CN105783722B - A kind of range sensor method arrow measuring method based on tetrahedral configuration - Google Patents

A kind of range sensor method arrow measuring method based on tetrahedral configuration Download PDF

Info

Publication number
CN105783722B
CN105783722B CN201610225230.7A CN201610225230A CN105783722B CN 105783722 B CN105783722 B CN 105783722B CN 201610225230 A CN201610225230 A CN 201610225230A CN 105783722 B CN105783722 B CN 105783722B
Authority
CN
China
Prior art keywords
msub
mrow
curved surface
cos
centerdot
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN201610225230.7A
Other languages
Chinese (zh)
Other versions
CN105783722A (en
Inventor
陈文亮
潘国威
齐振超
王珉
丁力平
屈龙强
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Nanjing University of Aeronautics and Astronautics
Original Assignee
Nanjing University of Aeronautics and Astronautics
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Nanjing University of Aeronautics and Astronautics filed Critical Nanjing University of Aeronautics and Astronautics
Priority to CN201610225230.7A priority Critical patent/CN105783722B/en
Publication of CN105783722A publication Critical patent/CN105783722A/en
Application granted granted Critical
Publication of CN105783722B publication Critical patent/CN105783722B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • 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

Abstract

A kind of range sensor method arrow measuring method based on tetrahedral configuration, it is characterized in that：First, three laser range sensors arranged in equilateral triangle are installed on the end effector of lathe or robot, and fix the measurement direction of three laser range sensors so that its laser beam converges at same point, and a space tetrahedron is formed with three laser range sensors；Secondly, three kinds of position relationships of utilization space tetrahedron top and curved surface to be measured：Summit is in curved surface, summit on curved surface, summit outside curved surface, with reference to laser range sensor measure numerical value, can in the hope of drilling curved surface to be measured method swear n；Finally, treat that drilling method swears information according to obtained by above-mentioned survey calculation, by anti-resolving Algorithm, try to achieve the drive volume of each axle of lathe or robot, posture adjustment campaign is realized for control system.Invention has that solving precision is high, can efficiently and rapidly response control system demand.

Description

A kind of range sensor method arrow measuring method based on tetrahedral configuration
Technical field
The present invention relates to a kind of method to swear e measurement technology, and especially a kind of method for aircraft skin drilling swears measuring method, Specifically a kind of range sensor method arrow measuring method based on tetrahedral configuration.
Background technology
About 150~2,000,000 connecting holes, aircaft configuration mainly pass through the riveting at this some holes on one frame large aircraft Connect and be spirally connected and mechanically connected to realize.According to statistics, the 70% of airframe fatigue failure accident is derived from structural connection position, its In 80% fatigue crack result from connection hole.Boeing is connected to fastener using analysis shows are carried out, and works as fastener When being tilted more than 2 ° along external load function direction, fatigue life reduces about 47%；When being tilted more than 5 °, fatigue life reduces 95%, it will thus be seen that connecting hole quality strong influence the life-span of aircraft.Therefore, to ensure that aircraft assembles quality, carry The fatigue life of high body, increasing automation equipment are used in the assembling process of large aircraft, as automatic drill riveter, Flexible rail drilling mechanism, climbing robot drilling mechanism and mechanical arm drilling mechanism etc..
During automation equipment drilling, the perpendicularity in hole depend on drill axis whether the normal weight with drilling point Close.At present, equipment is difficult the direction of normal drilling for making drill bit along boring point by itself control, it is necessary to the measurement of utilization method arrow and end Posture adjusting device adjusts the posture of drill bit.Measurement is sweared for the method for curved surface, common are vector cross product method, Quadratic Surface Fitting Method, nurbs curve method and Triangular meshes method etc..Above method in engineer applied, it is necessary to measure substantial amounts of point can be only achieved compared with High precision, be not suitable for accurate measurement in real time.
The present invention proposes a kind of three laser range sensors based on tetrahedral configuration for the problem of appearing above Eyes with non-contact method arrow measuring method, the method measurement accuracy is high, speed is fast, and will not damage testee surface.
The content of the invention
The purpose of the present invention is not high for precision present in existing method arrow measuring method, the problem of poor real, hair A kind of bright range sensor method arrow measuring method based on tetrahedral configuration, it is realized pair by three laser range sensors The quick realization measurement of the hole method arrow of aircraft skin drilling.
The technical scheme is that：
A kind of range sensor method arrow measuring method based on tetrahedral configuration, it is characterized in that it comprises the following steps：
First, installation passes in three laser rangings of equilateral triangle arrangement on the end effector of lathe or robot Sensor, and fix the measurement direction of three laser range sensors so that its laser beam converges at same point, with three laser Distance measuring sensor forms a space tetrahedron；
Secondly, three kinds of position relationships of utilization space tetrahedron top and curved surface to be measured：Summit is in curved surface, summit is in song On face, summit outside curved surface, with reference to laser range sensor measure numerical value, can in the hope of drilling curved surface to be measured method swear n；
Finally, treat that drilling method swears information according to obtained by above-mentioned survey calculation, by anti-resolving Algorithm, try to achieve lathe or machine The drive volume of each axle of device people, posture adjustment campaign is realized for control system.
In order that the measurement result for obtaining drilling surface normal vector n to be measured is more accurate, make following constraint：lmin≤li≤ lmax
(i=1,2,3)
L in formulaiDistance for three laser range sensor laser emission points to drilling curved surface to be measured, lminAnd lmaxRespectively L during to meet that drilling method swears required precisioniMinimum range and ultimate range, its concrete numerical value can swash by laser range sensor The distance of light launch point to laser beam convergent point is obtained with the accuracy class for treating drilling method arrow.Work as liAfter meeting above-mentioned constraint, treat Surveying the method arrow n of drilling curved surface can specifically solve according to following three kinds of situations.
Situation one：Tetrahedron top is in curved surface to be measured
When surface intersection where space tetrahedron and position to be detected, coordinate system as shown in Figure 2 is established, coordinate is former Point is established in cutter end points, and described 3 laser range sensors A, B, C are distributed in cutter surrounding in equilateral triangle, setting xtDirection was OtPoint points to B directions, y parallel to AB and by AtDirection is OtC directions, ztObtained according to right hand theorem in direction .First, according to design and installation, the installation site of 3 laser range sensors is determined, and 3 laser rangings are passed 3 laser of sensor converge at a point D, i.e., before laser range sensor measures to surface normal vector, are tied by machinery Structure and assembling ensure known to tetrahedron D-ABC configurations.Then A, B, C are in OtxtytztCoordinate under coordinate system is respectivelyC(0,CD·cos∠DCOt, 0),
The curved surface where the position to be detected intersects with tetrahedron, can be in the hope of according to geometrical relationship
A1(-A1D·cos∠DAOt·cos∠OtAB,-A1D·cos∠DAOt·sin∠OtAB,AA1·sin∠DAOt)
B1(B1D·cos∠DBOt·cos∠OtBA,1B1D·cos∠DBOt·sin∠OtBA,BB1·sin∠DBOt)
C1(0,DC1·cos∠DCOt,CC1·sinDCOt)
Make A1(xa1,ya1,za1), B1(xb1,yb1,zb1), C1(xc1,yc1,zc1), then A1B1(xb1-xa1,yb1-ya1,zb1- za1), A1C1(xc1-xa1,yc1-ya1,zc1-za1), B1C1(xb1-xc1,yb1-yc1,zb1-zc1), if plane A1B1C1Normal direction coordinate For (l1,m1,n1), then, according to the definition of normal vector
By above formula, (l can be solved1,m1,n1), wherein n1As unprocessed hole location law vector.
Situation two：Summit is on curved surface
When tetrahedron top overlaps with curved surface where position to be detected, as shown in the figure.It is considered that A1, B1, C13 points with D points overlap, i.e.,
By the Chinese style of situation one (1), (l solved1,m1,n1) there are an infinite multiple combinations, therefore hole to be processed in situation two Position law vector unsolvable.
Situation three：Summit is outside curved surface
Surface intersection is when on the extended line of space tetrahedron top where position to be detected, as illustrated, according to several What relation can be in the hope of
A2(DA2·cos∠DAOt·cos∠OtAB,DA2·cos∠DAOt·sin∠OtAB,AA2·sin∠DAOt)
B2(-DB2·cos∠DBOt·cos∠OtBA,DB2·cos∠DBOt·sin∠OtBA,BB2·sin∠DBOt)
C2(0,-DC2·cos∠DCOt,CC2·sinDCOt)
Make A2(xa2,ya2,za2), B2(xb2,yb2,zb2)C2(xc2,yc2,zc2), then A2B2(xb2-xa2,yb2-ya2,zb2-za2), A2C2(xc2-xa2,yc2-ya2,zc2-za2), B2C2(xb2-xc2,yb2-yc2,zb2-zc2), if plane A2B2C2Normal direction coordinate be (l2, m2,n2), then, according to the definition of normal vector
By above formula (3), (l can be solved2,m2,n2), wherein n2As unprocessed hole location law vector.
The beneficial effects of the invention are as follows：
The inventive method is simple, passes through the geometrical relationship and laser ranging sensing based on tetrahedral configuration arranged in advance The data that device measures can be achieved to treat the method arrow measurement in processing hole.Again by anti-resolving Algorithm, can very easily realize to machine Bed or robot realize the drive volume of each axle of drilling processing, and posture adjustment campaign is realized for control system.Therefore, the present invention has Solving precision is high, can efficiently and rapidly response control system demand.
Brief description of the drawings
Fig. 1 is the method arrow measurement procedure of the present invention.
Fig. 2 is that method arrow of the tetrahedron top of the present invention in curved surface to be measured solves schematic diagram.
Fig. 3 is that method arrow of the tetrahedron top of the present invention on curved surface solves schematic diagram.
Fig. 4 is that method arrow of the tetrahedron top of the present invention outside curved surface to be measured solves schematic diagram.
Embodiment
The present invention is further illustrated with reference to the accompanying drawings and examples.
Referring to the accompanying drawing for showing the embodiment of the present invention, the present invention is described in more detail.However, the present invention can be with Many multi-forms are realized, and should not be construed as being limited by the embodiment herein proposed.On the contrary, these embodiments proposed It is for abundant and complete disclosure, and those skilled in the art is understood the scope of the present invention completely.
As Figure 1-4, a kind of range sensor method arrow measuring method based on tetrahedral configuration, it includes following step Suddenly：
First, before the arrow measurement of parts to be processed method is carried out, essence is carried out to mounted three laser range sensors Scale is determined, and adjusts the assembly precision of laser range sensor, three laser range sensors is converged at same point, that is, forms One tetrahedron.
Secondly as the size of the tetrahedron of the three laser range sensors composition pre-set in space is limited, And laser range sensor measurement accuracy and measurement distance are in inverse ratio, therefore, lathe or robot are driven so that laser measurement passes Sensor tentatively realizes that method arrow is aligned with part to be detected, and adjusts to suitable distance, meets distance constraints.
3rd, the value surveyed using three laser range sensors, the selection of method vector calculus method is carried out, if three Laser Measurings The tetrahedron top of formation away from sensor in part surface to be measured, is then finely adjusted to end effector just；If summit exists Below part to be measured, then selection algorithm one realizes the calculating for treating machined surface method arrow；If summit is selected above part to be measured Select algorithm two and realize the calculating for treating machined surface method arrow.
Finally, the face method to be processed being calculated according to above-mentioned measurement swears information, by inverse kinematic algorithm, obtains Lathe or robot reach each axle drive volume of drilling method arrow, and posture adjustment campaign is realized for control system.
Details are as follows：
Coordinate system as depicted is established, the origin of coordinates is established in cutter end points, described 3 laser range sensors A, B, C are distributed in cutter surrounding in equilateral triangle, set xtDirection was OtPoint points to B directions, y parallel to AB and by AtDirection For OtC directions, ztDirection obtains according to right hand theorem.First, according to design and installation, the peace of 3 laser range sensors is determined Holding position, and cause 3 laser range sensors, 3 laser to converge at a point D, i.e., in laser range sensor to Surface Method Before arrow measures, ensured by mechanical structure and assembling known to tetrahedron D-ABC configurations.Then A, B, C are in OtxtytztCoordinate System under coordinate be respectively C(0,CD·cos∠ DCOt, 0),
The curved surface where the position to be detected intersects with tetrahedron, can be in the hope of according to geometrical relationship
A1(-A1D·cos∠DAOt·cos∠OtAB,-A1D·cos∠DAOt·sin∠OtAB,AA1·sin∠DAOt)
B1(B1D·cos∠DBOt·cos∠OtBA,1B1D·cos∠DBOt·sin∠OtBA,BB1·sin∠DBOt)
C1(0,DC1·cos∠DCOt,CC1·sinDCOt)
Make A1(xa1,ya1,za1), B1(xb1,yb1,zb1)C1(xc1,yc1,zc1), then A1B1(xb1-xa1,yb1-ya1,zb1-za1), A1C1(xc1-xa1,yc1-ya1,zc1-za1), B1C1(xb1-xc1,yb1-yc1,zb1-zc1), if plane A1B1C1Normal direction coordinate be (l1, m1,n1), then, according to the definition of normal vector
By above formula (4), (l can be solved1,m1,n1), wherein n1As unprocessed hole location law vector.
Curved surface and tetrahedron are non-intersect where the position to be detected, can be in the hope of according to geometrical relationship
A2(DA2·cos∠DAOt·cos∠OtAB,DA2·cos∠DAOt·sin∠OtAB,AA2·sin∠DAOt)
B2(-DB2·cos∠DBOt·cos∠OtBA,DB2·cos∠DBOt·sin∠OtBA,BB2·sin∠DBOt)
C2(0,-DC2·cos∠DCOt,CC2·sinDCOt)
Make A2(xa2,ya2,za2), B2(xb2,yb2,zb2)C2(xc2,yc2,zc2), then A2B2(xb2-xa2,yb2-ya2,zb2-za2), A2C2(xc2-xa2,yc2-ya2,zc2-za2), B2C2(xb2-xc2,yb2-yc2,zb2-zc2), if plane A2B2C2Normal direction coordinate be (l2, m2,n2), then, according to the definition of normal vector
By above formula (5), (l can be solved2,m2,n2), wherein n2As unprocessed hole location law vector.
Although describing the embodiment of the present invention above, it will be appreciated by those of skill in the art that these It is merely illustrative of, protection scope of the present invention is defined by the appended claims.Those skilled in the art is not carrying on the back On the premise of principle and essence from the present invention, various changes or modifications can be made to these embodiments, but these are changed Protection scope of the present invention is all fallen within modification.

Claims (4)

  1. A kind of 1. range sensor method arrow measuring method based on tetrahedral configuration, it is characterized in that it comprises the following steps：
    First, installation senses in three laser rangings of equilateral triangle arrangement on the end effector of lathe or robot Device, and fix the measurement direction of three laser range sensors so that its laser beam converges at same point, by three Laser Measurings A space tetrahedron is collectively formed away from sensor and described convergent point；The origin of coordinates is established in cutter tips point, three Laser range sensor is distributed in cutter surrounding in equilateral triangle；
    Secondly, three kinds of position relationships of utilization space tetrahedron top and curved surface to be measured：Summit is in curved surface, summit is in curved surface , with reference to the numerical value of laser range sensor measurement, try to achieve outside curved surface and treat drilling central point on drilling curved surface to be measured in upper, summit Method swears n；
    Finally, information is sweared according to the method for treating drilling central point obtained by above-mentioned survey calculation, by anti-resolving Algorithm, tries to achieve lathe Or the drive volume of each axle of robot, posture adjustment campaign is realized for control system, the method arrow for making tool axis and trying to achieve is consistent.
  2. 2. the method according to claim 11, it is characterized in that：In order that obtain drilling surface normal vector n to be measured measurement result more Add accurately, make following constraint：lmin≤li≤lmax(i=1,2,3)
    L in formulaiDistance for three laser range sensor laser emission points to drilling curved surface to be measured, lminAnd lmaxIt is respectively full L during sufficient drilling method arrow required precisioniMinimum range and ultimate range, its concrete numerical value can send out by laser range sensor laser The distance of exit point to laser beam convergent point is obtained with the accuracy class for treating drilling method arrow；Work as liAfter meeting above-mentioned constraint, system to be measured The method arrow n of hole curved surface should according to tetrahedron top in curved surface to be measured, tetrahedron top is outside curved surface to be measured and tetrahedron top Three kinds of situations specifically solve on curved surface to be measured.
  3. 3. according to the method for claim 1, it is characterized in that when tetrahedron top is in curved surface to be measured, set xtDirection was Origin of coordinates OtPoint points to B directions, y parallel to AB and by AtDirection is OtC directions, ztDirection obtains according to right hand theorem；It is first First, according to design and installation, the installation site of three laser range sensors is determined, and causes three laser range sensors three Bar laser converges at a point D, i.e., before laser range sensor measures to surface normal vector, passes through mechanical structure and assembling Ensure known to tetrahedron D-ABC configurations；Then A, B, C are in OtxtytztCoordinate under coordinate system is respectively AC(0,CD·cos∠DCOt, 0),
    The curved surface where the position to be detected intersects with tetrahedron, can be in the hope of according to geometrical relationship：
    A1(-A1D·cos∠DAOt·cos∠OtAB,-A1D·cos∠DAOt·sin∠OtAB,AA1·sin∠DAOt)
    B1(B1D·cos∠DBOt·cos∠OtBA,1B1D·cos∠DBOt·sin∠OtBA,BB1·sin∠DBOt)
    C1(0,DC1·cos∠DCOt,CC1·sinDCOt)
    Make A1(xa1,ya1,za1), B1(xb1,yb1,zb1), C1(xc1,yc1,zc1), then A1B1(xb1-xa1,yb1-ya1,zb1-za1), A1C1 (xc1-xa1,yc1-ya1,zc1-za1), B1C1(xb1-xc1,yb1-yc1,zb1-zc1), if plane A1B1C1Normal direction coordinate be (l1,m1, n1), then, according to the definition of normal vector
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>a</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>b</mi> <mn>1</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    By above formula, (l can be solved1,m1,n1), wherein n1As treat drilling position law vector.
  4. 4. according to the method for claim 1, it is characterized in that tetrahedron top is outside curved surface, curved surface phase where position to be detected , can be in the hope of according to geometrical relationship when meeting on the extended line of space tetrahedron top：
    A2(DA2·cos∠DAOt·cos∠OtAB,DA2·cos∠DAOt·sin∠OtAB,AA2·sin∠DAOt)
    B2(-DB2·cos∠DBOt·cos∠OtBA,DB2·cos∠DBOt·sin∠OtBA,BB2·sin∠DBOt)
    C2(0,-DC2·cos∠DCOt,CC2·sinDCOt)
    Make A2(xa2,ya2,za2), B2(xb2,yb2,zb2)C2(xc2,yc2,zc2), then A2B2(xb2-xa2,yb2-ya2,zb2-za2), A2C2 (xc2-xa2,yc2-ya2,zc2-za2), B2C2(xb2-xc2,yb2-yc2,zb2-zc2), if plane A2B2C2Normal direction coordinate be (l2,m2, n2), then, according to the definition of normal vector
    <mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>a</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>x</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>l</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>y</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>y</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>m</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>(</mo> <msub> <mi>z</mi> <mrow> <mi>b</mi> <mn>2</mn> </mrow> </msub> <mo>-</mo> <msub> <mi>z</mi> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>n</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    By above formula (3), (l can be solved2,m2,n2), wherein n2As treat drilling position law vector.
CN201610225230.7A 2016-04-12 2016-04-12 A kind of range sensor method arrow measuring method based on tetrahedral configuration Expired - Fee Related CN105783722B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201610225230.7A CN105783722B (en) 2016-04-12 2016-04-12 A kind of range sensor method arrow measuring method based on tetrahedral configuration

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201610225230.7A CN105783722B (en) 2016-04-12 2016-04-12 A kind of range sensor method arrow measuring method based on tetrahedral configuration

Publications (2)

Publication Number Publication Date
CN105783722A CN105783722A (en) 2016-07-20
CN105783722B true CN105783722B (en) 2018-04-06

Family

ID=56396313

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201610225230.7A Expired - Fee Related CN105783722B (en) 2016-04-12 2016-04-12 A kind of range sensor method arrow measuring method based on tetrahedral configuration

Country Status (1)

Country Link
CN (1) CN105783722B (en)

Families Citing this family (11)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106553086B (en) * 2016-10-27 2018-06-08 大连理工大学 The complex-curved drilling point law vector measuring method of quick high accuracy
CN107052909A (en) * 2017-05-23 2017-08-18 电子科技大学 A kind of borehole perpendicularity monitoring system
CN107462883A (en) * 2017-08-04 2017-12-12 中车青岛四方机车车辆股份有限公司 Method and laser range finder of the measurement point to any dimension plan range in space
CN110285757B (en) * 2019-07-23 2020-12-22 广州海洋地质调查局 Method and system for measuring distance and size of target object
CN111409023B (en) * 2020-03-17 2021-06-22 天津大学 Three-laser displacement sensor clamp convenient for angle adjustment
CN111623711B (en) * 2020-05-14 2021-06-01 深圳市地质环境研究院有限公司 Landslide area detection method and device
CN111664813B (en) * 2020-05-15 2021-08-03 成都飞机工业（集团）有限责任公司 Free surface arbitrary hole normal vector measuring device and method and compensation method
CN112033307B (en) * 2020-07-15 2021-08-03 成都飞机工业（集团）有限责任公司 Farnet vector measuring device
CN112525131B (en) * 2020-10-23 2021-09-14 清华大学 Method and system for measuring curvature of workpiece by non-contact distance sensor array
CN114111672A (en) * 2021-11-26 2022-03-01 南京航空航天大学 Method for quickly calibrating sensor installation position parameters measured by multiple displacement sensors in normal direction
CN115365545B (en) * 2022-10-24 2023-02-28 山东联投工具股份有限公司 Drilling machine punching device capable of automatically calibrating and positioning

Family Cites Families (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS63169509A (en) * 1987-01-06 1988-07-13 Komatsu Ltd Inclination measuring instrument
JP2787891B2 (en) * 1993-09-08 1998-08-20 三菱電機株式会社 Automatic teaching device for laser robot
CN100418108C (en) * 2006-08-14 2008-09-10 东南大学 Figure reconstruction method in 3D scanning system
CN101957175B (en) * 2010-09-14 2012-03-28 西安交通大学 Three-point micro-plane-based normal detection method
CN102322793B (en) * 2011-05-12 2013-06-05 浙江大学 Real-time radius compensation method and measuring head device applied to portable coordinate measuring machines
CN104625162B (en) * 2015-01-27 2017-01-25 南京航空航天大学 Aligning method and aligning system based on hole drilling normal vector of laser transmitters

Also Published As

Publication number Publication date
CN105783722A (en) 2016-07-20

Similar Documents

Publication Publication Date Title
CN105783722B (en) A kind of range sensor method arrow measuring method based on tetrahedral configuration
CN102284956B (en) Normal centering method of automatic drilling and riveting robot
US10065318B2 (en) Methods and systems of repairing a structure
Tian et al. Auto-normalization algorithm for robotic precision drilling system in aircraft component assembly
US7774083B2 (en) Methods and systems for position sensing
CN102636110B (en) Reference detecting device of automatic drilling and riveting system of airplane components and detecting method thereof
CN104128846B (en) A kind of high-precision cutter bias On-line Measuring Method
CN104816307B (en) The four-point method of the accurate drilling of industrial robot is to leveling method
CN102322857B (en) Position and posture measuring system and method for mechanical equipment
CN100538261C (en) Unknown free curved face self-adapting measuring method and gauge head unit based on the method for exploring the way
CN109163675B (en) Method for detecting angular pendulum shaft position accuracy based on laser tracker
US20200011167A1 (en) Optimal trajectory control for rotary steerable systems
KR20150125553A (en) System and method for positioning an automated assembly tool relative to a structure
CN104625162B (en) Aligning method and aligning system based on hole drilling normal vector of laser transmitters
CN103737433B (en) Large-size components combined type accuracy measurement method
Yu et al. Research on surface normal measurement and adjustment in aircraft assembly
CN104102173A (en) Numerical Controller
CN105345600A (en) Normal measurement and adjustment method for drilling of free-form surface of aviation thin-wall piece
Zhao et al. Kinematic modeling and base frame calibration of a dual-machine-based drilling and riveting system for aircraft panel assembly
CN103900528A (en) Detection method for three-dimensional space section roundness of large component
CN105222711A (en) A kind of gathering pipe field measurement apparatus based on laser ranging technique and measuring method
CN103900510A (en) Detection path modeling method of coordinate measuring machine
CN104764415A (en) Steel bridge structure three-dimensional measurement and detection system and measurement method
EP3045394B1 (en) Method and system for repairing a structure
CN107957234A (en) A kind of method and device for measuring normal vector of arbitrary point of free-form surface

Legal Events

Date Code Title Description
C06 Publication
PB01 Publication
C10 Entry into substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20180406

Termination date: 20190412

CF01 Termination of patent right due to non-payment of annual fee