CN110487217A - A kind of spherical hinge three dimensional angle detection method - Google Patents
A kind of spherical hinge three dimensional angle detection method Download PDFInfo
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- CN110487217A CN110487217A CN201910734999.5A CN201910734999A CN110487217A CN 110487217 A CN110487217 A CN 110487217A CN 201910734999 A CN201910734999 A CN 201910734999A CN 110487217 A CN110487217 A CN 110487217A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
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- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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Abstract
The invention discloses a kind of spherical hinge three dimensional angle detection methods.Currently, optics angle measurement mode is limited.The present invention can calculate the space two-dimensional corner of bulb, i.e. deflection angle and azimuth according to the principle of four-quadrant photo detector and simple triangle relation by one laser emitter of arrangement and several four-quadrant photo detectors.The present invention is of less demanding to the installation site of laser emitter, and implementation is relatively simple, it can be achieved that non-cpntact measurement, obtains higher resolution ratio and measurement accuracy.
Description
Technical field
The invention belongs to field of measuring technique, and in particular to a kind of flexural pivot chain space based on four-quadrant photo detector turn
Angle detection method.
Background technique
Spherical hinge is a kind of Three Degree Of Freedom mechanical joint generallyd use, has compact-sized, movement flexibly and bearing capacity
The advantages that strong, becomes the key member in the mechanical equipments such as parallel institution, industrial robot (mechanical arm) and auto parts and components.Example
Such as, parallel machine is as novel numerical control machining equipment, and wherein each branch passes through hinge and is connected with dynamic and static platform, is
Influence of the quasi-static error of system to machine tool accuracy accounts for about 70%, and spherical hinge error alignment static error has an important influence.
Since the movement of spherical hinge is limited by joint space and the structural rigidity etc. of hinge, caused kinematic error influences the transmission of system
Precision, therefore the detection of flexural pivot space angle of revolution is very necessary to systematic error forecast analysis, feedback and compensation, is conducive to transport
The optimization of dynamic mechanism controls.
Traditional angle measurement usually has mechanical angle measurement, electromagnetic type angle measurement and light based on single dof mobility object
Learn the methods of angle measurement.Wherein, the research of optical measuring technique is comparatively fast developed with application, since angle-measuring method difference causes to examine
Instrument wide variety, such as photoelectric encoder method, Circular gratings method, laser interferance method, loop laser method are surveyed, it is most of applied to small
In the accurate measurement of angle, higher resolution ratio and measurement accuracy can be obtained, however 360 ° of complete cycle angle measurement are also needed
It is suitably modified.For example, Japanese Duomochuan Fine Machinary Co., Ltd shore letter controls the measurement method for proposing sphere absolute angle, wherein
Sphere is by transparent material or is transmissive to be made by the electromagnetism wave material that pattern recognition device identifies, can spray on spherome surface
Painting pattern is QRTwo dimension or one-dimensional bar code, the information such as record position in coding.Pass through setting figure outside sphere
As identification device, sphere angle information is obtained after handling for the pattern detected, however the measurement method is actually being answered
With not yet finding in occasion, actual effect need to be discussed.
Summary of the invention
The purpose of the present invention is in view of the deficiencies of the prior art, propose a kind of spherical hinge based on four-quadrant photo detector
Three dimensional angle detection method realizes spherical hinge deflection angle and azimuthal measurement.
The specific steps of the present invention are as follows:
1) hemispherical shell is fixed on bulb output rod, so that hemispherical shell is concentric with bulb, and hemispherical shell
Body is towards bulb.
2) laser emitter is fixedly installed at ball-and-socket.
3) the n four-quadrant photo detector group arranged along warp direction, four-quadrant are arranged in hemispherical shell Internal Spherical Surface
Photodetector group is made of the N number of four-quadrant photo detector for being uniformly fixed on hemispherical shell Internal Spherical Surface along weft direction；
The four-quadrant photo detector of adjacent four-quadrant photo detector group is aligned one by one along warp direction；Each four-quadrant photodetection
Coincidence side side length in device group along the two neighboring four-quadrant photo detector of same warp alignment is equal；It is right on a warp
The warp direction symmetrical center line of neat all four-quadrant photo detectors is the side of the inscribe regular polygon of the warp；Then
Sequential organization is carried out to the four-quadrant photo detector of arrangement, it is specific as follows: in the minimum four-quadrant photo detector group of latitude
Each four-quadrant photo detector successively serial number from 1 to N, n four-quadrant photo detector group according to latitude from low to high according to
Secondary number, in i-th of four-quadrant photo detector group j-th four in first four-quadrant photo detector group minimum with latitude
Quadrant photodetector is j+ (i-1) N, 1≤j≤N, 2≤i≤n along the four-quadrant photo detector number that warp direction is aligned；
N >=20, n >=8；
4) cartesian coordinate system O-XYZ is established, coordinate origin O is arranged at bulb center, and X-axis and Y-axis constitute flat
Face XY is parallel with plane where weft, and plane where weft is parallel to ball-and-socket bottom surface；Z axis is perpendicular to plane XY.
5) when the point M on bulb output rod central axis goes to point M ', before bulb rotation and azimuth is turned overLaser afterwards
The laser of transmitter transmitting is beaten on two four-quadrant photo detectors, according to four-quadrant photo detector measuring principle, is measured
Imaging facula center of energy P of the laser emitter emergent light on a wherein four-quadrant photo detector1Apart from the four-quadrant
The broadwise of photodetector geometric center biases dx1With through to biasing dy1And laser emitter emergent light is in another four-quadrant
Limit the imaging facula center of energy P on photodetector2Broadwise apart from the four-quadrant photo detector geometric center biases dx2
With through to biasing dy2.The first quartile of four-quadrant photo detector, the second quadrant, third quadrant and fourth quadrant and plane coordinates
Four quadrant division modes in system are consistent, set P1The d in first, fourth quadrantx1It is positive, the d in second, third quadrantx1
It is negative, P1The d in the first, second quadranty1It is positive, the d in third, fourth quadranty1It is negative；Set P2In first, fourth quadrant
When dx2It is positive, the d in second, third quadrantx2It is negative, P2The d in the first, second quadranty2It is positive, in third, fourth quadrant
dy2It is negative.
6) in the same four-quadrant photo detector group each four-quadrant photo detector along broadwise in the positive N being encircled into
The interior angle ω of shape solves as follows:
7) work as P1And P2When two four-quadrant photo detectors at place are in adjacent warp, the azimuth that turns overAccording to
Formula (2) calculates, and works as P1And P2When two four-quadrant photo detectors at place are in non-conterminous warp, the azimuth that turns over
It is calculated according to formula (3)；
In formula (3), m1For P1And P2Four-quadrant between two four-quadrant photo detectors at place along weft direction apart
Limit photodetector number；Set P1The broadwise edge lengths of place four-quadrant photo detector are k, P2Place four-quadrant photoelectricity is visited
Survey broadwise edge lengths v=k ± c of device1× p, P2Place four-quadrant photo detector is located at P1On the four-quadrant photo detector of place
Fang Shi takes positive sign, otherwise takes negative sign, c1The value in 0.02~0.05, the unit of broadwise edge lengths are mm, p P1And P2Place
The number difference of four-quadrant photo detector group；P1Place four-quadrant photo detector is close to P2Place four-quadrant photo detector
Broadwise side be set as E1, P2Place four-quadrant photo detector is close to P1Place four-quadrant photo detector broadwise side is set as E2, then
P1To E1Distance a=0.5k-dx1, P2To E2Distance b=0.5v-dx2。P1With broadwise side E1Intersection point, P1And coordinate system is former
In the triangle of point O composition, the corresponding angle of the side length that length is a isP2With broadwise side E2Intersection point, P2And coordinate system is former
In the triangle of point O composition, the corresponding angle of the side length that length is b is
Regardless of P1And P2Whether two four-quadrant photo detectors at place are in adjacent warp,WithAccording to as follows
Process solves:
Coordinate origin O to P is solved according to formula (4) according to the cosine law1Distance L1, according to the cosine law according to public affairs
Formula (5) solves coordinate origin O to P2Distance L2；Then, it is solved according to sine according to formula (6)According to sine
Theorem is solved according to formula (7)
In formula (4) and (5), r is the inner sphere radius of hemispherical shell.
8) set all four-quadrant photo detectors through being all t to edge lengths, then along adjacent two four of warp direction
The angle of quadrant photodetector is 180 ° of-α, and angle [alpha] is solved according to formula (8):
9) work as P1And P2Two four-quadrant photo detectors at place are in two adjacent four-quadrant photo detector groups
When, the deflection angle θ turned over is calculated according to formula (9), works as P1And P2Two four-quadrant photo detectors at place are non-conterminous two
When in a four-quadrant photo detector group, the deflection angle θ turned over is calculated according to formula (10)；
θ=θ1+θ2 (9)
In formula (10), m2For P1And P2Between two four-quadrant photo detectors at place along warp direction apart four
Quadrant photodetector number, T are the warp direction symmetrical centre for all four-quadrant photo detectors being aligned on a warp
The number of edges of regular polygon, the solution of T are as follows where line:
By
It releases
P1Place four-quadrant photo detector is close to P2Place four-quadrant photo detector through being set as E to side3, P2Place
Four-quadrant photo detector is close to P1Place four-quadrant photo detector is through being set as E to side4, then P1To E3Distance c=0.5t-
dx2, P2To E2Distance d=0.5t-dy2。P1With broadwise side E3Intersection point, P1And in the triangle of coordinate origin O composition,
The corresponding angle of the side length that length is c is θ1；P2With broadwise side E4Intersection point, P2And in the triangle of coordinate origin O composition,
The corresponding angle of the side length that length is d is θ2。
Regardless of P1And P2Two four-quadrant photo detectors at place in two adjacent four-quadrant photo detector groups,
θ1And θ2Solve as follows:
Coordinate origin O to P is solved according to formula (11) according to the cosine law1Distance L3, according to the cosine law according to public affairs
Formula (12) solves coordinate origin O to P2Distance L4；Then, θ is solved according to formula (13) according to sine1, according to sine
Theorem solves θ according to formula (14)2。
Further, the four-quadrant photo detector size of the same four-quadrant photo detector group is identical.
Further, four-quadrant photo detector spacing adjacent in the same four-quadrant photo detector group is less than
0.05mm。
Further, four-quadrant photo detector group is not covered with entire hemispherical shell Internal Spherical Surface.
The invention has the advantages that:
1, the present invention is visited by one laser emitter of arrangement and several four-quadrant photo detectors according to four-quadrant photoelectricity
The principle and simple triangle relation for surveying device, can calculate the space two-dimensional corner of bulb, i.e. deflection angle and azimuth, and
And it is of less demanding to the installation site of laser emitter, implementation is relatively simple.
2, the achievable non-cpntact measurement of the present invention, obtains higher resolution ratio and measurement accuracy.
3, cost is relatively low by the present invention, and not high to equipment requirement, practicability is big.
Detailed description of the invention
Fig. 1 is the assembling schematic diagram of hemispherical shell in the present invention, laser emitter, bulb, bulb output rod and ball-and-socket；
Fig. 2 is four-quadrant photo detector arrangement schematic diagram in hemispherical shell body of the invention；
Fig. 3 be measure-ball of the present invention deflection angle and azimuthal schematic diagram；
Fig. 4 is P in the method for the present invention1Place four-quadrant photo detector schematic diagram；
Fig. 5 is P in the method for the present invention2Place four-quadrant photo detector schematic diagram；
Fig. 6 is P in the method for the present invention1And P2Measurement side when two four-quadrant photo detectors at place are in adjacent warp
The schematic diagram of parallactic angle；
Fig. 7 is P in the method for the present invention1And P2Two four-quadrant photo detectors at place measure when being in non-conterminous warp
Azimuthal schematic diagram；
Fig. 8 is P in the method for the present invention1And P2Two four-quadrant photo detectors at place are in two adjacent four-quadrant light
The schematic diagram of deflection angle is measured when in electric explorer group；
Fig. 9 is P in the method for the present invention1And P2Two four-quadrant photo detectors at place are not in two adjacent four-quadrants
The schematic diagram of deflection angle is measured when in photodetector group.
Specific embodiment
Below in conjunction with the accompanying drawings and embodiment the invention will be further described.
A kind of spherical hinge three dimensional angle detection method, the specific steps are as follows:
1) as shown in Figure 1, hemispherical shell 3 is fixed on bulb output rod 1, so that hemispherical shell 3 and bulb 4 are same
The heart, and hemispherical shell 3 is towards bulb 4.
2) laser emitter 2 is fixedly installed at ball-and-socket 5.
3) as shown in Fig. 2, arranging the n four-quadrant photodetection arranged along warp direction in 3 Internal Spherical Surface of hemispherical shell
Device group, four-quadrant photo detector group is by being uniformly fixed on N number of four-quadrant photoelectricity of 3 Internal Spherical Surface of hemispherical shell along weft direction
Detector 6 forms；The four-quadrant photo detector size of the same four-quadrant photo detector group is identical；The same four-quadrant
It limits four-quadrant photo detector spacing adjacent in photodetector group and is less than 0.05mm, can be approximately 0, and will not influence to sharp
The reception of 2 emergent light of optical transmitting set；The four-quadrant photo detector of adjacent four-quadrant photo detector group along warp direction one by one
Alignment；Along the coincidence side of the two neighboring four-quadrant photo detector of same warp alignment in each four-quadrant photo detector group
Side length is equal；The warp direction symmetrical center line for all four-quadrant photo detectors being aligned on a warp is the warp
Inscribe regular polygon side；Four-quadrant photo detector group does not need to be covered with entire 3 Internal Spherical Surface of hemispherical shell, it is only necessary to protect
The laser that laser emitter 2 emits during card hemispherical shell 3 rotates can be beaten in the four-quadrant photodetection arranged
On device 6.Then sequential organization is carried out to the four-quadrant photo detector of arrangement 6, in this, as four-quadrant photo detector
Mark, specific as follows: each four-quadrant photo detector is successively suitable from 1 to N in the minimum four-quadrant photo detector group of latitude
Sequence number, n four-quadrant photo detector group is according to latitude number consecutively from low to high, i-th of four-quadrant photo detector group
In in first four-quadrant photo detector group minimum with latitude j-th of four-quadrant photo detector be aligned along warp direction
Four-quadrant photo detector number is j+ (i-1) N, 1≤j≤N, 2≤i≤n；N >=20, n >=8；
4) as shown in figure 3, establishing cartesian coordinate system O-XYZ, coordinate origin O is arranged at 4 center of bulb, X-axis and Y
The plane XY that axis is constituted is parallel with plane where weft, and plane where weft is parallel to 5 bottom surface of ball-and-socket；Z axis is perpendicular to plane XY；
Then coordinate of the point M on 1 central axis of bulb output rod in cartesian coordinate system O-XYZ are as follows:
Wherein,For azimuth, θ is deflection angle, and R is point M at a distance from coordinate origin O；According to above-mentioned formula, R is
What point M was just directly determined after choosing, it is therefore possible for the detected that azimuthWith deflection angle θ, the three dimensional angle (side of spherical hinge can be solved
Parallactic angleThree dimensional angle is collectively referred to as with deflection angle θ).
5) as shown in Fig. 3,4 and 5, when the point M on 1 central axis of bulb output rod goes to point M ', before bulb 4 rotates and turn
Cross azimuthThe laser that laser emitter 2 emits afterwards is beaten on two four-quadrant photo detectors 6, is visited according to four-quadrant photoelectricity
6 measuring principle of device is surveyed, imaging facula energy of 2 emergent light of laser emitter on a wherein four-quadrant photo detector 6 is measured
Amount center P1Apart from 6 geometric center O of the four-quadrant photo detector1The broadwise of point biases dx1With through to biasing dy1And laser
Imaging facula center of energy P of 2 emergent light of transmitter on another four-quadrant photo detector 62Apart from the four-quadrant photoelectricity
6 geometric center O of detector2The broadwise of point biases dx2With through to biasing dy2, dx1And dy1And dx2And dy2According to four-quadrant photoelectricity
The solution procedure of 6 measuring principle of detector be four-quadrant photo detector 6 inside ripe algorithm, as Wang Ganfa in 2008
Page 7 to page 11 in paper disclosed in Changchun University of Science and Technology " quick, the precise detection technology research based on the QD laser optical axis "
Solution procedure.In Fig. 4, S1、S2、S3And S4Respectively P1The first quartile of place four-quadrant photo detector, the second quadrant, third
Quadrant and fourth quadrant area；In Fig. 5, S5、S6、S7And S8Respectively P2The first quartile of place four-quadrant photo detector,
Two quadrant, third quadrant and fourth quadrant area, the first quartile of four-quadrant photo detector, the second quadrant, third quadrant and
Fourth quadrant is consistent with four quadrant division modes in plane coordinate system.Set P1The d in first, fourth quadrantx1It is positive, In
D when second, third quadrantx1It is negative, P1The d in the first, second quadranty1It is positive, the d in third, fourth quadranty1It is negative；Setting
P2The d in first, fourth quadrantx2It is positive, the d in second, third quadrantx2It is negative, P2The d in the first, second quadranty2It is positive,
The d in third, fourth quadranty2It is negative.
6) as shown in Figures 6 and 7, in the same four-quadrant photo detector group each four-quadrant photo detector along the side of broadwise
The interior angle ω for the n-shaped being encircled into solves as follows:
7) as shown in Figures 6 and 7, work as P1And P2Two four-quadrant photo detectors 6 at place are in adjacent warp (can not
In the same four-quadrant photo detector group) when, the azimuth that turns overIt is calculated according to formula (2), works as P1And P2The two of place
When a four-quadrant photo detector 6 is in non-conterminous warp, the azimuth that turns over(two four-quadrants are calculated according to formula (3)
Photodetector not in the same four-quadrant photo detector group,WithIt should be asked respectively in two different n-shapeds
Solution, but Fig. 6 and 7 has only drawn a n-shaped for rough schematic view)；
In formula (3), m1For P1And P2Four-quadrant between two four-quadrant photo detectors at place along weft direction apart
Limit photodetector number；Since the present invention handles (four-quadrant light for all four-quadrant photo detectors 6 are approximately rectangle
Electric explorer 6 is in isosceles trapezoid, but since 6 size of four-quadrant photo detector is little, is approximately that rectangle influences precision
In allowed band), so regardless of P1And P2The position of four-quadrant photo detector wherein, P1Place four-quadrant photodetection
Pass through P on device1And the broadwise edge lengths of the four-quadrant photo detector, P are equal to along the straight length of weft direction2Place four
Pass through P on quadrant photodetector2And the broadwise of the four-quadrant photo detector is also equal to along the straight length of weft direction
Edge lengths；Set P1The broadwise edge lengths of place four-quadrant photo detector are k, P2The broadwise of place four-quadrant photo detector
Edge lengths v=k ± c1× p, P2Place four-quadrant photo detector is located at P1When above the four-quadrant photo detector of place, take just
Number, otherwise take negative sign, c1The value in 0.02~0.05, the unit of broadwise edge lengths are mm, p P1And P2Place four-quadrant light
The number difference of electric explorer group；P1Place four-quadrant photo detector is close to P2The broadwise side of place four-quadrant photo detector
It is set as E1, P2Place four-quadrant photo detector is close to P1Place four-quadrant photo detector broadwise side is set as E2, then P1To E1's
Distance a=0.5k-dx1, P2To E2Distance b=0.5v-dx2。P1With broadwise side E1Intersection point, P1And coordinate origin O composition
Triangle in, the corresponding angle of the side length that length is a isP2With broadwise side E2Intersection point, P2And coordinate origin O composition
Triangle in, the corresponding angle of the side length that length is b is
Regardless of P1And P2Whether two four-quadrant photo detectors at place are in adjacent warp,WithAccording to as follows
Process solves:
Coordinate origin O to P is solved according to formula (4) according to the cosine law1Distance L1, according to the cosine law according to public affairs
Formula (5) solves coordinate origin O to P2Distance L2；Then, it is solved according to sine according to formula (6)According to sine
Theorem is solved according to formula (7)
In formula (4) and (5), r is the inner sphere radius of hemispherical shell 3.
8) as shown in FIG. 8 and 9, set all four-quadrant photo detectors 6 through being all t to edge lengths, then along warp side
Angle to two adjacent four-quadrant photo detectors is 180 ° of-α, and α is solved according to formula (8):
9) as shown in FIG. 8 and 9, work as P1And P2Two four-quadrant photo detectors 6 at place are in two adjacent four-quadrant light
When (can be not at adjacent warp position) in electric explorer group, the deflection angle θ turned over is calculated according to formula (9), works as P1And P2Institute
Two four-quadrant photo detectors 6 in non-conterminous two four-quadrant photo detector groups when, the deflection angle θ that turns over by
Calculated according to formula (10) (when two four-quadrant photo detectors are in non-conterminous two four-quadrant photo detector groups, θ1And θ2
It should be solved respectively in the two different positive side T shapes, but Fig. 8 and 9 has only drawn the n item of the positive side a T shape for rough schematic view
Side)；
θ=θ1+θ2 (9)
In formula (10), m2For P1And P2Between two four-quadrant photo detectors at place along warp direction apart four
Quadrant photodetector number, T are the warp direction symmetrical centre for all four-quadrant photo detectors being aligned on a warp
The number of edges of regular polygon, the solution of T are as follows where line:
By
It releases
P1Place four-quadrant photo detector is close to P2Place four-quadrant photo detector through being set as E to side3, P2Place
Four-quadrant photo detector is close to P1Place four-quadrant photo detector is through being set as E to side4, then P1To E3Distance c=0.5t-
dx2, P2To E2Distance d=0.5t-dy2。P1With broadwise side E3Intersection point, P1And in the triangle of coordinate origin O composition,
The corresponding angle of the side length that length is c is θ1；P2With broadwise side E4Intersection point, P2And in the triangle of coordinate origin O composition,
The corresponding angle of the side length that length is d is θ2。
Regardless of P1And P2Two four-quadrant photo detectors 6 at place in two adjacent four-quadrant photo detector groups,
θ1And θ2Solve as follows:
Coordinate origin O to P is solved according to formula (11) according to the cosine law1Distance L3, according to the cosine law according to public affairs
Formula (12) solves coordinate origin O to P2Distance L4；Then, θ is solved according to formula (13) according to sine1, according to sine
Theorem solves θ according to formula (14)2。
Claims (4)
1. a kind of spherical hinge three dimensional angle detection method, it is characterised in that: specific step is as follows for this method:
1) hemispherical shell is fixed on bulb output rod, so that hemispherical shell is concentric with bulb, and hemispherical shell court
To bulb；
2) laser emitter is fixedly installed at ball-and-socket；
3) the n four-quadrant photo detector group arranged along warp direction, four-quadrant photoelectricity are arranged in hemispherical shell Internal Spherical Surface
Detector group is made of the N number of four-quadrant photo detector for being uniformly fixed on hemispherical shell Internal Spherical Surface along weft direction；It is adjacent
The four-quadrant photo detector of four-quadrant photo detector group is aligned one by one along warp direction；Each four-quadrant photo detector group
The coincidence side side length of the middle two neighboring four-quadrant photo detector along the alignment of same warp is equal；It is aligned on a warp
The warp direction symmetrical center line of all four-quadrant photo detectors is the side of the inscribe regular polygon of the warp；Then to cloth
The four-quadrant photo detector set carries out sequential organization, specific as follows: each four in the minimum four-quadrant photo detector group of latitude
Quadrant photodetector from 1 to N, successively successively compile from low to high according to latitude by serial number, n four-quadrant photo detector group
Number, j-th of four-quadrant in first four-quadrant photo detector group minimum with latitude in i-th of four-quadrant photo detector group
Photodetector is j+ (i-1) N, 1≤j≤N, 2≤i≤n along the four-quadrant photo detector number that warp direction is aligned；N≥
20, n >=8；
4) cartesian coordinate system O-XYZ is established, coordinate origin O is arranged at bulb center, the plane XY that X-axis and Y-axis are constituted
Parallel with plane where weft, plane where weft is parallel to ball-and-socket bottom surface；Z axis is perpendicular to plane XY；
5) when the point M on bulb output rod central axis goes to point M ', before bulb rotation and azimuth is turned overLaser emission afterwards
The laser of device transmitting is beaten on two four-quadrant photo detectors, according to four-quadrant photo detector measuring principle, measures laser
Imaging facula center of energy P of the transmitter emergent light on a wherein four-quadrant photo detector1Apart from the four-quadrant photoelectricity
The broadwise of geometric center of detector biases dx1With through to biasing dy1And laser emitter emergent light is in another four-quadrant light
Imaging facula center of energy P on electric explorer2Broadwise apart from the four-quadrant photo detector geometric center biases dx2And warp
To biasing dy2；In the first quartile of four-quadrant photo detector, the second quadrant, third quadrant and fourth quadrant and plane coordinate system
Four quadrant division modes it is consistent, set P1The d in first, fourth quadrantx1It is positive, the d in second, third quadrantx1It is negative,
P1The d in the first, second quadranty1It is positive, the d in third, fourth quadranty1It is negative；Set P2The d in first, fourth quadrantx2For
Just, the d in second, third quadrantx2It is negative, P2The d in the first, second quadranty2It is positive, the d in third, fourth quadranty2For
It is negative；
6) each four-quadrant photo detector is encircled into along the side of broadwise in the same four-quadrant photo detector group n-shaped
Interior angle ω solves as follows:
7) work as P1And P2When two four-quadrant photo detectors at place are in adjacent warp, the azimuth that turns overAccording to formula
(2) it calculates, works as P1And P2When two four-quadrant photo detectors at place are in non-conterminous warp, the azimuth that turns overAccording to
Formula (3) calculates；
In formula (3), m1For P1And P2Four-quadrant light between two four-quadrant photo detectors at place along weft direction apart
Electric explorer number；Set P1The broadwise edge lengths of place four-quadrant photo detector are k, P2Place four-quadrant photo detector
Broadwise edge lengths v=k ± c1× p, P2Place four-quadrant photo detector is located at P1Above the four-quadrant photo detector of place
When, positive sign is taken, negative sign, c are otherwise taken1The value in 0.02~0.05, the unit of broadwise edge lengths are mm, p P1And P2Place four
The number difference of quadrant photodetector group；P1Place four-quadrant photo detector is close to P2Place four-quadrant photo detector
Broadwise side is set as E1, P2Place four-quadrant photo detector is close to P1Place four-quadrant photo detector broadwise side is set as E2, then P1
To E1Distance a=0.5k-dx1, P2To E2Distance b=0.5v-dx2；P1With broadwise side E1Intersection point, P1And coordinate system is former
In the triangle of point O composition, the corresponding angle of the side length that length is a isP2With broadwise side E2Intersection point, P2And coordinate system is former
In the triangle of point O composition, the corresponding angle of the side length that length is b is
Regardless of P1And P2Whether two four-quadrant photo detectors at place are in adjacent warp,WithAs follows
It solves:
Coordinate origin O to P is solved according to formula (4) according to the cosine law1Distance L1, according to the cosine law according to formula (5)
Solve coordinate origin O to P2Distance L2；Then, it is solved according to sine according to formula (6)It is pressed according to sine
It is solved according to formula (7)
In formula (4) and (5), r is the inner sphere radius of hemispherical shell；
8) set all four-quadrant photo detectors through being all t to edge lengths, then two four-quadrants adjacent along warp direction
The angle of photodetector is 180 ° of-α, and angle [alpha] is solved according to formula (8):
9) work as P1And P2When two four-quadrant photo detectors at place are in two adjacent four-quadrant photo detector groups, turn
The deflection angle θ crossed is calculated according to formula (9), works as P1And P2Two four-quadrant photo detectors at place are at non-conterminous two four
When in quadrant photodetector group, the deflection angle θ turned over is calculated according to formula (10)；
θ=θ1+θ2 (9)
In formula (10), m2For P1And P2Four-quadrant between two four-quadrant photo detectors at place along warp direction apart
Photodetector number, T are the warp direction symmetrical center line institute for all four-quadrant photo detectors being aligned on a warp
It is as follows in the solution of the number of edges of regular polygon, T:
By
It releases
P1Place four-quadrant photo detector is close to P2Place four-quadrant photo detector through being set as E to side3, P2Place four-quadrant
Photodetector is close to P1Place four-quadrant photo detector is through being set as E to side4, then P1To E3Distance c=0.5t-dx2, P2It arrives
E2Distance d=0.5t-dy2；P1With broadwise side E3Intersection point, P1And in the triangle of coordinate origin O composition, length c
The corresponding angle of side length be θ1；P2With broadwise side E4Intersection point, P2And in the triangle of coordinate origin O composition, length d
The corresponding angle of side length be θ2；
Regardless of P1And P2Two four-quadrant photo detectors at place are in two adjacent four-quadrant photo detector groups, θ1And θ2
Solve as follows:
Coordinate origin O to P is solved according to formula (11) according to the cosine law1Distance L3, according to the cosine law according to formula
(12) coordinate origin O to P is solved2Distance L4；Then, θ is solved according to formula (13) according to sine1, fixed according to sine
Reason solves θ according to formula (14)2；
2. a kind of spherical hinge three dimensional angle detection method according to claim 1, it is characterised in that: the same four-quadrant light
The four-quadrant photo detector size of electric explorer group is identical.
3. a kind of spherical hinge three dimensional angle detection method according to claim 1, it is characterised in that: the same four-quadrant light
Adjacent four-quadrant photo detector spacing is less than 0.05mm in electric explorer group.
4. a kind of spherical hinge three dimensional angle detection method according to claim 1, it is characterised in that: four-quadrant photodetection
Device group is not covered with entire hemispherical shell Internal Spherical Surface.
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