Mechanical model construction method for robot-assisted kirschner wire bone drilling

Abstract

The invention provides a mechanical model construction method for robot-assisted kirschner wire bone drilling, which comprises the following steps: analyzing a robot-assisted kirschner wire bone drilling process to obtain a mechanical analysis geometric model for robot-assisted kirschner wire bone drilling; according to a mechanical analysis geometric model, a finite element analysis model for robot-assisted Kirschner wire bone drilling is established, and the influence rule of the Kirschner wire rotating speed, the Kirschner wire feeding speed and the relative angle of the Kirschner wire and the bone surface on the drilling force is obtained; according to a mechanical analysis geometric model and finite element model data, a mechanical model for robot-assisted kirschner wire placement is established, and mathematical representations between drilling force and the rotating speed and the feeding speed of the kirschner wire and between the kirschner wire and the bone surface angle are obtained. According to the technical scheme provided by the invention, the construction of the mechanical model of the robot-assisted kirschner wire bone drilling can be realized.

Description

Technical Field

[0001] The present invention relates to a method for constructing a mechanical model of robot-assisted Kirschner wire bone drilling, belonging to the field of robot bone drilling and machining.

Background Art

[0002] In orthopedic surgeries, using Kirschner wires for bone drilling is a common clinical operation. Due to the complexity of the bone surface structure, the Kirschner wire often forms a certain angle with the bone surface during drilling. In this inclined drilling process, slippage is likely to occur, making it difficult for the Kirschner wire to accurately enter the expected position, thus requiring doctors to frequently adjust the drilling site during the surgery. To address this issue, establishing a mechanical model of Kirschner wire bone drilling is of great value for predicting the deflection force of slippage when the guide wire is inserted obliquely, and can provide a theoretical basis for slippage correction.

[0003] The drilling force can be constructed through theoretical modeling and empirical analysis methods. Theoretical modeling obtains the integral form of the drilling force by analyzing the microscopic geometric structure, motion state, and force conditions of the Kirschner wire. However, this method ignores the characteristics of different bone structures, making it difficult to intuitively observe the relationship between the drilling force and drilling parameters such as feed speed, rotational speed, and inclination angle, and it is also difficult to directly apply it to actual robot control. The empirical analysis method establishes an empirical formula or regression model between the drilling force and parameters such as feed speed, rotational speed, and inclination angle through a large amount of experimental data. However, the limitation of the empirical analysis method is the lack of a profound understanding of the microscopic physical process and the difficulty in explaining the fundamental mechanism of the generation of the drilling force. In summary, conducting research on a method for constructing a mechanical model of robot-assisted Kirschner wire bone drilling is of important research significance.

Summary of the Invention

[0004] In view of this, the present invention provides a method for constructing a mechanical model of robot bone drilling to achieve mechanical modeling of robot bone drilling.

[0005] The present invention provides a method for constructing a mechanical model of robot bone drilling, including:

[0006] Analyze the process of robot-assisted Kirschner wire bone drilling to obtain a mechanical analysis geometric model of robot-assisted Kirschner wire bone drilling;

[0007] According to the mechanical analysis model of Kirschner wire bone drilling, the resultant force of Kirschner wire bone drilling can be decomposed into: radial component force F R , tangential component force F P , axial component force F Q Among them, the axial force is generated by the feeding of the robotic arm and is responsible for maintaining the feeding of the Kirschner wire; the tangential component force is generated by the rotation of the Kirschner wire and acts as the cutting force to cut the bone tissue; the radial component force is generated by the insufficient contact between the tip of the Kirschner wire and the bone tissue, which will cause slippage at the initial stage of the guide wire insertion.

[0008] Based on the mechanical analysis geometric model, a finite element analysis model for robot-assisted Kirschner wire bone drilling is established to obtain the influence laws of the rotational speed of the Kirschner wire, the feed speed, and the relative angle between the Kirschner wire and the bone surface on the drilling force.

[0009] Based on the mechanical analysis geometric model and the finite element model data, a mechanical model for robot-assisted Kirschner wire bone drilling is established to obtain the mathematical representation between the drilling force and the rotational speed of the Kirschner wire, the feed speed, and the relative angle between the Kirschner wire and the bone surface.

[0010] In the above method, the step of establishing a finite element analysis model for robot-assisted Kirschner wire bone drilling based on the mechanical analysis geometric model to obtain the influence laws of the rotational speed of the Kirschner wire, the feed speed, and the relative angle between the Kirschner wire and the bone surface on the drilling force includes:

[0011] Based on the mechanical analysis geometric model of robot bone grinding, a solid geometric model of the Kirschner wire and the femur is constructed using 3D modeling software, and the generated model is imported into the finite element simulation software. In the assembly, the relative positions of the femur model and the Kirschner wire model are set.

[0012] Based on the material essential properties of the femur model and the Kirschner wire model, the material properties and constitutive models of the femur model and the Kirschner wire model are constructed.

[0013] Based on the geometry and stress state of the simulation model, a multi-density grid structure of the femur model and the Kirschner wire model is constructed.

[0014] Based on the actual bone drilling state, the drilling contact constraints of the Kirschner wire and the femur model are set respectively. Among them, the Kirschner wire is regarded as a rigid body with a reference point (RP); the bottom surface of the femur model is constrained and fixed to realize the modeling of the actual scene of robot bone drilling.

[0015] Based on the above conditions, the explicit dynamics is used to analyze the complex dynamic behaviors of the Kirschner wire and the femur, and the radial force F of the Kirschner wire is collected. R observing the changing trend of the radial force, and it is found that the radial force F R shows a trend of increasing first and then decreasing with time, and the maximum value increases with the increase of the angle between the Kirschner wire and the bone.

[0016] Based on the above finite element analysis model, the drilling radial force data are collected under different spindle speeds, different feed speeds, and different inclination angles between the Kirschner wire and the bone surface to provide sufficient experimental data.

[0017] In the above method, based on the mechanical analysis geometric model and finite element model data, a mechanical model for robot-assisted Kirschner wire bone drilling is established, and the mathematical representations of the drilling force with respect to the rotational speed of the Kirschner wire, the feed rate, and the relative angle between the Kirschner wire and the bone surface are obtained, including:

[0018] According to the mechanical analysis model of Kirschner wire bone drilling, the resultant force of Kirschner wire bone drilling can be decomposed into: a radial component force F R , a tangential component force F P , and an axial component force F Q Among them, the axial force is generated by the feeding of the robotic arm and is responsible for maintaining the feeding of the Kirschner wire; the tangential component force is generated by the rotation of the Kirschner wire and acts as the cutting force to cut through the bone tissue; the radial component force is generated by the insufficient contact between the tip of the Kirschner wire and the bone tissue, which will cause a slippage phenomenon at the initial stage of the guide wire placement.

[0019] Based on the relationship between the above drilling force and the spindle speed, feed rate, and tilt angle, as well as the finite element simulation data, a mechanical model is established using the response surface method, which will serve as the basis for the optimization and control of the robotic bone drilling motion parameters.

[0020] It can be seen from the above technical solutions that the present invention has the following beneficial effects:

[0021] In the technical solution of the present invention, a mechanical analysis geometric model for robotic bone drilling is obtained; based on the mechanical analysis geometric model, a finite element analysis model for robotic bone drilling is established to obtain the influence law of the spindle speed and feed rate of the Kirschner wire and the relative angle between the Kirschner wire and the femur on the grinding force; based on the mechanical analysis geometric model and finite element model data, a mechanical model for robotic bone drilling is established to obtain the mathematical representations of the radial force on the Kirschner wire with respect to the spindle speed, feed rate, and the angle formed by the Kirschner wire and the bone, providing a model basis for the slip control of robotic Kirschner wire drilling and, at the same time, providing a theoretical basis for the research of the robotic bone drilling system.

BRIEF DESCRIPTION OF THE DRAWINGS

[0022] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative and laborious efforts.

[0023] Figure 1 is a schematic flow chart of the method for constructing the force model of robotic bone drilling provided by the embodiment of the present invention;

[0024] Figure 2 is a schematic diagram of the bone grinding robot system provided by the embodiment of the present invention;

[0025] Figure 3 It is a schematic diagram of the geometric model for mechanical analysis provided in the embodiments of the present invention;

[0026] Figure 4 It is a schematic diagram of finite element analysis provided in the embodiments of the present invention: (a) 3D model of bone; (b) 3D model of Kirschner wire; (c) mesh of bone; (d) mesh of Kirschner wire; (e) load constraint of bone; (f) load constraint of Kirschner wire;

[0027] Figure 5 It is a schematic diagram of the spatio-temporal distribution of finite element simulation provided in the embodiments of the present invention: (a) unimplanted state; (b) partially implanted state; (c) stably implanted state;

[0028] Figure 6 It is a response surface diagram of the grinding mechanical model provided in the embodiments of the present invention;

[0029] Figure 7 It is a schematic diagram of the change of the radial force of the Kirschner wire with time at different feed speeds in the finite element simulation provided in the embodiments of the present invention;

[0030] Figure 8 It is a schematic diagram of the change of the radial force of the Kirschner wire with time at different spindle speeds in the finite element simulation provided in the embodiments of the present invention;

[0031] Figure 9 It is a schematic diagram of the change of the radial force of the Kirschner wire with time at different tilt angles in the finite element simulation provided in the embodiments of the present invention;

[0032] Figure 10 It is a residual analysis diagram provided in the examples of the present invention.

Specific Embodiment

[0033] For a better understanding of the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0034] It should be clear that the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0035] The embodiments of the present invention provide a method for constructing a mechanical model for robot bone drilling. Please refer to Figure 1 , which is a flow schematic diagram of the force model construction method for robot drilling provided by the present invention. As shown in Figure 1As shown, without being limited to the foregoing, the method for constructing a mechanical model of robotic bone drilling is applicable to the field of orthopedic surgery and provides a radial contact force output model for robotic bone drilling during a surgical procedure, so as to more accurately control the robotic parameters such that the radial force during bone drilling is within a certain range, thereby reducing the occurrence of slippage during autonomous robotic bone drilling and improving the accuracy of bone drilling. The method includes the following steps:

[0036] Step 101: Analyze the process of robotic bone drilling and establish a geometric model for mechanical analysis of robotic bone drilling.

[0037] Referring to Figure 2 , the bone grinding robotic system 201 includes a robotic arm 202, a six-axis force sensor 213, a high-speed grinding drill 215, and a Kirschner wire 216. The bone grinding robotic system 201 can be arranged for autonomous drilling. What the bone grinding robotic system 201 provides is to fully control the autonomous movement of the robotic arm 202, the high-speed grinding drill 215, and the Kirschner wire 216 equipment. At the same time, the grinding force collected by the six-axis force sensor 213 is used as a feedback signal.

[0038] The robotic arm 202 is a six-degree-of-freedom robotic arm, including a base flange 203, a rotary joint 1 204, a rotary joint 2 205, a link 1 206, a rotary joint 3 207, a link 2 208, a rotary joint 4 209, a rotary joint 5 210, a rotary joint 6 211, and a tip flange 212. The six-axis force sensor 213 is fixedly installed on the tip flange 212. The high-speed grinding drill fixing component 214 is fixedly installed on the six-axis force sensor 213. The high-speed grinding drill 215 is fixedly installed on the high-speed grinding drill fixing component 214. The Kirschner wire 216 is fixedly installed at the end of the high-speed grinding drill 215.

[0039] Specifically, analyze the process of robotic bone drilling. Referring to Figure 3 , construct the X-axis, Y-axis, and Z-axis of the Kirschner wire. The Z-axis is the axial direction of the Kirschner wire. The negative direction of the Z-axis is the feed direction, the Y-axis is perpendicular to the Z-axis direction, and the X-axis satisfies the right-hand screw rule and is perpendicular to the Y-axis and the Z-axis.

[0040] According to the coordinate axes of the robotic bone grinding process, construct a geometric model for mechanical analysis of robotic bone grinding. As shown in Figure 3 , the axial drilling force F Q of the Kirschner wire in the Z-axis direction, the radial drilling force F R of the Kirschner wire in the Y-axis direction, the circumferential drilling force F P received by the Kirschner wire, the angle θ between the Kirschner wire and the bone surface, the spindle speed n of the Kirschner wire, the feed speed f of the Kirschner wire. The diameter d of the Kirschner wire, the drilling edge lengths l1 and l2 of the Kirschner wire, and the cutting half angle k a of the Kirschner wire.

[0041] Step 102: Based on the mechanical analysis geometric model, establish a finite element analysis model for robot-assisted Kirschner wire bone drilling to obtain the influence laws of the rotational speed of the Kirschner wire, the feed speed, and the relative angle between the Kirschner wire and the bone surface on the drilling force;

[0042] Specifically, according to the mechanical analysis model of robot bone drilling, use Solidworks 3D modeling software to construct the geometric model of the Kirschner wire, and use ITK-snap software to construct the bone model, as shown in Figure 4 (a) Figure 4 (b) respectively. Import both into the Abaqus finite element simulation software, and set the relative position between the bone model and the Kirschner wire in the assembly, with an angle θ between the two.

[0043] Furthermore, set the material properties and constitutive models of the bone model and the Kirschner wire. During the drilling process of the Kirschner wire, it first contacts the cortical bone. The material properties of the cortical bone are: density of 1640 kg / m 3 , elastic modulus of 17 GPa, and Poisson's ratio of 0.35. See Table 1 for details. The material of the Kirschner wire is TC4 titanium alloy, and its properties are: density of 8640 kg / m 3 , elastic modulus of 210 GPa, and Poisson's ratio of 0.3. See Table 2 for details.

[0044] The constitutive model establishes the stress and strain relationship in the grinding area, can predict the stress distribution and strain accumulation in the grinding area, and is a key factor in finite element analysis.

[0045] According to the Johnson-Cook material model, as shown in the following formula,

[0046]

[0047] where σ is the equivalent flow stress, and ε is the equivalent plastic strain; and are the equivalent plastic strain rate and the reference plastic strain rate; T is the temperature at the bone grinding site; T r is the melting point of the material; T m is the room temperature; n is the strain hardening index; m is the thermal softening index; A, B, and C are the yield strength, strain, and strain sensitivity rate of the material. Design the strain parameters of the bone model as shown in Table 3.

[0048] According to the Johnson-Cook damage model, as shown in the following formula,

[0049]

[0050] where ε fThe strain equivalent at material failure, D1, D2, and D3 are damage coefficients related to quasi-static failure, and the D4 coefficient is related to the influence of strain rate. The damage parameters of the bone model are designed as shown in Table 4.

[0051] Next, set the multi-density network structure of the bone model and the Kirschner wire. As Figure 4 (c) and Figure 4 (d) show, the C3D4 linear eight-node hexahedron element is used to mesh the bone model, with the seed point size set to 1.2, and the entire model is divided into 407,251 cells. The C3D10M quadratic tetrahedron element is used to mesh the Kirschner wire, with the seed point size set to 0.5, and it is divided into 19,576 cells.

[0052] Next, set the drilling contact constraints for the bone model and the Kirschner wire. As Figure 4 (e) and Figure 4 (f) show, in the bone drilling simulation, the bone model is fixed, and the boundary conditions of the bone model are to constrain the six degrees of freedom of the bottom surface (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0), where U1, U2, and U3 are the velocities in the X, Y, and Z directions respectively, and UR1, UR2, and UR3 are the rotational velocities around the X, Y, and Z axes respectively, all set to 0. The Kirschner wire needs to complete drilling, including rotation around the axis and feeding along the axis. Different feeding velocities in the negative Z-axis direction and different spindle speeds in the Z-axis direction are applied at the reference point of the Kirschner wire to ensure the simulation of the actual bone drilling scenario.

[0053] According to the above conditions, the explicit dynamics analysis is used to analyze the complex dynamic behavior of the interaction between the Kirschner wire and the bone. The entire bone drilling process is divided into three stages: not inserted, partially inserted, and fully inserted, and each stage is analyzed, as Figure 5 shown, and the axial drilling force F of the Kirschner wire is collected R (Y-axis drilling force).

[0054] Step 103, based on the mechanical analysis geometric model and finite element model data, use the response surface method to establish a mechanical model for robot-assisted Kirschner wire bone drilling, and obtain the mathematical representation between the drilling force and the rotational speed, feeding speed, and relative angle between the Kirschner wire and the bone surface.

[0055] Based on the relationship between the above drilling force and the spindle speed, feeding speed, and tilt angle, as well as the finite element simulation data, use the response surface method to establish a mechanical model, as Figure 6 shown, which will be used as the basis for optimizing and controlling the motion parameters of robot bone drilling.

[0056] According to the response surface analysis method, first, the sequential model sum of squares analysis is carried out. The results of the sequential model sum of squares analysis are shown in Table 5. The p-values of the linear model, the second-order interaction model, and the quadratic model are 0.0300, 0.4928, and 0.0335, respectively. Among them, the p-value of the linear model is significant (less than 0.05), indicating that the linear model has a strong ability to explain the data. However, the p-value of the second-order interaction model is not significant (greater than 0.05), while the p-value of the quadratic model is significant, indicating that the quadratic model has a better fitting effect than the linear model and the second-order interaction model. The p-value of the cubic model is 0.7937, indicating that the contribution of its higher-order terms to the model is not significant, and there is a confounding problem in the cubic model, so it is not adopted.

[0057] Next, the lack-of-fit analysis is carried out. The results of the lack-of-fit analysis are shown in Table 6. The lack-of-fit p-values of the linear model and the second-order interaction model are 0.3702 and 0.3409, respectively, both greater than 0.05, indicating that their lack-of-fit terms are not significant. However, the lack-of-fit p-value of the quadratic model is 0.7937, further verifying its high fitting degree with the experimental data.

[0058] Based on the comprehensive results of the sequential model sum of squares, the lack-of-fit analysis, and the model summary statistics, the quadratic model is selected as the optimal model. The obtained model regression equation is:

[0059] F = 3.13 - 0.60A - 0.32B + 0.16C

[0060] - 0.26AB - 0.13AC + 0.26BC

[0061] - 0.14A 2 + 0.62B 2 - 0.17C 2

[0062] where A, B, and C represent the coding factors of the angle between the Kirschner wire and the bone surface, the rotational speed of the Kirschner wire, and the feeding speed of the Kirschner wire, respectively.

[0063] To further evaluate the effectiveness of the model, a physical experiment is carried out. Different parameters are changed to collect the force signals during the drilling process, and the changes in the maximum radial drilling force under different parameters are observed.

[0064] In the first case, under the condition of keeping the Kirschner wire angle and the spindle speed constant, the radial drilling force on the Y-axis increases with the increase of the feeding speed of the Kirschner wire, as Figure 7 shown;

[0065] In the second case, under the condition of keeping the Kirschner wire angle and the feeding speed constant, the radial drilling force on the Y-axis decreases with the increase of the rotational speed of the Kirschner wire, as Figure 8 shown;

[0066] In the third case, under the condition of keeping the spindle speed and feed rate constant, the radial drilling force of the Y-axis increases with the decrease of the Kirschner wire angle, as Figure 9 shown;

[0067] The external studentized residual is used to evaluate the bone drilling mechanical model. The calculation formula of the external studentized residual is as follows:

[0068]

[0069] where e i is the ordinary residual of the i-th observation value, that is MSE -i is the residual standard deviation of the remaining observation values in the model after excluding the i-th observation value, and the calculation method is:

[0070]

[0071] where n is the total number of observation values, p is the number of independent variables in the model, e j is the residual of the j-th observation value after excluding the i-th observation value; H ii is the leverage value of the i-th observation value of the model.

[0072] The studentized residual values of 15 repeated experiments are as Figure 10 shown. The residuals are randomly distributed within the range of the actual values of the response variable without an obvious trend, indicating that there is no significant heteroscedasticity or non-linear relationship in the model, and the absolute values of all residuals are less than 2, indicating that there are no significant outliers, and the fitting effect of the bone drilling mechanical model is good.

[0073] Table 1 Physical properties of bone

[0074]

[0075] Table 2 Physical properties of spherical grinding head

[0076]

[0077] Table 3 Main parameters of Johnson-cook material model

[0078]

[0079]

[0080] Table 4 John-cook damage model parameters

[0081]

[0082] Table 5 Analysis results of sequential model sum of squares

[0083]

[0084] Table 6 Analysis Results of Lack-of-Fit Terms

[0085]

Claims

1. A method for constructing a mechanical model of robot-assisted Kirschner wire bone drilling, characterized in that: The method comprises: Analyze the process of robot-assisted Kirschner wire bone drilling and establish the mechanical analysis geometric model of robot-assisted Kirschner wire bone drilling; Based on the mechanical analysis geometric model, a finite element analysis model of robot-assisted Kirschner wire bone drilling was established to obtain the influence of Kirschner wire rotation speed, feed speed, and the relative angle between the Kirschner wire and the bone surface on the drilling force. Based on the mechanical analysis geometric model and finite element model data, a mechanical model of robot-assisted K-wire bone drilling was established using response surface analysis to obtain the mathematical representation of the drilling force and K-wire rotation speed, feed speed, and the relative angle between the K-wire and the bone surface.

2. The method according to claim 1, characterized in that The process of robot-assisted Kirschner wire bone drilling was analyzed, and the mechanical analysis geometric model of robot-assisted Kirschner wire bone drilling was established, including: The process of robot-assisted Kirschner wire bone drilling was analyzed, and the X-axis, Y-axis, and Z-axis of the Kirschner wire were constructed. The negative direction of the Z-axis was the feeding direction, the Z-axis coincided with the Kirschner wire rotation axis, the X-axis was perpendicular to the Z-axis, and the Y-axis, X-axis, and Z-axis were perpendicular to each other, which conformed to the right-hand screw rule. According to the coordinate axes of the robot-assisted Kirschner wire bone drilling process, the mechanical analysis geometric model of robot-assisted Kirschner wire bone drilling is constructed. The resultant force F exerted on the Kirschner wire when drilling the bone is tilted, and the axial force F along the feeding direction of the Kirschner wire is Q , radial force F R , tangential force F P , the angle between the K-wire and the bone surface θ, the K-wire spindle speed n, the K-wire feed speed f, the K-wire diameter d, the K-wire cutting half angle k a , feed per revolution s, projection of K-wire diameter w, length of cutting edge where K-wire is partially inserted l1, l2. Radial force F R With the tangential force F P As shown below: The lengths of the cutting edges l1 and l2 of the partially inserted K-wire are as follows:

3. The method according to claim 1, characterized in that Based on the mechanical analysis geometric model, a finite element analysis model of robot-assisted Kirschner wire bone drilling was established to obtain the influence of Kirschner wire rotation speed, feed speed, and the relative angle between the Kirschner wire and the bone surface on the drilling force, including: According to the mechanical analysis geometric model, the geometric model of the Kirschner wire and the femur was constructed using 3D modeling software, and the generated model was imported into the finite element simulation software. In the assembly, the relative position between the femur model and the Kirschner wire model was set; According to the material essential properties of the femur model and the Kirschner wire model, the material properties and constitutive model of the femur model and the Kirschner wire model are constructed; According to the geometric state of the simulation model and the interaction state between the assemblies, a multi-density mesh structure of the femur model and the Kirschner wire model is constructed; According to the actual K-wire placement status, the interaction between the femoral model and the K-wire model is constructed, and the drilling contact constraints between the K-wire and the femoral model are set respectively. The K-wire model is regarded as a rigid body bound to the reference point, and its motion law is the same as the reference point motion law. Fixed constraints are set on the femoral model to realize the modeling of the actual scene of robot-assisted K-wire placement. The explicit dynamics analysis function provided by Abaqus software was used to analyze the dynamic interaction between the Kirschner wire model and the femoral model in the drilling environment. The radial force during the Kirschner wire drilling process was collected and its signal was analyzed. According to the finite element analysis model, the radial drilling force data under different spindle speeds, feed speeds, and angles between the Kirschner wire and the femur were collected to provide data support for the mechanical model.

4. The method according to claim 1, characterized in that: Based on the mechanical analysis geometric model and finite element analysis model data, a mechanical model of robot-assisted Kirschner wire bone drilling was constructed using response surface analysis to obtain the mathematical representation of the radial force of bone drilling and the spindle speed and feed speed, including: According to the mechanical analysis model of Kirschner wire bone drilling, the resultant force of Kirschner wire bone drilling can be decomposed into: radial force F R , tangential force F P , axial force F Q The axial force is generated by the feeding of the robotic arm and is responsible for maintaining the feeding of the Kirschner wire; the tangential component is generated by the rotation of the Kirschner wire and acts as a cutting force to cut the bone tissue; the radial component is generated by the insufficient contact between the tip of the Kirschner wire and the bone tissue, which will cause slippage in the initial stage of guide wire insertion. According to the relationship between the drilling force and the Kirschner wire rotation speed, the Kirschner wire feed speed, the angle between the Kirschner wire and the bone surface, and the finite element simulation data, the response surface method was used to establish a mechanical model, and the model regression equation was obtained as follows: F=3.13-0.60A-0.32B+0.16C-0.26AB-0.13AC+0.26BC-0.14A 2 +0.62B 2 -0.17C 2 A, B, and C represent the coding factors of the angle between the K-wire and the bone surface, the rotation speed of the K-wire, and the feeding speed of the K-wire, respectively.

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