CN103673976A - Method and system for converting and unifying composite type precision measuring coordinate system - Google Patents

Method and system for converting and unifying composite type precision measuring coordinate system Download PDF

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CN103673976A
CN103673976A CN201310643714.XA CN201310643714A CN103673976A CN 103673976 A CN103673976 A CN 103673976A CN 201310643714 A CN201310643714 A CN 201310643714A CN 103673976 A CN103673976 A CN 103673976A
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倪俊
陈小弟
汤红涛
陈伟男
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Shanghai Institute of Satellite Equipment
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    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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Abstract

The invention provides a system and method for converting and unifying a composite type precision measuring coordinate system, wherein the method comprises: building a theodolite measurement coordinate system by intersection measurement of theodolite space point coordinates; building a machine tool measurement coordinate system; calculating a coordinate of a common reference point; converting the theodolite measurement coordinate system into the machine tool measurement coordinate system. The invention further provides a relative system. The method and system combine the coordinate systems of the machine tool and the theodolite measurement system coordinate systems, build a fusion measurement system, and successfully solve the measurement demand in a product assembling stage, wherein the measurement precision and measurement performance all well satisfy requirements; by introduce a high precisionreference ball to provide a common reference point, the machine tool measurement coordinate system and the theodolite coordinate system are converted and unified one coordinate system, thereby implementing data operation and process under a same coordinate system; and by system error correction, the measurement precision is obviously raised, and the method and system has good applications under special conditions.

Description

Method and system for converting and unifying combined type precision measurement coordinate system
Technical Field
The invention belongs to the technical field of industrial measurement, and particularly relates to a method and a system for converting and unifying a combined type precision measurement coordinate system.
Background
The space coordinate measurement of large-size workpieces of aviation and spacecraft mainly adopts two measurement methods, namely contact measurement and non-contact measurement. The contact type measuring equipment takes on-line detection finishing equipment or three-coordinate as a representative; non-contact measurement is represented by an optical electronic theodolite. However, when these two measuring devices work independently, there are some inevitable disadvantages due to the limitations of the inherent functions of the devices:
(1) contact-type measuring method
On-line detection finishing equipment (or three-coordinate) is taken as a representative, the advantages of large measurement range, strong universality and capability of generating a numerical control machining program in real time according to a measurement result to correct a workpiece, but the following defects exist:
1. due to the position limitation of the measuring head, the profile of a workpiece with a special configuration, such as a hole, a hole and the like, cannot be measured;
2. the measuring arm is limited by the size of the processing shaft and mechanical interference of a space structure, and measurement on the internal structure of the truss or the internal structure of the platform cabin cannot be implemented.
(2) Non-contact measuring method
The optical electronic theodolite is taken as a representative, has the advantages of high measurement precision and flexible measurement azimuth angle, can measure the inside of a truss or a platform cabin, but has the following defects:
1. limited by the intersection measurement principle of theodolites, a target or a prism must be adhered to the position of a measured point;
2. the dimensional accuracy of the measured space distance is not as good as that of online detection correction equipment (or three-coordinate);
3. the workpiece cannot be processed and corrected in real time based on the measurement result.
In view of the above practical problems, the existing contact and non-contact measurement methods must be combined, so as to exert respective technical advantages to the maximum extent, make up for the deficiencies, and obtain more comprehensive and accurate precision data of the workpiece to be measured, which is of great significance for ensuring precision measurement of large-size tools and products in the future.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for converting and unifying a combined type precision measurement coordinate system.
In order to realize the purpose of composite measurement, key technologies such as coordinate system conversion and unification of electronic theodolite intersection measurement and machine tool measurement, calculation of spatial data, fusion of a composite measurement system and the like must be broken through.
The invention relates to a resolving method for contact and non-contact measurement systems, which comprises the steps of machine tool measurement coordinate system construction, theodolite system calibration, introduction and conversion of 3 common datum points, space data transmission, space data resolving and the like.
The invention aims to solve the technical problem that a contact type measuring system (namely three-coordinate) and a non-contact type measuring system (namely theodolite) can not meet the requirement of point position measurement in the same coordinate system. The invention provides a coordinate system conversion and unification method of combined type precision measurement aiming at the problem, the method can exert the technical advantages of each measurement system, make up for the deficiencies, not only solve the measurement problem under each independent coordinate system, but also solve the measurement problem of common coordinate system conversion caused by combined type precision measurement.
According to one aspect of the present invention, there is provided a method for converting and unifying a combined precision measurement coordinate system,
the method comprises the following steps:
step 1: establishing a theodolite measurement coordinate system through intersection measurement of the spatial point coordinates of the theodolite;
step 2: establishing a machine tool measurement coordinate system;
and step 3: acquiring coordinates of a plurality of common datum points of a theodolite measurement coordinate system and a machine tool measurement coordinate system;
and 4, step 4: converting and unifying a theodolite measurement coordinate system and a machine tool measurement coordinate system by using the coordinates of the plurality of common reference points;
the step 1 comprises the following steps:
step 1.1: determining a theodolite measurement coordinate system, specifically, taking the projection of a connecting line of a theodolite A and a theodolite B on a horizontal plane as an X axis, taking the reverse direction of a vertical line passing through the center of a transit latitude instrument A as a Z axis, and determining a Y axis by a right-hand rule, thereby forming the theodolite measurement coordinate system;
step 1.2: reading out horizontal direction observation value gamma of mutual aiming between theodolite A and theodolite BABBAAnd the vertical direction observation value alphaABBAReading out the horizontal direction observation value and the vertical direction observation value gamma of the observation target point P of the theodolite AAPAPAnd the horizontal direction observed value and the vertical direction observed value of the theodolite B observation target point PObserved value gamma in straight directionBPBP
Step 1.3: calculating the three-dimensional coordinates of the target point P, specifically, setting the horizontal angles alpha and beta as
<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>AB</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>AP</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>BP</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>BA</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </math>
The three-dimensional coordinates (x, y, z) of the target point P are then
<math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>z</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>[</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AP</mi> </msub> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BP</mi> </msub> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> <mo>+</mo> <mi>h</mi> <mo>]</mo> </mrow> </math>
Wherein B is the base length, i.e., the horizontal separation distance between theodolite A and theodolite B, and h is the height difference between theodolite A and theodolite B.
Preferably, the step 3 comprises the steps of:
step 3.1: calculating longitude and latitude coordinates of the common datum point in a theodolite measurement coordinate system;
step 3.2: calculating machine coordinates of the common reference point in a machine measurement coordinate system;
wherein steps 3.1 to 3.2 are repeated to obtain at least three common reference point coordinates.
Preferably, the step 4 comprises the steps of:
step 4.1: converting the theodolite measurement coordinate into the machine tool measurement coordinate, specifically, setting the theodolite measurement coordinate system O-XYZ to translate first (X)0,Y0,Z0) Then rotate (epsilon)x,εy,εz) After the scaling is carried out by k times, the coordinate system is converted into a machine tool measurement coordinate system O ' -X ' Y ' Z ', and then the coordinate of the common reference point in O-XYZ is (X, Y, Z) and the coordinate in O ' -X ' Y ' Z ' is (X ', Y ', Z ');
step 4.2: calculating a matrix equation after the coordinate conversion,
<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Y</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Z</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>k</mi> <msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>-</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
wherein, a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 converting the matrix parameters;
step 4.3: and (4) substituting the coordinates of the three common reference points into the matrix equation in the step (4.2) to calculate the parameter relation between the theodolite measurement coordinate system and the machine tool measurement coordinate system.
Preferably, the coordinates of the common reference point are acquired in step 3 using the target ball as a reference.
According to another aspect of the present invention, there is provided a system for converting and unifying a combined precision measurement coordinate system, comprising:
the transit measuring coordinate system data acquisition device is used for acquiring data under a transit measuring coordinate system established by intersection measurement of transit space point coordinates;
the machine tool measuring coordinate system data acquisition device is used for acquiring data in a machine tool measuring coordinate system;
coordinate calculation means for acquiring coordinates of the plurality of common reference points from the theodolite-measured coordinate system data acquisition means and the machine-tool-measured coordinate system data acquisition means;
the coordinate system conversion device is used for converting and unifying the theodolite measurement coordinate system and the machine tool measurement coordinate system by using the coordinates of the plurality of common reference points;
establishing a theodolite measurement coordinate system, specifically, taking the projection of a connecting line of a theodolite A and a theodolite B on a horizontal plane as an X axis, taking the reverse direction of a vertical line passing through the center of a transit latitude instrument A as a Z axis, and determining a Y axis by a right-hand rule, thereby forming the theodolite measurement coordinate system;
the transit coordinate coefficient data acquisition device comprises the following modules:
a target point observation value reading module for collecting horizontal observation value gamma of mutual aiming between theodolite A and theodolite BABBAAnd the vertical direction observation value alphaABBAReading out the horizontal direction observation value and the vertical direction observation value gamma of the observation target point P of the theodolite AAPAPAnd the horizontal direction observation value and the vertical direction observation value gamma of the theodolite B observation target point PBPBP
A three-dimensional coordinate calculation module for calculating the three-dimensional coordinate of the target point P, specifically, setting the horizontal angles alpha and beta as
<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>AB</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>AP</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>BP</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>BA</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </math>
The three-dimensional coordinates of the target point P are
<math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>z</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>[</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AP</mi> </msub> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BP</mi> </msub> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> <mo>+</mo> <mi>h</mi> <mo>]</mo> </mrow> </math>
Wherein B is the base length, i.e., the horizontal separation distance between theodolite A and theodolite B, and h is the height difference between theodolite A and theodolite B.
Preferably, the coordinate calculation device comprises the following modules:
the longitude and latitude coordinate calculation module is used for calculating longitude and latitude coordinates of the common datum point in a theodolite measurement coordinate system;
and the machine tool coordinate calculation module is used for calculating the machine tool coordinates of the common datum points in the machine tool measurement coordinate system.
Preferably, the coordinate system conversion apparatus includes the following modules:
a coordinate conversion module for converting the theodolite measurement coordinate into the machine tool measurement coordinate, specifically, setting O-XYZ translation (X) of the theodolite measurement coordinate system0,Y0,Z0) Then rotate (epsilon)x,εy,εz) After the scaling is carried out by k times, the coordinate system is converted into a machine tool measurement coordinate system O ' -X ' Y ' Z ', and then the coordinate of the common reference point in O-XYZ is (X, Y, Z) and the coordinate in O ' -X ' Y ' Z ' is (X ', Y ', Z ');
a matrix equation calculating module for calculating the matrix equation after the coordinate conversion,
<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Y</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Z</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>k</mi> <msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>-</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
wherein, a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 converting the matrix parameters;
and the parameter relation calculation module is used for substituting the coordinates of the three common reference points into the matrix equation to calculate and obtain the parameter relation between the theodolite measurement coordinate system and the machine tool measurement coordinate system.
Preferably, the coordinates of the common reference point are calculated in a coordinate calculation device using the target ball as a reference.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention combines the coordinate systems of the machine tool and the theodolite measuring system to construct a fusion measuring system, successfully solves the measuring requirement of the product in the assembling stage, and has better measuring precision and measuring performance to meet the requirement;
2. according to the invention, a common datum point is provided by introducing a high-precision datum ball, and a machine tool measurement coordinate system and a theodolite coordinate system are converted and unified into one coordinate system, so that data calculation and processing of the same coordinate system are realized, and the measurement precision is obviously improved through system error correction, so that the method has good application under special conditions;
3. the coordinate system conversion and unification method can be popularized and derived to the composition of contact and non-contact measurement systems in industrial measurement.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a cross-measurement principle of spatial point coordinates of theodolite in the present invention;
FIG. 2 is a schematic diagram of the coordinate system transformation of the composite measuring system of the present invention;
FIG. 3 is a schematic diagram of a data transmission and processing architecture of the hybrid measurement system of the present invention;
FIG. 4 is a flow chart of the steps of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.
The method mainly comprises the steps of establishing a theodolite standard, establishing a machine tool measuring coordinate system, fitting a common datum point, converting the coordinate system, calculating spatial data and the like. The method comprises the following steps that a theodolite measurement coordinate system is established by theodolite space intersection measurement technology through theodolite on-line communication, a measurement reference ruler and software resolving, and then target point information pasted on a part to be measured is collected to solve three-dimensional point coordinates; in the measurement of a machine tool coordinate system, a workpiece coordinate system is often required to be generated to facilitate measurement, and contact measurement of a space point to be measured is realized through axis alignment and space fitting. The common datum point is a common parameter converted from a theodolite coordinate system and a machine tool coordinate system, more than 3 datum coordinate points are required, and the common datum point is fitted by introducing a high-precision datum ball; the transformation and unification of the coordinate system are realized by transforming the translation, rotation and scaling of the spatial rectangular coordinate system on the basis of the establishment of the independent coordinate system.
The main calculation and conversion processes of the present invention are described below with reference to fig. 1,2 and 4.
Step 1: and (4) establishing a theodolite measurement coordinate system through intersection measurement of the coordinates of the spatial points of the theodolite. Specifically, the measurement principle of the theodolite measurement system is a spatial forward intersection, and a system formed by two theodolites will now be described as an example. As shown in fig. 1, two theodolites a and B, a coordinate system is formed by using the intersection point of the central axes of the theodolite a as the origin of coordinates, using the projection of the A, B connecting line on the horizontal plane as the X axis, using the reverse direction of the perpendicular line passing through the center of the theodolite a as the Z axis, and determining the Y axis by the right-hand rule.
Reading out horizontal direction observation value gamma of mutual aiming between theodolite A and theodolite BABBAAnd the vertical direction observation value alphaABBAReading out the horizontal direction observation value and the vertical direction observation value gamma of the observation target point P of the theodolite AAPAPAnd the horizontal direction observation value and the vertical direction observation value gamma of the theodolite B observation target point PBPBP
Calculating the three-dimensional coordinates of the target point P, specifically, setting the horizontal angles alpha and beta as
<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>AB</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>AP</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>BP</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>BA</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </math>
The three-dimensional coordinate (x, y, z) of the point P is
<math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>z</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>[</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AP</mi> </msub> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BP</mi> </msub> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> <mo>+</mo> <mi>h</mi> <mo>]</mo> </mrow> </math>
In the formula, B is the base length, namely the horizontal distance between theodolites A and B, and can be obtained by inverse calculation by measuring a certain reference by using two theodolites and also can be directly measured by a high-precision distance measuring system, and h is the height difference of the two theodolites:
<math> <mrow> <mi>h</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mrow> <mo>(</mo> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AB</mi> </msub> <mo>-</mo> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BA</mi> </msub> <mo>)</mo> </mrow> <mi>b</mi> </mrow> </math>
it can be known that the three-dimensional coordinate value of any point in space can be obtained by only carrying out the orientation of the theodolite system, establishing a measuring coordinate system and obtaining the coordinate value of the A, B survey station.
Step 2: and establishing a machine tool measurement coordinate system.
And step 3: acquiring coordinates of a plurality of common datum points of a theodolite measurement coordinate system and a machine tool measurement coordinate system; . Specifically, in the composite measurement software, when the theodolite measures the target ball, the mode of single-point coordinate measurement is set as 'circle center measurement', the cross wire of the fourth quadrant of the 1 st theodolite is used for aligning the upper left edge of the reference target ball, and the horizontal angle value and the zenith distance are respectively recorded as (Hz)11,V11) Then the right lower edge of the reference target ball is cut by the second quadrant of the theodolite, and the horizontal angle value and the zenith distance are respectively recorded as (Hz)12,V12) Averaging the observed values and ordering;
Hz1=(Hz11+Hz12)/2
V1=(V11+V12)/2
angular value (Hz)1,V1) Passing through the center of sphere, and obtaining the observed value of the angle of the second theodolite passing through the center of sphere in the same way as (Hz)2,V2) And by using the coordinate intersection measurement principle of the space points, the coordinates of the target sphere center can be obtained through intersection, namely the longitude and latitude coordinates of the common datum point are (x, y, z).
When the machine tool measures the reference sphere, the center of the target sphere is indirectly obtained by measuring a plurality of points on the surface of the target sphere and utilizing a least square fitting method. The coordinate value of n (n is more than or equal to 4) measuring points on the surface of the measuring target ball is Pi(xi,yi,zi) Where i =1,2,3, …, n. The three-dimensional coordinates of the target sphere center in the machine tool measuring system, namely the machine tool coordinates of the common datum point, can be obtained through fitting.
And respectively collecting the coordinates of more than three common reference points according to the steps.
And 4, step 4: theodolite surveying instrument using coordinates of multiple common reference pointsThe standard system and the machine tool measurement coordinate system are converted and unified. Specifically, a theodolite measurement coordinate system O-XYZ is set to translate firstly (X)0,Y0,Z0) Then rotate (epsilon)x,εy,εz) And finally, after scaling by k times, converting the coordinate system into a machine tool measurement coordinate system O '-X' Y 'Z'. The coordinates of the point P in O-XYZ are (X, Y, Z), the coordinates in O ' -X ' Y ' Z ' are (X ', Y ', Z '), and through a matrix equation, when the number of the obtained coordinates of the common reference point is more than or equal to 3, the parameter relation between the theodolite coordinate system and the machine tool measurement coordinate system can be obtained, namely, the conversion between the theodolite measurement coordinate system and the machine tool measurement coordinate system is realized.
<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Y</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Z</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>k</mi> <msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>-</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>
Wherein, a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 to transform the matrix parameters.
In this embodiment, the present invention provides a system for converting and unifying a composite measurement coordinate system, including the following devices:
the transit measuring coordinate system data acquisition device is used for acquiring data under a transit measuring coordinate system established by intersection measurement of transit space point coordinates;
the machine tool measuring coordinate system data acquisition device is used for acquiring data in a machine tool measuring coordinate system;
coordinate calculation means for acquiring coordinates of the plurality of common reference points from the theodolite-measured coordinate system data acquisition means and the machine-tool-measured coordinate system data acquisition means;
and a coordinate system converting device for converting and unifying the theodolite measurement coordinate system and the machine tool measurement coordinate system from the coordinates using the plurality of common reference points.
The method comprises the following steps of establishing a theodolite measurement coordinate system, specifically, taking the projection of a connecting line of a theodolite A and a theodolite B on a horizontal plane as an X axis, taking the reverse direction of a vertical line passing through the center of a transit latitude instrument A as a Z axis, and determining a Y axis by a right-hand rule, thereby forming the theodolite measurement coordinate system.
The transit coordinate coefficient data acquisition device comprises the following modules:
a target point observation value reading module for collecting horizontal observation value gamma of mutual aiming between theodolite A and theodolite BABBAAnd the vertical direction observation value alphaABBAReading out the horizontal direction observation value and the vertical direction observation value gamma of the observation target point P of the theodolite AAPAPAnd the horizontal direction observation value and the vertical direction observation value gamma of the theodolite B observation target point PBPBP
A three-dimensional coordinate calculation module for calculating the three-dimensional coordinate of the target point P, specifically, setting the horizontal angles alpha and beta as
<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>AB</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>AP</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>BP</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>BA</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </math>
The three-dimensional coordinates of the target point P are
<math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>z</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>[</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AP</mi> </msub> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BP</mi> </msub> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> <mo>+</mo> <mi>h</mi> <mo>]</mo> </mrow> </math>
Wherein B is the base length, i.e., the horizontal separation distance between theodolite A and theodolite B, and h is the height difference between theodolite A and theodolite B.
Preferably, the coordinate calculation device comprises the following modules:
the longitude and latitude coordinate calculation module is used for calculating longitude and latitude coordinates of the common datum point in a theodolite measurement coordinate system;
and the machine tool coordinate calculation module is used for calculating the machine tool coordinates of the common datum points in the machine tool measurement coordinate system.
Wherein the coordinates of the common reference point are calculated using the target ball as the reference.
Preferably, the coordinate system conversion apparatus includes the following modules:
a coordinate conversion module for converting the theodolite measurement coordinate into the machine tool measurement coordinate, specifically, setting O-XYZ translation (X) of the theodolite measurement coordinate system0,Y0,Z0) Then rotate (epsilon)x,εy,εz) After the scaling is carried out by k times, the coordinate system is converted into a machine tool measurement coordinate system O ' -X ' Y ' Z ', and then the coordinate of the common reference point in O-XYZ is (X, Y, Z) and the coordinate in O ' -X ' Y ' Z ' is (X ', Y ', Z ');
a matrix equation calculating module for calculating the matrix equation after the coordinate conversion,
<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Y</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Z</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>k</mi> <msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>-</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow> </math>
wherein, a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 to transform the matrix parameters.
And the parameter relation calculation module is used for substituting the coordinates of the three common reference points into the matrix equation to calculate and obtain the parameter relation between the theodolite measurement coordinate system and the machine tool measurement coordinate system.
The data transmission of the invention is as shown in fig. 3, the measured data of the theodolite 1 is transmitted to the T-LINK controller through the communication serial port 1 and the measured data of the theodolite n is transmitted to the computer through the communication serial port n. The machine tool measurement data are stored in the data storage device, then transmitted to the data transmitter through the USB communication interface, and transmitted to the computer by the data transmitter. The computer calculates the longitude and latitude coordinates of a common reference ball, namely a target ball, by the triangulation calculation of original measurement data of the theodolite, and calculates the machine coordinates by the original measurement data of the machine tool. And then, unifying and converting the coordinates, and finally, storing the data into an angle and coordinate database after data processing and resolving.
The invention not only can solve the problems of coordinate system transformation, unification, resolving and processing in the compound operation of machine tool measurement and theodolite measurement, but also can solve the key technical problem of coordinate system operation in contact and non-contact fusion measurement in industrial measurement, and the method mainly comprises the following steps: the method comprises the steps of machine tool measurement coordinate system construction, theodolite system calibration, public datum point conversion, space data calculation and the like. Wherein, the theodolite measurement coordinate system is established by a theodolite measurement device; the machine tool measurement coordinate system is established by a machine tool or three coordinates; the common datum point is obtained by fitting an introduced common datum ball and is used for resolving common parameters for converting and unifying a theodolite measurement coordinate system and a machine tool measurement coordinate system; finally, the measured data is provided to the combined special measuring software through the data transmitter and the power supply controller, and the space data is resolved and processed
In conclusion, the method integrates non-contact and contact measurement technologies, provides a common reference point by using the reference ball, converts and unifies a machine tool measurement coordinate system and a theodolite coordinate system into one coordinate system, and meets the combined measurement requirement required by products. The method provides powerful support for solving the problem of precision measurement in the processes of assembly of large aerospace components and the like.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.

Claims (8)

1. A method for converting and unifying a composite precision measurement coordinate system is characterized by comprising the following steps:
step 1: establishing a theodolite measurement coordinate system through intersection measurement of the spatial point coordinates of the theodolite;
step 2: establishing a machine tool measurement coordinate system;
and step 3: acquiring coordinates of a plurality of common datum points of a theodolite measurement coordinate system and a machine tool measurement coordinate system;
and 4, step 4: converting and unifying a theodolite measurement coordinate system and a machine tool measurement coordinate system by using the coordinates of the plurality of common reference points;
the step 1 comprises the following steps:
step 1.1: determining a theodolite measurement coordinate system, specifically, taking the projection of a connecting line of a theodolite A and a theodolite B on a horizontal plane as an X axis, taking the reverse direction of a vertical line passing through the center of a transit latitude instrument A as a Z axis, and determining a Y axis by a right-hand rule, thereby forming the theodolite measurement coordinate system;
step 1.2: reading out horizontal direction observation value gamma of mutual aiming between theodolite A and theodolite BABBAAnd the vertical direction observation value alphaABBAReading out the horizontal direction observation value and the vertical direction observation value gamma of the observation target point P of the theodolite AAPAPAnd the horizontal direction observation value and the vertical direction observation value gamma of the theodolite B observation target point PBPBP
Step 1.3: calculating the three-dimensional coordinates of the target point P, specifically, setting the horizontal angles alpha and beta as
<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>AB</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>AP</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>BP</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>BA</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </math>
The three-dimensional coordinates (x, y, z) of the target point P are then
<math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>z</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>[</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AP</mi> </msub> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BP</mi> </msub> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> <mo>+</mo> <mi>h</mi> <mo>]</mo> </mrow> </math>
Wherein B is the base length, i.e., the horizontal separation distance between theodolite A and theodolite B, and h is the height difference between theodolite A and theodolite B.
2. The method of converting and unifying a composite precision measurement coordinate system according to claim 1, wherein said step 3 comprises the steps of:
step 3.1: calculating longitude and latitude coordinates of the common datum point in a theodolite measurement coordinate system;
step 3.2: calculating machine coordinates of the common reference point in a machine measurement coordinate system;
wherein steps 3.1 to 3.2 are repeated to obtain at least three common reference point coordinates.
3. The method of converting and unifying a composite precision measurement coordinate system according to claim 1, wherein said step 4 comprises the steps of:
step 4.1: converting the theodolite measurement coordinate into the machine tool measurement coordinate, specifically, setting the theodolite measurement coordinate system O-XYZ to translate first (X)0,Y0,Z0) Then rotate (epsilon)x,εy,εz) After the scaling is carried out by k times, the coordinate system is converted into a machine tool measurement coordinate system O ' -X ' Y ' Z ', and then the coordinate of the common reference point in O-XYZ is (X, Y, Z) and the coordinate in O ' -X ' Y ' Z ' is (X ', Y ', Z ');
step 4.2: calculating a matrix equation after the coordinate conversion,
<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Y</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Z</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>k</mi> <msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>-</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
wherein, a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 converting the matrix parameters;
step 4.3: and (4) substituting the coordinates of the three common reference points into the matrix equation in the step (4.2) to calculate the parameter relation between the theodolite measurement coordinate system and the machine tool measurement coordinate system.
4. A method of transformation and unification of a compound precision measurement coordinate system according to claim 1, wherein coordinates of a common reference point are obtained in step 3 using a target ball as a reference.
5. A system for converting and unifying a composite precision measurement coordinate system is characterized by comprising the following devices:
the transit measuring coordinate system data acquisition device is used for acquiring data under a transit measuring coordinate system established by intersection measurement of transit space point coordinates;
the machine tool measuring coordinate system data acquisition device is used for acquiring data in a machine tool measuring coordinate system;
coordinate calculation means for acquiring coordinates of the plurality of common reference points from the theodolite-measured coordinate system data acquisition means and the machine-tool-measured coordinate system data acquisition means;
the coordinate system conversion device is used for converting and unifying the theodolite measurement coordinate system and the machine tool measurement coordinate system by using the coordinates of the plurality of common reference points;
establishing a theodolite measurement coordinate system, specifically, taking the projection of a connecting line of a theodolite A and a theodolite B on a horizontal plane as an X axis, taking the reverse direction of a vertical line passing through the center of a transit latitude instrument A as a Z axis, and determining a Y axis by a right-hand rule, thereby forming the theodolite measurement coordinate system;
the transit coordinate coefficient data acquisition device comprises the following modules:
a target point observation value reading module for collecting horizontal observation value gamma of mutual aiming between theodolite A and theodolite BABBAAnd the vertical direction observation value alphaABBAReading out the horizontal direction observation value and the vertical direction observation value gamma of the observation target point P of the theodolite AAPAPAnd the horizontal direction observation value and the vertical direction observation value gamma of the theodolite B observation target point PBPBP
A three-dimensional coordinate calculation module for calculating the three-dimensional coordinate of the target point P, specifically, setting the horizontal angles alpha and beta as
<math> <mfenced open='' close='}'> <mtable> <mtr> <mtd> <mi>&alpha;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>AB</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>AP</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mi>&beta;</mi> <mo>=</mo> <msub> <mi>&gamma;</mi> <mi>BP</mi> </msub> <mo>-</mo> <msub> <mi>&gamma;</mi> <mi>BA</mi> </msub> </mtd> </mtr> </mtable> </mfenced> </math>
The three-dimensional coordinates of the target point P are
<math> <mrow> <mi>x</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cos</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>y</mi> <mo>=</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>sin</mi> <mi>&alpha;</mi> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> </mrow> </math>
<math> <mrow> <mi>z</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>[</mo> <mfrac> <mrow> <mi>sin</mi> <mi></mi> <mi>&beta;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>AP</mi> </msub> <mo>+</mo> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cot</mi> <msub> <mi>&alpha;</mi> <mi>BP</mi> </msub> </mrow> <mrow> <mi>sin</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>+</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>b</mi> <mo>+</mo> <mi>h</mi> <mo>]</mo> </mrow> </math>
Wherein B is the base length, i.e., the horizontal separation distance between theodolite A and theodolite B, and h is the height difference between theodolite A and theodolite B.
6. The system for transformation and unification of a composite precision measurement coordinate system according to claim 5, wherein said coordinate calculation means comprises the following modules:
the longitude and latitude coordinate calculation module is used for calculating longitude and latitude coordinates of the common datum point in a theodolite measurement coordinate system;
and the machine tool coordinate calculation module is used for calculating the machine tool coordinates of the common datum points in the machine tool measurement coordinate system.
7. A combined measurement and co-ordination system as claimed in claim 5, wherein the coordinate system transformation means comprises the following modules:
a coordinate conversion module for converting the theodolite measurement coordinate into the machine tool measurement coordinate, specifically, setting O-XYZ translation (X) of the theodolite measurement coordinate system0,Y0,Z0) Then rotate (epsilon)x,εy,εz) After the scaling is carried out by k times, the coordinate system is converted into a machine tool measurement coordinate system O ' -X ' Y ' Z ', and then the coordinate of the common reference point in O-XYZ is (X, Y, Z) and the coordinate in O ' -X ' Y ' Z ' is (X ', Y ', Z ');
a matrix equation calculating module for calculating the matrix equation after the coordinate conversion,
<math> <mrow> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msup> <mi>X</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Y</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mi>Z</mi> <mo>&prime;</mo> </msup> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mi>k</mi> <msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mn>3</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>c</mi> <mn>1</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>2</mn> </msub> </mtd> <mtd> <msub> <mi>c</mi> <mn>3</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mfenced open='(' close=')'> <mtable> <mtr> <mtd> <mi>X</mi> <mo>-</mo> <msub> <mi>X</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Y</mi> <mo>-</mo> <msub> <mi>Y</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mi>Z</mi> <mo>-</mo> <msub> <mi>Z</mi> <mn>0</mn> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow> </math>
wherein, a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 converting the matrix parameters;
and the parameter relation calculation module is used for substituting the coordinates of the three common reference points into the matrix equation to calculate and obtain the parameter relation between the theodolite measurement coordinate system and the machine tool measurement coordinate system.
8. A combined precision measurement coordinate system transformation and unification system according to claim 5, wherein the coordinates of the common reference points are calculated in a coordinate calculation device using target balls as reference.
CN201310643714.XA 2013-12-03 2013-12-03 Method and system for converting and unifying composite type precision measuring coordinate system Pending CN103673976A (en)

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CN111189391A (en) * 2020-01-10 2020-05-22 天津大学 Coordinate unification method based on measurement of central point of axis of carbon fiber
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