JPS6135998A - Method of forming curve of secondary degree and forming tool - 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 method and tool for creating a quadratic curve suitable for application to geometry teaching materials and polishing and forming a quadratic curved surface.

Traditionally, instruments for drawing and forming quadratic curves have used link mechanisms or many gears, but these have complex structures and are extremely difficult to manufacture and difficult to operate. It had the following drawback.

The present invention uses a common principle of quadratic curves, which is different from conventional ones, to create quadratic curves that are easy to manufacture and can draw accurate quadratic curves, such as parabolas, ellipses, and hyperbolas, with simple operations. The main purpose of this invention is to provide a method and a tool for creating the next curve.

FIG. 1 is a route map showing an example of a creation tool suitable for use in a method for creating a parabola, which is an example of the method for creating a quadratic curve according to the present invention.

Reference numeral 10 indicates an L-shaped member, which is composed of a first member 11 and a second member 12 that are perpendicular to each other, with a support shaft 1 at each intersection point.
There are three. The support shaft 13 represents an arbitrary point P on the quadratic curve. The first member 11 is formed to extend in the direction of a point N where the normal line at an arbitrary point P intersects with the optical axis, and
A sliding groove 11a is bored on which the slider S1 slides on a line connecting the line segment N, and the second member 12 is formed as a tangent at an arbitrary point P, and is therefore formed in an L-shape perpendicular to the line segment PN. , slider S on the line of parallel line T'T',
A sliding groove 12a for sliding is provided.

The slider S2 sliding in the sliding groove 12a of the second member 12 is connected to the first link piece 14 that regulates the distance from the focal point F.
and a second link piece 15 that regulates the distance from an arbitrary point P to the vertical line D'D'. . The other end of the first link piece 14 is rotatably attached to a fixing pin 16 on the focal point F.
is fixed. One of the second link pieces 15 is a slider S2
The other end is rotatably supported on a support shaft 18 provided at the point of the link piece 20 provided on the vertical line D'D'. The link piece 20 is formed into a T-shape for convenience in depicting a parabola among quadratic curves. Then, the point where the vertical line D'D' and the link piece 20 intersect at right angles is designated as D, and the slider slides in the groove 21a of the sliding groove body 21 fixedly provided on the vertical line D'D', and at any arbitrary point. P and D
A sliding groove body 22 extending on a line parallel to the optical axis connecting the two is bored. The support shaft 13 of the L-shaped member 10 is slidably fitted into the groove body 22.

The support shaft 13 further has a vertical groove 31 formed extending on a line connecting an arbitrary point P and a foot M placed perpendicularly to the light MON from this point P.
is mated to. The vertical grooves 31 and the horizontal grooves 32 formed on the optical axis connecting the focal points F and N are bored in a grooved plate, for example, the triangular plate 3( ), in order to regulate the orthogonal relationship (see FIG. 2). A support shaft for supporting the slider S1 is provided on the triangular plate 3 at a point N on the optical axis (point MN=2f (=constant)).

Next, the creation of a parabola, which is an example of the method of the present invention, will be explained.

First, as shown in FIG. 1, the fixing pin 16 is rotatably fixed on the drawing surface at a position that should be the focal point F of the parabola 1A, and a straight line passing through the focal point F of the parabola A and the inflection point O is set. The sliding groove body 21 is arranged and fixed vertically. In this state, any point P
That is, a writing instrument such as a pencil or pen or a quadratic curve generating means such as a cutter is provided at the tip of the support shaft 13 as desired.

By sliding the link piece 20 along the sliding groove 21, for example, in the downward direction in FIG.
0 is the first link piece 14. The second link piece 15 biases the fixing pin 16 in a counterclockwise direction.

Along with this, the triangular plate 30 is deflected (leftward in the figure) due to the movement of the support shaft 13 fitted in the vertical groove 31 and the slider s1 fitted in the horizontal groove 32.

In this case, the triangle connecting the fixed pin 16, the slider s2, and the support shaft 13 and the triangle connecting the support shaft 13, the support shaft 18, and the slider S2 maintain a congruent relationship with each other, so that the support shaft 13 and the fixed pin 16 The distance between the support shaft 13 and the support shaft 18 is kept constant, and due to the structure of the L-shaped member 10, the line connecting any point P and the slider Sl, and the distance between the arbitrary point P and the slider In order to maintain the orthogonal relationship between the lines connecting S2,
A parabola A will be created.

Next, creation of an ellipse using the above creation tool will be explained. The difference with the creation of a parabola is that in a parabola, the second focal point is at infinity, so the line connecting arbitrary points P and D must be placed parallel to the optical axis, whereas in the case of an ellipse, , the second focal point is any point P.

]) should intersect with the second focal point. Also, for a parabola, MN = 2f (=constant), but for an ellipse, MN = x (1e'-), so add a pantograph 4 () with lines at points M, 0, and N. It is important to form it.

That is, as shown in FIG. 3, the fixing pin 16 is rotatably fixed at the position that should be the j-th focal point F of the ellipse B, and
The end of the link piece 20 opposite to the end where the support shaft 18 is provided is rotatably fixed to a second focal point F' on the optical axis. In this state, a writing instrument such as a pencil or pen or a cutting tool such as a canter is attached to an arbitrary point P, that is, the tip of the support shaft 13, as desired, and the link piece 20 is moved counterclockwise around the second focal point F'. By rotating the L-shaped member 10, the first link piece 14. The triangular plate 30 is rotated clockwise around the optical axis 16 by the second link piece 15, and the triangular plate 30 is moved as shown in the figure by the movement of the support shaft 13 fitted in the vertical groove 31 and the slider S1 fitted in the horizontal groove 32. deviate to the left. In this case, the triangle connecting the fixed pin 16, slider S2, and support shaft 13 is also connected to the support shaft 1.
3. The triangles connecting the support shaft 18 and the slider S2 maintain a congruent relationship with each other, so that the distance between the support shaft 13 and the fixed pin 16 and the support shaft 13 and the support shaft 18 is kept constant, and the L-shape is maintained. Depending on the structure of the member 10, an arbitrary point P and slider S1
Since the line connecting , the arbitrary point P, and the line connecting the slider S2 maintain an orthogonal relationship, the left half of the diagram of the ellipse B is created. Therefore, by using the first and second focal points inversely, the right half of the building will be created.

Next, creation of a hyperbola using the above creation tool will be explained. The difference with the creation of a parabola is that the second focus of a parabola is at infinity, so any point P.

The line connecting D needs to be placed parallel to the optical axis, whereas a hyperbola has a second focal point, and the second focal point has an eccentricity greater than the power bow, so the L-shaped member 10 and each First link piece 14. In addition to inverting IS and using any point P,
The line connecting D should intersect with the second focal point. Also, while a parabola has h4N = 2 f (= constant), a hyperbola changes as MN = It is important to form it.

That is, as shown in FIG. 4, the fixing pin 16 is
is rotatably fixed at the position that should be the second focal point F2 of the link piece 20, and one end 2 (la of the link piece 20
It is rotatably fixed at the focal point F1.

In this state, a pencil is placed at an arbitrary point P, that is, at the tip of the support shaft 13.
A writing instrument such as a pen or a cutter such as a cutter may be provided as desired.

By rotating the link piece 2 () counterclockwise around the first focal point F1, the L-shaped member 10 is rotated clockwise around the support shaft 13 by the first link piece 14 and the second link piece 15. As the triangular plate 3 ( ) rotates in the direction, the triangular plate 3 ( ) is deflected to the left in the figure by the movement of the support shaft 13 fitted in the vertical groove 31 and the slider S1 fitted in the horizontal groove 32 . In this case, the triangle connecting the fixed pin 16, the slider S2, and the support shaft 13 and the triangle connecting the support shaft 13, the support shaft 18, and the slider S2 maintain a congruent relationship with each other, so that the support shaft 13 and the fixed pin 1
6 and the support shafts 13 and 18 are kept constant, and due to the structure of the L-shaped member 10, a line connecting any point P and the slider S1, and a line connecting any point P and the slider S2. Since the connecting lines maintain an orthogonal relationship, a hyperbola C will be created. Therefore, a corresponding hyperbola will also be created by using the first and second focal points inversely, respectively.

As described above, according to the present invention, a first line segment extending from an arbitrary point P on the quadratic curve to a point where the normal line at the arbitrary point P is the optical axis is provided, and from the focal point A second line segment perpendicular to the normal line is constructed in an L shape with the arbitrary point P as the intersection, and a second line segment perpendicular to the normal line is configured in an L shape with the arbitrary point P as the intersection, and a second line segment on the line passing through one focal point (including infinity) of the quadratic curve and the arbitrary point P The distance between an arbitrary point R and the arbitrary point P is regulated to match the distance between the arbitrary point P and the other focal point, and the first line segment is defined as a straight line passing through the focal point and orthogonal to this. Since the system moves along a straight line and creates a quadratic curve at the arbitrary point P, it is easy to create various properties of the quadratic curve without having to use many auxiliary lines as in the past. Since you can create a quadratic curve while understanding
Perfect for teaching.

Further, according to the present invention, the first
and a second member perpendicular to the normal line from the focal point, configured in an L shape with the arbitrary point P as the intersection point, and a focal point on the - side of the quadratic curve (infinity ) and a first point connected to the rectangular member that makes the distance between an arbitrary point R on a line passing through the arbitrary point P and the arbitrary point P equal to the distance between the arbitrary point P and the other focal point. and a second link piece, and a groove plate having a groove in which the first member of the rectangular member slides on a straight line passing through the focal point and a straight line orthogonal thereto, and at the arbitrary point. Since it is equipped with a quadratic curve generating means, there are far fewer components than in the past, making it easy to manufacture, making it possible to form, polish, and cut the surfaces of various lenses in large-scale optical systems. Therefore, when applied to teaching materials, it can be supplied at low cost.

[Brief explanation of the drawing]

FIG. 1 is an explanatory diagram showing the creation of a parabola as an example of the creating tool of the present invention, FIG. 2 is a diagram showing an example of a groove plate, and FIG. 3 is an explanatory diagram of creating a shield circle using the creating tool of the present invention. FIG. 4 is an explanatory diagram of creating a hyperbola using the creating tool of the present invention. 10...L-shaped member, 11...@1 member, 12...
Second member, 13... Support shaft, 14... First link piece, 15... Second link piece, 30... Groove plate, 31...
...Vertical groove, 32...Horizontal groove. Applicant's agent Patent attorney Takashi Akiyama Figure 1 Figure 3 Prisoner Figure 4

Claims (1)

[Claims] 1. Provide a first line segment extending from an arbitrary point P on the quadratic curve to a point where the normal line at the arbitrary point P intersects with the optical axis, and the second perpendicular line segment and the arbitrary point P
The distance between any point R on the line passing through one focus (including infinity) of the quadratic curve and the arbitrary point P and the arbitrary point P is set to an arbitrary point. The first line segment is controlled so as to match the distance between the point P and the other focal point, and the first line segment is moved on a straight line passing through the focal point and a straight line perpendicular thereto, and at the arbitrary point P. A method for creating a quadratic curve, characterized in that a quadratic curve is created. 2. A first member extending from an arbitrary point P on the quadratic curve to a point where the normal line at the arbitrary point P intersects with the optical axis, and a second member perpendicular to the normal line from the focal point. An L-shaped member configured in an L-shape with the arbitrary point P as the intersection, an arbitrary point R on a line passing through one focus (including infinity) of the quadratic curve and the arbitrary point P, and the arbitrary point P. First and second link pieces connected to the L-shaped member that make the distance from point P match the distance between any point P and the other focal point, and on a straight line passing through the focal point and a straight line orthogonal thereto. above L
A quadratic curve generating tool comprising: a groove plate having a groove in which a first member of the rectangular member slides; and a quadratic curve generating means is provided at the arbitrary point.