Rope Coiling Research Articles

3D‐Printed Soft Proprioceptive Graded Porous Actuators with Strain Estimation by System Identification

Integration of both actuation and proprioception into the robot body leads to a single integrated system that can deform and sense. Within this work, liquid rope coiling is used to 3D‐print soft graded porous actuators. By fabricating these actuators from a conductive thermoplastic elastomer, piezoresistive sensing is directly integrated. These sensor‐integrated actuators exhibit nonlinearities and hysteresis in their resistance change. To overcome this challenge, a novel approach that uses identified Wiener–Hammerstein (WH) models is proposed to estimate the strain based on the resistance change. Three actuator types were investigated, namely, a bending actuator, a contractor, and a three degrees of freedom bending segment. By using the design freedom of additive manufacturing to set the porosity, the actuation and sensing behavior of a contracting actuator can be programmed. Furthermore, the WH models can provide strain estimation with on average high fits (83%) and low root mean square (RMS) errors (6%) for all three actuators, which outperformed linear models significantly (76.2/9.4% fit/RMS error). In these results, it is indicated that combining 3D‐printed graded porous structures and system identification can realize sensor‐integrated actuators that can estimate their strain but also tailor their behavior through the porosity.

PolyStokes: A Polynomial Model Reduction Method for Viscous Fluid Simulation

Standard liquid simulators apply operator splitting to independently solve for pressure and viscous stresses, a decoupling that induces incorrect free surface boundary conditions. Such methods are unable to simulate fluid phenomena reliant on the balance of pressure and viscous stresses, such as the liquid rope coil instability exhibited by honey. By contrast, unsteady Stokes solvers retain coupling between pressure and viscosity, thus resolving these phenomena, albeit using a much larger and thus more computationally expensive linear system compared to the decoupled approach. To accelerate solving the unsteady Stokes problem, we propose a reduced fluid model wherein interior regions are represented with incompressible polynomial vector fields. Sets of standard grid cells are consolidated into super-cells, each of which are modelled using a quadratic field of 26 degrees of freedom. We demonstrate that the reduced field must necessarily be at least quadratic, with the affine model being unable to correctly capture viscous forces. We reproduce the liquid rope coiling instability, as well as other simulated examples, to show that our reduced model is able to reproduce the same fluid phenomena at a smaller computational cost. Futhermore, we performed a crowdsourced user survey to verify that our method produces imperceptible differences compared to the full unsteady Stokes method.

Modeling for silicone foam material extrusion with liquid rope coiling

This research demonstrates a Modeling idea using parametric Modeling and considering the process to predict coiling patterns effectively in open-cell foams material extrusion (MEX) with liquid rope coiling (LRC) effect. The model consists of three sub-models, including pneumatic extrusion model, liquid rope coiling model, and geometric model, considering material properties, material extrusion, falling, LRC, pattern formation process and device structure. The model uses four MEX process parameters (back pressure, moving speed, inner nozzle diameter, and nozzle height) to predict three geometric parameters of the coiling pattern. The capability to predict pattern shape (period length, width, and loop length) accurately is validated by comparing the fit of predicted and experimental values when adjusting the process parameters, with R-squared coefficients up to 0.957. Then, application value is demonstrated by printing silicone open-cell foams under the guidance of the proposed model and studying the compression properties of these foams. The obtained three-region stress-strain curves indicate the feasibility of variable stiffness foam fabrication by adjusting the process parameters according to the proposed model during the printing process. Based on the results, the proposed model demonstrates accuracy in predicting geometric parameters of translational coiling pattern, makes predictable manufacturing of complex cellular structures available, and provides a foundation for design and fabrication of load-based variable stiffness silicone open-cell foam.

3D printing of soft fluidic actuators with graded porosity

New additive manufacturing methods are needed to realize more complex soft robots. One example is soft fluidic robotics, which exploits fluidic power and stiffness gradients. Porous structures are an interesting type for this approach, as they are flexible and allow for fluid transport. In this work, the infill foam (InFoam) method is proposed to print structures with graded porosity by liquid rope coiling (LRC). By exploiting LRC, the InFoam method could exploit the repeatable coiling patterns to print structures. To this end, only the characterization of the relationship between nozzle height and coil radius and the extruded length was necessary (at a fixed temperature). Then by adjusting the nozzle height and/or extrusion speed the porosity of the printed structure could be set. The InFoam method was demonstrated by printing porous structures using styrene-ethylene-butylene-styrene (SEBS) with porosities ranging from 46% to 89%. In compression tests, the cubes showed large changes in compression modulus (more than 200 times), density (-89% compared to bulk), and energy dissipation. The InFoam method combined coiling and normal plotting to realize a large range of porosity gradients. This grading was exploited to realize rectangular structures with varying deformation patterns, which included twisting, contraction, and bending. Furthermore, the InFoam method was shown to be capable of programming the behavior of bending actuators by varying the porosity. Both the output force and stroke showed correlations similar to those of the cubes. Thus, the InFoam method can fabricate and program the mechanical behavior of a soft fluidic (porous) actuator by grading porosity.

High-Throughput and Controllable Fabrication of Helical Microfibers by Hydrodynamically Focusing Flow.

Due to the unique spiral geometry, different functional helical fibers are fabricated to perform vital tasks, including cargo transportation, medical treatment, cell manipulation, and so on. Although microfluidic techniques are widely used to fabricate helical fibers, the problems of channel blockage and spinning instability have not been well solved, which limits the mass preparation and practical application of spiral microfibers. In addition, the spinning mechanism is simply limited to liquid rope coiling, which has little impact on the design of microfluidic devices. Here, new types of microfluidic devices, which were easy to make and exhibited excellent spiral spinning performance, were designed. It was found that adding a sleeve layer outside the inner core needle in a coaxial microfluidic device could effectively promote the stable formation of helical microfibers. This novel microchannel could fabricate helical microfibers of more than 100 m in length continuously at one time with almost no blockage or deformation, and the key parameters of the fibers could be precisely adjusted. Combined with micro-particle image velocimetry (micro-PIV) measurements, it was confirmed that the improvement in the spinning performances was mainly attributed to the emergence of a focusing flow in the presence of the sleeve layer. After loading magnetic nanoparticles, the helical microfibers exhibited excellent motion manipulation capabilities, which showed great potential for drug delivery, cargo transportation, clogging removal, etc. This new design not only realized the high-throughput fabrication of helical microfibers but also provided deeper insights into the underlying mechanisms of spiral generation and new ideas for the design of microfluidic devices.

A unified second-order accurate in time MPM formulation for simulating viscoelastic liquids with phase change

We assume that the viscous forces in any liquid are simultaneously local and non-local , and introduce the extended POM-POM model [McLeish and Larson 1998; Oishi et al. 2012; Verbeeten et al. 2001] to computer graphics to design a unified constitutive model for viscosity that generalizes prior models, such as Oldroyd-B, the Upper-convected Maxwell (UCM) model [Sadeghy et al. 2005], and classical Newtonian viscosity under one umbrella, recovering each of them with different parameter values. Implicit discretization of our model via backward Euler recovers the variational Stokes solver of [Larionov et al. 2017] for Newtonian viscosity. For greater accuracy, however, we introduce the second-order accurate Generalized Single Step Single Solve (GS4) scheme [Tamma et al. 2000; Zhou and Tamma 2004] to computer graphics, which recovers all prior second-order accurate time integration schemes to date. Using GS4 and our generalized constitutive model, we present a Material Point Method (MPM) for simulating various viscoelastic liquid behaviors, such as classical liquid rope coiling, buckling, folding, and shear thinning/thickening. In addition, we show how to couple our viscoelastic liquid simulator with the recently introduced non-Fourier heat diffusion solver [Xue et al. 2020] for simulating problems with phase change, such as melting chocolate and digital fabrication with 3D printing. While the discretization of heat diffusion is slightly different within GS4, we show that it can still be efficiently solved using an assembly-free Multigrid-preconditioned Conjugate Gradients solver. We present end-to-end 3D simulations to demonstrate the versatility of our framework.

Adapted SIMPLE Algorithm for Incompressible SPH Fluids With a Broad Range Viscosity.

In simulating viscous incompressible SPH fluids, incompressibility and viscosity are typically solved in two separate stages. However, the interference between pressure and shear forces could cause the missing of behaviors that include preservation of sharp surface details and remarkable viscous behaviors such as buckling and rope coiling. To alleviate this problem, we introduce for the first time the semi-implicit method for pressure linked equations (SIMPLE) into SPH to solve incompressible fluids with a broad range viscosity. We propose to link incompressibility and viscosity solvers, and impose incompressibility and viscosity constraints iteratively to gradually remove the interference between pressure and shear forces. We will also discuss how to solve the particle deficiency problem for both incompressibility and viscosity solvers. Our method is stable at simulating incompressible fluids whose viscosity can range from zero to an extremely high value. Compared to state-of-the-art methods, our method not only produces realistic viscous behaviors, but is also better at preserving sharp surface details.

Helical hollow fibers via rope coiling: Effect of spinning conditions on geometry and membrane morphology

Helical hollow fiber membranes from poly(ether sulfone) were spun via dry-wet spinning, making use of the liquid rope coiling phenomenon. The polymer solution composition was changed by varying the coagulation value and adding PEG400 as pore former. The bore liquid composition, outer coagulation bath temperature, air gap, polymer dope and bore liquid flowrates were varied to map the conditions where helical fibers form. It was observed that increasing air gap changed fiber geometry from straight to helical. Increasing the outer coagulation bath temperature caused helical geometries to become irregular or straight under identical spinning conditions, possibly due to the higher water vapour absorption in the air gap. Regularly helical fibers could, however, be spun with a coagulation bath at 50 °C under a variety of conditions. Comparing fibers spun under the same conditions with different solutions, it was observed that as the solution's viscosity increased, the geometry shifted towards helical. Increasing the bore liquid solvent strength so as to form the skin on the bore side yielded straight fibers due to the fast solidification of the fibers before curling and all helical fibers fabricated had a denser skin on the shell side. During filtrations of yeast suspensions, the helical fibers experienced less fouling with the feed on either the bore or the shell side of the membrane, which shows that using liquid rope coiling to spin helical fibers is a promising, practical method of alleviating fouling in membrane filtrations.

Slip Morphology of Elastic Strips on Frictional Rigid Substrates.

The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which-when the bending elasticity dominates over the effect of gravity-are classified into three distinct types of states: pinned, partially slipped, and completely slipped, depending on the magnitude of the vertical strain and the coefficient of static friction. We develop a theory of elastica under mixed clamped-hinged boundary conditions combined with the Coulomb-Amontons friction law and find excellent quantitative agreement with simulations and controlled physical experiments. We also discuss the effect of gravity in order to bridge the difference in the qualitative behaviors of stiff strips and flexible strings or ropes. Our study thus complements recent work on elastic rope coiling and takes a significant step towards establishing a unified understanding of how a thin elastic object interacts vertically with a solid surface.

Silicone Foam Additive Manufacturing by Liquid Rope Coiling

This study investigates the additive manufacturing (AM) of a porous silicone foam by liquid rope coiling, a method in which a thin viscous fluid stream generates a helical coil structure while extruding from a specific height onto a moving surface. The moisture-cured silicone liquid rope coiling experiments were conducted to identify effects of four parameters, height, flow rate, nozzle size, and travelling speed, on the regime diagram and dimensions of coiling patterns, including steady, meandering, figure-of-eight, coiling, and side kicks. The coiling pattern was demonstrated to be feasible for layer-by-layer AM of silicone foams.

Liquid rope coiling: a synoptic view

In liquid rope coiling, a slender jet of viscous fluid falling onto a rigid surface builds a rotating corkscrew-like structure. Here, I use a numerical continuation method to construct a complete regime diagram for liquid rope coiling. I first consider the onset of coiling, and show that a suitable onset criterion is that the radius $a_{1}$ of the rope itself be just equal to the radius $R$ of the coil. Numerical calculation of the critical surface $a_{1}=R$ in the space of the dimensionless fall height $\unicode[STIX]{x1D6F1}_{H}$, flow rate $\unicode[STIX]{x1D6F1}_{Q}$ and nozzle diameter $\unicode[STIX]{x1D6F1}_{d}$ shows that the surface has four distinct asymptotic limits corresponding to a viscous (V) mode, a gravitational (G) mode and two inertial modes (I1, I2) which are distinguished by how much the tail of the jet is stretched by gravity. Exact expressions for the onset frequencies in each of these four modes are determined. Finally, the regime diagram is constructed in the form of contour plots of the dimensionless coiling frequency as a function of $\unicode[STIX]{x1D6F1}_{H}$ and $\unicode[STIX]{x1D6F1}_{Q}$ for several values of $\unicode[STIX]{x1D6F1}_{d}$. The diagram exhibits a total of six modes: V, G, I1, I2, a multivalued inertio-gravitational (IG) mode and a third inertial mode I3 with viscosity-dominated stretching of the tail. The regime diagram permits prediction of the coiling frequency for given values of the fall height, flow rate, viscosity and nozzle diameter, and should therefore be useful in practical applications ranging from non-woven textile production to 3D printing.

Facile fabrication of helical microfluidic channel based on rope coiling effect

A rapid and simple fabrication approach to achieve helical microfluidic channels with circular cross section using template-assisted method is proposed in this article based on rope coiling effect in the extrusion process of a desktop 3D printer. Rope coil effect is a common phenomenon in the falling process of a slender string of viscous fluid and is used to fabricate helical microstructures served as the templates in the sacrificial template-assisted method, which holds great promise to fabricate micro-channels with desired vascular architectures. The helical microstructures are fabricated with the high viscous PVA (Polyvinyl alcohol) paste extruded out of the nozzle orifice from a certain falling height. After the PDMS block embedded with PVA helical template has been fabricated, the template would then be removed by melting in hot water easily to obtain the microfluidic channels. Two major processing parameters, falling height and flow rate are studied in relation to two main geometric features of helical structures: coil diameter and wire diameter. Besides, the dimension and the shape of helical microstructures are further studied for fabrication of microfluidic channels with varying geometric parameters. The presented method facilitates the rapid and convenient construction of three-dimensional (3D) helical microfluidic channels for a wide variety of lab-on-chip applications.

Preparation of helical fibers from cellulose–cuprammonium solution based on liquid rope coiling

A new method for large-scale mimicking of the helical structure of plant tendrils from cellulose solution was proposed based on liquid rope coiling of viscous fluid. In the spinning process, cellulose–cuprammonium solution was extruded from a certain height above a mobile coagulating bath. Helical structure was shown to form spontaneously at the surface of the coagulating bath as a result of buckling instability, and regenerated cellulose helical fiber was obtained after treatment with acid and air-drying. Spinning parameters, such as spinning height, flow rate and moving speed of the coagulating bath were examined in relation to the size and structure of the helical fiber. The microstructure of the helical fiber was further investigated by SEM. The diameters of the fiber and helix were found in the range of 100–400 and 300–700 μm, respectively. The helical fibers demonstrated high elongation at break and elasticity within a certain range of strain, which were attributed to the coiling structure. The microporous feature of the regenerated cellulose helical fiber shows potential as a helical scaffold and template for inorganic materials.

Buckling of Liquid Columns

Under appropriate conditions, a column of viscous liquid falling onto a rigid surface undergoes a buckling instability. Here we show experimentally and theoretically that liquid buckling exhibits a hitherto unsuspected complexity involving three different modes-viscous, gravitational, and inertial-depending on how the viscous forces that resist bending of the column are balanced. We also find that the nonlinear evolution of the buckling exhibits a surprising multistability with three distinct states: steady stagnation flow, "liquid rope coiling," and a new state in which the column simultaneously folds periodically and rotates about a vertical axis. The transitions among these states are subcritical, leading to a complex phase diagram in which different combinations of states coexist in different regions of the parameter space.

Validity test of a Stokes flow solver by fluid rope coiling: Toward plate-mantle simulation

In this study, we propose a so-called fluid rope coiling to use as a validity test of our simulation scheme designed to solve the plate-mantle problem in the Eulerian frame of reference. In a plate-mantle unified system, a subducting plate is known to show various large and complex deformations. A numerical simulation for the plate-mantle problem is required to solve such plate motions properly without serious numerical errors. Fluid rope coiling, in which a coiling motion of viscous fluid is poured onto a horizontal plane from a certain height with the shape of a thin rope, is known to be one such motion. We reproduced the coiling rope of a Stokes flow by two different methods: a three-dimensional simulation and simplified one-dimensional solution. Quantitative comparison of these methods enables us to evaluate the accuracy of the simulation scheme for large non-linear deformation problems.

The Broken Obelisk

The purpose of the present note is to alert scholars to the fact that following a cleaning programme undertaken in the late 1960s certain iconographic details apparently visible on the decorated face of the monument known as the Broken Obelisk should be treated with caution.As recounted by C. J. Gadd, the Broken Obelisk was found by Hormuzd Rassam in August 1853 at Nineveh, about halfway between Sennacherib's Palace and Ashurbanipal's Palace (Gadd 1936: 123; Rassam 1897: 9). It was probably in or near the Ishtar Temple (ibid.; Reade 2005: 373). The Obelisk was drawn on site (Fig. 1), either by Charles Hodder (Gadd 1936: 123) or by William Boucher, who arrived at Nineveh in March 1854 in order to help Rassam record some of the important sculptures he had found at Kouyunyik (Barnett 1975: 22; Rassam 1897: 37). Gadd describes how the obelisk was shipped with other sculptures from Basra to Bombay in the steam-frigate Acbar in March 1854, and from Bombay to London in the ship Merchantman, arriving in February 1855 (Gadd 1936: 123). It now has the British Museum number 118898 (56-9-9, 59).It is known as the Broken Obelisk because it is the upper part only of an obelisk with a stepped top. At the bottom it measures 65 × 41 cm, and it has an overall surviving height of 63 cm. There is a lengthy cuneiform inscription on three of the four sides (the short left side is blank) and on one of the long sides there is, in addition to the cuneiform inscription, a panel of carved decoration showing a king holding a rod and ring or (more likely) a mace and a coil of rope. In front of the king are two pairs of prisoners roped together. In the field above the prisoners, and in front of the king, are five divine symbols, comprising a horned cap, a crescent, a winged disc from which emerge two hands, one of them holding a bow, a bolt of lightning, and a rosette. The text (Grayson 1991: 99–105) recounts the achievements of a king who is thought to be Ashur-bel-kala (1073–1056 BC). It is usually inferred from the text that the obelisk was originally set up at Ashur.

Loops and and Illusions

Loops and and Illusions

SACRED NOISE IN DON DELILLO'S FICTION

SACRED NOISE IN DON DELILLO'S FICTION

The promotion and prevention of recoiling in a maximally snaillike vermetid gastropod: a case study for the centenary of Dollo's Law

The Neogene speciesPetaloconchus sculpturatuspresents a contradiction in terms, for it grows whorl “packages” of nearly perfect regularity, but ranks within the most geometrically irregular family of uncoiled gastropods, the Vermetidae. We perform a first biometric study of vermetids (only possible because sufficient regularity of growth permits us to number and identify whorls) to specify and characterize the factors on both sides of this “exquisite tension” between promotion and prevention of recoiling. Promoting factors include the older phyletic heritage of preserved dextral coiling, and the more immediate vermetid (or specifically petaloconchid) features of growth toward open spaces (where regular coiling might proceed in an unimpeded fashion); radular excision of discordant feeding tubes with shaping of the resulting scar so that growth may proceed in conformity with previous whorls; and locking of subsequent whorls upon a keel formed by longitudinal bead-rows of the previous whorl. Preventing factors include prominent phyletic heritage of all vermetids—maximal early irregularity enjoined by discordance between larval and subsequent growth (with teleoconch wrapping itself around the protoconch), thus precluding an ordered substrate to act as a foundation for regular whorl “packages” of intermediary growth—and a set of features specific to this lineage and acting as geometric constraints. In this category, we particularly document the exceedingly low rate of whorl expansion and the consequently wide umbilical space that produces a shell akin to winding a cylindrical coil of narrow-diameter rope around the periphery of a wide circular platform. This complex combination of promoting and preventing factors produces a shell that is tantalizingly close to fully regular, but cannot truly reattain this previous phyletic state—thus providing a fine example of Dollo's Law at the centenary of his formation of irreversibility.

The Case of the Mysterious Coil of Rope: Street Life and Jewish Persona in Rome in the Middle of the Sixteenth Century

The Case of the Mysterious Coil of Rope: Street Life and Jewish Persona in Rome in the Middle of the Sixteenth Century