/asymmetry of its energy wells. By incorporating the concept of pretensioned torsional springs, we also demonstrate the existence of tristable cases for the waterbomb fold pattern. We then apply the analysis of a single waterbomb to study quasi-one-dimensional arrays of waterbombs, where we discover a conserved geometric-kinematic quantity in which the number of popped-up and popped-down vertices is determined uniquely through analysis of the origami structure’s boundaries. This culminates with a discussion of how the quasi-one-dimensional array may be designed to achieve stable states with various degeneracies, kinematics and gaps between energy levels. Collectively, this work presents an alternative approach for characterizing origami multistability properties and reveals an origami design motif that has potential applications in physically reconfigurable structures, mechanical energy absorption and metamaterials.

Evolution of the Hybrid Aerial Underwater Robotic System (HAUCS) for Aquaculture: Sensor Payload and Extension Development

While robotics have been widely used in many agricultural practices such as harvesting, seeding, cattle monitoring, etc., aquaculture farming is an important, fast-growing sector of agriculture that has not seen significant adoption of advanced technologies such as robotics and the Internet of Things (IoT). In particular, dissolved oxygen (DO) monitoring, a practice in pond aquaculture essential to the health of the fish crops, remains labor-intensive and time-consuming. The Hybrid Aerial Underwater robotiCs System (HAUCS) is an IoT framework that aims to bring transformative changes to pond aquaculture. This paper focuses on the latest development in the HAUCS mobile sensing platform and field deployment. To address some shortcomings with the current implementation, the development of a novel rigid Kirigami-based robotic extension subsystem that can expand the functionality of the HAUCS platform is also being discussed.

Untethered Origami Worm Robot with Diverse Multi-Leg Attachments and Responsive Motions under Magnetic Actuation

Nowadays, origami folding in combination with actuation mechanisms can offer deployable structure design, yield compliance, and have several properties of soft material. An easy complex folding pattern can yield an array of functionalities in actuated hinges or active spring elements. This paper presents various cylinder origami robot designs that can be untethered magnetically actuated. The different designs are analyzed and compared to achieve the following three types of motion: Peristaltic, rolling, and turning in different environments, namely, board, sandpaper, and sand. The proposed origami robot is able translate 53 mm in peristaltic motion within 20 s and is able to roll one complete cycle in 1 s and can turn ≈180∘ in 1.5 s. The robot also demonstrated a peristaltic locomotion at a speed of ≈2.5 mm s−1, ≈1.9 mm s−1, and ≈1.3 mm s−1 in board, sandpaper, and sand respectively; rolling motion at a speed of 1 cycle s−1, ≈0.66 cycles s−1, and ≈0.33 cycles s−1 in board, sandpaper, and sand respectively; and turning motion of ≈180∘, ≈83∘, and ≈58∘ in board, sandpaper, and sand respectively. The evaluation of the robotic motion and actuation is discussed in detail in this paper.

Multistable inflatable origami structures at the metre scale

From stadium covers to solar sails, we rely on deployability for the design of large-scale structures that can quickly compress to a fraction of their size^1-4. Historically, two main strategies have been used to design deployable systems. The first and most frequently used approach involves mechanisms comprising interconnected bar elements, which can synchronously expand and retract^5-7, occasionally locking in place through bistable elements^8,9. The second strategy makes use of inflatable membranes that morph into target shapes by means of a single pressure input^10-12. Neither strategy, however, can be readily used to provide an enclosed domain that is able to lock in place after deployment: the integration of a protective covering in linkage-based constructions is challenging and pneumatic systems require a constant applied pressure to keep their expanded shape^13-15. Here we draw inspiration from origami-the Japanese art of paper folding-to design rigid-walled deployable structures that are multistable and inflatable. Guided by geometric analyses and experiments, we create a library of bistable origami shapes that can be deployed through a single fluidic pressure input. We then combine these units to build functional structures at the metre scale, such as arches and emergency shelters, providing a direct route for building large-scale inflatable systems that lock in place after deployment and offer a robust enclosure through their stiff faces.

Harnessing the Multistability of Kresling Origami for Reconfigurable Articulation in Soft Robotic Arms

This study examines a biology-inspired approach of using reconfigurable articulation to reduce the control requirement for soft robotic arms. We construct a robotic arm by assembling Kresling origami modules that exhibit predictable bistability. By switching between their two stable states, these origami modules can behave either like a flexible joint with low bending stiffness or like a stiff link with high stiffness, without requiring any continuous power supply. In this way, the robotic arm can exhibit pseudo-linkage kinematics with lower control requirements and improved motion accuracy. A unique advantage of using origami as the robotic arm skeleton is that its bending stiffness ratio between stable states is directly related to the underlying Kresling design. Therefore, we conduct extensive parametric analyses and experimental validations to identify the optimized Kresling pattern for articulation. The results indicate that a higher angle ratio, a smaller resting length at contracted stable state, and a large number of polygon sides can offer more significant and robust bending stiffness tuning. Based on this insight, we construct a proof-of-concept, tendon-driven robotic arm consisting of three modules and show that it can exhibit the desired reconfigurable articulation behavior. Moreover, the deformations of this manipulator are consistent with kinematic model predictions, which validate the possibility of using simple controllers for such compliant robotic systems.

Plasticity and aging of folded elastic sheets

We investigate the dissipative mechanisms exhibited by creased material sheets when subjected to mechanical loading, which comes in the form of plasticity and relaxation phenomena within the creases. After demonstrating that plasticity mostly affects the rest angle of the creases, we devise a mapping between this quantity and the macroscopic state of the system that allows us to track its reference configuration along an arbitrary loading path, resulting in a powerful monitoring and design tool for crease-based metamaterials. Furthermore, we show that complex relaxation phenomena, in particular memory effects, can give rise to a nonmonotonic response at the crease level, possibly relating to the similar behavior reported for crumpled sheets. We describe our observations through a classical double-logarithmic time evolution and obtain a constitutive behavior compatible with that of the underlying material. Thus the lever effect provided by the crease allows magnified access to the material's rheology.

Equilibria and bifurcations of a foldable paper-based spring inspired by Kresling-pattern origami

Origami-inspired design has recently emerged as a major thrust area of research in the fields of science and engineering. One such design utilizes Kresling-pattern origami to construct nonlinear springs that can act as mechanical bit memory switches, wave guides, fluidic muscles, and vibration isolators. The main objective of this work is to characterize the static equilibria of such springs, their stability, and bifurcations as the geometric parameters of the Kresling pattern are varied. To this end, a mathematical model which assumes that the different panels can be represented by axially deformable truss elements is adopted. The adopted model demonstrates that the shape of the potential energy of the spring is very sensitive to changes in its geometric parameters. This causes the static configuration to undergo several bifurcations as one or more of the geometrical parameters are varied. In particular, it is shown that the geometric parameter space of the Kresling pattern can be divided into five regions, each of which results in a qualitatively different spring behavior. Results of the axial truss model are verified experimentally demonstrating that, for the most part, the model is capable of predicting the loci and bifurcations of the spring's equilibria. Nevertheless, it is also observed that, away from the equilibrium points, the quasistatic behavior of the spring is not well-approximated by the axial truss model. To overcome this issue, a modified model is developed which accounts for (i) the rotary stiffness of the creases, (ii) self avoidance due to panel contact at small angles between the panels, and (iii) buckling of the creases under compressive loads. It is shown that the modified model is capable of providing a better overall qualitative approximation of the quasistatic behavior.

Structure, design, and mechanics of a paper spring

A paper spring is a simple paper craft popular with children. It can be constructed by interfolding and gluing two long strips of paper of equal sizes, with the simplest possible crease patterns. In addition to its curious springy response, this origami-based composite exhibits a twist deformation during its extension. Although its interlocking structure is expected to underly the strong stretch-twist coupling, a detailed understanding of it remains elusive. Here we quantify the kinematics and mechanics of a paper spring during its extensional actuation by combining experimental, numerical, and analytical approaches. We directly link the nonlinear mechanics of a paper spring with its structural design and the sheet elasticity. We show that the unique interlocking provides an enhanced structural rigidity because the thin sheets suffer from geometric frustrations and must locally bend and stretch during extension. This structural design allows for a reversible transformation between the rotatory and linear motions solely by controlling forces and moments applied at the ends of the structure. Such deployment kinematics could provide a unique avenue of the mode conversion for potential applications and will broaden the possibilities of future designs of origami-based springs with tunable functionalities.

Local mechanical description of an elastic fold

To go beyond the simple model for the fold as two flexible surfaces or faces linked by a crease that behaves as an elastic hinge, we carefully shape and anneal a crease within a polymer sheet and study its mechanical response. First, we carry out an experimental study that involves recording both the shape of the fold in various loading configurations and the associated force needed to deform it. Then, an elastic model of the fold is built upon a continuous description of both the faces and the crease as a thin sheet with a non-flat reference configuration. The comparison between the model and experiments yields the local fold properties and explains the significant differences we observe between tensile and compression regimes. Furthermore, an asymptotic study of the fold deformation enables us to determine the local shape of the crease and identify the origin of its mechanical behaviour.

Overcurvature induced multistability of linked conical frusta: how a 'bendy straw' holds its shape

We study the origins of multiple mechanically stable states exhibited by an elastic shell comprising multiple conical frusta, a geometry common to reconfigurable corrugated structures such as 'bendy straws'. This multistability is characterized by mechanical stability of axially extended and collapsed states, as well as a partially inverted 'bent' state that exhibits stability in any azimuthal direction. To understand the origin of this behavior, we study how geometry and internal stress affect the stability of linked conical frusta. We find that tuning geometrical parameters such as the frustum heights and cone angles can provide axial bistability, whereas stability in the bent state requires a sufficient amount of internal pre-stress, resulting from a mismatch between the natural and geometric curvatures of the shell. We provide insight into the latter effect through curvature analysis during deformation using X-ray computed tomography (CT), and with a simple mechanical model that captures the qualitative behavior of these highly reconfigurable systems.

Basins of attraction of the bistable region of time-delayed cutting dynamics

This paper investigates the effects of bistability in a nonsmooth time-delayed dynamical system, which is often manifested in science and engineering. Previous studies on cutting dynamics have demonstrated persistent coexistence of chatter and chatter-free responses in a bistable region located in the linearly stable zone. As there is no widely accepted definition of basins of attraction for time-delayed systems, bistable regions are coined as unsafe zones (UZs). Hence, we have attempted to define the basins of attraction and stability basins for a typical delayed system to get insight into the bistability in systems with time delays. Special attention was paid to the influences of delayed initial conditions, starting points, and states at time zero on the long-term dynamics of time-delayed systems. By using this concept, it has been confirmed that the chatter is prone to occur when the waviness frequency in the workpiece surface coincides with the effective natural frequency of the cutting process. Further investigations unveil a thin "boundary layer" inside the UZ in the immediate vicinity of the stability boundary, in which we observe an extremely fast growth of the chatter basin stability. The results reveal that the system is more stable when the initial cutting depth is smaller. The physics of the tool deflection at the instant of the tool-workpiece engagement is used to evaluate the cutting safety, and the safe level could be zero when the geometry of tool engagement is unfavorable. Finally, the basins of attraction are used to quench the chatter by a single strike, where the resultant "islands" offer an opportunity to suppress the chatter even when the cutting is very close to the stability boundary.