CN107945877B - Arch bar system structure construction method based on arch living body bone inertia main shaft - Google Patents
Arch bar system structure construction method based on arch living body bone inertia main shaft Download PDFInfo
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Abstract
The invention provides an arch of foot structure of rod system structure construction method based on arch live bone inertia main axis, solve the inertia main axis of the live bone according to the particular order of rotation based on the mass center of arch live bone; establishing a three-dimensional rectangular coordinate system according to the mass center and the inertia main shaft of the arch living bone; selecting six maximum and minimum marking points along three coordinate axes in the established three-dimensional rectangular coordinate system; reversing the six marking points according to a specific rotation reverse sequence; connecting six points to form a rod structure of the arch living bone; the rod structure connecting 7 tarsal bones and 5 metatarsal bones forms an arch rod system; a new method for statics and dynamics analysis and optimization calculation of the foot wearing object structure is formed, a foot mechanics model is provided with a rod piece structure, and mechanics analysis can be carried out according to needs.
Description
Technical Field
The invention relates to the technical field of biomedical engineering, in particular to an arch bar system structure construction method based on an arch living body bone inertia main shaft.
Background
Many bones of the human body are present in pairs, and tarsal bones and metatarsal bones which are symmetrical to the left and right feet constitute a symmetrical arch of the foot. Is there a difference in the symmetry of the arch structure of our left and right feet? How does this difference, if any, affect our basic behavior? Is it still in line with the principle of "structure and function are unified? To address these issues, it is necessary to build a mechanical model of the arch structure for mechanical analysis.
For the regular analysis of stress and force transmission of the structure, the finite element method not only has high calculation precision, but also can adapt to various complex shapes, so that the finite element is widely applied to arch structure analysis. However, the finite element method is very troublesome in terms of the arrangement of structural constraints between tarsal bones and metatarsal bones constituting the arch, etc. for a complicated biological structure such as the arch, and lacks a corresponding standard, which deteriorates the reliability of the calculation result.
Therefore, how to construct a standardized arch-bar structure and improve the reliability of the calculation result of the arch-bar structure are key technologies to be urgently broken through. Solving the problem makes new progress in theoretical research of bone biomechanics, arch structure mechanics analysis method in the technical field of biomedical engineering and the like.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the arch skeleton structure construction method based on the arch living bone inertia main shaft solves the problem that the existing method using finite element is used for the arch, and the like complex biological structure has poor reliability in calculating structure.
In order to solve the technical problems, the invention adopts the technical scheme that: an arch bar system structure construction method based on inertia main shafts comprises the following steps:
s1: acquiring a three-dimensional model of an arch living bone;
s2: dividing the obtained three-dimensional model of the arch living bone into a set of a plurality of volume microelements, and then obtaining the centroid of the three-dimensional model of the arch living bone according to the coordinates and the density of each volume microelement in the image;
s3: respectively establishing a first three-dimensional rectangular coordinate system with a coordinate origin on the arch living bone mass center;
s4: sequentially rotating the arch living bone along x, y and z axes of a first three-dimensional rectangular coordinate system to sequentially obtain corresponding inertia moment;
s41: rotating the arch living bone along an x axis in a first three-dimensional rectangular coordinate system by alpha to obtain a first moment of inertia of each volume infinitesimal element of the arch living bone relative to the x axis;
s42: rotating the arch living bone by beta along a y axis in a first three-dimensional rectangular coordinate system to obtain a second inertia moment of each volume infinitesimal element of the arch living bone relative to the y axis;
s43: rotating the arch living bone along a z axis in a first three-dimensional rectangular coordinate system to obtain a third inertia moment of each volume infinitesimal element of the arch living bone relative to the z axis;
s5: obtaining inertia products of all volume infinitesimal elements of the arch living bone according to the obtained first inertia moment, the second inertia moment and the third inertia moment;
s6: repeating the steps S4-S5, and when the inertia product of each volume infinitesimal element of the obtained arch living bone is zero, taking the main shaft of the arch living bone with the inertia product of zero as an inertia main shaft;
s7: establishing a second three-dimensional rectangular coordinate system according to the obtained mass center and inertia main shaft of the arch living bone;
s8: respectively obtaining 6 marking points in the living bone relative to the three-dimensional rectangular coordinate system, wherein the 6 marking points are (x)max,0,0),(xmin,0,0),(ymax,0,0),(ymin,0,0),(zmax,0,0),(zmin,0,0)；
S9: respectively rotating the 6 coordinate points along the z, y and x of the second three-dimensional rectangular coordinate system by-gamma, -beta and-alpha,
s10: connected in rod form (x)max0,0) and (x)min0,0) in the form of rods (y)max0,0) and (y)min0,0) in the form of rods (z)max0,0) and (z)min0,0) to obtain an arch living body bone rod structure based on the inertia main shaft;
s11: the rod structure connecting with the living arch bone forms the living arch bone rod system structure.
The invention has the beneficial effects that: in the arch rod system structure construction method based on the inertia main shaft, the inertia main shaft of the living bone is solved according to a specific rotation sequence based on the center of mass of the living bone of the arch; establishing a three-dimensional rectangular coordinate system according to the mass center and the inertia main shaft of the arch living bone; selecting six maximum and minimum marking points along three coordinate axes in the established three-dimensional rectangular coordinate system; reversing the six marking points according to a specific rotation reverse sequence; connecting six points to form a rod structure of the arch living bone; the rod structure connecting 7 tarsal bones and 5 metatarsal bones forms an arch rod system; the novel method for forming statics and dynamics analysis of the foot and optimization calculation of the structure of the foot wearing article is characterized in that a rod piece structure has a mechanical model of the foot, mechanical analysis can be carried out according to needs, such as comfort analysis of shoes, comfort analysis of basketball center shoes and simulation of rotation load of one foot, the fact that the lower part of a metatarsophalangeal joint is designed to be in a round shape can be found, and friction force is reduced so as to facilitate rotation; the above method has higher reliability in a complex structure such as an arch than the existing method using finite elements.
Drawings
Fig. 1 is a schematic view of an arch living bone and a bar system structure thereof obtained by an arch bar system structure construction method based on inertia principal axes according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of an arch bar system obtained by an arch bar system structure construction method based on inertia principal axes according to an embodiment of the present invention;
Detailed Description
In order to explain technical contents, achieved objects, and effects of the present invention in detail, the following description is made with reference to the accompanying drawings in combination with the embodiments.
The most key concept of the invention is as follows: solving an inertia main shaft of the living bone according to a specific rotation sequence based on the center of mass of the arch living bone; establishing a three-dimensional rectangular coordinate system according to the mass center and the inertia main shaft of the arch living bone; selecting six maximum and minimum marking points along three coordinate axes in the established three-dimensional rectangular coordinate system; reversing the six marking points according to a specific rotation reverse sequence; and connecting six points to form a rod structure of the arch living bone.
Referring to fig. 1 and 2, the invention relates to a method for constructing an arch bar system structure based on inertia principal axes, comprising the following steps:
s1: acquiring a three-dimensional model of an arch living bone;
s2: dividing the obtained three-dimensional model of the arch living bone into a set of a plurality of volume microelements, and then obtaining the centroid of the three-dimensional model of the arch living bone according to the coordinates and the density of each volume microelement in the image;
s3: respectively establishing a first three-dimensional rectangular coordinate system with a coordinate origin on the arch living bone mass center;
s4: sequentially rotating the arch living bone along x, y and z axes of a first three-dimensional rectangular coordinate system to sequentially obtain corresponding inertia moment;
s41: rotating the arch living bone along an x axis in a first three-dimensional rectangular coordinate system by alpha to obtain a first moment of inertia of each volume infinitesimal element of the arch living bone relative to the x axis;
s42: rotating the arch living bone by beta along a y axis in a first three-dimensional rectangular coordinate system to obtain a second inertia moment of each volume infinitesimal element of the arch living bone relative to the y axis;
s43: rotating the arch living bone along a z axis in a first three-dimensional rectangular coordinate system to obtain a third inertia moment of each volume infinitesimal element of the arch living bone relative to the z axis;
s5: obtaining inertia products of all volume infinitesimal elements of the arch living bone according to the obtained first inertia moment, the second inertia moment and the third inertia moment;
s6: repeating the steps S4-S5, and when the inertia product of each volume infinitesimal element of the obtained arch living bone is zero, taking the main shaft of the arch living bone with the inertia product of zero as an inertia main shaft;
s7: establishing a second three-dimensional rectangular coordinate system according to the obtained mass center and inertia main shaft of the arch living bone;
s8: respectively obtaining 6 marking points in the living bone relative to the three-dimensional rectangular coordinate system, wherein the 6 marking points are (x)max,0,0),(xmin,0,0),(ymax,0,0),(ymin,0,0),(zmax,0,0),(zmin,0,0)；
S9: respectively rotating the 6 coordinate points along the z, y and x of the second three-dimensional rectangular coordinate system by-gamma, -beta and-alpha,
s10: connected in rod form (x)max0,0) and (x)min0,0) in the form of rods (y)max0,0) and (y)min0,0) in the form of rods (z)max0,0) and (z)min0,0) to obtain an arch living body bone rod structure based on the inertia main shaft;
s11: the rod structure connecting with the living arch bone forms the living arch bone rod system structure.
The arch bar system structure construction method based on the inertia main shaft has the beneficial effects that: in the arch rod system structure construction method based on the inertia main shaft, the inertia main shaft of the living bone is solved according to a specific rotation sequence based on the center of mass of the living bone of the arch; establishing a three-dimensional rectangular coordinate system according to the mass center and the inertia main shaft of the arch living bone; selecting six maximum and minimum marking points along three coordinate axes in the established three-dimensional rectangular coordinate system; reversing the six marking points according to a specific rotation reverse sequence; connecting six points to form a rod structure of the arch living bone; the rod structure connecting 7 tarsal bones and 5 metatarsal bones forms an arch rod system; the novel method for forming statics and dynamics analysis of the foot and optimization calculation of the structure of the foot wearing article is characterized in that a rod piece structure has a mechanical model of the foot, mechanical analysis can be carried out according to needs, such as comfort analysis of shoes, comfort analysis of basketball center shoes and simulation of rotation load of one foot, the fact that the lower part of a metatarsophalangeal joint is designed to be in a round shape can be found, and friction force is reduced so as to facilitate rotation; the above method has higher reliability in a complex structure such as an arch than the existing method using finite elements.
Further, in the method for constructing an arch bar system structure based on principal axes of inertia, after S11, the method further includes the steps of:
s12: and setting the connection relationship among the rod piece structures in the arch living body bone rod system structure, wherein the connection relationship comprises a spherical hinge or a cylindrical hinge.
Further, in the method for constructing an arch bar system structure based on principal axes of inertia, after S12, the method further includes the steps of:
s13: assigning the elastic modulus of each rod piece material in the arch living body bone rod system structure, including the Young elastic modulus;
further, in the method for constructing an arch bar system structure based on principal axes of inertia, after S13, the method further includes the steps of:
s14: according to the requirement of human motion analysis, the arch living body skeleton system structure is subjected to statics and dynamics analysis, and quantitative parameters are provided for optimizing the shape and the structure of the foot wearing object according to the law of structural stress and force transmission.
Further, in the arch bar system structure construction method based on inertia principal axes, the step S1 is specifically:
and according to the sectional image of the arch living bone, performing three-dimensional reconstruction on the arch living bone to obtain a three-dimensional model of the arch living bone.
Further, in the arch bar system structure construction method based on inertia principal axes, the step S1 is specifically:
according to the cross-sectional image of the arch living bone, performing three-dimensional reconstruction on the arch living bone to obtain a three-dimensional model of the arch living bone; the arch living bones include 7 tarsal bones and 5 metatarsal bones.
Further, the arch bar system structure construction method based on the inertia principal axis specifically comprises the following steps:
s1: according to the cross-sectional image of the arch living bone, performing three-dimensional reconstruction on the arch living bone to obtain a three-dimensional model of the arch living bone; the arch living bones comprise 7 tarsal bones and 5 metatarsal bones;
s2: dividing the obtained three-dimensional model of the arch living bone into a set of a plurality of volume microelements, and then obtaining the mass center of each volume infinitesimal three-dimensional model of the arch living bone according to the coordinates and the density of each volume infinitesimal in the image;
s3: respectively establishing a first three-dimensional rectangular coordinate system with a coordinate origin on the arch living bone mass center;
s4: sequentially rotating the arch living bone along x, y and z axes of a first three-dimensional rectangular coordinate system to sequentially obtain corresponding inertia moment;
s41: rotating the arch living bone along an x axis in a first three-dimensional rectangular coordinate system by alpha to obtain a first moment of inertia of each volume infinitesimal element of the arch living bone relative to the x axis;
s42: rotating the arch living bone by beta along a y axis in a first three-dimensional rectangular coordinate system to obtain a second inertia moment of each volume infinitesimal element of the arch living bone relative to the y axis;
s43: rotating the arch living bone along a z axis in a first three-dimensional rectangular coordinate system to obtain a third inertia moment of each volume infinitesimal element of the arch living bone relative to the z axis;
s5: obtaining inertia products of all volume infinitesimal elements of the arch living bone according to the obtained first inertia moment, the second inertia moment and the third inertia moment;
s6: repeating the steps S4-S5, and when the inertia product of each volume infinitesimal element of the obtained arch living bone is zero, taking the main shaft of the arch living bone with the inertia product of zero as an inertia main shaft;
s7: establishing a second three-dimensional rectangular coordinate system according to the obtained mass center and inertia main shaft of the arch living bone;
s8: respectively obtaining 6 marking points in the living bone relative to the three-dimensional rectangular coordinate system, wherein the 6 marking points are (x)max,0,0),(xmin,0,0),(ymax,0,0),(ymin,0,0),(zmax,0,0),(zmin,0,0)；
S9: respectively rotating the 6 coordinate points along the z, y and x of the second three-dimensional rectangular coordinate system by-gamma, -beta and-alpha,
s10: connected in rod form (x)max0,0) and (x)min0,0) in the form of rods (y)max0,0) and (y)min0,0) in the form of rods (z)max0,0) and (z)min0,0) to obtain an arch living body bone rod structure based on the inertia main shaft;
s11: a rod member structure connected with the arch living bone to form an arch living bone rod system structure;
s12: setting the constraint relation between rod structures in the arch living body bone rod system structure, wherein the constraint relation comprises spherical hinge or cylindrical hinge connection;
s13: assigning the elastic modulus of each rod piece material in the arch living body bone rod system structure, including the Young elastic modulus;
s14: according to the requirement of human motion analysis, the arch living body skeleton system structure is subjected to statics and dynamics analysis, and quantitative parameters are provided for optimizing the shape and the structure of the foot wearing object according to the law of structural stress and force transmission.
Example 1
An arch bar system structure construction method based on inertia main shafts comprises the following steps:
s1: according to the cross-sectional image of the arch living bone, performing three-dimensional reconstruction on the arch living bone to obtain a three-dimensional model of the arch living bone; the arch living bones comprise 7 tarsal bones and 5 metatarsal bones;
s2: dividing the obtained three-dimensional model of the arch living bone into a set of a plurality of volume microelements, and then obtaining the mass center of each volume infinitesimal three-dimensional model of the arch living bone according to the coordinates and the density of each volume infinitesimal in the image; the arch living bones comprise 7 tarsal bones and 5 metatarsal bones;
s3: respectively establishing a first three-dimensional rectangular coordinate system with a coordinate origin on the arch living bone mass center;
s4: sequentially rotating the arch living bone along x, y and z axes of a first three-dimensional rectangular coordinate system to sequentially obtain corresponding inertia moment;
s41: rotating the arch living bone along an x axis in a first three-dimensional rectangular coordinate system by alpha to obtain a first moment of inertia of each volume infinitesimal element of the arch living bone relative to the x axis;
s42: rotating the arch living bone by beta along a y axis in a first three-dimensional rectangular coordinate system to obtain a second inertia moment of each volume infinitesimal element of the arch living bone relative to the y axis;
s43: rotating the arch living bone along a z axis in a first three-dimensional rectangular coordinate system to obtain a third inertia moment of each volume infinitesimal element of the arch living bone relative to the z axis;
s5: obtaining inertia products of all volume infinitesimal elements of the arch living bone according to the obtained first inertia moment, the second inertia moment and the third inertia moment;
s6: repeating the steps S4-S5, and when the inertia product of each volume infinitesimal element of the obtained arch living bone is zero, taking the main shaft of the arch living bone with the inertia product of zero as an inertia main shaft;
s7: establishing a second three-dimensional rectangular coordinate system according to the obtained mass center and inertia main shaft of the arch living bone;
s8: respectively obtaining 6 marking points in the living bone relative to the three-dimensional rectangular coordinate system, wherein the 6 marking points are (x)max,0,0),(xmin,0,0),(ymax,0,0),(ymin,0,0),(zmax,0,0),(zmin,0,0)；
S9: respectively rotating the 6 coordinate points along z, y and x of a second three-dimensional rectangular coordinate system by-gamma, -beta and-alpha;
s10: connected in rod form (x)max0,0) and (x)min0,0) in the form of rods (y)max0,0) and (y)min0,0) in the form of rods (z)max0,0) and (z)min0,0) to obtain an arch living body bone rod structure based on the inertia main shaft;
s11: a rod member structure connected with the arch living bone to form an arch living bone rod system structure;
s12: setting the constraint relation between rod structures in the arch living body bone rod system structure, wherein the constraint relation comprises spherical hinge or cylindrical hinge connection;
s13: assigning the elastic modulus of each rod piece material in the arch living body bone rod system structure, including the Young elastic modulus;
s14: according to the requirement of human motion analysis, the arch living body skeleton system structure is subjected to statics and dynamics analysis, and quantitative parameters are provided for optimizing the shape and the structure of the foot wearing object according to the law of structural stress and force transmission.
Example 2
The calculation principle of the arch bar system structure construction method based on the inertia main shaft is as follows:
solving the mass center and the inertia principal axis of the arch living bone, wherein the inertia principal axis is respectively wound on the order of x, y, y, x, y, z and … …, and the angular displacement of the rotation is recorded as alpha1,β1,γ1,α2,β2,λ2,……；
The centroid of the arch bone is calculated by reconstructing the centroid of the arch bone based on the tomogram from the following equation:
in the formula (x)c,yc,zc) Is the center of mass of the arch bone, (x)iyi,zi) Indicating the location and mass of the ith volume element of the arch bone.
The arch bone is prescribed to rotate in the x → y → z order.
Rotation about the x-axis;
a spatial rectangular coordinate system for reconstructing the centroid of the arch bone based on the tomogram is represented by oxyz, the arch bone reconstructed by the tomogram consists of a finite number of volume elements, and is represented by Ix,Iy,IzRepresenting moments of inertia for the x, y, z axes, respectively.
Moment of inertia of the arch bone is:
product of inertia of arch bone:
where dV denotes a volume voxel, ρ denotes a gray value of the volume voxel, and (x, y, z) denotes a position coordinate of the volume voxel.
Reconstructing the body coordinate of the center of mass of the arch bone by the tomography image and rotating alpha around the X axis to form a new coordinate system oxαyαzαCoordinates (x) of volume elementsα,yα,zα) The relationship to (x, y, z) is:
substituting equations (4b) and (4c) into moments of inertia about the x-axis
In (1), obtaining:
from equation (5), the moment of inertia about the x-axis is constant.
Substituting equations (4a), (4b) and (4c) into the sum of the moments of inertia about the y-axis and z-axis
In (1), obtaining:
from equation (5), equation (6) can be expressed as:
from equation (7), rotation about the x-axis is invariant to the sum of the moments of inertia of the y-axis and z-axis. In combination with equation (5), the moment of inertia of the arch bone reconstructed by the tomography is invariant around the x-axis.
Substituting equations (4a) and (4c) into
In (1), obtaining:
substituting equations (4a) and (4b) into
In (1), obtaining:
the following equations are established:
from equations (8) and (9), equation (10) can be expressed as:
f(α,β,γ)α＝∫(y2(sin2α-cos2α)+4yzsinαcosα+z2(cos2α-sin2α))ρdV (11)
since 2sin α cos α ═ sin2 α, cos2α-sin2α — cos2 α, equation 11 can be expressed as:
f(α,β,γ)α＝∫(-y2cos2α+2yzsin2α+z2cos2α)ρdV (12)
order to
Equation (12) becomes:
thus is provided with
sin2α∫y2ρdV+2cos2α∫yzρdV-sin2α∫z2ρdV＝0 (14)
Due to the fact that
sin2α∫x2ρdV-sin2α∫x2ρdV＝0 (15)
Substituting equation (15) into equation (14) yields the following equation:
sin2α∫y2ρdV+sin2α∫x2ρdV+2cos2α∫yzρdV-sin2α∫z2ρdV-sin2α∫x2ρdV＝0
(16) from equation (2), equation (16) can be expressed as:
sin2αIz+2cos2αIyz-sin2αIy＝0 (17)
both sides of equation (17) are divided by cos2 α to obtain
tan2αIz+2Iyz-tan2αIy＝0 (18)
Further, there are:
solving the inverse function of equation (19) yields:
rotating about the y-axis
After rotating alpha around the x-axis, using ox by a spatial rectangular coordinate system for reconstructing the center of mass of the arch bone based on tomogramsαyαzαShow, by
Respectively represent a pair xα,yα,zαMoment of inertia of the shaft.
Moment of inertia of the arch bone is:
the product of inertia of the arch bone is:
where dV represents a volume voxel and ρ represents a gray value of the volume voxel, (x)α,yα,zα) Representing the position coordinates of the volume element.
Reconstructing the body coordinate of the center of mass of the arch bone through the tomogram and rotating beta around the y axis to form a new coordinate system oxαβyαβzαβCoordinates (x) of volume elementsαβ,yαβ,zαβ) And (x)α,yα,zα) The relationship of (1) is:
substituting equations (23a) and (23c) into moments of inertia about the y-axis
In (1), obtaining:
by equation (24), the moment of inertia about the y-axis is invariant.
Substituting equations (23a), (23b), and (23c) into the sum of the moments of inertia about the x-axis and z-axis
In (1), obtaining:
from equation (24), equation (25) can be rewritten as:
from equation (26), the moment of inertia about the y-axis is invariant to the sum of the moments of inertia about the x-axis and the z-axis. In conjunction with equation (24), the moment of inertia of the arch bone is constant, rotating about the y-axis.
Substituting equations (23b) and (23c) into
In (1), obtaining:
substituting equations (23a) and (23b) into
In (1), obtaining:
the following equations are established:
from equations (27) and (28), equation (29) can be expressed as:
since 2sin β cos β ═ sin2 β, cos2β-sin2β cos2 β, equation (30) can be expressed as:
order to
Due to the fact that
Thus is provided with
Due to the fact that
Substituting equation (34) into equation (33) yields the following equation:
from equation (21), equation (45) can be expressed as:
both sides of equation (36) are divided by cos2 β to obtain
Further, there are:
solving the inverse function of equation (38) to obtain
Rotating about the z-axis
After rotating alpha around the x axis and then rotating beta around the y axis, using ox through a space rectangular coordinate system for reconstructing the center of mass of the arch bone based on the tomogramαβyαβzαβShow, by
Respectively represent a pair xαβ,yαβ,zαβMoment of inertia of the shaft.
Moment of inertia of the arch bone is:
the product of inertia of the arch bone is:
where dV represents a volume voxel and ρ represents a gray value of the volume voxel, (x)αβ,yαβ,zαβ) Representing the position coordinates of the volume element.
Reconstructing the body coordinate of the center of mass of the arch bone by the tomography image and rotating gamma around the z axis to form a new coordinate system oxαβγyαβγzαβγCoordinates (x) of volume elementsαβγ,yαβγ,zαβγ) And (x)αβ,yαβ,zαβ) The relationship of (1) is:
substituting equations (42a) and (42b) into moments of inertia about the z-axis
In (1), obtaining:
from equation (43), the moment of inertia about the z-axis is invariant.
Substituting equations (42a), (42b), and (42c) into the sum of the moments of inertia about the x-axis and z-axis
In (1), obtaining:
from equation (44), it can be seen that the rotation around the z-axis has invariance to the sum of the moments of inertia of the x-axis and the y-axis. In conjunction with equation (43), the moment of inertia of the arch bone is constant, rotating about the z-axis.
Substituting equations (42b) and (42c) into
In (1), obtaining:
substituting equations (42a) and (42b) into
In (1), obtaining:
the following equations are established:
from equations (45) and (46), equation (47) can be expressed as:
since 2sin γ cos λ ═ sin2 γ, cos2γ-sin2γ ═ cos2 γ, equation (48) can be expressed as:
order to
Due to the fact that
Thus is provided with
Due to the fact that
Substituting equation (52) into equation (51) yields the following equation:
from equation (40), equation (53) can be expressed as:
both sides of equation (54) are divided by cos2 γ to obtain
Further, there are:
solving the inverse function of equation (68) to obtain
And (3) rotating in the sequence of x → y → z, stopping rotating if the inertia product of the arch bone is zero, and continuing rotating in the sequence of x → y → z until the inertia product of the arch bone is zero if the inertia product of the arch bone is not zero, wherein the main shaft of the arch bone is the main shaft of inertia.
Establishing a three-dimensional rectangular coordinate system by using the mass center and the inertia main shaft of the arch living bone;
for a non-symmetric body, the rotation sequence is different, six marking points are respectively obtained in the living bone relative to the three-dimensional rectangular coordinate system, and the coordinate points are respectively (x)max,0,0),(xmin,0,0),(ymax,0,0),(ymin,0,0),(zmax,0,0),(zmin,0,0)。
x → y → z rotation
From equation (4), equation (23) can be changed to:
from equation (42), equation (58) can be rewritten as:
(59) y → z → x rotation
From equation (42), equation (23) can be rewritten as:
from equation (4), equation (60) can be rewritten as:
z → x → y rotation
From equation (4), equation (42) can be rewritten as:
from equation (23), equation (62) can be rewritten as:
it can be seen from equations (59), (61) and (63) that the results of rotating in different orders are different. The posture before rotation is recovered to a mode that the posture can be reversed only reversely.
Marking the six coordinate points, and then respectively rotating the six coordinate points by … … z, y, x, z, y, x in the sequence of … … -lambda2,-β2,-α2,-γ1,-β1,-α1；
Connected in rod form (x)max0,0) and (x)min0,0) in the form of rods (y)max0,0) and (y)min0,0) in the form of rods (z)max0,0) and (z)min,0,0)；
The rod structure of 7 tarsal bones and 5 metatarsal bones forms an arch rod system, the constraint relation (such as spherical hinge and column hinge connection) among the rods is set, the elastic modulus (such as Young elastic modulus) of the rod material is assigned, the structure of the arch rod system is analyzed statically and dynamically according to the requirement of human motion analysis, and quantitative parameters are provided for optimizing the form and the structure of the foot wearing object according to the law of structural stress and force transmission.
In conclusion, in the construction method of the arch bar system structure based on the inertia main shafts, the inertia main shafts of the living bones are solved according to a specific rotation sequence based on the mass center of the living bones of the arch; establishing a three-dimensional rectangular coordinate system according to the mass center and the inertia main shaft of the arch living bone; selecting six maximum and minimum marking points along three coordinate axes in the established three-dimensional rectangular coordinate system; reversing the six marking points according to a specific rotation reverse sequence; connecting six points to form a rod structure of the arch living bone; the rod structure connecting 7 tarsal bones and 5 metatarsal bones forms an arch rod system; the novel method for forming statics and dynamics analysis of the foot and optimization calculation of the structure of the foot wearing article is characterized in that a rod piece structure has a mechanical model of the foot, mechanical analysis can be carried out according to needs, such as comfort analysis of shoes, comfort analysis of basketball center shoes and simulation of rotation load of one foot, the fact that the lower part of a metatarsophalangeal joint is designed to be in a round shape can be found, and friction force is reduced so as to facilitate rotation; the above method has higher reliability in a complex structure such as an arch than the existing method using finite elements.
The above description is only an embodiment of the present invention, and not intended to limit the scope of the present invention, and all equivalent changes made by using the contents of the present specification and the drawings, or applied directly or indirectly to the related technical fields, are included in the scope of the present invention.
Claims (6)
1. An arch bar system structure construction method based on an arch living body bone inertia main shaft is characterized by comprising the following steps:
s1: acquiring a three-dimensional model of an arch living bone;
s2: dividing the obtained three-dimensional model of the arch living bone into a set of a plurality of volume microelements, and then obtaining the centroid of the three-dimensional model of the arch living bone according to the coordinates and the density of each volume microelement in the image;
s3: respectively establishing a first three-dimensional rectangular coordinate system with a coordinate origin on the arch living bone mass center;
s4: sequentially rotating the arch living bone along x, y and z axes of a first three-dimensional rectangular coordinate system to sequentially obtain corresponding inertia moment;
s41: rotating the arch living bone along an x axis in a first three-dimensional rectangular coordinate system by alpha to obtain a first moment of inertia of each volume infinitesimal element of the arch living bone relative to the x axis;
s42: rotating the arch living bone by beta along a y axis in a first three-dimensional rectangular coordinate system to obtain a second inertia moment of each volume infinitesimal element of the arch living bone relative to the y axis;
s43: rotating the arch living bone along a z axis in a first three-dimensional rectangular coordinate system to obtain a third inertia moment of each volume infinitesimal element of the arch living bone relative to the z axis;
s5: obtaining inertia products of all volume infinitesimal elements of the arch living bone according to the obtained first inertia moment, the second inertia moment and the third inertia moment;
s6: repeating the steps S4-S5, and when the inertia product of each volume infinitesimal element of the obtained arch living bone is zero, taking the main shaft of the arch living bone with the inertia product of zero as an inertia main shaft;
s7: establishing a second three-dimensional rectangular coordinate system according to the obtained mass center and inertia main shaft of the arch living bone;
s8: respectively obtaining 6 marking points in the living bone relative to the three-dimensional rectangular coordinate system, wherein the 6 marking points are (x)max,0,0),(xmin,0,0),(ymax,0,0),(ymin,0,0),(zmax,0,0),(zmin,0,0)；
S9: respectively rotating the 6 coordinate points along z, y and x of a second three-dimensional rectangular coordinate system by-gamma, -beta and-alpha;
s10: connected in rod form (x)max0,0) and (x)min0,0) in the form of rods (y)max0,0) and (y)min0,0) in the form of rods (z)max0,0) and (z)min0,0) to obtain an arch living body bone rod structure based on the inertia main shaft;
s11: the rod structure connecting with the living arch bone forms the living arch bone rod system structure.
2. The method for constructing an arch bar system structure based on principal axes of inertia of living bones in the arch according to claim 1, further comprising the step of, after the step of S11:
s12: and setting the connection relationship among the rod piece structures in the arch living body bone rod system structure, wherein the connection relationship comprises a spherical hinge or a cylindrical hinge.
3. The method for constructing an arch bar system structure based on principal axes of inertia of living bones in the arch according to claim 2, further comprising the step of, after the step of S12:
s13: and assigning the elastic modulus of each rod piece material in the arch living body bone rod system structure, including the Young's modulus of elasticity.
4. The method for constructing an arch bar system structure based on principal axes of inertia of living bones in the arch according to claim 3, further comprising the step of, after the step of S13:
s14: according to the requirement of human motion analysis, the arch living body skeleton system structure is subjected to statics and dynamics analysis, and quantitative parameters are provided for optimizing the shape and the structure of the foot wearing object according to the law of structural stress and force transmission.
5. The method for constructing an arch bar system structure based on the principal axis of inertia of living bones in the arch according to claim 1, wherein the step S1 is specifically as follows:
and according to the sectional image of the arch living bone, performing three-dimensional reconstruction on the arch living bone to obtain a three-dimensional model of the arch living bone.
6. The method for constructing an arch bar system structure based on the principal axis of inertia of living bones in the arch according to claim 1, wherein the step S1 is specifically as follows:
according to the cross-sectional image of the arch living bone, performing three-dimensional reconstruction on the arch living bone to obtain a three-dimensional model of the arch living bone; the arch living bones include 7 tarsal bones and 5 metatarsal bones.
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