CN108340211A - Numerically-controlled machine tool profile errors method for three-dimensional measurement based on monocular vision - Google Patents
Numerically-controlled machine tool profile errors method for three-dimensional measurement based on monocular vision Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
- B23Q17/24—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves
- B23Q17/2452—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves for measuring features or for detecting a condition of machine parts, tools or workpieces
- B23Q17/2471—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves for measuring features or for detecting a condition of machine parts, tools or workpieces of workpieces
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B23—MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
- B23Q—DETAILS, COMPONENTS, OR ACCESSORIES FOR MACHINE TOOLS, e.g. ARRANGEMENTS FOR COPYING OR CONTROLLING; MACHINE TOOLS IN GENERAL CHARACTERISED BY THE CONSTRUCTION OF PARTICULAR DETAILS OR COMPONENTS; COMBINATIONS OR ASSOCIATIONS OF METAL-WORKING MACHINES, NOT DIRECTED TO A PARTICULAR RESULT
- B23Q17/00—Arrangements for observing, indicating or measuring on machine tools
- B23Q17/24—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves
- B23Q17/2428—Arrangements for observing, indicating or measuring on machine tools using optics or electromagnetic waves for measuring existing positions of tools or workpieces
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Abstract
The present invention is based on the numerically-controlled machine tool profile errors method for three-dimensional measurement of monocular vision to belong to computer vision measurement technical field, is related to a kind of profile errors numerically-controlled machine tool method for three-dimensional measurement based on monocular vision.Monocular camera is mounted on measuring system mounting bracket by this method first, and positioned at the oblique upper of platen.In conjunction with Zhang Zhengyou standardizations and high-precision gridiron pattern scaling board, the intrinsic parameter and distortion parameter of monocular camera are demarcated.Measuring basis is installed after calibration, lathe operation is driven to generate dynamic trajectory, the movement sequence image of four encoded points on monocular camera shooting measuring basis is triggered simultaneously, data processing calculating benchmark space of points coordinate is carried out to every frame image using iterative algorithm, Processing Algorithm is traversed and can be obtained machine tool motion track under camera coordinates system per connection datum mark after frame image.Then this track is projected under lathe coordinate system, is compared with theory locus to solve lathe contoured three-dimensional error.Method is easy to operate, and measurement has good stability.
Description
Technical field
The invention belongs to computer vision measurement technical fields, are related to a kind of profile errors numerical control machine based on monocular vision
Bed method for three-dimensional measurement.
Background technology
The extensive use in modern production field and product short cycle complex parts high-precision with high-performance equipment manufacturing
Production requirement proposes challenge to numerical control machine tooling ability, and five-axle number control machine tool complete can carry out complicated variable curvature part high
Quality, high efficiency processing.But due to lathe by design, manufacture, the factors such as processing environment are influenced, not by machine dynamic characteristics
NC Machine Error is very prominent caused by foot, makes center cutter point physical location deviation theory position, reduces work pieces process essence
Degree, if being unable to fully react and improve the machining accuracy of lathe using lathe static characteristic assessment equipment and method.Lathe
Dynamic characteristic can preferably be characterized by profile errors, and profile errors periodic detection is evaluation numerical control machine dynamic performance, protects
The important leverage of part processing precision is demonstrate,proved, accurate evaluation lathe profile errors need high-precision to solve machine tool motion track.Therefore,
Research five-axle number control machine tool dynamic trajectory high-precision measuring method is of great significance for accurately solving lathe profile errors.
University Of Tianjin Liu lacks the " numerical control based on LaserTRACER of the Patent No. CN106141814A of friend et al. invention
Lathe translation shaft geometric error detects and discrimination method ", using the system being made of numerically-controlled machine tool and LaserTRACER, establish
Mapping model between 21 geometric errors and numerically-controlled machine tool end position and attitude error, in conjunction with the survey of LaserTRACER position and attitude errors
Data are measured, complete the identification of Geometric Error for Computerized Numerical Control Milling Machine, but the system is not suitable for measuring lathe dynamic outline track.Fujian
" a kind of five-axle number control machine tool rotation axis error of engineering college's leaf Jian Hua, the yellow Patent No. CN105382631A for defending east invention
Detection device and method ", invented and be made of the standard ball of binocular machine vision non-contact measurement head and position adjustable
Device drives being accurately positioned for measuring system using lathe linear axis, and to detect the error of rotary shaft, this method can only be realized flat
The profile error measure of face inner circle track.
Invention content
The technical problem to be solved in the present invention is to overcome the deficiencies of existing technologies, and has invented a kind of wheel based on monocular vision
Wide error method for three-dimensional measurement solves lathe arbitrary trajectory and profile errors three-dimensional measurement problem.This method installs a list
Mesh camera keeps measuring visual field and machine tool motion track is completely covered in the depth of field, and in lathe worker in the top of five-axle number control machine tool
Make that measuring basis is installed on platform, the movement sequence image of measuring basis is acquired using monocular camera.In image procossing, for every
On one frame imagery exploitation measuring basis this corresponding frame is solved at four encoded point combination monocular position-pose measurements of fan-shaped array
Machine tool motion spatial position.By each in above-mentioned image processing process ergodic sequence image, camera coordinates system can be obtained
Under lathe running orbit, finally by track project under lathe coordinate system with theory locus compare, complete the three of profile errors
Dimension solves.The characteristics of this method is calculated using monocular vision without Stereo matching avoids and measures robustness caused by error hiding
The problem of difference, while being expanded compared with binocular vision and measuring the depth of field and measurement range.In addition, in conjunction with the imaging model of four encoded points
And iterative algorithm, it can be achieved that machine tool track and profile errors three-dimensional measurement, machine dynamic characteristics can be assessed on various dimensions, should
Method is easy to operate, and integration is good.
The technical solution adopted by the present invention is a kind of numerically-controlled machine tool profile errors method for three-dimensional measurement based on monocular vision,
It is characterized in that：Monocular camera is mounted on measuring system mounting bracket by this method first, and is located at numerically-controlled machine tool lathe workbench
Oblique upper demarcate the intrinsic parameter and distortion parameter of monocular camera in conjunction with Zhang Zhengyou standardizations and high-precision gridiron pattern scaling board.
Measuring basis is installed after calibration, lathe operation is driven to generate dynamic trajectory, while being triggered on monocular camera shooting measuring basis
The movement sequence image of four encoded points carries out the data processing calculating benchmark space of points to every frame image using iterative algorithm and sits
Processing Algorithm is traversed and can be obtained machine tool motion track under camera coordinates system per connection datum mark after frame image, then will by mark
This track is projected under lathe coordinate system, is compared with theory locus to solve lathe contoured three-dimensional error.The tool of the measurement method
Steps are as follows for body：
The first step builds experiment measuring table
It includes monocular camera 1, measuring basis 2, platen 3, measuring system mounting bracket 4 to test measuring table；It will folder
Tool 5 is mounted on platen 3, so as to the replacement clamping of measuring basis 2 and scaling board；
Monocular camera 1 is mounted on measuring system mounting bracket 4, and positioned at the oblique upper of platen 3, according to measurement
The motion range of track and the position for measuring depth of field adjustment monocular camera 1；Gridiron pattern scaling board is first clamped in platen 3
On prepare for camera calibration；It is replaced with measuring basis 2 after calibration is good, and is fixed on platen 3；Measuring basis 2 is
Photoetching glass plate, upper surface photoetching have four circle codification points 119,125,127,151 in fan-shaped distribution, set central point
Point on the basis of 119, and lathe coordinate system is established using it as origin, this four circle codification points are used for the movement of the accurate transmission lathe
Information；When measurement by its clamping on platen 3, by X, Y two-axle interlocking of lathe under certain feed speed
Interpolation equiangular spiral line tracking；
Second step, camera calibration
According to Zhang Shi standardization combined high precision gridiron pattern scaling boards, the intrinsic parameter and distortion parameter of monocular camera 1 are demarcated,
Selection one point coordinates of space is (Xw,Yw,Zw), it is (x, y) to project point coordinates in image plane, considers actual imaging mistake
The radial distortion and centrifugal distortion of camera lens in journey, the non-linear perspective projection model expression of determining video camera are as follows：
Wherein, f is the focal length of monocular camera 1, αx=f/dx and αy=f/dy is respectively defined as the normalization on two axis of x, y
Focal length, (x0, y0) it is image coordinate system origin, by αx、αy、u0、v0The projective transformation matrix M that four parameters are constituted0For phase
Machine Intrinsic Matrix, the unit rotating orthogonal battle array that R is 3 × 3, t is translation vector, 0T=(0,0,0)T, the M of composition1For camera
Outer parameter matrix；I.e. first formula is linear projection imaging model, by intrinsic parameter αx、αy、u0、v0And outer parameter R, t determines machine
The relationship of bed coordinate system and image coordinate system；Point (x, y) is the ideal position of subpoint, and (x ', y ') is the reality for considering distortion
Coordinate, δx、δyFor the nonlinear distortion variate of horizontal axis and the longitudinal axis, r is that subpoint is at a distance from origin under image coordinate system, k1、k2With
k3Respectively single order, second order and three rank coefficient of radial distortion, p1、p2It is single order, second order centrifugal distortion coefficient；By demarcating monocular
Camera can obtain intrinsic parameter αx、αy、u0、v0And distortion parameter k1、k2、k3、p1、p2, and then determine camera projection imaging model.
Third walks, and machine tool track is solved with profile errors three-dimensional
It is that measuring basis 2 utilizes four on measuring basis 2 according to iterative algorithm characteristic that scaling board is replaced after camera calibration
A circle codification point and the perspective projection relationship in two-dimentional image plane between corresponding points are solved；It is realized using Newton iteration method
Monocular vision solves lathe three-dimensional track and initially sets up associated coordinates system and obtain two-dimentional picpointed coordinate；Then primary Calculation is three-dimensional
The pose of object point solves machine tool motion track；Error vector is re-defined, error function is obtained with least square method and optimizes and ask
Solution；Detailed process is as follows：
According to formula (1), the correspondence of three-dimensional object point P and picture point (x, y, z) under camera coordinates system in lathe coordinate system are write out
Projection relation is as follows
To keep the correspondence result of solution more accurate, error function need to be built to solve the minimal error of conversion variable, then
Partial derivatives of image point coordinates u, the v to parametric variable need to be calculated, using Dx、Dy、DzThree corrected parameters indicate translation transformation：Dx
And DyProject objects are represented in the position of image plane, DzIt indicates distance of the object to image plane in z-axis, then can obtain
To indicate rotation transformation, it is defined around camera coordinates system Xc、Yc、ZcThe rotation angle θ of three axisx、θy、θzJoin to correct
Variable h=[Δ D are corrected in number, definitionx,ΔDy,ΔDz,Δθx,Δθy,Δθz], by u, v to the partial derivative of each component with it is unknown
The multiplication of Parameters variation amount can respectively obtain two error equations, by taking the error equation of u components as an example：
Above formula is written as to the form of matrix equation：Jh=e, wherein J are the Jacobian matrixes for including partial derivative, and e is to scheme
The error vector of correspondence as in.When system by it is polynary determining when, can pass through and solve corresponding normal equation formula and execute error
The least square fitting of vector
min||Jh-e||2 (5)
Containing there are six unknown corrected parameter in above formula, one group of corresponding points of foundation can obtain two equations, minimum three groups pairs of needs
Should put can solve all unknown parameters, to ensure solving precision, be solved using four groups of corresponding points to calculate in the present invention；Foundation
Iterative method gradually restrains the characteristic approached, and each iterative projection model parameter amendment can reduce about an order of magnitude, with iteration
Number increases, and acquires the high-precision of machine tool track point under camera coordinates system as a result, every image path point of connection is lathe fortune
Dynamic rail mark, profile errors can be solved by being projected into compare with theory locus in machine tool motion plane.
The invention has the beneficial effects that carrying out data acquisition using a monocular camera, avoid in Binocular vision photogrammetry
Error hiding problem, it is using flexible, easy to adjust, increase measurement range compared with binocular vision and measure the depth of field, enhancing equipment is suitable
Equipment cost is also reduced while with property, also enhances the robustness of equipment, passes through consolidating for measuring basis and platen
Determine the accurate transmission machine tool motion information, pose solution is carried out with the imaging model of four circle codification points of iterative algorithm pair, it is real
The three-dimensional measurement of machine tool track and profile errors is showed.Experimental system is easy to operate, and measurement has good stability.
Description of the drawings
Fig. 1 is machine tool track and profile errors three-dimension measuring system based on monocular vision.Wherein, 1- monocular cameras, 2-
Measuring basis, 3- platens, 4- measuring system mounting brackets, 5- fixtures.
Fig. 2 is the position relationship of central area on measuring basis 2.Wherein, point on the basis of setting central point 119,125,
127,151- is respectively other 3 points.
Tetra- circle codification point images of Fig. 3.
Fig. 4 is to measure machine tool track and profile errors experiment flow figure.
Specific implementation mode
Describe the specific implementation mode of the present invention in detail below in conjunction with technical solution and attached drawing.
Fig. 1 is the profile errors three-dimension measuring system based on monocular vision.Wherein, 1 is monocular camera, and 2 be measuring basis,
3 be platen.It is the photoetching glass plate of 125mm × 125mm × 3mm, upper surface that the present invention, which uses measuring basis 2, shape,
Its clamping is passed through X, Y of lathe when measurement there are four the circle codification point in fan-shaped distribution by photoetching on platen 3
Two-axle interlocking interpolation equiangular helical spiral track under the feed speed of 1000mm/min；Monocular camera 1 shoots measuring basis 2 and generates
Sequence image is handled frame by frame using iterative algorithm, is solved with imaging model in conjunction with four encoded points, is obtained machine tool track point and exist
High-acruracy survey under camera coordinates system is thrown as a result, every image of traversal and connect tracing point and obtain lathe actual motion track
Shadow carries out projection with theory locus under lathe coordinate system and compares, and the profile errors of lathe can be acquired according to definition.Experimental method
Flow as shown in figure 3, being as follows：
The first step builds experiment measuring table
Measurement object is the numerically-controlled machine tool in laboratory, fixture 5 is mounted on platen 3 first, so as to measurement base
The replacement clamping of standard 2 and scaling board；Experiment using monocular camera 1 model EoSens 25CXP, resolution ratio be 5000 ×
5000 pixels, cooperation Nikon24-70mm camera lenses form optical imaging system, to coordinate the feed speed of lathe 1000mm/min,
It is 80fps to select shooting frame frequency, and the camera exposure time is 3000 μ s, and monocular camera 1 is fixed on to the measurement built by aluminium section bar
It on system mounting bracket 4, keeps stablizing and adjusts camera position, make viewing field of camera that machine tool motion rail be completely covered with the depth of field is measured
Mark, it is ensured that the encoded point energy accurate characterization machine tool motion information on measuring basis 2.
Second step, camera calibration
According to Zhang Shi standardizations, combined high precision gridiron pattern scaling board carries out camera calibration, by adjusting light-source brightness and
Camera focus clearly observes tessellated black and white lattice line of demarcation on scaling board in computer capacity, to ensure stated accuracy, when calibration
Control lathe make scaling board measure visual field different location and shoot 16 photos, according to formula (1) bring into imaging model into
Row calculates, and it is (α to find out inner parameter resultx, αy, u0, v0)=(14959.25397,14959.68660,2557.11076,
2599.79356)；The distortion parameter result of solution is (k1, k2, k3, p1, p2)=(0.10328, -0.23054,0.00045,
0.00012,0.00000) imaging model of monocular camera, is finally determined.
Third walks, and machine tool track and the three-dimensional of profile errors solve
After calibration, replacement scaling board is measuring basis 2, and control lathe interpolation under the feed speed of 1000mm/min is set
Good equiangular spiral line tracking, monocular camera are continuously shot acquisition sequence image, are carried out to each frame image using iterative algorithm
Processing：By taking the 100th frame image as an example, for solve four of the pose value numbers in fan-shaped distributed code point be " 119 ",
" 151 ", " 127 ", " 125 ", as shown in Figure 2,3, No. 119 encoded point central points of setting are as datum mark, the center according to each point
Away from for 25mm, it is known that the space coordinate under its lathe coordinate system is respectively (0.000mm, 0.000mm, 0.000mm),
(0.000mm, 25.000mm, 0.000mm), (17.678mm, 17.678mm, 0.000mm), (25.000mm, 0.000mm,
0.000mm), according to formula (2) to (5), the perspective projection relationship of four groups of corresponding points can be obtained using encoded point, by successive ignition
Solve, solve the track of camera coordinates system and project to the datum mark space coordinate under lathe coordinate system be (5.653mm ,-
5.569mm, -0.016mm), 750 figures for traversing shooting obtain the track under the machine coordinates of vision measurement, are marked according to the world
Standard is by that can solve the contoured three-dimensional error of numerically-controlled machine tool, experiment final result compared with theory locus：Vision measurement
The largest contours error that equiangular helical spiral interpolation generates is 17.1 μm, and mean profile error is 3.1 μm；
The precision that machine tool track and profile errors measure is solved for verification iterative algorithm, is missed using commercialization lathe profile
Aberration measuring apparatus-plane grating device under the same conditions solves machine tool motion track, because plane grating measurement accuracy is less than
0.1 μm, measured movement locus is regarded as lathe theory locus, and the largest contours error that the device measures is learnt through experiment
It it is 72.4 μm, mean error is 13.4 μm, and application condition, the largest contours error that iterative algorithm solves are carried out according to above-mentioned data
And mean profile error is respectively less than the one third that plane grating solves error, it was demonstrated that reliable experiment result, i.e. the method for the present invention
The three-dimensional measurement of machine tool track and profile errors can be achieved, and can preferably reflect the dynamic characteristic of lathe.
Monocular camera is combined by the present invention with numerically-controlled machine tool, is expanded compared with binocular vision and is measured visual field and measure the depth of field,
The error hiding problem caused by Stereo matching, and then the robustness of lifting means are avoided, has that flexibility is strong, equipment cost is low
Advantage complete lathe rail in conjunction with position orientation relation of four encoded points in imaging model on iterative algorithm and measuring basis
The high-precision of mark solves the three-dimensional measurement with profile errors, it can be achieved that the various dimensions of machine dynamic characteristics are assessed, and method operation is simple
Single, measurement has good stability.
Claims (1)
1. a kind of numerically-controlled machine tool profile errors method for three-dimensional measurement based on monocular vision, it is characterized in that：This method first will be single
Mesh camera is mounted on measuring system mounting bracket, and positioned at the oblique upper of numerically-controlled machine tool lathe workbench, is demarcated in conjunction with Zhang Zhengyou
Method and high-precision gridiron pattern scaling board, demarcate the intrinsic parameter and distortion parameter of monocular camera；Measuring basis is installed after calibration, is driven
Lathe operation generates dynamic trajectory, while triggering the motion sequence figure of four encoded points on monocular camera shooting measuring basis
Picture carries out data processing calculating benchmark space of points coordinate to every frame image using iterative algorithm, Processing Algorithm is traversed per frame figure
Connection datum mark can be obtained machine tool motion track under camera coordinates system as after, this track is then projected on lathe coordinate system
Under, it is compared with theory locus to solve lathe contoured three-dimensional error；The measurement method is as follows：
The first step builds experiment measuring table
It includes monocular camera (1), measuring basis (2), platen (3), measuring system mounting bracket (4) to test measuring table；
Fixture (5) is mounted on platen (3), so as to the replacement clamping of measuring basis (2) and scaling board；
Monocular camera (1) is mounted on measuring system mounting bracket (4), and positioned at the oblique upper of platen (3), according to survey
Measure the motion range of track and the position for measuring depth of field adjustment monocular camera (1)；Gridiron pattern scaling board is first clamped in lathe worker
Make to prepare for camera calibration on platform (3)；It is replaced with measuring basis (2) after calibration is good, and is fixed on platen (3)；
Measuring basis (2) is photoetching glass plate, upper surface photoetching have four circle codification points 119 in fan-shaped distribution, 125,127,
151, point on the basis of central point 119 is set, and lathe coordinate system is established using it as origin, this four circle codification points are for accurate
Transmit the movable information of lathe；When measurement by its clamping on platen (3), by X, Y two-axle interlocking of lathe one
Interpolation equiangular helical spiral track under fixed feed speed；
Second step, camera calibration
According to Zhang Shi standardization combined high precision gridiron pattern scaling boards, the intrinsic parameter and distortion parameter of calibration monocular camera (1), choosing
It is (X to take one point coordinates of spacew, Yw, Zw), it is (x, y) to project point coordinates in image plane, considers actual imaging process
The radial distortion and centrifugal distortion of middle camera lens, the non-linear perspective projection model expression of determining video camera are as follows：
Wherein, f is the focal length of monocular camera 1, αx=f/dx and αy=f/dy is respectively defined as the normalization focal length on two axis of x, y,
(x0, y0) it is image coordinate system origin, by αx、αy、u0、v0The projective transformation matrix M that four parameters are constituted0For camera internal reference
Matrix number, the unit rotating orthogonal battle array that R is 3 × 3, t is translation vector, 0T=(0,0,0)T, the M of composition1For the outer parameter of camera
Matrix；I.e. first formula is linear projection imaging model, by intrinsic parameter αx、αy、u0、v0And outer parameter R, t determines machine coordinates
The relationship of system and image coordinate system；Point (x, y) is the ideal position of subpoint, and (x ', y ') is the actual coordinate for considering distortion,
δx、δyFor the nonlinear distortion variate of horizontal axis and the longitudinal axis, r is that subpoint is at a distance from origin under image coordinate system, k1、k2With k3Respectively
For single order, second order and three rank coefficient of radial distortion, p1、p2It is single order, second order centrifugal distortion coefficient；It can by demarcating monocular camera
Obtain intrinsic parameter αx、αy、u0、v0And distortion parameter k1、k2、k3、p1、p2, and then determine camera projection imaging model；
Third walks, and machine tool track is solved with profile errors three-dimensional
It is that measuring basis (2) utilizes four on measuring basis (2) according to iterative algorithm characteristic that scaling board is replaced after camera calibration
A circle codification point and the perspective projection relationship in two-dimentional image plane between corresponding points are solved；It is realized using Newton iteration method
Monocular vision solves lathe three-dimensional track and initially sets up associated coordinates system and obtain two-dimentional picpointed coordinate；Then primary Calculation is three-dimensional
The pose of object point solves machine tool motion track；Error vector is re-defined, error function is obtained with least square method and optimizes and ask
Solution；Detailed process is as follows：
According to formula (1), writes out three-dimensional object point P in lathe coordinate system and projected with the corresponding of picture point (x, y, z) under camera coordinates system
Relationship is as follows
To keep the correspondence result of solution more accurate, error function need to be built to solve the minimal error of conversion variable, then need to count
Nomogram picpointed coordinate u, v is to the partial derivative of parametric variable, using Dx、Dy、DzThree corrected parameters indicate translation transformation：DxAnd DyGeneration
Table project objects are in the position of image plane, DzIt indicates distance of the object to image plane in z-axis, then can obtain
To indicate rotation transformation, it is defined around camera coordinates system Xc、Yc、ZcThe rotation angle θ of three axisx、θy、θzIt is fixed for corrected parameter
Positive variable h=[the Δ D of justice-reparationx, Δ Dy, Δ Dz, Δ θx, Δ θy, Δ θz], by u, partial derivatives and unknown parameter of the v to each component
Variable quantity multiplication can respectively obtain two error equations, by taking the error equation of u components as an example：
Above formula is written as to the form of matrix equation：Jh=e, wherein J are the Jacobian matrixes for including partial derivative, and e is in the picture
The error vector of correspondence；When system by it is polynary determining when, can pass through and solve corresponding normal equation formula and execute error vector
Least square fitting；
min||Jh-e||2 (5)
Containing there are six unknown corrected parameter in above formula, one group of corresponding points of foundation can obtain two equations, at least need three groups of corresponding points
All unknown parameters can be solved, to ensure solving precision, are solved using four groups of corresponding points to calculate in the present invention；According to iteration
Method gradually restrains the characteristic approached, and each iterative projection model parameter amendment can reduce about an order of magnitude, with iterations
Increase, acquires the high-precision of machine tool track point under camera coordinates system as a result, every image path point of connection is machine tool motion rail
Mark, profile errors can be solved by being projected into compare with theory locus in machine tool motion plane.
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