JPS6058897A - Creating tool for curve of secondary degree - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

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

In the past, there were devices that used link mechanisms or many gears to draw quadratic curves, but these had the disadvantage of being complex, extremely difficult to manufacture, and difficult to operate. Was. The present invention provides a quadratic curve generator that is easy to manufacture and can draw accurate quadratic curves, such as parabolas, ellipses, and hyperbolas, with simple operations, using a principle different from conventional ones. And that's what gold is for.

First, the principle of this invention will be explained.

Parabolas, ellipses, and hyperbolas have two properties in common. In a parabola, as shown in Fig. 1, any point P on a parabola A, yoshi quasi #! If the solid line drawn at B is 4, and the focus of the parabola A is F, then the line segment -π2
There is a relationship expressed by the first equation between and the line segment.

P, RP = p, 〒 ・・・・・・・・・・・・・・・
(Rimata, P, the parabola &!A tangent at the point is the focal point F
Let Q be the point that intersects the straight line (optical axis) B' passing through the inflection point 0 of the parabola A, then there is a relationship of the second equation between the line segment evaluation and the line segment exposure.

(2) For an ellipse, as shown in Figure 2, the major axis α and the minor axis bf
One focal point F of the ellipse C, and an arbitrary point P2 of the ellipse C
If we take a point R,i equal to the distance from point P2 to the other focal point F2 on the @ line that passes through , the length of the line segment is always constant, and between line segment -6 and line segment q2. has the relationship of the fifth equation.

P2R,=92 ・・・・・・・・・・・・・・・
(3) Also, the tangent to the ellipse C at 22 points is the bifocal point F.

If the point that intersects the straight line X passing through F2 is 92, then the line segment 0
2 and the line segment 92 has the relationship expressed by the fourth equation.

Exposure, ±92・・・・・・・・・・・・・・・ (4) In a hyperbola, as shown in Figure 3, one focal point f of the hyperbola If we take a point Rh equal to the distance from point P to the other focal point f on the straight line connecting point P3, then the relationship between the line segment i and the line segment -7° is expressed by Equation 5. There is.

♀・=F72 ・・・・・・・・・・・・・・・
(5) Also, the tangent line of the hyperbola at 23 points is the bifocal point f
Let Q3 be the point that intersects the straight line

PSQll±Rhf2 ・・・・・・・・・・・・・・・
(6) The present invention provides that the three types of quadratic curves are:
Focusing on the fact that ``It'' has the property that the lengths of two specific line segments are equal, and that the two specific line segments of ``Iya'' have a perpendicular relationship, we created a mechanism that has the above properties. It has become concrete.

Next, regarding the embodiment of this invention, for each type of quadratic curve,
This will be explained with reference to Ekko.

FIG. 4 shows a quadratic curve generator drawn on the parabola 11'.

As shown in FIG. 4, the quadratic curve generator for drawing a parabola consists of a link element body l that always maintains an orthogonal relationship between the subdivision beam and line segments R and F, and a subdivision RFP.

and a first link member that maintains constant the line segment I;
It has a second link member J and a third link member a.

The link element body L is located on a tangent to the parabola A, and is a long tangential member formed into a plate shape, for example. It has a pair of plate-shaped arm members 6.7, for example, which extend orthogonally in a cross shape. The tangential section S is movably attached to the first groove g, and has a parabolic shape. It has a mover /θ of 411 for pivotally supporting the generating tool q, and a second mover l that is movably attached to the first groove and pivotally supporting the bottle //. Further, one arm member 6 has a second groove 13, for example, a groove-shaped opening, extending from one end in the longitudinal direction to the vicinity of the tangential portion S, and the second groove A third mover/3, which is pivotally supported by the fixed bin/Qf, is slidably fitted into the passage 13.

Similar to the arm member 6, the other arm member 7 has a fifth channel 16t-, in which a second bottle 77 is inserted.
A fourth mover/piece having a diameter is slidably fitted thereinto.

The first link member K is formed in the shape of a long plate, one end of which is pivoted to the first bin of the second mover, and the other end of the first link member K to the first link member K. It is pivoted to the fixed bottle of No. 3 mover/S. The second link member 3 is formed into a long plate shape, and has one end pivotally supported on the first bin of the second mover 12 and the other end attached to the fourth
is pivoted to the second bin/7 of the mover ig. The first link member and the second link member 3 are
so that the interval between the first bin // and the fixed bin /y is equal to the interval between the first bin 17 and the second bin 17,
Each pivot point is set. Therefore, when the second mover /λ moves in the first groove g, the third mover /3 and the fourth mover ig move in the second groove 13 and the third groove ll- wo, the link element body l will move at the same time while maintaining an equal distance from the cross-shaped intersection T.

The third link member l is formed into a long plate shape, one end of which is pivotally supported on the second bin 17 of the fourth mover ig, and a long fourth link member l in the middle part thereof. A groove path 19, for example, a groove-shaped opening is fully formed, and a fifth mover that pivotally supports the parabola generator 7 of the first mover 10 is slidably inserted into the fourth groove path 19. Fit, and then the other end GL! K is the 6th
Fix the mover 2/. This sixth mover 2/f,
J:, from one end of the long plate-shaped stator 22 in the longitudinal direction to the other end, it is slidable in a fifth groove 23 formed perpendicular to the fourth groove /7. is mated to. Therefore, when the sixth mover moves completely in the fifth rK path 2J of the stator, the third link member l that intersects with the fifth groove path 23 moves in parallel. Become.

The construction of a parabola using the quadratic curve generator constructed above will be described next.

First, the quadratic curve generation A having the above configuration is placed on the drawing surface, and rotatably fixed at the position that should be the focus F of the fixed bin/1It-parabola A, and the focus F and inflection point 0 of the parabola A are fixed. The stator 22 is arranged and fixed perpendicularly to a straight line passing through. In this state, a writing instrument such as lead or a pen, or a cutting tool such as a cutter is attached to the tip of the parabola generating tool as desired.

Therefore, by sliding the sixth mover 21 into the fifth groove 23, for example in the direction of the arrow in FIG. 4, the third link flit U is moved. , the link element body l rotates counterclockwise about the fixed pin/da as a fulcrum. The tangent line 111 member 5 and the pair of arm members 6.7 always have a rectangular relationship of the second formula, and the first
A link mechanism having a link member J, a second link member J, and a third link member, a parabola generator D,
A triangle connecting the first bin // and the second bin /7 and a parabola generator? , fixed bin IQ and first bin l/
The distance between the triangle connecting the parabola generator 7 and the second bin 17 is always maintained, and the distance between the parabola generator 7 and the fixed bin /4' and the total distance 1) i
If ll is kept constant, the relationship in the first equation is maintained, and the parabola generator draws the parabola A.Next, an example of the quadratic curve generator for drawing an ellipse is shown in the fifth example. As shown in the figure.

The difference between the quadratic curve generator for drawing an ellipse shown in FIG. 5 and the quadratic curve generator for drawing a parabola shown in FIG. 4 is that the third link member q and the stator 2. There is currently a plan for a third link member with the following configuration:
Is Rukoto. Boo, that is, the third link portion ifAλl
t is a long plate-like body, one end of which INB is pivotally supported on the second bin/7 of the fourth mover/8, and a long fourth groove is provided in the middle part of the body. 3.For example, form a groove-like 110 part,
Is there a quadratic curve generator of the first mover 10 in the fourth groove J? A fifth mover 26 that pivotally supports the ellipse C is slidably fitted therein, and the other end of the ellipse C is fixed with a focal point pinia X1 to be located at one focal point P of the ellipse C. In this section, members having the same functions as those in Figure 4 will be given the same symbol, and detailed explanations will be omitted.

Next, construction of the ellipse C using the quadratic curve generator configured as described above will be described.

First, the quadratic surface Aθ generating tool of 41/, , 27 are rotatably fixed at the position where they should be one focal point F of the ellipse C.

Next, when the sixth glue member 2y is rotated, for example, in the counterclockwise direction of the arrow in FIG. Rotate with force. Then, during rotation, the tangential portions 1 and 4S
Since the pair of arm members 6.7 are always perpendicular to each other, the relationship of the above-mentioned Edict 4 is maintained.
The link part t1, the second link member 3, and the third link member are evaluated as follows. Song l11
1 creation tool? Since the distance connecting the second bin 17 and the distance connecting the quadratic curve generating tool and the fixed bin llI are -7, the relationship of the fifth equation of 0116C is maintained.

Therefore, if the two songs are 1MbU, the third link s
One rotation of @2 will draw the p1 ellipse.

Figure 6 shows an example of the quadratic curved pattern "Crow" which depicts a hyperbola.

The fourth quadratic curve generator shown in Figure 6 is used to draw hyperbolas.
The difference from the quadratic curve generator for drawing a parabola shown in the figure is that the third link member 4 and the stator n
>JC% The third link member Mf has the following configuration.

That is, the fifth link part @2g is a long plate-like body, and the fourth groove 2 is long from one end to the middle part.
t, for example, an opening is formed, and a fifth groove 2t for pivotally supporting the quadratic curve generating device of the first mover 10 is provided in the fourth groove 2t.
Mover 301F! : Fits slidably, and the second bin/7i of the fourth mover/g is pivoted at the middle part, and one focal point f of the hyperbola is mounted at the other end. A focus bin J/ to be located at is rotatably fixed. In addition,
The pair of arm members 6.7 of the link element body l in the quadratic curve generating tool that creates the hyperbolic #il' are in contact lfi! compared to the link element body l shown in FIG. In Fig. 6, members having the same functions as those in Fig. 4 are given the same numbers, and their detailed information is explained. The explanation will be omitted.

First, a quadratic curve generator having the above configuration is placed on the drawing surface,
The fixing pin 4I is rotatably fixed at a position which should be the other focal point f2 of the hyperbolic curve, and the focusing pin 3/f is rotatably fixed at a position which should be one focal point f of the hyperbolic curve.

Next, when the third link member Mf is rotated, for example, in the counterclockwise direction of the arrow in FIG. 6, centering on the focal point pier 3/f, the link element body l rotates clockwise with respect to the fixed pin IQf. . During rotation, the tangential member S and the pair of arm members 6 and 6 are always perpendicular to each other, so that the sixth
The relationship of the formula is maintained, and the first link member K, the second link member J, and the third link EtIS@'J-
t, the conic curve generator d and the second bin 1, as in the quadratic curve generator of FIG.
Since the distance connecting 7 and the distance connecting the secondary surface a creating tool d and the fixed pin/da are constant, the relationship in equation 5 is maintained. Therefore, the quadratic curve generator draws a hyperbola Dt by rotating the third link member g.

Although the embodiments of this invention have been described in detail above, it goes without saying that this invention is not limited to the above embodiments, and can be practiced with appropriate modifications within the scope of the gist of this invention. do not have.

In the embodiment described above, each groove is a groove-shaped opening, and the slider is a fitting piece that can be slid into the opening. It may also be a moving wheel.

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

■ Can draw quadratic curves easily and accurately.

■ Three types of quadratic curves can be easily drawn by changing the function of the third link member.

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

■ Since the structure is simple, it is easy to manufacture and can be manufactured at low cost.

■ The principle of quadratic curves Since the entire principle can be clearly shown, it can be used as a teaching material for understanding the principle of quadratic curves.

■ Can also be used for forming, polishing, and cutting lens surfaces.

[Brief explanation of drawings]

Figures 1 to 3 are explanatory diagrams showing the principle of this invention, and Figure 4
6 to 6 are plan views showing an embodiment of the present invention. /...link element body, ko...first link member, 3
...Second link member, μ...Third link member,
S... Tangent member, 6.7... Arm member, g... First groove path, ? ... Quadratic curve generator, 10... First mover, l/... First pin, /λ... Second mover, /J... Second groove path , lri... fixed bottle, /3
...Third mover, /A...Third groove path, /7...
・Second pin, lI! r...Fourth mover, 19...
・Fourth groove path,〃...Fifth mover, 2/...Sixth
Mover, 2... Stator, 3... Fifth groove, 2'
l...Third link member, '8...Fifth groove, 2
6...Sixth mover, Koku...Focus bin, 3...
3rd link n@, 2t...5th groove, JO...
Sixth mover, 31... focus bin. Patent applicant Akira Shishido Part 1'

Claims (4)

[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, and the tangential member has a longitudinal side thereof. a first mover movably attached to a first groove extending from near one end to near the other end in a direction and pivotally mounting a quadratic curve generating pin; A second mover is provided that is movably attached to the groove and is located on the opposite side of the arm member from the first mover, and one of the pair of arm members includes: A third groove is movably attached to a second groove extending from the vicinity of the longitudinal end to the vicinity of the tangential member, and a fixed bin to be located at the focal point of the quadratic curve is pivoted. A mover is provided on the other arm member, and is movably attached to the third groove formed to extend from near the longitudinal end of the other arm member to near the tangential member, and is attached to the tangential member. On the other hand, there is provided a link element body including a fourth mover disposed symmetrically with the third mover, and a first link element body having the fixing pin pivotally attached to one end thereof and provided on the second mover. The first pin is pivotally connected to the other end.
a second link member to which a first pin provided on the second mover is pivotally connected to one end and a second pin provided to the fourth mover, a fourth groove in which a second pin provided on the fourth slider is pivotally connected, and a fifth slider is movable, the second pin provided on the first slider being pivotally connected; The third plate formed along the longitudinal direction
A quadratic curve generating tool comprising: a link member; (2) The quadratic curve is a parabola, and the third link member has a second pin provided on the fourth mover pivotally attached to one end thereof, and the other end thereof: A sixth movable movable element is fully fixed to a fifth groove extending in the longitudinal direction of the stator, which is disposed perpendicularly to the optical axis passing through the focal point and the inflection point of the parabola, and The quadratic curve generating tool according to claim 1, characterized in that it is movable in parallel to an axis. (3) The quadratic curve is an ellipse, and the third link member has a second link provided on the fourth mover at one end thereof.
A pin of the ellipse is pivotally attached to the ellipse, and a focus bin to be located at the other focal point of the ellipse is fixed to the other end of the ellipse, and the focus pin is rotatably movable around the entire center of the ellipse. The quadratic curve generator according to item 1. (4) The quadratic curve is a hyperbola, and the fifth link member has a second pin provided on the fourth mover pivotally connected to the middle part thereof, and has a hyperbola shape at one end thereof. /l\:F! is characterized in that a focusing pin to be located at the other focal point of is fixed and is rotatable around the focusing bin.
T. The quadratic curve generating tool according to claim 1.