Kinematics of Origami Structures with Creased Folds

Abstract

Having reviewed the existing and potential engineering applications of active origami structures in Chap. 1, it is evident that such structures have significant complexity in their geometry and motion. Therefore, mathematical models for origami are needed to enable the development of advanced active origami structures. The following assumptions generally apply to the development of mathematical models for origami: folds are straight creases (termed as creased folds), and planar faces bounded by the folds and the sheet boundary are rigid (i.e., these faces do not stretch or bend). In this chapter, we present a kinematic model for origami based on such assumptions. We also address the implementation of the model in a computational environment. 2.1 Introduction Traditionally, origami is known as the art of folding sheets of paper into decorative and often intriguing shapes, either abstract in form or representative of realistic objects (e.g., plants, animals) [1]. As reviewed in Chap. 1, origami is currently being applied to the development of novel engineering structures comprised of complex materials. Kinematic modeling of origami structures, which is the study of their motion without considering their constituent materials or the physical stimuli causing such a motion, is of high importance as it permits the understanding of the complex deformation of origami structures and the development of computational tools for their simulation [2-4]. Kinematic modeling of origami structures is also the first step towards the full physical modeling of such structures. The reader is referred to Sect. 1.4 for a review on previous efforts in kinematic modeling and simulation of origami structures. In this chapter, we present a kinematic model for origami and we also address the implementation of such a model in a computational framework. Electronic Supplementary Material The online version of this article (https://doi.org/10.1007/ 978-3-319-91866-2_2) contains supplementary material, which is available to authorized users.