Analysis method for artificial limb joint with concave spherical rough contact surface

Abstract

The embodiment of the invention discloses an analysis method for an artificial limb joint with a concave spherical rough contact surface, relates to the technical field of advanced manufacturing, and can efficiently analyze the non-fixed-axis sliding friction process of the artificial limb joint with the concave spherical rough contact surface. Therefore, the result whether the manufactured artificial limb joint is matched with the non-fixed-axis sliding friction process of the original skeleton joint of the human body or not is quickly fed back to the user, and the analysis result can be continuously improved according to parameter adjustment of the user, so that the artificial limb personalized customization efficiency for different people is improved.

Description

Technical Field

[0001] The invention relates to the field of advanced manufacturing technology, and in particular to an analysis method for a prosthetic joint with a concave spherical rough contact surface. Background Art

[0002] Human prosthetic joints are a common type of medical devices. Their complex multi-body structure, especially the unsteady friction torque at the joints, leads to a large number of complex dynamic phenomena, which have been highly valued by researchers. For example, some researchers have studied the influence of wheels on the motion law of the cable-traction ankle rehabilitation robot. By analyzing the robot's motion scheme under two working conditions, considering wheels and ignoring wheels, a mathematical model of the cable length considering wheels was established; some colleagues have proposed a human skeleton joint point estimation algorithm based on human posture characteristics under the constraints of human structure, and identified human behavior based on skeleton data; there is also a method to solve the coupling of rope-driven joint motion through mobile compensation, that is, the decoupling constraints are derived according to the motion coupling mechanism, and a two-degree-of-freedom rope-driven robot is designed accordingly, and the winch equation is used to establish a theoretical model of the influence of rope tension on joint rotation angle offset; and, there is also a basic For the ankle rehabilitation robot with 3-CPS / S parallel mechanism, the mathematical model of the mechanism is established using the screw theory, the input / output motion screw and the transmission / constraint force screw of the mechanism are derived, and the inverse position equation of the mechanism is obtained by the closed-loop vector method; when studying the human joint movement, the existing scheme also conducts a theoretical analysis of a rotating disk friction nanogenerator, establishes an angle sensing model of human joint movement, and derives the relationship between the electrical signal of the rotating disk friction nanogenerator and the rotor rotation angle under open and closed states; the DH parameter method is also used to establish the forward and inverse kinematic models of the exoskeleton robot in the sagittal plane, and the change of each joint is solved through posture transformation.

[0003] In the process of improving prosthetic joints through 3D printing technology, it is particularly important to analyze the kinematic characteristics of prosthetic joints efficiently and accurately. In particular, the production of prosthetic limbs often requires customized design and improvement for each disabled person, and each person's motion characteristics and actual usage are also very different. Therefore, it is necessary to develop an analysis method that can effectively present the relative displacement, motion characteristics of prosthetic joints, and the dynamic characteristics of the prosthetic rigid body under the action of time-varying sliding friction torque.

[0004] However, the existing analysis methods are still insufficient for the personalized customization of prosthetic joints, especially the non-fixed axis sliding friction process of prosthetic joints with concave spherical rough contact surfaces. This is the real-time stress state of human joints in real situations. Whether the manufactured prosthetic joints match the non-fixed axis sliding friction process of the original human bone joints directly determines the comfort of the prosthetic joints after installation. However, few research groups have conducted in-depth research in this area. Therefore, the current manufacturing of prosthetic joints still uses a trimming solution based on fixed size models, which requires doctors to have very rich experience, and therefore it is difficult to further improve the efficiency of personalized customization of prosthetics for different people. Summary of the invention

[0005] The embodiment of the present invention provides an analysis method for a prosthetic joint with a concave spherical rough contact surface, which can improve the efficiency of personalized customization of prosthetics for different people.

[0006] To achieve the above object, the embodiments of the present invention adopt the following technical solutions:

[0007] An analysis method for a prosthetic joint with a concave spherical rough contact surface, comprising:

[0008] S1. Establishing a prosthetic joint analysis model, wherein the prosthetic joint analysis model includes: a ball-rod rigid body mechanics model and a rough concave spherical surface mechanics model;

[0009] S2. Receive the vital sign data of the human body uploaded by the user terminal, convert the vital sign data into model parameters, and input them into the ball-rod rigid body model and the rough concave spherical surface model respectively to obtain the mechanical parameters of the joint surface of the human body, wherein the vital sign data include: bone density, the size of the articular head and the articular fossa constituting the articular surface; the size data of the articular head and the articular fossa include: the spherical radius of the articular head, the length of the bone connecting the articular head and the circular cross-sectional radius; the equivalent curvature radius of the micro-convex bodies on the rough concave spherical surface of the articular fossa, the area density of the micro-convex bodies, the Young's modulus of the rough concave spherical surface material, the Poisson's ratio of the rough concave spherical surface material and the hardness of the rough concave spherical surface material.

[0010] S3, manufacturing a prosthetic joint sample by 3D printing, and collecting sample data of the prosthetic joint sample, wherein the sample data includes: material density of the sample, and dimensions of the articular head and articular fossa of the articular surface constituting the prosthetic joint sample;

[0011] S4, converting the sample data into model parameters and inputting them into the ball-bar rigid body mechanics model and the rough concave spherical surface mechanics model respectively, to obtain the mechanical parameters of the joint surface of the prosthetic joint sample;

[0012] S5. Return the mechanical parameters of the human body and the mechanical parameters of the prosthetic joint sample to the user terminal, then modify the sample data according to the user operation and recalculate the mechanical parameters of the prosthetic joint sample until the mechanical parameters of the prosthetic joint sample are consistent with the mechanical parameters of the human body.

[0013] In S1, a ball-and-rod rigid body mechanical model is established, including: using a rigid smooth sphere to represent the joint head, using a cylindrical straight rod to represent the bones connecting the joint head, and establishing a dynamic model of the ball-and-rod rigid body in the body coordinate system: Where J represents the inertia tensor of the ball-rod rigid body relative to the origin of the body coordinate system, ω represents the angular velocity vector of the ball-rod rigid body relative to the body coordinate system, M represents the resultant external torque, J represents the inertia matrix of J relative to the body coordinate system, ω is the column vector expression of ω, represents the coordinate matrix of ω, M is the column vector expression of the resultant external torque.

[0014] According to the dynamic model of the ball-rod rigid body in the body coordinate system, the non-fixed axis motion model of the ball-rod rigid body is established: Λ represents the Euler column vector, represents the coordinate matrix of Euler parameters, T represents the matrix transpose operator, ω 4 represents the 4th-order array of ω; the “dot” on the parameter symbol represents the derivative of the parameter with respect to time t. A, B, and C are the principal moments of inertia of the ball-rod rigid body in three directions. ω x ,ω y ,ω z is the projection of the angular velocity vector ω in the body coordinate system, M x 、M y 、M z is the projection of the moment M in the body coordinate system, M = M sl +M c represents the total external torque, where M sl is the torque generated by sliding friction, M c is the external control torque acting on the ball-rod rigid body;

[0015] p1, p2, and p3 are the projections of the instantaneous rotation axis p in the body coordinate system, and θ represents the rotation angle of the body coordinate system of the ball-and-stick rigid body relative to the initial body coordinate system around the instantaneous rotation axis p.

[0016] In S1, a rough concave spherical surface mechanical model is established, including: dividing the rough concave spherical surface into micro-rings, and establishing a load model generated by the deformation of micro-convex bodies on the micro-rings: dF r p They are the contact loads caused by elastic, elastoplastic and plastic deformation of the micro asperities on the micro ring.

[0017] The moment model of the micro-ring is further established based on the load model: are the sliding friction torques corresponding to elastic, elastoplastic and plastic deformation on the micro-ring respectively; the mechanical model of the rough concave spherical surface is: A r Represents the area of ​​the microannulus.

[0018]

[0019] is the equivalent Young's modulus of the rough concave spherical material, E a is the Young's modulus of the rough concave spherical material, ν a is the Poisson's ratio of the rough concave spherical material, η a is the area density of the micro-asperities, R a is the equivalent radius of curvature of the convex body, dA r represents the area of ​​the micro-circle, χ(r) represents the completeness of the micro-circle, r is the radius of the micro-circle, H a represents the hardness of the rough concave spherical surface material, k represents the average contact pressure coefficient, δ represents the normal displacement of the micro-convex body, z represents the relative height of a single micro-convex body compared to the average height of the micro-convex body, and d0 represents the distance between the average height of the micro-convex body and the smooth spherical surface;

[0020] f(δ) is the template function, δ1 represents the critical normal deformation at the initial yield point, δ2 represents the critical normal deformation when complete plastic deformation occurs, and the height of the microconvex body σ s The ratio of the standard deviation σ of the rough surface distribution is β a is the surface morphology parameter of the rough concave spherical surface, φ(z) is the normal distribution function,

[0021] μ s Represents the sliding friction coefficient.

[0022] The embodiments of the present invention provide a method for efficiently analyzing the non-fixed-axis sliding friction process of a prosthetic joint containing a concave spherical rough contact surface, thereby quickly providing users with feedback on whether the non-fixed-axis sliding friction process of the manufactured prosthetic joint matches that of the original skeletal joint of the human body, and can also continuously improve the analysis results based on user parameter adjustments, thereby improving the efficiency of personalized customization of prosthetics for different people. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in 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. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0024] Figure 1 Schematic diagram of a prosthetic joint model with a concave spherical rough contact surface.

[0025] Figure 2 Schematic diagram of the contact deformation of a micro-convex body and a rigid spherical surface.

[0026] Figure 3 Schematic diagram of micro-circular division of a rough concave spherical surface.

[0027] Figure 4 Schematic diagram of the fixed-axis rotation of the ball-and-stick rigid body around the z-axis.

[0028] Figure 5 Schematic diagram of the fixed-axis rotation of the ball-and-stick rigid body around the y-axis.

[0029] Figure 6 Schematic diagram of the fixed-point rotation of a ball-and-stick rigid body towards rest.

[0030] Figure 7 Schematic diagram of irregular fixed-point rotation of the ball-and-stick rigid body. DETAILED DESCRIPTION

[0031] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. The embodiments of the present invention will be described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention. It can be understood by those skilled in the art that, unless specifically stated, the singular forms "one", "one", "said" and "the" used herein may also include plural forms. It should be further understood that the term "including" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their groups. It should be understood that when we say that an element is "connected" or "coupled" to another element, it can be directly connected or coupled to other elements, or there may also be intermediate elements. In addition, the "connection" or "coupling" used here may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items. It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as generally understood by those of ordinary skill in the art to which the present invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0032] The embodiment of the present invention provides an analysis method for a prosthetic joint with a concave spherical rough contact surface during a sliding friction process, which can accurately describe the relative displacement and motion characteristics of the prosthetic joint, and effectively reveal the dynamic influence of non-fixed axis sliding friction on the prosthetic rigid body. An accurate model that can simulate the dynamic behavior of a prosthetic joint with a concave spherical rough contact surface during a sliding friction process is derived. The model can effectively present the relative displacement and motion characteristics of the prosthetic joint, as well as the dynamic characteristics of the prosthetic rigid body under the action of time-varying sliding friction torque.

[0033] In the embodiment of the present invention, a prosthetic joint with a concave spherical rough contact surface is modeled. In order to more intuitively demonstrate the relative motion of such a joint, it is assumed that the acetabulum at the upper end of the prosthetic joint is a rough concave spherical surface and is fixed, and the lower end is a ball-rod rigid body that can rotate around any axis, such as Figure 1 The ball-rod rigid body is formed by a rigid smooth sphere (representing the femoral head) and a cylindrical straight rod (representing the femur), and the radius of the sphere is R. s , the density of the straight rod is ρ r, length is l r , the radius of the cross section is R r , the smooth spherical surface is in contact with a fixed rough concave spherical surface with the same radius. Fix the body coordinate system o-xyz to the ball-rod rigid body, and assume that the ball-rod rigid body rotates around the time-varying p axis at an instantaneous angular velocity ω. Obviously, when the ball-rod rigid body and the concave spherical surface have relative motion, a sliding friction torque will be generated, and the magnitude and direction of the friction torque are different for different instantaneous rotation axes.

[0034] For the ball-rod rigid body at the lower end, according to the Euler equation, the dynamic equation can be listed in the body coordinate system o-xyz

[0035]

[0036] Wherein, “point” represents the derivative with respect to time t, J represents the inertia tensor of the ball-rod rigid body with respect to point o, ω represents the angular velocity vector of the ball-rod rigid body relative to the body coordinate system o-xyz, and M=M sl +M c represents the total external torque, where M sl is the torque generated by sliding friction, M c is the external control torque acting on the ball-rod rigid body. For the convenience of calculation, we can fix the origin o of the body coordinate system at the center of mass of the smooth sphere, and the z axis coincides with the axis of the cylindrical straight rod, that is, we choose a principal axis coordinate system as the body coordinate system, then the dynamic equation (1) can be written as the following matrix form:

[0037]

[0038] in, is the inertia matrix of the inertia tensor J relative to the body coordinate system o-xyz, A, B, C are called the principal moments of inertia of the ball-rod rigid body, is the column vector expression of the angular velocity vector ω, ω x ,ω y ,ω z is the projection of the angular velocity vector ω in the body coordinate system, is called the coordinate matrix of the angular velocity vector ω, is the column vector expression of the resultant external torque, M x 、M y 、M z is the projection of the moment M in the body coordinate system.

[0039] In order to further demonstrate the motion law of the ball-rod rigid body, let p1, p2, and p3 be the projections of the instantaneous rotation axis p in the body coordinate system. The body coordinate system of the current ball-rod rigid body is obtained by rotating θ around the instantaneous rotation axis p relative to the initial body coordinate system. By introducing the following quaternion

[0040]

[0041] The kinematic equation describing the ball-rod rigid body is obtained

[0042]

[0043] in

[0044]

[0045] They are respectively called the Euler column vector, the coordinate matrix of Euler parameters, and the 4th-order matrix of the angular velocity vector ω.

[0046] Note that when the instantaneous angular velocity ω is not equal to 0, the sliding friction torque is equal to the maximum static friction torque; and when the instantaneous angular velocity ω is equal to 0, the sliding friction torque is equal to the current static friction or the reaction torque acting on the external control torque of the ball-bar rigid body, as shown in the following formula:

[0047]

[0048] For the non-fixed axis motion of the ball-rod rigid body, the sliding friction torque is usually not a constant. The following is a method for calculating the time-varying sliding friction torque.

[0049] The rough concave spherical surface and the smooth sphere in contact with each other are partially enlarged to discuss the contact mechanics between the micro-convex body on the concave spherical surface and the smooth contact surface. Since the size of the micro-convex body is much smaller than the smooth sphere, it is assumed that the local sphere in contact with the micro-convex body is a plane, such as Figure 2 As shown. Assume R a is the equivalent radius of curvature of the micro-convex body, z is the relative height of a single micro-convex body compared to the average height of the micro-convex body, d0 is the distance between the average height of the micro-convex body and the smooth spherical surface, δ = z-d0 is the normal displacement of the micro-convex body, η a is the area density of micro-asperities.

[0050] According to Hertz's theory, the contact area between a single microconvex body and the spherical surface can be calculated as:

[0051] A a =πR a δ (7)

[0052] Based on this, the normal contact load of a single asperity can be written as

[0053]

[0054] in, is the equivalent Young's modulus of the rough concave spherical material, E a is the Young's modulus of the rough concave spherical material, v a is the Poisson's ratio of the rough concave spherical material.

[0055] In order to calculate the torque generated by the ball-rod rigid body and the rough concave spherical surface in sliding friction, the intersection point o of the instantaneous rotation axis p and the rough concave spherical surface is p As the center of the circle, the rough concave spherical surface in contact is divided into a series of micro-circular rings, such as Figure 3 As shown. Since the intersection point o p Usually not at the center o of the rough concave spherical surface a Coincidentally, there are complete micro-circles and incomplete micro-circles. At the same time, since the instantaneous rotation axis p is time-varying, the division of each instantaneous micro-circle is also different. Obviously, the normal contact load of each micro-convex body on the same micro-circle to the moment centroid o p The distance is the same.

[0056] Here, we first calculate the normal contact load generated by the deformation of the micro-convex body on the micro-ring

[0057]

[0058] in, are the contact loads caused by elastic, elastoplastic and plastic deformation of the micro-convex body on the micro-annulus, respectively. Their specific expressions are written as

[0059]

[0060] Among them, dA r represents the area of ​​the micro-circle, χ(r) represents the completeness of the micro-circle, r is the radius of the micro-circle, H a represents the hardness of the rough concave spherical surface material, k represents the average contact pressure coefficient, is the normal distribution function, the sample function can be written as

[0061]

[0062] here, represents the critical normal deformation at the initial yield point, and δ2=110δ1 represents the critical normal deformation when complete plastic deformation occurs. The ratio of the height of the micro-convex body to the standard deviation of the rough surface distribution is

[0063]

[0064] Among them, β a =0.0339 is the surface morphology parameter of the rough concave spherical surface.

[0065] At this point, the torque generated by the micro-ring due to sliding friction relative to the instantaneous rotation axis p can be written as

[0066]

[0067] in, are the sliding friction moments corresponding to elastic, elastoplastic and plastic deformation on the micro-ring, respectively. Their specific expressions are written as

[0068]

[0069] Therefore, the total sliding friction torque can be written as

[0070]

[0071] At this point, only equations (2) and (4) need to be linked to complete the modeling of the prosthetic joint with a concave spherical rough contact surface with non-fixed axis rotation. The modeling method proposed in the present invention can accurately describe the dynamics of the prosthetic joint.

[0072] The actual effect of this embodiment is verified by specific experimental calculations below:

[0073] Consider a prosthetic joint. Let the radius of the smooth sphere representing the femoral head be R. s =0.025m, representing the straight rod density of the femur as ρ r =7.85×10 3 kg / m 3 , length l r =0.3m, the radius of the circular section is R r =0.0125m.

[0074] Assume that the equivalent curvature radius of the microconvex body on the rough concave spherical surface representing the acetabulum is R a =5.427×10 -6 m, the area density of the micro-convex body is η a =4.459×10 10 m -2 , the Young's modulus of the rough concave spherical material is E a =207GPa, the Poisson's ratio of the rough concave spherical material is ν a =0.29, the hardness of the rough concave spherical material is H a =1.96GPa, the average contact pressure coefficient is k=0.4.

[0075] Example 1: Select the initial angular velocity vector of the ball-rod rigid body as ω0 = [00-20rad / s] T , that is, the ball-rod rigid body rotates only around the z-axis. According to equations (13)-(15), it can be calculated that when rotating around the z-axis, the torque generated by sliding friction is M sl =0.1458Nm, so the external control torque can be kept constant at M c =[000.15Nm] T , which is obviously greater than the current sliding friction torque. The numerical simulation results are as follows Figure 4As shown, the rigid body has no rotation relative to the x-axis and y-axis of the body coordinate system. Figure 4 (a) is the time history of the angular velocity of the ball-rod rigid body. It can be observed that under the action of the reverse torque on the z-axis, the rigid body quickly changes from clockwise to counterclockwise rotation. Figure 4 (b) is the time history of the sliding friction torque. When the direction of the angular velocity of the ball-bar rigid body changes, the direction of the sliding friction torque also changes.

[0076] Example 2: Select the initial angular velocity vector of the ball-rod rigid body as ω0 = [0-20rad / s 0] T , that is, the ball-rod rigid body rotates only around the y-axis. It can be calculated that when rotating around the y-axis, the torque generated by sliding friction is M sl =0.2119Nm, so the external control torque in Example 1 cannot be driven. At this time, the external control torque can be set to be constant at M. c =[00.25Nm 0] T The numerical simulation results are as follows: Figure 5 shown. Figure 5 (a) is the time history of the angular velocity. It can be observed that under the action of the reverse torque on the y-axis, the rigid body changes from clockwise to counterclockwise rotation. Figure 5 (b) is the time history of the sliding friction torque. When the direction of the angular velocity of the ball-bar rigid body changes, the direction of the sliding friction torque also changes.

[0077] Example 3: Select the initial angular velocity vector of the ball-rod rigid body as ω0 = [-20rad / s 0-20rad / s] T , the external control torque is M c =[000.16Nm] T The numerical simulation results are as follows: Figure 6 As shown, this is a typical fixed-point motion. Figure 6 (a) is the time history of angular velocity, and it is found that the angular velocity eventually tends to 0. Figure 6 (b) is the time history of the ball-rod rigid body quaternion, which eventually tends to a constant value. Figure 6 (c) is the time history of the control torque and sliding friction torque. It can be found that the external control torque remains unchanged, while after 8.5s, the rigid body remains stationary and the sliding friction torque also oscillates within a certain range. This example shows that insufficient external control torque output may cause the prosthetic joint to fail to move.

[0078] Example 4: Select the initial angular velocity vector of the ball-rod rigid body as ω0 = [-20rad / s 0-20rad / s] T , the external control torque is M c =[000.17Nm] T, this input torque is only slightly different from Example 3. The numerical simulation results are shown in Figure 7 shown. Figure 7 (a) is the time history of the angular velocity. It can be found that the angular velocity does not approach 0. Figure 7 (b) is the time history of the quaternion of the ball-rod rigid body, and the quaternion changes irregularly. Figure 7 (c) is the time history of the control torque and the sliding friction torque. It can be found that the control torque remains unchanged, and the sliding friction torque also oscillates back and forth. This example shows that it is necessary to consider the sliding friction torque of the prosthetic joint.

[0079] The above four groups of examples fully demonstrate the relative displacement and motion characteristics of the prosthetic joints under different initial conditions. The numerical results are consistent with the actual situation, thereby illustrating the correctness of the prosthetic joint model constructed by the present invention.

[0080] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The above is only a specific implementation method of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or replacements that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. An analysis method for a prosthetic joint with a concave spherical rough contact surface, characterized in that: include: S1. Establishing a prosthetic joint analysis model, wherein the prosthetic joint analysis model includes: a ball-rod rigid body mechanics model and a rough concave spherical surface mechanics model; S2, receiving the physical sign data of the human body uploaded by the user terminal, converting the physical sign data into model parameters, and inputting the physical sign data into the ball-bar rigid body model and the rough concave spherical surface model respectively, to obtain the mechanical parameters of the human joint surface, wherein the physical sign data include: bone density, and the size of the articular head and the articular fossa constituting the articular surface; S3, manufacturing a prosthetic joint sample by 3D printing, and collecting sample data of the prosthetic joint sample, wherein the sample data includes: material density of the sample, and dimensions of the articular head and articular fossa of the articular surface constituting the prosthetic joint sample; S4, converting the sample data into model parameters and inputting them into the ball-bar rigid body mechanics model and the rough concave spherical surface mechanics model respectively, to obtain the mechanical parameters of the joint surface of the prosthetic joint sample; S5. Return the mechanical parameters of the human body and the mechanical parameters of the prosthetic joint sample to the user terminal.

2. The method according to claim 1, characterized in that: In S1, a ball-bar rigid body mechanics model is established, including: The joint head is represented by a rigid smooth sphere, and the bones connecting the joint head are represented by a cylindrical straight rod. The dynamic model of the ball-rod rigid body in the body coordinate system is established: Where J represents the inertia tensor of the ball-rod rigid body relative to the origin of the body coordinate system, ω represents the angular velocity vector of the ball-rod rigid body relative to the body coordinate system, M represents the resultant external torque, J represents the inertia matrix of J relative to the body coordinate system, ω is the column vector expression of ω, represents the coordinate matrix of ω, M is the column vector expression of the resultant external torque.

3. The method according to claim 2, characterized in that Also includes: According to the dynamic model of the ball-rod rigid body in the body coordinate system, the non-fixed axis motion model of the ball-rod rigid body is established: Λ represents the Euler column vector, represents the coordinate matrix of Euler parameters, T represents the matrix transpose operator, ω 4 represents the 4th-order array of ω; the "dot" on the parameter symbol represents the derivative of the parameter with respect to time t.

4. The method according to claim 2 or 3, characterized in that: A, B, and C are the principal moments of inertia of the ball-rod rigid body in three directions. ω x ,ω y ,ω z is the projection of the angular velocity vector ω in the body coordinate system, M x 、M y 、M z is the projection of the moment M in the body coordinate system, M = M sl +M c represents the total external torque, where M sl is the torque generated by sliding friction, M c is the external control torque acting on the ball-rod rigid body.

5. The method according to claim 4, characterized in that p1, p2, and p3 are the projections of the instantaneous rotation axis p in the body coordinate system, and θ represents the rotation angle of the body coordinate system of the ball-and-stick rigid body relative to the initial body coordinate system around the instantaneous rotation axis p.

6. The method according to claim 1, characterized in that In S1, a rough concave spherical surface mechanical model is established, including: The rough concave spherical surface is divided into micro-rings, and the load model generated by the deformation of the micro-convex body on the micro-ring is established: They are the contact loads caused by elastic, elastoplastic and plastic deformation of the micro asperities on the micro ring.

7. The method according to claim 1, characterized in that Also includes: The moment model of the micro-ring is further established based on the load model: are the sliding friction torques corresponding to elastic, elastoplastic and plastic deformation on the micro-ring respectively; the mechanical model of the rough concave spherical surface is: A r Represents the area of ​​the microannulus.

8. The method according to claim 6 or 7, characterized in that: is the equivalent Young's modulus of the rough concave spherical material, E a is the Young's modulus of the rough concave spherical material, v a is the Poisson's ratio of the rough concave spherical material, η a is the area density of the micro-asperities, R a is the equivalent radius of curvature of the convex body, dA r represents the area of ​​the micro-circle, χ(r) represents the completeness of the micro-circle, r is the radius of the micro-circle, H a represents the hardness of the rough concave spherical surface material, k represents the average contact pressure coefficient, δ represents the normal displacement of the micro-convex body, z represents the relative height of a single micro-convex body compared to the average height of the micro-convex body, and d0 represents the distance between the average height of the micro-convex body and the smooth spherical surface; f(δ) is the template function, δ1 represents the critical normal deformation at the initial yield point, δ2 represents the critical normal deformation when complete plastic deformation occurs, and the height of the microconvex body σ s The ratio of the standard deviation σ of the rough surface distribution is β a is the surface morphology parameter of the rough concave spherical surface, φ(z) is the normal distribution function, 9. The method according to claim 8, characterized in that μ s Represents the sliding friction coefficient.

10. The method according to claim 1, characterized in that The dimensional data of the articular head and the articular socket include: the spherical radius of the articular head, the length of the bone connecting the articular head and the circular cross-sectional radius; the equivalent curvature radius of the micro-asperities on the rough concave spherical surface of the articular socket, the area density of the micro-asperities, the Young's modulus of the rough concave spherical surface material, the Poisson's ratio of the rough concave spherical surface material and the hardness of the rough concave spherical surface material.

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