Method for calculating the opening force of a slipknot

Abstract

The application relates to a control method of a slipknot opening force, which comprises the following steps: inputting the Young's modulus, the wire diameter and the self-friction coefficient of a wire and the structure of a slipknot into a constructed calculation model of the slipknot opening force; and calculating the slipknot knotting force. The application can directly predict the size of the slipknot opening force through the process parameters of knotting the slipknot, and can perform inverse solution to prepare the slipknot with an arbitrary knotting force. Meanwhile, the application can realize the force output and measurement of any specified size by relying on the structure of the slipknot without depending on a sensor.

Description

Technical Field

[0001] This invention belongs to the field of slip knot technology, and in particular, a method for calculating the opening force of a slip knot. Background Technology

[0002] Knotting is an essential method for ligation and hemostasis, and for tissue suturing. Knotting requires accuracy, reliability, and speed. Accuracy means clearly identifying the tissue site requiring knotting; knots should not be tied where ligation is unnecessary, as this can easily damage the tissue. Reliability means using the correct knotting method to prevent the knot from loosening, which could cause bleeding or suture tearing, resulting in patient pain or even endangering life. Inexperienced knotting skills will significantly prolong surgical time; therefore, knotting is a technique that surgeons often practice diligently. There are several types of knots, including single knots, square knots, surgical knots, and triple knots, each used for different sites. There are two knotting methods: simple hand knotting and instrument knotting. The former is suitable for most surgical procedures; the latter is suitable for superficial suturing and some delicate surgeries.

[0003] Existing rope slipknot tying methods and mechanisms fail to consider the force factor during the slipknot weaving process. The resulting slipknots can only achieve a preset topological structure and cannot be customized to set the force required to open the slipknot. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and propose a method for calculating the opening force of a slip knot, which can quickly and accurately calculate the knotting force of a slip knot and use this as a basis to prepare a slip knot structure with a specific opening force.

[0005] The technical problem solved by this invention is achieved through the following technical solution:

[0006] A method for controlling the opening force of a slipknot includes the following steps:

[0007] Step 1: Obtain the Young's modulus, wire diameter, and coefficient of self-friction of the wire.

[0008] Step 2: Define the structure of the slipknot;

[0009] Step 3: Construct a calculation model for the opening force of the swivel knot. Input the Young's modulus, diameter, friction coefficient of the wire and the structure of the swivel knot into the database, train the model, and compare and optimize it with the measured value of the opening force of the swivel knot to reduce the calculation error.

[0010] Step 4: Based on the trained model, input the Young's modulus, wire diameter, and self-friction coefficient obtained in Step 1, and the knot structure in Step 2, to calculate the live knot force.

[0011] Furthermore, step 3 involves constructing a calculation model for the opening force of a live knot using Kirchhoff.

[0012] Furthermore, step 3 includes the following steps:

[0013] Step 3.1: According to the Kirchhoff rod theory, the live knot is decomposed into a Kirchhoff rod with a total length of 2L and a rigid ring with a diameter of D;

[0014] Step 3.2: Construct the governing equations based on the relationship between the Kirchhoff rod and the rigid ring;

[0015] Step 3.3: Construct the corresponding boundary conditions based on the governing equations constructed in Step 3.2.

[0016] Furthermore, the governing equation in step 3.2 is:

[0017]

[0018] Where θ1(s) belongs to the variable s∈[0,l], while θ2(s) belongs to the interval (l,L], E is the Young's modulus of the rod, I is the polar moment of inertia of the rod, and F is the external force on the end of the rod. c This represents the resultant force of the rigid ring on the rod. When the external force F acts at the coordinate s = L, the rigid ring remains in static equilibrium at s = l.

[0019] Furthermore, the boundary conditions in step 3.3 include:

[0020] θ1(0)=0,

[0021]

[0022] EIθ1′(l)=EIθ2′(l), EIθ2′(L)=0.

[0023]

[0024] In this equation, EI, the product of Young's modulus E and the relational moment I, represents the bending stiffness of the rod; D represents the radius of the rigid circular ring constraint; and μ is the coefficient of friction between the rod and the ring. The mechanical meaning of the boundary conditions is as follows: due to the model's symmetry, the rotation angle is always 0 at s = 0; at s = l, the continuity of rotation angle and bending moment is satisfied, and the rod is subject to the pose constraint of the rigid circular ring. At s = L, the condition of no external bending moment is satisfied. Based on this combination of governing equations and boundary conditions, the external force F corresponding to each given l can be obtained.

[0025] The advantages and positive effects of this invention are:

[0026] This invention constructs a calculation model for the opening force of a slipknot, and inputs the Young's modulus, wire diameter, and self-friction coefficient of the wire, along with the structure of the slipknot, into the model to calculate the slipknot knotting force. This invention can directly predict the opening force of a slipknot based on the process parameters of knotting, and can perform inverse knives to prepare slipknots with arbitrary knotting forces. Furthermore, this invention can achieve arbitrary force output and measurement based on the structure of the slipknot without relying on sensors. Attached Figure Description

[0027] Figure 1 This is a schematic diagram illustrating the principle of the present invention;

[0028] Figure 2 This is a schematic diagram showing the comparison between experimental measurement and model calculation of the single-ring structure of the present invention;

[0029] Figure 3 This is a schematic diagram showing the comparison between experimental measurement and model calculation of the two-ring structure of the present invention;

[0030] Figure 4 This is a schematic diagram showing the comparison between experimental measurement and model calculation of the three-ring structure of the present invention;

[0031] Figure 5 This is a schematic diagram showing the comparison between experimental measurement and model calculation of the opening force of the live knot with different wire diameters according to the present invention;

[0032] Figure 6 This is a schematic diagram showing the comparison between experimental measurement and model calculation of the opening force of the live knot with different preloads according to the present invention; Detailed Implementation

[0033] The present invention will be further described in detail below with reference to the accompanying drawings.

[0034] The opening force of a slipknot is directly related to the process of making the slipknot; the structure of the slipknot and the force used to make it directly affect the opening force. However, this mechanical relationship is an extremely complex nonlinear one. This invention, starting from theory, directly derives the nonlinear mathematical relationship between the slipknot opening force and the preparation process, and verifies it experimentally with excellent results.

[0035] A method for controlling the opening force of a slipknot includes the following steps:

[0036] Step 1: Obtain the Young's modulus, wire diameter, and coefficient of self-friction of the wire.

[0037] Step 2: Define the structure of the slipknot.

[0038] Step 3: Construct a calculation model for the opening force of the swivel knot. Input the Young's modulus, diameter, friction coefficient of the wire and the structure of the swivel knot into the database, train the model, and compare and optimize it with the measured value of the opening force of the swivel knot to reduce the calculation error.

[0039] In this invention, Kirchhoff's rod theory is used to establish a calculation model for the opening force of a live knot. In this model, the length of the rod is defined as L, and the diameter as d. It is assumed that the rod is slender, i.e., satisfying the condition L >> d, thus simplifying the 3D rod model to a 1D case, i.e., a line. The bending stiffness of the rod is defined as EI, where E refers to the Young's modulus of the rod, and I refers to the polar moment of inertia. To simplify the calculation, it is assumed that the rod can undergo bending deformation, but it is inextensible and shear-resistant. This ensures that when the rod undergoes bending deformation, its centerline neither expands nor contracts, and the cross-section always remains orthogonal to the centerline. Furthermore, the effects of torsional deformation and all possible out-of-plane deformations of the rod are ignored.

[0040] like Figure 1 As shown, this invention provides a mechanical model for analyzing the unraveling process of a slipknot under external force. The model decomposes the slipknot into a Kirchhoff rod of total length 2L and a rigid ring of diameter D, represented by a black curve and an orange ring, respectively. The rod is a straight line in its natural state without external force. In the model, the end of the rod is subjected to an external force F, representing the opening force applied to the slipknot. Due to the symmetry of the geometry and the loading state, an appropriate half-structure can be used for analysis to simplify the calculation. A Frenet-Serret coordinate system is established along the rod, where s represents the arc length and θ(s) represents the rotation angle. When the external force F acts at coordinate s = L, it is assumed that the rigid ring is in static equilibrium at s = l. Since the rigid ring is in contact with the rod, both normal force and friction are generated at the contact point. The Coulomb friction coefficient between the rod and the ring can be represented by μ, and the symbol F... c This represents the resultant force exerted by the rigid ring on the rod.

[0041] The shape of the deformed elastic rod can be described by the radius vector equation of the centerline, namely r(s) = x(s)e1 + y(s)e2, where e i This refers to the basis vector along the i- direction. In the non-scalable case, the relationship between the position and angle of the centerline, and the transformation between the Frenet-Serret coordinate system and the Cartesian coordinate system, can be described as follows:

[0042]

[0043] The relationship between the rotation angle θ and the curvature κ can be written as κ(s)=θ′(s)e³, where the symbol ' denotes differentiation with respect to s. The internal loads along the centerline of the rod are simplified to internal forces N and internal bending moments M. The moment-curvature constitutive relation of the rod is:

[0044] EIκ(s)=M(s). (2)

[0045] Since it is assumed that the contact area between the rod and the rigid ring is only at one point, no distributed force will be generated in the contact area. The equilibrium condition of the internal forces and moments of the rod can be expressed as:

[0046] N′(s)=0, (3)

[0047] M′(s)+r′(s)×N(s)=0, (4)

[0048] in

[0049] r′(s)=cosθ(s)e1+sinθ(s)e2, (5)

[0050] r′(s) is the derivative of the position vector. At coordinates s = l, assume the normal force exerted by the rigid circular ring on the rod is F. n The Coulomb friction force is F τ Since the external force F is applied along the x-direction, and due to the symmetry of the structure, the force F exerted by the rigid ring on the rod is... c It must also be along the x-axis. Therefore, the expression for the internal force N(s) is:

[0051]

[0052] Substituting equations (5) and (6) into equation (4), we finally obtain a piecewise second-order differential algebraic equation concerning the rotation angle θ. To avoid any possible ambiguity, we define θ1(s) as belonging to the variable s∈[0,l], and θ2(s) as belonging to the interval (l,L], thus obtaining:

[0053]

[0054] To calculate the critical force F corresponding to each l, a total of 6 boundary or constraint conditions are required. First, due to the symmetry of the structure, we can obtain:

[0055] θ1(0)=0, (8)

[0056] Based on Coulomb's law of friction, when nearing sliding, the relationship F is given. t =μF n Where μ represents the coefficient of friction between the rod and the ring. Since the resultant force of the ring is along the x-direction, we obtain:

[0057] F τ=F c cosθ(l),F n =F c sinθ(l), (9)

[0058] Therefore, we get:

[0059]

[0060] Since the derivative of s is used in formula (7), boundary conditions for the bending moment are required. Because the diameter of the rod is relatively small, it is assumed that the frictional force acts directly on the centerline and does not affect the continuity of the bending moment at s = l. Therefore, the boundary conditions for the bending moment are:

[0061] EIθ1′(l)=EIθ2′(l), EIθ2′(L)=0. (11)

[0062] Finally, the rigid ring will generate a positional constraint along the x-direction:

[0063]

[0064] Therefore, the governing equation (7) and the boundary conditions (8) and (10)-(12) constitute the calculation model for the opening force of the live knot.

[0065] In this model, the maximum value of force F, i.e., F open Satisfy the following relationship

[0066]

[0067] For a rod with a circular cross-section, we have I = πd 4 / 64. Where f(μ) represents the fitting parameters related to μ. This equation shows that F open and present D 2 Inverse relationship, such as Figure 1 As shown. Furthermore, the accuracy of this formula has been further verified through experimental and simulation methods, such as... Figure 2-6 As shown. Figure 2 Figures 3 and 4 show experimental measurements, simulations, and model calculations for single-ring, two-ring, and three-ring slack knot structures, respectively. As can be seen from the figures, regardless of how the structural parameters (number of rings) of the slack knot are adjusted, the predicted data from the model of this invention basically match the experimental data, and are even closer to the actual experimental measurement data than the finite element prediction data. Figure 5 The effect of changing the wire diameter on the opening force of the live knot was studied. As can be seen from the figure, the thicker the wire diameter, the greater the corresponding opening force, and this behavior can be predicted by the formula of the model of this invention. Figure 6The effect of changing the preload on the opening force of the slack knot was studied. As shown in the figure, the greater the preload, the greater the corresponding opening force. This trend can also be characterized by the formula of the model in this invention. Comparative experiments and simulation results with the calculation results of this model show that the model of this invention can quickly and accurately calculate the opening force of the slack knot.

[0068] Step 4: Based on the trained model, input the Young's modulus, wire diameter, and self-friction coefficient obtained in Step 1, and the knot structure in Step 2, to calculate the live knot force.

[0069] It should be emphasized that the embodiments described in this invention are illustrative rather than limiting. Therefore, this invention includes, but is not limited to, the embodiments described in the specific implementation. Any other implementations derived by those skilled in the art based on the technical solutions of this invention are also within the scope of protection of this invention.

Claims

1. A method of calculating a slipknot opening force, characterized by: The method comprises the following steps: Step 1, obtaining the Young's modulus, wire diameter and self-friction coefficient of the wire, Step 2, setting the structure of the live knot; Step 3, constructing a calculation model of the opening force of the live knot, inputting the Young's modulus, diameter and friction coefficient of the wire and the structure of the live knot in the database respectively, training the model, comparing and optimizing with the measured value of the opening force of the live knot, and reducing the calculation error; Step 3 uses Kirchhoff to construct a calculation model of the opening force of the live knot; Step 3 comprises the following steps: Step 3.1, according to the Kirchhoff rod theory, the live knot is decomposed into a Kirchhoff rod with a total length of 2L and a rigid circular ring with a diameter of D; Step 3.2, according to the relationship between the Kirchhoff rod and the rigid circular ring, a calculation model of the opening force of the live knot is constructed; Step 3.3, according to the calculation model of the opening force of the live knot constructed in step 3.2, the corresponding boundary conditions are constructed; Step 4, according to the trained model, input the Young's modulus, wire diameter and self-friction coefficient obtained in step 1 and the knot structure in step 2, and calculate the knot force of the live knot.

2. A method of calculating the slipknot opening force according to claim 1, characterized in that: The calculation model of the opening force of the live knot in step 3.2 is: where s ∈ [0, l] in θ1(s) and s ∈ (l, L] in θ2(s), E is the Young's modulus of the rod, I is the moment of inertia of the rod, F is the external force applied to the end of the rod, F c represents the resultant force of the rigid circular ring on the rod, and when the external force F is applied at coordinate s = L, the rigid circular ring maintains static equilibrium at s = l.

3. The method of calculating the slipknot opening force of claim 1, wherein: The boundary conditions in step 3.3 include: θ1(0)=0, EIθ1′(l)=EIθ2′(l),EIθ2′(L)=0. Wherein, the product EI of the Young's modulus E and the moment of inertia I is the bending stiffness of the rod, D represents the radius of the rigid circular ring constraint, and μ is the friction coefficient between the rod and the ring; The mechanical meaning of the boundary condition is: according to the symmetry of the model, the angle is 0 at s=0, the continuity of the angle and the bending moment is satisfied at s=l, and the pose constraint of the rigid circular ring is required; At s=L, it satisfies the condition of no external bending moment; Based on the calculation model of the opening force of the live knot and the boundary conditions, the corresponding external force F of each given l is obtained.

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