Research On The Folding Interference And The Mechanical Properties Of Origami Mechanism

Origami mechanism is a kind of folding mechanism.It has a flexible and changeable structure,enable the deployment of large structures from small volumes,and are potentially reconfigurable.These origami mechanisms with various configurations have been applied to many engineering and technical fields,such as aerospace and medical technology.However,at present,the application of origami mechanism is still limited to a few limited configurations,while other rich and diverse configurations still remain at the theoretical level.There are two main reasons that restrict the transformation of these diverse configurations to actual mechanism design results.One is that when the configurations are complex and the angle of folding is not limited in the folding process,the paper surface is prone to cross-collision,leading to mechanism damage.Secondly,the mechanics theory is the basis of mechanism bearing capacity design.However,the research theory of origami mechanism mainly focuses on kinematics analysis,and the research results of mechanics analysis are very few.This paper focuses on the above two aspects.The main research work includes the following aspects:(1)Describe the fold pattern and analyse the configuration of origami mechanism.The symbolic marking method is used to express the fold pattern information of origami mechanism.The calculating equation of the angle between folds and the distinguishing method of mountain and valley folds are defined.The kinematic constraints needed to achieve effective folding of the mechanism are analyzed.The equation of developability constraint is derived based on zero Gaussian curvature condition,and the equation of loop closure constraint is derived by coordinate transformation.Then the single-vertex origami mechanism and multi-vertex origami mechanism are studied separately.Combined with the equation of loop closure constraint and the degree of freedom of the mechanism,the folding kinematic variables used to describe the arbitrary instantaneous configuration of the mechanism are analyzed,including the folding angles and the position coordinates of any point on the paper surface,and the calculation method is studied.(2)Based on the configuration description method of origami mechanism,the paper surface interference is studied.Firstly,the form of interference is analyzed.According to the idea of geometric segmentation,the interference problem of various shapes of paper surface is simplified to the intersection judgment problem of space triangle face pairs,and four kinds of spatial position relations of face pairs are concluded.According to the mapping relationship between vectors and spatial positions,the corresponding judgment methods are studied for each spatial position relationship.The corresponding interference judgment program is compiled to analyze the calculation amount,calculation speed and accuracy of the algorithm.(3)Taking Miura origami mechanism unit as the research object,according to the folding trajectory and geometric characteristics of the mechanism,the relationship between the folding angles is analyzed,and the bending moment of the fold acting on the paper surface is solved through the deformation analysis.Based on the geometric characteristics and the stress forms of the paper surface,the paper surface was modeled by a thin plate model.By analyzing the internal force,the relationship between stress and displacement,bending moment and displacement is deduced.Based on the bending theory of thin plate with small deflection,the expression of the deflection curve is solved by Levy’s method and superposition principle.Then the relationship between bending moment and stress is deduced.Finally,the analysis results of the mechanical characteristics of the Miura origami mechanism unit is verified by the calculation and simulation analysis of an example.