A method for modeling and analyzing an over-constrained spatial four-bar mechanism combination

Abstract

The application provides a modeling and analysis method of an over-constrained space four-bar linkage mechanism combination, acquires a plurality of unit bodies used for constructing the over-constrained space four-bar linkage mechanism combination, splits each unit body into set particles, constructs a basic unit of a model of each unit body according to particle combination of the set particles, and constructs an additional rotary hinge unit of each unit body, combines the model of each unit body through the additional rotary hinge unit to construct a combination model, improves the modeling speed, and then analyzes a beam unit, a rotary hinge unit, a contact constraint unit and a torsional spring unit in each unit body model to obtain corresponding flexible deformation and particle internal force, cross-section contact force and side contact force, deformation driving force and rotary displacement, so as to analyze the deformation expansion process of the over-constrained space four-bar linkage mechanism combination, and avoid the problem of inaccurate analysis caused by the analysis of the whole unit body, and improve the analysis accuracy.

Description

Technical Field

[0001] This application relates to the field of modeling and motion analysis technology, and in particular to a modeling and analysis method for an over-constrained space four-bar linkage assembly. Background Technology

[0002] Bennett linkages refer to a special type of single-degree-of-freedom spatial four-bar linkage, also known as over-constrained spatial four-bar linkages. It consists of four links and four rotating hinges connecting them. The axes of these hinges are neither parallel nor intersecting at a single point, and each hinge axis is perpendicular to the two links it connects. Derivatives of Bennett linkages refer to spatial four-bar linkages formed by extending any Bennett linkage from its endpoints by a certain length c and d, with equal lengths at opposite endpoints. Bennett linkage derivatives, under certain geometric conditions, possess the properties of complete folding and complete unfolding. For a closed ring-shaped body composed of n links with identical cross-sections, if the entire structure is required to fold completely, the cross-section must be a regular n-gon. Therefore, the cross-section of this four-bar linkage should be a square. Using Bennett linkage derivatives as basic units, they can be extended into mesh combinations covering larger planes through certain connection methods, such as oblique meshes, upright meshes, and cylindrical meshes, etc. Bennett linkage derivatives offer advantages such as simple and quick operation, small footprint when fully folded, reusability, and ease of transportation and storage. In practical engineering fields, such as construction, aerospace, emergency rescue, and medical equipment, there is a need for mechanisms that can fold to a minimum size during storage or transportation and unfold to cover a large area of ​​movable structure when in use. Therefore, Bennett linkage assemblies have broad application prospects in these fields. However, current modeling of Bennett linkage assemblies often involves solid modeling of the entire unit, which involves many angles, is slow, and because it only models the unit and does not consider the individual units that make up the unit, subsequent motion analysis cannot be performed on the individual units, leading to inaccurate results. Summary of the Invention

[0003] This application provides a modeling and analysis method for an over-constrained space four-bar linkage assembly.

[0004] According to a first aspect of this application, a modeling and analysis method for an over-constrained spatial four-bar linkage assembly is provided. The method includes: acquiring multiple unit bodies for constructing the over-constrained spatial four-bar linkage assembly, wherein each unit body is an over-constrained spatial four-bar linkage in an unfolded state; acquiring set mass points for splitting each unit body according to set conditions; constructing a reference coordinate system for the over-constrained spatial four-bar linkage assembly, and acquiring mass point coordinate information of each unit body's set mass points based on the reference coordinate system and the geometric parameters of each unit body; constructing a model and additional rotational hinge units for each unit body based on the mass point coordinate information of each unit body, wherein the model of each unit body includes basic units, including beam units, virtual beam units, rotational hinge units, contact constraint units, and torsion spring units; combining the models of the multiple unit bodies based on the additional rotational hinge units of each unit body to obtain a combined model of the over-constrained spatial four-bar linkage assembly; controlling the combined model to perform motion simulation of the deformation and unfolding process of the over-constrained spatial four-bar linkage assembly; and analyzing the basic units of each unit body to obtain the beam units of each unit body. The analysis results include the analysis results of the rotating hinge unit, the analysis results of the contact constraint unit, and the analysis results of the torsion spring unit. The analysis of the basic units of each unit includes: analyzing the beam unit of each unit to obtain the analysis results of the beam unit, which include flexible deformation and internal forces of the mass points; analyzing the contact constraint unit of each unit to obtain the analysis results of the contact constraint unit, which include cross-sectional contact forces and lateral contact forces; analyzing the torsion spring unit of each unit to obtain the analysis results of the torsion spring unit, which include deformation driving forces; and analyzing the rotating hinge unit of each unit to obtain the analysis results of the rotating hinge unit, which include rotational displacement. Based on the analysis results of the beam unit, rotating hinge unit, contact constraint unit, and torsion spring unit of each unit, the combined model is iteratively solved to perform kinematic analysis on the deformation and unfolding process of the over-constrained space four-bar linkage assembly.

[0005] According to one embodiment of this application, the four reference mass points include a first reference mass point, a second reference mass point, a third reference mass point, and a fourth reference mass point; correspondingly, constructing the reference coordinate system for each unit body includes: using the center of each unit body as the origin, the direction from the origin to the third reference mass point as the positive X-axis, and the direction from the first reference mass point to the third reference mass point as the positive Y-axis, to construct the reference coordinate system.

[0006] According to one embodiment of this application, the geometric parameters of each unit include the link length, unfolding angle, upward angle, and link tilt angle of the unit; the unfolding angle is the angle between the first line segment formed by the second reference mass point and the third reference mass point and the negative direction of the X-axis; the upward angle is the angle between the middle line segment formed by the origin and the third reference mass point and the positive direction of the Y-axis; the link tilt angle is the angle between the rectangular cross-section side of each unit and the set plane.

[0007] According to one embodiment of this application, the step of obtaining the set mass points for splitting each unit body according to the set conditions includes: obtaining four reference mass points of each unit body according to the connecting axis of each connecting rod of each unit body; obtaining a set number of connecting rod mass points between the two reference mass points of each connecting rod of each unit body; determining the end mass points of each end section of each unit body according to the four reference mass points of each unit body and the end sections where the four reference mass points are located; wherein, the set mass points include the reference mass points, connecting rod mass points and end mass points of each unit body.

[0008] According to one embodiment of this application, based on the mass point coordinate information of each unit body, a basic model unit and an additional rotational hinge unit for each unit body are constructed, including: constructing a sub-beam unit for each link of each unit body based on the coordinates of two reference mass points on each link of each unit body; the beam unit of each unit body includes all sub-beam units of each unit body; constructing a sub-virtual beam unit for each link based on the coordinates of two reference mass points and the coordinates of the end mass points at the end sections where the two reference mass points are located; the virtual beam unit of each unit body includes the sub-virtual beam units for each link of each unit body; constructing a sub-rotational hinge unit at each reference mass point based on the coordinates of each reference mass point, the coordinates of the four end mass points at the end sections where the reference mass point is located, and the first set bearing, first set journal, and first set rotation axis direction at each reference mass point; the rotational hinge unit of each unit body includes the sub-rotational hinge unit at each reference mass point; based on the coordinates of each unit body... Based on the coordinates of each reference mass point, the coordinates of the four end masses of the end section where each reference mass point is located, and the normal vector and side normal vector of the end section of the connecting rod where each reference mass point is located, a sub-contact constraint unit is constructed at each reference mass point; the contact constraint unit of each unit body includes the sub-contact constraint unit at each reference mass point; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end masses of the end section where each reference mass point is located, and the first set rotation axis of each reference mass point, a sub-torsion spring unit is constructed at each reference mass point; the torsion spring unit of each unit body includes the sub-torsion spring unit at each reference mass point; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end masses of the end section where each reference mass point is located, and the second set bearing, second set journal, and second rotation axis direction of each reference mass point, a sub-additional rotation hinge unit is constructed at each reference mass point; the additional rotation hinge unit of each unit body includes the sub-additional rotation hinge unit at each reference mass point.

[0009] According to one embodiment of this application, the method further includes: performing motion analysis on the combined model to obtain motion analysis results, the motion analysis results including beam element analysis results, rotational hinge element analysis results, contact constraint element analysis results, and torsion spring element analysis results for each unit; wherein, performing motion analysis on the combined model to obtain motion analysis results includes: analyzing the beam elements of each unit to obtain beam element analysis results for each unit, the beam element analysis results including link flexible deformation and mass internal force; analyzing the contact constraint elements of each unit to obtain contact constraint element analysis results for each unit, the contact constraint element analysis results including end section contact force and side contact force; analyzing the torsion spring elements of each unit to obtain torsion spring element analysis results for each unit, the torsion spring element analysis results including mechanism deformation driving force; and analyzing the rotational hinge elements of each unit to obtain rotational hinge element analysis results for each unit, the rotational hinge element analysis results including rotational displacement.

[0010] According to one embodiment of this application, the analysis of the beam element of each unit body includes: analyzing each sub-beam element of the beam element of each unit body; wherein, the analysis of each sub-beam element of the beam element of each unit body includes: constructing a first local motion coordinate system for each sub-beam element; determining the displacement increment of each link in each sub-beam element from a first moment to a second moment based on the virtual motion method and the first local motion coordinate system; determining the deformable link corresponding to each link based on the displacement increment of each link; and connecting each link and its corresponding deformable link. The deformation of each link is compared to obtain the local flexible deformation of each link in the first local motion coordinate system. The flexible deformation includes local compressive and tensile deformation and local bending deformation. Based on the flexible deformation of each link, the local mass point internal force of each link in the first local motion coordinate system is determined. The local mass point internal force includes the two local mass point internal forces corresponding to the two mass points of each link. Based on the first local motion coordinate system and the reference coordinate system, the local flexible deformation and the local mass point internal force are converted into the flexible deformation and mass point internal force of each link in the reference coordinate system.

[0011] According to one embodiment of this application, the analysis of the contact constraint unit of each unit body includes: analyzing each sub-contact constraint unit of the contact constraint unit of each unit body; wherein, the analysis of each sub-contact constraint unit of the contact constraint unit of each unit body includes: obtaining the side normal vector and the cross-sectional normal vector at each reference mass point; determining the dihedral angle at each reference mass point based on the side normal vector and the cross-sectional normal vector at each reference mass point; and determining the end cross-sectional contact force and the end side contact force at each reference mass point based on the penalty function and the dihedral angle at each reference mass point.

[0012] According to one embodiment of this application, the analysis of the torsion spring unit of each unit body includes: analyzing each sub-torsion spring unit of the torsion spring unit of each unit body; wherein, the analysis of each sub-torsion spring unit of the torsion spring unit of each unit body includes: obtaining the plane normal vector at each reference mass point; determining the torsion spring rotation angle at each reference mass point based on the plane normal vector and direction angle function of each reference mass point; and determining the mechanism deformation driving force at each reference mass point based on the torsion spring rotation angle at each reference mass point.

[0013] According to one embodiment of this application, the analysis of the rotational hinge unit of each unit body includes: analyzing each sub-rotational hinge unit of the rotational hinge unit of each unit body; wherein, the analysis of each sub-rotational hinge unit of the rotational hinge unit of each unit body includes: obtaining the first center mass and the second center mass corresponding to the second set bearing and the second set journal at each reference mass point of each unit body, wherein the translational degrees of freedom of the first center mass point and the second center mass point are coupled to each other; constructing a second local coordinate system with the first center mass point at each reference mass point as the origin and the second set rotation axis as the z-axis; constructing the motion equations and degree-of-freedom coupling equations of the first center mass point and the second center mass point based on the second local coordinate system; determining the local rotational displacement of each reference mass point of each link in the second local coordinate system according to the motion equations and the degree-of-freedom coupling equations; and determining the rotational displacement corresponding to the local rotational displacement in the reference coordinate system according to the reference coordinate system and the second local coordinate system.

[0014] In one embodiment of this application, the combined model is iteratively solved based on the beam element analysis results, rotation hinge element analysis results, contact constraint element analysis results, and torsion spring element analysis results of each unit to perform motion analysis on the deformation and unfolding process of the over-constrained space four-bar linkage assembly. This includes: determining the force information of a set mass point of each unit based on the beam element analysis results, rotation hinge element analysis results, contact constraint element analysis results, and torsion spring element analysis results of each unit; determining the mass point displacement of the set mass point of each unit at the current moment based on the force information of the set mass point of each unit; and obtaining the rear mass point displacement of the set mass point of each unit at the next moment based on the previous mass point displacement of the set mass point of each unit at the previous moment and the mass point displacement at the current moment.

[0015] The method and apparatus of this application embodiment provide a model construction and analysis method for an over-constrained space four-bar linkage assembly. It obtains multiple unit bodies for constructing the over-constrained space four-bar linkage assembly, and divides each unit body into four reference mass points. Based on the combinations of these reference mass points, it constructs the basic units that make up the model of each unit body. It also constructs the basic units and additional rotational hinge units for each unit body based on the reference mass points. By combining the models of each unit body using the additional rotational hinge units, a combined model is constructed, improving the modeling speed. Then, by analyzing the beam units, rotational hinge units, contact constraint units, and torsion spring units in each unit body model, the corresponding flexible deformation, internal forces of mass points, cross-sectional contact forces and side contact forces, deformation driving forces, and rotational displacements are obtained. This allows for motion analysis of the deformation unfolding process of the over-constrained space four-bar linkage assembly, avoiding the inaccuracy caused by analyzing only the unit body as a whole, and improving the accuracy of the analysis.

[0016] It should be understood that the teachings of this application are not required to achieve all the beneficial effects described above, but rather that a specific technical solution can achieve a specific technical effect, and other embodiments of this application can also achieve beneficial effects not mentioned above. Attached Figure Description

[0017] The above and other objects, features, and advantages of exemplary embodiments of this application will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of this application are illustrated in the drawings by way of example and not limitation, in which:

[0018] In the accompanying drawings, the same or corresponding reference numerals indicate the same or corresponding parts.

[0019] Figure 1A schematic diagram illustrating the implementation flow of the modeling and analysis method for the over-constrained spatial four-bar linkage provided in the embodiments of this application is shown.

[0020] Figure 2 A three-dimensional schematic diagram of the unit cell of the modeling and analysis method for over-constrained space four-bar linkage provided in the embodiments of this application is shown.

[0021] Figure 3 This illustration shows a three-dimensional schematic of the linkage of a unit cell in the modeling and analysis method for an over-constrained space four-bar linkage assembly provided in an embodiment of this application. Figure 1 ;

[0022] Figure 4 This illustration shows a three-dimensional schematic of the linkage of a unit cell in the modeling and analysis method for an over-constrained space four-bar linkage assembly provided in an embodiment of this application. Figure 2 ;

[0023] Figure 5 The diagram shows a sub-contact constraint unit and a sub-torsion spring unit of the modeling and analysis method for the over-constrained spatial four-bar linkage provided in the embodiments of this application;

[0024] Figure 6 This illustration shows a modeling and analysis method for over-constrained space four-bar linkages provided in an embodiment of this application, illustrating a constrained space four-bar linkage assembly. Figure 1 ;

[0025] Figure 7 This illustration shows a modeling and analysis method for over-constrained space four-bar linkages provided in an embodiment of this application, illustrating a constrained space four-bar linkage assembly. Figure 2 ;

[0026] Figure 8 This illustration shows a schematic diagram of the virtual reverse motion of the sub-beam unit in the modeling and analysis method of the over-constrained spatial four-bar linkage provided in the embodiments of this application;

[0027] Figure 9 A schematic diagram of a sub-rotation hinge unit is shown in the modeling and analysis method for an over-constrained spatial four-bar linkage assembly provided in an embodiment of this application.

[0028] Figure 10 This paper shows a schematic diagram of the composition structure of the model building device for the over-constrained space four-bar linkage provided in an embodiment of this application;

[0029] Figure 11 A schematic diagram of the composition structure of the electronic device provided in the embodiments of this application is shown. Detailed Implementation

[0030] To make the objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] In the following description, references are made to “some embodiments,” which describe a subset of all possible embodiments. However, it is understood that “some embodiments” may be the same subset or different subsets of all possible embodiments and may be combined with each other without conflict.

[0032] In the following description, the terms "first" and "second" are used merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first" and "second" may be interchanged in a specific order or sequence where permitted, so that the embodiments of this application described herein can be implemented in an order other than that illustrated or described herein.

[0033] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0034] In related technologies, existing methods for modeling and dynamic analysis of Bennett linkage assemblies often have the following shortcomings:

[0035] (1) Existing modeling methods for Bennett linkage assemblies often determine the geometric coordinates of key structural points by using the spatial geometric relationship of the linkages to model the unit body. The calculation process involves many angular relationships, which is not conducive to quickly determining the coordinates. The geometric relationship of the actual structure will change continuously with the deformation of the structure. Therefore, it is difficult to quickly complete the modeling of the full deformation process of the Bennett linkage mechanism. That is, the traditional method of determining the coordinates by spatial geometric relationship cannot quickly and accurately determine the coordinates of the Bennett linkage mechanism assembly model.

[0036] (2) Existing modeling methods for Bennett linkage combinations often only focus on individual units during the modeling stage. However, in actual engineering, Bennett linkages mostly appear in the form of linkage combinations. The modeling methods for individual units do not consider the additional rotational hinge units in the derivative combination of linkages. At the same time, the number of angles involved in the traditional modeling methods using geometric relationships increases exponentially, making it difficult to quickly determine the coordinates of all endpoints in the global coordinate system. This makes it difficult to apply to linkage combinations. In other words, existing modeling methods for Bennett linkages are not suitable for actual engineering modeling applications.

[0037] (3) Existing modeling methods for Bennett linkage combinations generally have certain defects. The modeling method of Bennett linkage composed of beam elements has a low computational cost, but it does not consider the cross-sectional dimensions of the beam elements and cannot reflect the actual deformation of the mechanism. Therefore, it is not applicable to the modeling of derivative forms. Discretizing the Bennett linkage into solid elements can simulate the size effect of the mechanism, but compared with the simplified method of modeling with beam elements, the number of elements increases significantly, and the explicit solution time step is reduced, resulting in excessively high computational cost.

[0038] (4) Existing analysis methods for the derivative combinations of Bennett linkage mechanisms are based on kinematics, considering the relationship between displacement, velocity and acceleration during the deformation process of the mechanism, but rarely involve the internal force problem of the mechanism; based on the finite element method, the stiffness matrix of the integrated variable mechanism is usually ill-conditioned, which makes it difficult to analyze variable mechanisms; based on multibody dynamics, the flexible deformation during the deformation process of the mechanism is not considered, and the analysis results have errors compared with the actual structure.

[0039] (5) Existing analysis methods for Bennett linkage assemblies do not consider the lateral contact constraints during structural deformation. Most analysis methods do not consider the contact constraints at the end sections of the linkages, which makes it impossible to determine whether the structure is fully extended or contracted during the analysis. The analysis results will show the phenomenon of linkage contraction and penetration, making it impossible to accurately simulate and analyze the structural deformation process.

[0040] (6) Existing analysis methods for Bennett linkage mechanisms do not consider the multi-module combination of unit bodies. The analysis of unit bodies does not consider the interaction between unit bodies in the derivative combination. At the same time, it cannot analyze the motion phenomena during the combination deformation process. The results of analyzing the derivative combination using existing methods are inaccurate.

[0041] Therefore, in order to address the shortcomings in the current modeling and motion analysis of Bennett linkage assemblies, this application provides a method and apparatus for modeling and analyzing over-constrained space four-bar linkage assemblies.

[0042] Figure 1The diagram illustrates the implementation flow of the modeling and analysis method for the over-constrained spatial four-bar linkage provided in this application.

[0043] refer to Figure 1 This application provides a modeling and analysis method for over-constrained space four-bar linkages, the method comprising:

[0044] Operation 101: Obtain multiple unit cells for constructing a constrained space four-bar linkage assembly. Each unit cell is a constrained space four-bar linkage in its unfolded state.

[0045] Specifically, an over-constrained spatial four-bar linkage (also known as a Bennett linkage) refers to a special type of single-degree-of-freedom spatial four-bar linkage. It consists of four links and four rotational hinges for each link. The axes of the rotational hinges are neither parallel nor intersecting at a single point, and each hinge axis is perpendicular to the two links it connects to. A Bennett linkage assembly refers to a spatial four-bar linkage formed by extending any Bennett linkage from its endpoints by a certain length c and d, with equal lengths for opposite endpoints. Under certain geometric conditions, a Bennett linkage assembly will possess the properties of complete folding and complete unfolding. For a closed ring-shaped body composed of n links with identical cross-sections, if the entire structure is required to fold completely, the cross-section must be a regular n-gon. Therefore, the cross-section of the Bennett linkages constituting a Bennett linkage assembly should be a square.

[0046] Furthermore, each Bennett linkage in the Bennett linkage assembly can be identical, and the Bennett linkage can be considered as a unit of the Bennett linkage assembly.

[0047] In this embodiment of the application, the Bennett linkage in its unfolded state is used as the unit body, and the unfolded state can be the complete unfolding of the Bennett linkage.

[0048] Operation 102: Based on the set conditions, obtain the set mass points used to split each unit body.

[0049] In one embodiment of this application, based on set conditions, set mass points for splitting each unit body are obtained: four reference mass points for each unit body are obtained based on the link axis of each link of each unit body; a set number of link mass points between the two reference mass points of each link of each unit body are obtained; and end mass points of each end section of each unit body are determined based on the four reference mass points of each unit body and the end sections where the four reference mass points are located; wherein, the set mass points include the reference mass points, link mass points, and end mass points of each unit body. Specifically, each Bennett linkage consists of four identical links, each link having a link axis, and the intersection point of the four link axes of the four links can be configured to represent the four reference mass points of the Bennett linkage mechanism.

[0050] For example, see reference. Figure 2 , Figure 2 This paper shows a three-dimensional schematic diagram of the unit cell of the modeling and analysis method for over-constrained space four-bar linkages provided in an embodiment of this application. Figure 2 In the figure, (a) is a rectangular cross-sectional view of the three-dimensional view of the unit body, (b) is a top view of the unit body, and (c) is a front view of the unit body. As shown in the figure, the connecting axis of each link divides the unit body into four reference mass points, namely A, B, C, and D.

[0051] In this embodiment of the application, in order to better represent each link with a mass point, the link can be split into two reference mass points on both sides, and then a set number of link mass points, such as 2, 3 or 4, can be determined between the two reference mass points of each link.

[0052] In this embodiment of the application, the end section of each reference mass is further divided into four end mass points based on the four reference mass points. The end section is the connection surface between the two connecting rods containing the reference mass points.

[0053] Specifically, each unit consists of four identical links, with a connecting surface between every two connected links. Each connecting surface includes four vertices, i.e., end mass points.

[0054] Operation 103: Construct a reference coordinate system for the four-bar linkage assembly in the constrained space, and obtain the mass coordinate information of the set mass point of each unit body based on the reference coordinate system and the geometric parameters of each unit body.

[0055] Specifically, in order to construct the basic unit of each unit body model, a reference coordinate system needs to be constructed.

[0056] In one embodiment of this application, the four reference mass points include a first reference mass point, a second reference mass point, a third reference mass point, and a fourth reference mass point. Constructing a reference coordinate system for each unit body includes: taking the center of each unit body as the origin, taking the direction from the origin to the third reference mass point as the positive X-axis, and taking the direction from the first reference mass point to the third reference mass point as the positive Y-axis, thus constructing a reference coordinate system.

[0057] For details, please refer to Figure 2 The first reference mass corresponds to A, the second reference mass corresponds to B, the third reference mass corresponds to C, and the fourth reference mass corresponds to D. The origin O can be defined as the midpoint of the diagonal BD of the unit cell ABCD, i.e., the center of the unit cell. OB is the x-axis, and the y-axis is parallel to AC.

[0058] It should be noted that this application does not impose specific limitations on the construction of the reference coordinate system. The reference coordinate system can also be constructed in other locations, as long as the coordinates of the four reference points can be obtained based on the constructed reference coordinate system. The above-mentioned method of constructing the reference coordinate system is only a preferred method to simplify the calculation process.

[0059] In one embodiment of this application, the mass coordinate information of the set mass point includes the coordinates of four reference mass points and the coordinates of the end mass point corresponding to each reference mass point. The coordinates of the four reference mass points can be obtained first, and then the coordinates of the end mass points corresponding to the four reference mass points can be obtained.

[0060] In one embodiment of this application, the geometric parameters of each unit include the link length, unfolding angle, upward angle, and link tilt angle. The unfolding angle is the angle between the first line segment formed by the second and third reference points and the negative X-axis; the upward angle is the angle between the middle line segment formed by the origin and the third reference point and the positive Y-axis; and the link tilt angle is the angle between the rectangular cross-section side of each unit and a predetermined plane.

[0061] For details, please refer to Figure 2 The link length L is the length of the link in each unit cell, where the link length is configured to represent the distance between two intersection points of the link, such as the length of BC. The unfolding angle ω is the angle between BC and the negative X-axis, and the upturn angle μ is the angle between OC and the Y-axis.

[0062] Further reference Figure 2 , Figure 2 Figure (a) shows a schematic diagram of the rectangular cross-section of link BC. This rectangular cross-section is obtained by taking four interconnected line segments from the four sides of the middle section of link BC, where each pair of connected segments is perpendicular to the other. For example, obtaining... Figure 2The S1S2, S2S3, S3S4, and S1S4 on the BC link shown form the rectangular section S1S2S3S4 of the BC link.

[0063] In one embodiment of this application, reference is made to Figure 2 In (a), the inclination angle λ of the connecting rod is the angle between the rectangular cross-section side S1S2 of the rod and the set plane. The set plane is a horizontal plane relative to the unit body, including point S1, and is parallel to the XOY plane of the coordinate axis.

[0064] In one embodiment of this application, the link length, unfolding angle, upward angle, and link tilt angle are configured by the designer according to the design requirements and specifications of the Bennett linkage mechanism when designing the Bennett linkage mechanism. This application does not specifically limit the configuration process and how to configure it. When the unit body is obtained, the geometric parameters of the unit body are included.

[0065] In this embodiment of the application, after the reference coordinate system is established, since the geometric parameters are fixed, the coordinates of the four reference points can be calculated using the geometric parameters.

[0066] For details, please refer to Figure 2 In the reference coordinate system (X, Y, Z), taking the coordinates of two reference points as an example, the coordinates of B and C are [L cos w, 0, 0] respectively. T ,[0,L sin w cosμ,L sin w sinμ] T The coordinates of A and D can be obtained using the methods described above, or by mirroring the coordinates of B and C. It should be noted that the method for mirroring coordinates can be referenced from the conventional coordinate calculation process, and will not be elaborated upon here.

[0067] Furthermore, after obtaining the coordinates of the four reference mass points of each unit body, the coordinates of the end mass points are obtained based on the coordinates of each reference mass point.

[0068] For details, please refer to Figure 2 and Figure 3 , Figure 3 This illustration shows a three-dimensional schematic of the linkage of a unit cell in the modeling and analysis method for an over-constrained space four-bar linkage assembly provided in an embodiment of this application. Figure 1 ,in, Figure 3 Figure (d) shows a schematic diagram of the local coordinate system of the rectangular cross-section. Specifically, Figure 3 The connecting rod shown is rod BC. The end sections of rod BC include the end section at reference mass point B and the end section at reference mass point C. The acquisition of the end sections at B and C, and the acquisition of the end mass points of the end sections, are illustrated by example. Figure 2 and 3 The end mass points at the end section at point C include E. C1 E C2 E C3 E C4 E C1 E C2 E c3 E C4 By utilizing the intersection of the four edges of the connecting rod with the YOZ plane, and considering the cross-sectional direction, a local coordinate system is established, and the directions of its three principal axes are defined as follows:

[0069] e z = [0, 0, 1] T

[0070] Around Rotate the axis by an angle λ to obtain direction Construct reference surfaces for the end sections at points B and C: planes B1B2B3B4 and C1C2C3C4. Plane B1B2B3B4 is obtained by translating rectangular section S1S2S3S4 along the BC link to point B, and plane C1C2C3C4 is obtained by translating rectangular section S1S2S3S4 along the BC link to point C. Obtain the coordinates of the reference points for the reference surfaces at points B and C from the local coordinate system.

[0071]

[0072] Using line x Bi x Ci The intersection with the YOZ plane yields the corresponding end mass point E. ci Coordinates, in x B1 x C1 For example, the line equation is The equation of the plane is (xx) O Given n = 0, find the intersection point E. Ci The coordinates are:

[0073]

[0074] Let x be the direction vector of BC. Bi Let x be the coordinates of the reference point in reference plane B1B2B3B4. O Let be the coordinates of the origin, and n be the normal vector of the YOZ plane. The method for determining the coordinates of the end section and end mass at point B is the same as that at point C, and will not be repeated here. Finally, according to the above scheme or the coordinate mirroring method, the coordinates of the end mass at points A and D can be obtained sequentially.

[0075] The method for obtaining the end mass of the reference mass point at the end section of each unit body that makes up the constrained space four-bar linkage can refer to the method for obtaining the end mass at point C, and will not be repeated here.

[0076] It should be noted that, in the embodiments of this application, after the end section corresponding to each reference mass point is determined, the coordinates of each reference mass point and the four end mass points corresponding to each reference mass point can also be obtained by any coordinate acquisition method. Any method that can obtain the coordinates of the reference mass point and the end mass points falls within the protection scope of this application.

[0077] Operation 104: Based on the mass point coordinate information of each unit body, construct the model of each unit body and the additional rotation hinge element. The model of each unit body includes basic elements, which include beam elements, virtual beam elements, rotation hinge elements, contact constraint elements and torsion spring elements.

[0078] Specifically, the basic elements of each element model can be constructed based on the reference mass points included in each element. To better facilitate the subsequent analysis of the elements, the basic elements can be configured to include beam elements, virtual beam elements, rotational hinge elements, contact constraint elements, and torsion spring elements.

[0079] Furthermore, multiple unit cells are connected by additional rotary hinge units to form a Bennett linkage mechanism assembly. Therefore, it is also necessary to construct an additional rotary hinge unit corresponding to each unit cell.

[0080] In one embodiment of this application, the specific operation of constructing the basic unit is as follows: Based on the coordinates of two reference mass points on each link of each unit body, a sub-beam unit is constructed for each link of each unit body; based on the coordinates of the two reference mass points on each link of each unit body and the coordinates of the end mass points at the end sections where the two reference mass points are located, a sub-virtual beam unit is constructed for each link; the virtual beam unit of each unit body includes the sub-virtual beam unit for each link of each unit body; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points at the end sections where the reference mass points are located, and the first set bearing, first set journal, and first set rotation axis direction at each reference mass point, a sub-rotation hinge unit is constructed for each reference mass point of each link; the rotation hinge unit of each unit body includes the sub-rotation hinge unit at each reference mass point; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points at the end sections where the reference mass points are located, and the coordinates of the end sections where the reference mass points are located, a sub-rotation hinge unit is constructed for each reference mass point of each link; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points at the end sections where the reference mass points are located, and the coordinates of the two reference mass points on each link, a sub-rotation hinge unit is constructed for each reference mass point of each link; the rotation hinge unit of each unit body includes the sub-rotation hinge unit at each reference mass point; based on the coordinates of each reference mass point of each unit body, the coordinates of the two reference mass points on the end sections where the reference mass points are located, and the coordinates of the two reference mass points on each link, a sub-rotation hinge unit is constructed for each reference mass point of each link; based on the coordinates of each reference mass point of each unit body, the coordinates of the two reference mass points on each link, and the coordinates of the two reference mass points on each link, a sub-rotation hinge unit is constructed Based on the coordinates of the four end mass points of the reference mass and the normal vectors of the end sections and sides of the connecting rod where each reference mass point is located, a sub-contact constraint unit is constructed at each reference mass point; the contact constraint unit of each unit body includes the sub-contact constraint unit at each reference mass point; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points of the end section where each reference mass point is located, and the first set rotation axis of each reference mass point, a sub-torsion spring unit is constructed at each reference mass point; the torsion spring unit of each unit body includes the sub-torsion spring unit at each reference mass point; based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points of the end section where each reference mass point is located, and the second set bearing, second set journal, and second rotation axis direction of each reference mass point, a sub-additional rotation hinge unit is constructed at each reference mass point; the additional rotation hinge unit of each unit body includes the sub-additional rotation hinge unit at each reference mass point.

[0081] In this embodiment of the application, each beam element of the unit body includes sub-link elements of each link, and each sub-link element of the link is composed of reference mass points at both ends of the corresponding link. Thus, the reference mass points are the endpoints of the link axis at both ends of each link.

[0082] For example, see reference. Figure 4 , Figure 4 This illustration shows a three-dimensional schematic of the linkage of a unit cell in the modeling and analysis method for an over-constrained space four-bar linkage assembly provided in an embodiment of this application. Figure 2 , Figure 4 In the diagram, 2 represents the beam element of the BC link, and reference mass points B and C are the components of the beam element. In addition to B and C, the beam element also includes multiple link mass points between BC. The number of link mass points can be specifically set according to actual needs, such as 2, 3, or 4.

[0083] In this embodiment of the application, reference is made to Figure 2 and Figure 4 Each link corresponds to two mass points and two end sections. The end mass points of the two end sections of each link and the two reference mass points form a sub-virtual beam element. The four sub-virtual beam elements of the four links form the virtual beam element of the unit body.

[0084] Furthermore, after determining the virtual beam element for each unit body, the virtual beam element can be constructed based on the reference mass coordinates and end mass coordinates determined above.

[0085] For example, see reference. Figure 4 , Figure 4 The fourth element is a virtual beam element. The end section at point B consists of the reference mass B and the end mass E. Bi The connection consists of a reference mass point and an end mass point E at point C. Ci The connection between the end sections at points B and C forms the sub-virtual beam element of rod BC.

[0086] In this embodiment of the application, the rotary hinge unit includes sub-rotary hinge units at each reference mass point. A first predetermined bearing, a first predetermined journal, and a first predetermined rotation axis direction can be configured for each reference mass point to construct a sub-rotary hinge unit for each reference mass point based on these configurations. The first predetermined bearing, first predetermined journal, and first predetermined rotation axis direction at each reference mass point can be configured according to the actual movement and forces acting on each mass point during the actual movement of the unit body.

[0087] In this embodiment of the application, the first set rotation axis direction can be configured as the set direction of the side of the end section where the reference mass is located, and the first set journal and the second set journal are determined as the points on the two connecting rods where the reference mass is located, where the side of the end mass is along the set direction. The set direction can be configured to face upwards.

[0088] Furthermore, after determining the rotational hinge element of each unit body, the rotational hinge element can be constructed based on the reference mass coordinates and end mass coordinates determined above.

[0089] For example, see reference. Figure 4 , Figure 4 In section 3, the sub-rotational hinge element is located at reference mass point C, and the sub-rotational hinge element at point C is formed by E of the BC connecting rod. c3 E of the CD linkage C3 For the first set bearing and the first set journal, E c4 E C3 The first setting is the rotation axis direction; the E of the BC link at point B. B3 E of the AB link B3 For the first set bearing and the first set journal, E B2 EB3 Set the first axis of rotation direction.

[0090] The construction method of the sub-rotational hinge elements at other reference mass points of the unit body is the same as that of the sub-rotational hinge elements at point C. The construction method of the sub-rotational hinge elements at point C represents the construction method of the sub-rotational hinge elements at each reference mass point, which will not be elaborated here.

[0091] In this embodiment of the application, the contact constraint unit of each unit body includes a sub-contact constraint unit at each reference mass point. Each sub-contact constraint unit includes the reference mass point at that point, the end mass point of the end section corresponding to the reference mass point, and the side normal vector of the connecting rod corresponding to the reference mass point.

[0092] Furthermore, the contact constraint element at each reference mass point can be constructed based on the coordinates of the reference mass point and the end mass point, as well as the corresponding side normal vector.

[0093] For example, see reference. Figure 5 , Figure 5 This diagram illustrates the sub-contact constraint element and sub-torsion spring element of the modeling and analysis method for an over-constrained spatial four-bar linkage provided in this embodiment. P1 and P2 represent the state of the reference mass point on the two links, M and N are the two end masses at the reference mass point whose positions remain unchanged during the movement of the two links, and m1 and m2 are the side normal vectors corresponding to the reference mass point. The sub-contact constraint element of the reference mass point consists of surfaces MNP1 and MNP2, and side normal vectors m1 and m2.

[0094] In this embodiment of the application, each unit's torsion spring unit includes a sub-torsion spring unit at each reference mass point. The sub-torsion spring unit includes a first predetermined axis of rotation for the reference mass point, two end masses corresponding to the first predetermined axis of rotation, and the reference mass point in its two-bar configuration. The first predetermined axis of rotation can be specifically set according to the actual movement of the unit, and can be set as the connecting line between the two connecting rods at the reference mass point.

[0095] For example, see reference. Figure 4 The torsion spring unit at point C is formed by mass point E at the pivot. C3 E C4 It is composed of point C of rods BC and CD, and can also be referenced. Figure 5 ,exist Figure 5 Taking point C as an example, M and N correspond to E. C4 and E C3 P1 and P2 correspond to the points of C on the BC link and CD link, respectively. Then the sub-torsion spring unit at C includes M, N, P1, P2 and the first rotating shaft where M and N are located.

[0096] In this embodiment of the application, additional rotational hinge units are also constructed. Each sub-additional rotational hinge unit at a reference mass point is composed of a second predetermined bearing, a second predetermined journal, and a second rotational axis direction at the reference mass point. The second predetermined bearing and the second predetermined journal are respectively an end mass point corresponding to the reference mass point and an end mass point corresponding to the reference mass point of a connecting rod adjacent to the connecting rod in an adjacent unit of the unit body containing the reference mass point. The second predetermined rotational axis direction is half of the first rotational axis direction.

[0097] Specifically, the sub-additional rotational hinge is simulated at the endpoint of the rotation axis by the cross-section formed by cutting the ends of two adjacent unit bodies.

[0098] For example, see reference. Figure 4 , of which E C5 E represents C4 E C3 The midpoint, E′ c5 E represents C5 At other points on the link, E B5 E represents B2 E B3 The midpoint, E′ B5 E represents B5 At points on other links, the second set axis of rotation of the sub-additional rotary hinge unit at point C is E. C5 E C3 The second bearing is set as unit BC connecting rod E. C3 The second set journal is the connecting rod E of the adjacent unit AB. A3 .

[0099] In one embodiment of this application, the individual elements of the unit body are set according to the actual force conditions of the unit body during its actual movement. Each element can also be simulated by other mass points that simulate that element. Each basic model element can be a combination of mass points that can simulate each element.

[0100] Specifically, beam elements, virtual beam elements, rotational hinge elements, contact constraint elements, and torsion spring elements can all be constructed by combining four reference mass points and the end mass points corresponding to the reference mass points.

[0101] Operation 105: Based on the additional rotational hinge unit of each unit, the models of multiple units are combined to obtain the combined model of the four-bar linkage in the constrained space.

[0102] Specifically, by adding rotating hinge units to connect the unit bodies, a combined model of the constrained space four-bar linkage is obtained. A schematic diagram of the combined model of the constrained space four-bar linkage can be found here. Figure 6 and Figure 7 , Figure 6 This illustration shows a modeling and analysis method for over-constrained space four-bar linkages provided in an embodiment of this application, illustrating a constrained space four-bar linkage assembly. Figure 1 , where 8, 9, 10, and 11 represent unit cells respectively. The four reference points of unit cell 8 are ABCD, the reference points of unit cell 9 are BEFC, the reference points of unit cell 10 are DCHI, and the reference point of unit cell 11 is CFGH. Figure 7 This illustration shows a modeling and analysis method for over-constrained space four-bar linkages provided in an embodiment of this application, illustrating a constrained space four-bar linkage assembly. Figure 2 ,in, Figure 7 The species comprises 25 units.

[0103] Operation 106: Control the combined model to perform motion simulation of the deformation and unfolding process of the constrained space four-bar linkage combination.

[0104] Specifically, after obtaining a combined model by combining multiple unit models, the deformation and unfolding process of the four-bar linkage assembly in the over-constrained space is simulated using the combined model, so as to conduct motion analysis on the deformation and unfolding process of the four-bar linkage assembly in the over-constrained space through subsequent motion analysis of the combined model.

[0105] Operation 107 analyzes the basic elements of each unit body, obtaining the analysis results for beam elements, rotational hinge elements, contact constraint elements, and torsion spring elements for each unit body. The analysis of the basic elements of each unit body includes: analyzing the beam elements, obtaining beam element analysis results including flexible deformation and mass internal forces; analyzing the contact constraint elements, obtaining contact constraint element analysis results including cross-sectional contact forces and lateral contact forces; analyzing the torsion spring elements, obtaining torsion spring element analysis results including deformation driving forces; and analyzing the rotational hinge elements, obtaining rotational hinge element analysis results including rotational displacements.

[0106] Specifically, during the process of simulating the deformation and unfolding of the four-bar linkage assembly in the constrained space using the combined model, the basic unit of each unit body is analyzed at any given time.

[0107] In one embodiment of this application, analyzing each beam element of a unit body is equivalent to analyzing each sub-beam element of the beam element of each unit body. Specifically, this includes: constructing a first local motion coordinate system for each sub-beam element; determining the displacement increment of each link in each sub-beam element from a first time to a second time based on the virtual motion method and the first local motion coordinate system; determining the deformable link corresponding to each link based on the displacement increment of each link; comparing the deformation of each link and its corresponding deformable link to obtain the local flexible deformation of each link in the first local motion coordinate system, wherein the flexible deformation includes local compressive-tensile deformation and local bending deformation; determining the local mass point internal force of each link in the first local motion coordinate system based on the flexible deformation of each link, wherein the local mass point internal force includes the two local mass point internal forces of the two mass points corresponding to each link; and converting the local flexible deformation and local mass point internal force into the flexible deformation and mass point internal force of each link in the reference coordinate system based on the first local motion coordinate system and the reference coordinate system.

[0108] For details, please refer to Figure 8 , Figure 8 This illustration shows a schematic diagram of the virtual reverse motion of the sub-beam element in the modeling and analysis method for the over-constrained spatial four-bar linkage provided in this application embodiment. The analysis of the sub-beam element of the AB linkage is used as an example for illustrative explanation. Figure 8 In the diagram, A and B are simply reference points for each link or two points among the link's mass points; they can be other diagrams, such as... Figure 2 The reference points A and B in the link can also be any two points on the link.

[0109] The deformation and motion of the sub-beam element are separated by setting a first local motion coordinate system that moves together with the AB rod sub-beam element. The initial axis of the first local motion coordinate system is...

[0110]

[0111] Determine time t a Translation coordinates in the reference coordinate system and rotation coordinates in the first local motion coordinate system With time t b (=t a Translation coordinates in the reference coordinate system and rotation coordinates in the first local motion coordinate system (+Δt) The translational displacement variable Δx within Δt is calculated. i and rotational displacement variable Δβ i :

[0112]

[0113] Determine the angle increment within Δt:

[0114]

[0115] Where, θ ba and They are t a Perpendicular to the principal axis of the unit at all times The vector and about the principal axis The rotation vector. Determined from time t by virtual reverse motion. b (=t a +Δt)A′B′ to time t a Displacement increment of A”B” -Δx A , -γ, compare the differences between A”B” and AB to determine the deformation of the sub-beam element, the axial deformation is t a and t b The difference in link length at any given moment, i.e., Δ e =l b -l a The bending angles of particles A and B are respectively and Axial deformation represents local compressive and tensile deformation, while bending angle represents local bending deformation. The internal forces of the sub-beam element are determined by the deformation of the sub-beam element.

[0116]

[0117]

[0118]

[0119]

[0120] in, The axial force at point A, The bending moment at point B, The axial force at point B, Let B be the bending moment at point B, E be the modulus of elasticity, and A be the cross-sectional area. Let be the first moment of the beam element area about the y-axis. Let Ω be the second moment of the beam element area about the z-axis. The internal force increment is transformed into the global coordinate system using the transformation matrix Ω and applied to the mass points B and C connected to the sub-beam element, thus obtaining the mass point internal forces. Furthermore, by determining the mass point internal forces and flexible deformation of each sub-beam element in the above manner, the flexible deformation of the beam element of each unit and the mass point internal forces of each mass point constituting the beam element are obtained.

[0121] In one embodiment of this application, analyzing the contact constraint element of each unit body, i.e., analyzing each sub-contact constraint element of the contact constraint element of each unit body, specifically includes: obtaining the side normal vector and cross-sectional normal vector at each reference mass point; determining the dihedral angle at each reference mass point based on the side normal vector and cross-sectional normal vector at each reference mass point; and determining the end cross-sectional contact force and end side contact force at each reference mass point based on the penalty function and the dihedral angle at each reference mass point.

[0122] For details, please refer to Figure 5 Calculate the cross-sectional normal vector n at each reference mass point. i With the side normal vector m i ,For example Figure 4 n1, n2, m1, and m2 in the text

[0123]

[0124] Where Sgn(·) is the sign function, e r It is the direction of the axis of rotation, e i It refers to the direction of the side or cross-sectional edge (as shown by Q2P2 or Q1P1 in the figure), n′ i =(x Oi -x Pi )×e r m′ i =e r ×e i (i = 1, 2), cross-sectional rotation angle θ F φ F The range of values ​​is (-π, π], and the calculation yields:

[0125] θ F =atan2(e r ·(n2×n1), -n2·n1), φ F =atan2(e r ·(m2×m1), -m2·m1)

[0126] When the turning angle θ F Located at (-ε, 0) or φ f When the coordinates are (0, ε), it can be determined that contact occurs between the two cross sections containing the reference particle. ε is the angle threshold excluding obtuse angles, which is taken as π / 10 here. The torque generated by the contact is calculated using the penalty function.

[0127]

[0128] Where, k rc k r The calculated moment is the rotational stiffness of the end section and the side section. Apply forces to the corresponding particles O1 and O′1 respectively, and complete the force analysis of the particles, including the torque. These correspond to the end section contact force and the end side contact force, respectively. O1 and O2 correspond to the points of each reference mass in the two connecting rods. Furthermore, by using the above method, the end section contact force and end side contact force of each sub-contact constraint element of each unit can be determined. The analysis results of the contact constraint elements of each unit include the end section contact force and end side contact force of each sub-contact constraint element of each unit.

[0129] In one embodiment of this application, analyzing the torsion spring unit of each unit body is equivalent to analyzing each sub-torsion spring unit of the torsion spring unit of each unit body, specifically including: obtaining the plane normal vector at each reference mass point; determining the torsion spring rotation angle at each reference mass point based on the plane normal vector and direction angle function of each reference mass point; and determining the end deformation driving force at each reference mass point according to the torsion spring rotation angle at each reference mass point.

[0130] For specific examples, please refer to the following: Figure 5 By setting sub-torsion spring elements at the end sections of the connecting rods at the reference mass point, the end sections of two adjacent connecting rods can be represented by mass points as MNP1 and MNP2, with plane normal vectors n1 and n2 respectively; the sub-torsion spring elements are arranged at the intersection line MN of the two end sections, with direction vector e. r The torsional spring rotation angle (dihedral angle) θ between the end sections is calculated using the direction angle function (atan2 function). F :

[0131] θ = atan2(-e r ·(n2×n1), -n2·n1)

[0132]

[0133] The torsion spring rotation angle before θ correction, where [x] is a function rounded down. The bending moment and torsion spring length generated by the sub-torsion spring element are proportional to the angle between the sections, i.e., satisfying:

[0134] M F =K F l F (θ F -θ0)

[0135] Where θ0 is the torsion spring rotation angle (dihedral angle) when the torsion spring has zero torque, which is set to 0 here; K F l is the unit spring stiffness. F Let M be the length of the torsion spring. The bending moment generated by the torsion spring will be converted into a point mass force acting on the cross-sectional mass, thereby driving the mechanism to unfold. FThat is, the end deformation driving force. Furthermore, the end deformation driving force at the end of each reference mass point can be obtained through the above method. The analysis results of the torsion spring element of each unit cell include the end deformation driving force of the sub-torsion spring element at each reference mass point of each unit cell, that is, the deformation driving force includes all end deformation driving forces.

[0136] In one embodiment of this application, analyzing the rotational hinge unit of each unit body is equivalent to analyzing each sub-rotational hinge unit of the rotational hinge unit of each unit body. Specifically, this includes: obtaining the first center mass and the second center mass corresponding to the second set bearing and the second set journal at each reference mass point of each unit body, wherein the translational degrees of freedom of the first center mass and the second center mass are coupled to each other; constructing a second local coordinate system with the first center mass point at each reference mass point as the origin and the second set rotation axis as the z-axis; constructing the motion equations and degree-of-freedom coupling equations of the first center mass and the second center mass based on the second local coordinate system; determining the local rotational displacement of each reference mass point of each link in the second local coordinate system according to the motion equations and degree-of-freedom coupling equations; and determining the rotational displacement in the reference coordinate system corresponding to the local rotational displacement according to the reference coordinate system and the second local coordinate system.

[0137] For specific examples, please refer to the following: Figure 9 , Figure 9 This illustration shows a schematic diagram of a sub-rotation hinge element in the modeling and analysis method for an over-constrained spatial four-bar linkage assembly provided in an embodiment of this application. The sub-rotation hinge element is composed of corresponding mass points i and j at the bearing center and journal center, respectively, for example... Figure 9 The first central mass point corresponding to the second set bearing and the second central mass point 7 corresponding to the second set journal are shown in the figure. Here, i corresponds to 6 and j corresponds to 7. Their translational degrees of freedom are coupled, and their translational movements both follow the equation:

[0138]

[0139] Therefore, d can be obtained. i =d j , Establish the equations of translational motion:

[0140]

[0141] By rotating axis e r Set as The axis, and the other two orthogonal axes are Establish a local coordinate system (LCS) at point i along the axis. Rotating axis e r The initial value is set to The coordinates of the mass point are calculated using the transformation matrix Ω; the axis of rotation... Since the axis is freely rotating, the equations of motion for the two particles need to be solved independently. The equations are:

[0142]

[0143] Points i and j around The rotation equations require simultaneous solutions due to the coupling of related degrees of freedom:

[0144]

[0145]

[0146]

[0147] By obtaining the local rotational displacement in the local coordinate system The rotational displacement θ in the global coordinate system is obtained using the transformation matrix Ω. k (k = i, j). Furthermore, the rotational displacement of all sub-rotational hinge elements can be calculated in the above manner to obtain the rotational hinge element analysis results of each element body. The rotational hinge element analysis results of each element body include the rotational displacement of each sub-rotational hinge element.

[0148] Operation 108 involves iteratively solving the combined model based on the analysis results of the beam element, rotation hinge element, contact constraint element, and torsion spring element for each unit, in order to perform motion analysis on the deformation unfolding process of the four-bar linkage assembly in the over-constrained space.

[0149] In one embodiment of this application, the combined model is iteratively solved through the following operations to perform motion analysis on the deformation unfolding process of the four-bar linkage assembly in the over-constrained space: based on the analysis results of the beam element, the rotation hinge element, the contact constraint element, and the torsion spring element of each unit, the force information of the set mass point of each unit is determined; based on the force information of the set mass point of each unit, the mass point displacement of the set mass point of each unit at the current moment is determined; based on the previous mass point displacement of the set mass point of each unit at the previous moment and the mass point displacement at the current moment, the subsequent mass point displacement of the set mass point of each unit at the next moment is obtained.

[0150] Specifically, in the motion simulation of the combined model, it is necessary to perform displacement analysis on all mass points of the combined model during the motion simulation process.

[0151] Furthermore, based on conventional force distribution methods and the analysis results of the basic units of each unit body, the force information of all particles constituting each basic unit can be determined. This force information includes both external and internal forces. It should be noted that by referring to the analysis process of the basic units and using the force distribution method commonly used in mechanical analysis, the force information of all particles in the combined model during the motion simulation process of the combined model can be continuously determined; this will not be elaborated upon further here.

[0152] In this embodiment of the application, for any moment in the motion simulation process of the combined model, after obtaining the force information of each mass point, the motion equation of each mass point is constructed based on the force information. The previous mass point displacement and the current mass point displacement of each mass point are used to solve the motion equation of the mass point using the central difference method to obtain the subsequent mass point displacement of each mass point at the next moment. The above steps are repeated to perform dynamic analysis of the thick folded paper structure.

[0153] Specifically, the trajectory of any particle α in each Bennett linkage can be represented by its motion at discrete times [t0, t1, t2, ..., t]. n The position representation of the particle is given by [x0, x1, x2, ..., x]. n If the time interval is small enough, the variables of the origami structure (such as stress and strain) can be considered constant within the same time interval, changing only between different time intervals. Within any given time interval, particle α is in dynamic equilibrium, and its motion follows Newton's second law:

[0154]

[0155] Where, m α Let α be the mass of the point mass. and Let represent the external force, internal force, and damping force of mass α, respectively, and μ be the mass damping coefficient. Each term on the right-hand side of the above equation can be expressed explicitly; therefore, using an explicit time integration scheme can avoid iterative solutions within a single step. Using the second-order central difference method, the displacement of mass α at time n+1 can be expressed as:

[0156]

[0157] In the formula, d n+1 d n and d n-1 These are the particle α at time t n+1 t n and t n-1 The displacement at time step Δt is the time integration step size, and c1 = (1 + μΔt / 2). -1 c2 = c1(1-μΔt / 2).

[0158] Therefore, in the construction process of this application embodiment, the coordinates of the end mass points of the unit body are determined by the coordinate system and geometric parameters, reducing the number of parameters in the coordinate calculation process. The coordinates of the entire unit body are obtained by utilizing the mirror principle, and the calculation process is standardized and uniform, which can adapt to the calculation of the unit body position coordinates under various angles, greatly improving the modeling speed of the Bennett linkage mechanism. Moreover, in the modeling process, this application embodiment considers the multi-module combination problem, reduces the angular relationship between models, quickly determines the basic model unit of the unit body through algebraic methods, comprehensively considers the setting of connecting units between different units, and completes the modeling of the Bennett linkage mechanism combination in a modular way, which significantly improves the speed and accuracy of the overall modeling process. Furthermore, in the modeling process, this application embodiment does not use solid element modeling, but uses beam elements, hinge elements, contact constraint elements, and torsion spring elements as the basis, and adopts a modular modeling method, which reduces the calculation cost for subsequent simulation of the deformation process of the constrained space four-bar linkage combination under various conditions. Furthermore, in the analysis process of this application, the finite mass method is used to define beam elements. This not only employs dynamic analysis as a foundation but also considers the flexible deformation of the linkages under the condition of internal forces during the deformation process of the analyzed mechanism. The magnitude of the deformation of the four-bar linkage in the over-constrained space is calculated, allowing for a better analysis of the dynamic relationships during the deformation process and obtaining accurate motion and force analysis results. In addition, this application adds contact constraint elements during the analysis process. These elements simulate the contact constraints at the end sections and sides of the linkages, and the penalty function is used to calculate the reaction force after the section contact. This accurately determines whether contact occurs during the deformation of the element, and the reaction force acts on adjacent mass points, effectively improving the accuracy of the force analysis. Moreover, the analysis process also considers the multi-module combination problem. Torsion spring elements are used to consider the forces between different elements during the combined deformation process, and contact constraint elements are used to consider the deformation restrictions between combinations and obtain the reaction force. This effectively improves the analysis process of the Bennett linkage combination and enhances the accuracy of the analysis results.

[0159] Figure 10 A schematic diagram of the composition structure of the model building device for the over-constrained space four-bar linkage provided in the embodiment of this application is shown.

[0160] refer to Figure 10Based on the above-mentioned modeling and analysis method for over-constrained space four-bar linkages, this application embodiment also provides a modeling and analysis device for over-constrained space four-bar linkages. The device includes: a first acquisition module 201, used to acquire multiple unit bodies for constructing the over-constrained space four-bar linkage, wherein the unit bodies are over-constrained space four-bar linkages in an unfolded state; a second acquisition module 202, used to acquire, according to set conditions, set mass points for splitting each unit body; and a third acquisition module 203, used to construct a reference coordinate system for the over-constrained space four-bar linkage, and based on the reference coordinate system and the set mass points of each unit body... The parameters are used to obtain the mass coordinate information of each unit body's set mass point; the first construction module 204 is used to construct the model of each unit body and the additional rotation hinge unit based on the mass coordinate information of each unit body. The model of each unit body includes basic units, including beam units, virtual beam units, rotation hinge units, contact constraint units and torsion spring units; the combination module 205 is used to combine the models of multiple unit bodies based on the additional rotation hinge units of each unit body to obtain the combined model of the over-constrained space four-bar linkage; the control module 206 is used to control the combined model to perform the over-constrained space four-bar linkage assembly. The motion simulation of the deformation and unfolding process of the composite element; analysis module 207 is used to analyze the basic elements of each unit body, and obtain the analysis results of beam elements, rotational hinge elements, contact constraint elements, and torsion spring elements for each unit body; the analysis of the basic elements of each unit body includes: analyzing the beam elements of each unit body, and obtaining the beam element analysis results of each unit body, which include flexible deformation and mass internal forces; analyzing the contact constraint elements of each unit body, and obtaining the contact constraint element analysis results of each unit body, which include cross-sections. Contact forces and lateral contact forces; analysis of the torsion spring elements of each unit body to obtain the analysis results of the torsion spring elements of each unit body, including the deformation driving force; analysis of the rotational hinge elements of each unit body to obtain the analysis results of the rotational hinge elements of each unit body, including the rotational displacement; solution module 208 is used to iteratively solve the combined model based on the analysis results of the beam elements, rotational hinge elements, contact constraint elements, and torsion spring elements of each unit body to perform kinematic analysis on the deformation unfolding process of the four-bar linkage combination in the over-constrained space.

[0161] It should be noted that the description of the device in this application embodiment is similar to the description of the method embodiment above, and has similar beneficial effects as the method embodiment, therefore it will not be repeated. For any technical details not covered in the assisted driving device provided in this application embodiment, please refer to... Figures 1 to 9 The meaning is understood in accordance with the description of any of the accompanying drawings.

[0162] According to embodiments of this application, this application also provides an electronic device and a non-transitory computer-readable storage medium.

[0163] Figure 11 A schematic block diagram of an example electronic device 30 that can be used to implement embodiments of this application is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the application described and / or claimed herein.

[0164] like Figure 11 As shown, the electronic device 30 includes a computing unit 301, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 302 or a computer program loaded from a storage unit 308 into a random access memory (RAM) 303. The RAM 303 may also store various programs and data required for the operation of the electronic device 30. The computing unit 301, ROM 302, and RAM 303 are interconnected via a bus 304. An input / output (I / O) interface 305 is also connected to the bus 304.

[0165] Multiple components in electronic device 30 are connected to I / O interface 305, including: input unit 306, such as keyboard, mouse, etc.; output unit 307, such as various types of displays, speakers, etc.; storage unit 308, such as disk, optical disk, etc.; and communication unit 309, such as network card, modem, wireless transceiver, etc. Communication unit 309 allows electronic device 30 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0166] The computing unit 301 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 301 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 301 performs the various methods and processes described above, such as a method for modeling and analyzing over-constrained space four-bar linkages. For example, in some embodiments, a method for modeling and analyzing over-constrained space four-bar linkages can be implemented as a computer software program tangibly contained in a machine-readable medium, such as storage unit 308. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 30 via ROM 302 and / or communication unit 309. When the computer program is loaded into RAM 303 and executed by the computing unit 301, one or more steps of the method for modeling and analyzing over-constrained space four-bar linkages described above can be performed. Alternatively, in other embodiments, computing unit 301 may be configured by any other suitable means (e.g., by means of firmware) to perform a modeling and analysis method for an over-constrained space four-bar linkage assembly.

[0167] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), payload-programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0168] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0169] In the context of this application, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0170] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0171] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0172] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0173] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this application can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this application can be achieved, and this is not limited herein.

[0174] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A modeling and analysis method for over-constrained spatial four-bar linkages, characterized in that, The method includes: Obtain multiple unit cells for constructing an over-constrained space four-bar linkage assembly, wherein the unit cells are over-constrained space four-bar linkages in an unfolded state; Based on the set conditions, obtain the set mass points used to split each unit body; Construct a reference coordinate system for the over-constrained space four-bar linkage assembly, and obtain the mass coordinate information of a set mass point of each unit body according to the reference coordinate system and the geometric parameters of each unit body; Based on the mass point coordinate information of each unit body, a model of each unit body and an additional rotation hinge unit are constructed. The model of each unit body includes basic units, which include beam units, virtual beam units, rotation hinge units, contact constraint units, and torsion spring units. Based on the additional rotational hinge unit of each unit body, the models of the multiple unit bodies are combined to obtain the combined model of the over-constrained space four-bar linkage. The combined model is controlled to simulate the motion of the deformation and unfolding process of the over-constrained spatial four-bar linkage assembly; The basic elements of each unit body are analyzed to obtain the analysis results of beam elements, rotational hinge elements, contact constraint elements, and torsion spring elements for each unit body. The analysis of the basic elements of each unit body includes: analyzing the beam elements of each unit body to obtain beam element analysis results, which include flexible deformation and mass internal forces; analyzing the contact constraint elements of each unit body to obtain contact constraint element analysis results, which include cross-sectional contact forces and lateral contact forces; analyzing the torsion spring elements of each unit body to obtain torsion spring element analysis results, which include deformation driving forces; and analyzing the rotational hinge elements of each unit body to obtain rotational hinge element analysis results, which include rotational displacements. Based on the analysis results of the beam element, the rotation hinge element, the contact constraint element, and the torsion spring element of each unit, the combined model is iteratively solved to perform motion analysis on the deformation and unfolding process of the over-constrained space four-bar linkage assembly. The step of obtaining the set mass points for splitting each unit body according to the set conditions includes: Based on the link axis of each link of each unit body, obtain four reference mass points of each unit body; Obtain a predetermined number of link mass points between two reference mass points of each link in each unit body; Based on the four reference mass points of each unit body and the end cross-sections where the four reference mass points are located, determine the end mass points of each end cross-section of each unit body; The designated mass points include the reference mass point, the connecting rod mass point, and the end mass point of each unit body; Each over-constrained space four-bar linkage consists of four identical links, each with a link axis. The intersection points of the four link axes are configured to represent four reference mass points of the over-constrained space four-bar linkage; the four reference mass points include a first reference mass point, a second reference mass point, a third reference mass point, and a fourth reference mass point; correspondingly, the reference coordinate system for constructing the over-constrained space four-bar linkage assembly includes: The reference coordinate system is constructed with the center of each unit body as the origin, the direction from the origin to the third reference mass as the positive X-axis, and the direction from the first reference mass to the third reference mass as the positive Y-axis. The geometric parameters of each unit include the link length, unfolding angle, upward angle, and link tilt angle of the unit. The unfolding angle is the angle between the first line segment formed by the second reference mass and the third reference mass and the negative direction of the X-axis; The upward angle is the angle between the midline segment formed by the origin and the third reference particle and the positive direction of the Y-axis; The inclination angle of the connecting rod is the angle between the rectangular cross-section side of each unit body and the set plane.

2. The method according to claim 1, characterized in that, Based on the mass point coordinate information of each unit body, construct the model of each unit body and the additional rotational hinge element, including: Based on the coordinates of two reference mass points on each link of each unit body, a sub-beam element is constructed for each link of each unit body; the beam element of each unit body includes all the sub-beam elements of each unit body. Based on the coordinates of two reference mass points of each link in each unit body and the coordinates of the end mass points of the end sections where the two reference mass points are located, a sub-virtual beam unit for each link is constructed; the virtual beam unit of each unit body includes the sub-virtual beam unit of each link in each unit body; Based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points of the end section where each reference mass point is located, and the first set bearing, first set journal, and first set rotation axis direction at each reference mass point, a sub-rotation hinge unit at each reference mass point is constructed; the rotation hinge unit of each unit body includes the sub-rotation hinge unit at each reference mass point. Based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points of the end section where each reference mass point is located, and the end normal vector and side normal vector of the connecting rod where each reference mass point is located, a sub-contact constraint unit is constructed at each reference mass point; the contact constraint unit of each unit body includes the sub-contact constraint unit at each reference mass point. Based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points of the end section where each reference mass point is located, and the first set rotation axis of each reference mass point, a sub-torsion spring unit is constructed at each reference mass point; the torsion spring unit of each unit body includes the sub-torsion spring unit at each reference mass point; Based on the coordinates of each reference mass point of each unit body, the coordinates of the four end mass points of the end section where each reference mass point is located, and the second set bearing, second set journal, and second rotation axis direction of each reference mass point, a sub-additional rotation hinge unit is constructed at each reference mass point; the additional rotation hinge unit of each unit body includes the sub-additional rotation hinge unit at each reference mass point.

3. The method according to claim 2, characterized in that, The analysis of the beam element of each unit body includes: Analyze each sub-beam element of the beam element in each unit body; The analysis includes each sub-beam element of each beam element in each unit body, including: Construct the first local motion coordinate system for each sub-beam element; Based on the virtual motion method and the first local motion coordinate system, the displacement increment of each link in each sub-beam unit from the first moment to the second moment is determined; Based on the displacement increment of each link, determine the deformable link corresponding to each link; Each link and its corresponding deformable link are compared to obtain the local flexible deformation of each link in the first local motion coordinate system. The local flexible deformation includes local compressive and tensile deformation and local bending deformation. Based on the flexible deformation of each link, the local mass point internal force of each link in the first local motion coordinate system is determined. The local mass point internal force includes the two local mass point internal forces of the two mass points corresponding to each link. Based on the first local motion coordinate system and the reference coordinate system, the local flexible deformation and the local mass internal force are converted into the flexible deformation and mass internal force of each link in the reference coordinate system.

4. The method according to claim 2, characterized in that, The analysis of the contact constraint units of each unit body includes: Analyze each sub-contact constraint element of the contact constraint element of each unit body; The analysis includes examining each sub-contact constraint element of each unit body's contact constraint element, including: Obtain the side normal vector and cross-sectional normal vector at each reference mass point; The dihedral angle at each reference mass point is determined based on the side normal vector and the cross-sectional normal vector at each reference mass point. Based on the penalty function and the dihedral angle of each reference mass, the end section contact force and end side contact force at each reference mass are determined.

5. The method according to claim 2, characterized in that, The analysis of the torsion spring unit of each unit includes: Analyze each sub-torsional torsion spring unit of each unit body; The analysis includes each sub-torsional torsion spring unit of each unit body, including: Obtain the plane normal vector at each reference point; Based on the plane normal vector and direction angle function of each reference mass point, the torsion spring rotation angle at each reference mass point is determined; The end deformation driving force at each reference mass point is determined based on the torsion spring rotation angle at each reference mass point.

6. The method according to claim 2, characterized in that, The analysis of the rotational hinge element of each unit body includes: Analyze each sub-rotational hinge element of each unit body's rotational hinge element; The analysis includes each sub-rotational hinge element of each unit body's rotational hinge element, including: Obtain the first center mass and the second center mass corresponding to the second set bearing and the second set journal at each reference mass point of each unit body, wherein the translational degrees of freedom of the first center mass point and the second center mass point are coupled to each other; A second local coordinate system is constructed with the first central mass point at each reference mass point as the origin and the second set rotation axis as the z-axis. Based on the second local coordinate system, the equations of motion and degree-of-freedom coupling equations of the first and second central mass points are constructed. Based on the equations of motion and the coupling equations of degrees of freedom, determine the local rotational displacement of each reference mass point of each link in the second local coordinate system; Based on the reference coordinate system and the second local coordinate system, the rotational displacement corresponding to the local rotational displacement in the reference coordinate system is determined.

7. The method according to claim 1, characterized in that, Based on the analysis results of the beam element, rotation hinge element, contact constraint element, and torsion spring element of each unit, the combined model is iteratively solved to perform kinematic analysis on the deformation and unfolding process of the over-constrained space four-bar linkage assembly, including: Based on the beam element analysis results, rotation hinge element analysis results, contact constraint element analysis results, and torsion spring element analysis results of each unit body, the force information of the set mass point of each unit body is determined. Based on the force information of the designated mass point of each unit body, determine the mass point displacement of the designated mass point of each unit body at the current moment; Based on the displacement of the preceding mass point of each unit body at the previous moment and the displacement of the mass point at the current moment, the displacement of the following mass point of each unit body at the next moment is obtained.

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