Research On Mechanical Properties Of Rigid Origami Structure Based On Mobility Analysis

In recent years,the ancient origami technology has been gradually used in mathematics,physics,biology,engineering and other fields,and the rigid origami structure has received more attention.One of the important characteristics of rigid origami structure is mobility,and it is necessary to determine whether the origami structure is movable.Therefore,this paper proposes a set of theoretical analysis methods to judge the rigid mobility of origami structures.On this basis,the motion bifurcation path and motion path tracking of rigid origami structures are analyzed.At present,there is little research on non Euclidean origami in the origami field.Therefore,this paper systematically studies non Euclidean origami units,and proposes various combinations of rigid origami configurations based on non Euclidean origami units.The introduction of non Euclidean origami units provides a new design perspective and theoretical support for the design and application of rigid origami structures.The main research contents of this paper are as follows:Based on the Jacobian matrix and Moore Penrose generalized inverse matrix of the constraint equation,the sufficient and necessary conditions for determining the mobility of rigid origami structures were derived,and the expressions of the displacement of the mechanism and the corresponding first-order Jacobian matrix were derived.Through the expressions,the unknowns in the coefficient vector could be effectively separated,which was helpful for solving the multivariate quadratic equations.The bifurcation paths of the moving singular points in the rigid origami structure were analyzed,and the number of the bifurcation paths could be effectively obtained by using the proposed method.The general formula of the higher order derivative of the displacement of the mechanism was derived.The rigid motion path of the rigid origami structure was effectively tracked by using the time domain and the method of modifying the higher-order term of the bar length constraint.Through this method,the error of the system in the motion process and the whole process of tracking the system motion could be effectively controlled.Finally,three numerical examples were given to validate the proposed mobility determination,motion bifurcation path analysis and motion path tracking methods.The rigid folding movement process of non Euclid origami unit was analyzed,and it was concluded that there was no motion path bifurcation phenomenon of non Euclid origami unit in the movement process,and the relationship between dihedral angles was non monotonic.The non Euclid origami unit was placed on the space sphere,and the special crease was derivedΙAnd special crease II.Based on the relationship between the sector angles of non Euclidean origami units,non Euclidean origami units were divided into general non Euclidean origami units and special non Euclidean origami units.The special non Euclidean origami unit with collinear characteristics and plane folding characteristics was analyzed.On this basis,the non Euclidean origami basic combination unit was proposed,and various rigid origami configurations were combined,providing a richer basis for origami configuration design.Based on the non Euclidean origami unit,an origami gripper with bistable characteristics was designed.The gripper made use of the feature that the non Euclidean origami unit did not have a motion bifurcation path in the motion process,and avoided the failure of grasping task caused by the motion bifurcation path;At the same time,according to the non monotonic relationship between the adjacent dihedral angles of the non Euclidean origami unit,pre bending spring steel was arranged at the corresponding crease of the gripper to make it have the characteristics of bistability.With the characteristics of bistability,it was possible to maintain the grasp of the object after grasping it without the need to input external force.The geometry of the origami gripper was parametrically analyzed,and the influence of the parameters such as the sector angle and length of the non Euclidean origami unit was studied to realize the programmability of the configuration design.Based on the principle of minimum potential energy,the grasping force of the gripper was deduced,and the factors affecting the grasping force,such as the sector angle and the initial angle of pre bending spring steel,were parametrically analyzed.A real object was made for the origami gripper,and the pre bent spring steel was used at the end crease of the gripper,so that it had the characteristics of bistability.Under the action of not continuously inputting external force after grasping the object,it can keep grasping the object.Based on the non Euclidean origami unit,a geometrically equivalent non Euclidean origami tube was designed and combined with Euclidean origami tube to form a new cross origami tube.Then its mobility was judged.Its rigid mobility was verified through finite element numerical simulation,theoretical analysis of spatial rotation matrix and translation matrix.The length dimension L_e in the x direction,the width dimension W_e in the y direction and the height dimension H_e in the z direction of the cross origami tube were derived geometrically.The rigid movable range of cross origami tube in x,y and z directions was studied.In the x direction,when the cross origami tube was under pressure,due to the geometric self-locking feature,the previous section was rigid and movable.When the locked angle value was reached,the rigid mobility movement of the cross origami tube ends;In the y direction,when the cross origami tube was compressed,the structure was rigid and movable until it was flattened;In the z direction,when the cross origami tube was under pressure,due to the self-locking characteristic of contact,the previous section was rigid motion.When the face to face contact structure was self-locking,the rigid motion of the cross origami tube ends.The cross origami tube composed of Euclid origami tube and non Euclid origami tube was designed to form a new cross origami tube metamaterial structure.The motion characteristics in three directions and the rigid movable range of the cross origami tube metamaterial structure were studied.Due to the geometric self-locking of the structure in the x direction,the rigid movable section was small;The whole process of the structure was rigid and movable in the y direction;Due to contact self-locking in the z direction,the front section of the structure was rigid and movable,while the rear section was non rigid.The compression of the cross folding tube metamaterial structure in the z direction had two stages of deformation.The first stage of deformation was the rigid movement of the folding tube,which mainly consumes energy through the rotation of the crease;In the second stage,the deformation mainly showed the deformation mode of diamond honeycomb,and the deformation was mainly the buckling deformation of the panel.The accuracy of theoretical model calculation was verified by comparison of theoretical model calculation,finite element model simulation and experiment.Based on the theoretical calculation model,the geometric parameters that affect the compression performance of the cross origami tube metamaterial structure were analyzed parametrically.