Method for calculating opening force of slipknot

Abstract

The invention relates to a control method of a slipknot opening force, which comprises the following steps of: constructing a calculation model of the slipknot opening force, and inputting the Young modulus, the wire diameter and the self-friction coefficient of a wire rod and a set slipknot structure into the constructed calculation model of the slipknot opening force; and calculating to obtain the knotting force of the slipknot. According to the method, the opening force of the slipknot can be directly predicted through the parameters of the slipknot tying process, inverse solution can be carried out, and the slipknot with any tying force can be prepared. Meanwhile, on the premise of not depending on a sensor, force output and measurement of any specified magnitude can be achieved by means of the slipknot structure.

Description

Technical Field

[0001] The invention belongs to the technical field of slipknot tying, in particular to a method for calculating a slipknot opening force. Background Art

[0002] Knotting is one of the indispensable methods for ligation and hemostasis and tissue suturing. Knotting requires accuracy, reliability, and speed. Accuracy means clarifying the tissue site to be knotted, and not tying knots in places where ligation is not required, otherwise it is easy to damage the tissue. Reliability means that the correct knotting method must be used, and the knot must not be loosened, causing bleeding or rupture of sutured tissue, causing pain to the patient or even endangering his life. Unskilled knotting will greatly prolong the operation time, so knotting is often a technique that surgeons must practice hard. There are several types of knots, including single knots, square knots, surgical knots, and triple knots, and different types are used in different parts. There are two methods of knotting: simple hand knotting and instrument knotting. The former is suitable for most surgical operations; the latter is suitable for shallow sutures and some delicate operations.

[0003] The rope slipknot tying method and knotting mechanism involved in the prior art fail to consider the force factor during the slipknot weaving process. The prepared slipknot can only achieve a preset topological structure, and the force when the slipknot is opened cannot be set according to requirements. Summary of the invention

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

[0005] The present invention solves the technical problem by adopting the following technical solutions:

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

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

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

[0009] Step 3, construct a calculation model for the slipknot opening force, input the Young's modulus, diameter, friction coefficient of the wire and the structure of the slipknot in the database respectively, train the model, compare and optimize it with the measured value of the slipknot opening force, and reduce the calculation error;

[0010] Step 4: According to the trained model, the Young's modulus, wire diameter and self-friction coefficient obtained in step 1 and the knotted structure in step 2 are input to calculate the knotting force.

[0011] Furthermore, the step 3 constructs a computational model of the slipknot opening force by using Kirchhoff.

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

[0013] Step 3.1, according to the Kirchhoff rod theory, decompose the slipknot 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 control equation based on the relationship between the Kirchhoff rod and the rigid ring;

[0015] Step 3.3: Construct the corresponding boundary conditions according to the control equations constructed in step 3.2.

[0016] Moreover, the control equation in step 3.2 is:

[0017]

[0018] Among them, θ1(s) belongs to the variable s∈[0,l], and 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, F is the external force on the end of the rod, and F c It 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 maintains static equilibrium at s=l.

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

[0020] θ1(0)=0,

[0021]

[0022] EIθ1′(l)=EIθ2′(l), EIθ2′(L)=0.

[0023]

[0024] Among them, the product EI of Young's modulus E and the relationship moment I is the bending stiffness of the rod, D represents the radius of the rigid ring constraint, and μ is the friction coefficient between the rod and the ring. The mechanical meaning of the boundary condition is: from the symmetry of the model, it can be seen that the angle is always 0 at s = 0, the continuity of the angle and the bending moment is satisfied at s = l, and the posture constraint of the rigid ring is required. At s = L, the condition of no external bending moment is satisfied. Based on this combination of control equations and boundary conditions, the external force F corresponding to each given l can be obtained.

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

[0026] The present invention constructs a calculation model for the opening force of a slipknot, and obtains the Young's modulus, wire diameter and self-friction coefficient of the wire and sets the structure of the slipknot into the constructed calculation model for the opening force of the slipknot; the slipknot tying force is calculated. The present invention can directly predict the size of the opening force of the slipknot through the process parameters of the slipknot, and can perform reverse solution to prepare a slipknot with any tying force. At the same time, the present invention can achieve any specified size of force output and measurement by relying on the structure of the slipknot without relying on the sensor. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0028] Figure 2 It is a schematic diagram for comparing the experimental measurement and model calculation of the single-ring structure slipknot of the present invention;

[0029] Figure 3 It is a schematic diagram for comparing the experimental measurement and model calculation of the two-ring structure slipknot of the present invention;

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

[0031] Figure 5 A schematic diagram showing the comparison between the experimental measurement and model calculation of the opening force of slipknots with different wire diameters of the present invention;

[0032] Figure 6 It is a schematic diagram of the comparison between the experimental measurement and model calculation of the opening force of the slipknot with different pre-tightening forces of the present invention; DETAILED DESCRIPTION

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

[0034] The size of the slipknot opening force is directly related to the process of tying the slipknot. The structure of the slipknot and the size of the force used to make the slipknot will directly affect the size of the slipknot opening force. However, this mechanical relationship is an extremely complex nonlinear relationship. The present invention directly derives the nonlinear mathematical relationship between the slipknot opening force and the preparation process based on theory, and verifies it through experiments, with excellent results.

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

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

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

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

[0039] In the present invention, the Kirchhoff rod theory is used to establish a calculation model for the opening force of the slipknot. In this model, the length of the rod is defined as L and the diameter is defined as d. Assuming that the rod is slender, that is, it satisfies the condition of L>>d, the 3D rod model can be simplified to a 1D case, that is, a line. The bending stiffness of the rod is defined as EI, where the symbol E refers to the Young's modulus of the rod, and I refers to the polar moment of inertia of the rod. To simplify the calculation, it is assumed that the rod can bend and deform, but the rod is not stretchable or shearable, so that when the rod is bent and deformed, its center line neither expands nor contracts, and the cross section always remains orthogonal to the center line. In addition, the effects of torsional deformation of the rod and all possible out-of-plane deformations are ignored.

[0040] like Figure 1 As shown, the present invention provides a mechanical model for analyzing the untying process of a slipknot under external force. The model decomposes the slipknot into a Kirchhoff rod with a total length of 2L and a rigid ring with a diameter of D, which are represented by a black curve and an orange ring respectively. The rod is a straight line in a natural state without external force. In the model, the end of the rod is acted upon by an external force F, which represents the opening force applied to the slipknot. Due to the symmetry of the geometric configuration and the loading state, an appropriate semi-structure can be taken for analysis in order 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 angle of rotation. When an external force F acts at the coordinate s=L, it is assumed that the rigid ring maintains static equilibrium at s=l. Since the rigid ring is in contact with the rod, positive pressure and friction are simultaneously 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 represents the resultant force of the rigid ring on the rod.

[0041] The shape of the elastic rod after deformation can be described by the radial vector equation of the center line, that is, r(s) = x(s)e1 + y(s)e2, where e i refers to the basis vector along the i-direction. In the non-scalable case considered, the kinematic relationship between the position and angle of the centerline, and the transformation relationship between the Frenet-Serret coordinate system and the Cartesian coordinate system can be described as:

[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 ' represents the derivative of s. The internal load along the centerline of the rod is simplified to the internal force N and the internal bending moment M. The moment-curvature constitutive relation of the rod is:

[0044] EIκ(s)=M(s). (2)

[0045] Since the contact area between the rod and the rigid ring is assumed to be only at one point, the contact area does not cause any distributed force. The equilibrium condition of the internal forces and internal 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 the coordinate s = l, assume that the normal pressure exerted by the rigid ring on the rod is F n , Coulomb friction force is F τ Since the external force F is applied along the x-direction, and from 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 formula (5) and formula (6) into formula (4), we finally get a piecewise second-order differential algebraic equation about the rotation angle θ. To avoid any possible ambiguity, we define θ1(s) to belong to the variable s∈[0,l], and θ2(s) to belong to the interval (l,L], and we get:

[0053]

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

[0055] θ1(0)=0, (8)

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

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

[0058] Then we get:

[0059]

[0060] Since the derivative of s is used in equation (7), boundary conditions for the bending moment are required. Since the diameter of the rod is relatively small, the friction force is assumed to act directly on the center line and it is assumed that it has no effect on 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 have a position constraint along the x-direction:

[0063]

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

[0065] In this model, the maximum value of force F, that is, F open Satisfies the following relationship

[0066]

[0067] For a circular cross-section rod, I = πd 4 / 64. Where f(μ) represents the fitting parameter related to μ. This equation shows that F open and D 2 Inverse relationship, such as Figure 1 In addition, the accuracy of this formula has been further verified by experiments and simulation methods, such as Figure 2-6 shown. Figure 2 , 3, 4 are schematic diagrams of experimental measurement, simulation and model calculation comparison of single-ring, two-ring and three-ring structure slipknots. It can be seen from the figure that no matter how the structural parameters (number of rings) of the slipknot are adjusted, the predicted data of the model of the present invention are basically consistent with the experimental data, and are closer to the actual experimental measurement data than the finite element predicted data. Figure 5 The effect of changing the wire diameter on the opening force of the slipknot was studied. It can be seen from the figure that the thicker the wire diameter, the greater the corresponding opening force, and this behavior can be predicted by the formula of the model of the present invention. Figure 6The effect of changing the preload on the opening force of the slipknot is studied. It can be seen from the figure that the greater the preload, the greater the corresponding opening force. This trend can also be described by the formula of the model of the present invention. By comparing the calculation results of the experiment, simulation and the model, it can be seen that the model of the present invention can quickly and accurately calculate the opening force of the slipknot.

[0068] Step 4: According to the trained model, the Young's modulus, wire diameter and self-friction coefficient obtained in step 1 and the knotted structure in step 2 are input to calculate the knotting force.

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

Claims

1. A method for controlling the opening force of a slipknot, characterized in that: The following steps are involved: Step 1: Obtain the Young's modulus, wire diameter and self-friction coefficient of the wire. Step 2: Set the structure of the slipknot; Step 3, construct a calculation model for the slipknot opening force, input the Young's modulus, diameter, friction coefficient of the wire and the structure of the slipknot in the database respectively, train the model, compare and optimize it with the measured value of the slipknot opening force, and reduce the calculation error; Step 4: According to the trained model, the Young's modulus, wire diameter and self-friction coefficient obtained in step 1 and the knotted structure in step 2 are input to calculate the knotting force.

2. The method for calculating the knotting force of a movable joint according to claim 1, characterized in that: The step 3 constructs a calculation model of the slipknot opening force by using Kirchhoff.

3. The method for calculating the knotting force of a flexible joint according to claim 2, characterized in that: The step 3 comprises the following steps: Step 3.1, according to the Kirchhoff rod theory, decompose the slipknot into a Kirchhoff rod with a total length of 2L and a rigid ring with a diameter of D; Step 3.2, construct the control equation based on the relationship between the Kirchhoff rod and the rigid ring; Step 3.3: Construct the corresponding boundary conditions according to the control equations constructed in step 3.

2.

4. A method for calculating the knotting force of a live joint according to claim 3, characterized in that: The control equation in step 3.2 is: Among them, θ1(s) belongs to the variable s∈[0,l], and θ2(s) belongs to the interval (l,L], E is the Young's modulus of the rod, I is the moment of inertia of the rod, F is the external force on the end of the rod, and F c It 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 maintains static equilibrium at s=l.

5. The method for calculating the knotting force of a flexible joint according to claim 4, characterized in that: The boundary conditions in step 3.3 include: θ1(0)=0, EIθ1′(l)=EIθ2′(l), EIθ2′(L)=0. Among them, the product EI of Young's modulus E and the relationship moment 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: from the symmetry of the model, it can be seen that the angle is always 0 at s=0, the continuity of the angle and the bending moment is satisfied at s=l, and the position constraint of the rigid circular ring is required; at s=L, the condition of no external bending moment is satisfied; based on this combination of control equations and boundary conditions, the external force F corresponding to each given l is obtained.

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