JPH0424508A - Subtense bar for three-dimensional measurement - Google Patents

Abstract

PURPOSE:To prevent the occurrence of accumulated errors by providing three targets at specified intervals in a subtense bar which is used in measurement for obtaining the position of each point based on the observations at least of three points. CONSTITUTION:One theodolite 1 is provided at coordinate origin (0, 0, 0). Then a subtense bar 2 is disposed in S2. Three fixed points are set. Then, the fixed points S1, S2 and S3 of the subtense bar 2 are sighted from the theodolite 1, and their horizontal angles and elevation angles are measured. Error equations are formed based on the horizontal angle and the elevation angle from the observed data and the distances between the fixed points of the subtense bar 2. Then, the approximate values are obtained from the observed data and substituted into the error equations. There are 11 error equations for the eight unknown values. Therefore, when the method of least squares is utilized, the unknown coordinates can be theoretically operated. Since the three targets can be formed in spherical shapes furthermore, the sighting errors can be reduced.

Description

Detailed Description of the Invention "Field of Industrial Application" The present invention relates to a subtense bar used for three-dimensional measurement to measure the shape and dimensions of large structures, etc.
The present invention relates to a subtense bar for use in three-dimensional measurement, which allows efficient and highly accurate measurement by using only one heptadrite.

``Conventional technology'' Conventionally, three-dimensional measurements are performed by leveling a subtense bar with grooves on both ends horizontally and placing it at a reference point, using two observation instruments (transits), and using the following method: The points were found from the known points using the following procedure.

(a) First, find the position of the observation point from the reference point.

That is, a subtense bar with targets provided at both ends is placed horizontally at a reference point. Here, the subtense bar is arranged horizontally in order to simplify the calculation for determining the position of the observation point. Then, two transits will be installed at two observation points. In this state, from the first transit, the two ends of the subtense bar placed horizontally and the second transit placed at the second observation point are referenced, and the horizontal angle
Measure the altitude angle.

Next, from the second transit, the horizontal angle and altitude angle are measured by measuring three points: both ends of the subtense bar placed horizontally and the first transit placed at the first observation point.

Furthermore, the reference point position and the coordinates of the first and second observation points are determined by a geometric method using the above observation data.

(b) Next, find the point.

With the transit installed at the coordinates of the first and second observation points computed in step (a) above, a point to be sought is determined from the first transit, and the horizontal angle and altitude angle are measured.

Next, the desired point is determined from the second transit, and the horizontal angle and altitude angle are measured.

Then, the coordinates of the desired point were determined by a geometric method using the first and second observation point positions and observation data.

``Problems to be Solved by the Invention'' However, in the conventional measurement method described above, the observation point position is first determined from the reference point, and the desired point is determined from this observation point position, so measurement errors accumulate and accuracy decreases. There was a problem.

Since there are two observation positions, simultaneous observation is required to reduce errors, which makes the work complicated.

In addition, the reference target for observation points is transit,
The problem is that it is difficult to standardize and tends to include standard errors.

Furthermore, since the subtense bar must be horizontal,
There was a problem in that there were restrictions on where to work.

"Means for Solving the Problems" The present invention has been devised in view of the above problems, and is based on three points at predetermined intervals in a subtense bar used for measurement to determine the position of each point from observation between at least three points. It is characterized by a target.

Furthermore, in the present invention, the three targets can also be formed into spherical shapes.

"Operation" According to the present invention configured as described above, by forming three targets at predetermined intervals on the subtense bar, the position of each point can be determined from observation between at least three points.

Furthermore, the shapes of the three targets can also be made spherical.

"Example" An embodiment of the present invention will be described based on the drawings.

The measurement method using the subtense bar 2 of the present invention is a method in which each independent unknown quantity and several other quantities in a specific relationship are directly measured, and the unknown quantities are indirectly determined using these measured values. is adopted.

Here, X, Y, Z...T are unknown l, and M, , M
If l, . . . MN are quantities to be directly measured, the unknown quantity will be calculated from the following quantity formula.

M, = f, (X, Y, Z, ・ ・ ・ ・T) Ml
= fa (X, Y, Z, ・ ・ ・ ・T) Ml
, = fo(X, Y, Z, ・ ・ ・ ・T)・ ・
・ ・ (1) Let this first equation be the error equation (lE?1 equation).

Then let X be the true value and call X' the approximate value. Complement X If it is a positive amount, X=x'+x And similarly, y=y'+y T=t'tent ・　・　・　・　・(2) It can be expressed as.

Also, the first equation uses the second equation to obtain f,<X-Y,Z ・ ・ ・ Tn=f+(x'
−t' +t) (i = 1 ・ −・ ・n
)・・−(3) It can be written as Then, the third equation is expanded by Taylor,
If we omit (linearize) the quadratic terms and subsequent terms, we get f, (x'+x+
y'+y+ z'+z---t' +t) ζ ft (x', y'-z' ・ ・ ・1/
)3t'.

Here, M1' = fl (X', y', Z' ・
...If t', then M.

M　H’ + a IX + b 13/ + CtZ.

It can be expressed as.

The present invention provides x/, y/, z/...t'
(approximate value) is substituted with an approximate value obtained by a geometric method, and the correction amounts x, y, z...t are obtained by solving simultaneous equations.

However, between the number of unknown quantities x, y, z...t and the number (n) of error equations (first equation), the number of error equations (n) is larger, so the method of least squares is adopted. By this,
x, y, z...t can be found. Further, by substituting the correction amounts X, y, z, . . . t obtained by the least squares method into the second equation, the true value can be calculated.

Next, a specific measurement method will be explained.

Heptaodolite 1 and Subtense Bar 2 are used for measurement. Seven Odolite 1 is a type of transit, and is a precision single-axis type that can only move upward.

Note that the theodolite 1 corresponds to an observation instrument, and it is sufficient if it is a measuring instrument that can determine at least the horizontal angle and the altitude angle.

The subtense bar 2 is also called a standard standard or measuring rod, and as shown in FIG. It is formed. These first, second, and third targets 21, 22, and 23 are each formed at predetermined intervals, and all of the targets are spherical in shape.

The subtense bar 2 is desirably made of a material with a small tensile strength, and can be installed by being attached to an appropriate base.

It is desirable that a plurality of reticles 11, 11, . . . of the heptaodolite 1 for standardizing the subtense bar 2 of this embodiment are formed concentrically as shown in FIG. 2(a). The reason why multiple reticles 11, 11... are formed is that the distance between the heptaodolite 1 and the subtense bar 2 is not always constant due to the installation space, etc., so there is a difference in the size of the target imaged on the reticle 11. This is because it occurs. Therefore, when the heptaodolite 1 and the subtense bar 2 are far apart, an image is formed as shown in FIG. The image is formed as shown in c). Furthermore, the first, second, and third targets 2
1.22.23 are spherical, even if the subtense bar 2 is inclined, it can be accurately referenced as shown in FIG. 2(d).

Furthermore, conventional targets have been used that have marks formed in a conical shape or a flat surface. Therefore, it could not be used if the subtense bar 2 was tilted.

However, in the conventional method, it was not possible to tilt the subtense bar 2, so this did not pose a problem9.In contrast, in this embodiment, as will be described later, measurement can be performed even when the subtense bar 2 is tilted. Therefore, by making the target spherical, even if the subtense bar 2 is tilted, it can be easily measured.

Next, the measurement method will be explained in detail. In order to know the coordinates of the target point, we must know the position (coordinates) of Seven Odorite 1 itself. Therefore, determine the number of heptadite 1, the number of subtense bars 2, and the number of observations, and theodolite 1.
positioning. In this embodiment, the positioning of the heptaodolites 1 will be referred to as orientation, the number of heptaodolites 1 is th, and the number of subtense bars 2 is sub.

Next, from each theodolite 1.1... to subtense bar 2
Observe. In this case, the criteria for subtense bar 2 are:
Observe horizontal angle and altitude angle at the same time.

Here, observation equations regarding the horizontal angle, altitude angle, and spacing of the subtense bars 2 will be explained.

(Observation equation for horizontal angle) For theodolite i = 1 to th, direction (
OBi) When observing Mizuko angle H, OBi, the observation equation for the horizontal angle is Hi, oat 8. Then, Vl, O
Bi ・ ・ ・ ・ ・ ・ (8)

(Observation equation for the length of subtense bar 2) Since the number of subtense bars 2 is sub, point No. is 5b(th+(2i-1), th+2i) when the number of subtense bars 2 is i=1 to sub.・・・・・・
(9) It can be expressed as follows. Therefore, the observation equation is i=1~s
When ub, + (Ys+) (th+2t) Y&btth+t□
1-1)l) 2+ (Zab(th+2++ Zs
b+th++2+-t++) 2・ ・ ・ ・ ・
・(10) becomes.

(Observation equation for linearity between fixed points) The linearity of subtense bar 2 is an observation equation for the spatial angle formed by three fixed points, but when these three fixed points are projected onto a horizontal plane, Horizontal angle Ha and vertical plane (x-
It can be considered separately as the altitude angle Va when projected onto the z plane or the yz plane.

Note that these error equations have the same form as the horizontal angle-altitude angle equation shown below.

Next, error equations regarding the horizontal angle, altitude angle, and spacing of the subtense bars 2 will be explained.

(Error equation for horizontal angle) Here, the observed value is [□. □, and the observation error is ΔHi, 0I
If Ii, LHI 01! I=Q Ht, ogi+JMi, o old... (11). i in equation 11 is the number of theodolites 1,
i=1 to th. OBi is the number of observations when point No. 9 of theodolite 1 is i.

Therefore, if linearization is performed, Q 14i, 081+ΔHi, OBi”fHj.Bj
(X' OBi, Y' oat, X' ,, Y'
1).

Then, if the seventh equation (observation equation) is 0' + 4i, OBi, then Q10.
. 8° is obtained as an approximate value, and the 13th equation is the same as fHl in the 12th equation.

Therefore, the error equation for the horizontal angle is ΔMl +w, 1 becomes.

In addition, H1 Q′□ OBi QH4 It is.

here, The terms of variable differentiation are shown below.

0f□ θX'0Bi (Y'oa+ Y' I) (x'.□-X1) 2 10 (Y' oat Yt) ” θf Hi, oat 'dY'oBs X'oai X'(X' 081 Xs) 2 + (Y' ass Yt) 2 afH* 0X'Y'oBi-Y'(X' osiXt) 2 + (Y'O□-Yl) θf Hr, oat 8Y'(X' asI Xs) 2+ (Y' □ Bi Y
t)”・ ・ ・ ・ ・ ・ (19)

(Error equation for altitude angle) As with the horizontal angle, we will derive an error equation for the altitude angle. The number of observations for altitude angle is the same as for horizontal angle.

■ the altitude angle. If □, the observation equation becomes Equation 8. The observed value is Q v+, oat, and the observation error is Δ0
8. Then, Lvi, ogt= Q v+, oat+ΔVi, OBI
・ ・ (20) becomes.

Therefore, the error equation is Ov+, oBt+ΔVi, OI f Vl, 081 (X' oai, Y'oat,
Z'onIX'i, Y'technique, z' *) ・ ・ ・ ・ ・ (21) It can be transformed into.

Furthermore, the approximate value of Equation 8 is σ　Vi. ■If it is, Q　’　vs ＝tan” Therefore, the error equation for the altitude angle is ΔV5,0Bi GZ′ ・　・　・　・　・(23) becomes.

Here, Wvs,ogt=Q'vt,oat
Q vs. oBI.

Note that although the total differential term in Equation 23 can be calculated in the same way as the horizontal angle, it will be omitted.

(Error equation for the length of subtense bar 2) Next,
An error equation for the length of subtense bar 2 is derived.

If the observed value is Q, 1, and the observation error is Δci, then L
gt = Q = j + J S
1・ ・ ・ ・ ・ (24)

QEi+JS.

-f ci (X' cb(th41i), Y' 5
b(thyu2i), Z' cb(th+2i),X
'cb(th-2i)Y/, wow. h-2i), Z
/6ゎ. h-2i)) θX'Gt+Tth◆21n''3f□ Next, an approximate value is obtained from the first O equation (l[?11 method), and if this approximate value is set as Q'si, then Q'5i is obtained.

Therefore, Error in length of subtense bar 2 The equation is Δs1 θX' cbTth◆(2i-11) θf□ + VV s t ・　・　・　・(27) becomes.

here, W,”　　　　　　　　　　　si　-QcI ・　・　・　・　・(28) It is.

Note that although the variable differential term in Equation 27 can be calculated in the same way as the horizontal angle, it will be omitted.

In the above, an error equation was created by converting the linearity between fixed points into a horizontal angle and an altitude angle, but an error equation may be created directly for the angle (spatial angle) formed by three fixed points in space.

Next, a method of calculating the approximate value used in the second equation will be explained. In this embodiment, two approximate value calculation methods will be explained.

(First method) In FIG. 7(a), if a plane in the space created by T1, Sl, S2, and S3 is taken out, a triangle on the plane as shown in FIG. 7(b) can be obtained.

The backward intersection method is applied to the triangles T1, Sl, S2, and S3 to find ψ1 and ψ2.

(ψl+ψ2)=π−(θ1□+023)(ψ□−ψ2
)/2=jan-” (jan ((ψ1+ψ2)/2
＞/ (j an-1(L, -s i nH2/L2-
sinHl)+π/4)) ・ ・ ・ ・ ・ ・ (30) As described above, if all angles and side lengths of triangles TI, Sl, S2, and S3 are found, then T1.5l-32, S3 If any one of the points is set as a known point and the direction passing through that point is fixed as a coordinate axis, the three-dimensional positions of the other points can be determined.

(Second method) As shown in Figure 8, this method projects two direction lines onto a plane passing through each observation point, calculates the plane coordinates X and Y, and then
The altitude Z can be determined from the altitude angle.

That is, the distance from observation point TI to measurement point Q is xq=I
), ・cosHl yq=I)1・sinHI Zq=D1− tanVl ・ ・ (31) The distance from observation point T2 to measurement point Q is Xq=
D2・C08H2 Yq=[)z・s i n) (2 Zq=D2・tanV2 ・ (32) 9 Therefore, substitute the approximate value obtained by the above method into the error equation, and calculate the correction amount by the least squares method. By performing the calculation, it becomes possible to calculate the three-dimensional coordinates of the measurement point.

``Work'' Nozu explains the basic measurement method when there is only one observation point based on Figures 3 and 4. 9 The subtense bar 2 is equipped with three fixed points (measurement points). The fixed point coordinates are 5l(X,, Yl, Zl), S2
(X2, T2, Z2)-33(X3, T3, Z3). The distance between the fixed points of the subtense bar 2 is determined to be an arbitrary value. ! In this embodiment, the explanation will be made using S2 as a reference point, and here it is assumed that Y2=O.

First, as shown in Figure 3, step 1 (hereinafter abbreviated as S1)
Set one Seven Odolite 1 at the coordinate origin (0, 0, 0). (It is assumed to be a known point) That is, the WA measurement instrument is placed at the im measurement point.

Next, 82' place the subtense bar 2 and set three fixed points.6 The subtense bar 2 of this embodiment corresponds to the standard target.97 After the odorite 1 and the subtense bar 2 are set, in S3, The fixed points S1, S2, and S3 of the subtense bar 2 are respectively referenced from the theodolite 1, and the horizontal angle and altitude angle are measured.

Next, in step 84, an error equation is created from the horizontal angle and altitude angle (including those corresponding to the linearity of the fixed points) from the observation data, and the distance between the fixed points of the subtense bar 2.

The horizontal angle error equation is as follows:

Seen from the heptadrite 1, the horizontal angle H12 between fixed points Sl and S2, the horizontal angle 82B between fixed points S2 and S3, and the horizontal angle H3 between fixed points S3 and S1.
1, and a horizontal angle Ha when the spatial angle formed by the fixed point Sl, the fixed point S2, and the fixed point S3 is projected onto a horizontal plane.

The error equation for altitude angle is as follows.

Seen from the seventh odolite 1, the altitude angle between the fixed point Sl and the fixed point S2 ■□2, the altitude angle between the fixed point S2 and the fixed point S3 v23, the altitude angle between the fixed point Sl and the fixed point S2 V3
1, and the altitude angle Va when the spatial angle formed by the fixed points S1, S2, and S3 are projected onto the monument plane.

However, since the horizontal angle Ha and the altitude angle Va are the angles formed by the fixed point S2, the coordinate values substituted into the error equations (Equations 14 and 23) are obtained by subtracting the coordinate values of the fixed point S2, respectively. It is necessary to do so.

The following is an error equation for the distance between three fixed points.

Error equations are created for three points: distance iLl between fixed point $1 and fixed point S2, distance HL2 between fixed point S2 and fixed point S3, and distance HL3 between fixed point S3 and fixed point S1.

As described above, when there is one observation point, there are eight unknowns, so the present invention can be applied by creating nine or more types of error equations, which are greater than the number of unknowns.

Next, at 85, approximate values are determined from the observed data using the method described above and substituted into the error equation.

As shown in FIG. 4, since there are 8 unknowns and 11 error equations, the unknown coordinates can be calculated theoretically by using the method of least squares in S6.

In this example, there is no need to use two heptaodolites for standardization alternately as in the conventional method, and measurements can be made with one heptaodolite. Fixed points can also be freely determined, but the number of unknowns must be smaller than the number of error equations.

Next, an application example of this measurement method in the case where there are two observation points will be explained based on FIGS. 5 and 6.

First, as shown in FIG. 5, the theodolite 1 is set at the first observation point T1 using Sl. Next, at 82, the subtense bar 2 is installed to set three fixing points.

Further, in step 83, an arbitrary desired point P to be measured is set.

Then, in S4, three fixed points from the heptadrite 1 to the subtense bar 2 and a desired point P located at an arbitrary position are determined, and the horizontal angle and altitude angle of each are measured.

Next, in S5, the theodolite 1 is moved from the first observation point T1 to the second observation point T2, and in S6, the three fixed points of the subtense bar 2 and the desired point P at an arbitrary position are again referenced. , measure each horizontal and altitude angle.

Then, in S7, the observed horizontal angle and altitude angle (including those corresponding to the linearity of the fixed point), and the subtense bar 2
Error equation from the distance between fixed points of In this case, the following error equation can be created.

The horizontal angle error equation is as follows:

- The horizontal angle between fixed points S1 and S2, the horizontal angle between fixed points S2 and S3, the horizontal angle between fixed points S1 and S2, and other observation points when viewed from the observation point - The horizontal angle between fixed points S1 and S2, the horizontal angle between fixed points S2 and S3, the horizontal angle between fixed points S1 and S2, and the horizontal angle between fixed points S1 and S2 when viewed from Create an error equation for the horizontal angle when the spatial angle formed by the fixed point S3 is projected onto the horizontal plane.9 Error equations for the altitude angle include the following.

The altitude angle between fixed points Sl and S2 when viewed from the observation point -, the altitude angle between fixed points S2 and S3, the altitude angle between fixed points S] and S2, and other observations. The altitude angle between fixed point S1 and fixed point S2 when viewed from the point, the altitude angle between fixed point S2 and fixed point S3, the altitude angle between fixed point Sl and fixed point S2, and the fixed point S1 and fixed point S2 Error equations are created for seven altitude angles when the spatial angles formed by the fixed point S3 and the fixed point S3 are projected onto the vertical plane.

However, since the horizontal angle Ha and the altitude angle Va are the angles formed by the fixed point S2, the coordinate values substituted into the error equations (Equations 14 and 23) are obtained by subtracting the coordinate values of the fixed point S2, respectively. It is necessary to do so.

The error equation for the distance between the three fixed points is the same as that described for the case where there is one observation point, so the explanation will be omitted.

As described above, when there are two observation points, there are 11 unknowns, so the present invention can be applied by creating 12 or more types of error equations, which are greater than the number of unknowns.

Note that if the positions of the first observation point T1, the second observation point T2, or the subtense bar 2 are known, the above-mentioned observation is sufficient, but if all are unknown, the positions shown in Fig. 6 are used. It is necessary to give four arbitrary points (known points) and standardize them using the theodolite 1 from the first observation point T and the second observation point T2.

Then, in S8, an approximate value is obtained from the observed data.

Furthermore, in step 89, the approximate value is substituted into the error equation, and the least squares method is applied to obtain Ml of the sought point P.

This embodiment configured as described above can be used for three-dimensional measurement of aircraft and ships, observation of steeply sloping collapsed topography, deformation tests of large tank relics, and the like.

``Effects'' The present invention configured as described above has three targets provided at predetermined intervals on the subtense bar used for measurement to determine the position of each point from observation between at least three points, so that the cumulative This method has the effect of being able to perform a three-dimensional measurement method that does not cause errors.9 Furthermore, since there is no need to face the observation instrument directly, and there is no need for the subtense bar to be horizontal, the subtense bar can be set at any location. It has the effect of being able to. In particular, since there are no restrictions on the setting position of the subtense bar, it has the outstanding effect that it can be easily placed even in places with poor conditions. It has the outstanding effect of reducing the standard error even when it is placed at an angle.

[Brief explanation of drawings]

The figures show one embodiment of the present invention, and FIG. 1 is a diagram explaining the subtense bar of this embodiment, FIG. 2 is a diagram explaining a heptaodolite reticle, and FIG. 3 is a diagram explaining this embodiment. Figure 4 is a coordinate system for explaining the basic principle, Figure 5 is a diagram explaining the configuration of applied measurement in this embodiment, and Figure 6 is a diagram for explaining the configuration of applied measurement. The explanatory diagrams, FIGS. 7 and 8, are diagrams for explaining the calculation method of approximate values.・Second target ・Third target

Claims (2)

[Claims] (1) A subtense bar for three-dimensional measurement, characterized in that three targets are provided at predetermined intervals on a subtense bar used for measurement to determine the position of each point from observation between at least three points. (2) The subtense bar for three-dimensional measurement according to claim 1, wherein the three targets are spherical.