CN105758306B - The tracking of some movement locus and reproducting method on spatial movement rigid body - Google Patents
The tracking of some movement locus and reproducting method on spatial movement rigid body Download PDFInfo
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- CN105758306B CN105758306B CN201610118150.1A CN201610118150A CN105758306B CN 105758306 B CN105758306 B CN 105758306B CN 201610118150 A CN201610118150 A CN 201610118150A CN 105758306 B CN105758306 B CN 105758306B
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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
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
Abstract
The invention discloses the tracking of some movement locus on spatial movement rigid body and reproducting methods.In the measurement space layout 2 of tested component or more laser tracker, so that its measurement range is covered measured point successively in the motion range of different periods, so that measurement data is unified benchmark by coordinate conversion relation between each laser tracker local coordinate system and quiet coordinate system；By the way that each laser tracker measurement data after coordinate transform is shown in the same coordinate system with different line style or color, some movement locus move the accurate correspondence between the time on the tested spatial movement rigid body of final acquisition, solves the technical barrier that single laser tracker data acquire incomplete and more laser tracker measurement data redundancy, have the advantages that simply and intuitively, and each laser tracker measurement data is after data processing, the information of some movement locus on spatial movement rigid body included in it can neither repeat the accurate reproduction that do not omit again.
Description
Technical field
The invention belongs to spatial mechanism kinetics parameter measuring technical fields, specifically, the present invention relates to a kind of spaces
The tracking of some movement locus and reproducting method on motion rigid body.
Background technology
In space mechanism's transmission, because the movement of driving link is mostly pure rotation or pure movement, displacement sensor is arranged more
It is convenient；And it is mostly spatial complex movement to execute component, because displacement sensor difficult arrangement causes its kinematics parameters, such as line (angle)
Displacement, the on-line measurement of line (angle) speed and line (angle) acceleration are difficult to carry out.
Authorization Notice No. is that the patent of invention of CN103925854B discloses a kind of leading based on three-dimensional coordinate transfer principle
Level measurement method is played, is to be combined digital measuring technique with three-dimensional coordinate transfer principle, integrates and is applied to guided missile level
In measurement, high-precision is realized, efficient level of digital measures so that guided missile can obtain same under any attitude
The 3 d space coordinate of full-scale each measurement point of guided missile under coordinate system, and can not be in general assembly for the component where measuring basis
In the case that assembling process participates in horizontal measurement, areal survey is carried out to its process conditions, computational methods are converted finally by coordinate
Realize the assessment of measurement point coordinate position and the comparative analysis under same benchmark.
It is real that the patent of invention of Publication No. CN105241378A discloses a kind of substation 3D based on laser tracking technology
Scape redraws method, and being the single-point tracking measurement technology and line laser structured light technology by combining laser tracker realizes large size
The global measuring of static scene.
Two above patent of invention solves the problems, such as the static measurement of large-scale stationary body or large-scale static scene.Its technology
Feature is, using same laser tracker or electronic theodolite etc., to carry out segmentation and slicing and repeatedly measure, then under the same coordinate system
The space curved surface reconstruct for carrying out large-sized object or scene, to obtain global measuring result；It is repeatedly, non-simultaneous measurement, segmentation
Fragment sequence can be strictly not corresponding with time of measuring！
But when being changed using the kinematics parameters for being tested component in single laser tracker tracking space mechanism, because of its survey
Scope limitation is measured, tracking blind area is certainly existed and corresponding data acquires infull problem；According to single laser tracker repeatedly with
Track measures, and is difficult to obtain tested accurate correspondence between member position coordinate and tested component run duration.
Invention content
It measures for existing tracking blind area when solving to be tested component in single laser tracker tracking space mechanism and repeatedly
It is difficult to obtain the technical barrier that tested member position coordinate moves accurate correspondence between the time again, the invention discloses
The tracking of some movement locus and reproducting method on spatial movement rigid body.
To achieve the goals above, the technical solution that the present invention takes is：Some movement locus on spatial movement rigid body
Tracking and reproducting method, including step：
Tested component starts spatial movement, laser tracker gathered data；
The data of laser tracker acquisition are handled；
The graphic plotting that measured point movement locus reproduces.
Around tested component, i-th of laser tracker and i+1 laser tracker are placed respectively, and i is not less than 1
Integer, and the measurement range of multiple laser trackers is made to cover movement of the measured point on tested component in different periods successively
Range.
When handling the data that laser tracker acquires, note is fixedly arranged at the moving axes on i-th of laser tracker
System is OiXiYiZi, the gathered data of i-th of laser tracker of note is [xi(t),yi(t),zi(t)] quiet coordinate system, is transformed to
Respective coordinates in OXYZ be [jxi(t),jyi(t),jzi(t)]；
Wherein, xi0、yi0、zi0To be fixed on the moving coordinate system O on i-th of laser trackeriXiYiZiCoordinate origin Oi
3 coordinate components in quiet coordinate system OXYZ；
" " is that vector dot operation meets, e1 r、e2 r、e3 rThree reference axis OX, OY of respectively quiet coordinate system OXYZ,
Unit vector corresponding to OZ axis,For moving coordinate system OiXiYiZiOiXiUnit vector of the axis in quiet coordinate system OXYZ,
For moving coordinate system OiXiYiZiOiYiUnit vector of the axis in quiet coordinate system OXYZ,For moving coordinate system OiXiYiZi；OiZi
Unit vector of the axis in quiet coordinate system OXYZ.
In moving coordinate system OiXiYiZiOiXiAxis, OiYiAxis and OiZiP is taken on axis respectivelyi、Qi、Mi3 points, Pi、Qi、Mi3 points
Coordinate in quiet coordinate system is respectively Pi(xPi,yPi,zPi), Qi(xQi,yQi,zQi), Mi(xMi,yMi,zMi)；
When handling the data that laser tracker acquires, note is fixedly arranged at the dynamic seat on i+1 laser tracker
Mark system Oi+1Xi+1Yi+1Zi+1, remember that the gathered data of i+1 laser tracker is：[xi+1(t),yi+1(t),zi+1(t)] it, converts
To the respective coordinates in quiet coordinate system OXYZ be [jxi+1(t),jyi+1(t),jzi+1(t)]；
Wherein, xi+1,0, yi+1,0, zi+1,0To be fixed on the moving coordinate system O on i+1 laser trackeri+1Xi+1Yi+1Zi+1
Coordinate origin Oi+13 coordinate components in quiet coordinate system OXYZ；
" " is that vector dot operation meets, e1 r、e2 r、e3 rThree reference axis OX, OY of respectively quiet coordinate system OXYZ,
Unit vector corresponding to OZ axis,For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Unit of the axis in quiet coordinate system to
Amount,For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Yi+1Unit vector of the axis in quiet coordinate system,For moving coordinate system
Oi+1Xi+1Yi+1Zi+1Oi+1Zi+1Unit vector of the axis in quiet coordinate system.
In Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Axis, Oi+1Yi+1Axis and Oi+1Zi+1P is taken on axis respectivelyi+1、Qi+1、Mi+13 points,
Pi+1、Qi+1、Mi+13 points of coordinates in quiet coordinate system are respectively Pi+1(xPi+1,yPi+1,zPi+1), Qi+1(xQi+1,yQi+1,zQi+1),
Mi+1(xMi+1,yMi+1,zMi+1)；
Based on transform in quiet coordinate system OXYZ tested point coordinates [jxi(t),jyi(t),jzi(t)] it and transforms to and sits quietly
In mark system OXYZ tested point coordinates [jxi+1(t),jyi+1(t),jzi+1(t)] it, carries out graphical data to show, and i-th is swashed
The measurement data of optical tracker system is distinguish from the measurement data of i+1 laser tracker with different linear or color.
In plane right-angle coordinate, measured point x coordinate is drawn respectively and moves correspondence figure between the time, tested
Point y-coordinate moves correspondence figure and measured point z coordinate between the time and moves correspondence figure between the time.
In the same three-dimensional cartesian coordinate system, measured point path curves figure is drawn.
The tracking of some movement locus and reproducting method on the spatial movement rigid body of the present invention, using multiple (two sets or more)
Laser tracker is tracked the same space Moving Objects, and 2 or more laser trackers are carried out reasonable cloth measuring space
It sets, makes the measurement range of these laser trackers, successively fortune of the measured point in different periods on covering detected space moving link
Dynamic range, to solve the problems, such as that tracking blind area and the acquisition of corresponding data existing for single laser tracker be not complete.
Measurand (refer to serial manipulator mechanical arm, parallel robot moving platform, series-parallel robot execute system and
Space mechanism's connecting rod etc. makees the component of spatial complex movement) it equips assembly, participate in each laser tracker measured booting preheating, and
Set each laser tracker data precision, sampling time to identical numerical value, and pay attention to equipping the assembly setting in motion moment with it is each
Laser tracker starts the data acquisition moment and keeps identical, to solve sex chromosome mosaicism while each laser tracker measures.
The coordinate conversion relation between the local coordinate system of each laser tracker and quiet coordinate system is established, each laser is tracked
In measurement data (local coordinate) unification to quiet coordinate system of instrument.
Obviously, 2 kinds of situations are also necessarily will appear in measurement：(1) any laser tracker, because measurement range limits,
Measurement data may not include the total movement location information of measured point, and therefore, final measurement must will participate in measurement
The measurement data of more laser trackers is integrated；(2) adjacent two laser tracker is surveyed because its trace regions has overlapping
Measure the location information that data may jointly containing measured point within a certain range.Therefore, final measurement result takes all sharp
The union of optical tracker system measurement data.Specific method is that the measurement data (local coordinate) of each laser tracker is passed through coordinate
Shift conversion is mark of sitting quietly, by computer graphics techniques, by the measurement data (mark of sitting quietly) of different laser trackers with difference
Line style or color show, splice in quiet coordinate system, the lap data of synteny or color do not take its union；It is final real
Now on the spatial movement rigid body based on more laser trackers some movement locus tracking and reproduction, export tested spatial movement
On rigid body some x coordinates move correspondence figure between the time, on tested spatial movement rigid body some y-coordinates and its transport
Correspondence figure between the dynamic time, some z coordinates move correspondence figure between the time on tested spatial movement rigid body
With some path curves on spatial movement rigid body tested under quiet coordinate system.
The tracking of some movement locus and reproducting method, have the advantages that on the spatial movement rigid body of the present invention：
(1) movement locus of same point on spatial movement component is tracked by more laser trackers, and is become using coordinate
It changes and integrated treatment is subject to the measurement data of more laser trackers with Display Technique of Computer Graphics, may finally obtain tested
Spatial movement rigid body on some movement locus move the accurate correspondence between the time；It solves and adopts in the prior art
With measuring devices such as same laser trackers by multiple, non-simultaneous measurement, though and it is aided with data processing technique and can realizes static state
The space curved surface reconstruct of large-sized object or scene under the same coordinate system, but the dynamic position appearance of space motion object can not be obtained
State moves the technical barrier of accurate correspondence relationship information between the time；
(2) when more laser trackers track the movement locus of same point on spatial movement component simultaneously, because of every laser
The measurement data of tracker is that the opposite local coordinate system of its own provides, therefore there are the skimble-scamble problems of data base；Cause
The measurement range of every laser tracker is limited, certainly exists tracking blind area and corresponding data acquire infull problem；And it is adjacent
Two laser trackers certainly exist measurement data redundancy issue because measurement range has overlapping；The present invention is each sharp by establishing
Coordinate conversion relation solves the problems, such as that measurement data benchmark is skimble-scamble between optical tracker system local coordinate system and quiet coordinate system, leads to
Computer graphics techniques are crossed, each laser tracker measurement data after coordinate transform is shown in the same coordinate system, and
It sets the measurement data of different laser trackers to different line style or color, solves single laser tracker data acquisition not
Full problem and more laser tracker measurement data redundancy issues, have the advantages that simply and intuitively, and each laser tracker measures number
According to after data processing, included on spatial movement rigid body some movement locus information, can neither repeat not lose again
The accurate reproduction of leakage.
Description of the drawings
This specification includes the following drawings, and shown content is respectively：
System arrangement schematic diagram described in Fig. 1 technical solution of the present invention；
The measured points Fig. 2 x coordinate moves correspondence schematic diagram between the time；
The measured points Fig. 3 y-coordinate moves correspondence schematic diagram between the time；
The measured points Fig. 4 z coordinate moves correspondence schematic diagram between the time；
Fig. 5 measured point path curves under quiet coordinate system；
In figure label for：
1, it is tested component；2, laser tracker；3, reflective mirror；4, song corresponding with i-th of laser tracker measurement data
Line；5, curve corresponding with i+1 laser tracker measurement data.
Specific implementation mode
Below against attached drawing, by the description of the embodiment, making to the specific implementation mode of the present invention further details of
Explanation, it is therefore an objective to those skilled in the art be helped to have more complete, accurate and deep reason to the design of the present invention, technical solution
Solution, and contribute to its implementation.
The present invention provides a kind of tracking of some movement locus on spatial movement rigid body based on more laser trackers with
Reproducting method, implementation steps are as follows：
Step 1：Equipment prepares.As shown in Figure 1, around tested component, i+1 laser tracker is set altogether, i is not
Integer less than 1, these laser trackers be followed successively by the 1st laser tracker ..., i-th of laser tracker and i+1
Laser tracker.The measurement range of each laser tracker, centered on its follower head target mirror, by horizontal plane corner section and
The corner section of vertical guide is constituted；The range that the measurement light of each laser tracker is covered is in using follower head target mirror as vertex
Rectangular pyramid shape, adjacent with the vertex four planes are respectively the corner interval border of horizontal plane and the corner section of vertical guide
Boundary.Place principle in the spatial position of i+1 laser tracker：Using each laser tracker follower head target mirror as the tetragonous on vertex
The measurement range of cone-shaped cover successively the measured point on tested component different periods motion range.
Arrange that reflective mirror, reflective mirror position are measured point on tested component.Tested component is to do spatial movement
Rigid body is the component that assembly is equipped as measurand, as the mechanical arm of serial manipulator, the dynamic of parallel robot are put down
The connecting rod etc. of platform, the execution system of series-parallel robot and space mechanism makees the component of spatial complex movement.Measurand is equipped
Assembly participates in each laser tracker measured booting preheating, and sets each laser tracker data precision, sampling time to phase
Same numerical value.
Step 2：Tested component starts spatial movement, and each laser tracker starts gathered data.Measurand equipment is total
Operation is started simultaneously at each laser tracker, the measurand equipment assembly setting in motion moment is made to start with each laser tracker
It is identical that data acquire moment holding.During tested component does spatial movement, the 1st laser tracker to i+1 swashs
Optical tracker system can successively measure the measurement point being tested on component, carry out the acquisition of data.
Step 3：The measurement data of i+1 laser tracker is imported into computer, carries out data processing.
For the measurement data of the acquisition of i+1 laser tracker in total, when carrying out data processing, each laser is tracked
The processing procedure of the measurement data of instrument mainly transforms to each measurement data [x (t), y (t), z (t)] in quiet coordinate system OXYZ
Respective coordinates be [jx(t),jy(t),jZ (t)], obtain the measured point being tested on component different moments correspondence on movement locus
Coordinate.It is said by taking the detailed process that the measurement data to i-th, i+1 laser tracker is handled as an example below
It is bright.
Moving coordinate system is established on i-th of laser tracker, remembers that the moving coordinate system being fixedly arranged on i-th of laser tracker is
OiXiYiZi, remember that the measurement data (group) of i-th (i is not less than 1 integer) a laser tracker is：[xi(t),yi(t),zi
(t)], transform to respective coordinates in quiet coordinate system OXYZ be [jxi(t),jyi(t),jzi(t)]。
Moving coordinate system is established on i+1 laser tracker, note is fixedly arranged at the moving axes on i+1 laser tracker
It is Oi+1Xi+1Yi+1Zi+1, remember that the measurement data (group) of i+1 laser tracker is：[xi+1(t),yi+1(t),zi+1(t)], become
Change to respective coordinates in quiet coordinate system OXYZ be [jxi+1(t),jyi+1(t),jzi+1(t)]。
By moving coordinate system OiXiYiZiTo the coordinate transformation method of quiet coordinate system OXYZ, determined by following formula (1)-formula (8),
For：
Wherein：xi0、yi0、zi0To be fixed on the moving coordinate system O on i-th of laser trackeriXiYiZiCoordinate origin Oi
3 coordinate components in quiet coordinate system OXYZ.
Wherein, " " be vector dot operation meet, and the unit corresponding to three reference axis of quiet coordinate system OXYZ to
Amount is：
For moving coordinate system OiXiYiZiOiXiUnit vector of the axis in quiet coordinate system OXYZ；
For moving coordinate system OiXiYiZiOiYiUnit vector of the axis in quiet coordinate system OXYZ；
For moving coordinate system OiXiYiZiOiZiUnit vector of the axis in quiet coordinate system OXYZ.
If moving coordinate system OiXiYiZiOiXiAxis, OiYiAxis and OiZiP is taken on axis respectivelyi、Qi、Mi3 points, Pi、Qi、Mi3 points
Coordinate in quiet coordinate system is respectively Pi(xPi,yPi,zPi), Qi(xQi,yQi,zQi), Mi(xMi,yMi,zMi)；ThenWithComputational methods be such as following formula (6)-(8)：
By moving coordinate system Oi+1Xi+1Yi+1Zi+1To the coordinate transformation method of quiet coordinate system OXYZ, by following formula (9) to formula
(13) and formula (3) is determined to (5), is：
Wherein：xi+1,0、yi+1,0、zi+1,0To be fixed on the moving coordinate system O on i+1 laser trackeri+1Xi+1Yi+1Zi+1
Coordinate origin Oi+13 coordinate components in quiet coordinate system OXYZ.
Wherein, " " be vector dot operation meet, and the unit corresponding to three reference axis of quiet coordinate system OXYZ to
AmountWithIt is determined by formula (3)-formula (5)；
For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Unit vector of the axis in quiet coordinate system；
For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Yi+1Unit vector of the axis in quiet coordinate system；
For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Zi+1Unit vector of the axis in quiet coordinate system.
If moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Axis, Oi+1Yi+1Axis and Oi+1Zi+1P is taken on axis respectivelyi+1、Qi+1、
Mi+13 points, Pi+1、Qi+1、Mi+13 points of coordinates in quiet coordinate system are respectively Pi+1(xPi+1,yPi+1,zPi+1)、Qi+1(xQi+1,
yQi+1,zQi+1)、Mi+1(xMi+1,yMi+1,zMi+1)；ThenWithCalculation formula it is as follows：
I is the integer not less than 1, when 2 laser trackers are set altogether around tested component, i=1, and i-th of laser
Tracker is the 1st laser tracker, and i+1 laser tracker is the 2nd laser tracker；When the week of tested component
When enclosing total setting more than two laser tracker, for the measurement data of the 1st laser tracker to (i-1)-th laser tracker
Processing procedure is identical as the processing procedure of above-mentioned i-th, i+1 laser tracker, mainly by each measurement data [x (t), y
(t), z (t)] transform to respective coordinates in quiet coordinate system OXYZ be [jx(t),jy(t),jZ (t)], details are not described herein.
Step 4：The graphic plotting that measured point movement locus reproduces.
After the measurement data to i+1 laser tracker acquisition in total is imported in computer and handled, based on processing
The measurement data obtained afterwards carries out graphical data and shows, and pays attention to the test data of each laser tracker with different
Linear or color is distinguish.
As shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5, based on transform in quiet coordinate system OXYZ i-th (i be it is whole not less than 1
Number) a laser tracker measurement data [jxi(t),jyi(t),jzi(t)] and i+1 in quiet coordinate system OXYZ is transformed to
Laser tracker measurement data [jxi+1(t),jyi+1(t),jzi+1(t)] it, carries out graphical data to show, and pays attention to the i-th (i
For not less than 1 integer) measurement data of a laser tracker from the measurement data of i+1 laser tracker with different lines
Shape or color are distinguish.
As shown in Figure 2, Figure 3 and Figure 4, it is shown in progress graphical data, in plane right-angle coordinate, after processing
The measurement data of acquisition, draw respectively measured point x coordinate move correspondence figure between the time, measured point y-coordinate and its
Correspondence figure and measured point z coordinate move correspondence figure between the time between run duration.
As shown in figure 5, based on the measurement data obtained after processing, in the same three-dimensional cartesian coordinate system, use
Matlab (matrix＆laboratory) Software on Drawing measured point path curves figure.
Embodiment 1
As shown in Figure 1, in the present embodiment, it is serial manipulator that measurand, which equips assembly, the tested of spatial movement is done
Component is the mechanical arm of serial manipulator, the arrangement reflective mirror 3 (i.e. measurement point) on the mechanical arm (being tested component 1), and
I-th and i+1 laser tracker 2 are placed around mechanical arm.
When placing i-th of laser tracker, make moving coordinate system OiXiYiZiIt is in the same direction with three reference axis of quiet coordinate system OXYZ
It is parallel, that is, OX is parallel to OiXi, OY is parallel to OiYi, OZ is parallel to OiZi, and measure：xi0=0.20, unit is rice；yi0=-
2, unit is rice；zi0=0.40, unit is rice；Again in moving coordinate system OiXiYiZiOiXiAxis, OiYiAxis and OiZiIt is taken respectively on axis
Pi、Qi、Mi3 points, Pi、Qi、Mi3 points of coordinates in quiet coordinate system are respectively Pi(xPi,yPi,zPi)、Qi(xQi,yQi,zQi)、Mi
(xMi,yMi,zMi)；Being computed can obtain：
Therefore have：
When placing i+1 laser tracker, make moving coordinate system Oi+1Xi+1Yi+1Zi+1With the z coordinate axis of quiet coordinate system OXYZ
Cocurrent and parallel, remaining two reference axis are antiparallel, that is, OX is parallel to Xi+1Oi+1, OY is parallel to Yi+1Oi+1, OZ is parallel to Oi+ 1Zi+1, and measure：xi+1,0=0.25, unit is rice；yi+1,0=2, unit is rice；zi+1,0=0.40, unit is rice；Again dynamic
Coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Axis, Oi+1Yi+1Axis and Oi+1Zi+1P is taken on axis respectivelyi+1、Qi+1、Mi+13 points, Pi+1、
Qi+1、Mi+13 points of coordinates in quiet coordinate system are respectively Pi+1(xPi+1,yPi+1,zPi+1)、Qi+1(xQi+1,yQi+1,zQi+1)、Mi+1
(xMi+1,yMi+1,zMi+1)；Being computed can obtain：
Therefore have：
Sampling time is set as 0.2483s；The measurement data such as table 1 of i-th of laser tracker output.
The measurement data of i-th of the laser tracker of table 1 output (length unit is rice, and chronomere is the second)
| t | 0 | 0.24 83 | 0.49 66 | 0.74 48 | 0.99 31 | 1.24 14 | 1.48 97 | 1.73 79 | 1.98 62 | 2.23 45 | 2.48 28 | 2.73 10 | 2.97 93 | 3.22 76 | 3.47 59 |
| xi (t) | 0.50 00 | 0.50 50 | 0.50 99 | 0.51 49 | 0.51 99 | 0.52 48 | 0.52 98 | 0.53 48 | 0.53 97 | 0.54 47 | 0.54 97 | 0.55 46 | 0.55 96 | 0.56 46 | 0.56 95 |
| yi (t) | 2.20 00 | 2.20 02 | 2.20 09 | 2.20 19 | 2.20 34 | 2.20 53 | 2.20 77 | 2.21 04 | 2.21 35 | 2.21 70 | 2.22 08 | 2.22 51 | 2.22 96 | 2.23 45 | 2.23 96 |
| zi (t) | 0.60 00 | 0.60 50 | 0.60 99 | 0.61 48 | 0.61 96 | 0.62 42 | 0.62 88 | 0.63 32 | 0.63 74 | 0.64 13 | 0.64 51 | 0.64 85 | 0.65 17 | 0.65 46 | 0.65 71 |
1 continued of table
| t | 3.72 41 | 3.97 24 | 4.22 07 | 4.46 90 | 4.71 72 | 4.96 55 | 5.21 38 | 5.46 21 | 5.71 03 | 5.95 86 | 6.20 69 | 6.45 52 | 6.70 34 | 6.95 17 | 7.20 00 |
| xi (t) | 0.57 45 | 0.57 94 | 0.58 44 | 0.58 94 | 0.59 43 | 0.59 93 | 0.60 43 | 0.60 92 | 0.61 42 | 0.61 92 | 0.62 41 | 0.62 91 | 0.63 41 | 0.63 90 | 0.64 40 |
| yi (t) | 2.24 51 | 2.25 08 | 2.25 67 | 2.26 29 | 2.26 92 | 2.27 57 | 2.28 23 | 2.28 91 | 2.29 59 | 2.30 28 | 2.30 97 | 2.31 66 | 2.32 34 | 2.33 02 | 2.33 70 |
| zi (t) | 0.65 93 | 0.66 11 | 0.66 25 | 0.66 35 | 0.66 41 | 0.66 43 | 0.66 40 | 0.66 32 | 0.66 20 | 0.66 03 | 0.65 81 | 0.65 55 | 0.65 23 | 0.64 87 | 0.64 45 |
The measurement data such as table 2 of i+1 laser tracker output.
The measurement data of 2 i+1 laser tracker of table output (length unit is rice, and chronomere is the second)
| t | 5.71 03 | 5.96 89 | 6.22 76 | 6.48 62 | 6.74 49 | 7.00 35 | 7.26 22 | 7.52 08 | 7.77 95 | 8.03 81 | 8.29 68 | 8.55 54 | 8.81 40 |
| xi+1 (t) | - 0.56 42 | - 0.56 94 | - 0.57 46 | - 0.57 97 | - 0.58 49 | - 0.59 01 | - 0.59 52 | - 0.60 04 | - 0.60 56 | - 0.61 08 | - 0.61 59 | - 0.62 11 | - 0.62 63 |
| yi+1 (t) | 1.70 41 | 1.69 69 | 1.68 97 | 1.68 26 | 1.67 54 | 1.66 83 | 1.66 14 | 1.65 46 | 1.64 79 | 1.64 15 | 1.63 53 | 1.62 94 | 1.62 38 |
| zi+1 (t) | 0.66 20 | 0.66 02 | 0.65 79 | 0.65 51 | 0.65 17 | 0.64 78 | 0.64 34 | 0.63 84 | 0.63 29 | 0.62 69 | 0.62 03 | 0.61 33 | 0.60 57 |
2 continued of table
| t | 9.07 27 | 9.33 13 | 9.59 00 | 9.84 86 | 10.1 073 | 10.3 659 | 10.6 246 | 10.8 832 | 11.1 419 | 11.4 005 | 11.6 592 | 11.9 178 |
| xi+1 (t) | - 0.63 15 | - 0.63 66 | - 0.64 18 | - 0.64 70 | - 0.65 21 | - 0.65 73 | - 0.66 25 | - 0.66 77 | - 0.67 28 | - 0.67 80 | - 0.68 32 | - 0.68 84 |
| yi+1 (t) | 1.61 86 | 1.61 37 | 1.60 92 | 1.60 52 | 1.60 16 | 1.59 85 | 1.59 60 | 1.59 40 | 1.59 26 | 1.59 17 | 1.59 15 | 1.59 19 |
| zi+1 (t) | 0.59 77 | 0.58 92 | 0.58 03 | 0.57 09 | 0.56 12 | 0.55 10 | 0.54 06 | 0.52 97 | 0.51 86 | 0.50 72 | 0.49 56 | 0.48 38 |
I-th of laser tracker output data be coordinately transformed by formula (1) after data such as table 3.
I-th of laser tracker output data coordinate transform result of table 3 (length unit is rice, and chronomere is the second)
| t | 0 | 0.24 83 | 0.49 66 | 0.74 48 | 0.99 31 | 1.24 14 | 1.48 97 | 1.73 79 | 1.98 62 | 2.23 45 | 2.48 28 | 2.73 10 | 2.97 93 | 3.22 76 | 3.47 59 |
| jxi (t) | 0.70 00 | 0.70 50 | 0.70 99 | 0.71 49 | 0.71 99 | 0.72 48 | 0.72 98 | 0.73 48 | 0.73 97 | 0.74 47 | 0.74 97 | 0.75 46 | 0.75 96 | 0.76 46 | 0.76 95 |
| jyi (t) | 0.20 00 | 0.20 02 | 0.20 09 | 0.20 19 | 0.20 34 | 0.20 53 | 0.20 77 | 0.21 04 | 0.21 35 | 0.21 70 | 0.22 08 | 0.22 51 | 0.22 96 | 0.23 45 | 0.23 96 |
| jzi (t) | 1.00 00 | 1.00 50 | 1.00 99 | 1.01 48 | 1.01 96 | 1.02 42 | 1.02 88 | 1.03 32 | 1.03 74 | 1.04 13 | 1.04 51 | 1.04 85 | 1.05 17 | 1.05 46 | 1.05 71 |
The continued table of table 3
| t | 3.72 41 | 3.97 24 | 4.22 07 | 4.46 90 | 4.71 72 | 4.96 55 | 5.21 38 | 5.46 21 | 5.71 03 | 5.95 86 | 6.20 69 | 6.45 52 | 6.70 34 | 6.95 17 | 7.20 00 |
| jxi (t) | 0.77 45 | 0.77 94 | 0.78 44 | 0.78 94 | 0.79 43 | 0.79 93 | 0.80 43 | 0.80 92 | 0.81 42 | 0.81 92 | 0.82 41 | 0.82 91 | 0.83 41 | 0.83 90 | 0.84 40 |
| jyi (t) | 0.24 51 | 0.25 08 | 0.25 67 | 0.26 29 | 0.26 92 | 0.27 57 | 0.28 23 | 0.28 91 | 0.29 59 | 0.30 28 | 0.30 97 | 0.31 66 | 0.32 34 | 0.33 02 | 0.33 70 |
| jzi (t) | 1.05 93 | 1.06 11 | 1.06 25 | 1.06 35 | 1.06 41 | 1.06 43 | 1.06 40 | 1.06 32 | 1.06 20 | 1.06 03 | 1.05 81 | 1.05 55 | 1.05 23 | 1.04 87 | 1.04 45 |
I+1 laser tracker output data, the data after being coordinately transformed by formula (9), such as table 4.4 i+1 of table
A laser tracker output data coordinate transform result (length unit is rice, and chronomere is the second)
| t | 5.71 03 | 5.96 89 | 6.22 76 | 6.48 62 | 6.74 49 | 7.00 35 | 7.26 22 | 7.52 08 | 7.77 95 | 8.03 81 | 8.29 68 | 8.55 54 | 8.81 40 |
| jxi+1 (t) | 0.81 42 | 0.81 94 | 0.82 46 | 0.82 97 | 0.83 49 | 0.84 01 | 0.84 52 | 0.85 04 | 0.85 56 | 0.86 08 | 0.86 59 | 0.87 11 | 0.87 63 |
| jyi+1 (t) | 0.29 59 | 0.30 31 | 0.31 03 | 0.31 74 | 0.32 46 | 0.33 17 | 0.33 86 | 0.34 54 | 0.35 21 | 0.35 85 | 0.36 47 | 0.37 06 | 0.37 62 |
| jzi+1 (t) | 1.06 20 | 1.06 02 | 1.05 79 | 1.05 51 | 1.05 17 | 1.04 78 | 1.04 34 | 1.03 84 | 1.03 29 | 1.02 69 | 1.02 03 | 1.01 33 | 1.00 57 |
4 continued of table
| t | 9.07 27 | 9.33 13 | 9.59 00 | 9.84 86 | 10.1 073 | 10.3 659 | 10.6 246 | 10.8 832 | 11.1 419 | 11.4 005 | 11.6 592 | 11.9 178 |
| jxi+1 (t) | 0.88 15 | 0.88 66 | 0.89 18 | 0.89 70 | 0.90 21 | 0.90 73 | 0.91 25 | 0.91 77 | 0.92 28 | 0.92 80 | 0.93 32 | 0.93 84 |
| jyi+1 (t) | 0.38 14 | 0.38 63 | 0.39 08 | 0.39 48 | 0.39 84 | 0.40 15 | 0.40 40 | 0.40 60 | 0.40 74 | 0.40 83 | 0.40 85 | 0.40 81 |
| jzi+1 (t) | 0.99 77 | 0.98 92 | 0.98 03 | 0.97 09 | 0.96 12 | 0.95 10 | 0.94 06 | 0.92 97 | 0.91 86 | 0.90 72 | 0.89 56 | 0.88 38 |
As shown in Fig. 2, Fig. 3, Fig. 4 and Fig. 5, set when the measurement data pattern of i-th of laser tracker in table 3 is shown
It is set to green dotted line, the measurement data pattern of the i+1 laser tracker in table 4 is set as red solid line when showing.Flat
In the rectangular coordinate system of face, draw respectively measured point x coordinate move correspondence figure between the time, measured point y-coordinate and its
Correspondence figure and measured point z coordinate move correspondence figure between the time between run duration.
As shown in figure 5, in the same three-dimensional cartesian coordinate system, measured point path curves figure is drawn.
The present invention is exemplarily described above in association with attached drawing.Obviously, present invention specific implementation is not by above-mentioned side
The limitation of formula.As long as using the improvement of the various unsubstantialities of inventive concept and technical scheme of the present invention progress；Or not
It is improved, the above-mentioned design of the present invention and technical solution are directly applied into other occasions, in protection scope of the present invention
Within.
Claims (7)
1. the tracking of some movement locus and reproducting method on spatial movement rigid body, which is characterized in that including step：
Tested component starts spatial movement, laser tracker gathered data；
The data of laser tracker acquisition are handled；
The graphic plotting that measured point movement locus reproduces；
Wherein, around tested component, i+1 laser tracker is set altogether, i is the integer not less than 1, these laser trackers
Be followed successively by the 1st laser tracker ..., i-th of laser tracker and i+1 laser tracker, and make multiple laser with
The measurement range of track instrument cover successively the measured point on tested component different periods motion range；
During tested component does spatial movement, the 1st laser tracker to i+1 laser tracker can be successively to quilt
The measurement point surveyed on component measures, and carries out the acquisition of data；
When handling the data that laser tracker acquires, remember that the moving coordinate system being fixedly arranged on i-th of laser tracker is
OiXiYiZi, the gathered data of i-th of laser tracker of note is [xi(t),yi(t),zi(t)] it, transforms in quiet coordinate system OXYZ
Respective coordinates be [jxi(t),jyi(t),jzi(t)]；
Wherein, xi0、yi0、zi0To be fixed on the moving coordinate system O on i-th of laser trackeriXiYiZiCoordinate origin OiIt is sitting quietly
3 coordinate components in mark system OXYZ；
" " is that vector dot operation meets, e1 r、e2 r、e3 rThree reference axis OX, OY, OZ axis of respectively quiet coordinate system OXYZ
Corresponding unit vector,For moving coordinate system OiXiYiZiOiXiUnit vector of the axis in quiet coordinate system OXYZ,It is
Coordinate system OiXiYiZiOiYiUnit vector of the axis in quiet coordinate system OXYZ,For moving coordinate system OiXiYiZi；OiZiAxis exists
Unit vector in quiet coordinate system OXYZ；
When handling the data that laser tracker acquires, note is fixedly arranged at the moving coordinate system on i+1 laser tracker
Oi+1Xi+1Yi+1Zi+1, remember that the gathered data of i+1 laser tracker is：[xi+1(t),yi+1(t),zi+1(t)] it, transforms to quiet
Respective coordinates in coordinate system OXYZ be [jxi+1(t),jyi+1(t),jzi+1(t)]；
Wherein, xi+1,0, yi+1,0, zi+1,0To be fixed on the moving coordinate system O on i+1 laser trackeri+1Xi+1Yi+1Zi+1Seat
Mark origin Oi+13 coordinate components in quiet coordinate system OXYZ；
" " is that vector dot operation meets, e1 r、e2 r、e3 rThree reference axis OX, OY, OZ axis of respectively quiet coordinate system OXYZ
Corresponding unit vector,For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Unit vector of the axis in quiet coordinate system,For moving coordinate system Oi+1Xi+1Yi+1Zi+1Oi+1Yi+1Unit vector of the axis in quiet coordinate system,For moving coordinate system Oi+ 1Xi+1Yi+1Zi+1Oi+1Zi+1Unit vector of the axis in quiet coordinate system；
Based on transform in quiet coordinate system OXYZ tested point coordinates [jxi(t),jyi(t),jzi(t)] and quiet coordinate system is transformed to
In OXYZ tested point coordinates [jxi+1(t),jyi+1(t),jzi+1(t)], carry out graphical data show, and by i-th of laser with
The measurement data of track instrument is distinguish from the measurement data of i+1 laser tracker with different linear or color.
2. the tracking of some movement locus and reproducting method, feature exist on spatial movement rigid body according to claim 1
In, the measurement range of each laser tracker, centered on its follower head target mirror, the corner section by horizontal plane and vertical guide
Corner section is constituted；The range that the measurement light of each laser tracker is covered is in using follower head target mirror as the pyramid shape on vertex
Shape, adjacent with the vertex four planes are respectively the corner interval border of horizontal plane and the corner interval border of vertical guide.
3. the tracking of some movement locus and reproducting method, feature exist on spatial movement rigid body according to claim 2
In in moving coordinate system OiXiYiZiOiXiAxis, OiYiAxis and OiZiP is taken on axis respectivelyi、Qi、Mi3 points, Pi、Qi、Mi3 points quiet
Coordinate in coordinate system is respectively Pi(xPi,yPi,zPi), Qi(xQi,yQi,zQi), Mi(xMi,yMi,zMi)；
4. the tracking of some movement locus and reproducting method, feature exist on spatial movement rigid body according to claim 2
In in Oi+1Xi+1Yi+1Zi+1Oi+1Xi+1Axis, Oi+1Yi+1Axis and Oi+1Zi+1P is taken on axis respectivelyi+1、Qi+1、Mi+13 points, Pi+1、
Qi+1、Mi+13 points of coordinates in quiet coordinate system are respectively Pi+1(xPi+1,yPi+1,zPi+1), Qi+1(xQi+1,yQi+1,zQi+1), Mi+1
(xMi+1,yMi+1,zMi+1)；
5. according to the tracking of some movement locus and reproducting method on any spatial movement rigid body of claim 2 to 4,
It is characterized in that, in plane right-angle coordinate, draws measured point x coordinate respectively and move correspondence figure, quilt between the time
Measuring point y-coordinate moves correspondence figure and measured point z coordinate between the time and moves correspondence figure between the time.
6. the tracking of some movement locus and reproducting method, feature exist on spatial movement rigid body according to claim 5
In, in the same three-dimensional cartesian coordinate system, drafting measured point path curves figure.
7. according to the tracking of some movement locus and reproducting method on any spatial movement rigid body of claim 2 to 4,
It being characterized in that, the tested component for doing spatial movement is the mechanical arm of serial manipulator, arranges reflective mirror on the mechanical arm, and
I-th and i+1 laser tracker are placed around mechanical arm.
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