SearcharxivSearch

arXiv subjects

Simon D. Guest

Publications and source records attributed to Simon D. Guest.

9 recordsLinked to original sources

A new method for generalizing non-self-intersecting flexible polyhedra

A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting flexible closed polyhedral surfaces (i.e. flexible polyhedra). These flexible polyhedra can be non-triangulated, exhibit multiple kinematic degrees of freedom, and possess topologies beyond the sphere. The geometric result provides fresh insights into the geometry of origami and the design of engineering mechanisms, such as sealed-chamber robotics and distortion-free metamorphic grippers.

math.MG

Real and complexified configuration spaces for planar 4-bar linkages

This note is a complete library of symbolic parametrized expressions for both real and complexified configuration spaces of a planar 4-bar linkage. Building upon the previous work from Izmestiev (2015), this library expands on the expressions by incorporating all four rotational angles across all possible linkage length choices, along with the polynomial relation between diagonals. Furthermore, a complete MATLAB app script is included, enabling visualization and parametrization. The derivations are presented in a detailed manner, ensuring accessibility for researchers across diverse disciplines.

math.MG

On rigid origami III: local rigidity analysis

Rigid origami is examined from the perspective of rigidity theory. First and second order rigidity are defined from local differential analysis of the consistency constraint; while the static rigidity and prestress stability are defined after finding the form of internal force and load. This article will show that first-order or static rigidity implies prestress stability, which implies second-order rigidity, which implies rigidity, but none of these is reversible. Examples are given of rigid origami structures with these different kinds of rigidity. Examining the different aspects of the rigidity of origami might give a novel perspective for the development of new folding patterns, or for the design of origami structures where some rigidity is required.

math.MG

On Rigid Origami I: Piecewise-planar Paper with Straight-line Creases

We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First, we give definitions on important concepts in rigid origami, then focus on how to describe the configuration space of a creased paper. The shape and 0-connectedness of the configuration space are analyzed using algebraic, geometric and numeric methods, where the key results from each method are gathered and reviewed.

math.MG

Approximating a Target Surface with 1-DOF Rigid Origami

We develop some design examples for approximating a target surface at the final rigidly folded state of a developable quadrilateral creased paper, which is folded with a 1-DOF rigid folding motion from the planar state. The final rigidly folded state is reached due to the clashing of panels. Now we can approximate some specific types of non-developable surfaces, but we do not yet fully understand how to approximate an arbitrary surface with a developable creased paper that has limited DOFs. Our designs might have applications in areas related to the formation of a shell structure from a planar region.

math.MG

New Rigid-foldable Developable Quadrilateral Creased Papers

This article extends the range of 1-DOF rigid-foldable developable quadrilateral creased papers. In a previous article, we put forward a sufficient and necessary condition for a quadrilateral creased paper to be rigid-foldable, and introduce a special sufficient condition that is convenient for practical use, generating quadrilateral creased paper by stitching basic units. In this article we develop new flat-foldable units and show how these can be used to construct a series of more complex rigid-foldable developable quadrilateral creased papers.

math.MG

Keeping it Together: Interleaved Kirigami Extension Assembly

Traditional origami structures can be continuously deformed back to a flat sheet of paper, while traditional kirigami requires glue or seams in order to maintain its rigidity. In the former, non-trivial geometry can be created through overfolding paper while, in the latter, the paper topology is modified. Here we propose a hybrid approach that relies upon overlapped flaps that create in-plane compression resulting in the formation of "virtual" elastic shells. Not only are these structures self-supporting, but they have colossal load-to-weight ratios of order 10000.

cond-mat.mtrl-sci

On Rigid Origami II: Quadrilateral Creased Papers

Miura-ori is well-known for its capability of flatly folding a sheet of paper through a tessellated crease pattern made of repeating parallelograms. Many potential applications have been based on the Miura-ori and its primary variations. Here we are considering how to generalize the Miura-ori: what is the collection of rigid-foldable creased papers with a similar quadrilateral crease pattern as the Miura-ori? This paper reports some progress. We find some new variations of Miura-ori with less symmetry than the known rigid-foldable quadrilateral meshes. They are not necessarily developable or flat-foldable, and still only have single degree of freedom in their rigid folding motion. This article presents a classification of the new variations we discovered and explains the methods in detail.

math.MG

Contractile and mechanical properties in epithelia with perturbed actomyosin dynamics

Mechanics has an important role during morphogenesis, both in the generation of forces driving cell shape changes and in determining the effective material properties of cells and tissues. Drosophila dorsal closure (DC) has emerged as a model system for studying the interplay between tissue mechanics and cellular activity. Thereby, the amnioserosa (AS) generates one of the major forces that drive DC through the apical contraction of its constituent cells. We combined quantitation of live data, genetic and mechanical perturbation and cell biology, to investigate how mechanical properties and contraction rate emerge from cytoskeletal activity. We found that a decrease in Myosin phosphorylation induces a fluidization of AS cells which become more compliant. Conversely, an increase in Myosin phosphorylation and an increase in actin linear polymerization induce a solidification of cells. Contrary to expectation, these two perturbations have an opposite effect on the strain rate of cells during DC. While an increase in actin polymerization increases the contraction rate of AS cells, an increase in Myosin phosphorylation gives rise to cells that contract very slowly. The quantification of how the perturbation induced by laser ablation decays throughout the tissue revealed that the tissue in these two mutant backgrounds reacts very differently. We suggest that the differences in the strain rate of cells in situations where Myosin activity or actin polymerization is increased arise from changes in how the contractile forces are transmitted and coordinated across the tissue through ECadherin mediated adhesion. Our results show that there is an optimal level of Myosin activity to generate efficient contraction and suggest that the architecture of the actin cytoskeleton and the dynamics of adhesion complexes are important parameters for the emergence of coordinated activity throughout the tissue.

q-bio.CB