JPH0321845A - Curvature calculation device - Google Patents

Abstract

PURPOSE:To remove an unfavorable effect to a curvature calculation according to a measuring error and to perform the accurate measurement by introducing an evaluation function to evaluate the approximation degree of polynominal expression showing the displacement measured at each measuring point and calculating the curvature thereby. CONSTITUTION:The displacement is given to an object to be measured in an operation part 4 and the displacing amount is measured at the plural measuring points of the object to be measured in a measuring part 3, then the curvature is calculated in a curvature calculating part 5 based on the above measurements. At this time, a measuring area of the object to be measured is divided into the plural areas by an area division setting part 6 in accordance with a specified evaluation value. Outputs of the division polynominal expression including undecided coefficients showing the displacing amount of the object to be measured and the evaluation function evaluating the approximation degree are made for every area by an outputting part 2 for polynominal expression and function. Then, the undecided coefficients in the polynominal equation are decided by a coefficient deciding part 1 in accordance with the evaluation function, measured displacement amount and boundary condition between the areas. Thus, a suitability of the area division is discriminated by an evaluation amount discriminating part 7 based on the amount evaluated from the evaluation function, and a re-division of the setting part 6 is commanded when the area division is unsuitable.

Description

[Detailed description of the invention] [Table of contents] Overview Industrial field of application Conventional technology (Figs. 3, 6, 12, 13) Problems to be solved by the invention (Figs. 8, 11) Figure) Means for solving the problem (Figure 1) Effect (Figure 1) Examples (Figure 2, Figure 4, Figure 5, Figure 6, Figure 7, Figure 9, Figure 10) ) Effects of the invention [Summary] An action part that applies displacement to the object to be measured, a measurement unit that measures the amount of displacement at a plurality of measurement points of the object to be measured, and a curvature calculation that calculates the curvature based on the amount of displacement. The present invention relates to a curvature calculation device having a simple structure, which can eliminate the adverse effects of measurement errors in the amount of displacement obtained at a measurement point, and calculate the curvature of an object to be measured with high accuracy. A region division setting unit that divides the measurement region of the object to be measured into a plurality of regions based on a predetermined evaluation quantity, and a piecewise polynomial that includes an undetermined coefficient representing the amount of displacement of the object to be measured for each region. , a polynomial/function output unit that outputs an evaluation function that evaluates the degree of approximation by the polynomial, and a coefficient determination unit that determines undetermined coefficients based on at least the evaluation function, the measured displacement amount, and the boundary conditions between regions. and an evaluation amount determination unit that determines whether or not the area classification is appropriate based on the evaluation amount derived from the evaluation function, and instructs the setting unit to reclassify the measurement area if it is not appropriate. It is a placating structure.

(Industrial Application Field) The present invention relates to a curvature calculation device used for measuring material properties of flexible structures such as plastics, and in particular includes an action part that displaces an object to be measured, and a plurality of The present invention relates to a curvature calculation device that includes a measurement point that measures the amount of displacement at a measurement point, and a curvature calculation section that calculates curvature based on the displacement of an object to be measured.

In recent years, in response to demands for higher functionality and lighter weight products, the field of structural design has sought to reduce the thickness of materials using plastic molding technology, creating the ultimate design that provides the minimum necessary strength. is being attempted.

Generally, when a flexible structure undergoes bending deformation, if the material properties (Young's modulus and Boisson's ratio) are given, stress etc. can be determined by knowing the radius of curvature.

(Prior Art) Conventionally, in order to measure the mechanical properties of flexible structures such as thin plastic materials, the applicant has developed a "measuring robot" (
(Japanese Patent Application No. 63-228354).

The outline of the measuring robot is as shown in Figure 3.
Cartesian robot 31.3 with a three-axis movement mechanism
2, a rotation mechanism 34 provided on the robot 31,
An object to be measured 33 such as a thin plastic material, a load pressing rod 38 attached to the robot 32 via a capacitor 35, and a capacitor 3 at the tip of the robot 31.
Probe 37 for displacement detection attached via 5
It has the following.

When measuring the curvature of an object to be measured using the measuring robot, the present applicant has conventionally proposed a method using a supplementary formula for a spline function (Japanese Patent Application No. 1-67836).

FIG. 13 shows a conventional curvature calculation device.

As shown in the figure, the device includes a displacement measuring section 133 that measures the amount of displacement of the object to be measured at a plurality of measurement points in response to a load applied to the object, and a displacement measuring section 133 that applies displacement to the object to be measured. an action section 134; a compensation equation setting section 132 that sets a spline interpolation equation as a polynomial expressing displacement for each region (one dimension) with the measurement point as a node; It has a coefficient determining unit 131 that determines each coefficient of the supplementary formula based on the spline interpolation formula that has been determined, and a curvature calculation unit 135 that calculates the curvature based on the determined spline interpolation formula. .

Here, the displacement measuring section 133 corresponds to the probe 37 attached via the force sensor 35 provided to the robot 31 of the measuring robot shown in FIG. This corresponds to the above-mentioned force sensor 36 and rod 38 attached to 32.

A specific example of settings for measuring the object to be measured is shown in FIG. One side of the test plate 61 is fixed with fixing plates 64a and 64b, and the rod 38 is applied to a point 63 near the other side to apply a load, and the amount of displacement at each measurement point 62 is measured.

When calculating the curvature using the conventional device, as shown in the flowchart of FIG. In step SA2, a spline interpolation formula of a predetermined degree (lower than the number of measurement points, e.g., m = 3rd degree) can be continuously differentiated (m-1) times for each region in step SA2. Set it as follows.

Determining each coefficient by using the fact that the spline interpolation formula passes through the measurement points (nodes) measured by the displacement measurement unit 133 in step SA3 and that the derivative of the spline interpolation formula is continuous at the nodes. I can do it.

Based on the spline interpolation formula obtained in step SA4, the curvature calculation unit 135 calculates the curvature by performing calculations such as second-order differential of the compensation formula.

[Problem to be solved by the invention]

By the way, as explained above, in the conventional curvature calculation device, a second-order differentiable and continuous function can be obtained by approximating the interpolation formula in cubic terms, so the curvature can be easily calculated. I can do it.

However, as shown in FIG. 11, the spline interpolation formula always passes through each measurement point, and the measurement data generally includes errors.

Therefore, when the measurement error is small compared to the amount of displacement,
The radius of curvature can be calculated with some degree of accuracy using the spline interpolation formula, but if the amount of displacement is relatively small, the influence of measurement errors becomes large, and the spline interpolation formula cannot calculate the curvature with high accuracy. becomes difficult. 8th
The figure shows the results of calculating curvature using a conventional device.

In the figure, 80 is a reference plane with 0 curvature, 81 is the curvature in the X direction, 82 is the curvature in the Y direction, and 83 is the torsion rate. The problem was that the measurable range was limited.

Therefore, the present invention has a simple structure, eliminates as much as possible the negative influence on curvature calculation due to measurement errors of discrete displacement amounts obtained at measurement points, and can accurately calculate the curvature of the object to be measured. This was made for the purpose of providing a curvature calculation device.

(Means for Solving the Problems) In order to solve the above-mentioned technical problems, the present invention, as shown in FIG. In a curvature calculation device that includes a measurement unit 3 that measures the amount of displacement of the object to be measured and a curvature calculation section 5 that calculates the curvature based on the displacement of the object to be measured, the measurement area of the object to be measured is calculated based on a predetermined evaluation amount. A region segmentation setting unit 6 that segments a plurality of regions, a segmentation polynomial that includes an undetermined coefficient that represents the amount of displacement of the object to be measured for each region, and a polynomial that outputs an evaluation function that evaluates the degree of approximation by the polynomial. Function output section 2
a coefficient determining unit 1 that determines an undetermined coefficient of the polynomial based on at least an evaluation function, a measured displacement amount, and a boundary condition between regions; The configuration includes an evaluation amount determining section 7 that determines whether or not the classification is appropriate, and instructs the setting section 6 to reclassify the measurement area if it is not appropriate.

Here, "curvature" refers to ΔS → 0 when point P moves along curve r by arc length ΔS and reaches P', and the angle between the tangent at P and the tangent at P° is Δω. It means the limit.

As shown in FIG. 6, the curvature of the displacement surface along the X axis when bending deformation is applied to the object to be measured can be determined by second-order partial differentiation of the displacement surface with respect to X. The curvature along the y-axis can be similarly determined. The torsion rate can be determined by first-order partial differentiation on the displacement surfaces X and y, respectively.

(Function) When calculating the curvature according to the present invention, as shown in FIG. Measure the displacement at the point.

The polynomial/function output section 2 outputs a piecewise polynomial including undetermined coefficients for approximately expressing the displacement of the object to be measured for each region divided by the region section setting section 6.

If the highest degree of the piecewise polynomial is, for example, m-th degree, continuous differentiation is possible m-1 times at the boundary of each area.

As such a piecewise polynomial, each region (1; 1・1, 2,
, k), for example, the following spline function (m is an odd number) may be used.

f (X) ”at, .xlvI+at, +11-
I X'″″″”4 easeat, ,X +aj,
.

? Undetermined coefficient at+mmat. m-■,..., at,
. is determined by the conditions described below.

Furthermore, the term "area" refers to an area set on the object to be measured, which may be one-dimensional, two-dimensional, or three-dimensional. When a certain one-dimensional line segment [a, bl on an object is divided into k regions (intervals), [xo + xtl I [X
1 +X2] e"" t [Xk-1 tXkl
■It is written like this: a"Xo. b-xk.

Note that the node X of each boundary generated by dividing the area according to the present invention. , x1, ..., Xk are n +1 measured by the measuring section 3, unlike the conventional spline interpolation
The position of the node is not determined by where the measurement point is taken, but is determined based on the above-mentioned evaluation quantity or an external instruction, and generally the position of the node is determined based on the evaluation amount or external instructions. The number n11 does not match the number k of nodes.

On the other hand, the evaluation function is a function for evaluating the degree of approximation by the piecewise polynomial.

If we impose the condition that the spline interpolation formula always passes through the measurement points as in the past, an evaluation function is not particularly necessary.
For the following reasons, we decided to introduce an evaluation function without imposing the constraint that the measurement point must always be passed as in the past.

That is, the measurement of displacement by the measurement unit 3 generally involves measurement errors, and it is impossible to eliminate measurement errors from the discrete displacement amounts measured at each measurement point, and the polynomial is This is because if a restriction is imposed that the measurement point must be passed through, the calculation of curvature, which requires second-order differentiation, may actually deviate from reality.

Therefore, in the present invention, instead of requiring complete agreement between the displacement expressed by the piecewise polynomial and the measured displacement at each measurement point, an evaluation function that can evaluate the degree of approximation of the polynomial is provided. was introduced so that the polynomial can better approximate the real displacement.

As an example of such an evaluation function, for example, the polynomial 1
The sum obtained by squaring the difference between the amount of displacement expressed from this and the amount of displacement at the measurement point for all measurement points, the sum of the absolute value of the difference over all measurement points, and evaluations as mentioned in the examples. Function; σ1 Σ WI I (s(xi)−y5)
l 2 ■However, Wi: weight function, S(Xz)
; Spline function, Vi + measurement data, i; There are parameters indicating the position of the measurement point.

In this way, each coefficient of the piecewise polynomial set by the polynomial/function setting section 2 is determined by the evaluation function, the displacement measured at each measurement point by the displacement measuring section 3, and the area section setting section 6. It is determined by the m-1 times continuous differentiability condition that the piecewise polynomial should satisfy at the boundary of the area.

At this time, the evaluation amount determining unit 7 determines whether the set area classification is appropriate based on the evaluation value derived by the evaluation function determined based on the area classification set by the area classification setting unit 6. to judge.

In other words, if the evaluation function is the sum of the squares of the differences between the displacement amount expressed by the polynomial and the measured displacement amount over all measurement points as described above, there is no measurement error. In this case, the smaller the evaluation value, the better the approximation. However, if there is a measurement error, it cannot be said that the approximation is necessarily good even if the evaluation value is made smaller than necessary. This becomes clear if we consider that if there is a measurement error, the evaluation value will not be zero even if a true function is used. Therefore, if there is a measurement error, a certain threshold is set based on the error of the measurement system, and it is determined whether the classification is appropriate based on whether the evaluation value is larger or smaller than the threshold. If the evaluation value is large, a command is issued to the area classification setting section 6 to reclassify (more detailed classification).

(Example) Next, a curvature calculation device according to an example of the present invention will be described.

As shown in FIG. 2, the curvature calculation device according to this embodiment has the following features:
An action unit 14 that applies displacement to the object to be measured, a measurement unit 13 that measures the amount of displacement at a plurality of measurement points of the object to be measured, a microcomputer (MPU) 20, and other components necessary for calculating curvature, stress, etc. A data storage section 21 stores data, an output section 23 such as a display section or a printer device outputs data, and a setting section 18 includes a keyboard for inputting data.

As shown in the figure, the acting section 14 includes the aforementioned robot 14a (32), a force measuring section 14b (36), and a robot that controls the drive of the robot based on signals etc. from the force measuring section 14b. It has a control section 14c.

The measurement unit 13 includes a robot 13a (31), a displacement measurement unit 13b, and a control unit 13c that controls the drive of the robot 13a.

Furthermore, the functions of the MPU 20 include a calculation section 22 that performs calculations for calculating curvature, and a measurement section 13.
and a command section 24 that issues commands to the action section 14, and a stress calculation section 25 that calculates stress and the like from the obtained curvature.

Further, as shown in the figure, the calculation section 22 includes a curvature calculation section 15 that calculates the curvature based on a spline function as a piecewise polynomial expressing the displacement of the object to be measured as a function of position, and A region division setting unit 16 that divides the measurement region into a plurality of regions based on a predetermined evaluation quantity, the above-mentioned spline function as a piecewise polynomial including an undetermined coefficient that approximates the displacement of the object to be measured for each region, and the a polynomial/function output unit 12 that outputs an evaluation function for evaluating the degree of approximation of the spline function; and determining undetermined coefficients of the spline function based on at least the evaluation function, the measured displacement amount, and the boundary conditions between regions. a coefficient determining unit 11 that determines whether or not the area classification is appropriate based on the evaluation amount derived from the evaluation function, and if it is not appropriate, the setting unit 1
6, it has an evaluation amount determination unit 17 that instructs reclassification of the area.

Further, as shown in the figure, the polynomial/function output section 12 is configured to generate a spline function that determines the form of a spline function (piecewise polynomial) corresponding to each region based on the region section set by the region section setting section 16. A function form determining unit 12b, an evaluation function form determining unit 12c that determines the evaluation function form based on the area division, and a spline function determined by the spline function form determining unit 12b and the evaluation function form determining unit 12c. and a coefficient determining formula deriving unit 12a that derives a coefficient determining formula for determining the undetermined coefficient based on the evaluation function form.

The operation of the curvature calculation device according to this embodiment will be explained.

As shown in the flowchart of FIG. 5, in step SJI, the setting unit 18 sets the number k of area divisions and the measurement area [a, bl] to the area division setting unit 16 in advance.

For example, when the number of measurement points is n, k≠n (k
In the case of mn, it is the same as the conventional spline interpolation formula and there is no need to perform smoothing).
For example, k-2) is output.

When the region division setting section 16 sets the region division, the spline function form determination section 12b of the calculation section 22 sets an undetermined coefficient for each region based on the division and the setting of the setting section 18 in step SJ2. A polynomial of degree m (odd number, e.g. 3) containing ? make them respond.

Further, the evaluation function form determining unit 12c determines the form of the evaluation function by setting the number of measurement points and the like by the setting unit 18.

Here, σ1ΣWr I (S(Xt)-3'z)
I ” ■i However, town: Weight function, s(xt) #Spline function, i: A parameter indicating the position of the measurement point will be used.

In step SJ3, the coefficient determining formula deriving unit 12a generates a determining formula that should be satisfied by the undetermined coefficients of each polynomial based on the spline function and the evaluation function set for each region and the continuity condition that should be satisfied between each segmented region. will be derived.

That is, the correspondence of the set m (= 3) degree polynomial to each k segmented area j is SJ(X)-aJ, 3X3+aJ, 2X2+aJ,
IX+aJ, O, and each area [xo l X 1] * [xt sX
2] *”” * Boundary (node) of [Xk- 1 *Xk] XO (-a) #X1+X2+..., Xk-■+
At Xk (=b), the spline function and the derivative of the spline function s(0)(x) (c=1.2,...,
A determining formula to be satisfied by the undetermined coefficient is derived based on a formula derived from the variational principle from the boundary condition that m-1) should be continuous and the condition that the evaluation function should take a minimum value.

In step SJ4, the displacement amount measured at each measurement point determined by the measuring unit 13 is substituted into the determining formula and the displacement applied by the acting unit 14, and in step SJ5, each undetermined displacement amount is substituted into the determining formula. Determine the coefficients.

In step SJ6, the evaluation amount determining unit 17 substitutes the coefficient determined by the coefficient determining unit 11 into the evaluation function,
Derive the evaluation quantity σ.

A predetermined threshold value σ for the evaluation amount σ derived in step SJ7. If the evaluation amount σ is larger than the threshold σ0, it is determined that the area classification by the area classification setting unit 16 is not appropriate, and the area classification setting unit 16 is instructed to change the area classification in step SJ8. A more detailed reclassification is commanded, and the above procedure is repeated again using the relevant classification.

On the other hand, in step SJ7, the evaluation amount σ is the threshold value σ. If it becomes smaller than , the classification by the area division setting unit 16 is deemed to be sufficient, and in step SJ9, a division polynomial having the coefficients determined by the coefficient determining unit 11 is used to represent the displacement of the object to be measured. As the curvature calculation unit 1
It will be output to 5.

As shown in FIG. 4 when spline smoothing is performed according to this embodiment, fluctuations that are thought to be based on measurement errors are smaller than in the conventional case (FIG. 11).

FIG. 6 shows an outline of the object to be measured, and has a structure that allows easy comparison with theoretical values later. FIG. 7 shows the amount of displacement measured by the measuring section 13 when a highly linear metal is used as the object to be measured.

In FIG. 7, the outline 70 is a reference plane with zero displacement, and 71 indicates the amount of displacement measured in this example. For reference, the reference numeral 72 indicates the result of structural analysis using the limit element method, indicated by a dotted line.

FIG. 9 shows the curvature calculated by the curvature calculation device according to this embodiment.

In the figure, reference numeral 90 indicates a reference plane with a curvature of 0, 91 indicates a curvature in the X direction, 92 indicates a curvature in the Y direction, and 93 indicates a torsion rate.

FIG. 10 shows the curvature 101 in the X direction determined by this example.
, is compared with the theoretical solution 102 obtained by the toleration element method, and as shown in the figure, it can be seen that they almost match.

The reason why the values are slightly different at both ends of the fixed part is due to the difference in boundary conditions: in theory, the plate is fixed at one end, but in the experiment, it is fixed using bolts.

〔Effect of the invention〕

As explained above, in the present invention, instead of imposing the condition that the polynomial expressing the displacement measured at each measurement point always passes through the measurement point as in the conventional case, an evaluation function is used to evaluate the degree of approximation of the polynomial. By introducing this method, the curvature is calculated. Therefore, the curvature of the object to be measured can be calculated with high accuracy by eliminating as much as possible the negative effects of measurement errors associated with the amount of displacement measured at each measurement point.

In addition, according to the present invention, the curvature can be determined with high accuracy based on the amount of displacement measured at each measurement point, so it is possible to measure strain and stress of a harder object to be measured, and it is possible to perform highly accurate measurements at low cost. This means that it can be realized.

[Brief explanation of drawings]

The first is a block diagram of the principle of the present invention, FIG. 2 is a block diagram of an embodiment, FIG. 3 is a diagram showing a measuring robot according to an embodiment, and FIG. 4 is a diagram illustrating spline smoothing according to an embodiment. , FIG. 5 is a flowchart showing spline smoothing according to the embodiment, and FIG. 6 is a diagram showing the object to be measured according to the embodiment (conventional example).
FIG. 7 is a diagram showing the amount of displacement measured by the example, FIG. 8 is a diagram showing the curvature determined by the curvature calculation device according to the conventional example, and FIG. 9 is a diagram showing the curvature determined by the curvature calculation device according to the example. FIG. 10 is a diagram showing a comparison between the curvature obtained by the curvature calculation device according to the embodiment and a theoretical solution, FIG. 11 is a diagram showing spline interpolation according to the conventional example, and FIG. 12 is a diagram according to the conventional example. The flowchart and FIG. 13 are flowcharts according to a conventional example. 1, 11...Coefficient determination unit 2...Polynomial/function output unit 3...Measurement unit 4...Action unit 5...Curvature calculation unit 6...Area division setting unit 7...Evaluation Quantity discrimination part (a) (1)) Actual example, S word ↑5! Rerobot TL Claw T Diagram
3 Diagram whistle 5 Inside ×/6\Y Is there any measurement target in the embodiment (conventional example)? ! ! Figure 1 Figure 6 Figure 7i? ! Example ← 2yo 98 deletion I mi history 0L1 [and PuheT
Figure 7 Stress length 2I! ! Diagram 10 shows the curved pavilion and the structure of the pier number 2.Example 11
Figure No. 12 [

Claims (1)

[Claims] An action section (4) that applies displacement to the object to be measured, a measuring section (3) that measures the amount of displacement at a plurality of measurement points of the object to be measured, and an action section (3) that applies displacement to the object to be measured based on the amount of displacement of the object to be measured. The curvature calculation unit (
5) A curvature calculation device comprising: a region division setting unit (6) that divides the measurement region of the object to be measured into a plurality of regions based on a predetermined evaluation amount; a polynomial/function output unit (2) that outputs a piecewise polynomial including undetermined coefficients and an evaluation function for evaluating the degree of approximation by the polynomial; a coefficient determination unit (1) that determines an undetermined coefficient of the polynomial based on the evaluation function; and a coefficient determination unit (1) that determines whether or not the region division is appropriate based on the evaluation amount derived from the evaluation function, and if it is not appropriate, the setting unit A curvature calculation device characterized in that, in contrast to (6), the curvature calculation device further comprises an evaluation amount determination unit (7) that instructs reclassification of the measurement area.