A flexible parallel structure equivalent to a chain ring and a topological mechanics analysis method

Abstract

The application relates to a flexible parallel structure equivalent to a chain ring and a topological mechanics analysis method, and relates to the technical field of robots.The structure comprises a driving base, at least two flexible strips and a plurality of driving units arranged on the driving base; wherein each flexible strip has two end portions, and the two end portions are connected with corresponding driving units respectively; the at least two flexible strips are connected with each other in a predetermined interlaced sequence at one or more connection regions; the interconnection relationship formed by the at least two flexible strips at the connection regions is equivalent to a chain ring in topology, and the component number of the chain ring is equal to the number of the flexible strips. The flexible parallel structure provided by the application has a stable topological invariant connection relationship.

Description

Technical Field

[0001] This application relates to the field of robotics, and more specifically, to a topological mechanics analysis method for a flexible parallel structure equivalent to a chain link. Background Technology

[0002] Flexible parallel structures are a novel type of mechanism formed by combining multiple flexible units in parallel. These structures utilize the elastic deformation of flexible units such as slender rods, strips, and thin plates to transmit motion and force, combining the high stiffness, high precision, and high load-bearing capacity of parallel mechanisms with the advantages of lightweight, good compliance, and large deformation capabilities of flexible bodies. They have already shown broad application prospects in fields such as continuum robots, flexible electronics, aerospace deployment structures, and biomedical devices.

[0003] The existing structure does not construct connection relationships with stable topological invariants, such as chain links, which makes it difficult to quantitatively describe the transformation relationship between local torsion and overall entanglement during its deformation process, thus limiting its application in fields such as reconfigurable flexible mechanisms and intelligent drive-sensing integrated systems. Summary of the Invention

[0004] This application is provided to address the aforementioned problems in the prior art. The embodiments of this application provide a flexible parallel structure equivalent to a chain link, and a topological mechanics analysis method, exhibiting a connection relationship with stable topological invariants.

[0005] In a first aspect, embodiments of this application provide a flexible parallel structure equivalent to a chain link, comprising: a drive base, at least two flexible strips, and a plurality of drive units disposed on the drive base; Each of the flexible strips has two ends, and the two ends are respectively connected to the corresponding drive unit; The at least two flexible strips are connected to each other in one or more connection areas in a predetermined staggered order; The interconnection between the at least two flexible strips in the connection region is topologically equivalent to a chain link, and the number of components of the chain link is equal to the number of flexible strips.

[0006] Secondly, embodiments of this application provide a topological mechanics analysis method based on the above-mentioned flexible parallel structure equivalent to a chain link. The method includes: Obtain the geometric parameters, material parameters, connection area information, and end drive control parameters of each flexible strip; Based on the geometric parameters and the material parameters, the control equations for each of the flexible strips are established. Based on the connection region information, constraint conditions for each of the flexible strips in the connection region are generated; Based on the end drive control parameters, the boundary conditions for each end of each of the flexible strips are generated; By combining the governing equations, the constraints, and the boundary conditions, and solving them, a numerical solution is obtained. Based on the numerical solution, the topological parameters and mechanical response parameters are determined; Based on the topology parameters and the mechanical response parameters, a mapping relationship between the topology parameters and the mechanical response parameters is generated.

[0007] The embodiments of this application have the following technical effects: Since the connection relationship is topologically equivalent to a chain link, the number of turns of the structure remains unchanged during continuous deformation. This property is independent of specific geometric dimensions, material parameters, or the degree of deformation, providing a solid structural foundation for subsequent analysis of bending-torsional coupling behavior based on topological invariants. The chain link topological constraint ensures that when the driving unit applies a torsional load to the end of the strip, local torsion and overall winding can be mutually transformed, and the total transformation amount is conserved. This makes the structure have predictable and designable deformation modes, allowing it to be applied to fields such as reconfigurable mechanisms, mechanical logic, and variable stiffness flexible robots. Since the core characteristics are determined by topology rather than specific geometric parameters, the topology-mechanical mapping model established for this structure can be extended to any other structure with the same chain link connection relationship, thereby achieving a universal analysis capability that is difficult to achieve with traditional flexible parallel structures. Attached Figure Description

[0008] In drawings that are not necessarily drawn to scale, the same reference numerals may describe similar parts in different views. The same reference numerals with or without letter suffixes may indicate different instances of similar parts. The drawings illustrate various embodiments generally by way of example rather than limitation, and are used, together with the description and claims, to explain the disclosed embodiments. Where appropriate, the same reference numerals are used in all drawings to refer to the same or similar parts. Such embodiments are illustrative and not intended to be exhaustive or exclusive embodiments of the apparatus or method.

[0009] Figure 1 This application provides a flexible parallel structure equivalent to a chain link, as provided in one embodiment. Figure 2 This is another flexible parallel structure equivalent to a chain link, provided in one embodiment of this application; Figure 3 This is yet another flexible parallel structure equivalent to a chain link, provided in one embodiment of this application; Figure 4 This is a schematic diagram of a chain link provided in one embodiment of this application; Figure 5 This is a flowchart of a topological mechanics analysis method provided in one embodiment of this application; Figure 6 This application provides an embodiment of a flexible parallel structure under conditions of increased torsion angle, along with the coordinates of characteristic points in the connection region. The curve of change; Figure 7 This application provides an embodiment of the evolution relationship between the number of windings and the number of twists as a function of the end twist angle; Figure 8 This application provides an embodiment of the evolution relationship between the number of self-chains and the number of wraps as a function of the end twist angle; Figure 9 This is a schematic diagram of a topology analysis device provided in one embodiment of this application. Detailed Implementation

[0010] To enable those skilled in the art to better understand the technical solutions of this application, the application will be described in detail below with reference to the accompanying drawings and specific embodiments. The embodiments of this application will be further described in detail below with reference to the accompanying drawings and specific examples, but this is not intended to limit the application. The terms "first," "second," and "third" used in this application are merely intended to distinguish the corresponding features and do not imply a necessary order, nor do they necessarily represent only the singular form.

[0011] like Figure 1 As shown, this application embodiment provides a flexible parallel structure equivalent to a chain link, including: a drive base (not shown in the figure), two flexible strips (blue and red strips), and four drive units disposed on the drive base. Figure 1 (The gray cylinder in the middle).

[0012] Each flexible strip has two ends, and each end is connected to a corresponding drive unit.

[0013] Two flexible strips are connected to each other in a predetermined staggered sequence in the connection area.

[0014] The interconnection between two flexible strips in the connecting region is topologically equivalent to a chain link, and the number of chain link components is equal to the number of flexible strips.

[0015] The drive base is a foundation component used to support and fix the drive unit. It typically possesses sufficient rigidity and stability to ensure that the motion or force output by the drive unit is accurately transmitted to the end of the flexible strip without causing additional base deformation or displacement. The base can be made of metal plate, carbon fiber composite plate, or injection-molded polymer material. The base does not necessarily have to be flat; it can also be a frame, ring, or multi-layer structure. Sensors can be integrated into the base to monitor the drive status in real time. The base can be designed to be height or angle adjustable to adapt to different experimental or application scenarios.

[0016] Flexible strips are the core deformation elements of a structure, possessing elastic properties such as being slender, flexible, and torsional. The number of strips must be at least two, for example, two, three, four, or more. Figure 2-3 As shown in the figure, the drive base is omitted. Each flexible strip is typically straight in its undeformed state, but may also have initial curvature or pre-torsion angle. The cross-section of the flexible strip can be rectangular, circular, elliptical, or irregular in shape to adjust the ratio of bending and torsional stiffness. The material of the flexible strip can be polymer, metal, or fiber-reinforced composite material.

[0017] The number of drive units is equal to twice the number of flexible strips. Each drive unit independently controls the end of the flexible strip connected to it and can output at least one of angular displacement, angular velocity, or torque. The drive units typically use a motor with a reducer or direct drive, but can also use a rotary electromagnet, pneumatic / hydraulic rotary actuator, or piezoelectric rotary motor.

[0018] The two free ends of each flexible strip are fixed to the output shafts of two different drive units. The connection method can be mechanical clamping, bonding, or welding. The connection between the ends and the drive units should ensure that no relative slippage or rotation occurs during loading to guarantee the determinism of the boundary conditions. Figure 1 The two flexible strips in the figure are bonded together; therefore, the bonded area in the figure is the connection area.

[0019] The connection area is the spatial location where the flexible strips are fixed together, transmit forces, and deform. It can be a common area, such as all flexible strips connecting near a center point, or multiple independent connection areas, such as flexible strips A and B connecting at point P, and flexible strips A and C connecting at point Q. The predetermined interlacing sequence refers to the order in which the flexible strips intersect within the connection area, for example, flexible strip 1 passes over flexible strip 2 from above, and flexible strip 2 then passes over flexible strip 3 from above, and so on. The interlacing sequence determines the topological type of the connection relationship. Connection methods include bonding, thermoforming, mechanical clamping, or stitching.

[0020] A chain link is a concept in knot theory, consisting of several interlocking closed curves. Although the flexible strips in this embodiment have free ends, the connection relationships they form in the connection region—that is, the staggered order and the way they are mutually fixed—have the same topological invariants as the projection or connection diagram of a closed chain link. Specifically, if the two ends of each flexible strip are virtually connected to form a closed loop, the connection topology of the entire system is equivalent to a chain link, such as... Figure 4 As shown in the figure. This feature ensures that the connection topology of the structure does not change during continuous deformation, thus making topological invariants such as the number of turns constant, providing a theoretical basis for subsequent mechanical analysis based on topological parameters.

[0021] Since the connection relationships are topologically equivalent to chain links, the number of turns remains constant during continuous deformation. This property is independent of specific geometric dimensions, material parameters, or the degree of deformation, providing a solid structural foundation for subsequent analysis of bending-torsional coupling behavior based on topological invariants. The chain link topological constraints ensure that when the driving unit applies a torsional load to the end of the flexible strip, local torsion and overall winding can be mutually converted, and the total conversion is conserved. This gives the structure predictable and designable deformation modes. This allows the structure to be applied to reconfigurable mechanisms, mechanical logic, variable stiffness flexible robots, and other fields. Because the core characteristics are determined by topology rather than specific geometric parameters, the topology-mechanical mapping model established for this structure can be generalized to any other structure with the same chain link connection relationships, thus achieving a universal analytical capability that is difficult to achieve with traditional flexible parallel structures.

[0022] In one embodiment of this application, the drive unit can independently control at least one of output angular displacement, angular velocity and torque to apply synchronous torsional loading, asynchronous torsional loading or sequential torsional loading to the end of the flexible strip; the number of drive units is equal to twice the number of flexible strips, and each drive unit is connected to one end of the flexible strip.

[0023] Each drive unit features multiple control modes, selectable to operate in at least one of angular displacement control, angular velocity control, or torque control. Angular displacement control: precisely controls the end-end torsional angle, suitable for quasi-static deformation analysis or position servo control with well-defined displacement boundary conditions. Angular velocity control: controls the torsional rate, suitable for dynamic loading or applications requiring controlled deformation speed. Torque control: directly controls the end-end torque, suitable for force boundary condition analysis or force / resistance control.

[0024] This feature defines the cooperative loading modes in which the drive units apply torsion to the ends. The three modes correspond to different control strategies: Synchronous Torsional Loading: All drive units move simultaneously with the same angular displacement / velocity / torque. Asynchronous Torsional Loading: Each drive unit moves at a different rate or amplitude. Sequential Torsional Loading: The drive units operate in a time-sequential manner. For example, ends 1 and 2 are first torsioned to a certain angle, and after stabilization, ends 3 and 4 are then torsioned.

[0025] By independently controlling the angular displacement, angular velocity, or torque of each end, and enabling synchronous, asynchronous, and sequential torsional loading, this flexible parallel structure can simulate almost any torsional boundary condition at each end. Because the drive unit can be independently controlled, the torsional input at each flexible strip end can be precisely changed, thereby quantitatively controlling the distribution of torsional number within the flexible strip.

[0026] like Figure 5As shown, this application provides a topological mechanics analysis method based on a flexible parallel structure equivalent to a chain link, as described in any of the above embodiments. The method includes: Step 501: Obtain the geometric parameters, material parameters, connection area information, and end drive control parameters of each flexible strip.

[0027] Geometric parameters may include the following: the length, width, thickness, and initial shape of each flexible strip.

[0028] Material parameters may include one or more of the following: elastic modulus and shear modulus.

[0029] The connection area information may include the following: the arc length ranges involved in the connection on each flexible strip, the staggered order between the flexible strips, and the connection type.

[0030] The end drive control parameters include one or more of the following: the boundary condition type (displacement control / force control) and specific values ​​(such as torsional angle, angular velocity, torque) of each end, as well as the loading mode.

[0031] Step 502: Based on geometric and material parameters, establish the governing equations for each flexible strip.

[0032] Based on the theory of elastic rod mechanics, a set of differential equations describing the relationship between deformation and internal forces is generated for each flexible strip. Kirchhoff's rod theory is typically used, as it is applicable to large deformation and torsion problems in slender rods.

[0033] Step 503: Based on the connection region information, generate the constraint conditions for each flexible strip in the connection region.

[0034] Geometric and static constraints are generated based on the location and staggered order of the connected regions.

[0035] Geometric constraints: Within the connection region, the corresponding points of all flexible strips satisfy displacement continuity and rotation continuity, that is, different flexible strips are rigidly fixed in the connection region.

[0036] Static constraint condition: Within the connected region, the sum of the internal forces transmitted by all flexible strips is zero, and the sum of the internal moments is zero. This is the manifestation of Newton's third law under quasi-static conditions.

[0037] Step 504: Based on the end drive control parameters, generate the boundary conditions for each end of each flexible strip.

[0038] Step 505: Solve the simultaneous governing equations, constraints, and boundary conditions to obtain a numerical solution.

[0039] The governing equations of all flexible strips, the internal constraints of the connecting regions, and the external boundary conditions of the ends are combined into a large-scale boundary value problem, which is then solved using numerical methods. Commonly used methods include the target method, the finite difference method, and the finite element method.

[0040] Step 506: Based on the numerical solution, determine the topological parameters and mechanical response parameters.

[0041] Step 507: Generate the mapping relationship between topological parameters and mechanical response parameters based on topological parameters and mechanical response parameters.

[0042] The calculated topological parameters are correlated with the corresponding mechanical response parameters to obtain a quantitative functional relationship. This mapping relationship can be in tabular form, interpolation function, etc.

[0043] This method is independent of the specific dimensions, materials, and other details of the structure; it only requires input of basic parameters to automatically complete modeling, solving, parameter extraction, and mapping. Therefore, it can be reused across structures (as long as the topology is equivalent to a chain), solving the problem of traditional flexible parallel structure analysis depending on specific configurations.

[0044] In one embodiment of this application, the governing equations for each flexible strip are established based on geometric and material parameters, including: Based on the length in the geometric parameters, equilibrium control equations are generated for the corresponding flexible strip regarding the centerline position, direction, internal forces, and internal moments. Based on the width and thickness in the geometric parameters and the elastic modulus and shear modulus in the material parameters, the structural equation is generated.

[0045] Figure 1 Although the structure shown is composed of two flexible strips, to simplify the equation establishment process, the two flexible strips can be modeled as four strip segments according to the connection area, labeled as 1 to 4 respectively. Specifically, for the first... i A flexible strip is considered as a slender elastic body with finite width and thickness, and its centerline and local cross-sectional attitude are described using the Kirchhoff rod model. This model is derived from the geometric compatibility and moment balance relationships of slender flexible structures under quasi-static conditions.

[0046] Establish arc length parameters along the centerline of the flexible strip s ,in, , For the first i The length of the flexible strip. Let Indicates the first i The position vector of the centerline of the flexible strip in the global coordinate system. , , These represent the three unit direction vectors in the coordinate system of the local section of the flexible strip, where... Consistent with the tangential direction of the centerline and These correspond to the width and thickness directions of the flexible strip cross-section, respectively. Let... Represents the curvature-torsion vector. and Let represent the internal forces and moments on the cross-section of the flexible strip, respectively. Neglecting gravity, each flexible strip satisfies the following governing equations:

[0047] In the above equation, the first equation describes the geometric compatibility relationship of the centerline of the flexible strip, that is, the first derivative of the centerline is equal to the local tangential direction; the second equation describes the change of the cross-sectional orientation of the flexible strip with the rotation of the arc length; the third and fourth equations are the force balance equation and the moment balance equation, respectively.

[0048] For each strip itself, the constitutive equation establishes a quantitative relationship between its internal torque and curvature, and between torque and torsion:

[0049] in, To bypass Moment of inertia of axial section To bypass Moment of inertia of axial section Let be the torsional constant. For elastic modulus, Shear modulus , To bypass axis, The curvature of the axis, To bypass Shaft torque, , To bypass axis, Bending moment of the shaft, To bypass The torque of the shaft and the moment of inertia of the cross section are calculated from the width and thickness.

[0050] The structure of the equilibrium governing equations is universal and independent of materials; the constitutive equations, on the other hand, encapsulate material properties. When the material is changed, only the generation module of the constitutive equations needs to be modified, while the equilibrium governing equations remain unchanged, which is beneficial for code reuse.

[0051] In one embodiment of this application, constraint conditions for each flexible strip in the connection region are generated based on the connection region information, including: Based on the connection arc length interval and staggered sequence in the connection area information, the displacement continuity condition and rotation continuity condition of each flexible strip in the connection area are generated. Based on the connection arc length range in the connection area information, the force balance conditions and torque balance conditions of each flexible strip in the connection area are generated.

[0052] Displacement continuity condition: Within the connected region, the global position vectors of all corresponding material points in the flexible strips are equal. Rotation continuity condition: Within the connected region, the direction vectors of the local coordinate systems of all flexible strips are equal, meaning there is no relative rotation of the cross-section.

[0053] Force equilibrium condition: The sum of the internal forces transmitted by all flexible strips to the connecting region is zero, ignoring the inertia and external forces of the connecting region itself. Torque equilibrium condition: The sum of the internal moments transmitted by all flexible strips to the connecting region is zero.

[0054] The correct use of the staggered order ensures that the correspondence of material points in the connecting regions is consistent with the cross structure of the chain links, thus making the connection topology of the overall structure mathematically equivalent to that of the chain links.

[0055] In one embodiment of this application, the boundary conditions include: displacement constraint conditions and torsional loading conditions; The displacement constraint condition is that the translational displacement of the end is fixed, and the torsional loading condition is that the end has at least one of angular displacement, angular velocity or torque around the axis.

[0056] The position of each flexible strip end in space is completely constrained, preventing translation. This means the ends are rigidly fixed to the output shaft connection point of the drive base, disallowing movement in the X, Y, and Z directions. Here, the axis refers to the direction of the tangent to the centerline of the flexible strip end, i.e. The axis. Because the end orientation of the flexible strip changes during deformation, but the drive unit is typically fixed to the base, its output axis direction is fixed. Therefore, the actual applied torsion is around the fixed axis of the base's output axis, not the follower axis. This requires the user to define the initial end orientation to be consistent with the drive axis direction during modeling, or to project the torsional boundary conditions to the follower coordinate system through coordinate transformation. However, for simplicity, it is usually assumed that the end orientation change is small, or the initial tangent direction is directly used as the axis.

[0057] Fixed translational displacement eliminates the translational degrees of freedom of the rigid body, significantly simplifying the boundary treatment in numerical solutions; torsional loading conditions are applied directly to the ends, eliminating the need to introduce additional driving element models and reducing computational complexity.

[0058] In one embodiment of this application, the numerical solution is obtained by simultaneously solving the governing equations, constraints, and boundary conditions, including: The target shooting method is used to numerically solve the boundary value problem formed by the combination of the control equation, constraint conditions and boundary conditions, and obtain the numerical solutions of each flexible strip at discrete arc length points. The numerical solution includes: the centerline position vector and the direction vector.

[0059] The numerical solution is not a continuous function, but rather an approximation of the unknowns at discrete points along the arc length. The density of these discrete points can be adjusted based on accuracy and computational cost, typically being higher in regions with large deformation gradients. Centerline position vector: Spatial coordinates of the flexible strip's centerline at each discrete point. Direction vector: A unit vector describing the cross-sectional attitude.

[0060] The target shooting method transforms complex boundary value problems into iterative initial value problems, avoiding the direct solution of large nonlinear algebraic equation systems. It has fast calculation speed and low memory consumption, making it particularly suitable for the structure composed of multiple slender flexible strips in this invention.

[0061] In one embodiment of this application, determining topological parameters based on numerical solutions includes: Based on the centerline position vector in the numerical solution, the discrete point set of the centerline of each flexible strip is extracted; Based on the discrete point set of the centerline, the number of wraps for each flexible strip is calculated; The torsion number of each flexible strip is calculated based on the direction vector in the numerical solution or the torsion calculated from the direction vector. Based on the number of windings and the number of twists, calculate the number of self-chains for each flexible strip; Calculate the number of wraps between any two flexible strips based on the discrete point set of the centerline of any two flexible strips; The topology parameters include: the number of windings, twists, and self-chains of each flexible strip, as well as the number of wraps between any two flexible strips.

[0062] Number of wraps It is a geometric topological quantity describing the degree of self-entanglement of a space curve. For open curves with free ends, an approximate number of entanglements must be calculated using virtual closure or end correction methods. The commonly used formula is the Gaussian integral:

[0063] twist number The degree of local torsion of a flexible strip around its centerline is described by the torsion integral along the arc length:

[0064] The torsion can be calculated using the derivative of the direction vector. (Self-chain number) Then it is the number of wraps. and torsion number sum:

[0065] The wrap number is a topological invariant describing the degree of entanglement between different components in a multi-component chain link. For a chain link topological object composed of multiple flexible strips, the wrap number can be calculated from any two flexible strips (flexible strips...). i With flexible strip j The number of rings formed by ) According to C lug Reanu's theorem, the number of turns of a chain. It can be represented as:

[0066] The centerline position and direction vectors obtained from the solution are transformed into the number of windings, the number of torsions, the number of self-chains, and the number of wraps, establishing a bridge between continuous deformation and discrete topological invariants. By calculating the number of windings and the number of torsions separately, it is possible to quantitatively analyze how local torsion is transformed into overall winding.

[0067] In one embodiment of this application, determining the mechanical response parameters based on the numerical solution includes: Based on the centerline position vector and direction vector in the numerical solution, the overall compression and spatial torsion angle of the flexible parallel structure are calculated. The mechanical response parameters include: overall compression and spatial torsion angle.

[0068] Overall compression describes the total shortening of the entire flexible parallel structure along a principal axis under end torsional loading. For a typical four-end drive chain structure, overall compression is usually defined as the average distance change between the four end drive base planes, or the end displacement difference along the structural axis.

[0069] Spatial torsion angle describes the overall degree of torsion of the entire structure in space, that is, the relative rotation angle between the planes containing the two strips, or the relative torsion angle between the ends around the axis of the structure.

[0070] The number of twists and turns describes topological features, while the overall compression and spatial twist angle describe observable geometric deformation. Only by combining the two can we fully characterize the bending-torsional coupling behavior.

[0071] In one embodiment of this application, a mapping relationship between topological parameters and mechanical response parameters is generated based on topological parameters and mechanical response parameters, including: Based on the number of windings, the number of twists, and the number of self-chains, a self-chain constraint relationship is generated; Based on the number of turns, a number of turns conservation constraint relationship for multi-component chain loops is generated; Based on the self-chain constraint relationship and the wrap number conservation constraint relationship, a mapping relationship between topological parameters and mechanical response parameters is generated.

[0072] For closed curves, the number of self-chains equals the number of wraps plus the number of twists. For open curves (such as the flexible strips in the embodiments of this application), with appropriate end corrections, this relationship is approximately satisfied, or a more general conservation law is satisfied: the number of wraps of the chain links remains unchanged during continuous deformation. Using the calculated values ​​of the topological parameters, the functional relationship between them is verified or fitted.

[0073] Using the topological constraints obtained in the previous step, such as the number of self-chains = number of entanglements + number of torsions, the topological parameters are quantitatively correlated with the mechanical response parameters. Since the constraints reveal the linear correlation between the topological parameters, the mapping relationship can be simplified.

[0074] Because topological constraints reduce two independent variables to one, the number of experimental or computational data points required to establish the mapping is greatly reduced, and the fitted model is more stable and physically interpretable.

[0075] Figure 6 This diagram illustrates the evolution of the overall deformation mode of the flexible parallel structure under gradually increasing end torsion angles, as well as the coordinates of characteristic points in the connecting region of the flexible strips. The curve showing the change. From Figure 6 It can be seen that when the end torsion angle increases from 0° to 90°, the coordinates of the central feature point along the vertical direction gradually decrease, indicating that the structure undergoes overall compression. This change exhibits nonlinear characteristics, with a relatively slow change in the early stage and a significant increase in the later stage. This result shows that local end torsion can induce overall compression and spatial winding of the structure, reflecting that the flexible parallel structure has a significant bending-torsional coupling response.

[0076] Figure 7-8 The evolution of each topological parameter with respect to the end twist angle during the loading process described above is shown. Among them, Figure 7 This indicates that the number of entanglements gradually decreases as the twist angle increases, while the number of twists gradually increases as the twist angle increases, showing a synchronous evolution trend in opposite directions. Figure 8 This indicates that the number of self-chains and the number of chain loops between the two flexible strips remain constant during loading. Therefore, it can be seen that, with the topology type remaining unchanged, a continuous transformation occurs between the local torsional storage and the overall spatial winding amount, while the corresponding topological invariants remain unchanged.

[0077] In the specific verification process, the end torsion angles can be set to loading nodes such as 0°, 30°, 60°, and 90°, and the equilibrium configuration of the flexible parallel structure can be solved or measured at each loading node. By recording the displacement of characteristic points in the central connection region, the overall compression, and the corresponding topological parameters, a quantitative relationship between the end driving input and the overall structural configuration response can be established. When the number of windings and the number of torsions show continuous monotonic changes while the number of self-chains and the number of chain loops remain constant, it indicates that the topological type of the structure has not changed during loading, and the resulting configuration response mainly comes from the energy conversion between bending and torsional deformation. The verification results can be used to determine the correctness of the numerical model and can serve as a basis for the design of driving parameters, deformation prediction, and selection of stable configurations for flexible parallel structures.

[0078] like Figure 9 As shown, this application provides a topology analysis device based on a flexible parallel structure equivalent to chain links in any of the above embodiments. The device includes: The acquisition module 901 is configured to acquire the geometric parameters, material parameters, connection area information and end drive control parameters of each flexible strip; The generation module 902 is configured to establish the control equations for each flexible strip based on geometric and material parameters; generate the constraint conditions for each flexible strip in the connection area based on the connection area information; and generate the boundary conditions for each end of each flexible strip based on the end drive control parameters. Solver module 903 is configured to simultaneously solve the governing equations, constraints, and boundary conditions to obtain a numerical solution. Module 904 is configured to determine topological parameters and mechanical response parameters based on numerical solutions; and to generate a mapping relationship between topological parameters and mechanical response parameters based on the topological parameters and mechanical response parameters.

[0079] In one embodiment of this application, the generation module 902 is configured to generate equilibrium control equations for the corresponding flexible strip based on the length in the geometric parameters, regarding the centerline position, direction, internal force, and internal moment; and to generate structural equations based on the width and thickness in the geometric parameters and the elastic modulus and shear modulus in the material parameters.

[0080] In one embodiment of this application, the generation module 902 is configured to generate displacement continuity conditions and rotation continuity conditions for each flexible strip in the connection region based on the connection arc length interval and staggered order in the connection region information; and to generate force balance conditions and torque balance conditions for each flexible strip in the connection region based on the connection arc length interval in the connection region information.

[0081] In one embodiment of this application, the solution module 903 is configured to use the shooting method to numerically solve the boundary value problem formed by the combination of the control equation, constraint conditions and boundary conditions, and obtain the numerical solutions of each flexible strip at discrete arc length points; wherein, the numerical solutions include: centerline position vector and direction vector.

[0082] In one embodiment of this application, the determining module 904 is configured to: extract the discrete point set of the centerline of each flexible strip based on the centerline position vector in the numerical solution; calculate the number of windings of each flexible strip based on the discrete point set of the centerline; calculate the number of twists of each flexible strip based on the direction vector in the numerical solution or the twist calculated from the direction vector; calculate the number of self-chains of each flexible strip based on the number of windings and the number of twists; and calculate the number of wraps between any two flexible strips based on the discrete point set of the centerline of any two flexible strips. The topology parameters include: the number of windings, the number of twists, the number of self-chains of each flexible strip, and the number of wraps between any two flexible strips.

[0083] In one embodiment of this application, the determining module 904 is configured to calculate the overall compression and spatial torsion angle of the flexible parallel structure based on the centerline position vector and direction vector in the numerical solution; wherein the mechanical response parameters include: overall compression and spatial torsion angle.

[0084] In one embodiment of this application, the determining module 904 is configured to generate a self-chain constraint relationship based on the number of windings, the number of torsions, and the number of self-chains; generate a multi-component chain loop number conservation constraint relationship based on the number of wraps; and generate a mapping relationship between topological parameters and mechanical response parameters based on the self-chain constraint relationship and the number of wraps conservation constraint relationship.

[0085] Furthermore, although exemplary embodiments have been described herein, their scope includes any and all embodiments based on this application that have equivalent elements, modifications, omissions, combinations (e.g., schemes with overlapping embodiments), adaptations, or changes.

[0086] The elements in the claims will be interpreted broadly based on the language used in the claims and are not limited to the examples described in this specification or during the implementation of this application, the examples of which will be interpreted as non-exclusive. Therefore, this specification and examples are intended to be considered merely illustrative, and the true scope and spirit are indicated by the claims and the full scope of their equivalents.

[0087] The order of the steps in this application is merely exemplary and not restrictive. The execution order of the steps can be adjusted without affecting the implementation of this application (without disrupting the logical relationship between the required steps), and the various embodiments obtained after the adjustment still fall within the scope of this application.

[0088] The above description is intended to be illustrative and not restrictive. For example, the above examples (or one or more of them) can be used in combination with each other. Other embodiments may be used by those skilled in the art upon reading the above description. Furthermore, in the above detailed description, various features may be grouped together to simplify the application. This should not be construed as an intention that a disclosed feature not claimed is necessary for any claim. Rather, the subject matter of the invention may be less than all the features of a particular disclosed embodiment. Thus, the claims are incorporated herein by way of example or embodiment, wherein each claim is an independent, separate embodiment, and these embodiments are contemplated as being able to be combined with each other in various combinations or arrangements. The scope of the invention should be determined by reference to the appended claims and the full scope of their equivalents.

Claims

1. A flexible parallel structure equivalent to a chain link, characterized in that, include: A drive base, at least two flexible strips, and multiple drive units disposed on the drive base; Each of the flexible strips has two ends, and the two ends are respectively connected to the corresponding drive unit; The at least two flexible strips are connected to each other in one or more connection areas in a predetermined staggered order; The interconnection between the at least two flexible strips in the connection region is topologically equivalent to a chain link, and the number of components of the chain link is equal to the number of flexible strips. The drive unit can independently control at least one of the output angular displacement, angular velocity and torque to apply synchronous torsional loading, asynchronous torsional loading or sequential torsional loading to the end of the flexible strip; the number of drive units is equal to twice the number of flexible strips, and each drive unit is connected to one end of the flexible strip.

2. A topological mechanics analysis method, characterized in that, Based on the flexible parallel structure equivalent to a chain link as described in claim 1, the method includes: Obtain the geometric parameters, material parameters, connection area information, and end drive control parameters of each flexible strip; Based on the geometric parameters and the material parameters, the control equations for each of the flexible strips are established. Based on the connection region information, constraint conditions for each of the flexible strips in the connection region are generated; Based on the end drive control parameters, the boundary conditions for each end of each of the flexible strips are generated; By combining the governing equations, the constraints, and the boundary conditions, and solving them, a numerical solution is obtained. Based on the numerical solution, the topological parameters and mechanical response parameters are determined; Based on the topology parameters and the mechanical response parameters, a mapping relationship between the topology parameters and the mechanical response parameters is generated.

3. The method as described in claim 2, characterized in that, Based on the geometric parameters and the material parameters, the governing equations for each of the flexible strips are established, including: Based on the length in the geometric parameters, equilibrium control equations are generated for the corresponding flexible strip regarding the centerline position, direction, internal force, and internal moment. Based on the width and thickness in the geometric parameters and the elastic modulus and shear modulus in the material parameters, the structural equation is generated.

4. The method as described in claim 2, characterized in that, Based on the connection region information, constraint conditions are generated for each of the flexible strips in the connection region, including: Based on the connection arc length interval and staggered order in the connection area information, the displacement continuity condition and rotation continuity condition of each flexible strip in the connection area are generated. Based on the connection arc length interval in the connection area information, force balance conditions and torque balance conditions for each of the flexible strips in the connection area are generated.

5. The method as described in claim 2, characterized in that, The boundary conditions include: displacement constraint conditions and torsional loading conditions; The displacement constraint condition is that the translational displacement of the end is fixed, and the torsional loading condition is at least one of the angular displacement, angular velocity or torque of the end around the axis.

6. The method as described in claim 2, characterized in that, By simultaneously applying the governing equations, the constraints, and the boundary conditions, and solving them, a numerical solution is obtained, including: The target shooting method is used to numerically solve the boundary value problem formed by the combination of the control equation, constraint conditions and boundary conditions, and obtain the numerical solution of each flexible strip at the discrete arc length point; The numerical solution includes: the centerline position vector and the direction vector.

7. The method as described in claim 2, characterized in that, Based on the numerical solution, the topological parameters are determined, including: Based on the centerline position vector in the numerical solution, extract the discrete point set of the centerline of each of the flexible strips; Based on the discrete point set of the centerline, calculate the number of wraps for each of the flexible strips; The number of twists of each of the flexible strips is calculated based on the direction vector in the numerical solution or the twist calculated from the direction vector. Based on the number of windings and the number of twists, calculate the number of self-chains for each flexible strip; Calculate the number of wraps between any two flexible strips based on the discrete point set of the centerline of any two flexible strips; The topology parameters include: the number of windings, twists, and self-chains of each flexible strip, as well as the number of wraps between any two flexible strips.

8. The method as described in claim 2, characterized in that, Based on the numerical solution, the mechanical response parameters are determined, including: Based on the centerline position vector and direction vector in the numerical solution, the overall compression and spatial torsion angle of the flexible parallel structure are calculated. The mechanical response parameters include: overall compression and spatial torsion angle.

9. The method as described in claim 7, characterized in that, Based on the topological parameters and the mechanical response parameters, a mapping relationship between the topological parameters and the mechanical response parameters is generated, including: Based on the number of windings, the number of twists, and the number of self-chains, a self-chain constraint relationship is generated; Based on the number of turns, a number of turns conservation constraint relationship for multi-component chain loops is generated; Based on the self-chain constraint relationship and the wrap number conservation constraint relationship, a mapping relationship between topological parameters and mechanical response parameters is generated.

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