A design method of a centralized compliance hinge with length self-adaptive function

Abstract

The application discloses a design method of a concentrated flexibility type compliant hinge with length self-adapting function, and comprises the following steps: firstly, constructing the structure of the concentrated flexibility type compliant hinge; then, establishing a principle model of the concentrated flexibility type compliant hinge; next, calculating the arc length of a spring leaf and the total length of the spring leaf; then, proving that the ends of the compliant hinge are flush after rotation, that is, proving the length self-adapting function of the compliant hinge; finally, performing strength analysis on the concentrated flexibility type compliant hinge. The application can improve the problems of motion incoordination and low fatigue strength between ordinary flat plate type laminated compliant hinges when rotating and deforming.

Description

Technical Field

[0001] This invention belongs to the field of flexible mechanism technology, specifically relating to a concentrated flexibility type compliant hinge design method. Background Technology

[0002] Due to the broad application prospects of deformable wings, scholars both domestically and internationally have conducted in-depth research on compliant mechanisms. The internal mechanisms driving the deformation of deformable wings are generally classified into rigid mechanisms, flexible mechanisms, and rigid-flexible coupling mechanisms. The design concept of rigid-flexible coupling is to make the mechanism driving the deformable wing consist of rigid rods and locally concentrated compliant hinges. Compliant hinges can achieve large-angle rotation and possess a certain degree of flexibility in their functional direction, while possessing a certain degree of stiffness in non-functional directions. In other words, the comprehensive performance of concentrated compliant hinges can meet the deformation requirements of deformable wings while also withstanding large aerodynamic loads in non-functional directions.

[0003] In 1965, Paros and Paros first proposed a formula for calculating the stiffness of a compliant circular hinge. However, the formula they gave was applicable to situations where the cutting radius was much larger than the hinge thickness. When the hinge thickness was close to the cutting radius, it would produce a large error.

[0004] In 2002, HOWELL et al. proposed a cross-spring type flexible hinge, which has the advantage of a large turning angle, but also obvious disadvantages, such as low rotation accuracy and the need for assembly.

[0005] HENEIN et al. proposed a butterfly hinge that can simultaneously achieve large stroke (±15°) and high precision (axis drift less than 1μm).

[0006] Since compliant hinges used on deformable wings need to withstand large aerodynamic loads, they must have sufficient tensile strength and fatigue resistance. However, ordinary compliant hinges cannot meet the deformation requirements of deformable wings due to their low fatigue resistance. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention provides a design method for a concentrated flexibility compliant hinge with length adaptive function. First, the structure of the concentrated flexibility compliant hinge is constructed. Then, a principle model of the concentrated flexibility compliant hinge is established. Next, the arc length of the spring and the total length of the spring are calculated. Then, it is demonstrated that after rotation, the ends of the compliant hinge are aligned, thus proving the length adaptive function of the compliant hinge. Finally, a strength analysis of the concentrated flexibility compliant hinge is performed. This invention can improve the problems of motion incoordination and low fatigue strength that occur between ordinary flat laminated compliant hinges during rotational deformation.

[0008] The technical solution adopted by this invention to solve its technical problem includes the following steps:

[0009] Step 1: Construct the structure of a concentrated flexibility hinge, including a stacked spring 1, two identical fixed shaft groups, a spring fixing plate 5, a first hinge structure 6, and a second hinge structure 7.

[0010] One end of the stacked spring sheet 1 is fixed by a fixed shaft group and snapped into the first hinge structure 6, and the other end of the stacked spring sheet 1 is fixed by another fixed shaft group and snapped into the second hinge structure 7; each layer of spring sheet in the middle of the stacked spring sheet 1 is fixed by the spring sheet fixing plate 5.

[0011] Each fixed shaft group includes a first fixed shaft 2 and two second fixed shafts 3; the stacked spring 1 forms a closed ring at each of its two ends, the first fixed shaft 2 is inserted into the ring, and the two ends of the first fixed shaft 2 are fixed on the first hinge structure 6 or the second hinge structure 7; the two second fixed shafts 3 act on the stacked spring 1 on the left and right sides of the stacked spring 1 simultaneously with the first fixed shaft 2 to clamp the stacked spring 1;

[0012] When the concentrated flexibility hinge is used on the wing, the first hinge structure 6 is used to connect the wing main drive rod; the second hinge structure 7 includes a hinge upper cover 12 and a hinge lower cover 13, the hinge upper cover 12 is connected to the stringer of the wing structure, and the hinge lower cover 13 is used to fix the first fixed shaft 2.

[0013] When the main drive rod of the wing rotates, the first hinge structure 6 drives the stacked spring 1 to rotate. Due to its length self-adaptability, the elongation of each layer of spring after rotation is the same. The force and torque generated between the springs of the stacked spring 1 act on the second hinge structure 7, thereby causing the drive rod of the wing to rotate.

[0014] Step 2: Establish the principle model of a concentrated flexibility type compliant hinge;

[0015] In the structural geometry model of a compliant hinge with concentrated flexibility, let R be the sum of the radius R of the first fixed axis 2 and the thickness of the laminated spring 1. j The sum of the radius r of the second fixed shaft 3 and the thickness of the laminated spring is r. j C represents the reserved length of the spring, and C1 represents the length of the spring in the straight section after the hinge rotates by an angle θ.

[0016] Assuming the compliant hinge consists of i layers of spring steel sheets with a thickness of δ mm, the parameters in the geometric model satisfy the following relationship:

[0017] α+β=π / 2 (1)

[0018] r j =r+iδ (2)

[0019] R j =R+iδ (3)

[0020] l m =R+r+iδ (4)

[0021] l n =2(r+iδ) (5)

[0022] l r =r j α=(r+iδ)α (6)

[0023] l R =R j α=(R+iδ)(2π-2β) (7)

[0024] β=arcsin(r j / l m (8)

[0025] l i =l R +2l r +2C (9)

[0026] In the formula, α is the angle between the line connecting the center of the first fixed axis 2 and the center of the second fixed axis 3, and the line connecting the centers of the two second fixed axes 3; β is half of the angle between the center of the first fixed axis 2 and the lines connecting the centers of the two second fixed axes 3; m l is the distance between the center of the first fixed axis 2 and the center of the second fixed axis 3. n The distance between the centers of the two second fixed axes 3; l r and l R These represent the lengths of the arc segments corresponding to the central angles α and 2π - 2β, respectively; i This represents the length of the i-th layer of reeds;

[0027] Step 3: According to formulas (1) to (9), the arc length of the i-th reed corresponding to the central angles α and β and the total length of the i-th reed can be calculated;

[0028] l r =(π / 2-β)(r+iδ)=(π / 2-arcsin(r j / l m ))(r+iδ) (10)

[0029] l R =2(π-β)(r+iδ)=2(π-arcsin(r j / l m ))(r+iδ) (11)

[0030] l i =π(2R+r+3iδ)-πarcsin(r) j / l m(R+r+2iδ) / 2+2C (12)

[0031] Step 4: Prove that after rotation, the ends of the compliant hinge proposed in this invention are aligned, thus proving the length adaptive function of the compliant hinge.

[0032] Due to the length l of the arc segment of the spring plate with central angles α and β... m l n If the length remains unchanged, then the elongation of the i-th spring sheet after rotation is:

[0033] Δl i =π[2r+(i-1)δ+(2n-i)δ]θ=π[2r+(2n-1)δ]θ (13)

[0034] In the formula: n represents the number of layers of the compliant hinge.

[0035] As can be seen from equation (13), when the structural parameters of the compliant hinge are determined, i.e. r and δ are constants, the elongation of each spring of the compliant hinge is only related to the number of layers and the rotation angle of the compliant hinge, and is not related to the variable i. That is, the elongation of each spring after rotation is equal. Since the ends of each spring are flush before the compliant hinge rotates, when the elongation is the same, the ends of the compliant hinge are flush after rotation, which proves that the stacked spring steel sheets of the compliant hinge have the function of length self-adaptation.

[0036] Step 5: Strength analysis of concentrated flexibility hinges;

[0037] The maximum tensile force that a stacked compliant hinge can withstand is:

[0038] F=[σ]A (14)

[0039] In the formula: A represents the cross-sectional area of ​​the spring steel, A=Bnδ, B represents the width of the spring steel; [σ] represents the tensile strength of the spring steel;

[0040] Taking a safety factor into account, the maximum tensile force that the laminated springs of a compliant hinge can withstand is:

[0041] F s =[σ]A / S <F (15)

[0042] In the formula: S>1 represents the safety factor.

[0043] Preferably, the 65Mn spring steel strip with a thickness of 0.1mm is used as the laminate material for the compliant hinge, with an elastic modulus E = 196.5Gpa, a tensile strength σb = 825Mpa~925Mpa, a spring steel tensile strength σb = 825Mpa, and a safety factor S = 2.

[0044] The beneficial effects of this invention are as follows:

[0045] This invention proposes a concentrated flexibility type compliant hinge with good tensile strength, fatigue resistance, and length self-adaptive function. Its own length self-adaptive function can improve the problems of motion incoordination and low fatigue strength that occur between ordinary flat laminated compliant hinges during rotational deformation. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the principle of the concentrated flexibility type compliant hinge of the present invention.

[0047] Figure 2 This invention provides a stiffness analysis model for a compliant hinge with concentrated flexibility under small deformation.

[0048] Figure 3 This is a schematic diagram of the overall assembly of the compliant hinge of the present invention.

[0049] Figure 4 This is a schematic diagram of the first hinge structure of the present invention.

[0050] Figure 5 This is an assembly diagram of the second hinge structure of the present invention.

[0051] Figure 6 This is a schematic diagram of the hinge cover of the second hinge structure of the present invention.

[0052] Figure 7 This is a schematic diagram of the hinge lower cover of the second hinge structure of the present invention.

[0053] Figure 8 This is a distributed compliance mechanism used in embodiments of the present invention for conversion into a centralized compliance mechanism.

[0054] Figure 9 This is a concentrated flexibility-type compliant mechanism in the embodiment of the present invention, namely a rigid-flexible coupling prototype;

[0055] In the diagram, 1. Stacked spring; 2. First fixed shaft; 3. Second fixed shaft; 4. End clamp; 5. Spring fixing plate; 6. First hinge structure 1; 7. Second hinge structure; 8. Support plate nut; 9. Bolt small hole; 10. Bolt large hole; 11. Fixed half shaft; 12. Hinge upper cover; 13. Hinge lower cover. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0057] To achieve both good tensile strength and fatigue resistance in compliant hinges, this invention proposes a concentrated compliance hinge with length self-adaptive function, distinct from ordinary compliant hinges. This invention selects 65Mn laminated spring steel strips as the laminate material for the compliant hinge. The compliant hinge proposed in this invention can utilize its inherent length self-adaptive function to improve the problems of motion incoordination and low fatigue strength that occur between ordinary flat laminated compliant hinges during rotational deformation.

[0058] See Figures 1-7 The first fixed shaft 2 and the second fixed shaft 3 (in this embodiment, for ease of processing and assembly, the fixed shaft 3 is replaced with a fixed half shaft 11, but their radius and function are the same) are used to fix the stacked spring 1 and prevent shaft drift; the spring fixing plate 5 replaces the end clamp 4 in the schematic diagram and fixes each layer of spring stacked with bolt holes 9; the first hinge structure 6 serves as the upper cover connected to the rod and is mainly used to connect the main drive rod; the second hinge structure 7 includes a hinge upper cover 12 and a hinge lower cover 13, which are connected to the stacked spring 1 through the first fixed shaft 2; the hinge upper cover 12 is connected to the stringer of the wing structure with two bolt holes 9 and one bolt hole 10; the hinge lower cover 13 uses the first fixed shaft 2 to fix the stacked spring 1.

[0059] Working principle: When the main drive rod of the mechanism rotates, the first hinge mechanism 6 drives the stacked spring 1 to rotate. Due to its length self-adaptability, the elongation of each layer of spring after rotation is the same, there is almost no stress between the springs, and it has motion coordination. The generated force and torque can be fully applied to the second hinge mechanism 7, thereby causing the driven rod to rotate, and applying it to... Figure 8 and Figure 9 The mechanism shown can be converted from a distributed compliance mechanism to a concentrated compliance mechanism, which enables the wing drive mechanism to drive the trailing edge skin of the wing to achieve more precise deformation under conditions of greater load-bearing capacity and stronger fatigue resistance.

[0060] The design method for a compliant hinge with concentrated flexibility includes the following steps:

[0061] Step 1: Establish a principle model of the compliant hinge, such as... Figure 1 As shown; in the designed geometric model, let R be the sum of the thickness of the laminated spring and the thickness of the lamination. j The sum of r and the thickness of the laminated spring is r j C represents the reserved length of the spring, and C1 represents the length of the spring in the straight section after the hinge rotates by an angle θ. Among them, C is a constant determined based on the specific rotation angle, flexibility, and whether it interferes with other structures of the wing. It should not be designed to be too long, otherwise it will cause excessive drift of the hinge center and result in motion uncertainty.

[0062] Assumption Figure 1 The compliant hinge shown is composed of i layers of spring steel sheets with a thickness of δ mm (i = 1, 2, 3, ...). Then, in... Figure 1 The parameters in the geometric model shown should satisfy the following relationship:

[0063] α+β=π / 2 (1)

[0064] r j =r+iδ (2)

[0065] R j =R+iδ (3)

[0066] l m =R+r+iδ (4)

[0067] l n =2(r+iδ) (5)

[0068] l r =r j α=(r+iδ)α (6)

[0069] l R =R j α=(R+iδ)(2π-2β) (7)

[0070] β=arcsin(r j / l m (8)

[0071] l i =l R +2l r +2C (9)

[0072] In the formula: R and r represent the radii of the large and small circular axes, respectively; α and β represent the central angles corresponding to the arc segments with radii r and R, respectively; l m l n These represent the distances between the centers of the large and small circular axes and the two small circular axes, respectively; r and l R These represent the lengths of the arc segments corresponding to the central angles α and 2π - 2β, respectively; i This represents the length of the i-th layer of reeds;

[0073] Step 2: According to formulas (1) to (9), the arc length of the i-th spring sheet corresponding to the central angles α and β and the total length of the i-th spring sheet can be calculated;

[0074] l r =(π / 2-β)(r+iδ)=(π / 2-arcsin(r j / l m ))(r+iδ) (10)

[0075] l R =2(π-β)(r+iδ)=2(π-arcsin(r j / l m ))(r+iδ) (11)

[0076] l i =π(2R+r+3iδ)-πarcsin(r) j / l m (R+r+2iδ) / 2+2C (12)

[0077] Step 3: Using known parameters, prove that after rotation, the ends of the compliant hinge proposed in this invention are aligned, thus proving the length adaptive function of the compliant hinge.

[0078] Due to the length l of the arc segment of the spring plate with central angles α and β... m l n If the length remains unchanged, then the elongation of the i-th spring sheet after rotation is:

[0079] Δl i =π[2r+(i-1)δ+(2n-i)δ]θ=π[2r+(2n-1)δ]θ (13)

[0080] In the formula: n represents the number of layers of the compliant hinge.

[0081] As shown in equation (13), when the structural parameters of the compliant hinge are determined, i.e., r and δ are constants, the elongation of each spring in the laminated spring compliant hinge is only related to the number of layers and the rotation angle of the compliant hinge, and is independent of the variable i. That is, the elongation of each spring after rotation is equal. Since the ends of each spring are flush before rotation, when the elongation is the same, the ends of the compliant hinge are flush after rotation. This proves that the laminated spring steel sheets of the compliant hinge proposed in this paper have a length adaptive function and will not exhibit the "bulging" phenomenon of ordinary laminated compliant hinges.

[0082] Step 4: Strength analysis of concentrated flexibility hinges;

[0083] The compliant hinge with concentrated flexibility proposed in this invention uses 0.1mm thick 65Mn spring steel strips as the lamination material, with an elastic modulus E = 196.5 GPa and a tensile strength σ. b =825 MPa~925 MPa. Considering safety issues, this invention selects the tensile strength σ of the spring steel. b =825 MPa, and a safety factor of 2 is set. Therefore, the maximum tensile force that the stacked compliant hinge designed in this invention can withstand is:

[0084] F=[σ]A (14)

[0085] In the formula: A represents the cross-sectional area of ​​the spring steel, A=Bnδ, B represents the width of the spring steel, n represents the number of layers of the compliant hinge, δ represents the thickness of the laminated spring steel; [σ] represents the tensile strength of the spring steel.

[0086] according to Figure 1 As shown, considering the safety factor, the maximum tensile force that the laminated springs of a compliant hinge can withstand is:

[0087] F s =[σ]A / S=825×B×2nδ / 2=825Bnδ <F (15)

[0088] In the formula: S represents the safety factor, and the value of S in this invention is S = 2; F represents the actual force on the compliant hinge.

[0089] When selecting the compliant hinge for the deformable wing, it is only necessary to ensure that the actual force at that point is less than the maximum tension calculated by equation (15). Although multiple solutions can be obtained from equation (15), not every solution can satisfy the bending deformation of the trailing edge of the variable camber wing. This is because when the trailing edge of the variable camber wing undergoes bending deformation, the width B of the laminated spring will affect the stability of its deformation. The smaller the width B of the laminated spring, the worse the deformation stability of the trailing edge of the variable camber wing; the larger the width of the laminated spring, the fewer the number of layers of the spring, and the lower the fatigue strength of the compliant hinge. Therefore, the width of the spring cannot be too small or too small. This invention suggests that the width B of the laminated spring be 20 to 60 mm.

[0090] A further technical solution of the present invention is: to derive the stiffness under small deformation based on the proposed centralized flexibility compliant hinge structure with length adaptive function.

[0091] Step 5: Derive the stiffness theoretical model of this invention under small deformation; refer to the stiffness analysis model of the compliant hinge under small deformation. Figure 2 The specific steps are as follows:

[0092] Sub-step one: The assumptions of this invention under small deformations are given;

[0093] Small deformation refers to a hinge rotation angle of less than or equal to 5 degrees. Before deriving the theoretical stiffness for small deformation, considering the complex shape of compliant hinges and the difficulty in directly calculating their stiffness, four assumptions are proposed:

[0094] 1) The compliant hinge deformation designed in the article is mainly concentrated in the circular arc and straight beam parts, so other deformations outside these two parts are ignored;

[0095] 2) Ignore the fretting friction between the layers of the stacked compliant hinge and derive the theoretical stiffness as a whole;

[0096] 3) Based on the small deformation cantilever beam theory, the deformation of the compliant hinge is mainly generated by the bending moment about the z-axis. The shear and torsional effects during the rotation process are ignored, that is, only the deformation in the two-dimensional plane is considered, while the axial load is also considered.

[0097] 4) The hinge boundary condition can be considered as one end being fixed and the other end bearing bending moment and tension.

[0098] Sub-step two: Derivation of the rotational stiffness of the hinge under small deformation conditions;

[0099] Assuming the right end of the compliant hinge is at bending moment M z Small angle generated under action Deformation, tensile force F x If a small displacement Δs is generated along the positive x-direction under the action, the deformation relationship can be expressed in the form of a compliance matrix:

[0100]

[0101] In the formula: C m and C f These represent the bending compliance and tensile or compressive compliance of a compliant hinge with concentrated compliance, respectively.

[0102] Based on Castiglione's second theorem, the left-hand side of equation (16) can be expressed as:

[0103]

[0104] In the formula: U represents strain energy.

[0105] By combining equations (16) and (17), we can see that

[0106]

[0107] According to mechanics of materials, the deformation energy of a compliant hinge is:

[0108]

[0109] Combining equations (18) and (19), we obtain:

[0110]

[0111] In the formula: E represents the elastic modulus of the laminated spring; I represents the moment of inertia; A represents the cross-sectional area.

[0112] In equation (20), when x∈[0,S] x When h(x) is part of an arc with radius r = 3, let the coordinates of the center of the circle be (x...A ,y A ),but:

[0113]

[0114] y A =r+t

[0115] In equation (21), t = iδ.

[0116] In △ACF and △DCO, the lengths of line segments CF and CO can be calculated respectively:

[0117]

[0118]

[0119] Combining (8), (21), and (22), we get:

[0120]

[0121] Therefore, the standard equation of circle A is:

[0122] (xx A ) 2 +(yy A ) 2 =r 2 (twenty four)

[0123] By combining equations (24) and (23), we can conclude that:

[0124]

[0125] h(x) = t, x ∈ [S x ,S x +S y ]

[0126] Combining (20), (24), and (25), we can obtain the two integral results for rotational compliance as follows:

[0127]

[0128] The second integral in equation (26) is easy to obtain a general expression for, but the first integral is difficult to obtain a specific general expression for due to the large number of provisional unknowns. Therefore, it is necessary to use MATLAB to solve the problem based on the specific parameters of the compliant hinge structure selected during the calculation.

[0129] Since stiffness and flexibility are reciprocals of each other, the rotational stiffness of the hinge is ultimately derived as follows:

[0130]

[0131] Sub-step 3: Derivation of the tensile stiffness of a concentrated flexibility hinge under small deformation conditions;

[0132] Combining equations (20) and (25), we can obtain the two integral results for the tensile compliance:

[0133]

[0134] Therefore, the formula for calculating the tensile (or compressive) stiffness of a compliant hinge can be obtained:

[0135]

[0136] Step six: The distributed compliance mechanism is converted into a centralized compliance mechanism, that is... Figure 8 The area circled in red is designed as a compliant hinge with concentrated flexibility, such as... Figure 8 As shown; select the parameters of the compliant hinge according to equation (15), and then apply the concentrated compliance hinge to the trailing edge of the wing, such as Figure 9 As shown; among them, the overall assembly diagram of the concentrated flexibility type compliant hinge is as follows. Figure 3 As shown; a detailed structural diagram of a concentrated flexibility hinge is shown below. Figures 4-7 As shown.

Claims

1. A design method of a lumped flexibility compliant hinge with length adaptation function, characterized in that, It comprises the following steps: Step 1: constructing the structure of the concentrated flexibility type compliant hinge, including laminated spring, two identical fixed shaft groups, spring fixed plate, first hinge structure and second hinge structure; One end of the laminated spring is fixed by one fixed shaft group and clamped into the first hinge structure, and the other end of the laminated spring is fixed by the other fixed shaft group and clamped into the second hinge structure; the middle layers of the laminated spring are fixed by the spring fixed plate; Each fixed shaft group comprises a first fixed shaft and two second fixed shafts; the laminated spring forms a closed ring at each end, the first fixed shaft is inserted into the ring, and the two ends of the first fixed shaft are fixed on the first hinge structure or the second hinge structure; the two second fixed shafts clamp the laminated spring on the left and right sides of the laminated spring while the first fixed shaft acts on the laminated spring; When the concentrated flexibility type compliant hinge is used on the wing, the first hinge structure is used to connect the wing main driving rod; the second hinge structure comprises hinge upper cover and hinge lower cover, the hinge upper cover is connected with the longeron of the wing structure, and the hinge lower cover is used to fix the first fixed shaft; When the wing main driving rod rotates, the laminated spring rotates with the first hinge structure, and because of the length adaptability, the elongation of each layer of spring after rotation is the same, the force and torque generated between the laminated spring springs act on the second hinge structure, so that the wing driving rod rotates; Step 2: establishing the principle model of the concentrated flexibility type compliant hinge; In the structural geometry model of the centralized flexibility type compliant hinge, the sum of the radius R of the first fixed shaft and the thickness of the laminated spring sheet is R j , the sum of the radius r of the second fixed shaft and the thickness of the laminated spring sheet is r j , C represents the reserved length of the spring sheet, C 1 represents the hinge rotation angle θ the length of the spring sheet after the straight line portion; Assuming the compliant hinge is made of i The layer thickness is δ mm spring steel sheet, the parameters in the geometric model satisfy the following relationships: In the formula, α is the angle between the line connecting the center of the first fixed axis circle and the center of the second fixed axis circle and the line connecting the two centers of the second fixed axis circles; β is half of the angle between the line connecting the center of the first fixed axis circle and the center of the second fixed axis circle and the line connecting the two centers of the second fixed axis circles; l m is the distance between the center of the first fixed axis circle and the center of the second fixed axis circle, l n is the distance between the two centers of the second fixed axis circles; l r and l R respectively represent the central angles α and 2 π- 2 β corresponding arc segment lengths; l i represent the corresponding lengths of the first i layer of spring pieces; Step 3: Calculate the central angle of the circle according to formulas (1) to (9) α 、 β The corresponding first i The arc length of the first i The total length of the first Step 4: after the compliant hinge rotates, the ends of the compliant hinge are flush, i.e. the length adaptability function of the compliant hinge is proved; Because of the central angle α , β The length of the arc segment spring sheet l m , l n If it remains unchanged, then the first i The elongation of the spring sheet after rotation is: In the formulae: n n represents the number of layers of the compliant hinge; From equation (13), when the structure parameters of the compliant hinge have been determined, i.e. r and δ are constants, then the elongation of each spring leaf of the compliant hinge is only related to the number of layers and the rotation angle of the compliant hinge, and is not related to the variable i , i.e. the elongation of each spring leaf after rotation is equal; since the ends of each spring leaf are flush before rotation of the compliant hinge, when the elongations are equal, the ends of the compliant hinge are flush after rotation, i.e. the layered spring steel leaves of the compliant hinge have a length self-adapting function. Step 5: strength analysis of the concentrated flexibility type compliant hinge; The maximum tensile force that the laminated compliant hinge can withstand is: wherein: A represents the cross-sectional area of the leaf spring steel, A=Bnδ , B represents the width of the spring steel; [σ] represents the tensile strength of the spring steel; Under the consideration of safety factor, the maximum tensile force that the laminated spring of the compliant hinge can withstand is: In the formulae: S> 1 represents the safety factor.

2. The design method of a compliant hinge with lumped flexibility and length self-adaptation capability according to claim 1, wherein, The thickness of the 65Mn spring steel strip used as the laminated material of the compliant hinge is 0.1mm, the elastic modulus E=196.5Gpa, the tensile strength σb=825Mpa~925Mpa, the tensile strength of the spring steel σb=825Mpa, and the safety factor S=2.

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