SU938036A1 - Device for measuring flat figure moments - Google Patents

Description

The invention relates to a balancing technique for measuring the moments of bodies and can find application in a control and measuring technique for determining the axial moments of bodies of any order. ⁵

A device allowing to determine the moment of inertia of plane figures in their area, comprising a drum and drum drive ₁₀ kuyu optical system with a curved mirror [1].

A disadvantage of the device is the impossibility of determining higher-order moments due to the fact that the curved (elliptical) mirror is a reflector and provides illumination of the scanning line in the image plane and focusing of the rays of the optical system in the focus of the ellipse.

Closest to the invention in technical essence is a device for determining the moments of planar figures, containing a more transparent drum, a drum drive, a light source associated with the drum, and an optical system £ 2].

However, the device does not allow to determine the moments of a figure of a higher order due to line-by-line scanning of a figure mounted on a drum.

The purpose of the invention is the determination of higher order moments.

This goal is achieved by the fact that the device for measuring the moments of flat figures is equipped with a Reflector installed between the drum and the optical system, executions with a curved surface, the curvature of which is described by the equation / Xo “X /“ X where x, y are the coordinates of the reflector, · x, y_ - the coordinates of the Shgoi phi 0 o gury;

C is a linear coefficient i And is the order number of the determined moment; y ^{ is the angular coefficient.

The drawing shows a device for measuring the moments of flat figures, a General view.

The device comprises a transparent drum 1, on the surface of which a measured flat figure 2 is attached, a drive 3 of a drum 1 kinematically connected to the latter, a light source 4 located inside the drum 1, an optical system 5 with an optical probe and a photodetector (not shown) mounted on a carriage 6, which by means of a screw pair 7 and a worm pair 8 is connected with the shaft of the drum 1. Between the optical system 5 and the drum 1, a reflector 9 is installed, made with a curved surface, the curvilinearity of which is described by the equation iem where x, ^x 0 ^'I 0

- coordinates of the reflector 9J

- coordinates of a plane figure 2;

- linear coefficient

- order number of the determined moment;

- angular coefficient.

At

The device also contains an information processing circuit that includes a series-connected amplifier 10, a switch 11, a counter 12, while the input of the amplifier 10 is connected to a photodetector of the optical system 5, and the second input of the switch is connected to a constant-frequency generator 13.

The device operates as follows.

When you turn on the drive 3, the drum 1 comes into rotation. Together with it, the measured figure 2 rotates and its display in a curved reflector 9 ". At the same time, the carriage 6 with the stylus of the optical system 5 receives translational motion and the probe scans the image of figure 2 in the reflector 9. The signal of the photodetector of the optical system is amplified by an amplifier

10, after which the switch key (not shown) is opened

11. The frequency of filling from

IS

938036 4 of the generator 13 occurs at the input of the counter 12, and the measurement results of individual rows are accumulated. The result is proportional to the area 5 of figure 2. And since this area is equal to the moment of the order AND of figure 2, it follows that the desired moment is measured.

Denote the coordinate of figure 2, directed along the axis of the drum 1, by y ₀ , and the coordinate of the image in the reflector 9 in the direction of movement of the carriage through x. The second coordinate of figure 2 at the scanning point is directed perpendicular to the plane of the drawing and is the same for figure 2 and [its image in the curvilinear from ^{1 of the} reflector 9. Denote it by Ζ.

The condition for equal moments is written where (y _p , Ζ) is the moment of inertia of the order in the coordinate axes y _o , Ζ;

Μ (x, Ζ) is a moment of order 0 ⁰ (area) in the coordinate axes x, Ζ.

Equality (. I) can be written as _s ib5a, ^ U <Wi.

it follows either after integration

V ^th . 'And + 4 (g)

Expression (2) represents the law of change in scanning display of a plane figure 2 in the reflector 9.

For each order number of the determined moment (n = 1,2,3,4, ...), a reflector profile 9 is required, while its curvature is described by the equation

3-vc ^bM V / x _o -x / -y

The device, by determining the moments of plane bodies of any order, expands its functionality.

Claims (2)

The invention relates to a sizing technique for measuring the moments of bodies and the majority of applications in measurement and control technology for determining the axial momentum of body elements of any order. A device is known that allows determining the moment of inertia of flat figures by their area, containing a drum, a drum drive and an optical system with a curvilinear mirror l. The disadvantage of the device is the impossibility of determining the higher order moments due to the fact that the curvilinear (elliptic) mirror is a reflector and provides illumination of the scanning line in the image plane and focused rays of the optical systems in the focus of the ellipse. The closest to the invention in its technical essence is a device for determining moments of flat figures containing a transparent drum, a drum drive, a light source associated with the drum, and an optical system (2 J. However, the device does not allow to determine the moments of a higher-order figure from - for line-by-line scanning of a figure mounted on a drum. The purpose of the invention is to determine the highest order moments. The goal is achieved by the fact that the device dp of measuring the moments of flat figures is equipped with an established drum and optical system Reflector, made with curvilinear surface, the curvilinearity of which is described by the equation, -. Mn + c V / Vx / -x - coordinates, reflector, where x, y - coordinates Shyu fi "N gory; c - linear coefficient i And - the number of the order of the moment to be determined - the angular coefficient The figure shows a device for measuring the moments of flat figures, general view. The device contains a transparent drum I, on the surface of which the measured flat figure 2 is fixed, the drive 3 of drum I, kinematically 1st of last m, light source 4, located inside drum 1, optical system 5 with optical probe and photodetector (not shown) mounted on carriage 6, which by means of a screw pair 7 and a worm pair 8 is connected to the drum shaft 1. Between the optical system 5 and drum 1 has a reflector 9, made with a curved surface, the curvilinearity of which is described by the equation v. -coordinates of the reflector 9 where X, y-coordinates of a flat guru 2; -linear coefficient, -number of the moment to be determined; y is the angular coefficient. . The device also contains an information processing circuit that includes a series 10 connected amplifier 10, a switch 11, a counter 12, the input of the amplifier 10 is connected to the photoreceiver of the optical system 5, and the second input of the switch is connected to a constant frequency generator 13. The device works as follows When the drive 3 is turned on, the drum 1 comes into rotation. Together with, the measured figure 2 and its rotate. display in a curved reflector 9 "With this, the carriage 6 with the optical system probe 5 receives translational motion and the probe scans the image of figure 2 in the reflector 9, the signal of the photoreceiver of the optical system is amplified by the amplifier 10, after which a switch (not shown) of the switch 11 is opened The filling frequency from generator 4 13 occurs at the input of counter 12, and the results of measurements of individual lines are accumulated. The result is proportional to the area of figure 2. And since this area is equal to a moment of the order of 4 "guru 2, it follows that the required moment is measured. Denote the coordinate of figure 2, directed along the axis of the drum 1, by VO and the image coordinate in the support 9 in the direction of the carriage movement through x. The second coordinate of figure 2 at the scanning point is perpendicular to the plane of the drawing and is the same for figure 2 and its image in a curvilinear reflector 9. Denote it by Z. The condition of equality of moments is M (Vo, z) - Mo (X, y), Z ) where M (y, - moment of inertia of the order in coordinates 1x axis x y, Z; M (x, Z) - moment of order O (area) in coordinate axes x X, Z. Equality (. 1) can be written in JbSa ai JMydi. from here follows or after integration o) Expression (2) represents the law of the change in the scanning of the display of the flat figure 2 in the reflector 9. For The number of the order of the moment being determined (, 2,3,4,. ".) requires its reflector profile 9, while its curvilinearity is described by the equation VTx irT-x and З-So-.C Device by determining the moments of flat bodies of any the order extends its functionality. The invention The device for measuring the moments of flat figures, which contains the 1st drum, the drive of the drum, the light source associated with the drum. An optical system, characterized in that, with a chain of highest-order moments, the eye is provided with a reflector installed between the drum and the optical system, made 1g 1m with a curvilinear surface, the curvature of which is described by the equation 2 -Uo "-C av where X, y - the coordinates of the reflector; X, y - coordinates of a flat fig ry;  linear coefficient C And - the number of the order, defined 040th moment; the angular coefficient. Sources of information taken into account in the examination 1, USSR Author's Certificate 551503, cl. G 01 B P / 28, 1975. 2. Author's certificate. USSR № 268677, cl. G 01 B 11/28, 1966 (prototype).