CN112926182B

CN112926182B - Method and terminal for evaluating work efficiency of endurance running shoes

Info

Publication number: CN112926182B
Application number: CN202110064085.XA
Authority: CN
Inventors: 范毅方; 冯连世; 樊瑜波; 方千华; 林文弢; 陈学灿
Original assignee: Fujian Normal University
Current assignee: Fujian Normal University
Priority date: 2021-01-18
Filing date: 2021-01-18
Publication date: 2023-05-05
Anticipated expiration: 2041-01-18
Also published as: CN112926182A

Abstract

The invention discloses a method for evaluating work efficiency of a endurance running shoe, which comprises the steps of obtaining first test data of a target endurance running shoe, wherein the first test data comprise target parameters of the target endurance running shoe; acquiring second test data, wherein the second test data comprises foot print data of a target subject and foot tomograms of the target subject; the foot print data are standardized to obtain standard foot print data, and the foot data are standardized according to the foot tomographic image to obtain standardized foot data; performing a simulation experiment according to the standard foot print data, the standardized foot data and the target parameters to obtain an experimental result, and analyzing the experimental result to obtain an evaluation result of the target endurance running shoes; according to the invention, a simulation experiment is carried out, comparison of experimental results is convenient after standardization, experimental data under various preset scenes are provided for various parameters to be tested of the running shoes, and data support is provided for the work efficiency optimization design of the endurance running shoes.

Description

Method and terminal for evaluating work efficiency of endurance running shoes

Technical Field

The invention relates to the field of running shoe design, in particular to a method and a terminal for evaluating work efficiency of endurance running shoes.

Background

The optimization of the skill of running by means of a precision instrument is not the "root-finding" as described by rowland. Why is the "tightening of the ankle" to increase the supporting reaction force, why is the increase of the reaction force to increase the running speed? This is not explained by the researchers. In addition, the "endurance running hypothesis" (Bramble et al, 2004) of milestones (Pontzer, 2019) suggests that the use of the full-sole, forefoot landing approach can reduce lower limb motor injuries (Bramble et al, 2010), but the biomechanical mechanism behind it is not explored.

The human beings invent the language and realize communication; characters are created, and civilization is recorded; whereas mathematics created by humans are the tools for interpreting nature, mathematics thus bear the full natural science description (Stewart, 1998). In the medical field there is no universally applicable equation, only a large number of observations, locally valid knowledge (Garner, 2014), but the big data is not equal to the scientific law, since the big data itself does not explain itself (Ji Leilei, 2015; wilczek, 2019). In the field of physics, scientists use several equations to interpret everything (Garner, 2014), for example, based on BCS theory (Bardeen, cooper, schrieffer) and numerical modeling calculations, predict LaH10 to be a superconducting material, whereas LaH10 formed at 170 atmospheres is not only a superconducting material, but also so far the most approximate room temperature (Liu, et al, 2017). As another example, arikan 2008 established a mathematical method of polarization codes (Arikan, 2008), 2018, and developed a 5G communication technology based on this method, thereby occupying a powerful position of the 5G technology standard war.

Mathematics (equations) are also important in biomechanical studies, and kinetic equations can answer "how and why" (novachock, 1998). To date, almost all equations for running simplify the human body into particles (systems) (Haugen et al, 2019), and even to the inverted pendulum clock (Srinivasan, 2004), particle spring models (Geyer et al, 2005) reduce the support reaction force to a first order tensor of point force without exception. The differences in the manner of landing are kinetic analysis problems with respect to the lower limb structure, whereas the injuries are stress-strain problems with respect to bones, muscles and joints (Brown, 2014), which are biomechanical problems involving second order tensors.

Seemingly, human gait appears to be symmetrical. However, the various methods of measurement show different results. Motion capture, force stations, plantar pressure insoles, and ground pad pressure test systems all show different gait patterns for everyone, characterized by minor asymmetries in stride pattern, force and acceleration (Emerging Technology from the arXiv, 2009).

These characteristics are taste-seeking, but this also greatly complicates understanding gait, making it impossible for biomechanics to agree on the basic characteristics of gait. It seems to be surprising, but no consensus has been reached about the invariant parameters (gait constants) that all human walkers must share (Emerging Technology from the arXiv, 2009).

Without gait constants, it would be difficult to accurately model gait, nor agree on how to best recover the impaired gait. Gait analysis dynamics equations can be established according to boundary conditions and constraint forms of human running. When the landing timings of the left and right feet with respect to each other are not determined, the kinetic equation is an indefinite equation Diophantine Equation), which is not a universally applicable equation. The analysis of the function of the endurance running shoes is inexpedient without the general applicable equation.

The landing mode determines the work efficiency of endurance running. With respect to the manner in which endurance runs, previous studies have been largely focused around the foot landing patterns (three basic landing patterns, heel, ball and forefoot) (Lieberman et al, 2010), which have been largely agreed in the industry, but have been controversial with respect to each other.

In fact, the diversity of the transverse (front transverse composed of 5 metatarsal bottoms, rear transverse composed of inner wedge, middle wedge, outer wedge and cuboid) and longitudinal (medial and lateral longitudinal and basal longitudinal) arches makes the fall-down approach a "quaternion" problem (hamilton generalizes the complex numbers, introduces quaternions, describes the plane rotation problem). Describing rotation in three dimensions requires a four-dimensional quantity, the biggest feature of the quaternion is that the exchange law is not satisfied (Kruglov, 2001), which means that the ergonomics of the different landing patterns are different. Not only does Galois demonstrate that the 5-degree equation has no general solution, but also solves two of the three major drawing problems of ancient Greek, namely "unable to trisect any angle" and "times cube" are impossible. The group theory pulls the curtain of modern algebra. However, the group theory solves the problem of insufficient floor order because the order of rotation of the feet remains an undisolved puzzle because it does not satisfy either the exchange or the combination laws. Quaternion is known as the magic of hamilton (Houts, 1973). Gait constants and quaternions are rocentre stone tablets for describing and reading endurance running shoe functions and work efficiency.

The greatest difference in endurance running shoes is the requirement for their ergonomics (ergonomics, interactions between foot, shoe and environment), the core function of which is to increase running speed, and to guide the pleasure of the sport. While designing various problems in endurance running shoes requires a generalized equation of dynamics of endurance running to solve.

Disclosure of Invention

The technical problems to be solved by the invention are as follows: the method for evaluating the work efficiency of the running shoes for endurance running is provided, and a model for evaluating the work efficiency of the running shoes for endurance running is provided.

In order to solve the technical problems, the invention adopts a technical scheme that:

a method for evaluating work efficiency of endurance running shoes comprises the following steps:

s1, acquiring first test data of a target endurance running shoe, wherein the first test data comprise target parameters of the target endurance running shoe;

s2, acquiring second test data, wherein the second test data comprise foot print data of a target subject and foot tomograms of the target subject;

s3, normalizing the foot print data to obtain standard foot print data, and normalizing the foot data according to the foot tomographic image to obtain standardized foot data;

s4, performing simulation experiments according to the standard foot print data, the standardized foot data and the target parameters to obtain experimental results, and analyzing the experimental results to obtain the evaluation results of the target endurance running shoes.

In order to solve the technical problems, the invention adopts another technical scheme that:

the endurance running shoe work efficiency evaluation terminal comprises a memory, a processor and a computer program which is stored in the memory and can run on the processor, wherein the processor realizes the following steps when executing the computer program:

The invention has the beneficial effects that: the foot print data and the foot tomographic image of the target subject are acquired and then standardized, so that the foot print data and the foot tomographic image of the target subject can be directly subjected to simulation experiments with target parameters of the target endurance running shoes, comparison of experimental results is facilitated after standardization, limited target subjects can provide data with wider application range, experimental data in various preset scenes can be provided for various required test parameters of the running shoes, and data support is provided for the work efficiency optimization design of the endurance running shoes.

Drawings

FIG. 1 is a flow chart of steps of a method for evaluating the efficacy of a endurance running shoe according to an embodiment of the present invention;

fig. 2 is a schematic structural diagram of a endurance running shoe efficacy evaluation terminal according to an embodiment of the present invention;

FIG. 3 is a schematic diagram of three in-plane forces at different landing timings according to an embodiment of the present invention;

FIG. 4 is a diagram illustrating centroid speeds at different landing timings according to an embodiment of the present invention;

FIG. 5 is a schematic displacement diagram of different landing timings according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of mechanical energy at different landing timings according to an embodiment of the present invention;

FIGS. 7-9 are gait reports of three different subjects, respectively, in accordance with an embodiment of the invention;

FIGS. 10-12 are graphs showing the results of arch reconstruction by foot calcite;

FIG. 13 is a schematic view of a prior art footprint fossil corresponding to podocardite;

FIGS. 14-15 show the results of prior art studies on different landing patterns;

FIGS. 16-18 are gait analysis data for different landing modes according to embodiments of the present invention;

FIG. 19 is a diagram showing the force versus time for different landing modes according to an embodiment of the present invention;

FIG. 20 is a diagram showing the correspondence between acceleration and time in different landing modes according to an embodiment of the present invention;

FIG. 21 is a graph showing the velocity versus time for different landing modes according to an embodiment of the present invention;

FIG. 22 is a diagram showing the correspondence between displacement and time in different landing modes according to an embodiment of the present invention;

FIG. 23 is a diagram showing the mechanical energy versus time in different modes of falling according to an embodiment of the present invention;

FIG. 24 is a graph showing the normalized foot data according to an embodiment of the present invention;

FIGS. 25-27 are load normalization diagrams according to embodiments of the present invention;

FIG. 28 is a graph showing simulation results of various floor modes according to an embodiment of the present invention;

FIGS. 29-30 are graphs showing foot stress analysis results for barefoot and shoe wear in accordance with embodiments of the invention;

FIG. 31 is a graph showing the results of the analysis of the barefoot and Achilles tendon forces with shoes in accordance with the embodiments of the invention;

FIG. 32 is a chart showing the gait parameters of subject F convalescence;

FIG. 33 is a graph showing the gait parameters of subject G convalescence;

FIG. 34 is a chart showing the gait parameters of subject H at convalescence according to an embodiment of the invention;

FIG. 35 is a graph showing gait parameters of a healthy young and elderly person in accordance with an embodiment of the present invention

Description of the reference numerals:

1. a endurance running shoe efficacy evaluation terminal; 2. a processor; 3. a memory.

Detailed Description

In order to describe the technical contents, the achieved objects and effects of the present invention in detail, the following description will be made with reference to the embodiments in conjunction with the accompanying drawings.

Referring to fig. 1 and fig. 3-31, a method for evaluating work efficiency of a endurance running shoe is characterized by comprising the steps of:

From the above description, the beneficial effects of the invention are as follows: the foot print data and the foot tomographic image of the target subject are acquired and then standardized, so that the foot print data and the foot tomographic image of the target subject can be directly subjected to simulation experiments with target parameters of the target endurance running shoes, comparison of experimental results is facilitated after standardization, limited target subjects can provide data with wider application range, experimental data in various preset scenes can be provided for various required test parameters of the running shoes, and data support is provided for the work efficiency optimization design of the endurance running shoes.

Further, in S2, second test data is obtained, where the second test data includes footprint data of the target subject specifically includes:

foot print data of the target subject is obtained by the plantar pressure test equipment.

As can be seen from the above description, the plantar pressure test device is provided, and can acquire data such as pressure besides foot print image data, so that various analyses can be performed later.

Further, the plantar pressure test equipment comprises sensors arranged in an array;

the step of normalizing the foot print data in the step S3 to obtain standard foot print data includes:

the components of the foot print impulse in the x-axis and y-axis are calculated:

wherein ,Ip_ij Representing the sensor impulse of the sensor interacting with the foot, i, j representing the rank number of the sensor, respectively, (x, y) representing the position of the sensor;

the sensor impulse

wherein ,T_s Representing the support phase time, P _(i，j) (t) represents a pressure value of the sensor at position (i, j) at time t; (x, y) represents Ip _ij The position relative to the center of the foot print impulse, said center of foot print impulse being +.>

When Sigma xyIp _ij When the mark is zero, marking a vertical axis passing through the center of the foot print impulse as a foot print main axis;

Calculate the foot print impulse position (x _cl ，y _cl )：

wherein ,n_l Representing the number of sensors interacting with the foot at foot print length position l;

calculating the landing time and the lift-off time on the foot print spindle:

/>

wherein ,

respectively represents the landing time and the ground leaving time at the foot print length position l,

the landing time and the landing time of the sole position (x, y) are respectively indicated.

From the above description, it can be seen that the foot print spindle is calculated, and the uncorrelated influencing factors can be discharged for more accurate analysis according to the foot print spindle marking foot print impulse position, landing time and ground clearance time.

Further, the normalizing the foot data according to the foot tomographic image in S3 to obtain normalized foot data includes:

determining the mass center of the foot according to the foot tomogram, marking the mass center in the foot tomogram, and marking a first plane rectangular coordinate system and a first space rectangular coordinate system passing through the mass center;

rotating the first plane rectangular coordinate system by a first preset angle to obtain a standardized plane rectangular coordinate system;

and rotating the first space rectangular coordinate system by a second preset angle to obtain a standardized space rectangular coordinate system.

From the above description, after determining the centroid of the foot according to the foot tomogram, the two-dimensional plane rectangular coordinate system and the three-dimensional space rectangular coordinate system are standardized, and the data comparison can be performed more intuitively in the standardized coordinate system.

Further, the rotating the first plane rectangular coordinate system by a first preset angle to obtain a standardized plane rectangular coordinate system specifically includes:

rotating the first plane rectangular coordinate system by phi degrees to obtain a standardized plane rectangular coordinate system:

wherein ,I_x Representing moment of inertia on the x-axis, I _y Representing moment of inertia on the y-axis, I _xy Representing the product of inertia in the x-axis and y-axis:

where dA represents a planar element, ρ represents a gray value of the planar element, and (x, y) represents a position coordinate of the planar element.

From the above description, the rotation angle is determined according to the moment of inertia and the product of inertia, so as to realize the automatic standardization of the plane rectangular coordinate system;

further, the rotating the first space rectangular coordinate system by a second preset angle to obtain a standardized space rectangular coordinate system specifically includes:

and sequentially rotating the first space rectangular coordinate system along the x axis by an alpha angle, rotating the first space rectangular coordinate system along the y axis by a beta angle and rotating the first space rectangular coordinate system along the z axis by a gamma angle to obtain a standardized space rectangular coordinate system:

/>

wherein ,I_y Representing moment of inertia of voxel to y-axis in said first space rectangular coordinate system, I _z Representing moment of inertia of voxel to z-axis in said first space rectangular coordinate system, I _yz Representation ofThe product of inertia of the voxel on the y axis and the z axis in the first space rectangular coordinate system;

representing moment of inertia of voxel to x-axis in a second spatial rectangular coordinate system, +.>

Representing moment of inertia of the voxel to the z-axis in said second spatial rectangular coordinate system,/->

Representing the product of inertia of the voxel on the x-axis and the z-axis in the second space rectangular coordinate system; />

Representing moment of inertia of voxel to x-axis in a third spatial rectangular coordinate system, +.>

Representing moment of inertia of voxel to y-axis in said third spatial rectangular coordinate system,/->

Representing the product of inertia of the voxel on the x-axis and the y-axis in the third space rectangular coordinate system

The second space rectangular coordinate system is obtained after the first space rectangular coordinate system rotates around the x axis by an alpha angle; the third space rectangular coordinate system is obtained after the second space rectangular coordinate system rotates around a y-axis by beta angle;

from the above description, the rotation is sequentially performed according to the sequence of the x axis, the y axis and the z axis for standardization, and the automatic determination of the rotation angle is realized according to the moment of inertia and the product of inertia, so that the automatic standardization of the coordinate system is completed;

Further, the step S4 further comprises building a motion model of the foot bone:

marking a foot bone in the foot tomogram;

establishing a transformation matrix of the relative inertial reference system of the foot bones:

wherein ,S^(i，k) A coordinate transformation matrix representing the foot bones performing circular motion around an x-axis, a y-axis or a z-axis;

acquiring a position vector of the foot bone relative to an inertial reference system;

obtaining a foot mass center according to the transformation matrix and the position vector;

acquiring main moment of inertia of the foot bone relative to the mass center of the foot bone and an inertia tensor of the foot bone around the mass center of the link;

obtaining the moment of inertia I of the foot bone relative to an inertial reference system according to the main moment of inertia and the inertial tensor ^(o，k) ；

According to I ^(o，k) And the mass center of the foot obtains the main moment of inertia I of the foot relative to the mass center of the foot ^(c) ；

According to the mass center of the foot and the I ^(c) And (5) building a foot bone movement model.

From the above description, it is known that, unlike the prior art in which the feet are analyzed as a whole, the feet are split into structures composed of the feet bones, and a transformation matrix between the feet bones is constructed for analysis, so that finer data can be obtained;

further, in the step S4, a simulation experiment is performed according to the standard foot print data, the standardized foot data and the target parameter to obtain an experimental result specifically as follows:

And placing the standard foot print data, the standardized foot data and the target parameters into different model of the ground mode to obtain an experimental result.

The experimental results comprise stress, acceleration, speed and displacement of the feet.

According to the description, the target parameters are tested in the different landing mode models according to the standardized data, whether the target parameters of the running shoes with endurance reach the expected effect can be verified, and the target parameters can be compared with the data of the barefoot in the different landing mode models, so that richer data reference is provided for the design of the running shoes.

Further, the analyzing the experimental result in S4 includes:

obtaining experimental data in an experimental result, wherein the experimental data comprises the position of the landing time of one foot in the stride cycle of the other foot and the reaction force of the left/right support surface to the foot, and comparing the experimental data with a preset gait constant;

the gait constants are: the landing time of one foot is centered in the stride cycle of the other foot, and the left/right support faces are symmetrical with respect to the reaction force of the foot.

From the above description, it can be known whether the comparison time delay data reach the preset gait constant, so as to realize automatic analysis of the experimental result.

Referring to fig. 2, a endurance running shoe efficacy evaluation terminal includes a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor implements the following steps when executing the computer program:

Referring to fig. 1, a first embodiment of the present invention is as follows:

the method comprises the steps of obtaining second test data, wherein the second test data comprise foot print data of a target subject, and the second test data comprise the following specific steps:

acquiring foot print data of a target subject through plantar pressure test equipment;

the plantar pressure test equipment comprises sensors which are arranged in an array;

the step of normalizing the foot print data to obtain standard foot print data comprises the following steps:

(1) Calculating a foot print spindle and foot print impulse position, foot print landing time and foot print off-ground time on the foot print spindle:

wherein ,Ip_ij The sensor impulse of the sensor which is interacted with the foot is represented by i, j, the row number of the sensor is represented by the row number of the sensor, the plantar pressure acquisition system is a flat plate of L×W (L is the plate length and W is the plate width), the definition of a rectangular coordinate system is the same as that of a computer display, namely, the origin of coordinates is at the upper left corner, the y-axis direction is from top to bottom, the x-coordinate direction is from left to right, and (x, y) is Ip _ij A position on the plate;

the sensor impulse

When Sigma xyIp _ij When the mark is zero, marking a vertical axis passing through the center of the foot print impulse as a foot print main axis; specifically, assuming that the angular displacement of the foot print is alpha about a vertical axis passing through the impulse center of the foot print, an equation is established:

(I _x -I _y ) _α ＝∑[(x ² cosα-y ² sinα)-(x ² sinα+y ² cosα)]Ip _ij (2.2-2)

deriving equation (2.2-2) and letting the derivative be 0:

i.e.

The foot print morphology is asymmetric, which results in I always in equation 2.2-1 _x ≠I _y Exists. At [0, pi ]]Within the scope, an asymmetric foot print is achieved by limited rotation (around the moment of passing the foot printA vertical axis of rotation of the heart) can always be made to be Σxyip _ij Zero. At this time, the axis passing through the impulse center of the foot print is the main axis of the foot print;

calculate the foot print impulse position (x _cl ，y _cl )：

According to gait characteristics, the process of landing and landing the foot in running is continuous, namely the same position of the sole of the foot is landed and lifted once in one gait cycle;

wherein ,n_l Representing the number of sensors interacting with the foot at foot print length position l (where foot print length refers to the length of the distal phalange from the heel, starting at the first heel landing point and ending at the last phalange landing point);

calculating the landing time and the lift-off time on the foot print spindle:

wherein ,

respectively representing the landing time and the ground leaving time of the sole positions (x, y);

(2) Determining the mass center of the foot according to the foot tomogram, marking the mass center in the foot tomogram, and marking a first plane rectangular coordinate system and a first space rectangular coordinate system passing through the mass center;

(1) rotating the first plane rectangular coordinate system by a first preset angle to obtain a standardized plane rectangular coordinate system, wherein the standardized plane rectangular coordinate system is specifically as follows:

wherein dA represents a face element, ρ represents a gray value of the face element, and (x, y) represents a position coordinate of the face element;

specifically, the process of determining the phi angle is as follows:

the plane rectangular coordinate system passing through the mass center of the tomogram is expressed by oxy, the tomogram consists of finite plane microelements, and I is used _x ，I _y Respectively represent moment of inertia to x, y axis, I _xy Is the product of inertia, and the formula is:

where dA represents a surface element, ρ represents a gradation value of the surface element, and (x, y) represents a position coordinate of the surface element.

Rotating the coordinate system around the mass center of the tomographic image to form a new coordinate system ox _φ y _φ Coordinates of face infinitesimal (x _φ ，y _φ ) And (x, y) are the following relationships:

by using

Respectively represent the pair x _φ ，y _φ Moment of inertia of the shaft, the formula of which is:

substituting equation 2.5-2b into 2.5-3a to obtain

Substituting equations 2.5-2a into 2.5-3b yields:

equation 2.5-4 plus equation 2.5-5 gives

From equations 2.5-6, it can be seen that: the tomogram rotates around its centroid, and the sum of its moments of inertia is constant. This means that equations 2.5-6 are indefinite equations for which the following equations can be established:

Substituting equations 2.5-4 and 2.5-5 into equations 2.5-7 yields:

f(α)＝∫(x ² (sin ² φ-cos ² φ)-4xy sinφcosφ-y ² (sin ² φ-cos ² φ))ρdA(2.5-8)；

since 2sin Φcos Φ=sin 2 Φ, cos ² φ-sin ² Phi = cos 2 phi, substituting these relations into the square

Schemes 2.5-8 give:

f(φ)＝∫(-x ² cos 2φ-2xy sin 2φ+y ² cos 2φ)ρdA(2.5-9)

order the

The following equation is obtained

From equations 2.5-10, the following equations are derived

2sin 2φ∫x ² ρdA-4cos 2φ∫xyρdA-2sin 2φ∫y ² ρdA＝0(2.5-11)；

From equations 2.5-1 and 2.5-11:

2sin 2φI _y -4cos 2φI _xy -2sin 2φI _x ＝0(2.5-12)；

both sides of equations 2.5-12 are divided by 2cos 2 phi:

solving the inverse function of the tangent function to obtain:

(2) rotating the first space rectangular coordinate system by a second preset angle to obtain a standardized space rectangular coordinate system, which specifically comprises the following steps:

/>

wherein ,I_y Representing moment of inertia of voxel to y-axis in said first space rectangular coordinate system, I _z Representing moment of inertia of voxel to z-axis in said first space rectangular coordinate system, I _yz Representing the product of inertia of the voxel on the y-axis and the z-axis in the first space rectangular coordinate system;

Representing the product of inertia of the voxel on the x-axis and the z-axis in the second space rectangular coordinate system; / >

Representing moment of inertia of the voxel to the x-axis in a third spatial rectangular coordinate system,

specifically, the process of determining the alpha angle, the beta angle and the gamma angle includes:

1) Rotation about the x-axis

The tomographic reconstruction body consists of finite individual microelements and is represented by oxyz through a space rectangular coordinate system based on the mass center of the tomographic reconstruction body, and I is used for _x ，I _y ，I _z The moments of inertia for the x, y, z axes are shown, respectively.

The moment of inertia of the body is:

inertia product of body:

where dV represents the voxel, ρ represents the gray value of the voxel, and (x, y, z) represents the position coordinates of the voxel.

Rotating the body coordinates of the mass center of the reconstructed body around the x-axis by alpha to form a new coordinate system ox _α y _α z _α Coordinates of voxel (x _α ，y _α ，z _α ) And (x, y, z) are in the following relationship:

substituting equations 2.5-16b and 2.5-16c into moments of inertia relative to the x-axis

In (1), the following steps are obtained: />

From equations 2.5-17, the moment of inertia about the x-axis is constant.

Substituting equations 2.5-16a, 2.5-16b, and 2.5-16c into the sum of the moments of inertia relative to the y-axis and the z-axis

In (1), the following steps are obtained:

from equations 2.5-17, equations 2.5-18 can be expressed as:

by equations 2.5-19, rotation about the x-axis has invariance to the sum of the moments of inertia about the y-axis and the z-axis. In conjunction with equations 2.5-17, the moment of inertia of the tomogram reconstruction has invariance by rotating about the x-axis.

Substituting equations 2.5-16a and 2.5-16c into

In (1), the following steps are obtained:

substituting equations 2.5-16a and 2.5-16b into

In (1), the following steps are obtained:

the following equation is established:

from equations 2.5-20 and 2.5-21, equations 2.5-22 can be expressed as:

f(α，β，γ) _α ＝∫(y ² (sin ² α-cos ² α)+4yz sinαcosα+z ² (cos ² α- sin2αρdV(2.5-23)

since 2sin α cos α=sin 2α, cos ² α-sin ² α=cos 2α, equations 2.5-23 can be expressed as:

f(α，β，γ) _α ＝∫(-y ² cos 2α+2yz sin 2α+z ² cos 2α)ρdV(2.5-24)；

order the

Equations 2.5-24 become: />

Thus there is

sin 2α∫y ² ρdV+2cos 2α∫yzρdV-sin 2α∫z ² ρdV＝0(2.5-26)

Due to sin 2 alpha ≡x ² ρdV-sin 2α∫x ² ρdV＝0(2.5-27)；

Substituting equations 2.5-27 into equations 2.5-26 yields the following equations:

sin 2α∫y ² ρdV+sin 2α∫x ² ρdV+2cos 2α∫yzρdV-sin 2α∫z ² ρdV- sin2ax2ρdV＝0(2.5-28)；

from equations 2.5-14, equations 2.5-28 can be expressed as:

sin 2αI _z +2cos 2αI _yz -sin 2αI _y ＝0(2.5-29)；

equation 2.5-27 is divided by cos 2α on both sides to give:

tan 2αI _z +2I _yz -tan 2αI _y ＝0(2.5-30)；

further, there are:

solving the inverse function of equations 2.5-31 yields:

2) Rotated about the y-axis

After rotation of alpha about the x-axis, ox is used by reconstructing the spatial rectangular coordinate system of the centroid of the volume based on the tomogram _α y _α z _α The tomogram reconstruction is composed of finite individual microelements

Respectively represent the pair x _α ，y _α ，z _α Moment of inertia of the shaft. The moment of inertia of the body is:

the product of inertia of the body is:

wherein dV represents a voxel, ρ represents a gradation value of the voxel, (x) _α ，y _α ，z _α ) Representing the location coordinates of the voxel.

By rotating the body coordinates of the mass center of the tomographically reconstructed body around the y-axis by beta, a new coordinate system ox is formed _αβ y _αβ z _αβ Coordinates of voxel (x _αβ ，y _αβ ，z _αβ ) And (x) _α ，y _α ，z _α ) The following relationship is:

/>

substituting equations 2.5-35a and 2.5-35c into moments of inertia relative to the y-axis

In (1), the following steps are obtained:

by equations 2.5-36, the moment of inertia about the y-axis is invariant.

Substituting equations 2.5-35a, 2.5-35b, and 2.5-35c into the sum of the moments of inertia relative to the x-axis and the z-axis

In (1), the following steps are obtained:

from equations 2.5-36, equations 2.5-37 can be rewritten as:

from equations 2.5-38, rotation about the y-axis has invariance to the sum of the moments of inertia about the x-axis and the z-axis. In connection with equations 2.5-36, the moment of inertia of the body is constant, rotating about the y-axis.

Substitution of equations 2.5-35b and 2.5-35c into

In (1), the following steps are obtained:

substitution of equations 2.5-35a and 2.5-35b into

In (1), the following steps are obtained:

the following equation is established:

from equations 2.5-39 and 2.5-40, equations 2.5-41 can be expressed as:

since 2sin β cos β=sin 2β, cos ² β-sin ² Beta = cos 2β, equations 2.5-42 can be expressed as:

order the

Due to

Thus there is

Due to

Substituting equations 2.5-46 into equations 2.5-45 yields the following equations:

from equations 2.5-33, equations 2.5-47 can be expressed as:

equation 2.5-48 is divided by cos 2β on both sides to give:

further, there are:

solving the inverse function of equations 2.5-45 to obtain

3) Rotated about the z-axis

After rotation about the x-axis by alpha and then about the y-axis by beta, ox is used by reconstructing the spatial rectangular coordinate system of the centroid of the volume based on the tomogram _αβ y _αβ z _αβ The tomogram reconstruction is composed of finite individual microelements

Respectively represent the pair x _αβ ，y _αβ ，z _αβ Moment of inertia of the shaft.

The moment of inertia of the body is:

the product of inertia of the body is:

wherein dV represents a voxel, ρ represents a gradation value of the voxel, (x) _αβ ，y _αβ ，z _αβ ) Representing the location coordinates of the voxel.

By rotating the body coordinates of the mass center of the tomographically reconstructed body around the z-axis by gamma, a new coordinate system ox is formed _αβγ y _αβγ z _αβγ Coordinates of voxel (x _αβγ ，y _αβγ ，z _αβγ ) And (x) _αβ ，y _αβ ，z _αβ ) The following relationship is:

rotating gamma around the z axis, the relationship between the new and old coordinate systems is as follows:

substituting equations 2.5-54a and 2.5-54b into moments of inertia relative to the z-axis

In (1), the following steps are obtained:

by equations 2.5-55, rotating about the z-axis, the moment of inertia relative to the z-axis has invariance.

Equations 2.5-54a, 2.5-54b and 2.5-54c into the sum of the moments of inertia relative to the x-axis and the z-axis

From equations 2.5-56, rotation about the z-axis has invariance to the sum of moments of inertia about the x-axis and the y-axis. In connection with equations 2.5-55, the moment of inertia of the body is constant, rotating about the z-axis.

Substitution of equations 2.5-54b and 2.5-54c into

In (1), the following steps are obtained:

substituting equations 2.5-54a and 2.5-54b into

In (1), the following steps are obtained:

the following equation is established:

from equations 2.5-57 and 2.5-58, equations 2.5-59 can be expressed as:

since 2sin γcosλ=sin2γ, cos ² γ-sin ² γ=cos 2γ, equations 2.5-60) can be expressed as:

order the

Due to

Thus there is

Due to

Substituting equations 2.5-64 into equations 2.5-63 yields the following equations:

from equations 2.5-52, equations 2.5-65 can be expressed as:

equation 2.5-66 is divided by cos 2. Gamma. On both sides to obtain

Further, there are:

solving the inverse function of equations 2.5-68 to obtain

S4, performing a simulation experiment according to the standard foot print data, the standardized foot data and the target parameters to obtain an experimental result, and analyzing the experimental result to obtain an evaluation result of the target endurance running shoes;

the experimental result obtained by performing a simulation experiment according to the standard foot print data, the standardized foot data and the target parameter is specifically:

Placing the standard foot print data, the standardized foot data and the target parameters into different model of falling modes to obtain experimental results;

the experimental results comprise stress, acceleration, speed and displacement of the feet;

wherein said analyzing said experimental results comprises:

obtaining experimental data in experimental results, wherein the experimental data comprises the position of the landing time of one foot in another foot stride period and the reaction force of a left/right side supporting surface to the foot (specifically, a stride period comprises a left foot supporting phase and a right foot supporting phase, namely, the reaction force of a left foot supporting surface and the reaction force of a right foot supporting surface), and comparing the experimental data with preset gait constants;

The second embodiment of the invention is as follows:

the method for evaluating the work efficiency of the endurance running shoes is different from the embodiment in that:

the step S4 is also followed by establishing a motion model of the foot bones:

a1, marking a foot bone in the foot tomographic image;

wherein ,S^(i，k) The coordinate transformation matrix is represented when the foot bones perform circular motion around the x axis, the y axis or the z axis, the foot bones are hinged by feet, the two hinged bones can only rotate, the rotating point is the curvature center of the curved surface of the joint head or the joint socket, the body coordinates of the foot bones are established, when the origin of the body coordinates is the curvature center, the rotation of the bones can describe the relative motion between the bones through the body coordinate transformation (the absolute motion of the relative inertial reference system can be obtained through calculation of the traction motion);

specific:

the rotation point (joint) of the foot bone is represented by a Cartesian Oxyz coordinate system, and the coordinate of any point P on the foot bone is (x) ⁽¹⁾ ，y ⁽¹⁾ ，z ⁽¹⁾ ) The radius of rotation is

Initial angular displacement from the x-axis is θ; the angular displacement produced when P moves circumferentially about the x-axis is alpha. The following relationship holds:

/>

substituting the formula (2.4-1) into the formula (2.4-3), and substituting the formula (2.4-2) into the formula (2.4-4) to obtain the following formula:

y ⁽²⁾ ＝y ⁽¹⁾ cosα-y ⁽¹⁾ tgθsinα(2.4-5)

z ⁽²⁾ ＝z ⁽¹⁾ cosα+z ⁽¹⁾ ctgθ sinα(2.4-6)

due to z ⁽¹⁾ ＝y ⁽¹⁾ tgθ；y ⁽¹⁾ ＝z ⁽¹⁾ ctgθ

Thus, there are: y is ⁽²⁾ ＝y ⁽¹⁾ cosα-z ⁽¹⁾ sinα，z ⁽²⁾ ＝z ⁽¹⁾ cosα+y ⁽¹⁾ sinα；

Additionally, because P is motion about the x-axis in the Oyz plane, there are the following kinematic equations:

linear equation the linear equation (2.4-7) can be represented by a matrix:

assume that

Initial angular displacement from the y-axis and the z-axis are +.>

Phi is provided. The angular displacement generated when P makes circular motion around the y axis and the z axis is beta and gamma respectively, and the same method as the analysis of P around the x axis comprises the following steps:

The coefficient matrices in formulas 2.4-8, 2.4-9 and 2.4-10 may be used as alpha ^(1，2) ，β ^(1，2) ，γ ^(1，2) Expressed, then the rotation equation of P in the Oxyz coordinate system is:

(x ⁽²⁾ ，y ⁽²⁾ ，z ⁽²⁾ ) ^T ＝α ^(1，2) β ^(1，2) γ ^(1，2) (x ⁽¹⁾ ，y ⁽¹⁾ ，z ⁽¹⁾ ) ^T (2.4-11)；

let the coefficient matrix in 2.4-11 be S ^(1，2) ＝α ^(1，2) β ^(1，2) γ ^(1，2) ；

S (1, 2) is a transformation matrix in tensor analysis;

the foot is defined as a 15-rigid mechanical model according to the Naledi model, namely the foot is simplified into a rigid body, and links are connected through hinges, so that a multi-rigid foot model is formed. For two adjacent bones (adjoining segments) B of the foot bone _p And B is connected with _q Order-making

And->

To be respectively fixed at B _p 、B _q Mutually orthogonal body coordinates. Depending on the nature of the rigid body: the position of any point on the rigid body at its base coordinates is always a feature. The rotation of any point on the link around the joint point, namely the change relation between the body coordinates on the bone and the body coordinates of the adjacent bone, has the following steps: />

S ^(p，q) ＝α ^(p，q) β ^(p，q) γ ^(p，q) ＝e ^(p) (e ^(q) ) ^T (2.4-12)；

Suppose B _q One end of (B) is connected with B _p Adjacent to the other end is connected with B _r The adjacent one of the two adjacent layers is,

to be consolidated at B _r The body coordinates of the above are as follows according to the formula 2.4-12:

S ^(p，r) ＝α ^(p，r) β ^(p，r) γ ^(p，r) ＝e ^(p) (e ^(r) ) ^T (2.4-13)；

according to the matrix theory:

(e ^(r) ) ^T ＝(e ^(q) ) ^T S ^(q，r) (2.4-14)；

substituting the formula (14) into the formula (13) to obtain:

S ^(p，r) ＝e ^(p) (e ^(q) ) ^T S ^(q，r) ＝S ^(p，q) S ^(q，r) ；

by analogy, the "transfer rule" of the transformation matrix can be obtained:

according to the definition of the Naledi model, a transformation matrix relation of the foot bone relative to an inertial reference system can be established by a formula 2.4-15. The transformation matrix of the relative inertial frame of reference of the first metatarsal, for example, is:

S ^(o，12) ＝S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·S ^(4，12)

The transformation matrix for each link of the human body is (1 representing the inertial reference frame of the foot, 2 representing the talus, 3 representing the calcaneus, 4 representing the navicular bone, 5 representing the internal wedge, 6 representing the middle wedge, 7 representing the external wedge, 8 representing the cuboid, 9 representing the first metatarsal, 10 representing the second metatarsal, 11 representing the third metatarsal, 12 representing the fourth metatarsal, 13 representing the fifth metatarsal, 14 representing the proximal phalanges of the first metatarsophalangeal joint, 15 representing the distal phalanges of the first metatarsophalangeal joint):

S ^(o，1) ＝α ^(o，1) β ^(o，1) γ ^(o，1)

S ^(o，2) ＝S ^(o，1) ·S ^(1，2)

S ^(o，3) ＝S ^(o，1) ·S ^(1，3)

S ^(o，4) ＝S ^(o，1) ·S ^(1，3) ·S ^(3，4)

S ^(o，5) ＝S ^(o，1) ·S ^(1，5)

S ^(o，6) ＝S ^(o，1) ·S ^(1，5) ·S ^(5，6)

S ^(o，7) ＝S ^(o，1) ·S ^(1，2) ·S ^(2，7)

S ^(o，8) ＝S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ^(7，8)

S ^(o，9) ＝S ^(o，1) ·S ^(1，2) ·S ^(2，9)

S ^(o，10) ＝S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ^(9，10)

S ^(o，11) ＝S ^(o，1) ·S ^(1，11)

S ^(o，12) ＝S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·S ^(4，12)

S ^(o，13) ＝S ^(o，1) ·S ^(1，5) ·S ^(5，6) ·S ^(6，13)

S ^(o，14) ＝S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ^(7，8) ·S ^(8，14)

S ^(o，15) ＝S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ^(9，10) ·S ^(10，15) ；

a2, acquiring a position vector of the foot bone relative to an inertial reference system, and obtaining a foot mass center according to the transformation matrix and the position vector;

let xi ^(k) The test points are rotated for the foot bones and are the position vectors between the lower serial number foot bone rotation points of the adjacent foot bones. r is% ^k ) G is the position vector of the link centroid relative to the rotation point of the foot bone ^(o，k) Is the foot bone B _k Position vector of centroid relative to inertial reference system origin of coordinatesThe quantities, according to the defined structure of the Naledi model (Li et al, 2019), are:

for example, the first metatarsal position vector is:

G ^(o，12) ＝S ^(o，12) ξ ₁₂ +S ^(o，12) r ₁₂

＝S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·S ^(4，12) ·ξ ⁽¹²⁾ +S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·S ^(4，12) ·r ⁽¹²⁾

position vector of the foot bone relative to the inertial reference frame:

G ^(o，1) ＝α ^(o，1) ·β ^(o，1) ·γ ^(o，1) ·ξ ⁽¹⁾ +α ^(o，1) ·β ^(o，1) ·γ ^(o，1) ·r ⁽¹⁾

G ^(o，2) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·r ⁽²⁾

G ^(o，3) ＝S ^(o，1) ·S ^(1，3) ·ξ ⁽³⁾ +S ^(o，1) ·S ^(1，3) ·r ⁽³⁾

G ^(o，4) ＝S ^(o，1) ·S ^(1，3) ·ξ ⁽³⁾ +S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·ξ ⁽⁴⁾ +S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·r ⁽⁴⁾

G ^(o，5) ＝S ^(o，1) ·S ^(1，5) ·ξ ⁽⁵⁾ +S ^(o，1) ·S ^(1，5) ·r ⁽⁵⁾

G ^(o，6) ＝S ^(o，1) ·S ^(1，5) ·ξ ⁽⁵⁾ +S ^(o，1) ·S ^(1，5) ·S ^(5，6) ·ξ ⁽⁶⁾ +S ^(o，1) ·S ^(1，5) ·S ^(5，6) ·r ⁽⁶⁾

G ^(o，7) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·ξ ⁽⁷⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·r ⁽⁷⁾

G ^(o，8) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·ξ ⁽⁷⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ⁽⁷ ^，8) ·ξ ⁽⁸⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ^(7，8) ·r ⁽⁸⁾

G ^(o，9) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·ξ ⁽⁹⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·r ⁽⁹⁾

G ^(o，10) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·ξ ⁽⁹⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ⁽⁹ ^，10) ·ξ ⁽¹⁰⁾

+S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ^(9，10) ·r ⁽¹⁰⁾

G ^(o，11) ＝S ^(o，1) ·S ^(1，11) ·ξ ⁽¹¹⁾ +S ^(o，1) ·S ^(1，11) ·r ⁽¹¹⁾

G ^(o，12) ＝S ^(o，1) ·S ^(1，3) ·ξ ⁽³⁾ +S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·ξ ⁽⁴⁾ +S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·S ⁽⁴ ^，12) ·ξ ⁽¹²⁾ +S ^(o，1) ·S ^(1，3) ·S ^(3，4) ·S ^(4，12) ·r ⁽¹²⁾

G ^(o，13) ＝S ^(o，1) ·S ^(1，5) ·ξ ⁽⁵⁾ +S ^(o，1) ·S ^(1，5) ·S ^(5，6) ·ξ ⁽⁶⁾ +S ^(o，1) ·S ^(1，5) ·S ^(5，6) ·S ⁽⁶ ^，13) ·ξ ⁽¹³⁾ +S ^(o，1) ·S ^(1，5) ·S ^(5，6) ·S ^(6，13) ·r ⁽¹³⁾

G ^(o，14) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·ξ ⁽⁷⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ⁽⁷ ^，8) ·ξ ⁽⁸⁾

+S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ^(7，8) ·S ^(8，14) ·ξ ⁽¹⁴⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，7) ·S ^(7，8) ·S ⁽⁸ ^，14) ·r ⁽¹⁴⁾

G ^(o，15) ＝S ^(o，1) ·S ^(1，2) ·ξ ⁽²⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·ξ ⁽⁹⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ⁽⁹ ^，10) ·ξ ⁽¹⁰⁾

+S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ^(9，10) ·S ^(10，15) ·ξ ⁽¹⁵⁾ +S ^(o，1) ·S ^(1，2) ·S ^(2，9) ·S ^(9，10) ·S ⁽¹⁰ ^，15) ·r ⁽¹⁵⁾

by G ^(o，c) Position vector representing the centroid of the foot relative to the inertial reference frame, m _k The quality of the links is represented by the following theorem:

in the formula ∑G^(o，k) ·m _k The moment of the foot bone on the inertial reference system;

A3, acquiring the main moment of inertia of the foot bone relative to the mass center of the foot bone and the inertia tensor of the mass center of the foot bone around the link (the mass center of all foot bones);

obtaining the moment of inertia I of the foot bone relative to an inertial reference system according to the main moment of inertia and the inertial tensor ^(o，k)；

Let the moment of inertia of the foot bone relative to the inertial reference system be I ^(o，k) ，I ^(k) For the main moment of inertia of the foot bone relative to the mass center of the foot bone, J ^(k) Is the inertial tensor of the foot bone around the center of mass of the link.

According to Huygens-Stanna theorem, the principal moment of inertia I of the foot bone ^k And inertial tensor J ^k The relation of (2) is:

according to the parallel axis theorem there are:

I ^(o，k) ＝S ^(o，k) (S ^(o，k) ) ^T J ^(k) +(G ^(o，k) ) ² m _k (2.4-18)；

according to formulas 2.4-16, formulas 2.4-18 are:

the formula 2.4-19 is expressed by the component form:

with I ^(c) To represent the main moment of inertia of the foot relative to the centroid of the foot, which is obtained by 2.4-20 formulas according to the parallel axis theorem:

expressed in terms of components:

from the formulae 2.4 to 11 and 2.4 to 12, r ^(k) and ξ^(k) Calculating link basic morphological parameters of a human body position vector and a centroid position, and measuring 15 foot bone morphological parameters according to the requirements of a Naledi model in order to obtain the basic morphological parameters and human body inertia parameters;

a4, according to the mass center of the foot and the I ^(c) Building a foot bone movement model;

s4 further comprises:

load standardization:

referring to fig. 25-27, load normalization for endurance running, in-situ jump and bow-tie steps; (1) a, the position of a joint mark point of a lower limb in a stride period during endurance running, (1)b) the track of the joint mark point of the lower limb in the stride period during endurance running, (1)c) the acceleration, speed and displacement change of the mass center in the stride period during endurance running, (1)d) the triceps muscle of the middle leg in the stride period during endurance running, and (1)e) the surface matrix myoelectricity of the triceps muscle of the middle leg in the stride period during endurance running; (2) a, the position of a joint mark point of a lower limb in the in-situ longitudinal jump, (2)b the track of the joint mark point of the lower limb in the in-situ longitudinal jump, (2)c the acceleration, the speed and the displacement change of the mass center in the in-situ longitudinal jump, (2)d the triceps surae muscle in the in-situ longitudinal jump, and (2)e the surface matrix myoelectricity of the triceps surae muscle in the in-situ longitudinal jump); (3) a, the position of a joint mark point of a lower limb in an arch step, (3)b) the track of the joint mark point of the lower limb in the arch step, (3)c) the acceleration, the speed and the displacement change of the mass center in the arch step, (3)d) the triceps surae muscle in the arch step, (3)e) the surface matrix myoelectricity of the triceps surae muscle in the arch step;

The above items are standardized.

The third embodiment of the invention is as follows:

the method for evaluating the work efficiency of the endurance running shoes is different from the rest embodiments in that:

before the step S4, the method further comprises: acquiring gait constants:

s01, establishing a landing time objective function

wherein ,F_l Representing the reaction force of the left supporting surface, F _r The reaction force of the right supporting surface is represented, w represents the weight, and g represents the gravitational acceleration;

wherein, ψ represents a fluctuation function, ground resilience force during walking is a periodic fluctuation diagram synthesized by two double hump diagrams, and support counter force during running is a pulse fluctuation function;

s02, obtaining force relation of endurance running

Specifically, a first force relationship F is established according to the Dallangei principle _l +F _r Wg+wa=0, where a represents acceleration of the centroid and wa is inertial force; establishing a second force relationship according to the first force relationship during one stride period of endurance running

Because endurance running has periodicity, +.>

And then obtain

The execution sequence is not limited between S01 and S02, and the execution can be performed sequentially or simultaneously;

s03, obtaining a final objective function according to the landing time objective function and the force relation

Specifically, a first equation is obtained according to the landing time objective function and the force relationship

Bringing the first equation into the landing time objective function to obtain a final objective function; jumping S041 to obtain a force-related gait constant, and jumping S042 to obtain a foot landing time-related gait constant;

s041, deriving and analyzing the final objective function

I.e.

When the reaction force of the left supporting surface and the reaction force of the right supporting surface are symmetrical, the final objective function has an optimal solution, and the effect of the action of the force is optimal (the mechanical energy consumption is minimum in the vertical direction); the left supporting surface reaction force and the right supporting surface reaction force are symmetrically used as force-related gait constants;

s042, decomposing the vertical component of the left supporting surface reaction force in the vertical direction

/>

Taking the reaction force of the right supporting surface to be the same as that of the left supporting surface, the landing time objective function is +>

wherein ,T_s Representing the support phase time of the foot, T _s +T _w ＝T，T _w Indicating the swing phase time of the foot;

the objective function of the landing time at this moment is derived, and the other derivative is 0 to obtain an optimal solution, wherein the optimal solution is the relevant gait constant of the landing time;

specifically, t+t in the landing timing objective function at this time is to be ₀ Separating to obtain a second equation:

then at [0, T _w ]The integral of the second equation over the interval is:

at [ T ] _s ，T]The integral of the second equation above is:

obtaining an inter-partition landing time objective function according to the second equation and a few parts thereof:

deriving the inter-partition landing opportunity objective function and obtaining the other derivative as 0:

(1) At [0, T _w ]The upper part of the upper part is provided with a plurality of grooves,

solving to obtain t ₀ =0, let t ₀ =0 brings the landing timing objective function to the maximum +.>

(2) At [ T ] _w ，T _s ]The upper part of the upper part is provided with a plurality of grooves,

as can be seen from the nature of the trigonometric function,

then T is _s -t ₀ ＝t ₀ -T _w Solving to obtain

Carry the minimum value of the objective function of the landing time

/>

(3) At [ T ] _s ，T]The upper part of the upper part is provided with a plurality of grooves,

relieve->

Handle->

Carry-in landing timing objective function maximum +.>

1/2T is the optimal solution, i.e., the center position of the landing time of one foot in the stride cycle of the other foot is the landing time-dependent gait constant; the constant is irrelevant to physiological factors such as sex, age, height, weight and the like, is irrelevant to gait parameters such as step length, step frequency, support phase ratio, swing phase ratio and the like, and is only relevant to the health condition of a musculoskeletal system and a nervous system. Thus, based on gait constants, it becomes a commonly applicable equation to build a description of centroid acceleration, velocity, displacement and mechanical energy.

Referring to fig. 3 to 9, a fourth embodiment of the present invention is as follows:

After acquiring the gait constants, before step S4, the method further comprises:

verifying the gait constant:

(1) Calculating the magnitude of the rebound force of the vertical bottom surface under different landing occasions, verifying whether the change rate of the magnitude of the rebound force of the vertical bottom surface is the lowest when the landing occasion of one foot is at the central position in the stride cycle of the other foot (substituting the rebound force of one stride cycle into a kinetic equation one by one, calculating the acceleration, the speed and the displacement of the mass center, normalizing the rebound force by the weight, and normalizing the weight, so that the mechanical energy of the mass center is only related to the change of the mass center speed, calculating the mechanical energy of the mass center, and judging whether the minimum value of the mechanical energy of the mass center exists as a constant of the landing occasion of the foot or not

There are two main methods for studying human centroid dynamics during endurance running, one is a reverse dynamics method based on motion capture. The position of the link during running is obtained through the Mark points (Mark) on the links and joints of the human body, so that the kinematic quantities of the link such as acceleration, speed, displacement and the like are obtained; and measuring and calculating inertial parameters (link geometric dimensions, mass, rotational inertia and the like) of the human body link, and analyzing the kinematics and dynamics characteristics of the mass center of the human body. Because of factors such as influence of skin on the identification point, measurement of human body inertia parameters, calculation errors and the like, although the precision of the camera equipment is continuously improved, the precision of a final calculation result is always poor;

The other is based on the forward dynamics mode of a force measuring table, a plantar pressure plate (table) and the like, the motion and dynamics characteristics of the mass center of a human body are analyzed by the ground resilience force when the force measuring table and other devices acquire endurance running, errors are mainly limited by the precision of the devices, the endurance running is a compound motion mode, and the motion law of the mass center of the whole body is accurately expressed by a certain position of the body, so that the forward dynamics mode is adopted in the invention:

centroid dynamics during endurance running comprises the kinematics and dynamics of centroid, and the gravity is constant, so the centroid is subjected toThe force problem is the analysis of ground bounce. The rebound force is caused by the movement of the body member under the drive of the trans-articular muscle, ultimately through the contact of the foot with the ground. The ground reaction force of one foot includes the ground vertical reaction force, the friction force in the left-right direction, and the front-rear friction force. By F ^G (t) represents the ground rebound force at a point in the stride cycle, using

Components in three directions are respectively represented, and the relation among the components is that:

according to the characteristics of bipedal walking

The friction force in the front-back, left-right and the resilience force in the vertical direction of the left and right feet are expressed respectively, and then in the equation (2-1)

According to the force-dependent gait constants, the distribution of rebound forces of the left foot and the right foot in three directions in respective stride periods is assumed to be the same, so that the change of ground rebound force is only caused by landing time between the two feet; let T be the stride period time, the initial phase of one foot be zero, the initial phase of the other foot be T _o (timing of foot landing). The rebound force of one foot (such as the left foot) is

The ground reaction of the other foot is

Thus (2)

Namely +.>

Is about time t and landing time t _o Equation (2-1) can be rewritten as:

endurance running is a continuous periodic movement, when running speed is stable, if there is always F ^G (t，t _o )＝F ^G (t+nT，t _o +nt) (n=1, 2, …), the impact of ground resilience and gravity (wg) on the body mass during a stride period is characterized by:

the stride cycle of a foot comprises a support phase and a swing phase, the support phase being provided for a period of time T _s The time of the swing phase is T _w The method comprises the steps of carrying out a first treatment on the surface of the According to equations 2-2 and 2-3, in the front-rear direction, there are

And has

Since t=t _s +T _w Then->

Also due to->

Therefore there is->

In the left-right direction there is +.>

There is->

Due to->

Therefore there is->

In the vertical direction there is +.>

And have->

Then there is

Due to->

Thus (2)

This is the characteristic of the impact of a single foot in three directions during endurance running (the distribution characteristic of rebound force) under the condition that the distribution of rebound forces of the left and right feet is the same.

The resultant force of the ground resilience force on the horizontal, vertical and sagittal planes is used respectively

Representation, in the known +.>

Under the condition of ground rebound force in three directions, the magnitude and the direction of the resultant force of the plane rebound force can be obtained. In equation 2-2, at [0, T]T is within the range of (2) _o Taking a certain value, equation 2-2 becomes an indefinite equation for t, from which +.>

And->

The effect of the landing time of the foot on the resultant force on the three surfaces can be obtained. At [0, T]T is within the range of (2) _o Take values one by one, thereby establishing the relationship between the landing time of the foot and the resultant force on the three surfaces, and specifically, please refer to fig. 3:

no matter t _o How the force of the rebound force varies, the force of the rebound force varies in three planes, always being a continuous closed curve, which is exactly the same as the physical meaning expressed by equations 2-3, i.e. when the distribution of the rebound force of a single foot has been determined, the momentum of the centroid remains unchanged after a stride period of the force of the rebound and the force of gravity, regardless of the order of landing of the foot. FIG. 3 also reveals the geometry of the resultant force of the plane, in the horizontal plane, when t _o ＝0，t _o When T, the force becomes zero in the left-right direction and becomes a straight line, when the force becomes a bipedal jump

At this time, the resultant force becomes about +.>

An axisymmetric butterfly graph. In the vertical plane of the plate,when t _o When=0, the resultant force ∈0>

The closed curve formed is longest (closed curve length is # F ^G (t，t _o )dF _x dF _z Calculation), when->

When the closed curve approaches the minimum, then increases again, when t _o At =t, the closed curve formed by the resultant force becomes longest again. In the sagittal plane, when t _o ＝0，t _o When =t, the resultant force becomes a straight line, when +.>

At this time, the resultant force becomes about +.>

An axisymmetric butterfly graph;

(2) Calculating the speed and position change of the mass center under different landing occasions, and verifying whether the speed and position change degree of the mass center is minimum when the landing time of one foot is at the central position in the stride cycle of the other foot;

when endurance runs, air resistance is ignored and gravity is constant, no matter how the body links move, the movement of the body links finally acts on the ground through the feet, ground resilience is a result of the feet acting on the ground, and the ground resilience in turn determines the change of acceleration, speed and displacement of the mass center of the human body. Therefore, when the ground resilience force is determined, the stress of the mass center is also determined, and thus, the motion rule of the mass center is also determined. In the case where the ground bounce and the body weight are known, the acceleration of the centroid is calculated according to newton's second law. From equation 2-2, in the stride period, after the human body mass is normalized to 1, the acceleration of the centroid at a certain moment is:

a(t，t _o )＝F ^G (t，t _o )-g(3-1)

Equation 3-1 illustrates centroid acceleration and inverseThe same elastic force is about time t and landing time t _o Is a function of (2). With a _x (t，t _o )、α _y (t，t _o )、a _z (t，t _o ) Representing acceleration of the centroid in three directions, from equations 2-1 and 3-1, there is α _x (t，t ₀ )＝gF _x (t，t ₀ )、a _y (t，t ₀ )＝gF _y (t，t ₀ )、a _z (t，t ₀ )＝gF _z (t，t ₀ ) -g. It can be seen that the impact of the landing timing of the foot on the mass acceleration is the same as the impact of the landing timing of the foot on the ground rebound force. The acceleration and rebound force changes in the fore-and-aft and left-and-right directions are identical except for the units, and the pattern of acceleration translates downward a distance in the vertical direction (the magnitude of translation is related to gravity) in the same form as the rebound force. The force in equation 2-2 is replaced with acceleration and the resulting acceleration dispersion is exactly the same as the force dispersion in figure 3. Further, the impact of the landing timing of the foot on the mass acceleration in the direction, plane and its dispersion is the same as the ground bounce. The method comprises the following steps: the landing time of the foot determines the change of the mass center acceleration when

When the acceleration dispersion in the horizontal direction is close to minimum, the acceleration dispersion in the left-right direction is maximum, and the acceleration dispersion in the vertical direction is minimum; the closed curve formed by acceleration in the horizontal plane and sagittal plane is represented by a symmetrical butterfly graph; the length of a closed curve enclosed by two acceleration components on a vertical plane is nearly the shortest.

The absolute motion of the mass center of the human body relative to the inertial reference system consists of a traction motion and a relative motion, and endurance running is a repetition of a stride cycle. In this way, the pulling speed is always a constant, the moving speed of the coordinate fixed on the human body is defined as the pulling speed, the speed of the mass center relative to the coordinate is the relative speed, and the initial speed of the relative movement of the mass center at the beginning of the stride period is set as v ₀ (t _o ). From equation 3-1, when the floor is onAt t _o When the method is used, the relation between the centroid speed and the acceleration and the initial speed at any time t in the stride period is as follows:

by v _x 、v _y 、v _z Respectively represent the speeds of the mass center in three directions, then there are

On the surface, v in equation 3-2 cannot always be determined by a dynamic method ₀ (t _o ) The size of (each person is different in pace) and v when the ground bounce determines and follows the motion of equations 2-3 ₀ (t _o ) There must be a unique value. From equation 3-2, v ₀ (t _o ) Relates to the foot landing time t _o As a function of the initial velocity of the relative movement and the acceleration:

as can be seen from equations 2-3, there is any landing time

From equation 3-2 there is v (T, T _o )＝v ₀ (t _o ) This indicates that the periodicity of the centroid velocity is consistent with v (T+nT, T _o +nT)＝ v ₀ (t _o +nt) (n=1, 2, …), that is to say the end of one stride period, that is to say the beginning of another stride period, which is indicative of the periodic nature of the centroid velocity in gait. It should be noted that the initial velocity calculated by equation 3-3 refers to the initial velocity of the centroid relative to the moving reference frame when the human body is at a steady velocity at the beginning of the stride period, andnot the absolute velocity of the centroid with respect to the static frame of reference. From equations 3-1 and 3-3, the landing timing of the foot determines the initial velocity of the relative motion, independent of the involvement velocity. When at steady speed, the usual gait parameter "pace" is the traction speed, whereas pace is related to stride frequency, stride, and relative speed is independent of stride frequency, stride.

The components of the centroid velocity in three planes are defined as v _xy ，v _xz ，v _yz It shows that, given the velocity components in three directions, the magnitude and direction of the centroid velocity in three planes can be obtained by the parallelogram method, and the result is shown in fig. 4:

referring to FIG. 4, when v _xz (t，t _o )＝0，v _yz (t，t _o ) The centroid velocity is a straight line when v _xy (t，t _o )＝v _x (t，t _o )+v _y (t，t _o ) When the plane velocity becomes about v _xz (t，t _o )＝ v _x (t，t _o )+v _z (t，t _o ) An axisymmetric closed curve. On the vertical plane, when v (t) =v _x (t)i+v _y (t)j+ v _z (t)k＝0，v(t) ² ＝v _x (t) ² +v _y (t) ² +v _z (t) ² When the plane speed forms a closed curve which is longest;

On the horizontal plane, when t _o ＝0，t _o When T, the centroid speed is always zero in the left-right direction, the centroid speed is a straight line, when

When the resultant force becomes about v _x Axisymmetric, note that when v _x V when=0 _y Not 0, i.e. not symmetrical about the origin. On the vertical plane, when t _o ＝0，t _o At =t, the closed curve formed by the sum velocity is longest (closed curve length is equal to pi v (T, T _o )dv _x dv _z Calculation), when->

Near shortest (not shortest). In the sagittal plane, when t _o ＝0，t _o When =t, the resultant velocity becomes a straight line, when +.>

At the time, the resultant speed becomes about v _z Axisymmetric pattern, when v _z V when=0 _y ≠0；

The displacement of the centroid, like the speed of the centroid, also includes absolute displacement, displacement of the implication and relative displacement. The inventor defines the initial displacement of the relative movement of the mass center under different landing occasions as s ₀ (t _o ). In the stride period, after the speed of the mass center at any moment is obtained according to (3-2), the mass center displacement of the relative motion at any moment can be obtained:

by s _x 、s _y 、s _z The speeds of the mass center in the horizontal direction, the left-right direction and the vertical direction are respectively shown

From equations 3-4, s ₀ (t _o ) Relates to the foot landing sequence t _o Establishing a relation between the initial position and the speed of the stride period:

as with the initial speed of the relative movement, the initial displacement of the relative movement is related only to the landing timing, and is independent of the pace, stride frequency and step size. In this way, when t and t _o The variation ranges of (C) are all defined as [0, T ]]Within the interval, the equations 3-4 and 3-5 are respectivelyThe landing sequence of the foot and the position s of the mass center in three directions _x (t，t _o )、 s _y (t，t _o )、s _z (t，t _o ) As in fig. 5:

When the resultant force becomes about s _x Axisymmetric, note that when v _x V when=0 _y Not 0, i.e. not symmetrical about the origin. On the vertical plane, when t _o ＝0，t _o At =t, the closed curve formed by the sum of the speeds is longest (closed curve length is equal to pi s (T, T _o )ds _x ds _z Calculation), when->

At the moment, the resultant speed becomes about s _y Axisymmetric pattern, when v _z V when=0 _y ≠0。

It can be seen that when

The speed of the relative movement of the centroid exhibits a closed curve of symmetry in the horizontal and frontal planes, the length of the closed curve being nearly the smallest in the sagittal plane. The dispersion of the relative motion centroid velocity is a global minimum in the horizontal and vertical directions and a maximum in the left and right directions throughout the cycle. When->

When the centroid position shows a closed curve with symmetry on the horizontal and frontal planes, the characteristic is that Otherwise, the shape approaches Bernoulli lemniscate in the horizontal plane. On the other hand, dispersion of centroid positions of relative movement is globally minimum in the horizontal direction and the vertical direction, and maximum in the left-right direction. The influence of the landing time on the mass center speed and displacement of the relative motion is irrelevant to gait space-time parameters such as pace speed, step frequency and step length. The impact of landing timing on centroid acceleration is consistent with its impact on rebound force. The experimental study further verifies that the gait minimum action amount principle reveals a gait constant;

(3) Calculating the mechanical energy change of the mass center under different landing occasions, and verifying whether the consumption of the mechanical energy is minimum when the landing time of one foot is at the central position in the stride cycle of the other foot;

the nature always minimizes some important measures when physical processes occur. The human gait is evolved continuously by the vertical walking, the optimized gait is finally obtained, and the human behavior characteristics are formed. In this behavior, the resultant force acting on the centroid, the centroid acceleration and the centroid speed of the relative motion are

A global minimum is shown. What are the physical meanings of these gait laws of motion? Human advancement to bipedal exercise frees the hands and also for long distance movements, which involves energy expenditure problems. The energy consumption of biological exercise has the characteristics of the biological exercise, and in walking, the exercise of the human body link is completed by the combination of active muscles, antagonistic muscles and cooperative muscles, and the stretching and buckling actions of the human body link all need to consume mechanical energy. On the other hand, in one stride period, the sum of potential energy of the centroids of relative motion exists

Average potential energy present +.>

Kinetic energy of centroid at any moment of relative movement E _k (t) is not less than 0, and in one stride period,the sum of kinetic energy is->

Average kinetic energy is present->

The inventors therefore use the relative motion centroid kinetic energy to simplify the description of the mechanical energy expenditure in gait as follows:

by E _x 、E _y 、E _z Respectively represent the kinetic energy of the mass center in three directions, there are

Let t and t _o The variation ranges of (C) are all defined as [0, T ]]When the interval is up, the relation between the landing time of the foot and the mass center kinetic energy in three directions is established, as shown in fig. 6:

when (when)

The order of landing of the foot, when present, makes the centroid average kinetic energy appear as global minimum in the horizontal and vertical directions. Is globally maximum in the left-right direction. Due to min (E _x (t，t _o ))＞max(E _y (t，t _o ))， max(E _y (t，t _o ))＜min(E _z (t，t _o ) The average kinetic energy in the horizontal direction and the average kinetic energy in the vertical direction determine the average kinetic energy of the centroid. At the time t of determining the landing time of feet _o In (2), the velocity of the centroid at any moment in gait is v (t) =v _x (t)i+v _y (t)j+v _z (t) k, v (t) is the square of both sides ² ＝v _x (t) ² + v _y (t) ² +v _z (t) ² This means, speedThe calculation follows the principle of vector calculation, and the square of the speed follows the principle of algebraic operation. That is, the calculation of the average kinetic energy of the centroid is the algebraic sum of the kinetic energies in three directions, when +.>

The centroid has the smallest average kinetic energy, that is, the centroid consumes the least mechanical energy in the case, which is the physical meaning of gait constants;

(4) Verifying the rehabilitation assessment effect of gait constants on patients with sports injuries:

when "gait analysis" is entered in various search engines, a book "bible" appears "gait analysis: normal and pathological function (Gait Analysis: normal and Pathological Function) (Grant, 2010). Another book of this introduction is biological identification: personal identification in network society (biomerics: personal identification in networked society) (Jain et al, 1999). Except for these two books, all books on gait analysis are referred to a paper "Walking pattern of normal men" published in 1964 (Murray et al 1964). The study in the last 60 th century by Murray opened the way to capture gait parameters using a photographic system, although only one camera was used, not only was a stride, a stride frequency, but also a support phase, a swing phase and a dual support phase were successfully obtained due to the use of one mirror (Murray et al 1964). However, the meaning of gait parameters is not understood deeply in the morse, and the knowledge of gait parameters by researchers is mostly accumulated through experience.

The inventors added the swing phase time of the hundred differentiation to the dual Support phase time (Duration of Swing, duration of Double-Limb Support, first and Second Periods) in the paper published in morley 1964 (Murray et al 1964), resulting in several groups of values of 49.52%, 49.54%, 50.52%, 50.00% and 60-65 years, respectively, with average values of 49.92% for all. Next, in the paper published in the morale in 1966 (study of different pace) (Murray et al 1966) a further discussion was made of the addition of a hundred differentiated wobble phase to a double support phase, resulting in data for rapid and natural pace of 50.57%, 50.00% respectively, with average values of 50.29% for different pace. Since the photographing frequency is only 20Hz, the accuracy of the data is to be further explored.

In 2004, researchers performed step-wise analysis of healthy adults using advanced high-speed motion capture systems in combination with force stations (Cho et al 2004). The inventors added the phase of the hundred differentiated swing phase to the phase of the double support phase (Double support period) (divided by 2) to give values of 49.96% and 50.06% for female and male respectively, at which time the frequency of the device was 120Hz. Also in 2004, she Kajie Linna used a pad plantar pressure system to test the left and right lateral gait (tioanova et al 2004), separating the Swing time (Swing time) and the Double support time (Double support time) of the left and right feet, and the inventor's differentiated left Swing phase+right Double support phase (Double support), right Swing phase+left Double support phase (Double support) was 49.37%,49.36%, respectively.

Based on the study foundation and study hypothesis of the former, to ascertain gait constant characteristics in gait of a patient with sports injury, 8 men were selected including a convalescence subject with achilles tendon rupture and a subject with achilles tendon rupture in convalescence, wherein 5 persons of the convalescence subject are more than 4 years after surgery, and 3 persons of the subject in convalescence. All subjects informed consent was given to participate in the experiment. The basic information of the rehabilitator and the subject is shown in tables 1 and 2, and the ages in tables 1 and 2 are the ages at the time of operation:

TABLE 1

TABLE 2

A subject	Height (cm)	Body weight (kg)	Age of	Affected side	Surgical time
						F	170	70.0	50	Left side	2012/05
G	171	67.5	46	Right side	2017/04
						H	175	55.0	22	Left side	2017/05

In 2011, the inventor adopts a Zebris Gait Analysis FDM system to perform gait tests on more than 4 years of achilles tendon rupture rehabilitation persons after 5 operations, and test reports are shown in fig. 7-9. The landing timing results of the achilles tendon rupture healers walking according to gait reports are shown in table 3:

TABLE 3 Table 3

Wherein, I-LR and U-LR respectively represent load response periods (percentage of one gait cycle) of the affected side and the healthy side, and I-WP and U-WP respectively represent swing phases (percentage of one gait cycle) of the affected side and the healthy side. The test time is 11 months 2011 to 12 months 2011. The test site is in the scientific experiment center of the Guangzhou gym;

as can be seen from table 3, the differences (absolute values) between the falling timings of the affected sides and the healthy sides of the rehabilitators a to E are: 1.4%, 3.6%, 1.3%, 2.2% and 1.2%, all greater than 1%. Table 3 and fig. 7-9 reflect two problems: firstly, the landing time sequence of the foot does not accord with gait constants, and secondly, the pressure distribution difference under the phalanges of the healthy side and the affected side is obvious. To understand the course of two sequelae, one achilles tendon breaker F was invited to develop follow-up studies. Subject F underwent the first test at 7/3 2012 and 13 tests during the next 4 months of recovery, essentially once per week. Return visit tests were performed on

day

13, 5, 2014. The detailed gait parameters are shown in fig. 7, and the landing timing results during walking are shown in table 4:

TABLE 4 Table 4

Wherein, L-LR and R-LR respectively represent the load reaction periods of the left side and the right side (the percentage of one gait cycle), L-WP and R-WP respectively represent the swing phases of the left side and the right side (the percentage of one gait cycle); 12 in 12/X/X means 2012, and 14/05/13 means 5/13 in 2014. The test site is in the scientific experiment center of the Guangzhou gym;

subject G was tested for the first time, 15

days

6 and 6 in 2017, and then 9 times in the convalescence period of 2 months thereafter, essentially once per week. One year later, a return visit test was performed. The detailed gait parameters are shown in fig. 8, and the landing timing results during walking are shown in table 5:

TABLE 5

Wherein, L-LR and R-LR respectively represent the load reaction periods of the left side and the right side (the percentage of one gait cycle), L-WP and R-WP respectively represent the swing phases of the left side and the right side (the percentage of one gait cycle); 17 in 17/X/X means 2017, 18/09/20 means 2018, 9, 20. The test site is at the foot research laboratory at the university of fowledgeable university.

Subject H was tested for the first time on 2017, 9, 29, and then on 2017, 10, 14, 11, 18. A return visit test was performed on

day

20, 9, 2019. The detailed gait parameters are shown in fig. 9, and the landing timing results during walking are shown in table 6:

TABLE 6

The L-LR and R-LR respectively represent the load response periods (percentage of one gait cycle) of the left side and the right side, and the L-WP and the R-WP respectively represent the swing phases (percentage of one gait cycle) of the left side and the right side; 17 in 17/X/X means 2017, 19/09/17 means 2019, 9, 17. The test site is at the foot research laboratory at the university of fowledgeable university.

The Hibola base says: "it is more important for a doctor to know a patient than to know a patient's condition" (Hipola bottom, 2011). Subject F is a doctor specialized in sports training, especially in the theoretical and practical work of physical training. Therefore, the inventor does not make any suggestion, and only shares data with the subject F for him to revise the rehabilitation training scheme. In addition, the inventor tracks, tests, observes and knows the exercise rehabilitation process of the achilles tendon fracture person for the first time. Subject F convalescence detailed gait parameters are shown in figure 32.

In fig. 7, it is shown that the difference in the step parameters of the healthy side and the diseased side is gradually decreased as a whole in the step length, the step time, the supporting phase, the swinging phase, the double supporting phase, and the single supporting phase with the lapse of time. Notably, are: no other parameter differences were minimal after two years of rehabilitation compared to the previous recordings, except for the step size parameter. At the same time, subject F was already available for vigorous challenge exercise one year after surgery. Therefore, the rehabilitation of walking function and gait skills of the achilles tendon breaker in the rehabilitation period are treated separately, so that not only is the rehabilitation of the motor function required, but also the relearning of the motor skills is performed. The structure of the body movement system is symmetrical (Hannah et al, 1984) and the gait parameters of the achilles tendon breaker should be restored to symmetrical levels based on the principle that the structure and function are unified (Kosak et al, 2004). Thus, the inventors devised an equal step gait training, specifically: by means of metronomes, the same step-size grid (by means of adjustable rope ladders) is drawn on the runway, and the subject performs gait skill training according to the length of the grid according to the prescribed step frequency.

The inventors then invited subject G to perform an intervention training for 9 weeks, the first 4 weeks being gait function training, without gait pattern setting, and then to perform an equal step training with the objective of performing gait skill learning. A total of 9 tests were performed. One year later, a return visit test was performed. The detailed gait parameters of subject G convalescence are shown in figure 33.

In fig. 8, the first 4 weeks are walking training based on the change in gait parameters from subject F in fig. 32. From week 5 (day 7 of 2017, month 7), the inventors set 106 steps using metronomes, the step size was first set to 50cm, then increased every day by 2cm, and the step size difference decreased rapidly in the test results after 4 days. The symmetrical gait parameters were better than those obtained 4 months after subject F surgery (2012, 09, 13) just before the end of summer holidays (2017, 8, 22), but the step size differences were still large. Subject F was observed to have better symmetry results at 10/18/2012 and 10/23/2012, while the results at 5/13/2014 were not satisfactory. The inventor worry that subject G also has the same condition, and that the achilles tendon fracture is truly "nail pulled out and hole left" and difficult to achieve complete and real recovery of achilles tendon fracture?

Compensatory physiological phenomena occur in the lungs, kidneys, arteries and bones (Cowan et al 1975; fung 1990). Feng Yuanzhen stress-growth relationship is a theoretical basis for interpretation of compensatory phenomena in tissues and organs (Fung, 1990). Due to pain and self-protection, achilles tendon-broken persons also experience compensatory movements during walking, and the healthy side helps the affected side to bear loads during the early stages of rehabilitation (Cowan et al 1975; fung, 1990). By way of fig. 32-34, the achilles tendon breaker compensatory gait is defined as: the step length, the step time and the swing phase of the exercise are reduced, and the support phase, the double support phase and the single support phase are increased. The sequelae of compensatory gait are: the functional recovery of the affected metatarsophalangeal joints is insufficient, which is manifested by poor symmetry in the aspects of step length, step time, supporting phase, swing and the like after recovery.

The exercise training mode is not adopted, and the equal step training effect is not ideal. It appears that the principle of the design of the exercise prescription for persons with broken achilles tendon should be ascertained first. For diseases of the motor system, the purpose of motor rehabilitation is to eliminate, alleviate motor dysfunction, the content of which includes motor dysfunction level assessment and motor prescription design (petersen et al, 2006), which means that motor rehabilitation is directional and purposeful, and the theory of "use in and out of the back" of lamac is perhaps the motor prescription design principle (Zhang Zhongbao, 2000) of diseases of the motor system (specifically meaning "exercise is only recovered"). Therefore, the inventors hypothesize that the stress-growth relationship of Feng Yuanzhen (Fung, 1990) is the theoretical basis for the design of the exercise prescription for achilles tendon breakers.

Subject H was recruited to a post-achilles tendon rupture surgery for more than 4 months at 9 months 2017. The inventors first tested subject H. The results of fig. 9 demonstrate a closer approximation to the results of subject F tested on 13/9/2012. The inventor has increased the requirement for the capstan situation of the affected side metatarsophalangeal joint to increase the load of the affected side achilles tendon when the pedaling action during walking is required to be as close as possible. The inventor proposes an equal-step plantar-toe joint winch gait rehabilitation scheme, which is performed on a virtual feedback gait training system. The method specifically comprises the following steps: the training speed was set to 2km/H, which was based on the walking speed of subject H in FIG. 9 being 2.92km/H. In order to form the motion memory of the subject, after learning the walking skills, the subject H is required to perform walking exercise for at least 5km per day, without being continuous, but the total amount is required. After 2 weeks of engagement, and after 4 weeks of engagement, walking skill learning was performed using the "virtual feedback gait training system" after the test, and two years later, a return visit test was performed, the results of which are shown in fig. 34.

Figure 34 shows that subject H reached complete recovery after two years. Why are three subjects with differences in rehabilitation results?

In tables 4-6, test results for subject F, 13 days 5, 2014: the landing time of the right foot is 51.49%, and the landing time of the left foot is 49.04% (the absolute value of the left-right difference is 2.45%); 2018.

day

9 and 20, the landing time of the right foot of subject G was at 50.48% and the landing time of the left foot was at 49.51% (left-right difference of 0.97%); on day 17 of 9 2019, the landing time of the right foot of subject H was 50.05% and the landing time of the left foot was 50.25% (left-right difference of 0.2%).

A gait kinematics study of a normal adult covering the ages of 20 to 65 showed that: they were all at 50.0% of the time of landing (time of landing=op site top-off+ Duration of Swing), but not on the left and right sides. To reduce duplicate studies, the inventors rearranged the test results of healthy young and old in the literature published in 2016 (Fan et al 2016), see fig. 35. According to fig. 35, the landing time of the right foot is 50.07%, 50.23%, 50.00% and the landing time of the left foot is 49.95%, 50.05%, 50.00% at the normal, fast and slow three walking speeds of the healthy young person (the absolute values of the left and right differences are 0.12%, 0.18%, 0.00%, respectively); the landing time of the right foot is 49.69%, 50.11% and 49.64% and the landing time of the left foot is 50.53%, 50.20% and 50.45% of the healthy elderly people at three steps of normal, fast and slow speed (the absolute values of the left and right differences are 0.84%, 0.09% and 0.81% respectively).

The gait of a healthy person generally follows the gait minimum action principle (gait constant), which is defined as: in walking, when the landing time of the foot is half of the stride period of the other foot, the mechanical energy consumption of the human body in the vertical direction is minimal.

In this embodiment, the definitions of the parameters in fig. 32 to 35 are: step length, step time, foot rotation, support phase, load response, single support, pre-Swing, wobble phase, total double support phase, totaldouble support, stride length, stride time, stride width, stride frequency, stride speed, and pace speed;

due to quantitative analysis, science was stripped from philosophy. The plantar pressure test system can provide accurate and quantitative test data for structural injury persons of ankles. The inventors obtained zebris FDM v1.18.40 scientific edition, month 1 in 2020, and this software divided the sole into three zones and seven zones of pressure variation, with seven zones separating the metatarsophalangeal joint zones. The results of the three and seven area analysis in the return gait test report about 2 years post-surgery for subject F are shown in fig. 7.

The results of the analysis of the three and seven zones in the return gait test report about 1.5 years after subject G surgery are shown in fig. 8.

The results of the three and seven area analysis in the return gait test report about 2 years post-surgery for subject H are shown in figure 9.

Tables 4-6, figures 7-9 demonstrate that the symmetry of gait parameters is uniform with the consistency of the seven-zone plantar pressure changes on the healthy side, the affected side. As can be seen, the achilles tendon rupture diagnosis method based on the plantar pressure test system is effective. The landing time of the healthy side and the affected side is close to 50%, and the absolute value of the difference is smaller than 1% which is a key index for quantitatively evaluating the rehabilitation of the achilles tendon fracture patients.

Referring to fig. 14, as a result of a study on barefoot running in the prior art, barefoot runners mainly land on the forefoot and rarely land on the heel (Lieberman et al, 2010), and referring to fig. 15, the authors refine the landing patterns during running in another paper, including the heel landing pattern RFS (a), the forefoot landing pattern short stride (B), the forefoot landing pattern long stride (C), and the acceleration of the three different landing patterns with dynamics and vertical reaction force at 3.0 m/s-1, it can be seen that the heel landing pattern (a) has a significant impact peak, the long stride in the forefoot landing pattern (C) has a steeper loading rate than the short stride (B), and the external bending moment at the peak load rate of each impact, i.e., the moment arm of the product of the vertical ground (Fv) and the reaction force (Rext), is shown below fig. 15. RFS produces a high dorsiflexion moment, the large stride in forefoot landing mode (C) produces a much higher outer plantar force Qu Liju than in the short stride height (B); referring to fig. 16 to 23, a fifth embodiment of the present invention is as follows:

s4 further comprises: preliminarily analyzing the change conditions of force, acceleration, speed, displacement and mechanical energy under different running postures to obtain a preliminary analysis result;

specifically, referring to fig. 16-18, the test analysis results of three different running postures are shown in table 7, in which the key data are shown in the following table 7:

TABLE 7

Width of step, cm	2.95	2.73	3.01	2.50	2.53	2.07
							Step frequency, step/drink	164.10	2.32	161.57	3.42	159.80	2.30
Pace, km/h	10.36	0.26	10.30	0.38	10.69	0.37

As can be seen from table 7, the slowest is the forefoot landing mode; the heel landing mode is the smallest stride length; the fastest step frequency is the heel landing mode; the lateral arch landing mode has the fastest pace, the smallest pace frequency and the largest step length, and then the running economy is analyzed based on a gait constant (gait minimum action amount principle) to obtain figures 19-23;

referring to fig. 23, the first row of the mechanical energy for centering the mass center speed and weight under the three landing modes is respectively from left to right in the graph a to graph C, and the second row is respectively from left to right in the graph D to graph F, the speed of the mass center when the heel of the graph a lands on the ground, the mechanical energy of the mass center when the heel of the graph B lands on the ground, the speed of the mass center when the sole of the graph C lands on the ground, the mechanical energy of the mass center when the sole of the graph D lands on the ground, the speed of the mass center when the bow of the graph E lands on the outer side, and the mechanical energy of the mass center when the bow of the graph F lands on the outer side;

As can be seen from fig. 19 to 23, the outer bow landing mode does not increase the ground resilience, and in combination with table 7, the outer bow has less foot support time, which means that the flight time is longer, the mechanical energy should be maximum, and in fig. 23 the outer bow landing mechanical energy is 13.68908, which is maximum, which means that the support time is reduced, the flight time increases, and in the case of the best stride frequency, the outer bow landing mode steps at the fastest speed due to the increase in stride length;

s4 specifically comprises the following steps:

and carrying out a simulation experiment according to the standard foot print data, the standardized foot data and the target parameters to obtain an experimental result, and analyzing the experimental result and the preliminary analysis result to obtain an evaluation result of the target endurance running shoes.

Referring to fig. 10-13, a sixth embodiment of the present invention is as follows:

the step S3 of the method for evaluating the work efficiency of the endurance running shoes is used for normalizing the foot data according to the foot tomographic image to obtain normalized foot data, and the normalized foot data is applied to reconstructing an arch structure according to foot ossifies:

modern foot bones rotate in the order of x-y-z axis.

1) Rotation about the x-axis

The surface of the modern foot bone is composed of a limited number of points, expressed by oxyz through the space rectangular coordinate system of the centroid of the modern foot bone, and E is used _x ，E _y ，E _z The Euler moments for the x, y, and z axes are shown, respectively.

The euler moment of the modern foot bone is:

euler products of the bones of modern feet are:

where dp represents the point cloud and (x, y, z) represents the position coordinates of the point cloud.

By rotating the body coordinate of the centroid of the modern foot bone around the x-axis by alpha, a new coordinate system ox is formed _α y _α z _α Coordinates (x) _α ，y _α ，z _α ) The relationship with (x, y, z) is:

substitution of equations 2.1-3b and 2.1-3c to Euler moments relative to the x-axis

In (1), the following steps are obtained:

from equations 2.1-4, it is clear that the Euler moment relative to the x-axis is constant, rotating about the x-axis.

Substituting equations 2.1-3a, 2.1-3b and 2.1-3c into the sum of the relative y-axis and z-axis Euler moments

In (1), the following steps are obtained:

from equations 2.1-4, equations 2.1-5 can be expressed as:

from equations 2.1-6, rotation about the x-axis has invariance to the sum of the Euler moments of the y-axis and the z-axis. In connection with equations 2.1-4, the euler of modern foot bones has invariance, rotating around the x-axis.

Substituting equations 2.1-3 a) and (2.1-3 c) into

In (1), the following steps are obtained:

substituting equations 2.1-3 a) and (2.1-3 b) into

In (1), the following steps are obtained:

the following equation is established:

from equations 2.1-7 and 2.1-8, equations 2.1-9 can be expressed as:

f(α，β，γ) _α ＝∫(y ² (sin ² α-cos ² α)+4yz sinαcosα+z ² (cos ² α- sin2αdp(2.1-10)

since 2sin α cos α=sin 2α, cos ² α-sin ² α=cos 2α, equations 2.1-10 can be expressed as:

f(α，β，γ)α＝∫(-y ² cos 2α+2yzsin 2α+z2 cos 2α)dp (2.1-11)

Order the

Equation 11 becomes:

there is therefore a number of such methods as,

sin 2α∫y ² dp+2cos 2α∫yzdp-sin2α∫z ² dp＝0 (2.1-13)

due to

sin 2α∫x ² dp-sin 2α∫x ² dp＝0 (2.1-14)

Substituting equations 2.1-14 into equations 2.1-13 yields:

sin 2α∫y ² dp+sin 2α∫x ² dp+2cos 2α∫yzdp-sin 2α∫z ² dp- sin2αx2dp＝0 (2.1-15)

from equations 2.1-1, equations 2.1-15 can be expressed as:

sin 2αE _z +2cos 2αE _yz -sin 2αE _y ＝0 (2.1-16)

the two sides of equations 2.1-16 are divided by cos 2 alpha to obtain

tan 2αE _z +2E _yz -tan 2αE _y ＝0 (2.1-17)

Further, there are:

solving the inverse function of equations 2.1-18 yields:

2) Rotated about the y-axis

After rotation of alpha around the x-axis, ox is used by a space rectangular coordinate system based on the centroid of modern foot bones _α y _α z _α Representation by

Respectively represent the pair x _α ，y _α ，z _α Euler moment of the shaft.

The euler moment of the modern foot bone is:

euler products of the bones of modern feet are:

wherein dp represents a point cloud, (x) _α ，y _α ，z _α ) Representing the position coordinates of the point cloud.

By rotating the body coordinates of the centroid of the modern foot bone around the y-axis by beta, a new coordinate system ox is formed _αβ y _αβ z _αβ Coordinates (x) _αβ ，y _αβ ，z _αβ ) And (x) _α ，y _α ，z _α ) The relation of (2) is:

substituting equations 2.1-22a and 2.1-22c into the Euler moment relative to the y-axis

In (1), the following steps are obtained: />

By equations 2.1-23, the euler moment with respect to the y-axis is invariant, rotating around the y-axis.

Equations 2.1-22a, 2.1-22b and 2.1-22c are substituted into the sum of relative x-axis and z-axis Euler moments

In (1), the following steps are obtained:

from equation 36, equation 37 may be rewritten as:

from equations 2.1-25, rotation about the y-axis has invariance to the sum of the Euler moments about the x-axis and the z-axis. In connection with equations 2.1-23, the euler of modern foot bones is unchanged, rotating around the y-axis.

Substituting equations 2.1-22b and 2.1-22c into

In (1), the following steps are obtained:

substituting equations 22a and 22b into

In (1), the following steps are obtained:

the following equation is established:

from equations 2.1-26 and 2.1-27, equations 2.1-28 can be expressed as:

/>

since 2sin β cos β=sin 2β, cos ² β-sin ² Beta = cos 2β, equations 2.1-29 can be expressed as:

order the

Due to

Thus there is

Due to

Substituting equations 2.1-33 into equations 2.1-32 yields:

from equations 2.1-20, equations 2.1-34 can be expressed as:

the two sides of equation 2.1-35 are divided by cos 2 beta to obtain

Further, there are:

solving the inverse function of equations 2.1-37 to obtain

3) Rotated about the z-axis

After rotation about the x-axis and then about the y-axis by an ox based on the spatial rectangular coordinate system of the centroid of the modern foot bone _αβ y _αβ z _αβ Representation by

Respectively represent the pair x _αβ ，y _αβ ，z _αβ Euler moment of the shaft.

The euler moment of the modern foot bone is:

euler products of the bones of modern feet are:

wherein dp represents a point cloud, (x) _αβ ，y _αβ ，z _αβ ) Representing the position coordinates of the point cloud.

By rotating the body coordinates of the centroid of the modern foot bone around the z axis by gamma, a new coordinate system ox is formed _αβγ y _αβγ z _αβγ Coordinates (x) _αβγ ，y _αβγ ，z _αβγ ) And (x) _αβ ，y _αβ ，z _αβ ) The relation is:

substitution of equations 2.1-41a and 2.1-41b to Euler moments relative to the z-axis

In (1), the following steps are obtained:

by equations 2.1-42, the euler moment with respect to the z-axis has invariance, rotating around the z-axis.

Substituting equations 2.1-41a, 2.1-41b, and 2.1-41c into the sum of relative x-axis and y-axis Euler moments

In (1), the following steps are obtained:

from equations 2.1-43, rotation about the z-axis has invariance to the sum of the Euler moments of the x-axis and the y-axis. In connection with equations 2.1-42, the euler of modern foot bones is unchanged, rotating around the z-axis.

Substituting equations 2.1-41 b) and (2.1-41 c) into

In (1), the following steps are obtained:

substitution of equations 2.1-41a and 2.1-41b into

In (1), the following steps are obtained:

the following equation is established:

from equations 2.1-44 and 2.1-45, equation 46 can be expressed as:

since 2sin γcosλ=sin2γ, cos ² γ-sin ² γ=cos 2γ, equations 2.1-47 can be expressed as:

order the

Due to

Thus, there are:

due to

Substituting equations 2.1-51 into equations 2.1-50 yields:

from equations 2.1-39, equations 2.1-52 can be expressed as:

the two sides of equations 2.1-53 are divided by cos 2 gamma to obtain

Further, there are:

solving the inverse function of equations 2.1-55 yields:

rotation is stopped when the euler products of the bones of the modern foot are all zero. The bones of the foot of the Nalaidi human are rotated by the same method to make Euler's products all zero. Suppose that the euler products of the foot bones of modern people sequentially rotate alpha, beta and gamma according to the sequence of x-y-z axes are all zero. The podophyliths are then rotated sequentially-gamma, -beta, -alpha in the order of x+.y+.z-axis. The specific process is as follows:

Foot ossifite rotates around z axis-gamma

According to equations 2.1-41, equations 2.1-57 can be rewritten as:

since sin (- γ) = -sin (γ), cos (- γ) = cos (γ), equation 58) becomes:

equations 2.1-59 can be expressed as:

foot ossifite rotates around y axis-beta

According to equations 2.1-22), equations 2.1-61 are expressed as:

since sin (- β) = -sin β, cos (- β) = cos β, equation (2.1-62) can be expressed as:

due to

Equations 2.1-63) can be expressed as:

simplifying equation 64) yields:

podophyllotoxin rotates about the x-axis-alpha

According to equations 2.1-3, equations 2.1-66 are expressed as:

due to

Equations 2.1-67), can be expressed as

After the treatment, there are

From this, the modern foot bones rotate by alpha, beta, gamma, alpha in turn around the x-y-z-x-y-z … axis ₁ ，β ₁ ，γ ₁ … the calcite is rotated …, gamma sequentially in the order of axes x+.y+.z+.x+.y+.z … ₁ ，β ₁ ，α ₁ Gamma, beta, alpha can reconstruct the arch structure of the nano-foot ossified foot. This also means that a similar living arch structure can be used to reduce the human fossilised arch structure;

fig. 10-12 are schematic views of reduction results, and fig. 13 is a schematic view showing the correspondence between the reduced arch structure and the foot imprinting fossils;

the nalytical person is known as the champion of the three prehistoric ironmen (news. Nationlgeographic. Com, 2015). Exploring how the arch structure of the naratide runs and jumps on african thin-tree grasslands in a barefoot manner and avoids injuries not only provides new evidence for interpreting the evolution of human locomotor activity, but also has a enlightening effect on the biomechanical problem of exploring the ossified arch structure and ankle stability, as ankle instability is the main cause of ankle sprains (Hubbard, et al 2007;Delahunt,et al, 2010

Referring to fig. 2, a seventh embodiment of the present invention is as follows:

the endurance running shoe work efficiency evaluation terminal 1 comprises a processor 2, a memory 3 and a computer program stored in the memory 3 and capable of running on the processor 2, wherein the processor 2 realizes the steps from the first embodiment to the sixth embodiment when executing the computer program.

In summary, the invention provides a method and a terminal for evaluating work efficiency of endurance running shoes, which establish a relation between gait parameter interpretation lower limb structures and exercise functions; the gait minimum action amount principle is found and verified, a gait constant is revealed according to the principle, a endurance running mechanics equation is established based on the gait constant, and quantitative analysis of endurance running is realized; the concepts of Euler quantity, euler main shaft and the like are put forward, and coordinate standardization and fossil foot structure body coordinate standardization, geometric model standardization and load loading standardization (force magnitude, direction and action point) in the analysis process are realized based on the Euler main shaft; providing a theoretical basis for the endurance running shoe function and the work efficiency optimization design; through the standardization after obtaining the foot print data and the foot tomographic image of the target subject, the method can directly carry out simulation experiments with the target parameters of the target endurance running shoes, and is convenient for comparison of experimental results after standardization, so that the limited target subject can provide data with wider application range, can provide experimental data under various preset scenes for various required test parameters of the running shoes, and provides data support for the work efficiency optimization design of the endurance running shoes.

The foregoing description is only illustrative of the present invention and is not intended to limit the scope of the invention, and all equivalent changes made by the specification and drawings of the present invention, or direct or indirect application in the relevant art, are included in the scope of the present invention.

Claims

1. The method for evaluating the work efficiency of the endurance running shoes is characterized by comprising the following steps:

the step of normalizing the footprint data in the step S3 to obtain standard footprint data includes:

；

wherein ,

a sensor impulse representing a sensor interacting with the foot,i,jrespectively representing the row and column numbers of the sensor,/->

For said->

A position on the plate;

the sensor impulse

, wherein ,/>

Representing the support phase time, +.>

The expression position is +.>

Is at the sensor of (1)tA pressure value at a moment; />

Representation->

The position relative to the center of the foot print impulse, said center of foot print impulse being +.>

；

When (when)

When the mark is zero, marking a vertical axis passing through the impulse center of the foot print as a foot print main axis;

calculating the position of the foot print main shaftFoot print impulse position of (2)

：

；

wherein ,

representing the number of sensors interacting with the foot at foot print length position l; />

The impulse position at foot print length position l;

calculating the landing time and the lift-off time on the foot print spindle:

；

wherein ,

respectively expressed in the foot print length position +.>

Landing time and lift-off time on the floor, < >>

Respectively represent plantar position +.>

Landing time and ground leaving time of (2);

the normalizing the foot data according to the foot tomographic image in S3 to obtain normalized foot data includes:

rotating the first space rectangular coordinate system by a second preset angle to obtain a standardized space rectangular coordinate system;

in the step S4, a simulation experiment is performed according to the standard foot print data, the standardized foot data and the target parameter to obtain an experimental result specifically as follows:

placing the standard foot print data, the standardized foot data and the target parameters into different floor mode models to obtain an experiment result;

the analyzing the experimental result in S4 includes:

2. The method for evaluating the work efficiency of a endurance running shoe according to claim 1, wherein the second test data is obtained in the step S2, and the second test data includes footprint data of a target subject specifically:

Foot print data of the target subject are obtained through a plantar pressure test device.

3. The method for evaluating the work efficiency of a endurance running shoe according to claim 2, wherein the plantar pressure test equipment comprises sensors arranged in an array.

4. The method for evaluating the work efficiency of the endurance running shoes according to claim 1, wherein the step of rotating the first plane rectangular coordinate system by a first preset angle to obtain a standardized plane rectangular coordinate system is specifically:

rotating the first plane rectangular coordinate system

And (3) angle, obtaining a standardized plane rectangular coordinate system:

；

wherein ,I _x representation ofxMoment of inertia on the shaft and,I _y representation ofyMoment of inertia on the shaft and,I _xy representation ofxShaft and method for producing the sameyProduct of inertia on axis:

;

wherein ,

representing facial primordia, ->

Gray value representing said facial element, < >>

Representing the position coordinates of the surface bins.

5. The method for evaluating the work efficiency of the endurance running shoes according to claim 1, wherein the step of rotating the first space rectangular coordinate system by a second preset angle to obtain a standardized space rectangular coordinate system is specifically:

sequentially following the first space rectangular coordinate systemxRotation of the shaft

Angle, edgeyShaft rotation->

Angle, edge zShaft rotation->

And (3) angle, obtaining a standardized space rectangular coordinate system:

；

；

；

wherein ,I _y representing voxel pairs in the first space rectangular coordinate systemyMoment of inertia of the shaft and,I _z representing voxel pairs in the first space rectangular coordinate systemzMoment of inertia of the shaft and,I _yz expressed in the first space rectangular coordinate systemyShaft and method for producing the samezThe product of inertia of the on-axis voxel;

representing voxel pairs in a second spatial rectangular coordinate systemxMoment of inertia of shaft>

Is indicated at->

The second space rectangular coordinate system is provided with a voxel pairzMoment of inertia of shaft>

Is indicated at->

In the second space rectangular coordinate systemxShaft and method for producing the samezThe product of inertia of the on-axis voxel; />

Representing voxel pairs in a third space rectangular coordinate systemxMoment of inertia of shaft>

Is indicated at->

The third space rectangular coordinate system is provided with a voxel pairyMoment of inertia of shaft>

Is indicated at->

In the third space rectangular coordinate systemxShaft and method for producing the sameyThe product of inertia of the on-axis voxel;

the second space rectangular coordinate system is that the first space rectangular coordinate system rotates around the x axis

Obtaining after angulation; the third space rectangular coordinate system is that the second space rectangular coordinate system rotates around the y axis>

The angle is obtained.

6. The method for evaluating the work efficiency of a endurance running shoe according to claim 1, wherein the step S4 further comprises the step of building a foot bone movement model:

Marking a foot bone in the foot tomogram;

；

wherein ,S ^(i,k) a coordinate transformation matrix representing the foot bones performing circular motion around an x-axis, a y-axis or a z-axis;

obtaining the moment of inertia of the foot bone relative to an inertial reference system according to the main moment of inertia and the inertial tensor

；

According to

And said foot centroid obtains a main moment of inertia of the foot relative to said foot centroid>

；

According to the mass center of the foot and the

And (5) building a foot bone movement model.

7. The endurance running shoe work efficiency evaluation terminal comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, and is characterized in that the processor realizes the endurance running shoe work efficiency evaluation method according to any one of claims 1-6 when executing the computer program.