JPH0526670A - Three-axis reed spring type inclination measuring device - Google Patents

Abstract

PURPOSE:To provide a fixed inclination measuring device with a simple structure. CONSTITUTION:Strip type reed springs 1, 2, 3 fixed on three rectangular axes X, Y, Z of a coordinate body at one end and having loads at the other end are fitted with the reed longitudinal direction set perpendicular to the axis and the perpendicular line of both surfaces of the reed set parallel with the axis, electronic displacement or strain measuring means measuring the deflection or strain at the tips of the springs by the gravitational component forces applied to the tip loads are provided near the reed tips or on the reed surfaces, the gravitational component forces of three axes of the coordinate body are obtained, and the inclination data of the coordinate body are calculated.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electronic tilt measuring device, and more particularly to a fixed type device having electronic measuring means and having no movable part.

[0002]

2. Description of the Related Art Conventionally, various electronic tilt measuring devices having a built-in microcomputer and having no moving parts have been developed.

[0003]

However, the conventional electronic inclinometer has many components of the mechanism, and various specific calculations are required in order to adapt to the inclination calculation method.

An object of the present invention is to provide a fixed tilt measuring device having a simple structure.

[0005]

According to the present invention, as a basic element of tilt measurement, a small reed spring having a fixed end on each of the three axes of a coordinate body and a load on the free end is orthogonal to each of the axes. The vertical line of the lead surface is attached parallel to each axis, and the method of electronically measuring the displacement of the free end of the lead or the distortion of the lead surface by gravity component force is adopted. Figure 5 in general mechanics
As shown in (a) of FIG. 5 and (b) of FIG. 5, in the XYZ three-axis coordinate system, each axis positive oblique of the arbitrary space vector γ becomes each axial cosine, and each axis three component force (x, y, z) is determined. .. Further, the three-component forces x, y, z of this orthogonal coordinate system are converted into three elements γ, θ, τ of the polar coordinate system.

According to the present invention, when the gravity value is taken for the space vector corresponding to this, the positive oblique lines to the three axes become the output of each axis, and that becomes the force value of the three axes of gravity as it is.

[0007]

As described above, the fact that the triaxial component force of the gravity vector is based on the standard form of the coordinate value calculation of the Cartesian coordinate system of the dynamics makes it possible to combine these component force values and calculate the inclination specifications of this coordinate body. The mechanics formula can be applied as is.

That is, the 0XY plane of this XYZ coordinate body is the bottom surface, the orthogonal axis is the Z axis, and the inclination characteristics of the Z axis with respect to the vertical line are the front and rear inclination, the left and right inclination, and the maximum inclination. Including, the front and rear surfaces orthogonal to the floor surface, the left and right surfaces, and the maximum inclined surface. The inverse normal cut of the ratio of the gravity component force to the intersection line with the floor surface and the Z-axis gravity component force determines each inclination angle. However, no special arithmetic expression is required for this calculation, and the conversion formula between the orthogonal coordinate value and the polar coordinate value of general mechanics can be applied as it is.

[0009]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS An embodiment of the present invention will be described below with reference to the accompanying drawings.

FIG. 1 shows reed spring type gravity sensors 1, 2 and 3 mounted on the three axes of an XYZ triaxial coordinate body. The gravity sensor is an ultra-small rectangle, a strip type, and if an example is shown, the length is 6 m.
It is also possible to use a nickel-white lead spring made of a material having m, a width of 5 mm, and a thickness of 0.08 mm and having the size described below. In that case, the length, width, and thickness are almost proportionally small. This lead spring is attached to the mounts 10-1, 10-2 including the corresponding shaft,
10-3 is fixed to the short side of the lead and the free ends are weights m-1, m-2 and m- of 1.0 gram each.
3, the lead longitudinal direction is orthogonal to the applicable axis, and the orthogonal lines on the front and back surfaces of the lead are attached parallel to the applicable axis.

In this case, the loads m-1 and m of the respective lead springs
-Lead spring can be freely moved by gravity component acting in -2 and m-3.
The end is displaced positive and negative depending on the direction of the component force parallel to the relevant line, and
Positive and negative strain is generated on both surfaces of the lead spring. This displacement is maximum
It is about 0.2 mm. The force of each axis is gravity vector.
(W vector) is an orthographic shadow, and this value is W₁，
W ₂, W₃And the resulting displacement of each lead spring is δ
₁, Δ₂, Δ₃, Distortion S ₁, S₂, S₃If so,
Since the position is minute, it is proportional to each component force, so δ₁∝W₁, Δ
₂∝W₂, Δ₃∝W₃In the same way, S₁∝W₁, S
₂∝W₂, S₃∝W ₃Becomes That is, each axis lead spring
The displacement or strain of represents the gravity component of each axis.
It For the sake of simplicity, if the gravity value is set to 1, the gravity component of each axis will be
Since the direction cosine value of the gravity vector is shown, each axis lead spring
The displacement or strain of corresponds to each axial cosine of the gravity vector
The Rukoto.

When the above-mentioned triaxial lead spring is attached to each of the triaxial corresponding shafts, there is no difference in the direction of the longitudinal axis of the lead from each axial lead, even if it is the direction of the circumference of the applicable shaft. As shown in FIG. 1, the X-axis and Y-axis leads are attached below the 0X line and 0Y line, that is, the longitudinal axis direction is parallel to the -Z axis. The Z-axis lead is attached with the longitudinal axis parallel to the 0X or 0Y line. In the case shown, the Z-axis lead is attached parallel to the X-axis.

FIG. 2 shows an example of displacement measuring means of the gravity component force sensor. The component force displacement measuring means of FIG. 2 has the same structure as that of the XYZ triaxial lead springs of FIG. 1, and is shown as P ₁ , P ₂ and P _{3 in} FIG. 2 shows P ₁ corresponding to the X-axis lead spring. Therefore, in FIG. 2, the lead spring 1 is a cross-sectional view orthogonal to the thickness direction. Therefore, the XX axis is orthogonal to the longitudinal axis of the lead spring, and the vertical line on the lead surface of the spring is X.
-Parallel to the X-ray. Therefore, the movement of the load due to the gravity component force is parallel to the XX line.

Coil L₁And L₂Is the high frequency power supply OSC
A pair of adjacent inductors in the bridge circuit
Composing the system. Coil L₁And L₂Is the weight of the reed spring
The surfaces of m-1 are opposed to each other with a small distance from the left and right.
On the bridge arm facing these two inductances
Two sets of rectifiers D, which are unidirectional when viewed from the power supply OSC ₁
And D₂Are connected. In such a configuration,
The tip of the reed spring receives a gravitational force component in the XX direction,
When placed, each coil L₁And L₂And brass weight of weight m-1
The distance to the metal surface changes and the coil L₁And L₂Inn of
A difference in dactance is generated, and output is output to output terminals 31 and 32.
To live.

The lead spring displacement measuring means can be replaced with a lead spring strain measuring means. In FIG. 3, a strain gauge R ₁ , above and below the surface of the Z-axis reed spring,
Joining R ₂ . A strain gauge is similarly joined to the X-axis and Z-axis lead springs. The strains of the gauges R ₁ and R ₂ in FIG. 3 are measured by the bridge circuit as shown in FIG. In this case R _1, R ₂ becomes two neighboring resistance bridge arms which are arranged in the forward direction as viewed from the power source, the midpoint of R ₁ and R _2, second resistor arms facing the R _1, R ₂ The middle point is the bridge output terminals 41 and 42. While the distraction surface sides of the lead spring in such a circuit, the other strain to cause distortion of the positive and negative university by compression from the output terminals 41 for generating as a function of the algebraic difference between R ₁ and R ₂ The double output is generated and the strain measurement sensitivity is improved. On the other hand, the temperature error between R ₁ and R ₂ has the same sign, and therefore has the effect of being compensated.

In the above description, a high frequency variable inductance bridge type displacement gauge is used as the lead spring displacement measuring means and a strain gauge type strain gauge is used as the lead spring strain measuring means. In the former, photoelectric type or condenser type displacement is used. Alternatively, the latter may be replaced by a solid semiconductor type strain measuring means in which a storage resistance element is vapor-deposited on an elastic silicon substrate.

As described above, the component force of the XYZ triaxial gravity vector of the coordinate body can be measured by the triaxial reed spring type gravity sensor. This is the same as the relationship between the space vector in the XYZ coordinate system of general mechanics, the positive oblique shadows of each axis, and the component force values.

Further, by combining these gravitational force components of the three axes of XYZ, it is possible to calculate the X inclination specifications of the XYZ coordinate system with respect to the vertical line.

That is, in this case, as shown in FIG. 6, in the 0-XYZ coordinate system in which the 0-XY plane is the floor surface and the 0Z axis is the orthogonal axis, the front and rear surfaces, the left and right surfaces, and the maximum inclination that include the Z axis and are orthogonal to the floor surface. The angle formed by the projection of the vertical line on each surface to the Z axis in each surface is the inclination of the Z axis with respect to the vertical line in each surface, and this is the intersection line with the floor surface of each surface. Is the arctangent of the gravity component force and the Z-axis component force ratio to the front-back axis, the left-right axis, and the maximum inclination line.

No special calculation is required for the calculation of the front-back inclination, the left-right inclination, and the maximum inclination, and the formula for converting the rectangular coordinate value of general mechanics into a polar coordinate system can be applied as it is.

In order to show this, the following general mechanics literature General mechanics Translated by Planck, translated by Hirokazu Terasawa Cartesian coordinate system P3
0-31 Basic physics 1 Mechanics Kawaguchi, Mitsutoshi Drawings and various formulas are abstracted from the spherical coordinate system P25.

First, when abstracted from the above document, FIG. 5A shows that the coordinate value of the space point P is OP in the Cartesian coordinate system 0-XYZ.
It is represented by the three sides x, y, z of a right-angled hexahedron whose diagonal line is. Let ξ, η, and the direction cosine value of each side of the OP vector
Let ζ and OP = γ

[0023]

[Formula 1] γ ² = x ² + y ² + z ²

[0024]

## EQU2 ## x = γcoξ, y = γwoη, z = γcos
ζ

[0025]

## EQU3 ## cos ² ξ + cos ² η + cos ² ζ = 1

Further, when abstracted from the literature, in FIG. 5B, in the spherical coordinate system, the intersection point of the perpendiculars from the point P (x, y, z) to the xy plane is point B, and OP = γ, OP vector and Z The angle formed by the axis is θ, and the angle formed by the OP vector and the X axis is ψ. The relationship between the Cartesian coordinate system (x, y, z) and the spherical coordinate system (γ, θ, ψ) is

[0027]

X = γ sin θ cos ψ

[0028]

## EQU5 ## y = γ sin θ sin ψ

[0029]

## EQU6 ## z = γ cos θ

[0030]

(7) γ ² = x ² + y ² + z ²

[0031]

Tan ψ = y / x

[0032]

[Equation 9]

It becomes Returning to the description of this embodiment, FIG.
In (a) and (b) of Fig. 6 and Fig. 6 in which this is applied to this example, the gravity vector is taken as the W vector.

[0034]

(10) W = γ

Let the output value of the lead type gravity sensor be W ₁ ,
Assuming W ₂ and W ₃ ,

[0036]

[Equation 11] W ₁ = x

[0037]

[Equation 12] W ₂ = y

[0038]

[Equation 13] W ₃ = z

Therefore, according to the formula [1],

[0040]

[Equation 14] W ₁ ² + W ₂ ² + W ₃ ² = W ²

If the gravity value is constant and W = 1, then W ₁ , W ₂ , and W ₃ at that time are (W ₁ ) ₀ , (W ₂ ) ₀ ,
As (W ₃ ) ₀ , from the equation (2),

[0042]

(15) (W ₁ ) ₀ = cos ξ

[0043]

## EQU16 ## (w ₂ ) ₀ = cos η

[0044]

## EQU17 ## (W ₃ ) ₀ = cos ζ

Therefore, in this case, from the formula [3],

[0046]

[Equation 18] (W ₁ ) ₀ ² + (W ₂ ) ₀ ² + (W ₃ ) ₀ ² = 1

It becomes

Further, the front-back inclination is the Z-axis component force W on the 0XZ plane.
X of a right triangle whose base is ₃ and X-axis component force W ₁ is a vertical side
It is the axial force diagonal, and if this is P

[0049]

[Formula 19] P = tan ⁻¹ (W ₁ / W ₃ ).

Similarly, the left-right tilt angle is the Y-axis component force diagonal of a right triangle having the Z-axis component force W ₃ as the base and the Y-axis component force W ₂ as the vertical side in the 0YZ plane. ,

[0051]

[Equation 20] R = tan ⁻¹ (W ₁ / W ₃ ).

It becomes The 0 maximum inclination angle M Tosureba which the bottom of the Z-axis force component W ₃ at 0BP plane in FIG. 6
It is the included angle between the BP and the 0P vector of a vertical triangle 0BP having the component force 0B of the P line as the vertical side, and this is M. The above is based on the Cartesian coordinate system diagram of FIG. 5 (a).
The spherical coordinate system of

[0053]

(21) M = θ

It becomes Therefore, from the formula [Equation 9]

[0055]

[Equation 22]

It becomes Also, if the direction of maximum inclination is denoted by σ, then σ = ψ, which is given by the formula [Equation 8].

[0057]

(23) σ = tan ⁻¹ (W ₂ / W ₁ )

Is required. In addition, forward tilt P, left and right tilt
Between the maximum slope M and the maximum slope M

[0059]

TanP = tanM × cosσ

[0060]

(25) tanR = tanM × sin σ

Therefore,

[0062]

(26) P = tan ⁻¹ (tanM × cosσ)

[0063]

R = tan ⁻¹ (tan M × cos σ)

In the case of computing the tilt specifications by a computer, it is general to calculate and display four elements of the front-back tilt P, the left-right tilt R, the maximum tilt M, and the maximum tilt direction σ from the above-mentioned specifications.

7 and 8 are flowcharts of the calculation of the inclination specifications by the above-mentioned relational expression by the computer in this embodiment. Fig. 7 shows ± 4 both forward and backward and left and right
This is the case of 5 ° or less. At this time, the front and rear inclination P and the left and right inclination R are immediately calculated as shown in FIG.
Calculate by formula. Further, in the case where the front-rear and left-right inclination is ± 45 ° or less, it is generally sufficient to calculate the P and R values as the inclination measurement. Therefore, the maximum tilt M and its direction are calculated by P, R
After the calculation of, it is performed as necessary. This calculation is based on [Equation 22] and [Equation 23]. These results are displayed by adding P and R, and if necessary, M and σ.

Next, the front and rear and left and right inclinations are ± 45 ° or more ±
The flow chart of FIG. 8 shows the entire range including reversal, rollover, and somersault up to 360 °. In this case, since the range of motion is wide and the change in motion is severe, first, [Formula 22] and [Formula 23] are given. The maximum inclination M and its direction σ are calculated by the equations, and then the front-rear inclination P and the left-right inclination R are calculated by the equations [26] and [27]. This is because the output of inputs W ₁ , W ₂ and W ₃ is used in order to calculate the maximum slope of [Equation 22] and the calculation of the direction thereof by [Equation 23], in order to take the form of an inverse normal division operation of the ratio of the cosine. The error of is automatically deleted and the measurement accuracy is improved. Therefore, the P and R values calculated from M and σ can be improved in accuracy by the formulas [19] and [20], which are calculated as they are W ₁ , W ₂ and W ₃ . The display is a P, R, M, σ four-element system.

[0067]

The 3-axis lead type gravity sensor of the present invention has a simple structure and can accurately measure the 3-axis component force value of gravity with high response. In addition, using this, the inclination specifications can be calculated with high accuracy by using the mechanics formula as it is.

[Brief description of drawings]

FIG. 1 is a perspective view showing an example of a triaxial gravity sensor.

FIG. 2 is an explanatory diagram showing an example of displacement measuring means of a gravity sensor.

FIG. 3 is a perspective view showing an example including a strain measuring unit of a gravity sensor.

FIG. 4 is an explanatory diagram showing a circuit of a distortion measuring unit.

FIG. 5 (a) shows coordinate values x, y, in a Cartesian three-axis coordinate system.
FIG. 5B is an explanatory view showing z display, and FIG. 5B is an explanatory view showing display of three elements γ, θ, ψ of the spherical coordinate system.

FIG. 6 is an explanatory view of gravity component force and inclination specification display in the present invention.

FIG. 7 is a flowchart for calculating the tilt specifications when the tilt angle is 45 ° or less.

FIG. 8 is a tilt specification calculation flowchart in the case of the entire tilt angle range.

[Explanation of symbols]

0-XYZ 3-axis coordinate axis 0ζ Gravity line W Gravity vector W ₁ , W ₂ , W ₃ Gravity component force 1,2,3 Reed spring m-1, m-2, m-3 Weights 10-1, 10-2 , 10-3 Mounting seat P ₁ , P ₂ , P ₃ Displacement measuring means L ₁ , L ₂ coil D ₁ , D ₂ diode OSC power supply 31, 32 Output terminal R ₁ , R ₂ Strain gauge 41, 42 Output terminal P Before and after Inclination R Left-right inclination M Maximum inclination σ Maximum inclination direction

Claims (1)

Claim: What is claimed is: 1. A strip-shaped lead spring having one end fixed on each of the three orthogonal axes of the coordinate body and having a load on the other end, the longitudinal direction of the lead being the corresponding axis. Attaching the orthogonal lines of both surfaces of the lead in parallel to the axis concerned, and bending or strain of the spring tip due to gravity component force acting on the tip load is provided with electronic displacement or strain measuring means near the lead tip or on the lead surface. By doing so, the gravity component force of the three axes of the coordinate body is obtained, and the tilt specifications of the coordinate body are calculated from this
Axial lead spring type tilt measuring device.