CN109682304A - A kind of composition error modeling method based on CCD camera contraposition assembly system - Google Patents
A kind of composition error modeling method based on CCD camera contraposition assembly system Download PDFInfo
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Abstract
The invention discloses a kind of composition error modeling method based on CCD camera contraposition assembly system, include the following steps: that aligning assembly system according to CCD camera establishes system topological chain；Not kinematic error ideally, precalculate to obtain the transformation matrix in base part group and target part group between each coordinate system, the position vector P of base part and target part under reference frame be calculated31、P61, direction vector U31、U61；Under the situation there are kinematic error, the error of perpendicularity of linear between centers is considered, and it is P that the position vector of base part and target part under reference frame, which under the error converting into target part and base part coordinate system of CCD camera camera lens, will be calculated,3And P6；The direction vector of base part and target part under reference frame is U3And U6；Obtaining the position error vector of base part and target part under reference frame is respectively Δ P3=P3‑P31、ΔP6=P6‑P61It is respectively Δ U with deflection error vector3=U3‑U31、ΔU6=U6‑U61。
Description
Technical field
The invention belongs to assemble to execute Motion Technology field, and in particular to a kind of to align assembly system based on CCD camera
Composition error modeling method.
Background technique
For formed towards medium scale micro element precision, mini system, as non-in ammunition fuze assembling process
Silicon MEMS system, inertial confinement fusion system etc., Beijing Institute of Technology's precision Micro-manufacturing laboratory is in coaxial alignment
On the basis of, have developed the high-precision contraposition detector that can reach submicron order assembly aligning accuracy, the extension of achievable ICF component
The precision assembly of part component TMP component, although high-precision contraposition detector can reach Asia by high-precision micro-vision system
Micron-sized detection accuracy, but the assembly precision of part additionally depends on the mechanical movement precision after vision system detection, and vision
The error of kinematic axis in system also will affect detection accuracy, to influence assembly precision.
But for comprehensive visual detection and the error modeling of each kinematic axis, there has been no more accurate methods at present, this leads
It causes the later period not compensated effectively, and then influences assembly precision.
Summary of the invention
In view of this, the present invention provides a kind of composition error modeling method based on CCD camera contraposition assembly system, it should
Method comprehensively considers linear displacement error, straightness error, pitching, rolling, Run-out error and the linear between centers of each linear axes
Coordinate origin offset, the error of perpendicularity, finally obtained the higher position error vector of precision and deflection error vector.
In order to achieve the above object, the technical solution of the present invention is as follows: a kind of synthesis based on CCD camera contraposition assembly system
Error modeling method, it includes vibration isolation table and the base part group, the target that are mounted in vibration isolation table that CCD camera, which aligns assembly system,
Part group and CCD camera group establish a reference frame O-xyz in vibration isolation table, wherein base part group by from upper and
Under base part and control the direction the Z1 motion platform, the direction Y1 motion platform and the direction X1 motion platform group of its position
By top-down target part and the six-freedom micro displacement platform i.e. PI platform, the side Z2 of its position is controlled at, target part group
It is formed to motion platform, the direction Y2 motion platform and the direction X2 motion platform, CCD camera group is by CCD camera and controls its position
The direction Z3 motion platform, the direction Y3 motion platform and the direction the X3 motion platform composition set, which is characterized in that this method includes such as
Lower step:
Step 1: aligning assembly system according to CCD camera establishes system topological chain: being matrix from vibration isolation table to base part
Chain is object chain from vibration isolation table to target part, is camera chain from vibration isolation table to CCD camera；And vibration isolation table, the direction X1 are moved
Platform, the direction Y1 motion platform, base part, the direction X2 motion platform, the direction Y2 motion platform, target part, the direction X3 fortune
Moving platform, the direction Y3 motion platform and CCD camera establish coordinate system, and in the order described above to the coordinate system established into
The coordinate serial number of row 0~9 is numbered；Wherein coordinate system 0 is reference frame；
Have 6 linear axes in system topological chain, is respectively as follows: the direction X1 motion platform, the direction Y1 motion platform, the side X2
To motion platform, the direction Y2 motion platform, the direction X3 motion platform and the direction Y3 motion platform；And it will be each according to its coordinate serial number
Linear axes number is axis 1, axis 2, axis 4, axis 5, axis 7, axis 8；
Step 2: not kinematic error ideally, precalculate to obtain base part group and target part group
In transformation matrix between each coordinate system, will form and convert square between the corresponding coordinate system of component each from the bottom to top of base part group
Battle array, which is multiplied, obtains transformation matrix of the base part with respect to reference frameThe each group from the bottom to top of target part group will be formed
Transition matrix is multiplied between the corresponding coordinate system of part, obtains transformation matrix of the target part with respect to reference frameTherefrom extract
Obtain the position vector P of base part and target part under reference frame31、P61, direction vector U31、U61；
Step 3: obtaining the linear displacement error of each linear axes in advance under the situation there are kinematic error, straightness misses
Difference, pitch error, roll error, Run-out error, and precalculate the error of perpendicularity, axis 4 and the axis 5 obtained between axis 1 and axis 2
Between the error of perpendicularity, the error of perpendicularity between axis 7 and axis 8, and obtain the coordinate origin offset between each coordinate system；
It is established using above-mentioned each error there are under the situation of kinematic error, base part and target part are with respect to reference coordinate
The transformation matrix of system
The Run-out error and pitch error for considering CCD camera, establish the transformation matrix of the opposite reference frame of CCD cameraWherein θx、θy、θzRespectively roll error of the CCD camera in the direction x, the direction y
Pitch error and the direction z Run-out error；δx、δy、δzRespectively the linear displacement error of CCD camera in the x, y, z-directions and
The sum of straightness error；
When considering the kinematic error of CCD component, the error transformation matrix of camera lens need to be equivalent to target part and matrix zero
The error transformation matrix of part.The straight-line displacement error and roll error of camera lens only cause part image in the position as plane, and
Part imaging deviation is not influenced, considers the pitching and deflection of camera lens, then the deflection of camera lens is equivalent to deflection and the direction phase of part
Instead, the pitching of camera lens is equivalent to the pitching of part；
Equivalent transformation matrix be
It utilizesRespectively withBe multiplied the comprehensive transformation for obtaining base part and target part with respect to reference frame
Matrix, respectivelyWithIt therefrom extracts and obtains the position vector of base part and target part under reference frame and beWith
The direction vector of base part and target part under reference frame isWith
Step 4: obtaining position error vector and deflection error vector of the base part under reference frame is respectively Δ
P3=P3-P31、ΔU3=U3-U31；
Position error vector and deflection error vector of the target part under reference frame are respectively Δ P6=P6-P6、1
ΔU6=U6-U61。
Further, not kinematic error ideally, the transformation matrix of coordinates between coordinate system is respectively as follows:
For coordinate system i to the coordinate of coordinate system j
Transformation matrix, i, j=0~9；
Base part and target part phaseTransformation matrix to reference frame is respectivelyWith
Then the position vector of base part and target part under reference frame is respectively
The direction vector of base part and target part under reference frame is respectively
When there are kinematic error: the transformation matrix of coordinates between coordinate system is respectively as follows: For coordinate system
For matrix chain:
In formula, O0-1For the offset of the origin of coordinate system 1 and coordinate system 0 in a z-direction；δ1x、δ1y、δ1zRespectively X1Side
To the sum of motion platform linear displacement error in the x, y, z-directions and straightness error；θ1x、θ1y、θ1zRespectively X1Direction fortune
Run-out error of the moving platform in the rolling in the direction x, the pitching in the direction y and the direction z；x1For X1The displacement of direction motion platform；
In formula, O1-2For the offset of the origin of coordinate system 2 and coordinate system 1 in a z-direction；δ2x、δ2y、δ2zRespectively Y1Side
To the sum of motion platform linear displacement error in the x, y, z-directions and straightness error；θ2x、θ2y、θ2zRespectively Y1Direction fortune
Run-out error of the moving platform in the rolling in the direction x, the pitching in the direction y and the direction z；y2For Y1The displacement of direction motion platform；
For Y1Direction motion platform and X1The error of perpendicularity between the motion platform of direction；
O2-3For the offset of the origin of coordinate system 3 and coordinate system 2 in a z-direction；
For object chain:
In formula, O0-4It is the origin of coordinate system 4 and coordinate system 0 in the direction z
On offset；δ4x、δ4y、δ4zRespectively X2Direction motion platform linear displacement error in the x, y, z-directions and straightness miss
The sum of difference；θ4x、θ4y、θ4zRespectively X2Direction motion platform is missed in the beat of the rolling in the direction x, the pitching in the direction y and the direction z
Difference；x4For X2Transport the displacement of direction moving platform；
In formula, O4-5It is the origin of coordinate system 5 and coordinate system 4 in the side z
Upward offset；δ5x、δ5y、δ5zRespectively Y2The linear displacement error and straightness of direction motion platform in the x, y, z-directions
The sum of error；θ5x、θ5y、θ5zRespectively Y2Beat of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z
Error；y5For Y2The displacement of direction motion platform；For Y2Direction motion platform and X2Verticality between the motion platform of direction is missed
Difference；
O5-6For the offset of the origin of coordinate system 6 and coordinate system 5 in a z-direction；
For camera chain:
In formula, O0-7It is the origin of coordinate system 7 and coordinate system 0 in the side z
Upward offset；δ7x、δ7y、δ7zRespectively X3The linear displacement error and straightness of direction motion platform in the x, y, z-directions
The sum of error；θ7x、θ7y、θ7zRespectively X3Beat of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z
Error；x7For X3The displacement of direction motion platform；
In formula, O7-8It is the origin of coordinate system 8 and coordinate system 7 in the side z
Upward offset；δ8x、δ8y、δ8zRespectively Y3The linear displacement error and straightness of direction motion platform in the x, y, z-directions
The sum of error；θ8x、θ8y、θ8zRespectively Y3Beat of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z
Error；y8For Y3The displacement of direction motion platform；For Y3Direction motion platform and X3Verticality between the motion platform of direction is missed
Difference；
O8-9For the offset of the origin of coordinate system 9 and coordinate system 8 in a z-direction.
CCD camera is relative to the transformation matrix of reference frame
Wherein θx、θy、θzRespectively CCD camera is in the inclined of the roll error in the direction x, the pitch error in the direction y and the direction z
Put error；δx、δy、δzRespectively the sum of CCD camera linear displacement error in the x, y, z-directions and straightness error；
When considering the kinematic error of CCD component, the error transformation matrix of camera lens need to be equivalent to target part and matrix zero
The error transformation matrix of part.The straight-line displacement error and roll error of camera lens only cause part image in the position as plane, and
Part imaging deviation is not influenced, considers the pitching and deflection of camera lens, then the deflection of camera lens is equivalent to deflection and the direction phase of part
Instead, the pitching of camera lens is equivalent to the pitching of part；
Equivalent transformation matrix beθy、θzRespectively CCD camera bowing in the direction y
Face upward the Run-out error with the direction z；
Then base part and target part are respectively as follows: with respect to the synthesis transformation matrix of reference frame
With
The position vector of base part and target part under reference frame isWith
The direction vector of base part and target part under reference frame isWith
The utility model has the advantages that
The present invention obtains system motion error and assembles system to the contraposition for being based ultimately upon CCD camera when carrying out error modeling
It unites maximum displacement and angular deviation caused by the pose to be installed to replace the spare parts.Comprehensively consider the linear displacement error, straight of each linear axes
Dimension error, pitching, rolling, Run-out error, and coordinate origin offset, the error of perpendicularity of linear between centers, finally obtain
The higher position error vector of precision and deflection error vector, and carry out effective compensation in the later period and can be improved assembly system
Assembly precision.
Detailed description of the invention
Composition error modeling method implementation flow chart of Fig. 1 based on CCD camera contraposition assembly system；
Fig. 2 is based on CCD camera alignment system structural scheme of mechanism；
Fig. 3 alignment system topology chain.
Specific embodiment
The present invention will now be described in detail with reference to the accompanying drawings and examples.
Embodiment 1, a kind of composition error modeling method based on CCD camera contraposition assembly system, CCD camera contraposition assembly
System is as shown in Fig. 2, include vibration isolation table and the base part group being mounted in vibration isolation table, target part group and CCD camera
Group, wherein base part group by top-down base part and control the Z1 motion platform of its position, Y1 motion platform and
X1 motion platform composition, target part group by top-down target part and control the PI platform of its position, Z2 motion platform,
Y2 motion platform and X2 motion platform composition, CCD camera group is by CCD camera and controls the Z3 motion platform of its position, Y3 fortune
Moving platform and X3 motion platform composition.
This method is as shown in Figure 1, include the following steps:
Step 1: aligning assembly system according to CCD camera establishes system topological chain, as shown in Figure 3；It is established in vibration isolation table
Reference frame, from vibration isolation table to base part be matrix chain, from vibration isolation table to target part be object chain, from vibration isolation table to
CCD camera is camera chain；And vibration isolation table, X1 motion platform, Y1 motion platform, base part, X2 motion platform, Y2 are moved flat
Platform, target part, X3 motion platform, Y3 motion platform and CCD camera establish coordinate system, and in the order described above to being built
Vertical coordinate system carries out 0~9 coordinate serial number number；
Assembly system structural scheme of mechanism is aligned according to CCD camera, in assembling process, assembles executing agency and CCD camera
The geometric error of component pose is to influence the key factor of assembly precision.The system has a PI platform and 8 linear axes: X1、Y1、
Z1、X2、Y2、X3、Y3、Z3.The kinematic accuracy of six-freedom parallel system is very high, ignores its geometric error to assembly precision
It influences.Z1Axis and Z3Two freedom degrees of axis just for the sake of respectively provide target part and CCD camera component height, convenient for
The coaxial alignment of base part detects and assembly, after system initial alignment, is in static shape in contraposition detection and assembling process
State.The kinematic error of itself has no effect on system accuracy, therefore ignores the kinematic error of the two freedom degrees, passes establishing error
Its freedom degree is disregarded when passing model.
Based on theory of multi body system, by the analysis to aligning structure, the topological chain figure of the available system.From every battle array
Platform is known as matrix chain to base part, is known as object chain to target part from every battle array platform, is known as camera to CCD camera from every battle array platform
Chain.Wherein reference frame 0 be fixed on system every on battle array platform, and establish coordinate system on each component, be shown in Table 1.
1 aligning structure of table forms topological serial number and corresponds to table
Step 2: not kinematic error ideally, precalculate to obtain base part group and target part group
In transformation matrix between each coordinate system；
Not kinematic error ideally, the transformation matrix of coordinates of adjacent linear axis is respectively as follows: For coordinate system i to the transformation matrix of coordinates of coordinate system j, i, j=
0~9；
Base part and target part are respectively with respect to the transformation matrix of reference frameWith
Then the position vector of base part and target part under reference frame is respectively
The direction vector of base part and target part under reference frame is respectively
Step 3: obtaining the linear displacement error of each linear axes in advance under the situation there are kinematic error, straightness misses
Difference, pitch error, roll error, Run-out error, and precalculate the error of perpendicularity, axis 4 and the axis 5 obtained between axis 1 and axis 2
Between the error of perpendicularity, the error of perpendicularity between axis 7 and axis 8, and obtain the coordinate origin offset between each coordinate system；
When there are kinematic error: the transformation matrix of coordinates of adjacent linear axis is respectively as follows: For coordinate system i to the transformation matrix of coordinates of coordinate system j, i, j=0~9；
For matrix chain:
X1Motion platform (low sequence body 1) includes two parts: X relative to the homogeneous coordinate transformation of vibration isolation table (low sequence body 0)1
Offset transformation and kinematic error transformation matrix of coordinates of the motion platform coordinate origin relative to reference frame origin.Convert square
Battle array be
In formula, O0-1For the offset of the origin of coordinate system 1 and coordinate system 0 in a z-direction；δ1x、δ1y、δ1zRespectively X1Fortune
The sum of moving platform linear displacement error in the x, y, z-directions and straightness error；θ1x、θ1y、θ1zRespectively X1Motion platform exists
The Run-out error of the rolling in the direction x, the pitching in the direction y and the direction z；x1For X1The displacement of motion platform.
With X1Motion platform is compared, Y1The coordinate system of motion platform (low sequence body 2) increases 1 due to two motion platforms
Between verticalityTransformation matrix caused by error.Therefore Y1Motion platform is relative to X1The error transformation matrix of motion platform
Are as follows:
In formula, O1-2For the offset of the origin of coordinate system 2 and coordinate system 1 in a z-direction；δ2x、δ2y、δ2zRespectively Y1Fortune
The sum of moving platform linear displacement error in the x, y, z-directions and straightness error；θ2x、θ2y、θ2zRespectively Y1Motion platform exists
The Run-out error of the rolling in the direction x, the pitching in the direction y and the direction z；y2For Y1The displacement of motion platform；For Y1Motion platform and
X1The error of perpendicularity between motion platform；
Base part (low sequence body 3) is with respect to Y1The homogeneous coordinate transformation matrix of motion platform only includes the inclined of coordinate origin
Move transformation.Homogeneous coordinate transformation is
O2-3For the offset of the origin of coordinate system 3 and coordinate system 2 in a z-direction；
Similarly, the homogeneous coordinate transformation of object chain are as follows:
In formula, O0-4It is the origin of coordinate system 4 and coordinate system 0 in the direction z
On offset；δ4x、δ4y、δ4zRespectively X2Motion platform linear displacement error in the x, y, z-directions and straightness error it
With；θ4x、θ4y、θ4zRespectively X2Run-out error of the motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；x4For X2
The displacement of motion platform；
In formula, O4-5It is the origin of coordinate system 5 and coordinate system 4 in the side z
Upward offset；δ5x、δ5y、δ5zRespectively Y2The linear displacement error and straightness error of motion platform in the x, y, z-directions
The sum of；θ5x、θ5y、θ5zRespectively Y2Run-out error of the motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；y5For
Y2The displacement of motion platform；For Y2Motion platform and X2The error of perpendicularity between motion platform；
O5-6For the offset of the origin of coordinate system 6 and coordinate system 5 in a z-direction；
For camera chain:
In formula, O0-7It is the origin of coordinate system 7 and coordinate system 0 in the side z
Upward offset；δ7x、δ7y、δ7zRespectively X3The linear displacement error and straightness error of motion platform in the x, y, z-directions
The sum of；θ7x、θ7y、θ7zRespectively X3Run-out error of the motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；x7For
X3The displacement of motion platform；
In formula, O7-8It is the origin of coordinate system 8 and coordinate system 7 in the side z
Upward offset；δ8x、δ8y、δ8zRespectively Y3The linear displacement error and straightness error of motion platform in the x, y, z-directions
The sum of；θ8x、θ8y、θ8zRespectively Y3Run-out error of the motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；y8For
Y3The displacement of motion platform；For Y3Motion platform and X3The error of perpendicularity between motion platform；
O8-9For the offset of the origin of coordinate system 9 and coordinate system 8 in a z-direction.
When considering the kinematic error that vision system introduces, because the pose of CCD camera directly affects the picture deviation of part, from
And influence the precision of rigging error.Consider influence of the pose deviation of CCD camera camera lens to component assembly error, then camera lens is straight
Displacement of the lines error and roll error only cause part image in the position as plane, have no effect on base part and target part phase
To the deviation of pose；And the pitching of camera lens and Run-out error will cause the imaging deviation of part.
Due to only having the beat of camera lens and pitch error to cause the rigging error of part, then only consider matrix in beat and
Pitch error, remaining element are set to 0.Assume
δ9x、δ9y、δ9zRespectively CCD camera in the x, y, z-directions linear
The sum of displacement error and straightness error；θ9x、θ9y、θ9zRespectively CCD camera is in the rolling in the direction x, the pitching in the direction y and the side z
To Run-out error.
Then, when considering the kinematic error of CCD component, the error transformation matrix of camera lens need to be equivalent to target part and matrix
The error transformation matrix of part.The deflection of camera lens is equivalent to the deflection of part and contrary, and the pitching of camera lens is equivalent to part
Pitching.Equivalent transformation matrix be
θ9y、θ9zRespectively CCD camera is in the pitching in the direction y and the beat in the direction z
Error；
Then base part and target part are respectively as follows: with respect to the synthesis transformation matrix of reference frame
With
The position vector of base part and target part under reference frame isWith
The direction vector of base part and target part under reference frame isWith
Step 4: Assembly part position error vector and deflection error vector is calculated
Position error vector and deflection error vector of the base part under reference frame are respectively Δ P3=P3-P3、1
ΔU3=U3-U31；
Position error vector and deflection error vector of the target part under reference frame are respectively Δ P6=P6-P6、1
ΔU6=U6-U61。
Embodiment 2
Comprehensive error computation based on CCD camera contraposition assembly system
1. the geometric error parameter of kinematic axis
The P grade of the assembly executing agency of high-precision contraposition detector, selection THK company, Japan KR-30H model is (accurate
Grade) mould group, wherein X1、Y1、X2、Y2、Y3The stroke of axis is 100mm, X3The stroke of axis is 200mm.
The linear motion platform of KR-30H configures high-resolution grating scale feedback, and positioning accuracy reaches 3 μm, according to it
Precision index, and by the decoupling of its total travel progress straightness and angular deviation.Then stroke is the X of 100mm1、X2The six of axis are freely
Spend error (δx,δy,δz,θx,θy,θz) maximum value is taken as (0.003,0.003,0.003,0.002,0.002,0.002), stroke is
The X of 200mm3The six degree of freedom max value of error of axis is taken as (0.003,0.003,0.003,0.001,0.001,0.001), Y1、
Y2、Y3The six degree of freedom max value of error of axis is taken as (0.003,0.003,0.003,0.002,0.002,0.002).Wherein, line misses
The unit of difference is millimeter, and the unit of angle error is degree.
Remaining parameter in Error Propagation Model takes the actual installation of high-precision alignment system to require index and installation position
It sets.
2. the kinematic error based on CCD camera alignment system calculates
The sextuple error of the linear motion platform of system is maximized, systematic error TRANSFER MODEL is substituted into, is utilized
MATLAB calculates the secondly coordinate conversion matrix of target part and base part, obtains target part and base part is opposite with reference to seat
The maximum deviation of the position vector and direction vector of marking system is respectively as follows:
ΔP3=[0.0872, -1.0020,0.1107,0]T
ΔQ3=[0.0040, -0.0070,0,0]T
ΔP6=[0.0960, -1.0020,0.0057,0]T
ΔQ6=[0.0040, -0.0070,0,0]T
Then target part and collective's part in contraposition detection process and assemble the geometry in implementation procedure by linear motion platform
Maximum displacement departure caused by error is respectively
|Δx36|max=| Δ x3|max+|Δx6|max=0.1832mm
|Δy36|max=| Δ y3|max+|Δy6|max=2.0040mm
|Δz36|max=| Δ z3|max+|Δz6|max=0.1164mm
Target part and collective's part in contraposition detection process and assemble the geometry mistake in implementation procedure by linear motion platform
Maximum angle departure caused by difference is respectively
|Δθx36|max=| Δ θx3|max+|Δθx6|max=0.008 °
|Δθy36|max=| Δ θy3|max+|Δθy6|max=0.014 °
|Δθz36|max=| Δ θz3|max+|Δθz6|max≈0
According to calculated result, it is known that in the high-precision contraposition detector of design, the sextuple geometry that mechanical part introduces is missed
Difference is very big.In displacement, Y-direction maximum influences to assemble the axial assembly precision between object up to 2.004mm；X can to maximum
Up to 0.1832mm, Z-direction maximum influences to assemble the radial assembly precision between object up to 0.1164mm, with system accuracy requirement
Index differs greatly.But since the kinematic error regularity of distribution followed normal distribution of system is distributed, the list of each motion platform
Probability very little of the item error in maximum value, the error propagation through multiple degrees of freedom precision movement platform are introduced in part coordinate system
Maximum deviation is almost 0 in the probability of maximum value.
To sum up, the above is merely preferred embodiments of the present invention, it is not intended to limit the scope of the present invention.It is all
Within the spirit and principles in the present invention, any modification, equivalent replacement, improvement and so on should be included in protection of the invention
Within the scope of.
Claims (2)
1. a kind of composition error modeling method based on CCD camera contraposition assembly system, the CCD camera align assembly system packet
Base part group, target part group and the CCD camera group for including vibration isolation table and being mounted in vibration isolation table, in the vibration isolation table
A reference frame O-xyz is established, wherein base part group by top-down base part and controls the Z1 of its position
Direction motion platform, the direction Y1 motion platform and the direction X1 motion platform composition, target part group is by top-down target zero
Part and six-freedom micro displacement platform i.e. PI platform, the direction Z2 motion platform, the direction Y2 motion platform and the side X2 for controlling its position
Formed to motion platform, CCD camera group by CCD camera and control the direction the Z3 motion platform of its position, the direction Y3 move it is flat
Platform and the direction X3 motion platform composition, which is characterized in that this method comprises the following steps:
Step 1: aligning assembly system according to CCD camera establishes system topological chain: it is matrix chain from vibration isolation table to base part,
It is object chain from vibration isolation table to target part, is camera chain from vibration isolation table to CCD camera；And vibration isolation table, the direction X1 are moved flat
Platform, the direction Y1 motion platform, base part, the direction X2 motion platform, the direction Y2 motion platform, target part, the movement of the direction X3
Platform, the direction Y3 motion platform and CCD camera establish coordinate system, and carry out in the order described above to the coordinate system established
0~9 coordinate serial number number；Wherein coordinate system 0 is reference frame；
Have 6 linear axes in system topological chain, is respectively as follows: the direction X1 motion platform, the direction Y1 motion platform, the direction X2 fortune
Moving platform, the direction Y2 motion platform, the direction X3 motion platform and the direction Y3 motion platform；And it will be each linear according to its coordinate serial number
Axis number is axis 1, axis 2, axis 4, axis 5, axis 7, axis 8；
Step 2: not kinematic error ideally, precalculate to obtain in base part group and target part group each
Transformation matrix between coordinate system, by transition matrix phase between the corresponding coordinate system of component each from the bottom to top for forming base part group
The multiplied transformation matrix to base part with respect to reference frameThe component pair each from the bottom to top of target part group will be formed
Transition matrix is multiplied between the coordinate system answered, and obtains transformation matrix of the target part with respect to reference frameIt therefrom extracts and obtains
The position vector P of base part and target part under reference frame31、P61, direction vector U31、U61；
Step 3: under the situation there are kinematic error, obtain in advance the linear displacement errors of each linear axes, straightness error,
Pitch error, roll error, Run-out error, and precalculate obtain the error of perpendicularity, axis 4 and axis 5 between axis 1 and axis 2 it
Between the error of perpendicularity, the error of perpendicularity between axis 7 and axis 8, and obtain the coordinate origin offset between each coordinate system；
It is established using above-mentioned each error there are under the situation of kinematic error, base part and target part are with respect to reference frame
Transformation matrix
The Run-out error and pitch error for considering CCD camera, establish the transformation matrix of the opposite reference frame of CCD camera Wherein θx、θy、θzRespectively pitching of the CCD camera in the roll error, the direction y in the direction x
The Run-out error of error and the direction z；δx、δy、δzThe respectively linear displacement error and straightness of CCD camera in the x, y, z-directions
The sum of error；
Equivalent transformation matrix be
It utilizesRespectively withBe multiplied the comprehensive transformation square for obtaining base part and target part with respect to reference frame
Battle array, respectivelyWithIt therefrom extracts and obtains the position vector of base part and target part under reference frame and beWith
The direction vector of base part and target part under reference frame isWith
Step 4: obtaining position error vector and deflection error vector of the base part under reference frame is respectively Δ P3=
P3-P31、ΔU3=U3-U31；
Position error vector and deflection error vector of the target part under reference frame are respectively Δ P6=P6-P61、ΔU6=
U6-U61。
2. a kind of composition error modeling method based on CCD camera contraposition assembly system as described in claim 1, feature exist
In, not kinematic error ideally, the transformation matrix of coordinates between coordinate system is respectively as follows: Become for the coordinate of coordinate system i to coordinate system j
Change matrix, i, j=0~9；
Base part and target part are respectively with respect to the transformation matrix of reference frame 1With
Then the position vector of base part and target part under reference frame is respectively
The direction vector of base part and target part under reference frame is respectively
When there are kinematic error: the transformation matrix of coordinates between coordinate system is respectively as follows: For coordinate system i to the transformation matrix of coordinates of coordinate system j, i, j=0~9；
For matrix chain:
In formula, O0-1For the offset of the origin of coordinate system 1 and coordinate system 0 in a z-direction；δ1x、δ1y、δ1zRespectively X1Direction fortune
The sum of moving platform linear displacement error in the x, y, z-directions and straightness error；θ1x、θ1y、θ1zRespectively X1Direction movement is flat
Run-out error of the platform in the rolling in the direction x, the pitching in the direction y and the direction z；x1For X1The displacement of direction motion platform；
In formula, O1-2For the offset of the origin of coordinate system 2 and coordinate system 1 in a z-direction；δ2x、δ2y、δ2zRespectively Y1Direction fortune
The sum of moving platform linear displacement error in the x, y, z-directions and straightness error；θ2x、θ2y、θ2zRespectively Y1Direction movement is flat
Run-out error of the platform in the rolling in the direction x, the pitching in the direction y and the direction z；y2For Y1The displacement of direction motion platform；For Y1
Direction motion platform and X1The error of perpendicularity between the motion platform of direction；
O2-3For the offset of the origin of coordinate system 3 and coordinate system 2 in a z-direction；
For object chain:
In formula, O0-4In a z-direction for the origin of coordinate system 4 and coordinate system 0
Offset；δ4x、δ4y、δ4zRespectively X2Direction motion platform linear displacement error in the x, y, z-directions and straightness error it
With；θ4x、θ4y、θ4zRespectively X2Run-out error of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；x4
For X2Transport the displacement of direction moving platform；
In formula, O4-5In a z-direction for the origin of coordinate system 5 and coordinate system 4
Offset；δ5x、δ5y、δ5zRespectively Y2Direction motion platform linear displacement error in the x, y, z-directions and straightness error it
With；θ5x、θ5y、θ5zRespectively Y2Run-out error of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；y5
For Y2The displacement of direction motion platform；For Y2Direction motion platform and X2The error of perpendicularity between the motion platform of direction；
O5-6For the offset of the origin of coordinate system 6 and coordinate system 5 in a z-direction；
For camera chain:
In formula, O0-7In a z-direction for the origin of coordinate system 7 and coordinate system 0
Offset；δ7x、δ7y、δ7zRespectively X3The linear displacement error and straightness error of direction motion platform in the x, y, z-directions
The sum of；θ7x、θ7y、θ7zRespectively X3Run-out error of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；
x7For X3The displacement of direction motion platform；
In formula, O7-8In a z-direction for the origin of coordinate system 8 and coordinate system 7
Offset；δ8x、δ8y、δ8zRespectively Y3The linear displacement error and straightness error of direction motion platform in the x, y, z-directions
The sum of；θ8x、θ8y、θ8zRespectively Y3Run-out error of the direction motion platform in the rolling in the direction x, the pitching in the direction y and the direction z；
y8For Y3The displacement of direction motion platform；For Y3Direction motion platform and X3The error of perpendicularity between the motion platform of direction；
O8-9For the offset of the origin of coordinate system 9 and coordinate system 8 in a z-direction.
CCD camera is relative to the transformation matrix of reference frame
Wherein θx、θy、θzRespectively CCD camera is missed in the beat of the roll error in the direction x, the pitch error in the direction y and the direction z
Difference；δx、δy、δzRespectively the sum of CCD camera linear displacement error in the x, y, z-directions and straightness error；
Equivalent transformation matrix beθy、θzRespectively pitching and z of the CCD camera in the direction y
The Run-out error in direction；
Then base part and target part are respectively as follows: with respect to the synthesis transformation matrix of reference frameWith
The position vector of base part and target part under reference frame isWith
The direction vector of base part and target part under reference frame isWith
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