folding pattern
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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.

Abstract This study aims to investigate the phylogenetic relationships within the Juglandaceae family based on the Internal Transcribed Spacer's primary sequence and secondary structures (ITS2). Comparative analysis of 51 Juglandaceae species was performed across most of the defined seven genera. The results showed that the ITS2 secondary structure's folding pattern was highly conserved and congruent with the eukaryote model. Firstly, Neighbor-joining (N.J.) analysis recognized two subfamilies: Platycaryoideae and Engelhardioideae. The Platycaryoideae included the Platycaryeae (Platycarya+(Carya+ Annamocarya)) and Juglandeae (Juglans-(Cyclocarya + Pterocarya)). The Engelhardioideae composed the (Engelhardia+（Oreomunnea+Alfaroa)). The Rhoiptelea genus was generally regarded as an outgroup when inferring the phylogeny of Juglandaceae. However, it is clustered into the Juglandaceae family and showed a close relationship with the Platycaryoideae subfamily. Secondly, the folded 3-helices and 4-helices secondary structure of ITS2 were founded in the Juglandaceae family. Therefore, these ITS2 structures could be used as formal evidence to analyze Juglandaceae's phylogeny relationship. The morphology based on the secondary structure nicely coincided with previous investigations. This study further confirms that ITS2 can serve as a valid basis for parsing evolutionary relationships in higher woody fruit trees.

AbstractThe beetle horn primordium is a complex and compactly folded epithelial sheet located beneath the larval cuticle. Only by unfolding the primordium can the complete 3D shape of the horn appear, suggesting that the morphology of beetle horns is encoded in the primordial folding pattern. To decipher the folding pattern, we developed a method to manipulate the primordial local folding on a computer and clarified the contribution of the folding of each primordium region to transformation. We found that the three major morphological changes (branching of distal tips, proximodistal elongation, and angular change) were caused by the folding of different regions, and that the folding mechanism also differs according to the region. The computational methods we used are applicable to the morphological study of other exoskeletal animals.

The study of a thin-walled column structure has gained much attention due to its potential in many engineering applications, such as the crash box of a car. A thin-walled square column usually exhibits high initial peak force, which may become very dangerous to the driver or passenger. To address this issue, introducing some shape patterns, e.g., origami folding pattern, to the column may become a solution. The present work investigates the compressive properties and behavior of a square box column structure which adopts the Miura origami folding pattern. Several test pieces of single-cell Miura origami column with varying folding angle and layer height are fabricated by a 3D printer. The filament is made of Polylactic Acid (PLA), which is a brittle material. Then, compression tests are carried out to understand its compressive mechanical properties and behavior. The results show that introducing a Miura origami pattern to form a thin-walled square column can dramatically lower down the initial peak stress by 96.82% and, at the same time, increase its ductility, which eventually improves the energy absorption capacity by 61.68% despite the brittle fracture behavior.

Abstract The head horn of the Asian rhinoceros beetle develops as an extensively folded primordium before unfurling into its final 3D shape at the pupal molt. The information of the final 3D structure of the beetle horn is prefigured in the folding pattern of the developing primordium. However, the developmental mechanism underlying epithelial folding of the primordium is unknown. In this study, we addressed this gap in our understanding of the developmental patterning of the 3D horn shape of beetles by focusing on the formation of furrows at the surface of the primordium that become the bifurcated 3D shape of the horn. By gene knockdown analysis via RNAi, we found that knockdown of the gene Notch disturbed overall horn primordial furrow depth without affecting the 2D furrow pattern. In contrast, knockdown of CyclinE altered 2D horn primordial furrow pattern without affecting furrow depth. Our results show how the depth and 2D pattern of primordial surface furrows are regulated at least partially independently during beetle horn development, and how both can alter the final 3D shape of the horn.

Abstract Most microinsects have feather-like bristled wings, a state known as ptiloptery, but featherwing beetles (family Ptiliidae) are unique among winged microinsects in their ability to fold such wings. An asymmetrical wing folding pattern, found also in the phylogenetically related rove beetles (Staphylinidae), was ancestral for Ptiliidae. Using scanning electron, confocal laser scanning, and optical microscopy, high-speed video recording, and 3D reconstruction, we analyze in detail the symmetrical wing folding pattern and the mechanism of the folding and unfolding of the wings in Acrotrichis sericans (Coleoptera: Ptiliidae) and show how some of the smaller featherwing beetles have reverted to strict symmetry in their wing folding. The wings are folded in three phases by bending along four lines (with the help of wing folding patches on the abdominal tergites) and locked under the closed elytra; they unfold passively in two phases, apparently with the help of the elasticity provided by resilin unevenly distributed in the wing and of convexities forming in the cross-sections of the unfolding wing, making it stiffer. The minimum duration of folding is 3.5 s; unfolding is much more rapid (minimum duration lowest recorded in beetles, 0.038 s). The folding ratio of A. sericans is 3.31 (without setae), which is greater than in any beetle in which it has been measured. The symmetrical wing folding pattern found in A. sericans and in all of the smallest ptiliids, in which ptiloptery is especially pronounced, is the only known example of symmetry re-established during miniaturization. This direction of evolution is remarkable because miniaturization is known to result in various asymmetries, while in this case miniaturization was accompanied by reversal to symmetry, probably associated with the evolution of ptiloptery. Our results on the pattern and mechanisms of wing folding and unfolding can be used in robotics for developing miniature biomimetic robots: the mechanisms of wing folding and unfolding in Ptiliidae present a challenge to engineers who currently work at designing ever smaller flying robots and may eventually produce miniature robots with foldable wings.

Abstract The beetle horn primordium is a complex and compactly folded epithelial sheet located beneath the larval cuticle. Only by unfolding the primordium the complete 3D shape of the horn appears, suggesting that the morphology of beetle horns is coded in the primordial folding pattern. To decipher the folding pattern, we have developed a method to manipulate the primordial local folding, reproduced it on a computer, and clarified the contribution of the folding of each primordium region to transformation. We found that the three major morphological changes (branching of distal tips, proximodistal elongation, and angular change) were caused by the folding of different regions, and that the folding mechanism was also different depending on the region. The computational methods we used are applicable to the morphological study of other exoskeletal animals.

Abstract Mapping the relation between cortical convolution and structural/functional brain architectures could provide deep insights into the mechanisms of brain development, evolution and diseases. In our previous studies, we found a unique gyral folding pattern, termed a 3-hinge, which was defined as the conjunction of three gyral crests. The uniqueness of the 3-hinge was evidenced by its thicker cortex and stronger fiber connections than other gyral regions. However, the role that 3-hinges play in cortico-cortical connective architecture remains unclear. To this end, we conducted MRI studies by constructing structural cortico-cortical connective networks based on a fine-granular cortical parcellation, the parcels of which were automatically labeled as 3-hinge, 2-hinge (ordinary gyrus) or sulcus. On human brains, 3-hinges possess significantly higher degrees, strengths and betweennesses than 2-hinges, suggesting that 3-hinges could serve more like hubs in the cortico-cortical connective network. This hypothesis gains supports from human functional network analyses, in which 3-hinges are involved in more global functional networks than ordinary gyri. In addition, 3-hinges could serve as ‘connector’ hubs rather than ‘provincial’ hubs and they account for a dominant proportion of nodes in the high-level ‘backbone’ of the network. These structural results are reproduced on chimpanzee and macaque brains, while the roles of 3-hinges as hubs become more pronounced in higher order primates. Our new findings could provide a new window to the relation between cortical convolution, anatomical connection and brain function.