CN101907455A - Three-coordinate measuring method for positioning pin not vertical to reference surface - Google Patents

Three-coordinate measuring method for positioning pin not vertical to reference surface Download PDF

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Publication number
CN101907455A
CN101907455A CN 201010046565 CN201010046565A CN101907455A CN 101907455 A CN101907455 A CN 101907455A CN 201010046565 CN201010046565 CN 201010046565 CN 201010046565 A CN201010046565 A CN 201010046565A CN 101907455 A CN101907455 A CN 101907455A
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analogue
cylinder
digital
plane
point
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CN101907455B (en
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张无忧
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Chery Automobile Co Ltd
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SAIC Chery Automobile Co Ltd
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Priority to PCT/CN2010/080495 priority patent/WO2011088729A1/en
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01BMEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B21/00Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant
    • G01B21/02Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness
    • G01B21/04Measuring arrangements or details thereof, where the measuring technique is not covered by the other groups of this subclass, unspecified or not relevant for measuring length, width, or thickness by measuring coordinates of points

Abstract

The invention aims to provide a three-coordinate measuring method for a positioning pin not vertical to a reference surface. The method has the advantages of simpleness, practicality, convenience and rapidness, and comprises the following steps that: measuring software is provided and a corresponding digital model is imported into the measuring software, wherein the measuring software is used for comparing the measured data and theoretical data in real time so as to obtain an offset value of the measured object; during measurement, a plane is pierced by a cylinder, because the cylinder belongs to a linear element, the software defaults that the plane is pierced by the central axis of the cylinder, regardless of the obtained circle or ellipse, a center coordinate value of the circle or ellipse is obtained finally and is consistent with the directly obtained point coordinate, the spacial coordinate position of the point is evaluated, and the angle between the cylinder and the plane is evaluated so as to determine whether the angle is in an allowed tolerance range. The measuring method by constructing the point has the advantages of simpleness, practicality, convenience and rapidness.

Description

Three-coordinate measuring method with the reference field positioning pin not vertical
Technical field
The invention belongs to the technical field of three-dimensional coordinates measurement in the metrology, be specifically related to a kind of manual three-coordinate measuring method, equally also can use for reference use when the using method when promptly the joint arm measuring machine is measured and the three coordinate measuring engine measurement of other type.
Background technology
At present in the measurement of each positioning object of Cab Welding Jig, the wherein measurement of register pin, no matter it is vertical with reference field, still with the reference field off plumb, the element of its measurement all is a two-dimentional element---circle, this is the work characteristics according to this area, and technician or related personnel are simple in order to increase work efficiency, and have become those skilled in the art's custom now.There is not any problem in this kind measuring method at register pin vertical with reference field of measurement, because the register pin vertical with reference field, on the length direction of pin, its locus is not influence the sheet metal component assembling, so three directions in its space are as long as consider that two positions are just passable.But, measuring one and reference field off plumb register pin, many defectives that its measuring method obviously exists inconvenience that testee is adjusted, but also be subjected to providing the restriction of object being measured digital-to-analogue, accurately whether the result of its measurement is difficult to be verified, because when measuring with reference field off plumb register pin, the position of actual measurement and theoretical position be probably just in same position, corresponding one by one comparison that the data that cause measurement and theoretical data can't be correct.In addition, if the product digital-to-analogue of vehicle body is the sheet metal component digital-to-analogue, in fact this be exactly by the gross data than object, above-mentioned measuring method is clearly just inapplicable, the data that measured data need artificial and digital-to-analogue to carry out complexity are relatively calculated, just can obtain the deviate of tested element, be subjected to the influence of extraneous factor, the result who relatively comes out is uncertain accurately.And the time of result who measures and the comparison of theoretical numerical value is long, and efficient is very low, the needs of adjusting after the measurement of the suitable on-the-spot anchor clamps of its method.From the anchor clamps operating position at scene, very pessimistic with the actual operating position of fixture datum positioning pin not vertical, its reason is exactly the bigger deviation of locus existence of register pin, is difficult to realize the intact assembling of vehicle body sheet metal component and register pin.There is bigger deviation in the locus of register pin, what refer to is exactly the volume coordinate of register pin, with respect to other register pins vertical with reference field, and the deviation that the most basic still measuring method causes, machining deviation also exists, but finally still will determine by three-dimensional coordinates measurement.
In addition, the function of utilizing " only dot pattern " and " searching theoretical value automatically " in the Survey Software as shown in Figure 2, also can realize measurement with the reference field positioning pin not vertical, promptly on the outside surface of register pin is the outside surface of cylinder, measure the single-point of some, realize point and the real-time deviate of putting that more also can obtain object being measured.This method just adopts the joint arm measuring machine that measurand is carried out the real data that obtains its position of measuring in kind earlier, Survey Software goes to search the theoretical value of this testee according to the measurement point of reality then, in fact these two processes are carried out simultaneously, the data of measuring have been come out, and itself and the theoretical value deviation after has relatively also just been come out.
Analyze for the shortcoming that three-coordinate measuring method traditional and the reference field positioning pin not vertical exists: through investigating the automobile body welding anchor clamps manufacturing plant of domestic several families, measurement for each setting element of weld jig, what anchor clamps manufacturing firm provided all is the anchor clamps digital-to-analogue that self designs, these anchor clamps digital-to-analogues are exactly that anchor clamps manufacturing firm designs according to the gross data that the vehicle body sheet metal component designs, has relation one to one with material object, measurement is exactly on the length direction of register pin with the method for fixture datum positioning pin not vertical, it on the plane vertical the position of key seat with register pin, point 1 among Fig. 1,2, three points of 3 position measurements, these 3 material object is measured, in Survey Software, construct a plane then, and as the projecting plane of measured circle, the peak of the face of cylinder material object on register pin and measure cross section circle respectively again near the position of key seat, shown in point among Fig. 14 and point 5 positions, in Survey Software, two cross sections circle projected on the same plane i.e. figure mid point 1 then respectively, 2, a plane of 3 structures, revalue the locus of justifying after its projection, can draw the deviate of the object of surveying, we are referred to as the cross section circule method this method.Mark 4,5 is cross section circles of two measurements among Fig. 1, and mark 6 is the reference fields on the anchor clamps.As if this kind method is at first sight quite reasonable, is that each measurement result is not unique but there is randomness in this method, result's repeatability was relatively poor when the repdocutbility of measurement result was promptly measured once more, and clearly there is very big objection in the result who measures.Otherwise, import again after measured result will being derived in the Survey Software in other the three-dimensional software with the product digital-to-analogue that is positioned carry out loaded down with trivial details data relatively after, could really find out the deviate of register pin, it is very low clearly to do efficient like this, is not suitable for very much the need of work of adjusting again after the measurement of on-the-spot automobile body welding anchor clamps setting element.
Two kinds of above-mentioned three-coordinate measuring methods all are to provide the design of Clamping Apparatus digital-to-analogue just can realize measuring the comparison of back data in Survey Software, if providing is the product digital-to-analogue of vehicle body, said method is also just powerless, only way be exactly must the data importing of measuring is other three-dimensional software in, carry out after loaded down with trivial details data relatively calculate with the product digital-to-analogue, just can obtain the deviate of testee.
Summary of the invention
The object of the present invention is to provide a kind of and three-coordinate measuring method reference field off plumb register pin, this method is simple and practical, convenient and swift.
For achieving the above object, provided by the invention and three-coordinate measuring method reference field off plumb register pin comprises following content:
A, provide Survey Software, will need the product digital-to-analogue of Measuring Object or design of Clamping Apparatus digital-to-analogue to import in the Survey Software, this Survey Software obtains the deviate of object being measured with the real-time comparison of measurement data and gross data;
B, set up workpiece coordinate system, an assigned work plane or current working face working face being set to give tacit consent to then, in Survey Software, it is cylinder that element is measured in order, is cylinder with joint arm measuring machine measurement practical position pin then;
C, measure at needs to appoint near the digital-to-analogue of cylinder position and get plane of 3 structures, this plane structure on the key seat of register pin or near sheet metal component digital-to-analogue hole that register pin is located structure;
D, in the digital-to-analogue of Survey Software, find out the register pin on the corresponding anchor clamps or the theoretical coordinate position in the hole that is positioned on the sheet metal component again, with its theoretical coordinate position as institute's survey register pin;
E, the plane of cylinder and structure is pierced through, construct a point, this point that pierces through has direction vector, and estimates the locus coordinate figure of this point, the real work position that this point is exactly a register pin;
Data are carried out relatively in the register pin on F, the point that will construct and the anchor clamps or the theoretical coordinate position in the hole that is positioned on the sheet metal component, just can draw actual deviate; Estimate the angle on this cylinder and plane then, see whether its angle satisfies the tolerance of design.
Because the error after the anchor clamps manufacturing is will weigh judgement by measuring certainly, next will manage to eliminate, surveying instrument displacement can occur after using a period of time, so three coordinate measuring machine must periodic calibration.Therefore, the measuring method of seeking a kind of automobile body welding anchor clamps register pin that is fit to be welded seems very necessary, technical scheme disclosed by the invention is exactly a kind of measuring method of solution and reference field off plumb register pin, Survey Software at first is provided, and with in the corresponding digital-to-analogue importing Survey Software, this Survey Software is used for the real-time comparison of measurement data and gross data, obtains the deviate of object being measured; During measurement, pierce through a plane with cylinder, because cylinder is to belong to linear element, the central axis of giving tacit consent in software with cylinder pierces a plane, what be not in control is a circle or an ellipse, still circle or the oval centre coordinate value that finally obtain, this is consistent with the coordinate figure that directly obtains a little, estimate the volume coordinate position of its point, and the angle on evaluation cylinder and plane, see it whether in the margin tolerance that allows, that the measuring method of this structure point method has is simple and practical, conveniently significantly have a few; Especially to the anchor clamps user, often do not have the design of Clamping Apparatus digital-to-analogue, the product design digital-to-analogue of oneself then is indispensable, and this implements to measure to actual practical anchor clamps and compares with the product design digital-to-analogue of oneself, and it is very convenient to operate.
This method need not manually to carry out the work relatively of loaded down with trivial details data again with importing other three-dimensional software after the measurement data derivation again.Measurement data refers to is exactly with measuring equipment testee to be measured the shown numerical value that comes out, can be understood as at this is exactly the data that the joint arm measuring machine is measured the actual measurement acquisition of testee, these data have only reflected the virtual condition of object, what differ with theoretical key element, whether qualified judge, still wants the support of Survey Software just can or to need the support of other three-dimensional software." other three-dimensional software " is meant the graphic operation software with data-handling capacity, as the PR0/E that uses in commonly used CATIA, the UG of automobile industry and Machine Design industry etc., personnel's participation beyond need not to measure, can directly calculate the deviate of testee by Survey Software, the efficient height, convenient and swift, alleviated the difficulty of labour intensity and operation greatly.
Description of drawings
Fig. 1 is a synoptic diagram of measuring two cross section circles in the prior art;
Measurement point and some situation synoptic diagram relatively in Fig. 2 prior art;
Fig. 3 is the measuring method synoptic diagram of the digital-to-analogue when utilizing jig Design;
Measuring method synoptic diagram when Fig. 4 provides vehicle body sheet metal component digital-to-analogue.
Mark the 1,2, the 3rd among Fig. 1, the point of selecting, the 4, the 5th, measures first and second cross section and justify, 6 is 6 to be the reference fields on the anchor clamps; Mark 1 among Fig. 2 is a key seat, the 2,3,4, the 5th, and the point of selecting, the 6th, the reference field on the anchor clamps;
Description of symbols among Fig. 3,4: the 1, the 2, the 3rd, the point of selecting, the 4th, the register pin that need measure, the 5th, by the positions, plane of point 1,2,3 structures, the 6th, the reference field on the anchor clamps, the 7th, vehicle body sheet metal component, 7a are the pilot holes on the vehicle body sheet metal component.
Embodiment
The three-coordinate measuring method of disclosed by the invention and reference field positioning pin not vertical comprises following content:
A, provide Survey Software, will need the product digital-to-analogue of Measuring Object or design of Clamping Apparatus digital-to-analogue to import in the Survey Software, this Survey Software obtains the deviate of object being measured with the real-time comparison of measurement data and gross data;
B, set up workpiece coordinate system, an assigned work plane or current working face working face being set to give tacit consent to then, in Survey Software, it is cylinder that element is measured in order, is cylinder with joint arm measuring machine measurement practical position pin then;
C, measure at needs to appoint near the digital-to-analogue of cylinder position and get plane of 3 structures, this plane structure on the key seat of register pin or near sheet metal component digital-to-analogue hole that register pin is located structure;
D, in the digital-to-analogue of Survey Software, find out the register pin on the corresponding anchor clamps or the theoretical coordinate position in the hole that is positioned on the sheet metal component again, with its theoretical coordinate position as institute's survey register pin;
E, the plane of cylinder and structure is pierced through, construct a point, this point that pierces through has direction vector, and estimates the locus coordinate figure of this point, the real work position that this point is exactly a register pin;
Data are carried out relatively in the register pin on F, the point that will construct and the anchor clamps or the theoretical coordinate position in the hole that is positioned on the sheet metal component, just can draw actual deviate; Estimate the angle on this cylinder and plane then, see whether its angle satisfies the tolerance of design.
Preferred scheme is: in steps A, importing Survey Software is the product digital-to-analogue of Measuring Object.In the B step, in Survey Software, if working face does not have appointed words, the plane that then is defaulted as Z positive dirction place is a working face, adopts space element of joint arm measuring machine manual measurement---cylinder.
Specifically describe in detail below in conjunction with Fig. 3,4.
Consider that all tested elements all are the elements in space, just sometimes, some testee only need be seen two coordinate figures in its space, measure a two-dimentional element so just without any problem, but importantly, one and reference field off plumb register pin, three coordinate positions in space need all to consider that it is just very unreasonable certainly to measure a two-dimentional element.So, for reference field off plumb register pin, measure a space element---cylinder.Circle belongs to two-dimentional element, not that the present invention discusses, and cylinder belongs to three-dimensional element, in Survey Software, before the measurement, be cylinder as long as element is measured in order, measure just passable then, then on a plane of placement configurations at cylinder place, if the anchor clamps digital-to-analogue, in Survey Software, key seat position near cylindrical base, appoint and get three points, point 1,2 as shown in Figure 3,3 positions, in Survey Software, construct a plane then, utilize cylinder to pierce through the plane again, construct a point with these three points.Piercing through is a kind of method of structure point in the Survey Software, its feature 1 must be a linear element, feature 2 is elements of curved surface class, must be that feature 1 pierces feature 2, obtaining a point is the point of first on the direction vector, if feature 2 is planes, still pierce through with intersecting, be a habit problem.Cylinder pierces through a plane, because cylinder is to belong to linear element, the central axis of giving tacit consent in software with cylinder pierces a plane, software has just been omitted middle process, what be not in control is a circle or an ellipse, still circle or the oval centre coordinate value that finally obtain, this is consistent with the coordinate figure that directly obtains a little, estimate the volume coordinate position of its point, and the angle on evaluation cylinder and plane, see it whether in the margin tolerance that allows, we just are referred to as a structure point method this method.
A, this kind method only need the support of Survey Software.The function of Survey Software of today from strength to strength, can realize the shape of object and evaluation and the online programming and the copying of position dimension, so the project that software is supported is also a lot, do not enumerate one by one at this, but, basic functions as Survey Software is exactly to realize the real-time comparison of measurement data and gross data, obtains the deviate of object being measured, and Here it is, and we need pay close attention to.Method provided by the invention does not need to increase any facility.At first only needing in Survey Software, is that the product digital-to-analogue imports in the Survey Software with the digital-to-analogue that needs Measuring Object, is providing under the design of Clamping Apparatus digital-to-analogue situation, and this measuring method equally also can be used.Software imports digital-to-analogue and just has only two kinds of situations; if import product digital-to-analogue and design of Clamping Apparatus digital-to-analogue simultaneously; there is not that necessity yet; when measuring; if guarantee that the digital-to-analogue of jig Design is correct; importing the anchor clamps digital-to-analogue also is fine; but; the design of all parts all designs according to the product digital-to-analogue; continue again for fear of mistake, detect, if the anchor clamps digital-to-analogue of design and product digital-to-analogue are issued to zero defect in theoretical situation assembling so preferred scheme imports the product digital-to-analogue with jig Design; with the product digital-to-analogue still is the anchor clamps digital-to-analogues, uses the inventive method measurement without any difference.
B, set up (its method of building coordinate system does not elaborate at this) behind the workpiece coordinate system, the working face that current then working face is set to give tacit consent to.In Survey Software, if working face does not have appointed words, be working face with regard to the plane that is defaulted as Z positive dirction place so, the direction vector of its working face decision Measuring Object, concrete condition is with reference to the setting of each Survey Software.Adopt the manual joint arm measuring machine of joint arm measuring machine to measure a space element---cylinder, as shown in Figure 3, Figure 4, other measuring machines equally also can be used for reference use.Be exactly in Survey Software, it is cylinder that element is measured in order, and measuring the practical position pin with the joint arm measuring machine then is cylinder.
C, near the digital-to-analogue of the cylinder position that needs are measured, appoint and get 3 points, as Fig. 3, point 1 shown in Figure 4,2, plane of 3 structures, if the words of anchor clamps digital-to-analogue, this point is just at the great circle place of key seat and the regional location between the right cylinder, if product digital-to-analogue, exactly near being positioned the peripheral region in hole, but it is not too far away, had better not surpass the distance of surveying bulb diameter, general 6mm gets final product, and this plane sees that it provides the jig Design digital-to-analogue still is the product digital-to-analogue, if the digital-to-analogue of jig Design, this plane can be constructed on the key seat of register pin, point 5 positions as shown in Figure 3; If the product digital-to-analogue of vehicle body is the sheet metal component digital-to-analogue of vehicle body, this plane just can be near sheet metal component digital-to-analogue hole that register pin is located structure, 8 positions as shown in Figure 4, there is note 8 position below figure, the 8 just effects of a mark, without any meaning, this plane must be into 90 ° angle with the axis of cylinder, as shown in Figure 3, Figure 4.Register pin is into 90 ° angle with the pilot hole of sheet metal component certainly under the situation of theory assembling.
D, finding out the be positioned theoretical coordinate position in hole of register pin again in the digital-to-analogue of Survey Software on sheet metal component, is the theoretical coordinate position of cylinder as institute's survey register pin with it.
E, utilize in the software function of structure point, the plane of cylinder and structure is pierced through, construct a point, its point that pierces through has direction vector, and estimate the locus coordinate figure of this point, the real work position that this point is exactly a register pin, the physical location when promptly register pin and sheet metal component assemble fully.
Data are carried out relatively in F, the point and the theoretical coordinate position in the hole that is positioned that will construct, and just can draw actual deviate.Estimate the angle on this cylinder and plane then, see whether its angle satisfies the tolerance of design.Actual request for utilization according to anchor clamps, this angle tolerance can be set to ± and 5 °, this step is very easy to accomplish in Survey Software, as softwares such as PC-DMIS, CAM2-Measure, PowerInspect, Metrology, as long as have the real-time comparing function of the most basic measurement data and gross data, obtain the Survey Software of object being measured deviate, the inventive method can be used.
In sum, this kind measuring method and cross section of the prior art circule method and only the dot pattern method have following difference: first, after deriving, the data that need not to measure import other three-dimensional softwares again, and then measurement data and gross data carried out loaded down with trivial details relatively calculating, just can obtain the hard work of the deviate of testee.Can obtain position and angular deviation value in real time, in time realize adjustment the automobile body welding anchor clamps.The second, except the three-dimensional coordinates measurement personnel, need not more personnel's participation.The 3rd, from the digital-to-analogue measurement data to the end of initial importing, all data all are simply to handle in Survey Software, are very easy to obtain the deviate of testee.The 4th, accurately under the situation, the digital-to-analogue that provides jig Design still is the product digital-to-analogue, also without any limitation in the digital-to-analogue that guarantees jig Design.The 4th, this method is easy to learn, understands easily, and is convenient and swift.
Facts have proved through actual measurement, the inventive method is promptly constructed a method and is had following advantage: first, under the situation that is not subjected to any condition restriction, can realize three-dimensional coordinates measurement with the reference field positioning pin not vertical, according to the relevant knowledge of cartesian geometry as can be known, the right cylinder that this kind method only need at first be measured in Survey Software, again provide the hole that is positioned on the product digital-to-analogue near plane of structure, the plane that pierces that structure with cylinder obtains a point then, taking out the theoretical coordinate value again on the hole that is positioned is the coordinate figure in the center of circle, the coordinate figure of structure point and the theoretical coordinate value in hole relatively must deviate, and estimate the angle of measured cylinder and institute's formation level and then.The application of this kind method just can very easily realize the measured value of actual testee and the comparison of theoretical value in Survey Software, obtain the position and the angular deviation value of testee.The second, under the situation of the product digital-to-analogue that object being measured is provided, the mistake that can effectively avoid the automobile body welding anchor clamps to cause when design effectively stops mistake to continue once more.No matter be the design of Clamping Apparatus digital-to-analogue, or the product digital-to-analogue of vehicle body, can realize not having circumscribed measurement data relatively.Can effectively people be freed personnel's participation beyond also need not to measure from the work that loaded down with trivial details uninteresting measurement data is relatively calculated.Can measure in real time and object being measured be adjusted at the scene, workshop, really reach the function of adjusting in real time behind the three-dimensional coordinates measurement.The 3rd, be not subjected to the restriction of Survey Software, the software that possesses fundamental measurement in the market all is suitable for.The 4th, as the main engine plants of automobile making, all be that product digital-to-analogue with vehicle body is a foundation from the design of initial all objects, really accomplish the unification of standard.Therefore, the any testee that utilizes the product digital-to-analogue to detect other is necessary, and so not only can detect the accuracy of jig Design, can also save artificial loaded down with trivial details data and relatively work, thereby alleviated laborer's labour intensity, improved the work efficiency of measuring.The 5th, this kind measuring method has been passed through multiple authentication, can also be applied to similarly testee such as other and reference field off plumb register pin or pilot hole etc., also can be used as such register pin measurement result and whether arbitrates foundation accurately.

Claims (5)

1. three-coordinate measuring method with the reference field positioning pin not vertical comprises following content:
A, provide Survey Software, will need the product digital-to-analogue of Measuring Object or design of Clamping Apparatus digital-to-analogue to import in the Survey Software, this Survey Software obtains the deviate of object being measured with the real-time comparison of measurement data and gross data;
B, set up workpiece coordinate system, an assigned work plane or current working face working face being set to give tacit consent to then, in Survey Software, it is cylinder that element is measured in order, is cylinder with joint arm measuring machine measurement practical position pin then;
C, measure at needs to appoint near the digital-to-analogue of cylinder position and get plane of 3 structures, this plane structure on the key seat of register pin or near sheet metal component digital-to-analogue hole that register pin is located structure;
D, in the digital-to-analogue of Survey Software, find out the register pin on the corresponding anchor clamps or the theoretical coordinate position in the hole that is positioned on the sheet metal component again, with its theoretical coordinate position as institute's survey register pin;
E, the plane of cylinder and structure is pierced through, construct a point, this point that pierces through has direction vector, and estimates the locus coordinate figure of this point, the real work position that this point is exactly a register pin;
Data are carried out relatively in the register pin on F, the point that will construct and the anchor clamps or the theoretical coordinate position in the hole that is positioned on the sheet metal component, just can draw actual deviate; Estimate the angle on this cylinder and plane then, judge whether its angle satisfies the tolerance of design.
2. the three-coordinate measuring method of according to claim 1 and reference field positioning pin not vertical is characterized in that: in steps A, importing Survey Software is the product digital-to-analogue of Measuring Object.
3. the three-coordinate measuring method of according to claim 1 and reference field positioning pin not vertical, it is characterized in that: in the B step, in Survey Software, if working face does not have appointed words, the plane that then is defaulted as Z positive dirction place is a working face, adopts space element of joint arm measuring machine manual measurement---cylinder.
4. the three-coordinate measuring method of according to claim 1 and 2 and reference field positioning pin not vertical, it is characterized in that: in the digital-to-analogue of Survey Software, find out the theoretical coordinate position of the pilot hole that cooperatively interacts on register pin and the sheet metal component again, its theoretical coordinate position as institute's survey register pin.
5. the three-coordinate measuring method of according to claim 1 and reference field positioning pin not vertical is characterized in that: described angle tolerance is set to ± and 5 °.
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