Fold Lines Research Articles

Fundamental conical defects: The d-cone, its e-cone, and its p-cone

We consider well-known surface disclinations by cutting, joining, and folding pieces of paper card. The resulting shapes have a discrete, folded vertex whose geometry is described easily by Gauss's mapping, in particular, we can relate the degree of angular excess, or deficit, to the size of fold line rotations by the area enclosed by the vector diagram of these rotations. This is well known for the case of a so-called "d-cone" of zero angular deficit, and we formulate the same for a general disclination. This method allows us to observe kinematic properties in a meaningful way without needing to consider equilibrium. Importantly, the simple vector nature of our analysis shows that some disclinations are primitive; and that other types, such as d-cones, are amalgamations of them.

Simultaneous optimisation of earwig hindwings for flight and folding.

ABSTRACTEarwig wings are highly foldable structures that lack internal muscles. The behaviour and shape changes of the wings during flight are yet unknown. We assume that they meet a great structural challenge to control the occurring deformations and prevent the wing from collapsing. At the folding structures especially, the wing could easily yield to the pressure. Detailed microscopy studies reveal adaptions in the structure and material which are not relevant for folding purposes. The wing is parted into two structurally different areas with, for example, a different trend or stiffness of the wing veins. The storage of stiff or more flexible material shows critical areas which undergo great changes or stress during flight. We verified this with high-speed video recordings. These reveal the extent of the occurring deformations and their locations, and support our assumptions. The video recordings reveal a dynamical change of a concave flexion line. In the static unfolded state, this flexion line blocks a folding line, so that the wing stays unfolded. However, during flight it extends and blocks a second critical folding line and prevents the wing from collapsing. With these results, more insight in passive wing control, especially within high foldable structures, is gained.

Multi-parametric stability investigation for thin spherical membranes filled with gas and fluid

The instability behavior of spherical membranes completely or partially filled with fluid, also with internal gas over-pressure, placed on a friction-less rigid plane was investigated. The two-parameter Mooney–Rivlin model was used for material description. A third order penalty function was used to describe the rigid support. Different problem settings were considered, and different instability responses were observed. For the partially fluid-filled membrane, a multi-parametric problem was defined and analyzed. Augmenting equations were introduced to impose control constraints on variables chosen. These equations also affect the instability analysis. A generalized eigenvalue analysis was used for the stability conclusions. Numerical simulations showed that appropriate control constraints are of essence to interpret the instability conclusions. Fold line evaluations were performed to analyze the dependence of the instability behavior on the parameters. A solution surface algorithm was utilized to analyze and visualize the mechanical responses to multi-variable loading.

Abstract P2-12-05: Trans-peri-areolar breast conservative surgery followed by endoscopic axillary lymph node dissection: A novel surgical option

Abstract Objective Endoscopic surgery currently is a standard method in most surgical fields. Although endoscopic breast surgery has been introduced since 1993, it is not widely applied due to limited benefits. Changing the conventional local treatment may require new attempts that enhance cosmetic outcomes and diminish complication rates. We report the cosmetic outcomes and postoperative complications of a breast conservative surgery (EBCS) procedure, which consists in using a 3cm peri-areolar incision to perform lumpectomy, and followed by endoscopic axillary lymph node dissection without liposuction. Patients and methods From Nov 2013 till May 2015, 53 patients diagnosed with early stage breast cancer were categorized into the conventional breast conservative surgical group (CBCS)and EBCS group. Indications for EBCS were 1.tumor/breast ratio below 20% 2.no distant metastasis 3.Tumor mass not located in the lower-inferior quadrant. Inform consents were obtained from all patients. 25 patients were enrolled in the EBCS and 28 patients in the CBCS group. Number of lymph nodes harvested, tumor size, intra-operative bleeding, drainage volume, pain score (10scale survey) were collected. The breast symmetrical score (BSS,direct distance from nipple to fovea jugularis,midclavicular, midsternal, inframammary fold and anterior axillary line of both breast was measured 3days after surgery and distance difference ratio of operated to contralateral site was calculated. BSS is the sum of each absolute value of distance difference ratio) and patient satisfaction (4scale survey) were used to evaluate cosmetic outcomes. Results There was no statistical difference in intra-operative bleeding(EBCS:36.00±17.08ml, CBCS:29.29±19.99ml,P=0.20) and drainage volume(EBCS:124.60±50.22, CBCS:120.82±74.58,P=0.832).An increased number of harvested lymph nodes was observed in the EBCS group(EBCS:17.88±6.21,CBCS:14.25±5.82,P=0.03). No statistical difference reported for lymph metastasis among two groups(EBCS:1.68±3.59, CBCS:0.96±1.45,P=0.34) .The average tumor size showed no difference(EBCS: 2.41±0.87, CBCS:1.96±0.95,P=0.07). The pain score (EBCS:3.88±1.53, CBCS:4.39±0.74, P=0.04) meanwhile BSS was significantly superior in the EBCS group(EBCS:0.097±0.084,CBCS:0.20±0.13,P=0.002). Patient satisfaction survey reported a positive feedback(EBCS:4.00±0.00,CBCS:3.68±0.48,P=0.001). Cosmetic outcomes and complications of endoscopic breast conservative surgery EBCSCBCSPbleeding36.00±17.0829.29±19.990.20drainage volume124.60±50.22120.82±74.580.832number of lymph nodes harvested17.88±6.2114.25±5.820.03pain score3.88±1.534.3±0.740.04breast symmetry score0.097±0.0840.20±0.130.002 Conclusions. We evaluated cosmetic outcome using a thorough BSS as an index plus adding the lack of scar in the axilla. EBCS patients displayed a significantly superior outcome in comparison with CBCS, which was further appraised by a considerable satisfied patient's feedback. Evaluation of long-term survival, complication rates and cosmetic results are mandatory in order to further estimate the applicability of this surgical management in treatment of breast cancer. EBCS may be a feasible surgical alternative with minimal invasiveness, suitable to patients demanding excellent cosmetic outcome. Citation Format: Yang W, Sejdinaj F, Shen L, Zhu W, Wang H, Zhang H. Trans-peri-areolar breast conservative surgery followed by endoscopic axillary lymph node dissection: A novel surgical option. [abstract]. In: Proceedings of the Thirty-Eighth Annual CTRC-AACR San Antonio Breast Cancer Symposium: 2015 Dec 8-12; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2016;76(4 Suppl):Abstract nr P2-12-05.

Origami tubes with reconfigurable polygonal cross-sections.

Thin sheets can be assembled into origami tubes to create a variety of deployable, reconfigurable and mechanistically unique three-dimensional structures. We introduce and explore origami tubes with polygonal, translational symmetric cross-sections that can reconfigure into numerous geometries. The tubular structures satisfy the mathematical definitions for flat and rigid foldability, meaning that they can fully unfold from a flattened state with deformations occurring only at the fold lines. The tubes do not need to be straight and can be constructed to follow a non-linear curved line when deployed. The cross-section and kinematics of the tubular structures can be reprogrammed by changing the direction of folding at some folds. We discuss the variety of tubular structures that can be conceived and we show limitations that govern the geometric design. We quantify the global stiffness of the origami tubes through eigenvalue and structural analyses and highlight the mechanical characteristics of these systems. The two-scale nature of this work indicates that, from a local viewpoint, the cross-sections of the polygonal tubes are reconfigurable while, from a global viewpoint, deployable tubes of desired shapes are achieved. This class of tubes has potential applications ranging from pipes and micro-robotics to deployable architecture in buildings.

Designing of self-deploying origami structures using geometrically misaligned crease patterns.

Usually, origami-based morphing structures are designed on the premise of 'rigid folding', i.e. the facets and fold lines of origami can be replaced with rigid panels and ideal hinges, respectively. From a structural mechanics viewpoint, some rigid-foldable origami models are overconstrained and have negative degrees of freedom (d.f.). In these cases, the singularity in crease patterns guarantees their rigid foldability. This study presents a new method for designing self-deploying origami using the geometrically misaligned creases. In this method, some facets are replaced by 'holes' such that the systems become a 1-d.f. mechanism. These perforated origami models can be folded and unfolded similar to rigid-foldable (without misalignment) models because of their d.f. focusing on the removed facets, the holes will deform according to the motion of the frame of the remaining parts. In the proposed method, these holes are filled with elastic parts and store elastic energy for self-deployment. First, a new extended rigid-folding simulation technique is proposed to estimate the deformation of the holes. Next, the proposed method is applied on arbitrary-size quadrilateral mesh origami. Finally, by using the finite-element method, the authors conduct numerical simulations and confirm the deployment capabilities of the models.

The Effect of Distal Location of the Volar Short Arm Splint on the Metacarpophalangeal Joint Motion.

BackgroundThe goals of this study were to compare maximal metacarpophalangeal joint (MCPJ) flexion angles after application of a volar short arm splint at 3 different locations and verify the relations between the three different physical and radiological locations.MethodsForty dominant hands of healthy subjects were analyzed in the study. We defined a transverse skin folding line as a line drawn from the radial aspect of the thenar crease to the ulnar aspect of the distal transverse palmar crease. The distal end of the volar short arm splint was applied on 3 parallel locations to this line. Location A was on this transverse skin folding line; location B was 1 cm proximal to location A; and location C was 1 cm distal to location A. Two orthopedic surgeons measured the maximal MCPJ flexion angles of each finger except the thumb with the application of a volar short arm splint at 3 different locations as well as without a splint as a control. Radiological locations of the 3 different distal ends of the volar short arm splint were also assessed by anteroposterior radiographs of the wrist.ResultsWhen the splint was applied at location A and C, the maximal MCPJ flexion angle decreased to a mean of 83° (91% of control value) and 56° (62% of control value), respectively (compared to the control, p < 0.001). At location B, the maximal MCPJ flexion angle was a mean of 90° (99% of control value); no significant difference was observed compared to the control or without the splint (p = 0.103). On radiography, the average length from the metacarpal head to the distal end of the splint at all fingers decreased in the order of location B, A, and C (29 mm, 19 mm, and 10 mm, respectively; p < 0.001).ConclusionsWe recommend applying the distal end of a volar short arm splint at proximal 1 cm to the transverse skin folding line to preserve MCPJ motion perfectly, which is located at distal 44% of the whole metacarpal bone length radiologically.

Quilt pattern inspired engineering: Efficient manufacturing of shelter topologies

Abstract Lightweight, thermally insulated, temporary shelters are essential for disaster relief and military operations. To minimize cost and increase sustainability, it is advantageous to reduce wasted material in manufacturing these shelters. This paper investigates quilt patterns – designs of interlocking geometric shapes – as inspiration for structural topologies that can be manufactured from flat sheets with minimal wasted material (shape interfaces serve as cut and fold lines). A series of quilt-inspired concepts based on established quilt patterns are developed into structural topologies using shape grammar rules. The detailed finite element analysis and design of three concepts is presented. To achieve a lightweight, thermally insulated design, the structures are comprised of sandwich panels (fiber-reinforced polymer faces and a foam core). The performance of each design is compared to an existing rigid wall shelter, demonstrating the efficacy of quilt-inspired forms. This paper is the first investigation of quilting as inspiration for structural systems.

Geometric design and mechanical behavior of a deployable cylinder with Miura origami

The folding and deployment of a cylinder with Miura origami patterns are studied in this paper. First, the geometric formulation of the design problem is discussed. Then the loading case of the axial strains and corresponding external nodal loads applied on the vertices of the top polygon during the motion is investigated analytically. The influence of the angle between the diagonal and horizontal fold lines α and β and the number of Miura origami elements n on the dynamic behavior of the basic segment is also discussed. Then the dynamic behavior is analyzed using numerical simulations. Finally, the deployment process of a cylinder with multi-stories is discussed. The numerical results agree well with the analytical predictions. The results show that the range of motion, i.e. the maximal displacement of top nodes, will also increase with the increase of angles α and β. This cylinder, with a smaller n, may have a bistable behavior. When n is larger, the influence of n on the axial strains and external nodal loads is slight. The numerical results agree well with the analytical predictions. Moreover, the deployment of the cylinder with multi-stories is non-uniform, which deploys from the upper story to the lower story.

Tumour localisation in ultrasound‐guided high‐intensity focused ultrasound ablation using improved gradient and direction vector flow

As one of the key technologies in ultrasound (US)-guided high-intensity focused ultrasound (HIFU) ablation systems, a precise and automatic US image segmentation method for tumour localisation can contribute to ablation of the diseased tissues and avoiding unwanted destruction of the healthy tissues. Owing to the speckle noise and the irregular shapes of target tumours in US images, traditional image segmentation methods are not suitable for tumour localisation. In this study, the authors proposed an improved gradient and direction vector flow (G&DVF) model to segment US images for tumour localisation. The conventional G&DVF model was improved in three aspects to obtain a better segmentation for tumour localisation. The straight lines were changed into fold lines to increase their flexibility in guiding the active contour. Several weighting parameters were added to the energy functional to control the influences of these different lines. Moreover, a novel vector field was defined to reduce the computational complexity and save the computation time. With these three aspects improved, the improved G&DVF model was applied in US image segmentation for tumour localisation. The experimental results demonstrate that this proposed model is reliable, accurate and time saving in US image segmentation for tumour localisation.

The role of Smad3 in the fibrotic phenotype in human vocal fold fibroblasts.

To investigate the role of Smad3 as a regulator of transforming growth factor (TGF)-β1-mediated cell activities associated with fibrosis in normal human vocal fold fibroblasts. We also sought to confirm the temporal stability of Smad3 knockdown via small inhibitor ribonucleic acid (siRNA). Vocal fold fibroblasts were employed to determine the effects of Smad3 knockdown on TGF-β1-mediated migration and contraction, as well as regulation of connective tissue growth factor (CTGF). We hypothesized that Smad3 is an ideal candidate for therapeutic manipulation in vivo based on its role in fibrosis. In vitro. Knockdown of Smad3 via siRNA was performed in our normal human vocal fold cell line. Three-dimensional collagen gel contraction and scratch assays were employed to determine the role of Smad3 on TGF-β1-mediated contraction and migration, respectively. The role Smad3 in the induction of CTGF was characterized via sodium dodecyl sulfate polyacrylamide gel electrophoresis. The effects of Smad3 signaling on Smad7 messenger (m)RNA and protein were also quantified. Smad3 knockdown was temporally-stable up to 72 hours (P < 0.001), diminished TGF-β1-mediated collagen gel contraction and migration, and blunted induction of CTGF, but it had no effect on TGF-β1-mediated Smad7 mRNA or protein induction. Transforming growth factor-β1 stimulated profibrotic cell activities in our cell line and these actions were largely reduced with Smad3 knockdown. These data provide continued support for therapeutic targeting of Smad3 for vocal fold fibrosis because it appears to regulate the fibrotic phenotype. N/A. Laryngoscope, 126:1151-1156, 2016.

Design of three-dimensional origami structures based on a vertex approach

Origami geometric design is fundamental to many engineering applications of origami structures. This paper presents a new method for the design of three-dimensional (3D) origami structures suitable for engineering use. Using input point sets specified, respectively, in the x − z and y − z planes of a Cartesian coordinate system, the proposed method generates the coordinates of the vertices of a folded origami structure, whose fold lines are then defined by straight line segments each connecting two adjacent vertices. It is mathematically guaranteed that the origami structures obtained by this method are developable. Moreover, an algorithm to simulate the unfolding process from designed 3D configurations to planar crease patterns is provided. The validity and versatility of the proposed method are demonstrated through several numerical examples ranging from Miura-Ori to cylinder and curved-crease designs. Furthermore, it is shown that the proposed method can be used to design origami structures to support two given surfaces.

New interpretation of the wings of the pterosaurRhamphorhynchus muensteribased on the Zittel and Marsh specimens

AbstractThe Zittel wing ofRhamphorhynchus muensteriis reinterpreted as preserving negative impressions of closely spaced broad flat actinofibrils that were replaced by calcite but were prepared away by the specimen’s finder. The Marsh specimen preserves positive impressions of the dorsal and ventral surfaces of the wing, which show that the skin was smooth with fine wrinkles and that actinofibrils were not on the wing surface. Based on comparisons of those specimens, the dactylopatagium consisted of dorsal and ventral skins of epidermis and dermis surrounding a common hypodermis core, and keratinous actinofibrils developed in place within the dorsal epidermis adjacent to a layer of linear collagen fibers in the dorsal dermis. The actinofibrils and linear collagen fibers together formed the main functional structure of the dactylopatagium. That structure made the dactylopatagium somewhat stiff and essentially inextensible so that it folded up along discrete fold lines that probably were genetically determined. A pneumatic retrophalangeal wedge behind the antebrachium through at least wing phalanx 3 streamlined the transition between the thick wing spar and thin patagium.

Regular Folding Pattern for Deployable Nonaxisymmetric Tubes1

This paper presents two techniques for modeling the folding patterns of deployable nonaxisymmetric tubes using regular arrangement of the fold lines and three different fundamental folding designs, namely, Miura folding, bellows folding, and torsional buckling-based folding. The first modeling technique involves the cutting and removal of unnecessary parts from the original folding pattern of the corresponding straight cylinder, and the second technique involves the design of additional fold lines for folding the unnecessary parts into the tube without being cut. The applicability and constraints of each folding design and modeling technique are discussed and summarized.

Planar locomotion of a vibration-driven system with two internal masses

A vibration-driven system is modelled to achieve the expected planar locomotion in the present paper. The system is composed of a main rigid body and two internal and movable masses. Coulomb dry friction and nonholonomic constraint of the body are considered to model stick-slip effect and to ensure the motion without sideslip. It is seen that driving periodically the two masses in two orthogonal directions leads to the expected planar locomotion. Correspondingly, the translational and rotary velocities of the system are analytically obtained. As a result, the system can move not only along oblique line in any given slope but also along folding lines derived from the oblique lines in the different slopes.

Design of Deployable Membranes Using Conformal Mapping

This paper proposes a new method for designing the crease patterns of deployable membranes that can be wrapped up compactly. The method utilizes conformal mapping and the origami folding technique. The mapping of the flow with circulation can be used to control the angles between the fold lines, produce elements of the same shape, and maintain regularity of the fold lines. The proposed method thus enables the systematic and efficient design of complex patterns based on simple ones. The proposed method was successfully used to produce the patterns of Nojima and other extended new patterns of deployable membranes consisting of discrete equiangular spirals. The patterns were wrapped and used to form pillars such as regular polygonal, rectangular, and diamond pillars. Toward the industrial application of the proposed method, this paper also discusses pattern design for space-saving storage and to reduce the effect of thickness when using versatile materials.

Triboelectric Nanogenerator Based on Biocompatible Polymer Materials

An attractive method to get a sustainable and green power source is to harvest energy from our living environment. However, most of devices for energy generation are fabricated by using bioincompatible materials, which limits their application in biomedical field. Here, we developed an arch-shaped biomedical triboelectric nanogenerator (TENG), which is fabricated by assembling two biocompatible polymer sheets made of materials having different triboelectric charactristics. The power generation mechanism and the electric output of the TENG, the thickness of the polymer sheet, and the style of lines loacated on the electrode were studied. The instantaneous output voltage and current density of the TENG can reach to 310.5 V and 16.2 μA, which can drive several commercial light-emitting diodes (LEDs). Additionally, we found that the appropriate thickness of the sheet and folding line’s design are both helpful to enhance the TENG’s performance. The survival rate of mouse L929 cells stimulated by TENG was significantly higher than that of the negative controlled test. Based on the TENG’s biomecical charateristic, such TENGs have the potential of harvesting energy from biological activities to drive biomedical devices possibly in vivo.

Surgical repair of excessive width, theatrical fold line and multiple eyelid after blepharoplasty

Objective To investigate the methods of repair of the excessive width, theatrical fold line or multiple eyelid following blepharoplasty. Methods From Mar. 2005 to Dec. 2013, 129 patients received repair because of their excessive width, theatirical fold line or multiple eyelid after blepharoplasty. Among them, 75 cases were repaired 2 times, 43 cases were repaired 3 times, 7 cases were repaired 4 times and 4 cases were repaired 5-7 times before this operation. The case history ranged from 6 months to 12 years. The orbital septum fat flap, orbital free fat graft and orbital filling were utilized. Results The repair results were very satisfactory in 87 cases (67.4%), satisfactory in 32 cases (24.8%), basically satisfactory in 7 cases (5.4%) and not satisfactory in 3 cases (2.3%). Conclusions It is a simple and effective approach that orbital septum fat flap, orbital free fat graft and orbital filling are used to repair the excessive width, theatrical fold line and multiple eyelid. Key words: Blepharoplasty; Post-operative deformities; Secondary repair

Locomotion analysis of a vibration-driven system with three acceleration-controlled internal masses

The controlled motion of a rigid body in the horizontal plane is investigated in this article. Three internal and acceleration-controlled masses are used to actuate the system. Dry friction acting between the system and the plane is isotropic. The dynamics of two basic motions of the system, that is, rectilinear and rotary motions, are first studied. Then by combining these two basic types of motions, planar locomotion of the system is constructed. Two typical planar trajectories of the system, that is, oblique lines and curve lines, are proposed and both approached with folding lines. The slope of the oblique lines and the curvature of the curves can be adjusted by varying the drive parameters, and the planar locomotion is thus controlled. To achieve a maximum average velocity, the drive parameters are optimized.

Regional dome evolution and its control on ore-grade distribution: Insights from 3D implicit modelling of the Navachab gold deposit, Namibia

We introduce a novel approach to analyse and assess the structural framework of ore deposits that fully integrates 3D implicit modelling in data-rich environments with field observations. We apply this approach to the early Palaeozoic Navachab gold deposit which is located in the Damara orogenic belt, Namibia. Compared to traditional modelling methods, 3D implicit modelling reduces user-based modelling bias by generating open or closed surfaces from geochemical, lithological or structural data without manual digitisation and linkage of sections or level plans. Instead, a mathematically defined spatial interpolation is used to generate 3D models that show trends and patterns that are embedded in large drillhole datasets. In our 3D implicit model of the Navachab gold deposit, distinctive high-grade mineralisation trends were identified and directly related to structures observed in the field. The 3D implicit model and field data suggest that auriferous semi-massive sulphide ore shoots formed near the inflection line of the steep limb of a regional scale dome, where shear strain reached peak values during fold amplification. This setting generated efficient conduits and traps for hydrothermal fluids and associated mineralisation that led to the formation of the main ore shoots in the deposit. Both bedding-parallel and highly discordant sets of auriferous quartz-sulphide veins are interpreted to have formed during the later lock-up stage of the regional scale dome. Additionally, pegmatite dykes crosscut and remobilise gold mineralisation at the deposit scale and appear to be related to a younger joint set. We propose that kilometre-scale active folding is an important deformation mechanism that influences the spatial distribution and orientation of mineralisation in ore deposits by forming structures (traps and pathways for fluids) at different preferred sites and orientations. We also propose that areas that experience high shear strain, located along the inflection lines of folds can act as preferred sites for syn-deformational hydrothermal mineralisation and should be targeted for regional scale exploration in fold and thrust belts. Our research also suggests that examination of existing drillhole datasets using 3D implicit modelling is a powerful tool for spatial analysis of mineralisation patterns. When combined with fieldwork, this approach has the potential to improve structural understanding of a variety of ore deposits.