RU2170659C1 - Method for marking out lines of square contour having area equal to that of predetermined circle - Google Patents

Abstract

FIELD: marking out systems. SUBSTANCE: method comprises steps of drawing by means of compass on surface of part circle with center O and with predetermined radius R; passing through center O two mutually normal axial lines by means of compass and ruler. EFFECT: simplification of marking out process. 1 cl, 2 dwg _

Description

 The invention relates to methods for marking contour lines in the form of a square with the given sizes of various parts blanks in mechanical engineering, in the textile industry and other sectors of the national economy of the Russian Federation.

 As a result of an information search conducted by the author, analogues of this method were not identified.

 The problem to which this invention is directed is the solution of a technical problem by simple technical means with increased marking accuracy.

The essence of the invention lies in the fact that on the surface of the workpiece, details with a compass describe the circumference of a given circle with center O of a given radius R _cr , two mutually perpendicular axial lines are drawn through the center O of this circle, using a compass and a ruler, and four semicircles of radius R _cr from the centers O ₁ , O ₂ , O ₃ and O ₄ formed from the intersection of the axial lines with the circle line of the circle, draw straight lines through the pairs of points a and b, c and d, e and f, g and h, formed from the intersections of four semicircles with a line about of circles of the circle to the intersection of the lines with each other at the points A ', B', C 'and D', which are the vertices of the first auxiliary square through which a solution of a compass, equal R _'q = OB', describe approximately a square circle O center then, in a similar way, mark the second auxiliary square for a circle with center O and radius R ' _q = OB', obtaining the vertices A '', B '', C '' and D '' of the second auxiliary square, through which a compass solution equal to R '' _sq = OB'', describe a circle with center O around the second square, continue straight lines it is the first and second auxiliary squares until they intersect with each other with the formation of four small squares, draw the diagonals of all squares, draw straight lines through the pairs of points A and B, B and C, C and D, D and A formed from the intersections of the diagonals of small squares between which are the vertices of the desired square, through which a solution of the compass equal to R _q = OB describe a circle with the center O around the square, and then check the correctness of the marking according to the formula
π = 2R $\genfrac{}{}{0ex}{}{\text{2}}{\text{sq}}$ / R $\genfrac{}{}{0ex}{}{\text{2}}{\text{sq}}$
where π is a constant, defined as the ratio of the circumference of a circle to its diameter;
R _kv is the radius of the circle circumscribed around the square;
R _cr - the radius of the circle of this circle.

The proposed marking method allows marking the contour line in the form of a square, equal in area to this circle, using simple technical means - a compass and a ruler and with increased marking accuracy. Based on the increased accuracy of the marking, a more accurate determination of the constant π is possible.
The invention is illustrated by drawings, where:
in FIG. 1 shows a sample markup of a workpiece blank;
in FIG. 2 - the same, the node at the vertices B 'and B''in an enlarged view.

 The method is as follows.

On the surface of the workpiece 1 parts compass 2 describe a circle with the center of the circle O. predetermined radius R _cr through the center O of the circle is carried out two mutually perpendicular axial lines 3 and 4, using a ruler and compass. To do this, through the center O draw an axial line 3 until it intersects with a circle 2 at points O ₂ and O ₄ .

With a solution of compass equal to R _cr , from the points O ₁ , O ₂ , O ₃ and O ₄ spend four semicircles 5 that intersect the line of circle 2 at points a, b, c, d, e, f, g, h. Using a ruler, draw straight lines 6 through pairs of points a and b, c and d, e and f, g and h until they intersect at points A ', B', C 'and D', which are the vertices of the first auxiliary square 7 Next, similarly mark the second auxiliary square 8. For this, through the vertices A ', B', C 'and D' of the first auxiliary square 7 with a compass solution equal to R ' _sq = OB', circle 9 with center O is described around square 7 The circle line 9 intersects with mutually perpendicular axial lines 3 and 4 at points O ' ₁ , O' ₂ , O ' ₃ and O' ₄ . With a solution of the compass equal to R ' _q , four semicircles 10 are drawn from points O' ₁ , O ' ₂ , O' ₃ and O ' ₄ , which intersect the circle line 9 at points a', b ', c', d ', e ', f', g ', h'. Using a ruler, draw lines 11 through pairs of points a 'and b', c 'and d', e 'and f', g 'and h' until they intersect at points A '', B '', C '' and D '', which are the vertices of the second auxiliary square 8. Through the vertices A '', B '', C '' and D '' of the second auxiliary square 8, with a compass solution equal to R '' _q = OB '', describe about the square 8 circle 12 with center O.

Continue straight lines 6 and 11 of the first and second auxiliary squares 7 and 8 until they intersect with each other to form four small squares 13. Draw the diagonals of all squares 7, 8 and 13. The points A, B, C and D of the intersection of the diagonals of small squares 13 are vertices of the desired square 14. Draw lines 15 through pairs of points A and B, B and C, C and D, D and A and get the desired square 14, equal in area to this circle with circle 2. Through the vertices A, B, C and D square 14 with a compass solution equal to R _q = OB, describe circle 16 around center 16 with center O.

After that, check the correctness of the markup according to the formula
π
where π = 2R $\genfrac{}{}{0ex}{}{\text{2}}{\text{sq}}$ / R $\genfrac{}{}{0ex}{}{\text{2}}{\text{cr}}$ - constant, defined as the ratio of the circumference of a circle to its diameter, π = 3,14159 ...;
R _kv is the radius of the circle 15 described around the square 14;
R _cr - the radius of the circle 2 of this circle.

 The invention allows marking of contour lines in the form of a square, equal in area to a given circle, using simple technical means and with increased marking accuracy, and also solves the scientific problem of the problem of squaring a circle.

Claims (1)

The method of marking the contour lines in the form of a square, equal in area to this circle, which consists in the fact that on the surface of the workpiece the details of the circle describe the circle of this circle with center O with a given radius R _cr , two mutually perpendicular axial lines are drawn through the center O of this circle using This compass and ruler, compass describe four semicircles of radius R _cr with the center O ₁ , O ₂ , O ₃ , O ₄ formed from the intersection of the axial lines with the circle line of the circle, draw straight lines through pairs of points a and b, c and d, e and f, g and h, formed from the intersections of four semicircles with the circle line of a given circle, to the intersection of straight lines at each other at points A ', B', C 'and D', which are the vertices of the first auxiliary square through which the compass solution equal to R ' _sq = OV', describe a circle with center O near the first square, then similarly mark the second auxiliary square for a circle with center O and radius R '' _sq = OB '', getting the vertices A '', B '', C '' and D of the second auxiliary square, through which a solution of the compass equal to R '' _sq = OV '', describe a circle with center O near the second square, continue the straight sides of the first and second auxiliary squares until they intersect with each other to form four small squares, draw the diagonals of all the squares, draw straight lines through the pairs of points A and B, B and C, C and D, D and a, formed by the intersection of the diagonals of small squares between itself and the required vertices are square, through which the solution compasses equal to _q R = OM, describe a square about the desired circle with a center O, afterwards check rules the formula markup Nosta
π = 2 R _sq ² / R _cr ² ,
where π is a constant, defined as the ratio of the circumference of a circle to its diameter;
R _kv is the radius of the circle circumscribed around the square;
R _cr - the radius of the circle of this circle.

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