Guest Editorial

J. Mechanisms Robotics. 2016;8(3):030301-030301-1. doi:10.1115/1.4032776.

Over the past few decades, the centuries-old art of origami and the centuries-old practice of engineering have been mixing in ways that have proven to be both fruitful and surprising, resulting in structures and mechanisms that fold, deploy, and transform. While the term “origami” captures the general sense of these forms, it should be interpreted broadly, as folding, in which multiple components rotate with respect to one another around reasonably well-defined axes of rotation: the “folds.” Unlike traditional origami (mostly paper), origami mechanisms are made from the materials of engineering: metals, polymers, plastics, and exotics, such as carbon fiber. The user of such mechanisms in the engineering domain requires the exploration of properties and parameters not considered in traditional origami: kinematics, effects of thickness and bending, stresses and strains, and methods of actuation far more sophisticated than the hands of a craftsman.

Topics: Robotics
Commentary by Dr. Valentin Fuster

Research Papers

J. Mechanisms Robotics. 2016;8(3):031001-031001-10. doi:10.1115/1.4031458.

This paper provides an approach to model the reaction force of origami mechanisms when they are deformed. In this approach, an origami structure is taken as an equivalent redundantly actuated mechanism, making it possible to apply the forward-force analysis to calculating the reaction force of the origami structure. Theoretical background is provided in the framework of screw theory, where the repelling screw is introduced to integrate the resistive torques of folded creases into the reaction-force of the whole origami mechanism. Two representative origami structures are then selected to implement the developed modeling approach, as the widely used waterbomb base and the waterbomb-based integrated parallel mechanism. With the proposed kinematic equivalent, their reaction forces are obtained and validated, presenting a ground for force analysis of origami-inspired mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031002-031002-11. doi:10.1115/1.4031953.

Rigid origami inspires new design technology in deployable structures with large deployable ratio due to the property of flat foldability. In this paper, we present a general kinematic model of rigid origami pattern and obtain a family of deployable prismatic structures. Basically, a four-crease vertex rigid origami pattern can be presented as a spherical 4R linkage, and the multivertex patterns are the assemblies of spherical linkages. Thus, this prismatic origami structure is modeled as a closed loop of spherical 4R linkages, which includes all the possible prismatic deployable structures consisting of quadrilateral facets and four-crease vertices. By solving the compatibility of the kinematic model, a new group of 2n-sided deployable prismatic structures with plane symmetric intersections is derived with multilayer, straight and curvy variations. The general design method for the 2n-sided multilayer deployable prismatic structures is proposed. All the deployable structures constructed with this method have single degree-of-freedom (DOF), can be deployed and folded without stretching or twisting the facets, and have the compactly flat-folded configuration, which makes it to have great potential in engineering applications.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031003-031003-6. doi:10.1115/1.4031954.

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly applicable algorithm to transform certain flat-foldable crease patterns into new crease patterns with similar folded structure but with a facet-separated folded state. We provide conditions on input crease patterns for the algorithm to produce a thickened crease pattern avoiding local self-intersection, and provide bounds for the maximum thickness that the algorithm can produce for a given input. We demonstrate these results in parameterized numerical simulations and physical models.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031004-031004-12. doi:10.1115/1.4032098.

The folding behavior of a prismatic mast based on Kresling origami pattern is studied in this paper. The mast consists of identical triangles with cyclic symmetry. Bar stresses and necessary external nodal loads of the mast during the motion are studied analytically. The results show that the mechanical behaviors are different when the initial height of the mast is different. Then the numerical analysis is used to prove the accuracy of the analytical results. The influence of the geometry and the number of sides of the polygon on the folding behavior of the basic segment is also investigated. The folding process of the mast with multistories was discussed. The effect of the imperfection based on the eigenvalue buckling modes on the folding behavior is also studied. It can be found that when the number of sides of the polygon is small, the imperfection in the axial direction affects the energy seriously by changing the folding sequence of the mast. When the number of sides of the polygon is larger, the imperfection in the horizontal plane has significant effect on the folding pattern, which leads to the sudden change of energy curve.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031005-031005-15. doi:10.1115/1.4032102.

We present the design for a family of deployable structures based on the origami flasher, which are rigidly foldable, i.e., foldable with revolute joints at the creases and planar rigid faces. By appropriate choice of sector angles and introduction of a cut, a single degree-of-freedom (DOF) mechanism is obtained. These structures may be used to realize highly compact deployable mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031006-031006-10. doi:10.1115/1.4031901.

A method is presented utilizing networks of lamina emergent joints, known as lamina emergent arrays, to accommodate large-curvature developable structures suited to deployable applications. By exploiting the ruling lines in developable surfaces, this method enables developable structures and mechanisms that can be manufactured with two-dimensional geometry and yet have a greater range of elastic motion than is possible with a solid sheet of material. Aligning the joints to the ruling lines also biases the structure to a specific deployment path. A mathematical model is developed to describe the resulting stiffness of the structure employing the lamina emergent arrays and equations are derived to facilitate stress analysis of the structure. Finite element results show the sensitivity of alignment of the elements in the array to the stress present in the developed structure. A specific technique for creating an array pattern for conical developable surfaces is described. Examples of developable structures and mechanisms, including curved-fold origami models transitioned to thick materials and two origami-inspired mechanisms, are examined.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031007-031007-11. doi:10.1115/1.4032271.

This work presents an analysis and validation of a foldable boom actuated by tape-spring foldable elastic hinges for space applications. The analytical equations of tape-springs are described, extending the classical equations for isotropic materials to orthotropic carbon-fiber composite materials. The analytical equations which describe the buckling of the hinge have been implemented in a multibody simulation software where the hinge was modeled as a nonlinear elastic bushing and the boom as a rigid body. In the experimental phase, the boom was fabricated using a thin layer carbon-fiber composite tube, and the residual vibrations after deployment were experimentally tested with a triaxial accelerometer. A direct comparison of the simulation with the physical prototype pointed out the dangerous effect of higher order vibrations which are difficult to capture in simulation. We observed that while the vibrational spectra of simulations and experiments were compatible at low frequencies during deployment, a marked difference was observed at frequencies beyond 30 Hz. While difficult to model, higher order frequencies should be carefully accounted for in the design of self-deployable space structures. Indeed, if tape-springs are used as a self-locking mechanism, the higher vibrational modes could have enough energy to unlock the structure during operation.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031008-031008-6. doi:10.1115/1.4031717.

This paper proposes a design method to obtain a family of rigidly foldable structures with one degree-of-freedom (DOF). The mechanism of flat-foldable degree-four cones and mutually compatible cones sharing a boundary is interpreted as the mechanism of Bricard's flexible octahedra. By sequentially concatenating compatible cones, one can design horn-shaped rigid-origami mechanisms. This paper presents a method to inversely obtain rigidly foldable horns that follow given space curves. The resulting rigidly foldable horns can be used as building blocks for a transformable cellular structure and attachments to existing rigidly foldable structures.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031009-031009-8. doi:10.1115/1.4032441.

Accordion patterns are widely used for deployable shelters, due to their simple construction, elegant deployment mechanism, and folded plate form with an inherent structural efficiency. This paper proposes two new accordion-type shelters that use modified geometries to improve on the structural stability and stiffness of the typical accordion form. The first shelter is termed a distributed frame accordion shelter and is generated by separating fully folded accordion frames between spacer plates aligned with the transverse direction. A transverse stiffness and increased flexural rigidity can therefore be achieved while maintaining a nonzero floor area. The second shelter is termed a diamond wall accordion shelter and is generated by inserting secondary wall elements that increase wall sectional depth and counteract the coupled rotational-transverse displacements at accordion roof–wall junctions. For both shelter types, a geometric parameterization and a full-scale prototype are presented. Good correlation is seen between the designed and constructed surfaces. A numerical investigation also shows that the new forms have substantially increased flexural rigidities compared to the typical accordion form.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031010-031010-9. doi:10.1115/1.4031808.

This paper presents a novel design of extensible continuum robots in light of origami-inspired folding techniques. The design starts from a modularized crease pattern, which consists of two triangular bases and three waterbomb bases, and generates a folding process for creating an origami waterbomb parallel structure. This further progresses to generating a compliant module with the origami parallel structure and a helical compression spring. A novel extensible continuum robot with the integrated compliant parallel modules is then proposed to imitate not only the bending motion but also the contraction of continuum creatures in nature. Mapping the origami parallel structure to an equivalent kinematic model, the motion characteristics of the origami structure are explored in terms of kinematic principles. The analysis reveals the mixed rotational and translational motion of the origami parallel module and the virtual axes for yaw and pitch motions. Following kinematics of the proposed continuum robot and features of the integrated helical spring in each module, three actuation schemes and resultant typical working phases with a tendon-driven system are presented. The design and analysis are then followed by a prototype of the extensible continuum robot with six integrated compliant modules connected in serial. The functionality of the proposed continuum robot with the origami parallel structure as its skeleton and the helical springs as the compliant backbone is validated by experimental results.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031011-031011-8. doi:10.1115/1.4032208.

Sandwich panels, for example, honeycomb structure, are widely used in various stages because they are lightweight and have high stiffness. Recently, an origami structure called truss core panel (TCP) has become known as a lightweight structure that has the same bending stiffness and better aspects in shear strength and in-plane compressive load than honeycomb panel. However, there are some difficulties in forming the TCP in general. In this study, a new forming process for TCP based on origami-forming is developed. In particular, the TCP is partitioned into several parts that can be developed into 2D crease patterns. After that, blanks of material are cut in the shape of these crease patterns and are formed by a robot system to get the desired 3D shape. In this paper, a partition method by dividing the TCP into pyramid cells and sheet plate is presented, which allows for the manufacture of a wider range of structure than before. Tool arrangement for a robot device and a countermeasure for springback are considered. By applying an origami unfolding technique, an improvement in the partition method is proposed by dividing the TCP into cell rows, and then searching for a crease pattern in order to fold that cell row. The cutting method of every cell is modified to reduce the number of facets, thereby simplifying the process. Finally, a crease pattern based on this new cutting method is presented for producing cell rows with any given number of cells.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031012-031012-12. doi:10.1115/1.4032406.

Self-folding origami has the potential to be utilized in novel areas such as self-assembling robots and shape-morphing structures. Important decisions in the development of such applications include the choice of active material and its placement on the origami model. With proper active material placement, the error between the actual and target shapes can be minimized along with cost, weight, and input energy requirements. A method for creating magnetically actuated dynamic models and experimentally verifying their results is briefly reviewed, after which the joint stiffness and magnetic material approximations used in the dynamic model are discussed in more detail. Through the incorporation of dynamic models of magnetically actuated origami mechanisms into the Applied Research Laboratory's trade space visualizer (atsv), the trade spaces of self-folding dynamic models of the waterbomb base and Shafer's frog tongue are explored. Finally, a design tradeoff is investigated between target shape approximation error and the placement of magnetic material needed to reach a target shape. These two examples demonstrate the potential use of this process as a design tool for other self-folding origami mechanisms.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031013-031013-6. doi:10.1115/1.4031809.

We study the kinematics of leaf-out origami and explore its potential usage as multitransformable structures without the necessity of deforming the origami's facets or modifying its crease patterns. Specifically, by changing folding/unfolding schemes, we obtain various geometrical configurations of the leaf-out origami based on the same structure. We model the folding/unfolding motions of the leaf-out origami by introducing linear torsion springs along the crease lines, and we calculate the potential energy during the shape transformation. As a result, we find that the leaf-out structure exhibits distinctive values of potential energy depending on its folded stage, and it can take multiple paths of potential energy during the transformation process. We also observe that the leaf-out structure can show bistability, enabling negative stiffness and snap-through mechanisms. These unique features can be exploited to use the leaf-out origami for engineering applications, such as space structures and architectures.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031014-031014-8. doi:10.1115/1.4032209.

Self-folding converts two-dimensional (2D) sheets into three-dimensional (3D) objects in a hands-free manner. This paper demonstrates a simple approach to self-fold commercially available, millimeter-thick thermoplastic polymer sheets. The process begins by first stretching poly(methyl methacrylate) (PMMA), polystyrene (PS), or polycarbonate (PC) sheets using an extensometer at elevated temperatures close to the glass transition temperature (Tg) of each sheet. Localizing the strain to a small strip creates a “hinge,” which folds in response to asymmetric heating of the sheet. Although there are a number of ways to supply heat, here a heat gun delivers heat to one side of the hinge to create the necessary temperature gradient through the polymer sheet. When the local temperature exceeds the Tg of the polymer, the strain in the hinged region relaxes. Because strain relaxation occurs gradually across the sheet thickness, the polymer sheet folds in the direction toward the heating source. A simple geometric model predicts the dihedral angle of the sheet based on the thickness of the sheet and width of the hinge. This paper reports for the first time that this approach to folding works for a variety of thermoplastics using sheets that are significantly thicker (∼10 times) than those reported previously.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):031015-031015-12. doi:10.1115/1.4031955.

Engineering inspired by origami has the potential to impact several areas in the development of morphing structures and mechanisms. Self-folding capabilities in particular are necessary in situations when it may be impractical to exert external manipulations to produce the desired folds (e.g., as in remote applications such as in space systems). In this work, origami principles are utilized to allow planar sheets to self-fold into complex structures along arbitrary folds (i.e., no hinges or pre-engineered locations of folding). The sheets considered herein are composed of shape memory alloy (SMA)-based laminated composites. SMAs are materials that can change their shape by thermal and/or mechanical stimuli. The generation of sheets that can be folded into the desired structures is done using origami design software such as Tachi's freeform origami. Also, a novel in-house fold pattern design software capable of generating straight and curved fold patterns has been developed. The in-house software generates creased and uncreased fold patterns and converts them into finite element meshes that can be analyzed in finite element analysis (FEA) software considering the thermomechanically coupled constitutive response of the SMA material. Finite element simulations are performed to determine whether by appropriately heating the planar unfolded sheet it is possible to fold it into the desired structure. The results show that a wide range of self-folding structures can be folded via thermal stimulus. This is demonstrated by analyzing the folding response of multiple designs generated from freeform origami and the newly developed in-house origami design software.

Commentary by Dr. Valentin Fuster

Technical Brief

J. Mechanisms Robotics. 2016;8(3):034501-034501-7. doi:10.1115/1.4032203.

Rigidly foldable origami tessellations exhibit interesting kinematic properties. Several tessellation types (most prominently Miura-ori) have shown potential for technical usage in aerospace and general lightweight construction. In addition to static (e.g., as core structures for sandwich components) and single-layer kinematic (e.g., deployable) applications, new possibilities arise from the combination of several layers of tessellations with congruent kinematics. This paper presents an analytical description of the kinematics of multilayered, or stacked, globally plane tessellations which retain rigid/isometric foldability by congruent, compatible movement.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):034502-034502-6. doi:10.1115/1.4032269.

Rolling joints, which are created by attaching two cylindrical surfaces of equal radius using two or more thin tapes or cable, are used for rigid origami considering the panel thickness. First, the concept and two implementation methods of this joint are given. Then planar linkages are chosen to study the mobility and kinematics of foldable plate structures with rolling joints. It can be found that the rolling joints preserve the full-cycle-motion of foldable plate structures. From the closure equations of linkages, the results show that the outputs of linkages with rolling joints are the same as that with traditional revolute joints if the lengths of links are equal. However, the results are different when the lengths of links are unequal. Moreover, the difference between linkages with rolling joints and revolute joints increases with an increase of the size of rolling joints.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2016;8(3):034503-034503-7. doi:10.1115/1.4032119.

This paper proposes a new family of single degree of freedom (DOF) deployable mechanisms derived from the threefold-symmetric deployable Bricard mechanism. The mobility and geometry of original threefold-symmetric deployable Bricard mechanism is first described, from the mobility characterstic of this mechanism, we show that three alternate revolute joints can be replaced by a class of single DOF deployable mechanisms without changing the single mobility characteristic of the resultant mechanisms, therefore leading to a new family of Bricard-derived deployable mechanisms. The computer-aided design (CAD) models are used to demonstrate these derived novel mechanisms. All these mechanisms can be used as the basic modules for constructing large volume deployable mechanisms.

Commentary by Dr. Valentin Fuster

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