Workspace Analysis of a Reconfigurable Mechanism Generated from the Network of Bennett Linkages

In this paper, a workspace triangle is introduced to evaluate the workspace of a reconfigurable mechanism generated from the network of Bennett linkages. Three evaluation indexes of workspace including movement locus of the joint, surface swept by the link and helical tube enveloped by the workspace triangle have been discussed. The comparison between the workspace of the reconfigurable mechanism and the sum of five resultant 5 R /6 R linkages including generalized Goldberg 5 R linkage, generalized variant of the L -shape Goldberg 6 R linkage, Waldron’s hybrid 6 R linkage, isomerized generalized L -shape Goldberg 6 R linkage and generalized Wohlhart’s double-Goldberg 6 R linkage is accomplished by using the evaluation indexes and mapping the workspace to the joint space which is defined by a vector whose components are joint variables

INFLUENCE OF PANEL ZONE SIZES ON ULTIMATE BEARING CAPACITY OF H-SHAPED STEEL FRAMES

In order to explore the influence of panel zone sizes on the ultimate bearing capacity of H-shaped steel frames, this study examines a steel frame structure with cross-shaped sections consisting of beams, columns and panel zones based on mechanical equilibrium principles. The area ratio of either side of the flange to the web is taken as the main parameter.The results show that the ultimate bearing capacity ratio curves can be grouped into three types. For the first type, the plastic hinge is formed in the panel zone. For the second type, when Rpcb, the strong column factor, is greater than 1.2, the plastic hinge is formed at the beam end; otherwise the plastic hinge is formed in the panel zone. For the third type, when Rpcb≤0.8, the plastic hinge is formed in the panel zone; otherwise the plastic hinge is formed at the beam end. The ultimate bearing capacity ratio curves of the local section of H-shaped steel largely fall in the first curve type, and the ultimate bearing capacity is larger when the panel zone size is excluded from the calculation than otherwise with the former being one to five times as large as the latter

Rigid Foldability of Generalized Triangle Twist Origami Pattern and Its Derived 6R Linkages

Rigid origami is a restrictive form of origami that permits continuous motion between folded and unfolded states along the predetermined creases without stretching or bending of the facets. It has great potential in engineering applications, such as foldable structures that consist of rigid materials. The rigid foldability is an important characteristic of an origami pattern, which is determined by both the geometrical parameters and the mountain-valley crease (M-V) assignments. In this paper, we present a systematic method to analyze the rigid foldability and motion of the generalized triangle twist origami pattern using the kinematic equivalence between the rigid origami and the spherical linkages. All schemes of M-V assignment are derived based on the flat-foldable conditions among which rigidly foldable ones are identified. Moreover, a new type of overconstrained 6R linkage and a variation of doubly collapsible octahedral Bricard are developed by applying kirigami technique to the rigidly foldable pattern without changing its degree-of-freedom. The proposed method opens up a new way to generate spatial overconstrained linkages from the network of spherical linkages. It can be readily extended to other types of origami patterns

A plane linkage and its tessellation for deployable structure

Deployable structures are widely used in space applications such as solar arrays and antennas. Recently, inspired by origami, more deployable structures have been developed. This paper outlined a novel design scheme for deployable structures by taking a plane linkage as an origami unit with a large deployable ratio. The mountain and valley (M-V) crease assignment and kinematics of the plane linkage were analyzed. Physical interference in the folding progress was discovered geometrically and resolved by the split-vertex technique. Finally, tessellation of the derived pattern was successfully used to create a large-deployable-ratio structure, which was found to exhibit considerable potential in future space applications

Folding of Tubular Waterbomb

Origami has recently emerged as a promising building block of mechanical metamaterials because it offers a purely geometric design approach independent of scale and constituent material. The folding mechanics of origami-inspired metamaterials, i.e., whether the deformation involves only rotation of crease lines (rigid origami) or both crease rotation and facet distortion (nonrigid origami), is critical for fine-tuning their mechanical properties yet very difficult to determine for origami patterns with complex behaviors. Here, we characterize the folding of tubular waterbomb using a combined kinematic and structural analysis. We for the first time uncover that a waterbomb tube can undergo a mixed mode involving both rigid origami motion and nonrigid structural deformation, and the transition between them can lead to a substantial change in the stiffness. Furthermore, we derive theoretically the range of geometric parameters for the transition to occur, which paves the road to program the mechanical properties of the waterbomb pattern. We expect that such analysis and design approach will be applicable to more general origami patterns to create innovative programmable metamaterials, serving for a wide range of applications including aerospace systems, soft robotics, morphing structures, and medical devices

Helical structures with switchable and hierarchical chirality

Chirality is present as a trend of research in biological and chemical communities for it has a significant effect on physiological properties and pharmacological effects. Further, manipulating specific morphological chirality recently has emerged as a promising approach to design metamaterials with tailored mechanical, optical, or electromagnetic properties. However, the realization of many properties found in nature, such as switchable and hierarchical chirality, which allows electromagnetic control of the polarization of light and enhancement of mechanical properties, in man-made structures has remained a challenge. Here, we present helical structures with switchable and hierarchical chirality inspired by origami techniques. We propose eggbox-based chiral units for constructing homogeneous and heterogeneous chiral structures and demonstrate a theoretical approach for tuning the chirality of these structures by modulating their geometrical parameters and for achieving chirality switching through mechanism bifurcation. Finally, by introducing a helical tessellation between the chiral units, we design hierarchical structures with chirality transferring from construction elements to the morphological level and discover a helix with two zero-height configurations during the unwinding process. We anticipate that our design and analysis approach could facilitate the development of man-made metamaterials with chiral features, which may serve in engineering applications, including switchable electromagnetic metamaterials, morphing structures, and bionic robots

Rigid Folding of Generalized Waterbomb Origami Tubes

The accurate theoretical description of the folding motion of origami structures is the foundation for their design and precise control in engineering applications. However, the folding behavior of most general origami structures is very difficult to analyze because of the lack of theoretical model and analysis methodology for the complex mobile assemblies of spherical linkages. This paper focuses on the widely-used Waterbomb origami tubes. Based on the kinematics and compatibility of spherical linkages, the rigid folding behavior of generalized Waterbomb tubes was systematically analyzed with analytical kinematics equations to describe their rigid contract and twist motion. The effect of various geometrical parameters on the rigid folding behaviour, bifurcation property as well as physical blockages of the Waterbomb origami tube was studied. This work lays a theoretical foundation for the design and control of programmable metamaterials, deformable structures, and robots based on Waterbomb origami tubes, while such kinematic model can be readily applied to other origami patterns

Reconfigurable mechanism generated from the network of Bennett linkages

A network of four Bennett linkages is proposed in this paper. Totally five types of overconstrained 5R and 6R linkages, including the generalized Goldberg 5R linkage, generalized variant of the L-shape Goldberg 6R linkage, Waldron's hybrid 6R linkage, isomerized case of the generalized L-shape Goldberg 6R linkage, and generalized Wohlhart's double-Goldberg 6R linkage, can be constructed by modifying this Bennett network. The 8R linkage formed by Bennett network serves as the basic mechanism to realise the reconfiguration among five types of overconstrained linkages by rigidifying some of the eight joints. The work also reveals the in-depth relationship among the Bennett-based linkages, which provides a substantial advancement in the design of reconfigurable mechanisms using overconstrained linkages