CN106871859B - Rigid space fixed shaft rotation angle detection method - Google Patents

Rigid space fixed shaft rotation angle detection method Download PDF

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CN106871859B
CN106871859B CN201710001869.1A CN201710001869A CN106871859B CN 106871859 B CN106871859 B CN 106871859B CN 201710001869 A CN201710001869 A CN 201710001869A CN 106871859 B CN106871859 B CN 106871859B
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coordinate system
rigid body
matrix
rotation
rigid
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CN106871859A (en
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丁杰雄
司朝阳
罗欣
胡维博
李菲
毕丹炀
丁启程
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University of Electronic Science and Technology of China
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    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention discloses a rigid body space dead axle rotation angle detection method, which provides a new solution for measuring rigid body position parameters in a large motion range by constructing a group of vectors by using coordinate values of mark points on the premise of measuring and positioning a total station instrument, namely measuring a horizontal angle and a vertical angle of the same mark point at two positions by using the total station instrument to obtain coordinate values of the corresponding mark point in a total station instrument coordinate system, determining the position of a space rigid body by using a double-vector position determination principle, and deducing and verifying a rotation angle calculation method on the basis.

Description

Rigid space fixed shaft rotation angle detection method
Technical Field
The invention belongs to the technical field of rigid body corner measurement, and particularly relates to a design of a rigid body space fixed shaft rotation angle detection method.
Background
Rigid bodies refer to objects with completely unchanged shapes and sizes under the action of any external force, and are ideal particle systems. The most basic motion forms of the rigid body are translation and rotation, any complex rigid body motion can be decomposed into superposition of translation and rotation, and the two simple motions are the most common motions in engineering and are also the basis for researching complex motions. Movements of certain objects in the project, for example: the motion of a piston in a cylinder, the motion of a tool rest on a lathe and the like belong to rigid body translation; the most common gears, main shafts of machine tools, rotors of motors, and the like belong to rigid body rotation around a fixed shaft.
The measurement of the rotation angle of the rigid body motion has been widely used in many fields such as industry, military, aerospace, navigation and the like, and the requirement for the measurement accuracy is higher and higher. In industrial control and measurement, angle is an important parameter, and measurement of the angle is necessary. For example, in some antenna servo systems of land base stations or sea base stations, in industrial production requiring turntables, and in real-time control of low rotation speed, the measurement of angles is not sufficient.
The main angle measurement methods existing in industry are: mechanical angle measurement method, electromagnetic angle measurement method, optical angle measurement method, and photoelectric angle measurement method. Mechanical goniometry is one of the earliest studied goniometry techniques, and is mainly represented by a multi-tooth index plate. The mechanical angle measuring method has the advantages of more early applications, simplicity and low cost. The electromagnetic indexing type angle measurement technology is used for measuring angles by utilizing the principle of electromagnetic induction, and mainly utilizes various parameters to carry out indexing angle measurement. The electromagnetic indexing technology is widely applied to further subdivision, so that the indexing and measuring range of the instrument is enlarged, the resolution is improved, and the application range is wide. At present, two types of angle measurement of a circular magnetic grid and angle measurement of an induction synchronizer are mainly adopted. Optical angle measurement methods have been paid attention to by people with their extremely high measurement accuracy, and their application is becoming more and more widespread. In addition to the well-known optical index head method and the polygon method, the conventional optical angle measurement method generally includes a moire fringe method, a parallel interference pattern method, a circular grating method, an optical internal reflection method, a laser interference method, and the like. In the photoelectric angle measurement method, the photoelectric sensors which are commonly applied at present comprise an optical code disc type sensor, an annular laser and an image sensor, and have the advantages of high precision, high reliability, simple realization, small volume, high angular sensitivity and the like.
The mechanical angle measuring method and the electromagnetic angle measuring method belong to traditional angle measuring methods, mostly adopt a manual contact measuring mode, and the measuring precision and stability are greatly influenced by the external environment. The optical angle measuring method and the photoelectric angle measuring method not only realize high-precision non-contact measurement of the corner, but also have simple operation and high system reliability because the method does not contact with the measured object in the measuring process, are convenient for measurement on site and can greatly reduce the labor intensity.
For the rotation of the fixed shaft, the rotation angle detection method can be divided into contact detection and non-contact detection. For example, in a gear transmission system, the axis is fixed, equipment such as an encoder and the like is convenient to install, and the rotation angle can be conveniently detected by applying contact detection; for example, in the detection of the rotation angle of an airplane control surface and the like, the axis is fixed but is not clear or a rotation angle measuring element is inconvenient to install, the detection method such as a conventional installation encoder and the like is not applicable any more, the common detection method is a non-contact detection method, for example, vision measurement, and most of the existing vision measurement methods are measurement technologies based on binocular stereo vision.
Measurement of attitude and position parameters of rigid body space motion has been an important content of rigid body motion analysis and control in the fields of multiaxial aircrafts, moving robots, robotic arms, aerospace and the like. The traditional method for measuring the motion parameters of the spatial rigid body is to install a gyroscope on the rigid body, measure the spatial attitude corner of the rigid body by using the gyroscope, or solve the spatial attitude information of the rigid body by combining a data fusion method of the gyroscope and the accelerometer, and in this way, measuring instruments such as the gyroscope and the like need to be installed on the rigid body, so that the corresponding measuring cost and equipment maintenance cost are high, and the precision is limited. In some cases, for example, when the surface of the rigid body is easily damaged or the rotation axis cannot be determined, the contact measurement method has great limitation, so in the rigid body motion parameter measurement method, the non-contact measurement cannot damage the measured surface or damage the measured surface because the measurement device is not in direct contact with the measured surface, and meanwhile, the measurement error caused by contact is avoided, so that the measurement method is widely concerned.
In a non-contact measurement method, the application research of vision measurement is the most extensive, and the vision measurement has good adaptability and higher measurement accuracy to complex environments and complex motions. Among them, the total station type electronic distance meter is widely used in the field of precision engineering measurement or deformation monitoring such as large-scale aboveground buildings and underground tunnel construction. The total station type electronic distance measuring instrument is a high-tech measuring instrument integrating light, machine and electricity into one body, and is a surveying instrument system integrating horizontal angle, vertical angle, distance (slant distance and flat distance) and height difference measuring functions into one body. Compared with an optical theodolite, the electronic theodolite changes an optical scale into a photoelectric scanning scale, and replaces manual optical micrometric reading with automatic recording and displaying of the reading, so that angle measurement operation is simplified, reading errors can be avoided, and all measurement work on the measuring station can be completed by arranging the instrument once.
Disclosure of Invention
The invention aims to solve the problems that the traditional contact type measuring method for the rotation angle of a rigid body has various defects under the conditions that the pose of a rotation shaft in a rigid body space is difficult to determine and the surface of the rigid body is complex, and provides a method for detecting the rotation angle of a fixed shaft in the rigid body space.
The technical scheme of the invention is as follows: a rigid space dead axle rotation angle detection method comprises the following steps:
s1, positioning the mark points on the surface of the rigid body;
s2, defining a world coordinate system and a rigid body rotation start-stop position coordinate system;
s3, constructing and representing the vector of rigid motion;
and S4, calculating the rotation angle of the rigid body.
Further, step S1 is specifically:
three mark points are arranged on the surface of the rigid body, two total stations arranged at different positions are adopted to measure each mark point respectively to obtain the horizontal angle and the vertical angle of each mark point, and the three-dimensional coordinate value of each mark point is obtained according to the measuring and positioning principle of the total stations and the horizontal angle and the vertical angle of each mark point.
Further, step S2 is specifically:
taking a coordinate system OXWYwZw of the measurement data of the characteristic points of the total station as a world coordinate system; setting the initial position and the final position of rigid body rotation as m and n positions respectively, and establishing a rigid body coordinate system O1XnYnZn of the n position and a rigid body coordinate system O1XmYmZm of the m position respectively by taking the rigid body rotation axis as a Z axis; the n-position rigid coordinate system O1XnYnZn has a rotation amount of an angle θ with respect to the m-position rigid coordinate system O1 XmYmZm.
Further, step S3 is specifically:
in the rigid body coordinate system O1XmYmZm, three mark points of the rigid body surface are taken as characteristic points pmiI 1,2,3, corresponding to a feature point p in the world coordinate system OXwYwZwwiI is 1,2, 3; from point pm1Connection point pm2、pm3To obtain a vector Lm1、Lm2Corresponding by point pw1Connection point pw2、pw3To obtain a vector Lw1、Lw2；
Let the conversion relation between the world coordinate system OXwYwZw and the rigid coordinate system O1XmYmZm be:
Figure BDA0001201796800000031
in the formula
Figure BDA0001201796800000032
A rotation matrix representing the rigid body coordinate system O1XmYmZm relative to the world coordinate system OXwYwZw, wherein T is a three-dimensional coordinate value of the origin of the rigid body coordinate system O1XmYmZm in the world coordinate system OXwYwZw;
corresponding feature point pmiAnd pwiThe transformation relationship of (a) is:
Figure BDA0001201796800000033
the vector construction method in the world coordinate system OXWYwZw includes:
Lw1＝pw2-pw1,Lw2＝pw3-pw1(3)
similarly, the rigid body coordinate system O1XmYmZm has:
Lm1＝pm2-pm1,Lm2＝pm3-pm1(4)
the following equations (2), (3) and (4) show:
Figure BDA0001201796800000034
constructing a third vector, selecting two vectors Lw1And Lw2Cross multiplication is performed, and the following relationship is satisfied:
Figure BDA0001201796800000035
definition vector JwAnd Jm：
Jw＝Lw1*Lw2,Jm＝Lm1*Lm2(7)
From equations (6) (7):
Figure BDA0001201796800000036
definition matrix DwAnd Dm：
Dw＝[Lw1Lw2Jw],Dm＝[Lm1Lm2Jm](9)
From equations (5), (8) and (9):
Figure BDA0001201796800000041
from matrix DwAnd DmThe construction process of (2) shows that both matrices are full rank matrices, so there is a reversible matrix, which is obtained by equation (10):
Figure BDA0001201796800000042
similarly, when the rigid body is at the n position, the rigid body coordinate system O1XnYnZn rotates the matrix relative to the world coordinate system OXwYwZw
Figure BDA0001201796800000043
Comprises the following steps:
Figure BDA0001201796800000044
wherein:
Dw′＝[Lw′ 1Lw′2Jw′],Dn＝[Ln1Ln2Jn](13)
in the actual rigid body rotation process, the final position n only rotates around the fixed shaft relative to the initial position m, and the rotation angle is theta, so that the position n isRigid body coordinate system O1XnYnZn relative to the rotation matrix of rigid body coordinate system O1XmYmZm of m position
Figure BDA0001201796800000045
Comprises the following steps:
Figure BDA0001201796800000046
the following equations (11), (12) and (14):
Figure BDA0001201796800000047
the vector mode has invariance in the coordinate transformation, so the following relationship exists:
|Lwi|＝|Lmi|＝|Lni|,i＝1,2 (16)。
further, step S4 is specifically:
as can be seen from the way the coordinate system is established, the feature points are fixed with respect to the rigid body coordinate system, and therefore the feature points are numerically identical in the coordinates of the n-position and the m-position, that is:
pni＝pmi,i＝1,2,3 (17)
because the coordinates of each feature point are the same, there are:
Dm＝Dn(18)
the following relationships are derived in conjunction with equations (11) (12) (15) (18):
Figure BDA0001201796800000051
known from the matrix construction process, DnIs a non-singular matrix, then it can be known from equation (19):
Figure BDA0001201796800000052
and
Figure BDA0001201796800000053
is a similarity matrix; from the properties of the similarity matrix: the similar matrices have the sameThe trace of (2); while
Figure BDA0001201796800000054
The point coordinates measured by the total station are constructed to be a known matrix, and the order is as follows:
Figure BDA0001201796800000055
then there are:
Figure BDA0001201796800000056
wherein
Figure BDA0001201796800000057
From the similarity matrix properties:
2cosθ+1＝a11+a22+a33(22)
as can be seen from the formula (22), θ is represented by
Figure BDA0001201796800000058
Obtaining the trace of (a) by11+a22+a33The expression of the obtained rigid body rotation angle theta is as follows:
Figure BDA0001201796800000059
the invention has the beneficial effects that: the invention adopts a non-contact measurement mode and is based on a double-vector attitude determination principle, and can conveniently solve the rotation angle of the rigid body fixed shaft according to two groups of coordinate values of the mark point on the rigid body measured by the total station, thereby providing a new solution for the measurement of rigid body attitude parameters in a large motion range.
Drawings
Fig. 1 is a flow chart of a rigid space fixed axis rotation angle detection method provided by the invention.
Fig. 2 is a schematic view of a total station measurement positioning principle according to an embodiment of the present invention.
FIG. 3 is a diagram illustrating a defined coordinate system according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of the structure of the feature points and the vectors according to the embodiment of the present invention.
Detailed Description
The embodiments of the present invention will be further described with reference to the accompanying drawings.
The invention provides a rigid space dead axle rotation angle detection method, as shown in figure 1, comprising the following steps:
and S1, positioning the mark points of the rigid surface.
As shown in FIG. 2, three mark points p are provided on the surface of the rigid body1、p2And p3The method comprises the steps of measuring each mark point by two total stations A, B arranged at different positions respectively to obtain a horizontal angle and a vertical angle of each mark point, and obtaining a three-dimensional coordinate value of each mark point according to the measurement positioning principle of the total stations and the horizontal angle and the vertical angle of each mark point.
And S2, defining a world coordinate system and a rigid body rotation starting and stopping position coordinate system.
As shown in fig. 3, a coordinate system OXwYwZw of the total station feature point measurement data is taken as a world coordinate system; setting the initial position and the final position of rigid body rotation as m and n positions respectively, and establishing a rigid body coordinate system O1XnYnZn of the n position and a rigid body coordinate system O1XmYmZm of the m position respectively by taking the rigid body rotation axis as a Z axis; the n-position rigid coordinate system O1XnYnZn has a rotation amount of an angle θ with respect to the m-position rigid coordinate system O1 XmYmZm. Because the rigid body is in any direction of space, the rigid body can always be obtained by three limited rotations around a coordinate axis, and the rotation angles, the pitch angles and the rotation amounts of deflection angles (representing postures by Euler angles) of an initial position coordinate system O1XmYmZm of the rigid body relative to a world coordinate system OXwYwZw are set.
And S3, constructing and representing the vector of the rigid body motion.
As shown in FIG. 4, in the rigid body coordinate system O1XmYmZm, three mark points of the rigid body surface are used as the characteristic points pmiI 1,2,3, corresponding to a feature point p in the world coordinate system OXwYwZwwiI is 1,2, 3; from point pm1Connection point pm2、pm3To obtain a vector Lm1、Lm2Corresponding by point pw1Connection point pw2、pw3To obtain a vector Lw1、Lw2。
Let the conversion relation between the world coordinate system OXwYwZw and the rigid coordinate system O1XmYmZm be:
Figure BDA0001201796800000061
in the formula
Figure BDA0001201796800000062
And T is a three-dimensional coordinate value of the origin of the rigid body coordinate system O1XmYmZm in the world coordinate system OXWYwZw.
Corresponding feature point pmiAnd pwiThe transformation relationship of (a) is:
Figure BDA0001201796800000063
the vector construction method in the world coordinate system OXWYwZw includes:
Lw1＝pw2-pw1,Lw2＝pw3-pw1(3)
similarly, the rigid body coordinate system O1XmYmZm has:
Lm1＝pm2-pm1,Lm2＝pm3-pm1(4)
the following equations (2), (3) and (4) show:
Figure BDA0001201796800000064
obviously, under the same coordinate system, two vectors constructed from the same point are not parallel, and two vectors L are selected to construct the required third vectorw1And Lw2Cross multiplication is performed, and the following relationship is satisfied:
Figure BDA0001201796800000071
for convenience of presentation, vector J is definedwAnd Jm：
Jw＝Lw1*Lw2,Jm＝Lm1*Lm2(7)
From equations (6) (7):
Figure BDA0001201796800000072
definition matrix DwAnd Dm：
Dw＝[Lw1Lw2Jw],Dm＝[Lm1Lm2Jm](9)
From equations (5), (8) and (9):
Figure BDA0001201796800000073
from matrix DwAnd DmThe construction process of (2) shows that both matrices are full rank matrices, so there is a reversible matrix, which is obtained by equation (10):
Figure BDA0001201796800000074
similarly, when the rigid body is at the n position, the rigid body coordinate system O1XnYnZn rotates the matrix relative to the world coordinate system OXwYwZw
Figure BDA0001201796800000075
Comprises the following steps:
Figure BDA0001201796800000076
wherein:
Dw′＝[Lw′1Lw′2Jw′],Dn＝[Ln1Ln2Jn](13)
during the actual rigid body rotationSince the final position n is only fixed-axis rotation with respect to the initial position m and the rotation angle is θ, the rotation matrix of the n-position rigid coordinate system O1XnYnZn with respect to the m-position rigid coordinate system O1XmYmZm
Figure BDA0001201796800000077
Comprises the following steps:
Figure BDA0001201796800000078
the following equations (11), (12) and (14):
Figure BDA0001201796800000081
the vector mode has invariance in the coordinate transformation, so the following relationship exists:
|Lwi|＝|Lmi|＝|Lni|,i＝1,2 (16)
as can be seen from formulas (15) and (16), there are 6 coordinate unknowns and 1 rotation angle unknowns, for a total of 7 unknowns; 13 relational expressions can be listed according to the corresponding relation of each element of the matrix and the equal relation of the vector mode, and the direct solving is complex, so that the matrix transformation is adopted to solve the rotation angle theta in the embodiment of the invention.
And S4, calculating the rotation angle of the rigid body.
As can be seen from the way the coordinate system is established, the feature points are fixed with respect to the rigid body coordinate system, and therefore the feature points are numerically identical in the coordinates of the n-position and the m-position, that is:
pni＝pmi,i＝1,2,3 (17)
because the coordinates of each feature point are the same, there are:
Dm＝Dn(18)
the following relationships are derived in conjunction with equations (11) (12) (15) (18):
Figure BDA0001201796800000082
constructed from a matrixThe process is known as DnIs a non-singular matrix, then it can be known from equation (19):
Figure BDA0001201796800000083
and
Figure BDA0001201796800000084
is a similarity matrix; from the properties of the similarity matrix: similar matrices have the same traces; while
Figure BDA0001201796800000085
The point coordinates measured by the total station are constructed to be a known matrix, and the order is as follows:
Figure BDA0001201796800000086
then there are:
Figure BDA0001201796800000087
wherein
Figure BDA0001201796800000088
From the similarity matrix properties:
2cosθ+1＝a11+a22+a33(22)
as can be seen from the formula (22), θ is represented by
Figure BDA0001201796800000089
Obtaining the trace of (a) by11+a22+a33The expression of the obtained rigid body rotation angle theta is as follows:
Figure BDA0001201796800000091
the accuracy of equation (23) is verified according to practical applications as follows:
(1) giving the position and attitude relationship between the rigid body coordinate system and the world coordinate system, the coordinates of three points under the rigid body coordinate system and the rotation of the rigid bodyAngle theta0。
(2) And calculating to obtain the coordinates of three points under two groups of world coordinate systems according to the coordinate transformation relation.
(3) According to the theoretical derivation process, a correlation matrix is constructed, and the rotation angle θ is obtained from equation (23).
(4) Discriminating theta and a given rotation angle theta0Whether they are consistent.
The verification results are shown in the following table, and the results prove that the rigid body space fixed-axis rotation angle detection method provided by the invention is feasible.
Figure BDA0001201796800000092
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (3)

1. A rigid space dead axle rotation angle detection method is characterized by comprising the following steps:
s1, positioning the mark points on the surface of the rigid body; the step S1 specifically includes:
setting three mark points on the surface of the rigid body, respectively measuring each mark point by adopting two total stations arranged at different positions to obtain the horizontal angle and the vertical angle of each mark point, and obtaining the three-dimensional coordinate value of each mark point according to the measuring and positioning principle of the total stations and the horizontal angle and the vertical angle of each mark point;
s2, defining a world coordinate system and a rigid body rotation start-stop position coordinate system; the step S2 specifically includes:
taking a coordinate system OXWYwZw of the measurement data of the characteristic points of the total station as a world coordinate system; setting the initial position and the final position of rigid body rotation as m and n positions respectively, and establishing a rigid body coordinate system O1XnYnZn of the n position and a rigid body coordinate system O1XmYmZm of the m position respectively by taking the rigid body rotation axis as a Z axis; the rigid body coordinate system O1XnYnZn at the n position has a rotation amount with an angle theta relative to the rigid body coordinate system O1XmYmZm at the m position;
s3, constructing and representing rigid motion vector to obtain rotation matrix of rigid coordinate system O1XnYnZn relative to world coordinate system OXwYwZw
Figure FDA0002408394770000011
The expression is as follows:
Figure FDA0002408394770000012
s4, according to
Figure FDA0002408394770000013
The expression to obtain the theta expression for calculating the rotation angle of the rigid body is as follows:
Figure FDA0002408394770000014
wherein a ═ a11+a22+a33，
Figure FDA0002408394770000015
xikIs a matrixElement (ii) ykjIs a matrix Dw＇And matrix of
Figure FDA0002408394770000017
And Dw＇And constructing point coordinates obtained by measuring the total station.
2. The rigid body space dead axle rotation angle detection method according to claim 1, wherein the step S3 specifically is:
in the rigid body coordinate system O1XmYmZm, three mark points of the rigid body surface are taken as characteristic points pmiI 1,2,3, corresponding to a feature point p in the world coordinate system OXwYwZwwiI is 1,2, 3; from point pm1Connection point pm2、pm3To obtain a vector Lm1、Lm2Corresponding by point pw1Connection point pw2、pw3To obtain a vector Lw1、Lw2；
Let the conversion relation between the world coordinate system OXwYwZw and the rigid coordinate system O1XmYmZm be:
Figure FDA0002408394770000018
in the formula
Figure FDA0002408394770000019
A rotation matrix representing the rigid body coordinate system O1XmYmZm relative to the world coordinate system OXwYwZw, wherein T is a three-dimensional coordinate value of the origin of the rigid body coordinate system O1XmYmZm in the world coordinate system OXwYwZw;
corresponding feature point pmiAnd pwiThe transformation relationship of (a) is:
Figure FDA0002408394770000021
the vector construction method in the world coordinate system OXWYwZw includes:
Lw1＝pw2-pw1,Lw2＝pw3-pw1(3)
similarly, the rigid body coordinate system O1XmYmZm has:
Lm1＝pm2-pm1,Lm2＝pm3-pm1(4)
the following equations (2), (3) and (4) show:
Figure FDA0002408394770000022
required for constructionA third vector of two vectors Lw1And Lw2Cross multiplication is performed, and the following relationship is satisfied:
Figure FDA0002408394770000023
definition vector JwAnd Jm：
Jw＝Lw1*Lw2,Jm＝Lm1*Lm2(7)
From equations (6) (7):
Figure FDA0002408394770000024
definition matrix DwAnd Dm：
Dw＝[Lw1Lw2Jw],Dm＝[Lm1Lm2Jm](9)
From equations (5), (8) and (9):
Figure FDA0002408394770000025
from matrix DwAnd DmThe construction process of (2) shows that both matrices are full rank matrices, so there is a reversible matrix, which is obtained by equation (10):
Figure FDA0002408394770000026
similarly, when the rigid body is at the n position, the rigid body coordinate system O1XnYnZn rotates the matrix relative to the world coordinate system OXwYwZw
Figure FDA0002408394770000027
Comprises the following steps:
Figure FDA0002408394770000028
wherein:
Dw′＝[Lw′1Lw′2Jw′],Dn＝[Ln1Ln2Jn](13)
in the actual rigid body rotation process, only the fixed axis rotation exists at the final position n relative to the initial position m, and the rotation angle is theta, so that the rotation matrix of the rigid body coordinate system O1XnYnZn at the n position relative to the rigid body coordinate system O1XmYmZm at the m position
Figure FDA0002408394770000031
Comprises the following steps:
Figure FDA0002408394770000032
the following equations (11), (12) and (14):
Figure FDA0002408394770000033
the vector mode has invariance in the coordinate transformation, so the following relationship exists:
|Lwi|＝|Lmi|＝|Lni|,i＝1,2 (16)。
3. the rigid body space dead axle rotation angle detection method according to claim 2, wherein the step S4 is specifically:
as can be seen from the way the coordinate system is established, the feature points are fixed with respect to the rigid body coordinate system, and therefore the feature points are numerically identical in the coordinates of the n-position and the m-position, that is:
pni＝pmi,i＝1,2,3 (17)
because the coordinates of each feature point are the same, there are:
Dm＝Dn(18)
the following relationships are derived in conjunction with equations (11) (12) (15) (18):
Figure FDA0002408394770000034
known from the matrix construction process, DnIs a non-singular matrix, then it can be known from equation (19):
Figure FDA0002408394770000035
and
Figure FDA0002408394770000036
is a similarity matrix; from the properties of the similarity matrix: similar matrices have the same traces; while
Figure FDA0002408394770000037
The point coordinates measured by the total station are constructed to be a known matrix, and the order is as follows:
Figure FDA0002408394770000038
then there are:
Figure FDA0002408394770000041
wherein
Figure FDA0002408394770000042
From the similarity matrix properties:
2cosθ+1＝a11+a22+a33(22)
as can be seen from the formula (22), θ is represented by
Figure FDA0002408394770000043
Obtaining the trace of (a) by11+a22+a33The expression of the obtained rigid body rotation angle theta is as follows:
Figure FDA0002408394770000044
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* Cited by examiner, † Cited by third party
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Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4269508A (en) * 1978-07-19 1981-05-26 Societe Anonyme De Telecommunications Device for adjusting the azimuthal and inclination directions of a wave reflector
CN101556704A (en) * 2009-05-19 2009-10-14 武汉一冶钢结构有限责任公司 Method for establishing temporary supporting frame system assembled by steel structures
CN203881346U (en) * 2014-03-25 2014-10-15 北京测科空间信息技术有限公司 Adjusting device for indoor triaxial calibration field
CN105136128A (en) * 2015-08-27 2015-12-09 中国航天空气动力技术研究院 Airframe structure measuring method based on two-point positioning
CN105424024A (en) * 2015-11-03 2016-03-23 葛洲坝易普力股份有限公司 Spatial target position and orientation calibration method based on total station
CN105549332A (en) * 2016-01-14 2016-05-04 哈尔滨工业大学 Method for three-degree-of-freedom displacement measurement of workpiece table

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7991575B2 (en) * 2009-01-08 2011-08-02 Trimble Navigation Limited Method and system for measuring angles based on 360 degree images

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4269508A (en) * 1978-07-19 1981-05-26 Societe Anonyme De Telecommunications Device for adjusting the azimuthal and inclination directions of a wave reflector
CN101556704A (en) * 2009-05-19 2009-10-14 武汉一冶钢结构有限责任公司 Method for establishing temporary supporting frame system assembled by steel structures
CN203881346U (en) * 2014-03-25 2014-10-15 北京测科空间信息技术有限公司 Adjusting device for indoor triaxial calibration field
CN105136128A (en) * 2015-08-27 2015-12-09 中国航天空气动力技术研究院 Airframe structure measuring method based on two-point positioning
CN105424024A (en) * 2015-11-03 2016-03-23 葛洲坝易普力股份有限公司 Spatial target position and orientation calibration method based on total station
CN105549332A (en) * 2016-01-14 2016-05-04 哈尔滨工业大学 Method for three-degree-of-freedom displacement measurement of workpiece table

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