Kinematic Analysis Of Rigid Origami Mechanism And Design Of Double Configuration Origami Robot

Rigid origami mechanism is an important branch of folding and unfolding mechanism.In the folding process,the rigid origami remain rigid except the crease.As it is easy to deform,fold and control,rigid origami has been widely used in the fields of architecture,super materials,aerospace,robot and so on.This paper mainly studies the folding process planning method of rigid origami,and designs a robot from rigid origami with walking and swimming configuration.This paper provides reliable theoretical support and design reference for promoting the practical application of origami mechanism in engineering field.Firstly,in order to analyze the folding configuration of rigid origami,the attached coordinate system is established on each creases.Through the transformation of coordinate systems,the constraint equations between the fold angles of a single vertex are derived,and the explicit expression of unknown fold angles are obtained.The interference solution is eliminated by the mutual check of the two equations,and the actual fold angles in folded state are obtained.The number of solutions of unknown fold angles are discussed by using geometric and numerical method,and the geometric significance of explicit expression method is analyzed.The calculation method of vertex position when the fold angles are known is analysed by coordinate transformation,then the various configuration states in folding process can be obtained.Based on the intersection test algorithm of triangle facets,the interference of folding mechanism is judged.Secondly,in order to obtain the free and dependent variables in folding process of rigid origami,a method using adjacency matrix is proposed to analyze the free fold angles.This method is applicable to the mechanism with redundant constraints,and can judge the number and distribution of redundant constraints.The relationship between free angle and number of crease of single vertex is analyzed by using the spiral theory.The topological relation between the vertices is expressed by adjacency matrix,and the elimination matrix is introduced to describe the process of determining the motion state of vertex by matrix product.By judging the sum of row elements in the adjacency matrix corresponding the vertex,the number of redundant constraints of the vertex is determined.The motion state of the cross crease vertex is analyzed.The method of classifying and simplifying configuration avoids the calculation error of free fold angles caused by the motion interlock at the cross crease vertex.By extending the crease in the loop configuraion and connecting the intersection points,the equivalent configuration of the loop configuration is obtained,and the free fold angles of the loop configuration is analyzed.Thirdly,a folding process planning algorithm is proposed by combining the rapidly exploring radom tree method and explicit expression method.The process planning problem with closed-loop constraints is solved.This algorithm can detect and avoid structural interference in the folding process.Using the continuously folding attribute,the reasonable folded state in the folding planning process is selected,and the redundancy solution of the unknown fold angles is avoided.Mountain valley(MV)assignment and pop-up and pop-down attribute are used to reduce the selectivity of the new folded state when the initial configuration is fully flattened.The critical state with only one solution of single vertex is defined,and the critical state of origami configuration is obtained by binary search method.With the help of Qt platform,the folding process simulation software is built using C++,and the folding process of origami configuration is analyzed with this software,which verifies the effectiveness of the planning algorithm.Finally,based on waterbomb pattern,the robot with walking and swimming configuration is designed by increasing cross creases.The folding process of the robot from swimming configuration to walking configuration is planned,and the transformation performance between two configurations is verified.In walking configuration,due to the difference of foot thrust,the ground contact points move alternately,so as to realize the advance of the whole configuration;In the swimming configuration,the tail is flexible structure,which provides forward thrust through the wave swing of the tail.The robot walking gait are studied,and the principle of walking is analyzed.The propulsion force during the period of tail fin swing is calculated by using the propulsion force formula,and the flexible deformation of the tail structure is analyzed.The walking and swimming experiments of the twoconfiguration robot are carried out,which test the walking and swimming performance of the origami and verify the rationality of this design.