Degree-of-freedom analysis-based six-dimensional force sensor configuration design method

Abstract

The invention discloses a six-dimensional force sensor configuration design method based on degree-of-freedom analysis, and relates to the technical field of six-dimensional force sensor configuration design, and the method comprises the following steps: determining a design target, a theoretical basis and a degree-of-freedom requirement of a six-dimensional force sensor configuration; performing degree-of-freedom analysis through a spiral theory-flexibility matrix method, and constructing a flexible module library; performing degree-of-freedom comprehensive design, decomposing a six-degree-of-freedom space target of the elastic branch chain into a plurality of low-dimensional subspaces, and selecting a flexible module to perform degree-of-freedom matching and combination to obtain a six-degree-of-freedom elastic branch chain; the n elastic branch chains are arranged into an n-branch-chain symmetrical elastic body, m groups of differential capacitors are arranged at symmetrical positions of the n elastic branch chains, and a six-dimensional force sensor is obtained; performing parameter optimization and verification on the six-dimensional force sensor; systematic design from a performance target to a topological structure is realized, a traditional design mode of trial and error depending on experience is got rid of, the sensitivity isotropy of the sensor is remarkably improved, and inter-dimensional coupling is reduced.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of six-dimensional force sensor configuration design, and particularly relates to a six-dimensional force sensor configuration design method based on degree of freedom analysis. BACKGROUND

[0002] In sensor optimization design, the design of an elastic body is a core part, the elastic body is composed of a plurality of six-degree-of-freedom elastic branches in parallel along a center loading table, and the configuration design directly determines the overall performance of the sensor, including sensitivity, isotropy, stiffness, and inter-dimensional coupling.

[0003] In the prior art, the traditional design method is mostly an innovative experience design, that is, a partial improvement is made on the basis of an existing mature structure, such as a cross-beam type, a spoke type, and a T-beam, for example, by means of punching and slotting to adjust the mechanical properties. Such a method highly depends on the experience accumulation of designers and a large number of finite element simulation trial and error, and is not only long in research and development cycle and high in cost, but also lacks a global topological structure generation theory, so that the design result is often a local optimal solution, and it is difficult to achieve a breakthrough in the performance of the sensor, and lacks a systematic theoretical guidance framework.

[0004] Although existing research proposes a parallel structure based on a Stewart platform or a flexible hinge, in order to overcome the disadvantages of rigid mechanisms, an integrated flexible mechanism is introduced into the design of a sensor, but the design itself is extremely challenging, and most of the existing flexible six-dimensional force sensor configurations are based on the flexible replacement of an existing parallel mechanism, or are based on the improvement of certain specific geometric shapes, and still lack a method of systematically synthesizing a new topological structure from the final performance target of the sensor.

[0005] Therefore, the present application provides a six-dimensional force sensor configuration design method based on degree of freedom analysis to solve the above problems. SUMMARY

[0006] The purpose of the present application is to provide a six-dimensional force sensor configuration design method based on degree of freedom analysis, which solves the problems of lack of systematic theoretical guidance, dependence on trial and error method, low design efficiency, and difficulty in achieving ideal sensitivity isotropy in the design of an existing capacitive six-dimensional force sensor elastic body.

[0007] To achieve the above purpose, the present application provides a six-dimensional force sensor configuration design method based on degree of freedom analysis, comprising the following steps: S1: determining the design target, theoretical basis, and degree of freedom requirement of the six-dimensional force sensor configuration; S2: performing degree of freedom analysis by the screw theory-flexibility matrix method, and constructing a flexible module library; S3: Perform a comprehensive design of degrees of freedom, decompose the six-degree-of-freedom spatial target of the elastic branch into multiple low-dimensional subspaces, select the corresponding flexible modules from the flexible module library for degree-of-freedom matching and combination, and obtain an elastic branch with six degrees of freedom. S4: Arrange n elastic branches around the central loading platform in a... A rotationally symmetric arrangement is formed to create an n-branch symmetric elastic body. According to the principle of symmetry, m sets of differential capacitors are set at the symmetrical positions of the n elastic branches, where n is not less than 3 and m is not less than 6, resulting in a six-dimensional force sensor. S5: Parameter optimization and verification of the six-dimensional force sensor.

[0008] Preferably, step S1 specifically includes the following steps: S11: Analyze the sensor input / output signal mapping matrix Mapping matrix Specifically set as follows: ; in, This represents the mapping matrix between the displacement of the moving plate of a capacitor and the change in capacitance. This matrix represents the mapping relationship between the displacement of the central loading stage caused by the elastic body and the displacement of the moving plate of the capacitor. Represents the flexibility matrix of an elastic body, and the mapping matrix. rank satisfy: ; in, The mapping matrix representing the relationship between the displacement of the moving plate of a capacitor and the change in capacitance. rank, The matrix representing the mapping relationship between the displacement of the central loading stage caused by the elastic body and the displacement of the moving plate of the capacitor. rank, Represents the flexibility matrix of an elastic body rank; S12: Obtain the mapping matrix condition number A necessary prerequisite is the elasticity matrix. It is a full-rank matrix, a mapping matrix. condition number Specifically set as follows: ; in, Represents the mapping matrix transpose, Representation matrix The largest eigenvalue, Representation matrix the minimum eigenvalue of the matrix S13: analyzing the elastomer flexibility matrix , defining a linear relationship between deformation and force, which is specifically set as: ; ; wherein, represents a motion matrix, represents a force matrix, represents the motion of the elastomer in the axis direction, represents the motion of the elastomer in the axis direction, represents the motion of the elastomer in the axis direction, represents the displacement of the elastomer in the axis direction, represents the displacement of the elastomer in the axis direction, represents the displacement of the elastomer in the axis direction, represents the matrix element of the elastomer flexibility matrix ; represents the load of the elastomer in the axis direction, represents the load of the elastomer in the axis direction, represents the load of the elastomer in the axis direction, represents the force of the elastomer in the axis direction, represents the force of the elastomer in the axis direction, represents the force of the elastomer in the axis direction, and expanding the first row to obtain: ; only considering the load of the elastomer in the axis direction to obtain: ; .

[0009] Preferably, step S2 specifically comprises the following steps: S21: constructing a basic flexible unit in a six-degree-of-freedom space by a flexibility matrix method, the basic flexible unit including a leaf spring, a plate strip and a thick plate; S22: connecting the basic flexible units in series to obtain a series flexible module, the series flexible module including a parallel type, a vertical type, a planar type and a normal type, and performing degree of freedom analysis on the series flexible module by using a screw theory; S23: connecting the basic flexible units in parallel to obtain a parallel flexible module, the parallel flexible module including a wheel type mechanism, a parallel four-bar mechanism, a planar type mechanism and a parallel four-bar planar type mechanism, and performing degree of freedom analysis on the parallel flexible module by using the screw theory.

[0010] Preferably, in step S21, the six-degree-of-freedom space includes a rotational degree of freedom in the axial direction , a rotational degree of freedom in the axial direction , a rotational degree of freedom in the axial direction , a translational degree of freedom in the axial direction , a translational degree of freedom in the axial direction and a translational degree of freedom in the axial direction , the leaf spring has three degrees of freedom, respectively , and , the plate strip has four degrees of freedom, respectively , , and , and the thick plate has five degrees of freedom, respectively , , , and .

[0011] Preferably, step S21 specifically includes the following steps: Step 1: defining a normalized flexibility matrix of the flexible beam , the normalized flexibility matrix is specifically set as: ; ; ; ; ; wherein , and all represent dimensionless constants, which are determined according to the geometric shape and material properties, represents the thickness of the beam, denotes the gyration constant of motion, denotes the width of the beam, denotes the length of the beam, denotes the shear modulus, denotes the Young's modulus, denotes the Poisson's ratio, denotes the polar moment of inertia, denotes the moment of inertia; Step 2: for a flexible beam with rectangular cross section, the gyration constant of motion is defined as: ; When varies from 1 to 0, the normalized flexibility matrix is obtained, and the main diagonal elements of the normalized flexibility matrix are: ; Step 3: according to and , the flexible beam is classified into basic flexible units, if , the , and are ignored, the flexible beam is a leaf spring, if , the and are ignored, the flexible beam is a strip, if , the is ignored, the flexible beam is a thick plate, and if , the thick plate is defined as a flexible rod.

[0012] Preferably, in step S22, the parallel type has 5 degrees of freedom, respectively , , , and , the vertical type has 5 degrees of freedom, respectively , , , and , the planar type has 3 degrees of freedom, respectively , and , and the orthogonal type has 5 degrees of freedom, respectively , , , and .

[0013] Preferably, in step S23, the wheel-shaped mechanism is radially connected in parallel by three basic flexible units, and the degrees of freedom are , the parallel four-bar mechanism is connected in parallel by two basic flexible units, and the degree of freedom is , the planar mechanism is connected in parallel by the free ends of two basic flexible units, has three degrees of freedom, respectively 、 and , the planar parallel four-bar mechanism is connected in parallel by two basic flexible units at 180°, and the degree of freedom is .

[0014] Preferably, step S3 specifically comprises the following steps: S31: decompose the six-degree-of-freedom space into a union of multiple low-dimensional, mutually independent degree-of-freedom subspaces, and the decomposition result is specifically set as: ; wherein represents an elastic support chain; S32: select a flexible module matching the first subspace from the flexible module library, and the selection result is a plate spring parallel planar mechanism, and the first subspace is specifically set as: = ; S33: select a flexible module matching the second subspace from the flexible module library, and the selection result is a thick plate parallel four-bar mechanism, and the second subspace is specifically set as: = ; S34: connect the plate spring parallel planar mechanism and the thick plate parallel four-bar mechanism in series to obtain an elastic support chain.

[0015] Preferably, step S5 specifically comprises the following steps: S51: set the range of the six-dimensional force sensor, and the range of the six-dimensional force sensor is specifically set as: ; S52: establish a three-dimensional model of the n-chain symmetric elastic body through a finite element simulation software, and apply a capacitive physical field at the corresponding position of the differential capacitor; S53: set the minimization of the condition number of the mapping matrix as an objective function, set the geometric parameters of the basic flexible units in the elastic support chain as design variables, the geometric parameters include thickness, width, length and initial polar distance, and perform iterative calculation on the design variables through a particle swarm algorithm, a genetic algorithm or a gradient descent method until the objective function converges; S54: perform result verification to obtain the mapping matrix condition number The optimal geometric parameters are close to 1, and a six-dimensional force sensor is constructed based on the optimal geometric parameters.

[0016] Therefore, the present invention employs the above-mentioned six-dimensional force sensor configuration design method based on degree-of-freedom analysis, which has the following beneficial effects: (1) This scheme addresses the problem that traditional six-dimensional force sensor configuration design relies on experience and trial and error. It proposes a systematic design method with degree of freedom analysis as the core. Based on degree of freedom theory and spiral theory, this method directly links performance objectives with structural requirements, providing a clear theoretical basis for configuration design and getting rid of the dependence on experience and trial and error. (2) This solution breaks down complex design problems into simple module selection and combination problems by establishing a flexible functional module library, which greatly simplifies the design process and improves design efficiency; (3) This scheme can systematically create a variety of novel and high-performance elastic body configurations through different degrees of freedom decomposition methods and module combinations, providing a broad space for innovative sensor design.

[0017] The method of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0018] Figure 1 This is a flowchart of a six-dimensional force sensor configuration design method based on degree-of-freedom analysis according to the present invention; Figure 2 This is a schematic diagram of the basic flexible unit in an embodiment of the present invention, wherein (a) is a leaf spring, (b) is a strip, and (c) is a thick plate; Figure 3 This is a schematic diagram of the structure of a series flexible module according to an embodiment of the present invention, wherein (a) is parallel type, (b) is vertical type, (c) is planar type, and (d) is orthogonal type; Figure 4 This is a schematic diagram of the structure of a parallel flexible module with a leaf spring as an example in an embodiment of the present invention, wherein (a) is a wheel-shaped mechanism, (b) is a parallel four-bar mechanism, (c) is a planar mechanism, and (d) is a planar parallel four-bar mechanism. Figure 5 This is a schematic diagram of the structure of the elastic branch in an embodiment of the present invention; Figure 6 This is a schematic diagram of the arrangement of the branched symmetrical elastomer and differential capacitor in Embodiment 3 of the present invention. Detailed Implementation

[0019] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, the methodological or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0021] The terms "comprising" or "including" as used in this invention mean that the element preceding the term encompasses the element listed after the term, and do not exclude the possibility of encompassing other elements. Terms such as "inner," "outer," "upper," and "lower" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention. When the absolute position of the described object changes, the relative positional relationship may also change accordingly. In this invention, unless otherwise explicitly specified and limited, the term "attached" and similar terms should be interpreted broadly. For example, it can refer to a fixed connection, a detachable connection, or an integral part; it can refer to a direct connection or an indirect connection through an intermediate medium; it can refer to the internal communication of two elements or the interaction relationship between two elements. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0022] Example Based on the sensor's sensing principle, to achieve completely decoupled measurement and high-sensitivity isotropic measurement of six-dimensional forces or torques in space, the influence mapping matrix is ​​analyzed. condition number Size factors and mapping matrix The internal parameters of the mapping matrix are found. A full-rank matrix is ​​a prerequisite for achieving isotropic sensitivity. Further analysis, considering the relationship between elastic body deformation and force, reveals that the matrix representing the elastic body's compliance is... When in full rank, an elastic body can completely and independently sense and measure the six force or torque components in space; all elastic bodies must have all six degrees of freedom.

[0023] like Figure 1 As shown, this invention provides a method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis, including the following steps: S1: Determine the design objectives, theoretical basis, and degree-of-freedom requirements for the six-dimensional force sensor configuration; Step S1 specifically includes the following steps: S11: Analyze the sensor input / output signal mapping matrix Mapping matrix Specifically set as follows: ; in, This represents the mapping matrix between the displacement of the moving plate of a capacitor and the change in capacitance. This matrix represents the mapping relationship between the displacement of the central loading stage caused by the elastic body and the displacement of the moving plate of the capacitor. Represents the flexibility matrix of an elastic body, and the mapping matrix. rank satisfy: ; in, The mapping matrix representing the relationship between the displacement of the moving plate of a capacitor and the change in capacitance. rank, The matrix representing the mapping relationship between the displacement of the central loading stage caused by the elastic body and the displacement of the moving plate of the capacitor. rank, Represents the flexibility matrix of an elastic body rank; S12: Obtain the mapping matrix condition number A necessary prerequisite is the elasticity matrix. It is a full-rank matrix, meaning the elastic body structure can independently sense six component forces; the elastic body flexibility matrix. Incomplete rank, mapping matrix It is impossible to achieve the full rank condition, nor is it possible to achieve isotropic sensitivity; the mapping matrix... condition number Specifically set as follows: ; in, Represents the mapping matrix transpose, Representation matrix The largest eigenvalue, Representation matrix The smallest eigenvalue; S13: Analyzing the Compliance Matrix of an Elastic Body Define the linear relationship between deformation and force, specifically set as follows: ; ; in, Represents the motion matrix. Represents the force matrix. Indicates that the elastomer in Movement in the axial direction Indicates that the elastomer in Movement in the axial direction Indicates that the elastomer in Movement in the axial direction Indicates that the elastomer in axial displacement, denotes the axial displacement of the elastic body, axial displacement, denotes the axial displacement of the elastic body, axial displacement, denotes the matrix element of the elastic body flexibility matrix , denotes the axial load of the elastic body, axial load, denotes the axial load of the elastic body, axial load, denotes the axial load of the elastic body, axial load, denotes the axial force of the elastic body, axial force, denotes the axial force of the elastic body, axial force, denotes the axial force of the elastic body, axial force, and the first row is expanded to obtain: ; only considering the axial load of the elastic body axial load obtained: ; .

[0024] When the sensor elastic body configuration satisfies six degrees of freedom, the elastic body flexibility matrix The main diagonal elements are approximately equal, which ensures that the elastic body flexibility matrix is a full rank invertible matrix, so that the pursuit of isotropic sensitivity is realized, so that the elastic body structure satisfies six degrees of freedom is the key prerequisite for realizing the isotropic sensitivity of the sensor, and is the key factor that must be considered when designing the elastic body configuration.

[0025] S2: Perform degree of freedom analysis by screw theory-flexibility matrix method, construct flexible module library, and six-degree-of-freedom elastic structure is composed of multiple six-degree-of-freedom elastic branches in parallel along the center loading platform, wherein each branch is composed of multiple flexible units or flexible modules in series, and each branch does not provide constraint to the platform, that is, the degree of freedom of each elastic branch is 6, therefore, the degree of freedom analysis of the basic flexible unit and the flexible module is a necessary preparation work for constructing the elastic branch; Step S2 specifically includes the following steps: S21: As shown in Figure 2 , a basic flexible unit is constructed in a six-degree-of-freedom space by a flexibility matrix method, and the basic flexible unit includes a leaf spring, a plate strip and a thick plate; In step S21, the six-degree-of-freedom space includes Rotational freedom in the axial direction 、 Rotational freedom in the axial direction 、 Rotational freedom in the axial direction 、 Translational freedom in the axial direction 、 Translational freedom in the axial direction and Translational freedom in the axial direction , the plate spring has 3 degrees of freedom, respectively 、 and , the plate has 4 degrees of freedom, respectively 、 、 and , the thick plate has 5 degrees of freedom, respectively 、 、 、 and .

[0026] Step S21 specifically includes the following steps: Step 1: Define the normalized flexibility matrix of the flexible beam The normalized flexibility matrix is specifically set as: ; ; ; ; ; wherein 、 and all represent dimensionless constants determined according to the geometric shape and material properties, represents the thickness of the beam, represents the motion screw constant, represents the width of the beam, represents the length of the beam, represents the shear modulus, represents the Young's modulus, represents the Poisson's ratio, represents the polar moment of inertia, represents the moment of inertia; Step 2: For a flexible beam with a rectangular cross section, the motion screw constant is defined as: ; When changes from 1 to 0, the normalized flexibility matrix is obtained The main diagonal elements of the normalized flexibility matrix are: ; Step 3: According to and , the basic flexible unit is classified, if , ignore , and , the flexible beam is a leaf spring, if , ignore and , the flexible beam is a strip, if , ignore , the flexible beam is a thick plate, if , the thick plate is defined as a flexible rod.

[0027] S22: As shown in Figure 3 , the basic flexible unit is connected in series to obtain a series flexible module, the series flexible module includes parallel type, vertical type, plane type and orthogonal type, and the degree of freedom of the series flexible module is analyzed by screw theory; In step S22, the parallel type has 5 degrees of freedom, respectively , , , and , the vertical type has 5 degrees of freedom, respectively , , , and , the plane type has 3 degrees of freedom, respectively , and , and the orthogonal type has 5 degrees of freedom, respectively , , , and .

[0028] S23: As shown in Figure 4 , the basic flexible unit is connected in parallel to obtain a parallel flexible module, the parallel flexible module includes a wheel-shaped mechanism, a parallel four-bar mechanism, a plane mechanism and a parallel four-bar mechanism plane, and the degree of freedom of the parallel flexible module is analyzed by screw theory.

[0029] In step S23, the wheel-shaped mechanism is connected in parallel by three basic flexible units in a radial manner, and the degree of freedom is Parallel four-bar mechanism is connected in parallel by two basic flexible units, and the degree of freedom is Parallel plane mechanism is connected in parallel by the free ends of two basic flexible units, and has three degrees of freedom, respectively 、 and Parallel four-bar mechanism plane is connected in parallel by two basic flexible units at 180°, and the degree of freedom is .

[0030] S3: The six-degree-of-freedom spatial target of the elastic support chain is decomposed into multiple low-dimensional subspaces, and corresponding flexible modules are selected from the flexible module library for degree of freedom matching and combination to obtain an elastic support chain with six degrees of freedom; Step S3 specifically includes the following steps: S31: The six-degree-of-freedom space is decomposed into multiple low-dimensional, independent degree-of-freedom subspaces, and the decomposition result is specifically set as: ; Wherein, represents the elastic support chain; S32: Selecting a flexible module matching the first subspace from the flexible module library, the selection result is a plate spring parallel plane mechanism, and the first subspace is specifically set as: = ; S33: Selecting a flexible module matching the second subspace from the flexible module library, the selection result is a thick plate parallel four-bar mechanism, and the second subspace is specifically set as: = ; S34: As shown in Figure 5 , the plate spring parallel plane mechanism and the thick plate parallel four-bar mechanism are connected in series to obtain an elastic support chain. In this embodiment, the elastic support chain is a compact structure, high stiffness, and easy to process, which is selected from multiple feasible configurations (such as L-shaped, T-shaped, three-plate spring series, etc.) based on factors such as processing feasibility, structural complexity and stiffness.

[0031] S4: The n elastic support chains are arranged in rotational symmetry around the center loading table to form an n-chain symmetric elastic body, and m groups of differential capacitors are arranged at the symmetric positions of the n elastic support chains according to the symmetry principle, wherein n is not less than 3, and m is not less than 6, to obtain a six-dimensional force sensor.

[0032] As shown in Figure 6As shown, in this embodiment, three elastic branches are arranged in a 120° rotational symmetry around the central loading platform to form a three-branch symmetrical elastic body. This symmetrical layout can effectively ensure the isotropy of the overall structure. According to the principle of symmetry, three sets of differential capacitors are set at the symmetrical positions of the three elastic branches to ensure that their arrangement also satisfies rotational symmetry, so as to obtain a linearly independent sensitivity matrix and obtain a six-dimensional force sensor. S5: Parameter optimization and verification of the six-dimensional force sensor.

[0033] Step S5 specifically includes the following steps: S51: Set the range of the six-dimensional force sensor. The specific range of the six-dimensional force sensor is set as follows: ; S52: Establish a three-dimensional model of an n-branched symmetric elastic body using finite element simulation software, and apply a capacitance physical field to the corresponding position of the differential capacitor. S53: Mapping matrix condition number Minimize the objective function and set the geometric parameters of the basic flexible unit in the elastic branch as design variables. The geometric parameters include thickness, width, length and initial polar moment. Iteratively calculate the design variables using particle swarm optimization, genetic algorithm or gradient descent method until the objective function converges. S54: Perform result verification to obtain the mapping matrix. condition number By finding the optimal geometric parameters close to 1, a six-dimensional force sensor is constructed based on these parameters, thereby obtaining a sensor design scheme that meets the requirements of high sensitivity and isotropy.

[0034] Therefore, this invention adopts the above-mentioned six-dimensional force sensor configuration design method based on degree of freedom analysis, realizing a systematic design from performance objectives to topology, breaking away from the traditional design mode that relies on experience and trial and error, significantly improving the isotropic sensitivity of the sensor, reducing interdimensional coupling, and providing theoretical basis and engineering methods for the innovative design of flexible parallel six-dimensional force sensors.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the method of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the method of the present invention, and these modifications or equivalent substitutions should not cause the modified method to deviate from the spirit and scope of the method of the present invention.

Claims

1. A method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis, characterized in that, Includes the following steps: S1: Determine the design objectives, theoretical basis, and degree-of-freedom requirements for the six-dimensional force sensor configuration; S2: Perform degree of freedom analysis using the spiral theory-compliance matrix method and construct a flexible module library; S3: Perform a comprehensive design of degrees of freedom, decompose the six-degree-of-freedom spatial target of the elastic branch into multiple low-dimensional subspaces, select the corresponding flexible modules from the flexible module library for degree-of-freedom matching and combination, and obtain an elastic branch with six degrees of freedom. S4: Arrange n elastic branches around the central loading platform in a... A rotationally symmetric arrangement is formed to create an n-branch symmetric elastic body. According to the principle of symmetry, m sets of differential capacitors are set at the symmetrical positions of the n elastic branches, where n is not less than 3 and m is not less than 6, resulting in a six-dimensional force sensor. S5: Parameter optimization and verification of the six-dimensional force sensor.

2. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 1, characterized in that, Step S1 specifically includes the following steps: S11: Analyze the sensor input / output signal mapping matrix Mapping matrix Specifically set as follows: ； in, This represents the mapping matrix between the displacement of the moving plate of a capacitor and the change in capacitance. This matrix represents the mapping relationship between the displacement of the central loading stage caused by the elastic body and the displacement of the moving plate of the capacitor. Represents the flexibility matrix of an elastic body, and the mapping matrix. rank satisfy: ； in, The mapping matrix representing the relationship between the displacement of the moving plate of a capacitor and the change in capacitance. rank, The matrix representing the mapping relationship between the displacement of the central loading stage caused by the elastic body and the displacement of the moving plate of the capacitor. rank, Represents the flexibility matrix of an elastic body rank; S12: Obtain the mapping matrix condition number A necessary prerequisite is the elasticity matrix. It is a full-rank matrix, a mapping matrix. condition number Specifically set as follows: ； in, Represents the mapping matrix transpose, Representation matrix The largest eigenvalue, Representation matrix The smallest eigenvalue; S13: Analyzing the Compliance Matrix of an Elastic Body Define the linear relationship between deformation and force, specifically set as follows: ； ； in, Represents the motion matrix. Represents the force matrix. Indicates that the elastomer in Movement in the axial direction Indicates that the elastomer in Movement in the axial direction Indicates that the elastomer in Movement in the axial direction Indicates that the elastomer in Displacement in the axial direction, Indicates that the elastomer in Displacement in the axial direction, Indicates that the elastomer in Displacement in the axial direction, Represents the flexibility matrix of an elastic body matrix elements, Indicates that the elastomer in Axial load, Indicates that the elastomer in Axial load, Indicates that the elastomer in Axial load, Indicates that the elastomer in Force in the axial direction, Indicates that the elastomer in Force in the axial direction, Indicates that the elastomer in Force along the axial direction, expanded from the first line, yields: ； Considering only the elastomer Axial load get: ； 。 3. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 2, characterized in that, Step S2 specifically includes the following steps: S21: Using the flexibility matrix method, basic flexible elements are constructed in a six-degree-of-freedom space. The basic flexible elements include leaf springs, strips, and thick plates. S22: Connect the basic flexible units in series to obtain a series flexible module. The series flexible module includes parallel, perpendicular, planar and orthogonal types. The degree of freedom of the series flexible module is analyzed by spiral theory. S23: Connect the basic flexible units in parallel to obtain a parallel flexible module. The parallel flexible module includes a wheel-shaped mechanism, a parallel four-bar mechanism, a planar mechanism, and a planar parallel four-bar mechanism. The degree of freedom of the parallel flexible module is analyzed using the spiral theory.

4. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 3, characterized in that, In step S21, the six-degree-of-freedom space includes Rotational degrees of freedom in the axial direction , Rotational degrees of freedom in the axial direction , Rotational degrees of freedom in the axial direction , Translational degrees of freedom in the axial direction , Translational degrees of freedom in the axial direction and Translational degrees of freedom in the axial direction The leaf spring has 3 degrees of freedom, namely , and The slats have 4 degrees of freedom, namely: , , and The thick plate has 5 degrees of freedom, namely: , , , and .

5. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 3, characterized in that, Step S21 specifically includes the following steps: Step 1: Define the normalized compliance matrix of the flexible beam. Normalized compliance matrix Specifically set as follows: ； ； ； ； ； in, , and All of these represent dimensionless constants, determined based on the geometry and material properties. Indicates the thickness of the beam. Represents the helical constant of motion. Indicates the width of the beam. Indicates the length of the beam. Indicates shear modulus, Indicates Young's modulus. Represents Poisson's ratio. Represents the polar moment of inertia. Represents the moment of inertia; Step 2: For a flexible beam with a rectangular cross-section, the motion helical constant is... Defined as: ； when When changing from 1 to 0, The normalized compliance matrix is ​​obtained. The main diagonal element is: ； Step 3: According to and The flexible beams are classified to obtain basic flexible elements. ,neglect , and The flexible beam is a leaf spring; if ,neglect and The flexible beam is made of slats, if ,neglect The flexible beam is a thick plate; if Thick plates are defined as flexible rods.

6. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 4, characterized in that, In step S22, the parallel type has 5 degrees of freedom, namely: , , , and The vertical type has 5 degrees of freedom, namely: , , , and The planar type has 3 degrees of freedom, namely , and The orthogonal form has 5 degrees of freedom, namely: , , , and .

7. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 4, characterized in that, In step S23, the wheel-shaped mechanism consists of three basic flexible units arranged radially in parallel, with a degree of freedom of [missing information]. The parallel four-bar linkage consists of two basic flexible units connected in parallel, with 100 degrees of freedom. The planar mechanism consists of two basic flexible units connected in parallel at their free ends, possessing three degrees of freedom: , and The planar parallel four-bar linkage consists of two basic flexible units connected in parallel at 180°, with a degree of freedom of [missing information]. .

8. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 4, characterized in that, Step S3 specifically includes the following steps: S31: Decompose the six-degree-of-freedom space into the union of multiple low-dimensional, mutually independent subspaces of freedom. The specific decomposition result is set as follows: ； in, Indicates a flexible branch; S32: Selection of the first subspace in the flexible module library The matched flexible module was selected as a parallel planar mechanism with leaf springs in the first subspace. Specifically set as follows: = ； S33: Selection of Flexible Module Library and Second Subspace The matched flexible module was selected as a thick plate parallel four-bar linkage mechanism, second subspace. Specifically set as follows: = ； S34: Connect the parallel planar mechanism of leaf springs with the parallel parallel four-bar mechanism of thick plates to obtain an elastic branch.

9. The method for designing a six-dimensional force sensor configuration based on degree-of-freedom analysis according to claim 4, characterized in that, Step S5 specifically includes the following steps: S51: Set the range of the six-dimensional force sensor. The specific range of the six-dimensional force sensor is set as follows: ； S52: Establish a three-dimensional model of an n-branched symmetric elastic body using finite element simulation software, and apply a capacitance physical field to the corresponding position of the differential capacitor. S53: Mapping matrix condition number Minimize the objective function and set the geometric parameters of the basic flexible unit in the elastic branch as design variables. The geometric parameters include thickness, width, length and initial polar moment. Iteratively calculate the design variables using particle swarm optimization, genetic algorithm or gradient descent method until the objective function converges. S54: Perform result verification to obtain the mapping matrix. condition number The optimal geometric parameters are close to 1, and a six-dimensional force sensor is constructed based on the optimal geometric parameters.

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