CN114218626A - Curved surface body positioning reference plane adjusting method based on nonlinear least square - Google Patents

Curved surface body positioning reference plane adjusting method based on nonlinear least square Download PDF

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CN114218626A
CN114218626A CN202111482742.9A CN202111482742A CN114218626A CN 114218626 A CN114218626 A CN 114218626A CN 202111482742 A CN202111482742 A CN 202111482742A CN 114218626 A CN114218626 A CN 114218626A
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curved surface
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关世玺
刘洋
沙业典
赵荣珍
王迅
张孟轲
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North University of China
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Abstract

The invention relates to a curved surface body positioning reference plane adjusting method based on nonlinear least squares, belonging to the field of curved surface body positioning reference plane adjustment; the technical problem to be solved is as follows: the improvement of a curved surface body positioning reference plane adjusting method based on nonlinear least squares is provided; the technical scheme for solving the technical problem is as follows: after the curved surface body is fixed on the workbench, coordinates of registration control points on the curved surface body are obtained through measurement of a laser tracker; in the Boolean sand model, a center auxiliary conversion coordinate system is established by translating the original points of the two coordinate systems to the central position of the reference control point; solving a center auxiliary coordinate conversion model based on a nonlinear least square method and a Gaussian-Newton iteration method to obtain seven parameters, adjusting based on offset and a scaling, compensating corresponding displacement and deflection angle values to a reference plane, and moving the curved surface body to an optimal working position; the method is applied to the field of positioning of the reference plane of the curved surface body.

Description

Curved surface body positioning reference plane adjusting method based on nonlinear least square
Technical Field
The invention discloses a curved surface body positioning reference plane adjusting method based on nonlinear least squares, and belongs to the field of curved surface body positioning reference plane adjusting.
Background
At present, when a machine tool is used for carrying out fine machining on a curved surface body, the difficulty in positioning the reference plane of the curved surface body is high, the curved surface body can be placed on a machine tool workbench or an attitude adjusting driver in any attitude, a certain position deviation exists between the reference plane and a coordinate system of the workbench, and displacement compensation operations such as origin offset and coordinate axis deflection need to be carried out.
At present, for the adjustment of a curved surface body positioning reference, a Boolean sand model is generally adopted to carry out coordinate conversion on the curved surface body positioning reference, in the process of calculating and solving parameters, secondary and above-secondary components are omitted from the conversion model, or a trigonometric function in a rotation matrix is approximately processed to form an angle, so that a larger truncation error is generated, the coordinate conversion precision is damaged, the calculation process is complicated, the influence of reference point selection on the parameters is larger, and the precision is lower because the calculation parameters omit a high-order term of an expansion formula, the adjustment method is only suitable for the condition of a tiny rotation angle, or a coordinate system conversion algorithm of a nonlinear least square method based on seven parameters, the calculation process is complicated, and the parameter deviation is increased.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to solve the technical problems that: the improvement of the method for adjusting the positioning reference plane of the curved surface body based on the nonlinear least square is provided.
In order to solve the technical problems, the invention adopts the technical scheme that: the method for adjusting the positioning reference plane of the curved surface body based on the nonlinear least square comprises the following adjusting steps:
the method comprises the following steps: and setting a theoretical coordinate system of a curved surface body as follows:
Figure 100002_DEST_PATH_IMAGE001
the theoretical coordinates of the three registration points A, B and C are respectively as follows:
Figure 683270DEST_PATH_IMAGE002
；
after the curved surface body is fixed on the workbench, coordinates of registration control points on the curved surface body are obtained through measurement of a laser tracker;
setting the actual coordinate system of the curved surface body as follows:
Figure 100002_DEST_PATH_IMAGE003
and the actual coordinates of the three registration points D, E and F are respectively as follows:
Figure 69252DEST_PATH_IMAGE004
；
the deviation of the actual coordinate system of the curved surface body from the theoretical coordinate system comprises 3 translation parameters
Figure 100002_DEST_PATH_IMAGE005
，
Figure 583410DEST_PATH_IMAGE006
，
Figure 100002_DEST_PATH_IMAGE007
Each parameter represents the translation along X, Y, Z axes, 3 rotation parameters alpha, beta and gamma represent the rotation angle around X, Y, Z axes, and the actual coordinate system
Figure 699658DEST_PATH_IMAGE003
Relative theoretical coordinate system
Figure 717292DEST_PATH_IMAGE001
The scale of (a) is k;
step two: in the Boolean Sand model, a center auxiliary conversion coordinate system is established by translating the original points of two coordinate systems to the central positions of respective reference control points:
the coordinate conversion model based on the Boolean-Walff model is constructed as follows:
Figure 805334DEST_PATH_IMAGE008
；
wherein:
Figure 100002_DEST_PATH_IMAGE009
；
Figure 541209DEST_PATH_IMAGE010
；
the method is simplified to obtain:
Figure 100002_DEST_PATH_IMAGE011
；
wherein:
Figure 208951DEST_PATH_IMAGE012
respectively as a theoretical coordinate system
Figure 100002_DEST_PATH_IMAGE013
Coordinate values of the upper reference point;
Figure 595938DEST_PATH_IMAGE014
respectively an actual coordinate system
Figure 100002_DEST_PATH_IMAGE015
Coordinate values of the upper reference point;
Figure 58144DEST_PATH_IMAGE016
the rotation matrixes are respectively a rotation matrix of a curved surface body actual coordinate system rotating around a Z axis by an angle alpha, rotating around a Y axis by an angle beta and rotating around a Z axis by an angle gamma;
Figure 100002_DEST_PATH_IMAGE017
as a theoretical coordinate systemGConversion to a real coordinate systemLA rotational transformation matrix of (a);
calculating the center point position of the registration point as follows:
Figure 281315DEST_PATH_IMAGE018
；
wherein:Xis the coordinates of the registration point in the coordinate system,Nin order to determine the number of registration points,
Figure 100002_DEST_PATH_IMAGE019
the central coordinates of the registration point set are obtained;
center point of three registration points on actual coordinates
Figure 487168DEST_PATH_IMAGE020
The coordinate values of (A) are:
Figure 100002_DEST_PATH_IMAGE021
；
wherein:
Figure 728662DEST_PATH_IMAGE022
is a central point
Figure 361769DEST_PATH_IMAGE020
The coordinate value of (a) on the X-axis,
Figure 100002_DEST_PATH_IMAGE023
is a central point
Figure 72236DEST_PATH_IMAGE020
The coordinate value of the Y-axis of (c),
Figure 612939DEST_PATH_IMAGE024
is a central point
Figure 459672DEST_PATH_IMAGE020
Z-axis coordinate values of (a);
center point of three registration points on theoretical coordinate
Figure 100002_DEST_PATH_IMAGE025
The coordinates of (a) are:
Figure 512948DEST_PATH_IMAGE026
；
wherein:
Figure 100002_DEST_PATH_IMAGE027
is a central point
Figure 710711DEST_PATH_IMAGE025
The coordinate value of (a) on the X-axis,
Figure 55104DEST_PATH_IMAGE028
is a central point
Figure 756344DEST_PATH_IMAGE025
The coordinate value of the Y-axis of (c),
Figure 100002_DEST_PATH_IMAGE029
is a central point
Figure 996833DEST_PATH_IMAGE025
Z-axis coordinate values of (a);
then, constructing a center auxiliary coordinate conversion model based on the Boolean-Walff model as follows:
Figure 213050DEST_PATH_IMAGE030
；
the abbreviation is:
Figure 100002_DEST_PATH_IMAGE031
；
wherein:
Figure 804876DEST_PATH_IMAGE032
；
Figure 100002_DEST_PATH_IMAGE033
；
in the formula:
Figure 626201DEST_PATH_IMAGE034
is the theoretical coordinate of the set of control points,
Figure 100002_DEST_PATH_IMAGE035
is the actual coordinates of the control point set;
step three: solving a center auxiliary coordinate conversion model based on a nonlinear least square method and a Gaussian-Newton iteration method to obtain seven parameters, and adjusting the position of the curved surface body to reach the optimal working position according to the seven parameters:
first order
Figure 37591DEST_PATH_IMAGE036
；
Wherein the three-dimensional coordinate transformation model
Figure 100002_DEST_PATH_IMAGE037
According to the least square principle, solving the minimum value as follows:
Figure 944367DEST_PATH_IMAGE038
；
the simplification is as follows:
Figure 100002_DEST_PATH_IMAGE039
is composed of
Figure 83093DEST_PATH_IMAGE040
；
Namely:
Figure 100002_DEST_PATH_IMAGE041
；
and solving again:
Figure 24505DEST_PATH_IMAGE042
；
in the formula:
Figure 100002_DEST_PATH_IMAGE043
；
in the resolving process, solving by adopting a Gaussian-Newton iteration method, wherein the specific steps are as follows;
step 3.1: will be provided with
Figure 810058DEST_PATH_IMAGE044
Linearization at the reference point
Figure 100002_DEST_PATH_IMAGE045
To pair
Figure 453398DEST_PATH_IMAGE044
Performing Taylor expansion to obtain:
Figure 943285DEST_PATH_IMAGE046
；
step 3.2: bringing the above into
Figure 100002_DEST_PATH_IMAGE047
In the above step, the next iteration is obtained as:
Figure 208044DEST_PATH_IMAGE048
；
in the iteration process, stopping iteration when one norm of two adjacent seven-parameter vector differences meets the precision requirement or is smaller than a certain threshold value, and obtaining the optimal solution under the least square rule;
step 3.3: solved forx,y,zThe offset of the actual coordinate system origin of the curved surface body and the theoretical coordinate origin is obtained;
the calculated alpha, beta and gamma are deflection angles of three coordinate axes of an actual coordinate system and three coordinate axes of a theoretical coordinate system of the curved surface body;
the calculated k is the scale scaling of the two coordinate systems;
step 3.4: and adjusting based on the offset and the scaling, compensating corresponding displacement and deflection angle values to the reference plane, and moving the curved surface body to the optimal working position.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a curved surface body positioning reference plane adjusting method based on a nonlinear least square center-aided space coordinate conversion algorithm, which comprises the steps of solving the center coordinates of a reference point on a theoretical model and a reference point measured by a laser tracker, and solving the optimal value of seven parameters by using the minimum value of a multivariate function, wherein the convergence speed is high under the condition of improving the precision, the calculation result is correct and stable, and a new solution is provided for solving the problem of curved surface body reference adjustment; through experimental calculation, the method can reduce iteration times and convergence, can obtain the same accurate seven-parameter explanation, and the method is effective in solving the problem of large rotation angle and has the characteristic of quick convergence.
Detailed Description
When the method is implemented, a registration reference point is planned in advance on a CAD model of the curved surface body, high-precision measuring equipment such as a laser tracker is adopted to detect the position of the registration reference point of the curved surface body on a workbench, after the position on the workbench of the reference surface is known, a mathematical model of a more accurate fitting pose of reference plane positioning is constructed by improving a seven-parameter Boolean sand coordinate conversion formula, and the position relation between the theoretical coordinate of the curved surface body and the actual coordinate of the curved surface body is solved, namely the displacement and the rotation angle of the positioning reference plane needing to be adjusted are obtained, so that the calculated amount can be effectively reduced, and the efficiency of the reference surface positioning of the curved surface body is improved; the method for adjusting the positioning reference plane of the curved surface body has universality and applicability, and can be used in the adjustment process of different reference planes of complex curved surface bodies.
The above-mentioned is a curved surface body registration control point, which refers to a model registration control point set planned in advance on a CAD or three-dimensional model of a curved surface body, and selects a feature point of the curved surface body as a model registration control point, and the selected target is: the method has the advantages that the characteristics can be identified as much as possible, the measurement is convenient, the registration is stable, and the registration positioning precision and efficiency are higher as much as possible under the condition of meeting the registration reliability requirement; such as the intersection of the curved surfaces, the supporting point under the curved surfaces, the characteristic point of the special structure of the curved surfaces, and the like; and selecting a proper reference control point, and taking three points which are not on the same straight line as reference points, wherein the three points are taken as a reference plane, namely the change of the posture of the curved body is reflected on the displacement and deflection of the reference plane.
In order to obtain the position of the reference surface of the actual curved body, the relative position of the actual coordinate system and the theoretical coordinate system of the curved body needs to be known, and then the coordinate conversion relation between the three actual registration points of the curved body and the three registration points of the theoretical model needs to be obtained, so that the conversion relation between the coordinate system of the curved body on a worktable and the coordinate system of the theoretical model needs to be obtained first, that is, the relative position of the reference surface of the curved body on the worktable is known, and the conversion parameters are the displacement and the rotation angle which need to be adjusted, and the optimal position of the curved body in work is achieved by adjusting the position of the reference surface; the invention is provided with a theoretical coordinate system of the curved surface body and a working coordinate system which are superposed (coordinate origin is superposed and coordinate axis is superposed), namely a reference surface on the theoretical coordinate system is an actual position to which a positioning reference plane of the curved surface body on a working table needs to be adjusted; in practical application, the position relationship between the theoretical coordinate system and the working coordinate system of the curved surface body needs to be specifically analyzed.
The invention provides a center auxiliary space coordinate conversion algorithm based on nonlinear least square, which is used for adjusting the surface body reference, solving the center coordinates of a reference point on a theoretical model and a reference point measured by a laser tracker, adopting a multivariate function minimum value to solve a seven-parameter optimal value, and providing a new solution for the surface body reference adjustment, wherein the method specifically comprises the following steps:
firstly, a theoretical coordinate system of a curved surface body is set as follows:
Figure 961237DEST_PATH_IMAGE001
the theoretical coordinates of three registration points A, B and C are respectively as follows:
Figure 639343DEST_PATH_IMAGE002
；
after the curved surface body is fixed on the workbench, coordinates of registration control points on the curved surface body are obtained through measurement of a laser tracker, and an actual coordinate system of the curved surface body is set as follows:
Figure 870604DEST_PATH_IMAGE003
and the actual coordinates of the three registration points D, E and F are respectively as follows:
Figure 317766DEST_PATH_IMAGE004
；
the deviation of the actual coordinate system of the curved body from the theoretical coordinate system comprises 3 translation parameters
Figure 959968DEST_PATH_IMAGE005
，
Figure 125371DEST_PATH_IMAGE006
，
Figure 894743DEST_PATH_IMAGE007
Representing the amount of translation along the X, Y, Z axes, respectively, and the 3 rotation parameters α, β, γ represent the rotation angles around the X, Y, Z axis, respectively;
actual coordinate system
Figure 461991DEST_PATH_IMAGE003
Relative theoretical coordinate system
Figure 25828DEST_PATH_IMAGE001
Is scaled by k. The theoretical coordinate system G of the curved surface body position and the origin of the actual position coordinate system L are not coincident, and the directions of all coordinate axes are different.
Then, a coordinate conversion model based on the Boolean-Walff model is constructed:
Figure DEST_PATH_IMAGE049
；
wherein:
Figure 881788DEST_PATH_IMAGE050
；
Figure 517169DEST_PATH_IMAGE010
；
the method is simplified to obtain:
Figure 863224DEST_PATH_IMAGE011
；
in the Boolean Sand model, the origin points of two coordinate systems are translated to the central position of a reference control point, and a central auxiliary conversion coordinate system is established to uniformly distribute the reference control point.
First, the position of the center point is calculated:
Figure 925858DEST_PATH_IMAGE018
；
center points of three registration points
Figure 737956DEST_PATH_IMAGE020
The coordinate coordinates of (a) are:
Figure 177028DEST_PATH_IMAGE021
；
similarly, the central point of three registration points on the theoretical coordinate
Figure 390971DEST_PATH_IMAGE025
Coordinates are as follows:
Figure 624507DEST_PATH_IMAGE026
；
then, constructing a center auxiliary coordinate conversion model based on the Boolean-Walff model as follows:
Figure 923901DEST_PATH_IMAGE030
；
the method is abbreviated as follows:
Figure 901084DEST_PATH_IMAGE031
；
wherein:
Figure DEST_PATH_IMAGE051
；
Figure 484381DEST_PATH_IMAGE052
；
Figure 826501DEST_PATH_IMAGE034
is the theoretical coordinate of the set of control points,
Figure 675508DEST_PATH_IMAGE035
is the actual coordinates of the control point set;
at the moment, the X, Y and Z axes of the central auxiliary conversion coordinate system are parallel to the X, Y and Z axes of the theoretical coordinate system;
then, solving a center auxiliary coordinate conversion model by using a nonlinear least square method and a Gaussian-Newton iteration method to obtain seven parameters:
first order
Figure 128486DEST_PATH_IMAGE036
；
Wherein the three-dimensional coordinate transformation model
Figure 379339DEST_PATH_IMAGE037
And solving a minimum value according to a least square principle:
Figure DEST_PATH_IMAGE053
；
the method is simplified as follows:
Figure 157939DEST_PATH_IMAGE039
is composed of
Figure 681193DEST_PATH_IMAGE040
；
And solving again:
Figure 179DEST_PATH_IMAGE042
；
in the formula:
Figure 43221DEST_PATH_IMAGE043
；
in the resolving process, solving by adopting a Gaussian-Newton iteration method:
firstly, the method is carried out
Figure 789461DEST_PATH_IMAGE044
Is linearized in
Figure 285164DEST_PATH_IMAGE054
Point pair
Figure 407841DEST_PATH_IMAGE044
Performing Taylor expansion to obtain:
Figure DEST_PATH_IMAGE055
；
bringing the above into
Figure 570969DEST_PATH_IMAGE047
In this way, the following iteration formula is obtained:
Figure 675060DEST_PATH_IMAGE048
；
in the iteration process, when one norm of the vector difference of two adjacent seven parameters is smaller than a certain threshold value, the iteration is stopped, and the optimal solution under the least square rule can be obtained.
Solved forx,y,zThe offset of the actual coordinate system origin of the curved surface body and the theoretical coordinate origin is obtained;
alpha, beta and gamma are deflection angles of three coordinate axes of an actual coordinate system and three coordinate axes of a theoretical coordinate system of the curved surface body;
k is the scale of two coordinate systems;
and finally, the optimal working position of the curved surface body is achieved by adjusting the corresponding displacement and deflection angle positions of the reference surface.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (1)

1. The method for adjusting the positioning reference plane of the curved surface body based on the nonlinear least square is characterized in that: the method comprises the following adjustment steps:
the method comprises the following steps: and setting a theoretical coordinate system of a curved surface body as follows:
Figure DEST_PATH_IMAGE001
the theoretical coordinates of the three registration points A, B and C are respectively as follows:
Figure 141140DEST_PATH_IMAGE002
；
after the curved surface body is fixed on the workbench, coordinates of registration control points on the curved surface body are obtained through measurement of a laser tracker;
setting the actual coordinate system of the curved surface body as follows:
Figure DEST_PATH_IMAGE003
and the actual coordinates of the three registration points D, E and F are respectively as follows:
Figure 464805DEST_PATH_IMAGE004
；
the deviation of the actual coordinate system of the curved surface body from the theoretical coordinate system comprises 3 translation parameters
Figure DEST_PATH_IMAGE005
，
Figure 510122DEST_PATH_IMAGE006
，
Figure DEST_PATH_IMAGE007
Each parameter represents the translation along X, Y, Z axes, 3 rotation parameters alpha, beta and gamma represent the rotation angle around X, Y, Z axes, and the actual coordinate system
Figure 95211DEST_PATH_IMAGE003
Relative theoretical coordinate system
Figure 581687DEST_PATH_IMAGE001
The scale of (a) is k;
step two: in the Boolean Sand model, a center auxiliary conversion coordinate system is established by translating the original points of two coordinate systems to the central positions of respective reference control points:
the coordinate conversion model based on the Boolean-Walff model is constructed as follows:
Figure 138571DEST_PATH_IMAGE008
；
wherein:
Figure DEST_PATH_IMAGE009
；
Figure 858134DEST_PATH_IMAGE010
；
the method is simplified to obtain:
Figure DEST_PATH_IMAGE011
；
wherein:
Figure 588192DEST_PATH_IMAGE012
respectively as a theoretical coordinate system
Figure DEST_PATH_IMAGE013
Coordinate values of the upper reference point;
Figure 398017DEST_PATH_IMAGE014
respectively an actual coordinate system
Figure DEST_PATH_IMAGE015
Coordinate values of the upper reference point;
Figure 922539DEST_PATH_IMAGE016
the rotation matrixes are respectively a rotation matrix of a curved surface body actual coordinate system rotating around a Z axis by an angle alpha, rotating around a Y axis by an angle beta and rotating around a Z axis by an angle gamma;
Figure DEST_PATH_IMAGE017
as a theoretical coordinate systemGConversion to a real coordinate systemLA rotational transformation matrix of (a);
calculating the center point position of the registration point as follows:
Figure 129398DEST_PATH_IMAGE018
；
wherein:Xis the coordinates of the registration point in the coordinate system,Nin order to determine the number of registration points,
Figure DEST_PATH_IMAGE019
the central coordinates of the registration point set are obtained;
center point of three registration points on actual coordinates
Figure 272935DEST_PATH_IMAGE020
The coordinate values of (A) are:
Figure DEST_PATH_IMAGE021
；
wherein:
Figure 61899DEST_PATH_IMAGE022
is a central point
Figure 491743DEST_PATH_IMAGE020
The coordinate value of (a) on the X-axis,
Figure DEST_PATH_IMAGE023
is a central point
Figure 185899DEST_PATH_IMAGE020
The coordinate value of the Y-axis of (c),
Figure 195443DEST_PATH_IMAGE024
is a central point
Figure 511018DEST_PATH_IMAGE020
Z-axis coordinate values of (a);
center point of three registration points on theoretical coordinate
Figure DEST_PATH_IMAGE025
The coordinates of (a) are:
Figure 580605DEST_PATH_IMAGE026
；
wherein:
Figure DEST_PATH_IMAGE027
is a central point
Figure 764986DEST_PATH_IMAGE025
The coordinate value of (a) on the X-axis,
Figure 578222DEST_PATH_IMAGE028
is a central point
Figure 872937DEST_PATH_IMAGE025
The coordinate value of the Y-axis of (c),
Figure DEST_PATH_IMAGE029
is a central point
Figure 51108DEST_PATH_IMAGE025
Z-axis coordinate values of (a);
then, constructing a center auxiliary coordinate conversion model based on the Boolean-Walff model as follows:
Figure 736167DEST_PATH_IMAGE030
；
the abbreviation is:
Figure DEST_PATH_IMAGE031
；
wherein:
Figure 149831DEST_PATH_IMAGE032
；
Figure DEST_PATH_IMAGE033
；
in the formula:
Figure 158107DEST_PATH_IMAGE034
is the theoretical coordinate of the set of control points,
Figure DEST_PATH_IMAGE035
is the actual coordinates of the control point set;
step three: solving a center auxiliary coordinate conversion model based on a nonlinear least square method and a Gaussian-Newton iteration method to obtain seven parameters, and adjusting the position of the curved surface body to reach the optimal working position according to the seven parameters:
first order
Figure 631814DEST_PATH_IMAGE036
；
Wherein the three-dimensional coordinate transformation model
Figure DEST_PATH_IMAGE037
According to the least square principle, solving the minimum value as follows:
Figure 476273DEST_PATH_IMAGE038
；
the simplification is as follows:
Figure DEST_PATH_IMAGE039
is composed of
Figure 428049DEST_PATH_IMAGE040
；
Namely:
Figure DEST_PATH_IMAGE041
；
and solving again:
Figure 556411DEST_PATH_IMAGE042
；
in the formula:
Figure DEST_PATH_IMAGE043
；
in the resolving process, solving by adopting a Gaussian-Newton iteration method, wherein the specific steps are as follows;
step 3.1: will be provided with
Figure 201019DEST_PATH_IMAGE044
Linearization at the reference point
Figure DEST_PATH_IMAGE045
To pair
Figure 532774DEST_PATH_IMAGE044
Performing Taylor expansion to obtain:
Figure 553820DEST_PATH_IMAGE046
；
step 3.2: bringing the above into
Figure DEST_PATH_IMAGE047
In the above step, the next iteration is obtained as:
Figure 271109DEST_PATH_IMAGE048
；
in the iteration process, stopping iteration when one norm of two adjacent seven-parameter vector differences meets the precision requirement or is smaller than a certain threshold value, and obtaining the optimal solution under the least square rule;
step 3.3: solved forx,y,zThe offset of the actual coordinate system origin of the curved surface body and the theoretical coordinate origin is obtained;
the calculated alpha, beta and gamma are deflection angles of three coordinate axes of an actual coordinate system and three coordinate axes of a theoretical coordinate system of the curved surface body;
the calculated k is the scale scaling of the two coordinate systems;
step 3.4: and adjusting based on the offset and the scaling, compensating corresponding displacement and deflection angle values to the reference plane, and moving the curved surface body to the optimal working position.
CN202111482742.9A 2021-12-07 2021-12-07 Curved surface body positioning reference plane adjusting method based on nonlinear least square Pending CN114218626A (en)

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