Research On Fitting Axisymmetric Target Surfaces Based On Waterbomb Origami

Origami refers to obtaining various three-dimensional target shapes from two-dimensional flat materials by folding crease patterns.Common types of origami include Miura-ori origami,Resch origami,Yoshimura origami,and Waterbomb origami.The study of waterbomb origami has always inspired the design of engineering structures and the realization of functions.Due to the high degree of freedom of waterbomb origami,the unfolding ratio of the six-fold waterbomb unit between the unfolded and closed states is large,so the flexible reverse design of the origami structure can be achieved by utilizing the waterbomb pattern.However,users cannot easily use this kind of origami to fit the target surface with axisymmetric characteristics,and there is a lack of research on waterbomb origami and its derivative structure.Then there is a certain optimization space for building 3D axisymmetric origami structures based on waterbomb origami.To solve these problems,this thesis proposes an interactive study based on waterbomb origami fitting of axisymmetric target surfaces,while solving two kinds of optimization problems,further expanding the exploration of axisymmetric deployable structures.The main research work of this thesis includes the following contents:(1)An interactive modeling method of waterbomb origami fitting axisymmetric target surfaces is proposed,which can flexibly design three-dimensional waterbomb origami structures.This method first uses interactive modeling to design two-dimensional contour curves,then uses the contour curves to rotate around a common axis to generate a threedimensional target surface,and obtains a base mesh model by tiling waterbomb units.Next,geometric constraints are added to the base mesh model to minimize the amount of flat-foldable residuals.Through symmetry and periodic repetition,the optimized model is accurately adjusted to obtain regular planar crease patterns,and ultimately a three-dimensional axisymmetric waterbomb origami structure that meets geometric constraints is obtained.At the same time,the study investigates the rigid folding of waterbomb origami structures and expands the exploration of waterbomb-derived origami structures.The experimental results indicate that this method provides an effective approach for reverse design of waterbomb origami structures and has good application prospects.(2)A multi-objective optimization method for modeling axisymmetric waterbomb origami structures is proposed.Firstly,constraint conditions are defined,and then apply constraints to the base mesh model to solve two types of optimization problems to minimize constraint residuals,thus obtaining a three-dimensional waterbomb origami structure,while demonstrating the origami structure that satisfies three constraints.In addition,the study also presents rigid folding sequence of waterbomb origami structures,data comparison of multiple optimization methods,and physical production of origami.The experimental results show that this method can achieve good results in constructing axisymmetric waterbomb origami structures.(3)Based on the above research,this thesis adopts a modular design approach and successfully develops and implements a prototype system for fitting axisymmetric target surfaces based on waterbomb origami.The prototype system embeds the above two methods,and the main functional modules include interactive interface,data processing module and algorithm module.The experimental results show that the system has good operability and effectiveness,provides comprehensive basic functions,and verifies the theoretical significance and practical value of this study.