JPH0216718B2 - - Google Patents

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. This invention is based on a principle different from conventional ones.
The object of the present invention is to provide a quadratic curve generator that is easy to manufacture and can draw accurate quadratic curves, such as parabolas, ellipses, and hyperbolas, with simple operations. First, the principle of this invention will be explained. Parabolas, ellipses, and hyperbolas have two types of properties in common. In a parabola, as shown in Fig. 1, if the foot of the solid line drawn from an arbitrary point P ₁ of the parabola A to the directrix B is R _P , and the focal point of the parabola A is F, then the line segment P ₁ There is a relationship between R _P and the line segment P ₁ F as shown in the first equation. P ₁ R _P = P ₁ F ………(1) Also, the tangent of the parabola A at the point _P is the focal point F
A straight line (optical axis) passing through and the inflection point O of the parabola A
If the point that intersects B′ is Q ₁ , line segment R _P F and line segment
The relationship between P ₁ Q ₁ is expressed by the second equation. _{P _ _ _}
If we take a point R _e equal to the distance from point P ₂ to the other focal point _{F 2 on} a straight line that passes through any point _{P 2} in There is a relationship expressed by the third equation between P ₂ R _e and the line segment P ₂ F ₂ . P _{2 Re} = P ₂ F ₂ ………(3) Also, the tangent of the ellipse C at the _two points P is the bifocal point F ₁ ,
If the point Q ₂ intersects the straight line X passing through F ₂ , then the line segment
There is a relationship expressed by the fourth equation between P ₂ Q ₂ and the line segment R _e F ₂ . P ₂ Q ₂ ⊥ R _e F ₂ ......(4) In a hyperbola, as shown in Figure 3, on the straight line connecting one focus F ₁ of the hyperbola D and any point P ₃ of the hyperbola D, If we take a point R _h that is equal to the distance from the point P ₃ to the other focal point F ₂ , then the relationship of equation 5 exists between the line segment R _h P ₃ and the line segment P ₃ F ₂ . R _h P ₃ = P ₃ F ₂ ………(5) Also, the tangent of the hyperbola D at _{the 3} points P is bifocal
If _{the intersection point with the straight line} P ₃ Q ₃ ⊥ R _h F ₂ ………(6) The present invention provides that the three types of quadratic curves have the same length of two specific line segments, and Focusing on the fact that the line segments have an orthogonal relationship, this embodiment embodies a mechanism having the above property. Next, embodiments of the present invention will be described 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 includes a link element body 1 that always maintains a perpendicular relationship between the line segment P ₁ Q ₁ and the line segment R _p F , and the line segment R p P 1 and the line segment R _p P ₁ . A first link member 2, a second link member 3, and a third link member 4 that always maintain the line segment P ₁ F constant.
It has The link element body 1 is located on a tangent to a parabola A, and includes an elongated tangential member 5 formed in a plate shape, for example, and a longitudinal direction of the tangential member 5 on both sides of an approximately intermediate portion of the tangential member 5. It has a pair of, for example, plate-shaped arm members 6 and 7 extending in a cross shape orthogonal to . The tangential member 5 is movably attached to an elongated first slideway 8 formed from one end to the other end in the longitudinal direction, for example, a groove-shaped opening, and the first slideway 8. It has a first slider 10 that pivotally supports the shaft pin 9, and a second slider 12 that is movably attached to the first slideway 8 and that pivotally supports the first pin 11. Further, one arm member 6 has a second slideway 1 formed extending from one end in the longitudinal direction to the vicinity of the tangential member 5.
3, the second slideway 1 having, for example, a groove-like opening;
3, a third mover 15 that pivotally supports the fixed pin 14;
be slidably fitted. Also, the other arm member 7
Like the arm member 6, it has a third slideway 16, and a fourth slider 18 having a second pin 17 is slidably fitted into the third slideway 16. . The third mover 15 and the fourth mover 18 are located symmetrically with respect to the tangential member 5. The first link member 2 is formed into a long plate shape, and one end thereof is connected to the first link member 2 of the second mover 12.
The other end is pivotally supported to the fixing pin 14 of the third movable element 15. Further, the second link member 3 is formed into a long plate shape, and one end thereof is pivotally supported on the first pin 11 of the second mover 12 coaxially with the first link member 2. , the other end is pivotally supported on the second pin 17 of the fourth mover 18. The first link member 2 and the second link member 3 are
Each pivot point is set so that the distance between the pin 11 and the fixed pin 14 is equal to the distance between the first pin 11 and the second pin 17. Therefore, the second
When the slider 12 moves on the first runway 8, the third
The mover 15 and the fourth mover 18 move the second slideway 13 and the third slideway 16 simultaneously, that is, symmetrically, while maintaining the same distance from the cross-shaped intersection T of the link element body 1. I will do it. The third link member 4 is formed into a long plate shape, and its tip is pivotally supported on the second pin 17 of the fourth mover 18, and a long fourth link member is provided in the middle part of the third link member 4. A slideway 19, for example, a groove-shaped opening is formed, and a fifth slider 20 is slidably fitted into the fourth slideway 19, and the fifth slider 20 and the first slider are slidably fitted into the fourth slideway 19. Child 1
0 and is coaxially supported by an axis pin 9. Furthermore, a sixth mover 2 is provided at the base end of the third link member 4.
Fix 1. The sixth slider 21 has a fifth slideway formed perpendicularly to the fourth slideway 19 from one end of the elongated plate-shaped stator 22 to the other end in the longitudinal direction. 23 is slidably fitted. Therefore, when the sixth mover 21 is moved along the fifth slideway 23 of the stator 22, the third link member 4 perpendicular to the fifth slideway 23 is moved in parallel. Parabola A using the quadratic curve generator with the above configuration
The drawing of is described next. First, the quadratic curve generator having the above configuration is placed on the drawing surface, and the fixing pin 14 is rotatably fixed at the position that should be the focal point F of the parabola A, and the focal point F and the inflection point O of the parabola A are The stator 22 is arranged and fixed perpendicularly to a straight line passing through. In this state, the shaft pin 9
If desired, a writing implement such as a pencil or pen or a cutter such as a cutter is attached to the tip of the handle. Therefore, when the third link member 4 is moved by sliding the sixth slider 21 along the fifth slideway 23, for example, in the direction of the arrow in FIG. rotates counterclockwise using the fixed pin 14 as a fulcrum. The tangential member 5 and the pair of arm members 6 and 7 always have a second orthogonal relationship, and during rotation, the first link member 2, the second link member 3, and the third link member 4, the shaft pin 9, the first pin 11, the second pin
The triangle connecting pins 17 of
The distance connecting the pin 17 and the distance connecting the shaft pin 9 and the fixed pin 14 are kept constant, the relationship of the first equation is maintained, and the trajectory of the shaft pin 9 becomes a parabola A.
will be drawn. Next, FIG. 5 shows an example of a quadratic curve generator for drawing an ellipse. 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. , the third link member 24 has the following configuration. That is, the third link member 24 is a long plate-shaped body, and its tip is connected to the fourth mover 18 by the second pin 17.
A long fourth slideway 25, for example, a groove-shaped opening, is formed in the middle part thereof, and the shaft pin of the first slider 10 is provided in the fourth slideway 25. A fifth mover 26 that pivotally supports 9 is slidably fitted,
Furthermore, an ellipse C is formed at the base end of the third link member 24.
A focus pin 27, which should be located at one focus _F1 , is fixed. In FIG. 5, members having the same functions as those in FIG. 4 are denoted by the same reference numerals, and detailed explanation thereof will be omitted. The construction of the ellipse C using the quadratic curve generator having the above configuration will be described next. First, the quadratic curve generator having the above configuration is placed on the drawing surface, and the fixing pin 14 is rotatably fixed at a position that should be the other focal point _F2 of the ellipse C, and the focal pin 27 is fixed at the position where the other focal point F2 of the ellipse C should be. It is rotatably fixed at the position where one focal point _F1 should be. Next, when the third link member 24 is rotated, for example, in the counterclockwise direction of the arrow in FIG.
Rotate counterclockwise around the center. Here, since the tangential member 5 and the pair of arm members 6 and 7 are always perpendicular to each other during rotation, the relationship of the fourth equation is maintained, and during rotation, the first link member 2, the second With the link mechanism having the link member 3 and the third link member 24, as in the quadratic curve generator shown in FIG. Since the distance between the fixed pin 14 and the fixed pin 14 is constant, the relationship of the third equation is maintained. Therefore, by swinging the third link member 24 up and down on the X axis around the focal point _F1 ,
The movement locus of the shaft pin 9 traces one half of an ellipse. And the focus pins 31 of each focus F ₁ and F ₂
The other half of the ellipse can be drawn by exchanging the positions of the fixed pin 14 and the other half of the ellipse and performing the same operation as above.
Further, the link element body 1 and each link member 2, 3,
If 24 is configured to have a sufficiently large length, it is also possible to draw the entire circumference of an ellipse by rotating the third link member 24. Next, FIG. 6 shows an example of a quadratic curve generator for drawing a hyperbola. The difference between the quadratic curve generator for drawing a hyperbola shown in FIG. 6 and the quadratic curve generator for drawing a parabola shown in FIG. , the third link member 28 has the following configuration. That is, the third
The link member 28 is an elongated plate-like member, and the fourth slideway 2 is elongated from the tip to the middle part.
9. Forming a groove-shaped opening, for example, and slidably fitting the fifth slider 30 to which the shaft pin 9 of the first slider 10 is pivotally connected to the fourth slideway 29; Further, a fourth link member 28 is provided at the intermediate portion of the third link member 28.
The second pin 17 of the mover 18 is pivotally supported, and further,
A focus pin 31 to be located at one focus F ₁ of the hyperbola D is rotatably fixed to the base end of the third link member 28 . Note that the pair of arm members 6 and 7 of the link element body 1 in the quadratic curve generator for creating a hyperbola are symmetrical with respect to the tangent member 5 as compared to the link element body 1 shown in FIG. In addition to being replaced, members in FIG. 6 that have the same functions as those in FIG. 4 are designated by the same reference numerals, and detailed explanation thereof will be omitted. First, place the quadratic curve generator having the above configuration on the drawing surface, and move the fixing pin 14 to the other focal point F ₂ of the hyperbola D.
At the same time, the focusing pin 31 is rotatably fixed at a position where one of the focal points _F1 of the hyperbola D should be. Next, when the third link member 28 is rotated, for example, in the counterclockwise direction of the arrow in FIG.
Rotate clockwise around the center. During rotation, the tangential member 5 and the pair of arm members 6 and 7 are always perpendicular to each other, so the relationship of the sixth equation is maintained,
In addition, the first link member 2, the second link member 3
and a link mechanism having a third link member 28, similarly to the quadratic curve generator shown in FIG. 4, the distance between the shaft pin 9 and the second pin 17,
Since the distance between the shaft pin 9 and the fixed pin 14 is constant, the relationship of the fifth equation is maintained. Therefore, the movement locus of the shaft pin 9 is the same as that of the third link member 2.
By rotating 8, one half of the hyperbola D is drawn. Then, the other half of the hyperbola can be drawn by replacing the focal pins 31 and fixed pins 14 of each focal point F ₁ and F ₂ and operating in the same manner as above. 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. Quadratic curves can be drawn easily and accurately. By changing the function of the third link member, three types of quadratic curves can be easily drawn. Since there are few components, it can be made very compact and does not take up much space. Since the configuration is simple, it is easy to manufacture and can be produced at low cost. 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. It can also be used for forming, polishing, and cutting lens surfaces.

[Brief explanation of drawings]

1 to 3 are explanatory diagrams showing the principle of the invention, and FIGS. 4 to 6 are plan views showing embodiments of the invention. 1 is a link element body, 2 is a first link member, 3
is the second link member, 4 is the third link member, 5
is a tangential member, 6 and 7 are arm members, 8 is a first slideway,
9 is a shaft pin, 10 is a first slider, 11 is a first pin, 12 is a second slider, 13 is a second slideway,
14 is a fixed pin, 15 is a third mover, 16 is a third slide, 17 is a second pin, 18 is a fourth mover, 19 is a fourth slide, and 20 is a fifth mover. child, 2
1 is a sixth slider, 22 is a stator, 23 is a fifth slideway, 24 is a third link member, 25 is a fourth slideway, 26 is a fifth slider, 27 is a focusing pin, 28
3 is a third link member, 29 is a fourth slideway, 30 is a fifth slider, and 31 is a focusing pin.

Claims (1)

[Claims] 1. A link element body 1 having a tangential member to be located on a tangent to a quadratic curve to be drawn and a pair of arm members 6 and 7 extending in a cross shape orthogonal to the tangential member 5.
, a first link member 2 movably pivotally connected to the link element body 1 via a slider, and a second link member 2 movably pivotally attached to the link element body 1 via a slider.
This is a quadratic curve generating tool consisting of a link member 3 and a third link member 4, 24, 28 which is movably pivotally connected to the link element body 1 via a slider. forms a first slideway 8 extending along the longitudinal direction, and a first slider 10 and a second slider 12 that are movable symmetrically about the midpoint are attached to the first slideway 8. Together with each arm member 6,
7 is formed with second and third slideways 13 and 16, and each slideway 13 and 16 is provided with a third and fourth slider 15,
18 are movably attached to each other, the second mover 12 and one end of the first link member 2 are pivotally supported by the first pin 11, and the other end of the first link member 2 and the first link member 2 are pivotally supported by the first pin 11. 3 mover 15 and fixing pin 14
The second movable element 12 and the third movable element 15 are connected by being pivoted by the first pin 11, and the second movable element 12 and one end of the second link member 3 are is coaxially supported with the link member 2 of
The other end of the second link member 3 and the fourth mover 1
8 is pivotally supported by the second pin 17 to connect the second mover 12 and the fourth mover 18, so that the third mover 15 and the fourth mover 18 are tangential. The third link members 4, 24, 28 are moved symmetrically and at right angles to the member 5.
A fourth slideway 19, 25, 29 is formed in the fourth slideway 19, 25, 29, and a fifth slider 2 is formed in the fourth slideway 19, 25, 29.
0, 26, 30 are movably mounted, and the fifth slider 20, 26, 30 and the first slider 10 mounted on the first slideway 8 of the tangential member 5 are connected to the shaft pin 9.
A part of the third link member 4, 24, 28 is pivotally supported coaxially with the fourth mover 18 by the second pin 17, and the third link member 4, A quadratic curve generating tool characterized in that when the shaft pins 24 and 28 are translated or rotated, the locus of movement drawn by the shaft pin 9 becomes a quadratic curve having a focal point at the position of the fixed pin 14. 2. The quadratic curve is a parabola, the fixing pin 14 is located at the focal point of the parabola, and the third
The link member 4 has a second pin 17 provided on the fourth slider 18 pivotally attached to its tip, and its base end is connected to the optical axis passing through the focal point and the inflection point of the parabola. The third link member 4 is fixed to the sixth slider 21 which is movably attached to the fifth slideway 23 formed to extend in the longitudinal direction of the stator 22 arranged orthogonally to each other. The quadratic curve generating tool according to claim 1, characterized in that it is movable parallel to the optical axis. 3 The quadratic curve is an ellipse, and the fixing pin 1
4 is located at one focal point of the ellipse, and the third link member 24 has a second pin 17 provided on the fourth slider 18 pivotally attached to its tip, and its base end. A quadratic curve generating tool according to claim 1, characterized in that a focusing pin 27 to be located at the other focal point of the ellipse is fixed to the ellipse, and is rotatably movable around the focusing pin 27. . 4. The quadratic curve is a hyperbola, the fixing pin 14 is located at one focal point of the hyperbola, and the third link member 28 has a second link member provided on the fourth mover 18 in the middle thereof. A pin 17 is pivotally attached, and a focusing pin 31 to be located at the other focal point of the hyperbola is fixed to the base end thereof, and the focusing pin 31 is rotatably movable around the focusing pin 31. A quadratic curve generator according to item 1 of the scope.