Method for manufacturing columnar body and columnar body manufactured by the same

Abstract

To provide a method for manufacturing a columnar body that enables the columnar body to be produced more easily and at lower cost.SOLUTION: The method includes the steps of: calculating the radius of curvature along a generatrix direction with respect to a columnar surface having a desired curved shape; producing a plate-shaped body whose cross-sectional area is determined along the generatrix direction in proportion to the radius of curvature; and bending the plate-shaped body along the generatrix direction. The generatrix may be any differentiable curve, preferably a parabola, an ellipse, or a hyperbola, and may also be a curve having an inflection point.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a technique for producing a cylindrical body, and more specifically to a method for producing a cylindrical body by calculating the radius of curvature of a cylindrical surface having a desired curved shape and curving a plate-like body having a cross-sectional area determined to be proportional to the radius of curvature. [Background technology]

[0002] Many improved reflecting telescopes have been developed, including Newtonian reflecting telescopes that use parabolic reflectors. However, the high level of precision required for polishing the parabolic reflectors used as primary mirrors and the complexity of the manufacturing process remain unchanged to this day. As a result, medium- to large-sized reflecting telescopes are expensive, and from both technical and cost perspectives, they are difficult to manufacture without a large-scale organization. Therefore, if it were possible to manufacture a high-light-gathering reflecting telescope that requires enormous investment, but is cheaper, easier, and lighter than conventional telescopes, even ordinary citizens would be able to own or build their own reflecting telescopes.

[0003] Techniques proposed to solve these problems in reflecting telescopes include those described in, for example, Patent Documents 1 to 3. These techniques use a reflector with a concave shape that is curved in only one direction, i.e., a cylindrical reflector. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2005-164881 [Patent Document 2] Patent No. 6602942

[0005] [Non-Patent Document 1] Kanazawa Institute of Technology, KIT Mathematics Navigation, URL https: / / w3e.kanazawa-it.ac.jp / math / category / kika / heimenkika / henkan-tex.cgi?target= / math / category / kika / heimenkika / radius_of_curvature.html&pcview=2 [Non-patent document 2] Shozo Koshi, Introduction to Calculus, Academic Press, January 1979 Summary of the Invention [Problem to be solved by the invention]

[0006] The techniques proposed in Patent Documents 1 to 3 require the fabrication of a cylindrical reflector that is curved in only one direction. While fabricating such a cylindrical reflector is not as difficult as fabricating the primary mirror of a parabolic reflector, it still requires expensive machine tools. On the other hand, cylindrical reflectors used in simple telescopes can be fabricated using, for example, a 3D printer, but this requires the surface to be mirror-finished or a mirror body to be attached to the surface. Furthermore, 3D CAD or the like must be created using data from the 3D printer, making it difficult to fine-tune the resulting product.

[0007] Therefore, an object of the present invention is to provide a method for producing a cylindrical body more easily and inexpensively. Another object of the present invention is to provide a cylindrical body that can be produced by this method and has a structure different from that of a cylindrical body that has a shape obtained by curving a rectangular plate in only one direction. [Means for solving the problem]

[0008] When a force F is applied to a rectangular plate with a cross-sectional area A parallel to its surface (cross-sectional area A), the distortion θ of the rectangle is proportional to F and inversely proportional to the cross-sectional area A. In other words, 1 / θ is proportional to the cross-sectional area A. Based on this relationship, the inventors discovered that if the cross-sectional area A is changed in advance along the curve of a certain differentiable function f so that θ is proportional to the radius of curvature r obtained from the function f when a force is applied to the plate with a cross-sectional area A, then θ will change inversely proportional to r in the direction along the curve, and therefore it is possible to create a cylindrical body using the function f, which is the basis of the radius of curvature r, as a conductor.

[0009] In one aspect, the present invention provides a cylindrical body manufacturing method for manufacturing a cylindrical body having a desired curved shape from a rectangular plate. The method includes the steps of calculating the radius of curvature of the cylindrical surface along the direction of a conductor line, fabricating a plate having a cross-sectional area along the direction of the conductor line that is proportional to the radius of curvature, and curving the plate along the direction of the conductor line. The conductor line can be any differentiable curve, preferably a parabola, ellipse, or hyperbola, and can also be a curve with an inflection point.

[0010] In one embodiment, the step of producing a plate-shaped body with a defined cross-sectional area includes producing a plate-shaped body with a uniform thickness and a length of a generatrix perpendicular to the conductor that is proportional to the radius of curvature. In another embodiment, the step of producing a plate-shaped body with a defined cross-sectional area includes producing a plate-shaped body with a uniform length of a generatrix perpendicular to the conductor and a thickness along the conductor that is proportional to the radius of curvature.

[0011] In one embodiment, the step of fabricating a plate-like body having a cross-sectional area determined along the direction of the conductor so as to be proportional to the radius of curvature includes fabricating a plate-like body having one straight side and the other curved side along the direction of the conductor, while in another embodiment, the step of fabricating a plate-like body having a cross-sectional area determined along the direction of the conductor so as to be proportional to the radius of curvature includes fabricating a plate-like body having two curved sides along the direction of the conductor.

[0012] In one embodiment, the step of bending the plate-like body along the conductor direction includes fixing at least two opposing points across the center of the plate-like body in the conductor direction while maintaining the bending. In another embodiment, the step of bending the plate-like body along the conductor direction includes fixing at least two opposing points across the center of the plate-like body in the conductor direction and a point corresponding to the inflection point.

[0013] In another aspect, the present invention provides a cylindrical body having a desired curved shape. The cylindrical body has a cross-sectional area determined along the direction of the conductor line so as to be proportional to a radius of curvature calculated along the direction of the conductor line of the cylindrical body having the desired curved shape. The cylindrical body may have a uniform thickness and the length of a generatrix perpendicular to the conductor line is determined to be proportional to the radius of curvature. Alternatively, the length of the generatrix perpendicular to the conductor line is constant and the thickness along the direction of the conductor line is determined to be proportional to the radius of curvature. The conductor line may be any differentiable curve, preferably a parabola, ellipse, or hyperbola, and may also be a curve having an inflection point.

[0014] In yet another aspect, the present invention provides a cylindrical body design method for designing a cylindrical body having a desired curved shape from a rectangular plate-like body, the method comprising the steps of calculating a radius of curvature along the direction of a conductor for the cylindrical surface having the desired curved shape, and determining a cross-sectional area of ​​the plate-like body along the direction of the conductor so as to be proportional to the radius of curvature. [Effects of the Invention]

[0015] According to the present invention, a cylindrical body can be produced more easily and inexpensively without using expensive machine tools or sophisticated mirror finishing. [Brief explanation of the drawings]

[0016] [Figure 1] 1 is a schematic diagram showing an example of the configuration of an optical system having a reflecting mirror that can be fabricated using a cylindrical body fabrication method according to an embodiment of the present invention. [Figure 2] 1A and 1B are schematic diagrams of a parabolic cylinder, which is an example of a cylinder that can be fabricated using a method for fabricating a cylinder according to an embodiment of the present invention, where (a) shows a plan view of the plate before bending, and (b) shows a perspective view of the plate after bending. This is a parabolic cylinder in which one side along the direction of the conductor is curved and the other side is straight. [Figure 3] FIG. 1 is a flow diagram showing a method for manufacturing a cylindrical body according to an embodiment of the present invention. [Figure 4] This shows a graph of the radius of curvature calculated in the creation of a parabolic cylinder with a focal length of 50 mm. [Figure 5] This shows a portion of a graph of the length of the parabola calculated when creating a parabolic cylinder with a focal length of 50 mm. [Figure 6] 1A and 1B are schematic diagrams of a parabolic cylinder, another example of a cylinder that can be fabricated using the method for fabricating a cylinder according to an embodiment of the present invention, in which (a) shows a plan view of the plate before bending, and (b) shows a perspective view of the plate after bending. This is a parabolic cylinder in which both sides along the direction of the conductor are curved. [Figure 7] 10 is a graph comparing the curved state of a cylindrical body whose width is determined according to the cylindrical body manufacturing method of the present invention and a cylindrical body that is curved without removing the ends in the width direction. [Figure 8] 1 is a photograph of a prototype of an elliptical cylinder manufactured according to the method for manufacturing a cylinder according to the present invention. [Figure 9] This is a trace of an actual rectangular plate showing the positions where the edges in the width direction are removed to create a parabolic cylinder with a focal length of 500 mm. [Figure 10] This shows an optical system constructed using a parabolic cylinder created by removing the edge of the plate of Figure 9 with the back surface traced and then bending it. [Figure 11] (a) is an image taken by the optical system of FIG. 10, and (b) is a photograph of an actual scene including (a). DETAILED DESCRIPTION OF THE INVENTION

[0017] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the following, the method for manufacturing a cylindrical body according to the present invention will be described using a cylindrical reflector that can be used in an optical system such as a telescope as an example. However, the method for manufacturing a cylindrical body according to the present invention can be used not only for designing and manufacturing reflectors for optical systems, but also for designing and manufacturing cylindrical bodies for various other applications. For example, the method for manufacturing a cylindrical body according to the present invention can be used for designing and manufacturing the shapes of exterior walls and roofs of buildings, designing and manufacturing automobile bodies, designing and manufacturing antenna shapes for receiving radio waves, and designing two cylindrical antennas arranged with their concave surfaces facing each other that can be used as an alternative to radar antennas.

[0018] (Example of optical system configuration) Fig. 1 shows an example of the configuration of an optical system that can use a cylindrical reflector manufactured by the manufacturing method according to the present invention (see Patent Document 2). Fig. 1 shows an example in which a cylindrical reflector is used as the primary mirror of an optical system.

[0019] The optical system shown in FIG. 1 includes a primary mirror M that reflects light from an object K, and a cylindrical lens L (concentrator) that is disposed on the optical axis of the light reflected from the primary mirror M and transmits the light reflected by the primary mirror M. The primary mirror M has a concave reflecting surface 12 that is curved in only one direction (i.e., only in the y-axis direction in the figure), and this reflecting surface 12 is a cylindrical reflecting mirror that can reflect light from the object K. An optical system in which the cylindrical lens L used in this optical system is replaced with a cylindrical reflecting mirror secondary mirror whose reflecting surface faces the direction of the primary mirror M, as disclosed in Patent Document 1, for example, is also possible. These primary mirrors and secondary mirrors can be fabricated using the fabrication method of the present invention.

[0020] (Definition of a cylinder) In this specification, a cylinder is an object with a curved surface (cylinder) that is created when a straight line that intersects a curve at a single point moves along the curve while maintaining a constant direction. The original curve is called the conductor, and the individual lines that make up the cylinder are called its generatrix.

[0021] (Creating a parabolic cylinder) [How to change the width in proportion to the radius of curvature] Figure 2 is a schematic diagram of a parabolic cylinder, which is an example of a cylinder that can be produced by a cylinder production method according to one embodiment of the present invention, where (a) shows a plan view of the plate before bending, and (b) is a perspective view after bending. Figure 3 is a flow chart showing a cylinder production method according to one embodiment of the present invention. The method for producing the cylinder of Figure 2 will now be described.

[0022] (1) Calculation of the radius of curvature of a parabolic cylinder First, for a cylindrical surface having a desired curved shape, the radius of curvature along the direction of the conductor is calculated (step S1 in Figure 3). In this case, since the cylindrical surface having the desired curved shape is a parabolic cylindrical surface, the conductor is a parabola. The parabola is expressed by the following equation (1). y=f(x)=ax 2 (1)

[0023] The radius of curvature r of a function y=f(x) that represents an arbitrary differentiable curve can be calculated from the following equation (2), as shown in, for example, Non-Patent Document 1 and Non-Patent Document 2.

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[0024] (2) Preparation of plate-shaped bodies Next, a plate-like body is produced whose cross-sectional area is determined along the direction of the conductor so as to be proportional to the radius of curvature calculated by the above method (step S2 in FIG. 3). The inventors have found that a cylindrical body having a generating line perpendicular to the curve of function f (which becomes the conductor of the cylindrical body) can be fabricated by calculating the radius of curvature r obtained from a function f that represents an arbitrary differentiable curve, and then curving the plate by varying the cross-sectional area of ​​the plate having a length direction along the curve of function f in proportion to the calculated radius of curvature r. In one embodiment, a method for determining the cross-sectional area of ​​the plate along the conductor so that it is proportional to the radius of curvature can be considered, in which the thickness is uniform and the length of the generating line perpendicular to the conductor (i.e., the width of the plate) is determined so that it is proportional to the radius of curvature.

[0025] As a specific example, a rectangular plate with a length of 450 mm, width of 150 mm, and thickness of 1 mm is prepared, and by changing the width of this rectangular plate along the length direction, a plate forming a parabolic cylinder with a focal length of f = 50 mm is produced. In the case of a parabola with a focal length of f = 50 mm, a in equation (1) is 1 / (4f)=a (4) From the above relationship, a = 0.005. By substituting this a into equation (3), the radius of curvature of the parabola at the position x can be calculated. Figure 4 shows a graph of the radius of curvature calculated in this way, plotting the radius of curvature r (parabola) corresponding to the value of x when the center of the length of the rectangular plate is set to 0 on the x-axis.

[0026] Next, if necessary, the position along the length of the rectangular plate corresponding to the position on the x-axis, i.e., the length of the plate from the center in the length direction to the position corresponding to the position on the x-axis, is determined. The radius of curvature r calculated by the above equation (3) is the radius of curvature of the parabola at the position corresponding to the value on the x-axis. However, since the cylinder is curved, the length along the plate from the center of the length of the plate (i.e., point 0 on the x-axis) toward the end to the position corresponding to the value of x is different from the length along the x-axis from point 0 to that value of x, and the length along the plate is longer than the length along the x-axis. Therefore, to determine the width of the rectangular plate so that it is proportional to the radius of curvature along its length, it may be necessary to calculate the relationship between the value p on the x-axis from the center of the length and the length L of the plate to the position corresponding to p. However, for a cylinder with a large radius of curvature (a cylinder with a long focal length), for example, there may be little difference between the length on the x-axis and the length along the cylinder within the range of the length in the conductor direction required as a reflector. Therefore, this step of calculating the relationship between p and L is not necessary.

[0027] In the parabola of equation (1), the length L of the parabola from the origin to the position x=p is

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[0028] Based on the above concept, a width is calculated along the conductor direction so as to be proportional to the radius of curvature, and a plate-like body having the calculated width is produced. Here, a method for producing a plate-like body having a width determined along the conductor direction so as to be proportional to the radius of curvature by physically removing the end portion from the original rectangular plate-like body is described. However, this is not limited to this, and a plate-like body having a width calculated along the conductor direction in advance may also be produced.

[0029] There are two methods for changing the width of a rectangular plate along the conductor direction by removing its edges: removing only one edge in the width direction of the rectangular plate, and removing both edges in the width direction. Using the method of removing only one edge in the width direction results in a plate with one straight edge and the other curved edge along the conductor direction. Using the method of removing both edges in the width direction results in a plate with both curved edges along the conductor direction. The parabolic cylinder shown in Figure 2 is a cylinder made using the former method, i.e., removing only one edge in the width direction of the rectangular plate.

[0030] Table 1 shows some of the values ​​used to fabricate the parabolic cylinder. In Table 1, p is the length (mm) from point 0 on the x-axis, L is the length (mm) of the conducting wire (parabola) to the position corresponding to p on the x-axis, and r is the radius of curvature (mm) of the conducting wire (parabola) at position p. The length of the conducting wire corresponds to the length of the plate. In the table, r(p) is the radius of curvature of the plate at position x = p, and r(pe) is the radius of curvature of the plate at the end of the length of the plate, i.e., at position L = 450 / 2 = 225 mm, when the center of the plate in the longitudinal direction is set to point 0 on the x-axis. r(p) / r(pe) indicates the ratio of the radius of curvature at position p to the radius of curvature at the end. Therefore, the width of the plate can be determined based on this ratio (step S2-1 in Figure 3). In order to simplify the table, Table 1 does not list all p and their corresponding values, but lists only representative values. The granularity of p can be determined depending on the size of the parabolic cylinder, the focal length, and other factors.

[0031] [Table 1]

[0032] FIG. 2(a) is a schematic plan view of a rectangular plate produced by removing only one widthwise end of the rectangular plate according to Table 1, and FIG. 2(b) is a schematic perspective view of the parabolic cylinder obtained by bending the plate shown in FIG. 2(a). Alternatively, a parabolic cylinder can be produced by removing both widthwise ends of the rectangular plate. In this case, a plate with both curved sides along the conductor direction can be obtained by removing both widthwise ends of the rectangular plate equally or by removing one widthwise end more than the other according to the ratios shown in Table 1. FIG. 6 is a schematic diagram of a parabolic cylinder obtained in this manner. FIG. 6(a) is a schematic plan view of a rectangular plate produced by removing both widthwise ends of the rectangular plate before bending, and FIG. 6(b) is a schematic perspective view of the cylinder obtained by bending the plate shown in FIG. 6(a).

[0033] [Method to change thickness in proportion to the radius of curvature] So far, we have described a method for producing a plate-like body whose width is determined to be proportional to the radius of curvature along the conductor direction. However, as another means for achieving a plate-like body whose cross-sectional area is proportional to the radius of curvature, the thickness of the plate-like body can be varied along the conductor direction (step S2-2 in Figure 3). The method for varying the thickness is not limited. For example, a plate-like body whose cross-sectional area is proportional to the radius of curvature can be produced by grinding one or both surfaces of the plate-like body. When producing a reflecting mirror, it is preferable to grind the surface opposite the reflecting surface. Alternatively, the thickness can be varied by applying, for example, putty to one or the other surface of the plate-like body. Alternatively, a plate-like body having a predetermined thickness along the conductor direction may be produced.

[0034] Furthermore, as a means for varying the thickness of the plate along the conductor direction, grooves extending perpendicular to the conductor can be formed with a density inversely proportional to the radius of curvature. Specifically, grooves extending perpendicular to the conductor from one end of the plate to the other can be formed with varying density along the length of the plate. Multiple grooves can be formed so that the spacing between adjacent grooves is wide near the ends of the plate and narrows toward the center. This groove density per unit length along the length of the plate gradually increases from the ends to the center. Within a certain range, areas with high groove density are equivalent to reducing the thickness of the plate, while areas with low groove density are equivalent to increasing the thickness of the plate.

[0035] (3) Curvature of the plate Next, the plate-like plate produced in (2) above, i.e., a plate-like body whose width changes along the conductor direction in proportion to the radius of curvature, or a plate-like body whose thickness changes along the conductor direction in proportion to the radius of curvature, is curved along the conductor direction and fixed in a curved state at least two points opposite each other across the center in the conductor direction, thereby producing a parabolic cylinder with the desired focal length (step S3 in Figure 3).

[0036] One method for bending a plate is to connect and fix both ends of the plate along the direction of the conductor (i.e., the length). The plate is fixed so that both ends of the conductor are located on the desired parabola when the center of the plate in the length direction is positioned at point 0 on the x-axis. For a plate with the values ​​shown in Table 1, both ends of the plate (each 225 mm long from the center) are fixed at points on the parabola corresponding to x = 166.07 and -166.07. If both ends of the plate are fixed so that they are located on the parabola in this way, the remaining parts of the plate automatically conform to the shape of the desired parabola, resulting in a parabolic cylinder with this parabola as its conductor. The fixing points can also be any two points on the parabola closer to the origin than the ends. In this case, the section between the two fixed points is a parabolic cylinder with a shape that conforms to the desired parabola, and the area outside these fixed points is not curved.

[0037] The two ends of the plate-like body can be fixed in the required position, i.e., on the desired parabola, for example, by connecting the two ends with one or more screw shafts and nuts, or by passing a tape, string, etc. between the two ends. Alternatively, for example, the two ends can be fixed in the required position by preparing a flat plate corresponding to the size of the plate-like body, fixing the central part of the plate-like body in the longitudinal direction to the flat plate, and supporting the two ends of the plate-like body with support members extending from the surface of the flat plate.

[0038] As described above, according to the present invention, it is possible to obtain a parabolic cylinder having a cross-sectional area determined along the direction of the conductor so as to be proportional to the radius of curvature calculated along the direction of the conductor. By varying the width of a plate of uniform thickness along the direction of the conductor, it is possible to obtain a parabolic cylinder whose width is determined so as to be proportional to the length of the generatrix perpendicular to the conductor, i.e., the radius of curvature. Furthermore, by varying the thickness of a plate of constant width along the direction of the conductor, it is possible to obtain a parabolic cylinder whose generatrix perpendicular to the conductor is constant and whose thickness is determined so as to be proportional to the radius of curvature.

[0039] (4) Comparison with a rectangular cylinder with no edges removed A cylinder whose width is determined to be proportional to the radius of curvature according to the method of the present invention is compared with a cylinder whose widthwise ends have not been removed, i.e., a cylinder obtained by simply bending a rectangular plate. Figure 7 is a graph comparing the bending states of the two. In Figure 7, line B is a line tracing the edge of a cylinder obtained by bending a rectangular plate of the same size as the above example, i.e., 450 mm long x 150 mm wide x 1 mm thick. Line A is a line tracing the unremoved edge of a cylinder of the same size as the cylinder of line B, but with one widthwise end removed according to Table 1 (i.e., the cylinder shown in Figure 2(b)). The black circles in the graph of Figure 7 represent the calculated values ​​of a parabola using equations (1) and (4) with f = 50. Both ends of both lines lie on the parabola.

[0040] The line A of the cylinder fabricated by the method of the present invention closely matches the calculated value of the parabola (●), which is the desired curved shape, while the line B bulges outward from the parabola between the fixed part and the origin. This is because the cross-sectional area of ​​the cylinder of line A varies depending on the longitudinal position, i.e., the cross-sectional area is determined so that it conforms to the parabola when curved, whereas the cross-sectional area of ​​the cylinder of line B does not change with the longitudinal position. Therefore, the cross-sectional area of ​​the cylinder of line B is larger than that of the cylinder of line A at the same longitudinal position, and when fixed at both longitudinal ends and curved, it experiences a stronger tendency to expand outward than the cylinder of line A. This result also demonstrates that, according to the present invention, it is possible to fabricate a cylinder using a differentiable function f as a conductor by previously varying the cross-sectional area A along the curve of the function f so that it is proportional to the radius of curvature r obtained from the function f.

[0041] (Creating other prisms) In the above, a parabola has been described as an example of an arbitrary differentiable curve, but such curves are not limited to parabolas, and a cylinder can be similarly created for various curves. For example, an elliptical cylinder can be created in the same way as the parabolic cylinder described above by calculating the radius of curvature from the following ellipse formula (9), creating a plate-like body whose cross-sectional area is determined along the direction of the conductor so that it is proportional to the radius of curvature, and then curving the plate-like body.

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[0042] Specifically, the radius of curvature r (of the ellipse) obtained using the ellipse formula (9) to formula (2) is expressed by the following formula (10).

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[0043] Based on this equation (10), the width is calculated along the conductor direction so that it is proportional to the radius of curvature, and an elliptical cylinder is created using the ellipse as the conductor. The values ​​used to create an elliptical cylinder by physically removing one end from the original rectangular plate are shown in Table 2. These values ​​were calculated for an ellipse with a major axis of 2a and a minor axis of 2b, with a = 60 and b = 30. [Table 2]

[0044] In this table, p is the x-coordinate value on the ellipse (p = 0 corresponds to (0, b) on the ellipse). L is the arc length (mm) of the ellipse from the coordinate (0, b) or (0, -b) to the position corresponding to the value of x = p. The arc length of the ellipse corresponds to the length along one side from the longitudinal end of the plate-like body when the elliptical cylinder is expanded. r is the radius of curvature (mm) of the ellipse at the position corresponding to the value of p. In the table, r(p) is the radius of curvature of the ellipse at the position x = p, and r(pe) is the radius of curvature of the ellipse at the position p = 0. r(p) / r(pe) is the ratio of the radius of curvature at the position p to the radius of curvature at the position p = 0, and the width of the plate-like body can be determined according to this ratio.

[0045] When the elliptical cylinder is expanded into a plate, the length of the plate from the position x=0 on the ellipse (coordinates (0, b) or (0, -b)) to the position corresponding to x=p (i.e., the arc length of the ellipse) can be calculated, for example, by using equation (11), which is well known to those skilled in the art for calculating the arc length of an ellipse. Here, θ is the angle between the line connecting the point x=p on the ellipse to the origin and the minor axis of the ellipse (the central angle of the sector).

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[0046] By bending the plate thus fabricated, i.e., a plate whose width varies in proportion to the radius of curvature along the wire direction, and fixing both ends together, an elliptical cylinder with an elliptical wire can be fabricated. Figure 8 shows a photograph of a prototype elliptical cylinder fabricated in this way. The wire of the prototype elliptical cylinder nearly coincides with the elliptical equation (9). The elliptical cylinder mirror fabricated in this way can be used in its entirety or, as needed, in a portion along the wire direction, as a reflecting mirror in a floating zone furnace used in the floating zone method, a single crystal growth method.

[0047] Similarly, a bipolar cylinder can be created based on the following formula:

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[0048] In general, according to the present invention, a cylinder can be fabricated using any differentiable curve as a conductor. A curve having an inflection point can be expressed by the following formula:

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[0049] As an example, a parabolic cylindrical reflector with a focal length of f=500 mm was fabricated, and an optical system was constructed using this reflector. An actual landscape was photographed using the constructed optical system. To fabricate a parabolic cylindrical reflector, an acrylic mirror with a length of 270 mm, width of 150 mm, and thickness of 2 mm was prepared. The parabola with a focal length of f = 500 mm can be expressed by the following equation (14) from equations (1) and (4). y=(5×10 -4 )x 2 (14) The radius of curvature of this parabola is given by equation (3):

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[0050] [Table 3]

[0051] The width of the plate was calculated based on the ratio calculated in this way, and a line indicating the position of the edge to be removed was marked on the back surface (the surface opposite the reflective surface) of the prepared acrylic mirror. Figure 9 is a diagram tracing the back surface of an actual acrylic mirror with the line indicating the removal position. Next, the edge of the acrylic mirror was removed along this line. Both longitudinal ends of the acrylic mirror from which the edge was removed were fixed with two screw shafts and nuts. By using both screw shafts and nuts, fine adjustments could be made so that the longitudinal end was positioned on the desired parabola. The parabolic cylindrical reflector thus fabricated was used to construct the optical system shown in Figure 10. The optical system in Figure 10 is a realization of the optical system shown in Figure 1(a). It uses the fabricated parabolic cylindrical reflector as a primary mirror that reflects light from the subject, and includes a cylindrical convex lens (focal length f = 200 mm) that is positioned on the optical axis of the light reflected from the primary mirror and serves as a secondary mirror that transmits and refracts the light reflected by the primary mirror M, and an oblique mirror as a light receiving unit that receives the light transmitted through the cylindrical convex lens.

[0052] Figure 11(a) shows a photograph taken using the optical system in Figure 10. This photograph was obtained by capturing the image reflected by the light receiving section of the optical system with a camera. The roof of the building seen in the center of the scene shown in Figure 11(b) is clearly visible in this photograph. Note that Figure 11(b) was taken with a standard digital camera. In the photograph in Figure 11(a), the roof appears vertically stretched compared to the actual scene. This is a distortion caused by the difference in focal lengths between the primary mirror (a parabolic cylindrical reflector) and the secondary mirror (a cylindrical convex lens) of this optical system. This distortion can be easily corrected, if necessary, by placing another lens after the secondary mirror (i.e., downstream in the light propagation direction) or by using correction software.

Claims

1. A cylindrical body manufacturing method for manufacturing a cylindrical body having a desired curved shape from a square plate-like body, comprising the steps of: Calculating the radius of curvature along the direction of the conductor for a cylindrical surface having a desired curved shape; a step of preparing a plate-like body having a cross-sectional area determined along the direction of the conductor so as to be proportional to the radius of curvature; bending the plate-like body along the direction of the conductor; A method for manufacturing a cylindrical body, comprising:

2. The step of producing a plate-shaped body having a defined cross-sectional area includes: and producing a plate-like body having a uniform thickness and a length of a generating line perpendicular to the conductor that is determined to be proportional to the radius of curvature. The method for manufacturing a cylindrical body according to claim 1 .

3. The step of producing a plate-shaped body having a defined cross-sectional area includes: and producing a plate-like body having a constant length of a busbar perpendicular to the conductor and a thickness along the direction of the conductor that is determined to be proportional to the radius of curvature. The method for manufacturing a cylindrical body according to claim 1 .

4. The conductor is any differentiable curve. The method for manufacturing a cylindrical body according to any one of claims 1 to 3.

5. The conductor is either a parabola, an ellipse, or a hyperbola. The method for manufacturing a cylindrical body according to claim 4.

6. The conductive line is a curve having an inflection point. The method for manufacturing a cylindrical body according to claim 4.

7. The step of producing a plate-like body having a cross-sectional area determined along the direction of the conductor so as to be proportional to the radius of curvature includes: and producing a plate-like body in which one side of the plate-like body along the direction of the conductor is a straight line and the other side is a curved line. The method for manufacturing a cylindrical body according to claim 2 .

8. The step of producing a plate-like body having a cross-sectional area determined along the direction of the conductor so as to be proportional to the radius of curvature includes: and producing a plate-like body in which two sides of the plate-like body along the direction of the conductor wire are both curved. The method for manufacturing a cylindrical body according to claim 2 .

9. The step of bending the plate-like body along the direction of the conductor wire includes: and fixing at least two points of the plate-like body that are opposite to each other across the center of the plate-like body in the direction of the conductor while maintaining the curve. The method for manufacturing a cylindrical body according to claim 4.

10. The step of bending the plate-like body along the direction of the conductor wire includes: and fixing the plate-like body at at least two locations facing each other across the center of the plate-like body in the direction of the conductor and at a location corresponding to the inflection point. The method for manufacturing a cylindrical body according to claim 6.

11. A cylindrical body having a desired curved shape, a cross-sectional area determined along the direction of the conductor line of a cylindrical body having a desired curved shape, the cross-sectional area being proportional to a radius of curvature calculated along the direction of the conductor line; Cylindrical body.

12. The thickness is uniform, and the length of the generating line perpendicular to the conductor is determined to be proportional to the radius of curvature. The cylindrical body according to claim 11.

13. The length of the busbar perpendicular to the conductor is constant, and the thickness along the direction of the conductor is determined to be proportional to the radius of curvature. The cylindrical body according to claim 11.

14. The conductor is any differentiable curve. The cylindrical body according to any one of claims 11 to 13.

15. The conductor is either a parabola, an ellipse, or a hyperbola. The cylindrical body according to claim 14.

16. The conductive line is a curve having an inflection point. The cylindrical body according to claim 14.

17. A cylindrical body design method for designing a cylindrical body having a desired curved shape from a quadrangular plate, comprising: Calculating the radius of curvature along the direction of the conductor for a cylindrical surface having a desired curved shape; determining a cross-sectional area of ​​the plate-like body in proportion to the radius of curvature along the direction of the conductor; A cylindrical body design method including:

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