CN111678476B - Method for measuring direction and spatial position of rotation center of rotating shaft - Google Patents

Method for measuring direction and spatial position of rotation center of rotating shaft Download PDF

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CN111678476B
CN111678476B CN202010534564.9A CN202010534564A CN111678476B CN 111678476 B CN111678476 B CN 111678476B CN 202010534564 A CN202010534564 A CN 202010534564A CN 111678476 B CN111678476 B CN 111678476B
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rotating shaft
plane
axis
equation
intersection point
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CN111678476A (en
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杨小君
訾进锋
梁晨涛
吴平
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Xi'an Zhongke Weijing Photon Technology Co ltd
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Xi'an Micromach Technology Co ltd
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23K—SOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
    • B23K26/00—Working by laser beam, e.g. welding, cutting or boring
    • B23K26/70—Auxiliary operations or equipment
    • B23K26/702—Auxiliary equipment
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/22—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes
    • G01B21/24—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring angles or tapers; for testing the alignment of axes for testing alignment of axes
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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Abstract

The invention discloses a method for measuring the rotation center direction and the spatial position of a rotating shaft, which comprises the following steps: s101: the rotating shaft A and the rotating shaft C are arranged at zero positions, and an inclined plane is arranged on a working table top of the rotating shaft C; s102: the rotation axis A is fixed, the rotation axis C rotates, a lattice is measured on a plane through a distance measuring sensor, a plane equation is fitted, and then a space focus of the plane and a normal focus of the plane are calculated to obtain the axis of the rotation axis C; s103: c, the rotating shaft is fixed, the rotating shaft A rotates, a dot matrix is measured on a plane through a distance measuring sensor, a plane equation is fitted, and then a space focus of the plane and a normal focus of the plane are calculated to obtain the axis of the rotating shaft A; the invention can measure the space position and geometric error of the rotating shaft of the movable machine tool.

Description

Method for measuring direction and spatial position of rotation center of rotating shaft
Technical Field
The invention relates to the field of laser processing, in particular to a method for measuring the rotation center direction and the spatial position of a rotating shaft.
Background
The beam scanning module of the laser processing equipment adopts non-contact processing, so that laser directly acts on the surface of a workpiece, and the laser processing equipment has the characteristics of small heat influence, flexible processing, wide material and the like.
The movable measuring device is internally provided with three linear shafts X, Y, Z and two rotating shafts A, C, the light beam scanning module and the point laser ranging sensor are arranged on the Z shaft and perform linear motion along with the Z shaft, and the processing table surface is parallel to the rotating plane of the C shaft.
When the machining position and the machining direction vector are known, the attitude of each axis of the machine tool to be machined can be obtained by simple calculation assuming that the axis of each rotating axis completely coincides with the theoretical axis, but since the axis of the rotating axis inevitably has a certain error during the assembly of the machine tool, the position and the direction of the axis of the rotating axis of the machine tool need to be measured, and the machining attitude needs to be analyzed under known conditions to calculate the position of each axis of the machine tool.
Disclosure of Invention
The invention provides a method for measuring the rotation center direction and the spatial position of a rotating shaft, which can measure the rotation center position of the rotating shaft of a movable machine tool relative to the zero point of a distance measuring sensor of the machine tool and the axial direction of the rotating shaft in a machine tool coordinate system.
To achieve these objects and other advantages in accordance with the purpose of the invention, there is provided a rotation axis rotation center direction and spatial position measuring method including the steps of:
s101: the rotating shaft A and the rotating shaft C are arranged at zero positions, and an inclined plane with an inclination angle of 10-30 degrees is arranged on a working table surface of the rotating shaft C;
s102: the rotation axis A is fixed, the rotation axis C rotates for multiple times, a rectangular lattice is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation is static, then a space plane equation of a plurality of inclined planes and the value of a normal vector thereof are fitted through the measured lattice, and a plane intersection point P can be calculated through the information1Axial to the C axis
Figure BDA0002536565640000011
P1And
Figure BDA0002536565640000012
the formed space straight line is the axis of the C rotating shaft;
s103: c, the rotating shaft is fixed, the rotating shaft A rotates for multiple times, a rectangular lattice is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation is static, then space plane equations of a plurality of inclined planes and values of normal vectors of the space plane equations are fitted through the measured lattice, and a plane intersection point P can be calculated through the information2Axial to the A axis
Figure BDA0002536565640000021
P2And
Figure BDA0002536565640000022
the formed space straight line is the axis of the rotating shaft A;
wherein the A rotating shaft performs rotating motion around the axis of the X shaft; the C rotating shaft is installed on the A rotating shaft and integrally and simultaneously rotates along with the A rotating shaft, and when the A rotating shaft is located at 0 degree, the C rotating shaft rotates around the axis of the Z shaft.
Further, in the step S102, the plane equation and the normal vector of the plane thereof
Figure BDA0002536565640000023
The calculation method of (2) is as follows:
the space plane coefficients A, B, C, D satisfy equation XiA+YiB+ZiC + D is 0(i is less than or equal to m, and m is more than or equal to 4), wherein (X)i,Yi,Zi) For the spatial coordinates of each point in the rectangular lattice, the plane equation coefficients A, B, C, D are obtained by solving the least squares solution of the following linear equation set, and the normal vector of the plane is obtained
Figure BDA0002536565640000024
Namely (A, B, C);
Figure BDA0002536565640000025
further, in step S102, at least three slopes are in accordance with the plane directionDistance XiA+YiB+ZiC + D is 0, and the normal vectors of the plane intersection point and the respective plane are calculated
Figure BDA0002536565640000026
The calculation method of the plane intersection point is as follows:
Figure BDA0002536565640000027
the intersection point of the spatial planes is obtained by solving the least square solution of the linear equation system.
Further, in step S102, at least three normal vectors are passed
Figure BDA0002536565640000028
Calculating the axial direction of the C-axis
Figure BDA0002536565640000029
The calculation method is as follows:
make the axial unit vector of the rotating shaft
Figure BDA00025365656400000210
Expressing, unit vector for each plane normal vector
Figure BDA00025365656400000211
Is shown, wherein, due to
Figure BDA00025365656400000212
Is obtained by rotating the same plane around a rotating shaft
Figure BDA00025365656400000213
And optionally
Figure BDA00025365656400000214
Included angles are equal because
Figure BDA00025365656400000224
And
Figure BDA00025365656400000225
are all unit vectors (length 1), i.e.
Figure BDA00025365656400000217
Is provided with
Figure BDA00025365656400000218
And
Figure BDA00025365656400000219
the included angle is alpha, and the included angle is alpha,
Figure BDA00025365656400000220
and
Figure BDA00025365656400000221
multiplication of phase points
Figure BDA00025365656400000222
For any i (i is less than or equal to n, n is more than or equal to 3), the following can be obtained:
Figure BDA00025365656400000223
order to
Figure BDA0002536565640000031
Wherein
Figure BDA0002536565640000032
And
Figure BDA0002536565640000033
for the same direction vector, we can obtain:
Figure BDA0002536565640000034
it is known that
Figure BDA0002536565640000035
Has a value of (A)Ni,BNi,CNi) Is provided with
Figure BDA0002536565640000036
Is (X, Y, Z), the following linear system of equations can be established:
Figure BDA0002536565640000037
solving the least squares solution of the above equations to obtain
Figure BDA0002536565640000038
Will be provided with
Figure BDA0002536565640000039
And (3) performing unitization treatment, wherein the obtained unit vector is the axial direction of the rotating shaft:
Figure BDA00025365656400000310
further, the plane intersection point P is calculated in the step S1032Axial to the A axis
Figure BDA00025365656400000311
And calculating the plane intersection point P in S1021Axial to the C axis
Figure BDA00025365656400000312
The calculation method is the same.
Preferably, in step S101, the zero positions of the a and C rotation axes are reference-positioned by a point laser ranging sensor.
Preferably, in step S102, the number of rotations of the C rotation shaft is not less than three.
Preferably, in step S102, the rotation range of the C rotation axis is 0 ° to 360 °.
Preferably, in step S103, the number of rotations of the a rotation axis is not less than three.
Preferably, in step S103, the rotation range of the C rotation axis is-45 to 45.
Compared with the prior art, the invention can calculate the rotation center position of each rotating shaft relative to the zero point of the distance measuring sensor of the machine tool and the axial direction of the rotating shaft in the coordinate system of the machine tool through the plane equation of the lattice fitting of the planes under different angles, and can calculate the attitude of each shaft of the machine tool when the five-shaft machine tool processes any point in the machine tool through the rotation center of the rotating shaft and the axial direction of the rotating shaft in the coordinate system of the machine tool.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of one embodiment of the present invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
It will be understood that terms such as "having," "including," and "comprising," as used herein, do not preclude the presence or addition of one or more other elements or groups thereof.
The invention provides a method for measuring the rotation center direction and the space position of a rotating shaft, which comprises the following steps as shown in figure 1:
s101: firstly, the rotating shaft A rotates around the axis of the shaft X; the C rotating shaft is arranged on the A rotating shaft and integrally rotates along with the A rotating shaft at the same time, and when the A rotating shaft is positioned at 0 degree, the C rotating shaft rotates around the axis of the Z shaft;
then, the rotating shaft A and the rotating shaft C are arranged at zero positions, and an inclined plane with an inclination angle of 10-30 degrees is arranged on a working table surface of the rotating shaft C; and the zero positions of the rotating shaft A and the rotating shaft C are subjected to reference positioning by a point laser ranging sensor.
S102: the rotating shaft A is fixed, the rotating shaft C rotates for multiple times, a rectangular lattice is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation is static, and then a space plane equation of a plurality of inclined planes is fitted through the measured lattice. Wherein the spatial plane equation is of the form Aix+Biy+Ciz+Di0, (i ≦ n, n ≧ 3), where the plane normal vector
Figure BDA0002536565640000041
Has a value of (A)i,Bi,Ci) Calculating the spatial intersection point P of the above planes1And the axial direction of the C axis can be calculated through the normal vector of the plane
Figure BDA0002536565640000042
P1And
Figure BDA0002536565640000043
the spatial straight line is the axis of the C rotating shaft, i.e. P1The position of the rotation center of the C rotating shaft relative to the zero point of the distance measuring sensor of the machine tool,
Figure BDA0002536565640000044
the axial direction of the rotating shaft C under the machine tool coordinate system; the number of rotations of the C-axis is not less than three, and the rotation range of the C-axis is 0-360 deg.
S103: and C, the rotating shaft is fixed, the rotating shaft A rotates for multiple times, a rectangular lattice is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation is static, and then a space plane equation of a plurality of inclined planes is fitted through the measured lattice. Wherein the spatial plane equation is of the form Ajx+Bjy+Cjz+Dj0, (j is less than or equal to n, n is more than or equal to 3), wherein the normal vector of the plane
Figure BDA0002536565640000045
Has a value of (A)j,Bj,Cj) Calculating the spatial intersection point P of the above planes2And the axial direction of the A axis can be calculated through the normal vector of the plane
Figure BDA0002536565640000046
P2And
Figure BDA0002536565640000047
the spatial straight line is the axial center of the rotating shaft A, namely P2The position of the revolution center of the rotating shaft A relative to the zero point of the distance measuring sensor of the machine tool,
Figure BDA0002536565640000051
is the axial direction of the rotating shaft A under a machine tool coordinate system; the rotating frequency of the rotating shaft A is not less than three times, and the rotating range of the rotating shaft C is-45 degrees.
Wherein the A rotating shaft performs rotating motion around the axis of the X shaft; the C rotating shaft is installed on the A rotating shaft and integrally and simultaneously rotates along with the A rotating shaft, and when the A rotating shaft is located at 0 degree, the C rotating shaft rotates around the axis of the Z shaft.
In the step S103, the plane intersection point P is calculated2Axial to the A axis
Figure BDA0002536565640000052
And calculating the plane intersection point P in S1021Axial to the C axis
Figure BDA0002536565640000053
The method for calculating the plane equation by the rectangular lattice is as follows, so that only the step S102 is taken as an example for explanation:
the space plane coefficients A, B, C, D satisfy equation XiA+YiB+ZiC + D is 0(i is less than or equal to m, and m is more than or equal to 4), wherein (X)i,Yi,Zi) For the spatial coordinates of each point in the rectangular lattice, the least squares solution is obtained by solving the following system of linear equationsTo the plane equation coefficient A, B, C, D, and obtains the normal vector of the plane
Figure BDA0002536565640000054
The value of (A, B, C);
Figure BDA0002536565640000055
sequentially measuring A, C rectangular lattices on n (n is more than or equal to 3) planes of a rotating shaft under different angles and calculating a plane equation, wherein n (n is more than or equal to 3) planes have unique intersection points under ideal conditions, and the method for calculating the plane intersection points comprises the following steps:
the point in space satisfying n (n is more than or equal to 3) space plane equations is the intersection point of the n (n is more than or equal to 3) space planes, and the space plane equation is Aix+Biy+Ciz+Di0, (i is not more than n, n is not less than 3), and the intersection point of the space plane can be obtained by solving the least square solution of the following linear equation set;
Figure BDA0002536565640000056
and, a normal vector passing through the above plurality of spatial planes
Figure BDA0002536565640000057
The axial direction of the rotating shaft can be calculated as follows:
make the axial unit vector of the rotating shaft
Figure BDA0002536565640000058
Expressing, unit vector for each plane normal vector
Figure BDA0002536565640000059
Therein, are shown. Due to the fact that
Figure BDA00025365656400000510
Is obtained by rotating the same plane around a rotating shaft
Figure BDA00025365656400000511
And optionally
Figure BDA00025365656400000512
Included angles are equal because
Figure BDA00025365656400000513
And
Figure BDA00025365656400000514
are all unit vectors (length 1), i.e.
Figure BDA00025365656400000515
Is provided with
Figure BDA00025365656400000516
And
Figure BDA00025365656400000517
the included angle is alpha, and the included angle is alpha,
Figure BDA00025365656400000518
and
Figure BDA00025365656400000519
multiplication of phase points
Figure BDA0002536565640000061
For any i (i is less than or equal to n, n is more than or equal to 3), the following can be obtained:
Figure BDA0002536565640000062
Figure BDA0002536565640000063
order to
Figure BDA0002536565640000064
Wherein
Figure BDA0002536565640000065
And
Figure BDA0002536565640000066
for the same direction vector, we can obtain:
Figure BDA0002536565640000067
it is known that
Figure BDA0002536565640000068
Has a value of (A)Ni,BNi,CNi) Is provided with
Figure BDA0002536565640000069
Is (X, Y, Z), the following linear system of equations can be established:
Figure BDA00025365656400000610
solving the least squares solution of the above equations to obtain
Figure BDA00025365656400000611
Will be provided with
Figure BDA00025365656400000612
And (3) performing unitization treatment, wherein the obtained unit vector is the axial direction of the rotating shaft:
Figure BDA00025365656400000613
the invention also provides an embodiment, and the measuring method comprises the following steps:
s201: the rotating shaft A and the rotating shaft C are arranged at zero positions, the reference positioning is carried out by a point laser ranging sensor, and an inclined plane with an inclination angle of 10-30 degrees is arranged on a working table top of the rotating shaft C;
s202: the rotating shaft A is fixed and the rotating shaft C rotatesSix times, namely 60 degrees, 120 degrees, 180 degrees, 240 degrees, 300 degrees and 360 degrees respectively, measuring a rectangular lattice on the inclined plane by using a machine tool distance measuring sensor after each rotation and rest, and then fitting a space plane equation of six inclined planes through the measured lattice, wherein the form of the space plane equation is Aix+Biy+Ciz+Di0, (i ≦ 6), where the plane normal vector
Figure BDA00025365656400000614
Has a value of (A)i,Bi,Ci) Calculating the spatial intersection point P of the above six planes1And the axial direction of the C axis can be calculated through the normal vector of the plane
Figure BDA00025365656400000615
P1And
Figure BDA00025365656400000616
the spatial straight line is the axis of the C rotating shaft, i.e. P1The position of the rotation center of the C rotating shaft relative to the zero point of the distance measuring sensor of the machine tool,
Figure BDA00025365656400000617
the axial direction of the rotating shaft C under the machine tool coordinate system;
s203: the C rotating shaft is not moved, the A rotating shaft rotates for seven times, the rotation angles are respectively 0 degrees, 15 degrees, 30 degrees, 45 degrees, 15 degrees, 30 degrees and 45 degrees, a rectangular dot matrix is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation and rest, and the form of the space plane equation is Ajx+Bjy+Cjz+Dj0, (j is less than or equal to n, n is more than or equal to 3), wherein the normal vector of the plane
Figure BDA00025365656400000618
Has a value of (A)j,Bj,Cj) Calculating the spatial intersection point P of the above seven planes2And the axial direction of the A axis can be calculated through the normal vector of the plane
Figure BDA0002536565640000071
P2And
Figure BDA0002536565640000072
the spatial straight line is the axial center of the rotating shaft A, namely P2The position of the revolution center of the rotating shaft A relative to the zero point of the distance measuring sensor of the machine tool,
Figure BDA0002536565640000073
is the axial direction of the A rotating shaft under the coordinate system of the machine tool.
And finally, calculating the processing attitude of the workpiece according to the axis of the A shaft and the axis of the C shaft obtained in the steps S202 and S203.
While embodiments of the invention have been disclosed above, it is not limited to the applications listed in the description and the embodiments. It can be applied to all kinds of fields suitable for the present invention. Additional modifications will readily occur to those skilled in the art. It is therefore intended that the invention not be limited to the exact details and illustrations described and illustrated herein, but fall within the scope of the appended claims and equivalents thereof.

Claims (8)

1. A method for measuring the rotation center direction and the space position of a rotating shaft is characterized by comprising the following steps:
s101: the rotating shaft A and the rotating shaft C are arranged at zero positions, and an inclined plane with an inclination angle of 10-30 degrees is arranged on a working table surface of the rotating shaft C;
s102: the rotation axis A is fixed, the rotation axis C rotates at least three times, a rectangular lattice is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation is static, then a space plane equation of at least three inclined planes and the value of a normal vector thereof are fitted through the measured lattice, and a plane intersection point P can be calculated through the information1Axial to the C axis
Figure FDA0003157913550000011
P1And
Figure FDA0003157913550000012
the formed space straight line is the axis of the C rotating shaft;
s103: c, the rotating shaft is fixed, the rotating shaft A rotates at least three times, a rectangular lattice is measured on the inclined plane by using a machine tool distance measuring sensor after each rotation is static, then a space plane equation of at least three inclined planes and the value of a normal vector of the space plane equation are fitted through the measured lattice, and a plane intersection point P can be calculated through the information2Axial to the A axis
Figure FDA0003157913550000013
P2And
Figure FDA0003157913550000014
the formed space straight line is the axis of the rotating shaft A;
wherein the A rotating shaft performs rotating motion around the axis of the X shaft; the C rotating shaft is installed on the A rotating shaft and integrally and simultaneously rotates along with the A rotating shaft, and when the A rotating shaft is located at 0 degree, the C rotating shaft rotates around the axis of the Z shaft.
2. The method as claimed in claim 1, wherein the plane equation and the normal vector of the plane are determined in step S102
Figure FDA0003157913550000015
The calculation method of (2) is as follows:
the space plane coefficients A, B, C, D satisfy equation XiA+YiB+ZiC + D is 0(i is less than or equal to m, and m is more than or equal to 4), wherein (X)i,Yi,Zi) For the spatial coordinates of each point in the rectangular lattice, the plane equation coefficients A, B, C, D are obtained by solving the least squares solution of the following linear equation set, and the normal vector of the plane is obtained
Figure FDA0003157913550000016
Namely (A, B, C);
Figure FDA0003157913550000017
3. the method as claimed in claim 2, wherein in step S102, at least three inclined planes are formed according to the plane equation XiA+YiB+ZiC + D is 0, and the normal vectors of the plane intersection point and the respective plane are calculated
Figure FDA0003157913550000018
The calculation method of the plane intersection point is as follows:
Figure FDA0003157913550000021
the intersection point of the spatial planes is obtained by solving the least square solution of the linear equation system.
4. The method as claimed in claim 3, wherein in step S102, at least three normal vectors are passed
Figure FDA0003157913550000022
Calculating the axial direction of the C-axis
Figure FDA0003157913550000023
The calculation method is as follows:
make the axial unit vector of the rotating shaft
Figure FDA0003157913550000024
Expressing, unit vector for each plane normal vector
Figure FDA0003157913550000025
Is shown, wherein, due to
Figure FDA0003157913550000026
Is obtained by rotating the same plane around a rotating shaft
Figure FDA0003157913550000027
And optionally
Figure FDA0003157913550000028
Included angles are equal because
Figure FDA0003157913550000029
And
Figure FDA00031579135500000210
are all unit vectors (length 1), i.e.
Figure FDA00031579135500000211
Is provided with
Figure FDA00031579135500000212
And
Figure FDA00031579135500000213
the included angle is alpha, and the included angle is alpha,
Figure FDA00031579135500000214
and
Figure FDA00031579135500000215
multiplication of phase points
Figure FDA00031579135500000216
For any i (i is less than or equal to n, n is more than or equal to 3), the following can be obtained:
Figure FDA00031579135500000217
Figure FDA00031579135500000218
order to
Figure FDA00031579135500000219
Wherein
Figure FDA00031579135500000220
And
Figure FDA00031579135500000221
for the same direction vector, we can obtain:
Figure FDA00031579135500000222
it is known that
Figure FDA00031579135500000223
Has a value of (A)Ni,BNi,CNi) Is provided with
Figure FDA00031579135500000224
Is (X, Y, Z), the following linear system of equations can be established:
Figure FDA00031579135500000225
solving the least squares solution of the above equations to obtain
Figure FDA00031579135500000226
Will be provided with
Figure FDA00031579135500000227
And (3) performing unitization treatment, wherein the obtained unit vector is the axial direction of the rotating shaft:
Figure FDA00031579135500000228
5. the method as claimed in claim 1, wherein the step S103 is performed by calculating the plane intersection point P2Axial to the A axis
Figure FDA00031579135500000229
And calculating the plane intersection point P in S1021Axial to the C axis
Figure FDA00031579135500000230
The calculation method is the same.
6. The method as claimed in claim 1, wherein the zero positions of the a-axis and the C-axis are reference-positioned by a point laser ranging sensor in step S101.
7. The method as claimed in claim 1, wherein the rotation range of the C-axis is 0 ° to 360 ° in step S102.
8. The method as claimed in claim 1, wherein the rotation range of the C-axis is-45 ° to 45 ° in step S103.
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