Kinematics of Origami Structures With Smooth Folds

Abstract

Origami provides both inspiration and potential solutions to the fabrication, assembly, and functionality of various structures and devices. Kinematic modeling of origamibased objects is essential to their analysis and design. Models for rigid origami, in which all planar faces of the sheet are rigid and folds are limited to straight creases having only zeroth-order geometric continuity, are available in the literature. Many of these models include constraints on the fold angles to ensure that any initially closed strip of faces is not torn during folding. However, these previous models are not intended for structures with non-negligible fold thickness or with maximum curvature at the folds restricted by material or structural limitations. Thus, for general structures, creased folds of merely zeroth-order geometric continuity are not appropriate idealizations of structural response, and a new approach is needed. In this work, a novel model analogous to those for rigid origami with creased folds is presented for sheets having realistic folds of nonzero surface area and exhibiting higher-order geometric continuity, here termed smooth folds. The geometry of smooth folds and constraints on their associated shape variables are presented. A numerical implementation of the model allowing for kinematic simulation of sheets having arbitrary fold patterns is also described. Simulation results are provided showing the capability of the model to capture realistic kinematic response of origami sheets with diverse fold patterns.

Design and simulation of origami structures with smooth folds

“…As the faces of the origami structures are assumed planar and rigid (see Definition 2.1), the order of geometry continuity of the origami structures is considered in Continuity conditions and parametric formulations of the curves c i (ζ 1 ) for various orders of geometric continuity are provided in [33]. Schematics of folds having various orders of geometric continuity and their associated signed curvature fields κ(s) as functions of arc-length are shown in figure 2.…”

“…Such constraints are presented in detail in [33] and summarized in this section. First, let the angles between centrelines of folds adjacent to a common interior fold intersection be denoted as α jk , j ∈ {1, .…”

“…A model for the kinematics of origami structures with smooth folds and rigid faces was fully addressed by the authors in [33]. There, a detailed description of the geometry of smooth folds having arbitrary order of geometric continuity and their associated kinematic variables were provided.…”

“…In addition, the mapping between reference and current configurations fully determined by the kinematic variables of the smooth folds was also derived. Finally, Peraza et al [33] provides an approach for kinematic simulation of origami structures with smooth folds having arbitrary reference configuration and subject to arbitrary folding motion. Such a model and simulation approach are described in more detail in §2.…”

“…The outline of this paper is as follows: a review of the main aspects of the kinematic model for origami with smooth folds presented by the authors in [33] is provided in §2. The description of the origami design problem addressed here is presented in §3.…”