JPH0239997B2 - NIJIKYOKUSENSOSEIGU - Google Patents

Description

[Detailed description of the invention] The present invention relates to a quadratic curve generator.

Conventionally, there were devices that used link mechanisms or many gears to draw quadratic curves, but these used many parts, had complex configurations, were extremely difficult to manufacture, and were difficult to operate. It also had the disadvantage of being difficult. This invention utilizes a principle different from the conventional one, and is not only easy to manufacture, but also allows accurate quadratic curves such as parabolas, ellipses, etc. to be created with simple operation.
The purpose of this invention is to provide a quadratic curve generator capable of drawing a hyperbola.

First, the principle of this invention will be explained.

Parabolas, ellipses and hyperbolas have properties in common. In a parabola, as shown in Figure 1, the leg of a solid line drawn from an arbitrary point P1 of parabola A to directrix B is Rp, the focal point of parabola A is F, and the leg parallel to directrix B is the origin O. Let Q be the intersection of the line A' passing through and the tangent to point P1, and let D be the intersection of the straight line (optical axis) B' passing through the focal point F and the origin O of the parabola A and the directrix B, then P1F=P1Rp, Since P1Q⊥FRp, QRp=QF and OF=OD. Therefore, since OQDRp and OQ=1/2DRp, FQ=QRp...(1) holds, and point Q is always located on line A'.

In an ellipse, as shown in Fig. 2, on a straight line passing through one focal point F1 of an ellipse C having a major axis 2a and a minor axis 2b and an arbitrary point P2 of the ellipse C, there is a line from point P2 to the other focal point F2. Take a point Re equal to the distance,
Let Q be the intersection of the tangent to point P2 and line segments Re and F2, and let O be the origin of the ellipse. Since P2F2=P2Re, P2Q⊥F2Re, and OF1=OF2, QF2=QRe, OQ=1/ 2F1Re, F2Q=QRe...(2) holds, and the point Q is always located on the circumcircle C' of the ellipse C.

In a hyperbola, as shown in Figure 3, on the straight line connecting one focus F1 of hyperbola D and any point P3 of hyperbola D, take a point Rh equal to the distance from point P3 to the other focus F2, Let Q be the intersection of the tangent to point P3 and line segment F2Rh, and let O be the origin of hyperbolas D and D, then P3Rh=P3F2, P3Q⊥F2Rh, and OF1=OF2, QF2=QRh, so OQF1Rh, OQ = 1/2F1Rh, and F2Q=QRh (3) holds, and the point Q is always located on the inscribed circle D' of the hyperbola D.

The present invention provides the above three types of quadratic curves,
Using the fact that equations (1), (2), and (3) are common principles, the cross-shaped link element placed at point Q is connected to lines A', C',
By moving along D′, parabola, ellipse,
This method allows hyperbolas to be created accurately and extremely easily.

Embodiments of the present invention will be described below for each type of quadratic curve with reference to the drawings.

FIG. 4 shows a quadratic curve generator for drawing a parabola.

As shown in FIG. 4, the quadratic curve generator for drawing a parabola consists of a cross-shaped link element body 1 that always maintains a line segment P1Q and a line segment RpF in an orthogonal relationship, and a first link element body located on the directrix B. It has a guide member 2, a second guide member 3 located on the line A', and a first link element 4 that can move along the first guide member 2 and maintain the line segment RpP1.

The link element body 1 includes an elongated tangential member 5 located on a tangent to a parabola A and formed, for example, in a plate shape, and a tangential member 5 on both sides of a substantially intermediate portion of the tangential member 5 in the longitudinal direction of the tangential member 5. It has a pair of plate-shaped arm members 6 and 7, for example, which extend orthogonally in a cross shape. The tangential member 5 is movably attached to a long first slideway 8 formed in the longitudinal direction, for example, a groove-shaped opening, and a first slideway 8 that pivotally supports the parabola generating tool 9. 1 mover 10, and a stator 12 located approximately in the center of the first slideway 8 and provided with a first pin 11. Further, one arm member 6 includes a second slideway 13 formed to extend from one end in the longitudinal direction to the vicinity of the tangential member 5;
For example, the second slideway 13 has a groove-like opening.
The second mover 15, which pivotally supports the fixing pin 14, is slidably fitted into the second mover 15. Similar to the arm member 6, the other arm member 7 has a third slideway 16, and a third slider 18 having a second pin 17 is disposed in the third slideway 16.
are slidably fitted.

The first guide member 2 has a long plate shape and forms a fourth slideway 19 in the length direction.
9 is slidably provided with a fourth mover 20, and the fourth mover 20 is pivotally attached to the second pin 17 of the third mover 18 so as to be rotatable.

The second guide member 3 is also the same as the first guide member 2.
Similarly, it has a long plate shape and has a fifth runway 2 in the length direction.
1, and a fifth slider 22 is formed on this fifth slideway 21.
is provided so that it can slide freely. And this fifth mover 2
The first pin 11 of the tangential element 5 described above is pivotally connected to the link element 2, and the link element body 1 is rotatably supported around the first pin 11 as a fulcrum, and is movable along the fifth slideway 21. Make it.

The first link element 4 described above has a horizontal T-shape consisting of a vertical portion 23 and a horizontal portion 24, and the vertical portion 23 is fixed to the fourth slider 20 of the first guide member 2.
A sixth slideway 25 is formed in the lateral portion 24 in the length direction, and a sixth slider 26 is slidably fitted therein.
The sixth mover 26 is pivotally connected to the parabola generator 9 of the tangential element 5.

When creating a parabola A using the quadratic curve creation tool having the above-mentioned configuration, the process is as follows.

First, the above-mentioned quadratic curve generator is placed on the drawing surface, the fixing pin 14 is rotatably supported at a position that should be the focal point F of the parabola A, and the first guide member 2 is placed on the directrix B of the parabola A. In addition, the second guide member 3 is placed on a line A' that passes through the origin O of the parabola A and is parallel to the directrix B,
Support each. Then, the length from the fixed pin 14 to the first pin 11, and the length from the first pin 11 to the second pin 1.
If the lengths up to 7 are made equal, the above equation (1) is completed, and the first pin 11 is at point Q in FIG.
The second pin 17 coincides with the point Rp, and the generating tool 9 coincides with the point P1. In this state, a writing instrument such as a pencil or pen or a cutting tool such as a cutter is attached to the tip of the parabola generating tool 9. Therefore, link element body 1
When moving along the fifth slideway 21 of the second guide member 3, since the fixed pin 14 is fixed in position, the link element body 1 moves while rotating around the first pin 11, and the tangential line As the direction of the member 5 gradually changes, the first link element 4 also moves along the first guide member 2. The tangential member 5 and the left and right arm members 6 and 7 are always orthogonal, and the length from the fixed pin 14 to the first pin 11 and the length from the first pin 11 to the second pin 17 are always equal. Since the parabola generator 9 is maintained, the locus of the parabola generator 9 draws the parabola A.

Next, an example of a quadratic curve generator for drawing an ellipse will be explained with reference to FIG.

In FIG. 5, the structure of the cross-shaped link element body 1 is the same as that of the link element body 1 of FIG. 4, so the same reference numerals are given and the explanation will be omitted. In addition to the link element 1 described above, this ellipse generating tool also includes a third guide member 27 and a second link element 2.
Use 8.

The third guide member 27 has a long plate shape, and one end is connected to the first pin 12 of the stator 12 of the tangential member 5.
1, and an origin pin 29 located at the origin O of the ellipse C is provided at the other end. Moreover, the second link element 2
Reference numeral 8 is a long plate having one end attached to the link element body 1.
The second pin 1 of the third mover 18 provided on the arm member 7 of
7, and a focusing pin 30 located at the focal point F1 of the ellipse C is provided at the other end. A seventh slideway 31 is formed in the second link element 28 along the length direction, and a seventh slider 32 is slidably provided thereon, and the seventh slider 32 is attached to the generating tool 9 of the tangential member 5. pivot.

Using the quadratic curve generator with the above configuration, create an ellipse C
If you want to create , it is as follows.

The quadratic curve generator described above is placed on the drawing surface, the fixed pin 14 is rotatably supported at the position that should be the focal point F2 of the ellipse C, and the origin pin 29 is set at the origin O of the ellipse C.
The focusing pin 30 is rotatably supported at the position where it should be the focus F1 of the ellipse C, and at the position where the focus pin 30 is the focus F1 of the ellipse C.

Then, when a writing instrument or the like is attached to the creation tool 9 and the length from the fixed pin 14 to the first pin 11 is made equal to the length from the first pin 11 to the second pin 17, the above equation (2) is completed. , 1st pin 1
1 corresponds to the point Q of the ellipse, the second pin 17 corresponds to the point Re, and the generating tool 9 corresponds to the point P2.

In this state, move the third guide member 27 to the origin pin 2.
9, the first pin 11 draws a circumscribed circle C' centered on the origin pin 29, and the link element body 1 rotates about the first pin 11 as a fulcrum due to the action of the second link element 28. while rotating around the origin pin 29 as a fulcrum. The second mover 15 moves on the second slideway 13, but since the position of the fixed pin 14 is fixed, the second mover 15 always moves from the fixed pin 14 to the first pin 1.
1 and the length from the first pin 11 to the second pin 17
When the lengths up to 9 are equal, equation (2) is always completed, and the locus of the creating tool 9 draws an ellipse C.
In this case, if the stator 12 is provided on the lower surface of the tangential member 5 so that the first mover 10 can move the entire length of the first runway 8, the entire circumference of the ellipse C can be drawn with the generator 9. .

Next, an example of a quadratic curve generator for drawing a hyperbola will be explained with reference to FIG. 6.

Comparing the construction of the creating tool of FIG. 6 with the creating tool of FIG. 5, the necessary components of the link element body 1, the third guide member 27, and the second link element 28 are the same. The difference between the two generating tools is that, in FIG. 6, the second link element 28 is pivotally connected to the second pin 17 of the link element body 1 in the middle of its length, and the second link element 28 is pivotally connected to the second pin 17 of the second pin 17 on the distal side from the pivotally connected part. A seventh slideway 31 is formed and a seventh slider 32 is slidably provided. A focusing pin 30 is attached to the other end of the second guide member 28.
is provided, and the seventh mover 32 is pivotally connected to the generating tool 9 of the tangential member 5.

Note that the symbols not explained in FIG. 6 are the same as the structures of the same symbols shown in the embodiment of FIG. 5 or FIG. 4, so a detailed explanation will be omitted.

When creating a hyperbola D using the quadratic curve generator having the above configuration, the procedure is as follows.

The above-mentioned quadratic curve generator is placed on the drawing surface, the fixing pin 14 is rotatably supported at the position that should be the focal point F2 of the hyperbola, and the origin pin 29 is set at the origin O of the hyperbola.
Place the focal pin 30 in the position where it should be.
Each is rotatably supported at the position that should be F1.

Then, by attaching a writing instrument or the like to the creation tool 9 and making the length from the fixed pin 14 to the first pin 11 equal to the length from the first pin 11 to the second pin 17, the above equation (3) is completed. , 2nd pin 1
7 corresponds to point Rh, and creation tool 9 corresponds to point P3.

In this state, move the third guide member 27 to the origin pin 2.
9, the first pin 11 draws an inscribed circle D' of a hyperbola D centered on the origin pin 29,
Further, due to the action of the second link element 28, the link element body 1 rotates around the first pin 11 as a fulcrum and revolves around the origin pin 29 as a fulcrum. and second mover 15
moves along the second slideway 13, but the position of the fixed pin 14 is fixed, so the length from the fixed pin 14 to the first pin 11 and the length from the first pin 11 to the second
If the lengths up to pin 17 are equal, the above formula (3)
is completed, and the locus of the creation tool 9 will draw one side of the hyperbola D. In this case, if the stator 12 is provided on the lower surface of the tangential member 5 so that the first mover 10 can move the entire length of the first runway 8, the entire length of one hyperbola can be drawn using the generator 9. . In addition, when drawing the other hyperbola, the focus pin 30 is
What is necessary is to rotatably fix the fixing pin 14 at the position where the focal point F2 should be and the fixing pin 14 at the position where the focal point F1 should be the focus point.

The embodiments of this invention have been described in detail above, but
It goes without saying that this invention is not limited to the embodiments described above, and can be implemented with appropriate modifications within the scope of the gist of the invention.

In the above embodiment, each slideway is a groove-shaped opening, and the slider is a fitting piece that can be slid into the opening, but each slideway is a rail, and the slider is rolled on the rail. It can also be used as a wheel.

According to the configuration of the present invention detailed above, the following effects can be achieved.

(1) Quadratic curves can be drawn easily and accurately.

(2) Can draw almost the entire length of a parabola, ellipse, and hyperbola at once.

(3) Since there are very few components, it can be made very compact and does not take up much space.

(4) Since the configuration is simple, it is easy to manufacture and can be manufactured at low cost.

(5) Since the principle of quadratic curves can be clearly demonstrated, it can be used as a teaching material for understanding the principle of quadratic curves.

(6) It can also be used for forming, polishing, and cutting lens surfaces.

[Brief explanation of drawings]

Figure 1 is a diagram to explain the principle of a parabola, Figure 2 is a diagram to explain the principle of an ellipse, Figure 3 is a diagram to explain the principle of a hyperbola, and Figure 4 is a diagram to explain the principle of a hyperbola.
5 is a plan view of the parabola generator, FIG. 5 is a plan view of the ellipse generator, and FIG. 6 is a plan view of the hyperbola generator. 1... Link element body, 2... First guide member,
3... Second guide member, 4... First link element,
5... Tangent member, 6, 7... Arm member, 8... First
Runway, 9... Quadratic curve generator, 10... First mover, 11... First pin, 12... Stator, 13...
...Second runway, 14...Fixed pin, 15...Second mover, 16...Third runway, 17...Second pin, 1
8...Third mover, 19...Fourth runway, 20...
4th mover, 21...5th slide, 22...5th mover, 25...6th slide, 26...6th mover,
27... Third guide member, 28... Second link element, 29... Origin pin, 30... Focus pin.

Claims (1)

[Scope of Claims] 1. A tangential member to be located on a tangent to a quadratic curve, and a pair of arm members extending in a cross shape perpendicular to the tangential member, wherein the tangential member has a A first slider is provided to be movably attached to a first slideway formed to extend in the direction and to support a quadratic curve generating pin, and a first pin is provided in the center, and one of the pair of arm members is provided. The arm member is provided with a second mover that is movably attached to a second slideway formed in the longitudinal direction of the arm member and has a fixing pin located at the focal point of the quadratic curve. a link element body provided with a third mover movably attached to a third slideway formed in the longitudinal direction and arranged symmetrically with the second mover with respect to the tangential member; A guide member rotatably supports the first pin of the link element body and guides the movement of the link element body; 1. A quadratic curve generating tool comprising: a link element that is attached to the link element and rotates the link element body. 2. The quadratic curve is a parabola, and the guide member includes a first guide member located on the directrix of the parabola and a second guide member located on a line parallel to the directrix and passing through the origin, and the link element is connected to the first guide member. The quadratic curve generating tool according to claim 1, wherein the quadratic curve generating tool is movable along a guide member. 3. Claim 1, wherein the quadratic curve is an ellipse, and the link element body can be rotated around the first pin and revolved along the circumcircle of the ellipse. The quadratic curve generator described in section. 4. Claim 4, characterized in that the quadratic curve is a hyperbola, and the link element body can be rotated around the first pin and revolved along the inscribed circle of the hyperbola. The quadratic curve generator according to item 1.