JP6524441B2 - Attitude correction method of inter-surface distance measuring device - Google Patents

Description

The present invention relates to an attitude correction method of an inter-plane distance measuring device .

In a measuring device capable of measuring the distance to the object and determining the posture with respect to the object, the initial posture may affect the measurement accuracy.
In the following, the inter-surface distance measuring device for measuring the distance between two surfaces proposed by the present applicant will be described first, and then the influence of the initial attitude on the measurement accuracy will be described. .
As one of the management of a rolling mill, it is performed to measure and manage the distance (referred to as a housing window width) between two facing surfaces of a housing window of a rolling mill housing (see, for example, Patent Document 1). During rolling by a rolling mill, it is necessary to periodically measure and control the width of the housing window because rolling load generated on the roll causes wear and deformation in the rolling mill housing and liner.
Conventionally, measurement of the housing window width is often performed using an inside micro gauge or the like. However, since the measurement work using the inside micro gauge or the like requires two or more people and the grease cleaning work of the portion to be measured is required, it is a burdensome work. In addition, skills are required for measurement work using an inside micro gauge (when it is difficult to visually determine the direction in which the measurement surface and the gauge are perpendicular, when the gauge is moved in the vicinity of the vertical) There is also a problem that measurement error due to human error is likely to occur.

Patent No. 5332606 Patent No. 5610443 gazette JP 2005-37353 A

The applicant of the present invention, as a measuring instrument suitable for use in the measurement of the housing window width, in Japanese Patent Application No. 2015-72118, a support that can be inserted between two opposing surfaces, and one end of the support Three or more distance measuring sensors for measuring a distance from a predetermined position of the inter-surface distance measuring device to one of the two surfaces, and provided at the other end of the support An inter-plane distance measuring device is proposed, comprising: three or more other distance measuring sensors for measuring the distance from a predetermined position of the inter-surface distance measuring device to the other of the two surfaces. .
The inter-surface distance measuring device calculates the inter-point distance between two surfaces and calculates the inter-surface distance from the angle between the line segment and the surface. This eliminates the need to maintain the orthogonal relationship with the surface of the housing window at the time of distance measurement, and enables measurement independent of the measurer.

  In addition, as a measuring instrument for measuring the distance to an object, for example, Patent Document 2 discloses a non-contact three-dimensional measuring instrument. The non-contact three-dimensional measuring device is composed of a rotary motor with two encoders and a laser ranging system. The encoder measures two angles φ and θ, and the laser ranging system measures the distance to the measurement target By doing this, coordinate information of the measurement point is obtained, and three-dimensional shape data of the entire shape of the measurement target is generated. Further, for example, Patent Document 3 discloses a surface texture measuring machine provided with a detector capable of taking a plurality of measurement postures with respect to a work.

  Since the angular resolution of the inter-plane distance measuring apparatus proposed by the present applicant as described above is 0.0004 ° (sin 0.0004 = 7/1000000), highly accurate measurement can be expected. In the case of the present invention, the expected accuracy is 0.04.degree. However, the actual measurement accuracy (error) before application of the present invention is 0.025 °, and it can be seen that assuming all the errors as calibration errors, it is not possible to secure double accuracy of expected accuracy. From this, the present calibration method has a problem that the measurement performance can not be sufficiently exhibited.

  In the present invention, when using a measuring instrument capable of measuring the distance to an object and obtaining the attitude with respect to the object, the attitude is corrected using its function to reduce the measurement accuracy (error). The purpose is to make it possible to ensure double precision of expected precision, improve measurement precision, and sufficiently exhibit measurement performance.

The posture correction method of the inter-surface distance measuring device according to the present invention comprises: a support that can be inserted between two opposing surfaces; and one end of the support, provided from the predetermined position of the inter- surface distance measuring device Three or more distance measuring sensors for measuring the distance to one of the two surfaces, and the other end of the support, provided on the other end of the support, from the predetermined position of the inter-surface distance measuring device Distance measuring device for measuring the distance between the two surfaces by determining the inclination with respect to the two opposing surfaces and three or more other distance measuring sensors for measuring the distance to the other surface of In order to correct the attitude of the sensor, the distance between two parallel planes is measured by changing the inclination from the state where the distance between two planes is set to a known calibrator, and measuring error is acquired. Distance measurement device based on the measurement procedure and the measurement error A procedure for determining the initial angle, and having a procedure for correcting the initial angle.
Further, another feature of the posture correction method of the inter-surface distance measuring device according to the present invention is that, in the procedure for acquiring the measurement error, the surface is measured with the inter-surface distance measuring device set in the calibrator. The inclination is changed on one end side of the inter-distance measuring device to perform distance measurement, and the measurement error at a predetermined inclination is determined. Next, the inclination is changed on the other end side of the inter-surface distance measuring device to perform distance measurement. The point is to determine the measurement error at the predetermined inclination. In this case, in the procedure for acquiring the measurement error, a neutral value of the measurement error at the predetermined inclination obtained at the one end side and the measurement error at the predetermined inclination obtained at the other end side Preferably, in the procedure of calculating the measurement error with respect to the neutral value and calculating the initial angle, the initial angle is obtained based on the measurement error with respect to the neutral value.
Further, another feature of the posture correction method of the inter-plane distance measuring device of the present invention is that, in the procedure for obtaining the initial angle, a measurement error Δ, a distance L between two surfaces of the calibrator, and an inclination θ The initial angle θ ′ is expressed by the following equation θ ′ = tan ⁻¹ (Δ · 180 / L · π · θ)
In terms of

  According to the present invention, when using a measuring instrument capable of measuring the distance to the object and obtaining the attitude with respect to the object, the function is used to correct the attitude and reduce the measurement accuracy (error) Therefore, double precision of expected precision can be secured, measurement precision can be improved, and measurement performance can be sufficiently exhibited.

It is a figure which shows schematic structure of the inter-surface distance measuring device which concerns on embodiment. It is a figure which shows typically the use condition of the inter-surface distance measuring device which concerns on embodiment. It is a figure for demonstrating the usage example of a surface distance measuring device. It is a figure for demonstrating the calculation method of surface distance. It is a figure which shows an example of a calibrator. It is a flowchart which shows the procedure which calculates | requires the initial angle of the inter-surface distance measuring device set to the calibrator. It is a figure which shows the example of the relationship of the inclination and distance which were obtained by left-right operation of the inter-surface distance measuring device. It is a figure which shows the relationship of the inter-surface distance measuring apparatus and calibrator when one side is lifted. It is a characteristic view showing the relation between a measurement error and an initial angle. It is a figure which shows the example of the relationship of the inclination and distance after reducing an initial stage angle. It is a figure for demonstrating the case where a laser tracker is made into object as another embodiment.

Hereinafter, preferred embodiments of the present invention will be described with reference to the accompanying drawings.
First, with reference to FIGS. 1 to 4, an inter-plane distance measuring apparatus which is a measuring instrument to be targeted in the present embodiment will be described.
FIG. 1 shows a schematic configuration of the inter-surface distance measuring device 1 according to the embodiment. Moreover, the use condition of the inter-plane distance measuring apparatus 1 which concerns on FIG. 2 at embodiment is shown typically. The inter-plane distance measuring device 1 is used to measure the distance between the two opposing surfaces 101a and 101b, for example, the housing window width of the rolling mill housing 100 as shown in FIG.

  As shown in FIG. 2, the inter-surface distance measuring device 1 has a support 2 which can be inserted between two opposing surfaces 101 a and 101 b in a housing window, and one of three provided at one end of the support 2. And the other three distance measurement sensors 3 b provided at the other end of the support 2. Each one of the distance measuring sensors 3 a measures the distance from the predetermined position 4 of the inter-plane distance measuring device 1 to the one surface 101 a. The other distance measuring sensors 3 b measure the distance from the predetermined position 5 of the inter-surface distance measuring device 1 to the other surface 101 b.

  As shown in FIG. 1, the support 2 includes a rod 201 and a pair of support plates 202 a and 202 b provided at both ends of the rod 201.

  The rod body 201 is composed of a pipe material 201 a and a pair of sub-pipe materials 201 b inserted at both ends of the pipe material 201 a. If the sub-pipes 201b having a plurality of lengths are prepared, the total length of the rod 201 can be freely changed by selecting the sub-pipes 201 according to the distance between the surfaces to be measured.

Further, the support plates 202 a and 202 b are formed in a disk shape, and an insertion portion 203 provided at the center thereof is inserted into an end portion of the rod body 201 and arranged perpendicularly to the rod body 201.
A contact type displacement sensor is disposed on the support plate 202a as the distance measurement sensor 3a. Similarly, a contact type displacement sensor is disposed on the support plate 202b as the distance measurement sensor 3b. The contact-type displacement sensors 3a, 3b have a stroke-type probe 301, and the air can elongate the probe 301 in its axial direction (see arrow X in FIG. 1). By using the air drive structure as the drive structure of the probe, it is possible to miniaturize, and it is possible to control the contact pressure to the surfaces 101a and 101b of the probe 301 with high accuracy. In the present embodiment, in the support plate 202a, three contact displacement sensors 3a are disposed at each vertex of an equilateral triangle. Similarly, in the support plate 202b, three contact displacement sensors 3b are arranged at each vertex of an equilateral triangle.

  Here, as shown in FIG. 2, the predetermined position 4 of the inter-surface distance measuring device 1 is a non-movable portion of the inter-surface distance measuring device 1 and a position closest to the surface 101a, that is, the contact displacement sensor 3a. Among the casing portions 302 excluding the probe 301 which is the movable portion, the position closest to the surface 101a is referred to. Similarly, the predetermined position 5 of the inter-surface distance measuring device 1 is a non-movable portion of the inter-surface distance measuring device 1 and a position closest to the surface 101 b, that is, a movable portion of the contact displacement sensor 3 b. The position closest to the surface 101 b in the casing portion 302 excluding the probe 301 is referred to.

As shown in FIG. 1, a cylindrical protector 204 is mounted on the peripheral edge portions of the support plates 202a and 202b so as to protect the contact displacement sensors 3a and 3b.
Further, in order to prevent the support plates 202a and 202b from being inclined, the support plates 202a and 202b may be supported by a string or the like (not shown).
The rod 201 and the support plates 202a and 202b are preferably made of, for example, an aluminum alloy, and preferably have a weight such that the distance measuring device 1 can be lifted by one person in order to reduce the weight while securing the rigidity. .

Next, an outline of inter-surface distance measurement by the inter-surface distance measuring device 1 will be described.
As shown in FIG. 2, the inter-plane distance measuring device 1 is inserted between the two opposing faces 101 a and 101 b in the housing window. At this time, the inter-plane distance measuring device 1 may be inclined with respect to the two surfaces 101a and 101b.
In this case, the operator may lift the inter-surface distance measuring device 1 and insert it between the two surfaces 101a and 101b, or as shown in FIG. The distance measuring device 1 may be supported and inserted between the two surfaces 101a and 101b. The use of the support member 6 makes it possible to measure the height of the housing window width.

  In a state in which the inter-plane distance measuring device 1 is inserted between the two surfaces 101a and 101b, the probes 301 of the contact displacement sensors 3a and 3b are extended to be in contact with the surfaces 101a and 101b. That is, the probes 301 of the three contact displacement sensors 3a supported by the support plate 202a are extended and brought into contact with one surface 101a, and the probes 301 of the three contact displacement sensors 3b supported by the support plate 202b are extended And the other surface 101b is brought into contact. When grease is applied to the portion to be measured, the probe 301 is driven to penetrate the grease and make contact with the surfaces 101a and 101b.

Hereinafter, with reference to FIG. 4, a method of calculating the inter-plane distance will be described. The inter-plane distance is calculated on the premise that the two opposing faces 101a and 101b are parallel.
As shown in FIG. 2, the inter-plane distance L _HW is the inter-plane distance with the inter-plane distance measuring device 1 at an inclination of θ, and the probes 301 of the contact displacement sensors 3a and 3b in contact with the surfaces 101a and 101b. Assuming that the length of the distance measuring device 1 is L _m , it is expressed by the following equation (1).

As shown in FIG. 4, three contact displacement sensors 3a are disposed at each vertex a, b, c of an equilateral triangle, and three contact displacement sensors 3b are disposed at each vertex d, e, f of an equilateral triangle. Ru. The vertex a and the vertex d are arranged in the same phase around the axis of the inter-plane distance measuring device 1. The same applies to vertices b and e, and vertices c and f. Further, a length between a predetermined position 4 on one end side of the inter-plane distance measuring device 1 and a predetermined position 5 on the other end side is k. Further, the pitch between each of the contact type displacement sensors 3a and 3b is w. The distances measured by the contact displacement sensors 3a on one surface 101a are l, m, n, and the distances measured by the contact displacement sensors 3b on the other surface 101b are l ', m', n ' I assume.
The coordinates of each of the contact points P _{1 to} P ₆ are measured, and an average plane is formed by three points on one side 101 a and the other side 101 b respectively, and the normal distance to each point on the target plane is calculated. L _m is represented by the following equation (2). Although averaging is not necessary if the object surfaces are strictly parallel, averaging is preferable in practical use.

In addition, cos θ is, for example, the normal vector n ₁ → (where → is assumed to be on n ₁ ) of an equilateral triangle consisting of vertices a, b and c, and the normal vector n ₂ → of the surface 101 a (→ is assumed to be attached on the n ₂₎ by a, represented by the following formula (3).
Here, normal vector n ₁ → and n ₂ → are respectively given by the equation of the measuring machine inner point and the plane represented by the following equation (4) and the equations of the measuring plane point and the plane represented by the following equation (5) It is represented by the following equation (6) and the following equation (7).

The inter-plane distance L _HW can be calculated by substituting the distance L _m calculated by the equation (2) and cos θ calculated by the equation (3) into the equation (1).

  The calculation of the inter-plane distance described above is performed by a computer including, for example, a CPU, a ROM, a RAM, and the like. In this case, the computing device and the display device for displaying the calculation result by the computing device may be installed anywhere. For example, if a small computing device and a small display device are installed at appropriate positions of the inter-surface distance measuring device 1 and the support member 6, the operator can check the inter-surface distance while working. Alternatively, the distances measured by the contact displacement sensors 3a and 3b may be transmitted by wireless communication, for example, and the calculation and display of the inter-plane distance may be performed by a separately installed calculation device and display device.

In the inter-plane distance measuring device 1 as described above, the inter-point distance between each of the two planes is calculated, and the inter-plane distance is computed from the angle between the line segment and the plane. This eliminates the need to maintain the orthogonal relationship with the surface of the housing window at the time of distance measurement, and enables measurement independent of the measurer.
And since one person is enough for the measurement operation using the inter-surface distance measuring device 1 and the grease cleaning operation of the measured part is not necessary, the load of the operation can be reduced. Further, since only the inter-plane distance measuring device 1 is inserted between the two surfaces to extend the probe 301, a measurement error due to human error hardly occurs. In this manner, the distance between two opposing surfaces of a large structure or the like can be measured quickly without skill.

Next, the calibration of the inter-plane distance measuring device 1 will be described.
As preparation for use, calibration of the inter-plane distance measuring device 1 using a calibrator is performed. An example of the calibrator 7 is shown in FIG. The calibrator 7 has a bottom surface 7a and left and right side surfaces 7b, and is formed by, for example, a cutting process. The parallelism between the left and right side surfaces 7b is secured, and the distance L between the left and right side surfaces 7b is strictly managed to a fixed length. As the distance L, 1470 mm close to the width of the housing window is set as an example. Further, on the bottom surface 7a, left and right setting tables 7c for mounting the inter-surface distance measuring device 1 are provided. The left and right setting tables 7 have a levelness so that the inter-plane distance measuring device 1 can be placed horizontally.

The conditions required for calibration are orthogonal to the main axis of the inter-plane distance measuring device 1 (line segment connecting the centers of the contact displacement sensors at three points on one side) and the side surface 7 b of the calibrator 7.
However, due to manufacturing errors such as processing accuracy of aluminum alloy and attachment accuracy of contact type displacement sensors 3a and 3b, in a state where inter-plane distance measuring device 1 is set in calibrator 7, actually, slight inclination (initial angle Is called). Therefore, reduction of the initial angle is required at the time of calibration. In this case, although it is conceivable to reduce the initial angle using a spirit level or the like, it is difficult to measure and adjust a minute angle (for example, 0.05 ° or less).

Therefore, as described below, the distance is measured by changing the inclination from the state in which the inter-plane distance measuring device 1 is set in the calibrator 7, the measurement error is acquired, and the inter-plane distance measuring device 1 is obtained based on the measurement error. Find the initial angle of.
FIG. 6 shows a procedure for obtaining the initial angle of the inter-plane distance measuring device 1 set in the calibrator 7.
In step S1, distance measurement is performed while changing the inclination from the state in which the inter-plane distance measuring device 1 is set in the calibrator 7, and measurement errors, that is, errors with respect to the known distance L of the calibrator 7 are acquired.
Specifically, with the inter-plane distance measuring device 1 set in the calibrator 7, the distance measurement is performed by vertically lifting the right side of the inter-surface distance measuring device 1, and the inclination θ is also determined. Similarly, the left side of the inter-plane distance measuring device 1 is operated to be vertically lifted to perform distance measurement, and the inclination θ is also determined. As a result, for example, as shown in FIGS. 7 (a) and 7 (b), the measurement results at each inclination θ until lifting left and right by 3 ° can be obtained. An inclination of 3 ° was set to obtain an initial angle resolution of 0.0004 ° (on the order of 1/10 of 0.005 °). The degree of inclination may be determined according to the resolution of the required inclination or the like.

In step S2, the neutral value of the measurement error generated by the left and right operation is determined. As shown in FIGS. 7A and 7B, in the case of inclination θ = 3 °, the measurement error on the left is −0.05 mm, the measurement error on the right is 0.02 mm, and the neutral value is (−0.05 + 0 .02) /2=-0.015 mm.
In step S3, a value obtained by subtracting the neutral value obtained in step S2 from the measurement error generated by the left and right operation is determined as a measurement error. The measurement error on the left side is −0.05 − (− 0.015) = − 0.035 mm, and the measurement error on the right side is 0.02 − (− 0.015) = 0.035 mm, and the inclination θ The measurement error at 3 ° is ± 0.035 mm.
The measurement error generated by the inclination of the inter-plane distance measuring device 1 includes factors other than the initial angle (for example, thermal expansion and contraction due to temperature fluctuation). In order to eliminate factors other than the initial angle as much as possible, that is, in order to narrow down to the initial angle, the calculation accuracy of the initial angle can be calculated by using data from operations on both left and right sides instead of one side. It can be improved.

In step S4, based on the measurement error obtained in step S3, the initial angle of the inter-surface distance measuring device 1 is obtained.
FIG. 8 shows the relationship between the inter-plane distance measuring device 1 and the calibrator 7 when one side is lifted. As apparent from FIG. 8, the measurement error Δ (mm), the inter-plane distance L (mm), the inclination θ (°), and the initial angle θ ′ (°) are expressed by the following equation (8). θ ′ is obtained by the following equation (9).
Δ = (L · π · θ / 180) · tan θ ′ (8)
θ ′ = tan ⁻¹ (Δ · 180 / L · π · θ) (9)
FIG. 9 shows the relationship between the measurement error Δ expressed by the equation (9) and the initial angle θ ′. As can be seen from FIG. 9, in this example, the initial angle 0.25 ° is determined based on the measurement error of 0.035 mm.

  Although the calibration law for the vertical direction is described here, the calibration law for the horizontal direction is the same.

  After the initial angle is determined as described above, the initial angle is corrected. For example, a posture correction of the inter-plane distance measuring device 1 is physically performed by inserting a shim between the setting table 7 c and the inter-plane distance measuring device 1 or the like so as to reduce the initial angle. Alternatively, in order to reduce the initial angle, the correction terms may be incorporated into the calculation formulas shown in Formulas (1) to (7), or the like, and the correspondence may be taken from software.

  FIG. 10 shows the effect of reducing the initial angle. Even if the inter-plane distance measuring device 1 is inclined at an inclination angle θ of 3 ° with respect to the two surfaces, the measurement errors are respectively −0.02 mm on the left and right. That is, although the error range before the reduction of the initial angle was 0.02 to -0.05 mm, the error range after the reduction of the initial angle is 0.00 to -0.02 mm, and the distance measurement accuracy is improved. I was able to.

(Other embodiments)
Although the embodiment described above describes the initial angle with respect to the side surface 7b when the inter-plane distance measuring device 1 is set in the calibrator 7, any measuring instrument capable of acquiring the distance to the object and the angle may be used. The scope of application is not limited thereto.
For example, there is a laser tracker as a measuring instrument capable of measuring the distance to an object and determining the angle with respect to the object. As shown in FIG. 11, in the laser tracker, the laser tracker main body 8 irradiates the laser light to the target 9 brought into contact with the object, and the laser light reflected from the target 9 is received to measure the distance. The three-dimensional position of the target 9 is determined.

  In the present embodiment, the initial attitude of the laser tracker main body 8 with respect to a plane serving as a reference (hereinafter referred to as a reference plane) is determined, and the initial attitude is corrected. That is, the X, Y, Z axes of the laser tracker body 8 are aligned with the reference plane. The reference surface may be, for example, a measurement surface of an object or a surface on which the laser tracker main body 8 is placed.

As shown in FIG. 11, it is assumed that the X axis or Y axis of the laser tracker main body 8 has an inclination of the angle α and the Z axis has an inclination of the angle β as an initial attitude with respect to the reference plane.
In the reference plane, the distance is measured at a plurality of points (preferably three or more points) while shifting the target 9 in one direction. This allows vectors to be generated at the reference plane. Similarly, in the reference plane, the distance is measured at a plurality of points (preferably three or more points) while shifting the target in the direction orthogonal to the one direction. This allows vectors to be generated at the reference plane.
Then, the initial attitude of the laser tracker main body 8 is adjusted so that the X axis or Y axis of the laser tracker main body 8 and the Z axis match the vector generated in the reference plane, that is, the angles α and β are zero. to correct. For example, posture correction of the laser tracker body 8 is physically performed by inserting a shim between the surface on which the laser tracker body 8 is placed and the laser tracker body 8 or the like.
If measurement is performed with the X, Y, and Z axes of the laser tracker main body 8 shifted with respect to the measurement surface of the object, calculation such as coordinate conversion is required later, resulting in an increase in the number of operation steps and calculation operations. As a result, there is a risk of loss of precision. By correcting the initial attitude of the laser tracker main body 8 with respect to the reference plane, it is possible to eliminate the need for calculation such as coordinate conversion and to improve the measurement accuracy so as to prevent the occurrence of missing digits and the like.

  As mentioned above, although the present invention was explained with an embodiment, the above-mentioned embodiment shows only an example of the embodiment in the case of carrying out the present invention, and the technical scope of the present invention is interpreted restrictively by these. It is a must-have. That is, the present invention can be implemented in various forms without departing from the technical concept or the main features thereof.

1: Inter-surface distance measuring device 2: Support 3a, 3b: Distance measuring sensor (contact displacement sensor)
7: Calibrator 7b: Side 8: Laser tracker body 9: Target

Claims (4)

A support that can be inserted between two opposing surfaces, and one end of the support, which measures the distance from a predetermined position of the inter- surface distance measuring device to one of the two surfaces Three or more distance measurement sensors, and three other sensors provided at the other end of the support, for measuring the distance from a predetermined position of the distance measuring device to the other of the two surfaces A posture correction method for correcting the posture of an inter-surface distance measuring device, comprising: the other distance measurement sensor described above; determining an inclination with respect to the two opposing surfaces; and measuring a distance between the two surfaces.
A procedure for measuring a distance from a state in which the distance between two planes is set to a calibrator with a known distance between two parallel planes and changing a tilt to obtain a measurement error;
Determining an initial angle of the inter-surface distance measuring device based on the measurement error;
And a step of correcting the initial angle. In the procedure for acquiring the measurement error, in a state where the inter-plane distance measuring device is set to the calibrator, distance measurement is performed while changing the inclination at one end of the inter-surface distance measuring device, and a predetermined inclination is obtained. obtains a measurement error, then performs distance measurement by changing the inclination at the other side of the face distance measuring device, according to claim 1, wherein the obtaining the measurement error at the predetermined inclination Attitude correction method of inter-surface distance measuring device. In the procedure for acquiring the measurement error, a neutral value of the measurement error at the predetermined inclination obtained at the one end side and the measurement error at the predetermined inclination obtained at the other end side is obtained, Calculate the measurement error for the neutral value,
The method according to claim 2 , wherein in the step of obtaining the initial angle, the initial angle is determined based on a measurement error with respect to the neutral value. In the procedure for obtaining the initial angle, the initial angle θ ′ is given by the following equation θ ′ = tan ⁻¹ (Δ · 180 / L · π · θ) as the measurement error Δ, the distance L between the two surfaces of the calibrator, and the inclination θ. )
The posture correction method of the inter-surface distance measuring device according to any one of claims 1 to 3 , characterized by:

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