CN109612420A - A kind of determination method applied to the joint arm measuring machine optimum measurement area for realizing workpiece on-line measurement - Google Patents
A kind of determination method applied to the joint arm measuring machine optimum measurement area for realizing workpiece on-line measurement Download PDFInfo
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- CN109612420A CN109612420A CN201910021931.2A CN201910021931A CN109612420A CN 109612420 A CN109612420 A CN 109612420A CN 201910021931 A CN201910021931 A CN 201910021931A CN 109612420 A CN109612420 A CN 109612420A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B21/00—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
- G01B21/02—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
- G01B21/04—Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points
- G01B21/042—Calibration or calibration artifacts
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Abstract
A kind of determination method applied to the joint arm measuring machine optimum measurement area for realizing workpiece on-line measurement, is applied in coordinate measuring technology field.This method establishes the transfer equation between workpiece, measuring machine Two coordinate system first with homogeneous coordinates conversion, the measurement model and error model for passing through joint arm measuring machine again obtain measurement model and error model that joint arm measuring machine is applied to workpiece to be machined measuring system.Using Newton iteration method and it is appropriate layout and extended method, obtain the worst error partial picture in entire space.Then will entire measurement space is equally spaced is cut into several small cubes regions, each region maximum error of measuring is determined using PSO.Finally, finding the wherein the smallest region of maximum error of measuring by comparing.This method can rapidly and accurately determine the joint arm measuring machine optimum measurement area of workpiece on-line measurement, and the measurement accuracy of measuring machine can be improved, to improve the machining accuracy and processing quality of workpiece.
Description
Technical field
It is applied to realize workpiece on-line measurement applied to one of coordinate measuring technology field the present invention relates to a kind of
The determination method in joint arm measuring machine optimum measurement area
Background technique
Workpiece on-line measurement is to realize the effective way of intelligence manufacture, can be with for the not high workpiece of requirement on machining accuracy
On-line measurement is realized using joint arm measuring machine, to improve the machining accuracy and processing quality of part.
Joint arm measuring machine is the space fisher's formula cascaded structure that more bars are connected in series by multiple rotary joints, due to it
Have the advantages that measuring speed is fast, be convenient for carrying, measure that space is openr, measures that dead angle is less, requirement to environment is low, it is wide
It is general to be applied to vehicle complete vehicle and components, mold, aerospace, steam turbine, heavy-duty machine and other mechanical processing industries.
Six degree of freedom joint arm measuring machine is made of 3 measurement arms, 6 joints, 6 round encoders and 1 gauge head.It is each to survey
Measuring arm is the 1st arm, the 2nd arm and the 3rd arm respectively；Above-mentioned each joint be respectively the 1st joint, the 2nd joint, the 3rd joint, the 4th joint,
5th joint and the 6th joint；Circle encoder is the 1st circle encoder, the 2nd circle encoder, the 3rd circle encoder, the 4th circle coding respectively
Device, the 5th circle encoder and the 6th circle encoder；The angle of each articulation is obtained by circle encoder output mounted thereto；
Angle and measuring machine structural parameters that 6 encoders record determine the coordinate of measuring machine gauge head.
Due to the mechanical structure of joint arm measuring machine tandem, justify the error of encoder since amplification is transmitted to survey
When head, lead to its low measurement accuracy, the precision for improving articulated coordinate machine at present becomes key problem urgently to be resolved.
When joint arm measuring machine measures any point in space, it can go to be surveyed by a variety of different postures
Amount, the angle error of 6 round encoders will be there are many different combinations in different positions.It is possible thereby to be generalized to articulated type seat
The entire measurement space of co-ordinate measuring machine, the i.e. error change at any point therefore are entirely being surveyed with certain rule and continuous
There are the smallest cubical area of worst error, that is, optimum measurement areas in quantity space.Similarly joint arm measuring machine is surveyed applied to workpiece
There is also optimum measurement areas when amount.
Particle swarm algorithm, also referred to as particle swarm optimization algorithm or flock of birds foraging algorithm (Particle Swarm
Optimization), it is abbreviated as PSO, is evolution new by one kind of the exploitations such as J.Kennedy and R.C.Eberhart in recent years
Algorithm (Evolutionary Algorithm-EA).One kind that PSO algorithm belongs to evolution algorithm is similar with simulated annealing,
It is also from RANDOM SOLUTION, by iteration find optimal solution, it be also the quality of solution is evaluated by fitness, but it than lose
Propagation algorithm rule is more simple, it does not have " intersection " (Crossover) of genetic algorithm and " variation " (Mutation) operation, it
By follow current search to optimal value find global optimum.This algorithm realizes easy, precision is high, convergence is fast etc. with it
Advantage causes the attention of academia, and its superiority is illustrated in solving practical problems.Particle swarm algorithm be it is a kind of simultaneously
Row algorithm.
In order to improve the measurement accuracy of measuring machine, expand its application range, optimum measurement of the domestic and foreign scholars to measuring machine
Area (maximum error of measuring the is the smallest region) method of determination conducts a research, and Wang Xueying etc. sits articulated type using Monte Carlo method
The working space of co-ordinate measuring machine has done simulation analysis and has delineated working space point cloud chart, it is found that the working space of measuring machine is
With hollow sphere.Zheng great Teng etc. using support vector machines obtain optimum measurement area based on spot measurement and based on space away from
Optimum measurement area from measurement, it was demonstrated that the existence in optimum measurement area, but this method is not very practical, needs to survey a large amount of
Data.Hu Yi etc. obtains the optimum measurement area in measurement space with ant group algorithm.The optimum measurement that the above scholar is studied
Area determine method both for the entire ball-type working space of measuring machine, and work measuring machine being used on general precision process equipment
Part on-line measurement only need to determine optimum measurement area for processing locating for workpiece in process equipment and measurement space, so needing pair
Above-mentioned optimum measurement area determines that method is improved.
Summary of the invention
In order to overcome the shortcomings in the background art, the invention discloses a kind of applied to the joint for realizing workpiece on-line measurement
The determination method in arm measure machine optimum measurement area, the above method can solve the joint arm for being applied to realize workpiece on-line measurement
Workpiece is placed in measuring machine optimum measurement area and carries out on-line measurement by measuring machine optimum measurement area, and joint arm survey can be improved
The measurement accuracy of amount machine, to achieve the purpose that improve Workpiece Machining Accuracy and processing quality.
The present invention is a kind of determination method applied to the joint arm measuring machine optimum measurement area for realizing workpiece on-line measurement,
The joint arm measuring machine is six degree of freedom joint arm measuring machine, by 3 measurement arms, 6 joints, 6 round encoders and 1 survey
Head is constituted.Above-mentioned each measurement arm is the 1st arm, the 2nd arm and the 3rd arm respectively；Above-mentioned each joint be respectively the 1st joint, the 2nd joint,
3rd joint, the 4th joint, the 5th joint and the 6th joint；Circle encoder is the 1st circle encoder, the 2nd circle encoder, the 3rd circle respectively
Encoder, the 4th circle encoder, the 5th circle encoder and the 6th circle encoder；The angle of each articulation is by mounted thereto
Circle encoder output obtains；
The present invention realizes that goal of the invention adopts the following technical scheme that
Step 1: the measurement equation p of joint arm measuring machine is established using D-H method,
Wherein: c indicates that cos, s indicate sin, liIt is the length of rod piece；θiIt is each joint actual rotation amount；diIt is that joint is inclined
The amount of setting；aiIt is the windup-degree of adjacent segment axis；L is measuring machine gauge head length；
Step 2: demarcating circle encoder errors, obtain its error characteristics function ei(θi).Joint arm measuring machine structure is joined
Several and error characteristics function substitutes into it and measures equation p, obtains the coordinate formula with joint rotation angle error:
The then measurement error as caused by circle encoder are as follows:
Step 3: establishing the transfer equation between workpiece, measuring machine Two coordinate system using homogeneous coordinates conversion, then pass through joint
The measurement model and error model of arm measure machine obtain the measurement mould that joint arm measuring machine is applied to workpiece to be machined measuring system
Type q and error model q*.If three-dimensional coordinate deviant is (x between two coordinate originsT,yT,zT)=(500,100,100)).
Therefore R coordinate measuring error in workpiece coordinate system in measured point is δ (θ1,θ2,θ3,θ4,θ5,θ6)。
Step 4: measurement space is set as 400mm≤x in workpiece coordinate system≤600mm, 0mm≤y≤200mm, 0mm
≤ z≤200mm, three-dimensional coordinate interval 20mm take a little, and the point of three axis intersection is measurement point sampled point；Appoint and takes in workpiece coordinate system
Its coordinate is substituted into the measurement model that joint arm measuring machine is applied to workpiece to be machined measuring system, using ox by any sampled point
Solution by iterative method Nonlinear System of Equations, obtains a variety of measurement attitude integrations of the point, then substitutes into joint arm measuring machine application
In the error model of workpiece to be machined measuring system, the error distribution and maximum error of measuring of the sampled point are obtained；Then it promotes
To the overall situation, the worst error distribution of each point in designated space is obtained, takes maximum survey of each measurement point under different measurement postures
Error is measured, each measurement point maximum error of measuring distribution in specified measurement space is obtained；
Step 5: by Step 1: step 2 and step 3 can obtain worst error model:
Workpiece coordinate system specified measurement space is divided into several small solid spaces at equal intervals, is acquired using PSO each
Worst error in solid space, the worst error of more each solid space obtain the smallest solid space of worst error, i.e.,
For applied to the joint arm measuring machine optimum measurement area for realizing workpiece on-line measurement.
Compared with the prior art, the invention has the advantages that:
The structural parameters of circle encoder errors characterisitic function and joint arm measuring machine are substituted into joint arm measure in the present invention
In the measurement model of machine, the error model of the joint arm measuring machine based on circle encoder angle error is obtained；Utilize homogeneous coordinates
The transfer equation between workpiece, measuring machine Two coordinate system is established in conversion, then passes through the measurement model and error mould of joint arm measuring machine
Type obtains measurement model and error model that joint arm measuring machine is applied to workpiece to be machined measuring system；Utilize Newton iteration
The inverse multiple groups measurement attitude integration for solving any sampled point of method, and joint arm measuring machine is substituted into applied to workpiece to be machined measurement system
The error model of system obtains the measurement error distribution and maximum error of measuring of the point；It is layouted and extended method, is asked using appropriate
The distribution of single-point error and global worst error distribution in designated space are obtained, measuring data sample number in actual measurement is not only solved
Limited problem also reduces many workloads, improves work efficiency；Particle swarm algorithm (PSO) is applied into measurement of coordinates
Field, it is simple using particle swarm algorithm, search speed is fast, high-efficient, low optimization accuracy is high the advantages that, substantially increase computational efficiency
And precision.The present invention can acquire the optimum measurement region of workpiece in articulated coordinate machine measurement designated space, mention to be subsequent
It high six-freedom joint type coordinate measurement machine automatic measurement precision and establishes optimum measurement area database and lays a good foundation；In this base
On plinth, the optimal measurement posture of measuring machine measurement specified point can also be determined.
Detailed description of the invention
Fig. 1 is specified measurement space cloud point figure.
Fig. 2 is sampled point R (500,100,100) error point cloud chart in different positions.
Fig. 3 is each measurement point maximum error of measuring distribution map in specified measurement space.
Fig. 4 is algorithm optimizing effect under different population scale.
Fig. 5 is algorithm optimizing effect under different particle rapidities.
Fig. 6 is the flow chart for the worst error that PSO algorithm solves each solid space.
Fig. 7 is the structure chart of six degree of freedom joint arm measuring machine.
Specific embodiment
Explanation is further explained to the present invention below by way of specific embodiment.
Articulated coordinate machine is six-freedom joint type coordinate measurement machine in the present embodiment, by 3 measurement arms, 6
Joint, 6 round encoders and 1 gauge head are constituted.Above-mentioned each measurement arm is the 1st arm, the 2nd arm and the 3rd arm respectively；Above-mentioned each joint
It is the 1st joint, the 2nd joint, the 3rd joint, the 4th joint, the 5th joint and the 6th joint respectively；Circle encoder is that the 1st circle is compiled respectively
Code device, the 2nd circle encoder, the 3rd circle encoder, the 4th circle encoder, the 5th circle encoder and the 6th circle encoder；Each joint turns
Dynamic angle is obtained by circle encoder output mounted thereto；
Specific implementation step is as follows:
Step 1: the measurement equation p of articulated coordinate machine is established using D-H method,
Wherein: c indicates that cos, s indicate sin, liIt is the length of rod piece；θiIt is each joint actual rotation amount；diIt is that joint is inclined
The amount of setting；aiIt is the windup-degree of adjacent segment axis；L is measuring machine gauge head length.
Step 2: demarcating circle encoder errors, error distribution curve be meet Dirichlet condition using 2 π as the period
Class sine curve, its error distribution curve is set as three rank Fourier spaces, obtains its error characteristics function ei(θi)。
ei(θi)=ai+bicos(θi)+cisin(θi)+dicos(2θi)+eisin(2θi)+ficos(3θi)
+gisin(3θi)
Articulated coordinate machine structural parameters and error characteristics function are substituted into it and measure equation p, are obtained with joint
The coordinate formula of angular errors:
The then measurement error as caused by circle encoder are as follows:
Step 3: establishing the transfer equation between workpiece, measuring machine Two coordinate system using homogeneous coordinates conversion, then pass through joint
The measurement model and error model of arm measure machine obtain the measurement mould that joint arm measuring machine is applied to workpiece to be machined measuring system
Type q and error model q*.If three-dimensional coordinate deviant is (x between two coordinate originsT,yT,zT)=(500,100,100)).
Therefore R coordinate measuring error in workpiece coordinate system in measured point is δ (θ1,θ2,θ3,θ4,θ5,θ6)。
Step 4:
A, measurement space is set as 400mm≤x in workpiece coordinate system≤600mm, 0mm≤y≤200mm, 0mm≤z≤
200mm, three-dimensional coordinate interval 20mm take a little, and the point of three axis intersection is measurement point sampled point, then sampling point distributions such as Fig. 1 institute
Show.
B, sampled point R (500,100,100) are taken, its coordinate is substituted into joint arm measuring machine and is measured applied to workpiece to be machined
The measurement model of system solves Nonlinear System of Equations using Newton iteration method, obtains a variety of measurement attitude integrations of the point, then
The error model that joint arm measuring machine is applied to workpiece to be machined measuring system is substituted into, the error distribution of the sampled point is obtained.(such as
Shown in Fig. 2)
C, it then is generalized to the overall situation, obtains the worst error distribution of each point in designated space, takes each measurement point in difference
The maximum error of measuring under posture is measured, each measurement point maximum error of measuring distribution in specified measurement space is obtained.(such as Fig. 3 institute
Show)
Step 5:
A, by Step 1: step 2 and step 3 can obtain worst error model:
Above formula is converted are as follows:
Because being constrained optimization problem, constraint is handled using exterior penalty function, is become a kind of extrapunitiveness letter
Number, is then added in objective function.Remember feasible zone are as follows:
Construct penalty function are as follows:
Target augmented program are as follows:
Thus constrained optimization problem is converted for unconstrained optimization problem, then objective function are as follows:
B, objective function minimum value, the corresponding the smallest sampled point of point, that is, worst error are acquired using PSO algorithm.
Each measurement zoning objectives functional minimum value (maximum of i.e. each measurement subregion is solved using PSO algorithm herein
Error), joint arm measuring machine six round encoder angular values are characterized with particle position, are surveyed with particle fitness value characterization joint arm
Amount machine measurement error value.The principal element for influencing PSO algorithm performance is particle rapidity and location updating mode in an iterative process,
Basic PSO algorithm speed and location update formula are shown below.
In formula: d=1,2 ... D；I=1,2 ..., n；K is current iteration number.VidFor the speed of particle.r1And r2It is point
Random number of the cloth in [0,1].c1And c2For acceleration factor, herein with reference to pertinent literature and to multiple groups acceleration factor value
Under algorithm optimizing effect compare, take c1=c2=1.49445.
ω is inertia weight, indicates influence of the particle present speed to speed after iteration, is affected to algorithm performance.For
Influence of the different inertia weight selection methods of test to algorithm, herein using common several inertia weight selection methods to finger
The minimum value for determining the small objective function of solid space 580≤x≤600,0≤y≤20,60≤z≤80 in space is solved.The area
Between worst error be 0.11 or so, the solution in 0.1045~0.1145 range is considered as close to optimal solution, other, which are considered as, falls into
Suboptimal solution.Population scale sizepop=100, iteration maximum times maxgen=2000, speed maximin V are setmax=
0.5,Vmin=-0.5, penalty factor σ=1000, every kind of method setting are run 100 times.Test result is as follows shown in table:
Wherein: ωsFor initial inertia weight；ωeInertia weight when for iteration to maximum number of iterations；K is current iteration
Number；TmaxFor maximum number of iterations；Take ωs=0.9, ωe=0.4.
By test result it is found that the inertia weight dynamic obtaining value method of above formula has obtained preferable solution effect.
In order to further test other influences of algorithms of different parameter value to algorithm performance, advised herein using different population
Mould value and friction speed value are to solid space small in designated space 580≤x≤600,0≤target of y≤20,60≤z≤80
Functional minimum value is solved.It is respectively 100,140,180,220 that population scale sizepop, which is arranged, iteration maximum times
Maxgen=2000, speed maximin Vmax=0.5, Vmin=-0.5, penalty factor σ=1000, algorithm optimizing effect is such as
Shown in Fig. 4, as seen from the figure, when population scale is 220, algorithmic statement is very fast.Population scale sizepop=220 is set, and iteration is most
Big number maxgen=2000, speed maximin VmaxRespectively 0.5,1.5,2.5,3.5, VminRespectively -0.5, -
1.5, -2.5, -3.5, penalty factor σ=1000, algorithm optimizing effect is as shown in figure 5, as seen from the figure, Vmax=3.5, Vmin=-
When 3.5, algorithmic statement is very fast.
Joint arm measuring machine is applied to the optimum measurement area of workpiece to be machined measurement in order to obtain, first by workpiece to be machined
The processing space that place coordinate system need to measure is divided into multiple small solid spaces, and (each small area of space is 203Mm), use
PSO algorithm acquires the maximum error of measuring of each solid space, and wherein the smallest solid space of maximum error of measuring is as best
Measurement zone.It goes to solve the worst error of each solid space using PSO algorithm herein, detailed process is as shown in Figure 6.
Take particle populations scale sizepop=220, iteration maximum times maxgen=2000, speed maximin Vmax
=3.5, Vmin=-3.5, penalty factor σ=1000.(it is after segmentation to the separation result in specified measurement space according in step 4
1000 three-dimensional measurement spaces), optimizing is carried out in each three-dimensional measurement space after singulation, and it is empty to obtain each small three-dimensional measurement
Between worst error (measured zone selected by this paper in joint arm measuring machine measurement range, then do not have to reject three-dimensional measurement empty
Between).For the size of measurement of comparison error, choose that measurement error is larger and the data in lesser measurement space, as shown in the table.
As seen from the above table, worst error is within the scope of 0.056mm~0.11mm in region, and wherein worst error minimum value is
0.056mm, worst error Minimum Area are 500mm≤x≤520mm, 80mm≤y≤100mm, 100mm≤z≤120mm, the area
Domain is the optimum measurement area for the joint arm measuring machine studied herein.
In order to further increase the measurement accuracy of measuring machine, select in the optimum measurement area of above-mentioned determination worst error value for
The point (504,88,108) of 0.053mm, the measurement error analyzed under 4000 groups of measurement postures that comparison step four determines are big
It is small, it is known that when the posture of measuring machine is θ1=212.5260 °, θ2=111.1939 °, θ3=332.5388 °, θ4=
112.5932°,θ5=82.6842 °, θ6=90.3424 °, the minimum measurement error of the point is 0.0020mm, therefore the measurement appearance
State is the optimal measurement posture that measuring machine measures the point.
It is obvious to a person skilled in the art that invention is not limited to the details of the above exemplary embodiments, Er Qie
In the case where without departing substantially from spirit or essential attributes of the invention, the present invention can be realized in other specific forms.Therefore, no matter
From the point of view of which point, the present embodiments are to be considered as illustrative and not restrictive, and the scope of the present invention is by appended power
Benefit requires rather than above description limits, it is intended that all by what is fallen within the meaning and scope of the equivalent elements of the claims
Variation is included within the present invention.Any reference signs in the claims should not be construed as limiting the involved claims.
In addition, it should be understood that although this specification is described in terms of embodiments, but not each embodiment is only wrapped
Containing an independent technical solution, this description of the specification is merely for the sake of clarity, and those skilled in the art should
It considers the specification as a whole, the technical solutions in the various embodiments may also be suitably combined, forms those skilled in the art
The other embodiments being understood that.
Claims (1)
1. a kind of determination method applied to the joint arm measuring machine optimum measurement area for realizing workpiece on-line measurement, the joint arm
Measuring machine is six degree of freedom joint arm measuring machine, is made of 3 measurement arms, 6 joints, 6 round encoders and 1 gauge head.On
Stating each measurement arm is the 1st arm, the 2nd arm and the 3rd arm respectively；Above-mentioned each joint is the 1st joint, the 2nd joint, the 3rd joint, respectively
4 joints, the 5th joint and the 6th joint；Circle encoder is the 1st circle encoder, the 2nd circle encoder, the 3rd circle encoder, the 4th respectively
Circle encoder, the 5th circle encoder and the 6th circle encoder；The angle of each articulation is defeated by circle encoder mounted thereto
It obtains out；
It is characterized by comprising following steps:
Step 1: the measurement equation p of joint arm measuring machine is established using D-H method,
Wherein: c indicates that cos, s indicate sin, liIt is the length of rod piece；θiIt is each joint actual rotation amount；diIt is joint amount of bias；
aiIt is the windup-degree of adjacent segment axis；L is measuring machine gauge head length；
Step 2: demarcating circle encoder errors, obtain its error characteristics function ei(θi).By joint arm measuring machine structural parameters and
Error characteristics function substitutes into it and measures equation p, obtains the coordinate formula with joint rotation angle error:
The then measurement error as caused by circle encoder are as follows:
Step 3: establishing the transfer equation between workpiece, measuring machine Two coordinate system using homogeneous coordinates conversion, then surveyed by joint arm
The measurement model and error model of amount machine obtain the measurement model q that joint arm measuring machine is applied to workpiece to be machined measuring system
With error model q*.If three-dimensional coordinate deviant is (x between two coordinate originsT,yT,zT)=(500,100,100)).Therefore
R coordinate measuring error in workpiece coordinate system in measured point is δ (θ1,θ2,θ3,θ4,θ5,θ6)。
Step 4: measurement space is set as 400mm≤x in workpiece coordinate system≤600mm, 0mm≤y≤200mm, 0mm≤z≤
200mm, three-dimensional coordinate interval 20mm take a little, and the point of three axis intersection is measurement point sampled point；Appoint take it is any in workpiece coordinate system
Its coordinate is substituted into the measurement model that joint arm measuring machine is applied to workpiece to be machined measuring system, is changed using newton by sampled point
Nonlinear System of Equations is solved for method, obtains a variety of measurement attitude integrations of the point, joint arm measuring machine is then substituted into and is applied to quilt
The error model of workpieces processing measuring system obtains the error distribution and maximum error of measuring of the sampled point；Then it is generalized to complete
Office obtains the worst error distribution of each point in designated space, and maximum measurement of each measurement point under different measurement postures is taken to miss
Difference obtains each measurement point maximum error of measuring distribution in specified measurement space；
Step 5: by Step 1: step 2 and step 3 can obtain worst error model:
Workpiece coordinate system specified measurement space is divided into several small solid spaces at equal intervals, acquires each solid using PSO
Worst error in space, the worst error of more each solid space obtain the smallest solid space of worst error, as answer
For realizing the joint arm measuring machine optimum measurement area of workpiece on-line measurement.
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| CN112833783A (en) * | 2020-12-31 | 2021-05-25 | 杭州电子科技大学 | Variable measurement space method of joint type coordinate measuring machine based on jaw joint |
| CN114714348A (en) * | 2022-03-17 | 2022-07-08 | 浙江大学 | Industrial robot absolute positioning precision improving method |
| EP4025890A4 (en) * | 2019-11-19 | 2023-06-14 | Hewlett-Packard Development Company, L.P. | Determining a preferred region of a scanner |
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