Shaped article, shaped article design method, and shaped article production method

Abstract

To provide a shaped article capable of further improving the degree of freedom of shaping.SOLUTION: A shaped article W produced by a 3D printer has shaped parts W1a and W1b each having a loop shape defined based on a torus knot, the plurality of shaped parts W1a and W1b being connected to each other and forming at least a part of a porous structure.SELECTED DRAWING: Figure 21

Description

[Technical Field]

[0001] The present invention relates to a three-dimensional object, a method for designing an object, and a method for manufacturing an object. [Background technology]

[0002] BACKGROUND ART In recent years, fused deposition modeling 3D printers, for example, have become widely known as model manufacturing devices for manufacturing three-dimensional models (see, for example, Patent Document 1).

[0003] When it comes to objects manufactured using 3D printers, there is more freedom in design than with conventional methods, and they can handle complex shapes; however, the more complex the shape, the more support is required to support the parts of the model that need support during printing, and it is often difficult to remove support that is no longer needed after printing.

[0004] Furthermore, lattice structures have traditionally been used when manufacturing objects using 3D printers (see, for example, Patent Document 2). Lattice structures are structures in which branched lattices are periodically arranged, allowing the interior of the object to be hollow, making it easy to reduce weight. However, because each element (edge) of this lattice structure is linear, it lacks flexibility (elasticity), and multiple unit cells must be combined to create a curved surface (curve). Additionally, because lattice structures have vertices, the connection direction (angle) is limited. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Special Publication No. 2000-500709 [Patent Document 2] Japanese Patent Application Laid-Open No. 2015-93461 Summary of the Invention [Problem to be solved by the invention]

[0006] Therefore, one object of the present invention is to provide a shaped object, a shaped object design method, and a shaped object manufacturing method that can further improve the degree of freedom in shaping. [Means for solving the problem]

[0007] A shaped object according to an embodiment of the present invention is a shaped object manufactured by a shaped object manufacturing device, and has a shaped portion having a loop shape defined based on a torus knot, and is configured by connecting multiple shaped portions to form at least a part of a porous structure.

[0008] In the above-described shaped object, the plurality of shaped portions may be connected so that the loop shapes intersect with each other.

[0009] In the above-described shaped object, the plurality of shaped portions may be connected so that the closed loop shapes do not intersect with each other.

[0010] In the above-described shaped object, the plurality of shaped portions may have the same shape or mirror-symmetric shapes.

[0011] In the above-described shaped object, the plurality of shaped portions may have shapes that are different in size from one another.

[0012] Furthermore, the object design method of the present invention forms the modeling data of the modeling part by setting a thickness to a surface formed by connecting two adjacent torus knots with a line.

[0013] In the above-described method for designing a shaped object, the shaping data of the shaping portion may be formed by sweeping a predetermined cross-sectional shape along a torus knot having a loop shape.

[0014] A method for manufacturing a shaped object according to the present invention is a method for manufacturing a shaped object by using a shaped object manufacturing apparatus, based on the modeling data formed by the above-described method for designing a shaped object.

[0015] In the above-described method for manufacturing a shaped object, the shaped object manufacturing apparatus may be a 3D printing apparatus employing a fused deposition modeling method or a photolithography method. [Effects of the Invention]

[0016] According to the embodiment of the present invention, it is possible to further improve the degree of freedom in shaping. [Brief explanation of the drawings]

[0017] [Figure 1] 1 is a front view schematically illustrating a fused deposition modeling 3D printer, which is an apparatus for manufacturing a molded object according to an embodiment of the present invention. [Figure 2] FIG. 1 is an explanatory diagram showing a torus knot. [Figure 3] This figure shows a molded object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 4] This shows a first design method for one object shown in Figure 3, where (a) is an oblique view showing a surface connecting two torus knots with a line, and (b) is an oblique view showing modeling data with thickness added to (a). [Figure 5] 10A and 10B are diagrams showing other objects manufactured using a 3D printer based on the modeling data designed by the first design method, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 6] This figure shows yet another object manufactured using a 3D printer based on the modeling data designed by the first design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a partially enlarged view thereof. [Figure 7]This figure shows yet another object manufactured using a 3D printer based on modeling data designed using the first design method, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is an oblique view from one direction, and (e) is an oblique view from another direction. [Figure 8] This shows a first design method for yet another object shown in Figure 7, where (a) is an oblique view showing a surface connecting two torus knots with a line, and (b) is an oblique view showing modeling data with thickness added to (a). [Figure 9] 10A and 10B show still another object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 10] 10 shows a second design method for yet another object shown in FIG. 9, where (a) is a perspective view showing a torus knot that serves as a sweep line, (b) is a perspective view showing an enlarged portion of (a), (c) is a perspective view of the modeling data in which a cross-sectional shape is swept along the sweep line of (a), and (d) is a perspective view showing an example in which the side edge of the cross-sectional shape extends along the modeling table. [Figure 11] This figure shows yet another object manufactured using a 3D printer based on modeling data designed using the second design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position equivalent to II in (b). [Figure 12] This figure shows yet another object manufactured using a 3D printer based on modeling data designed using the second design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position equivalent to II-II in (b). [Figure 13]This figure shows yet another object manufactured using a 3D printer based on modeling data designed using the second design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position equivalent to III-III in (b). [Figure 14] This figure shows yet another object manufactured using a 3D printer based on modeling data designed using the second design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position equivalent to IV-IV in (b). [Figure 15] 10A and 10B show still another object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 16] This shows a first design method for yet another object shown in Figure 15, where (a) is an oblique view showing a surface connecting two torus knots with a line, and (b) is an oblique view showing modeling data with thickness added to (a). [Figure 17] This figure shows yet another object manufactured using a 3D printer based on modeling data designed using the second design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is an oblique view from one direction, (e) is an oblique view from another direction, (f) is an oblique view from yet another direction, (g) is an oblique view from yet another direction, and (h) is a cross-sectional view at a position equivalent to VV in (b). [Figure 18]10A and 10B show still another object manufactured using a 3D printer based on modeling data designed by the second design method described above, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, (f) is a perspective view from yet another direction, (g) is a perspective view from yet another direction, and (h) is a cross-sectional view at a position equivalent to VI-VI in (b). [Figure 19] This figure shows yet another object manufactured using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position equivalent to VII-VII in (b). [Figure 20] This figure shows yet another object manufactured using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position equivalent to VIII-VIII in (b). [Figure 21] 19A and 19B are diagrams showing yet another object produced by further connecting the yet another object shown in FIG. 18, where (a) is a plan view seen from the Z-axis direction, (b) is a side view seen from the X-axis direction, and (c) is a perspective view. [Figure 22] 21A and 21B are diagrams showing yet another object produced by further connecting the yet another object shown in FIG. 20, where (a) is a plan view seen from the Z-axis direction, (b) is a side view seen from the X-axis direction, and (c) is a perspective view. [Figure 23] 21A and 21B are diagrams showing yet another object produced by further connecting the yet another object shown in FIG. 20, where (a) is a plan view seen from the Z-axis direction, (b) is a side view seen from the X-axis direction, and (c) is a perspective view. [Figure 24] 21A and 21B are diagrams showing yet another object produced by further connecting the yet another object shown in FIG. 20, where (a) is a plan view seen from the Z-axis direction, (b) is a side view seen from the X-axis direction, and (c) is a perspective view. [Figure 25]24 is a photograph showing a manufacturing example of the shaped object shown in FIG. 23. [Figure 26] 10A and 10B show still another object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 27] 10A and 10B show still another object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 28] 10A and 10B show still another object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 29] 1A and 1B are diagrams showing an example of a torus knot that defines the loop shape of the shaped portion of the same object, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 30] 10A and 10B are diagrams showing another example of a torus knot that defines the loop shape of the shaped portion of the same object, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 31] 10A and 10B show still another object produced using the same 3D printer, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, (c) is a side view from the -Y-axis direction, (d) is a perspective view from one direction, and (e) is a perspective view from another direction. [Figure 32] 27(a) is a photograph showing an example of the shaped object shown in FIG. 26 in a deformed state, and FIG. 27(b) is a photograph showing an example of the shaped object shown in FIG. 26 in a restored state. [Figure 33]FIG. 10 is a cross-sectional view showing a reference example of the rising angle from the modeling table of an object that can be support-less modeled using the same 3D printer. [Figure 34] 34 is a photograph showing a manufacturing example of the reference example of FIG. 33. [Figure 35] 7 is a photograph showing a manufacturing example of the shaped object shown in FIG. 6. [Figure 36] 15 is a photograph showing a manufacturing example of the shaped object shown in FIG. 14. DETAILED DESCRIPTION OF THE INVENTION

[0018] An embodiment of the present invention will be described with reference to the drawings.

[0019] In Figure 1, 1 is a fused deposition modeling 3D printer, which is a device for manufacturing objects. This fused deposition modeling 3D printer (hereinafter sometimes simply referred to as "3D printer 1") is a modeling machine that produces a three-dimensional object W by sequentially layering resin, which is a modeling material that has been melted (dissolved) by heat, one layer at a time based on 3D modeling data.

[0020] The resin used as the modeling material in the 3D printer 1 is, for example, a thermoplastic resin, such as general-purpose plastic, engineering plastic, super engineering plastic, reinforced resin, recycled plastic, biomass plastic, or biodegradable plastic. More specifically, examples include PVC, POM, PBAT, AAS, PS, PLA, plant fiber-filled PLA, ABS, glass fiber-filled ABS, carbon fiber-filled ABS, PP, glass fiber-filled PP, carbon fiber-filled PP, PC, PC-ABS, ASA, TPE, TPU, cellulose acetate, PA, and PETG. Any shape of modeling material, such as pellets or filaments, may be used. Furthermore, the 3D printer 1 may have a single nozzle head, for example, and only one type of resin may be used for modeling; a dedicated resin for support (such as a water-soluble resin) is not required. The modeling material is not limited to resin; metal, ceramic, silicone, etc. may also be used. These molding materials may also have one or more of the following properties: flexibility, antibacterial properties, chemical resistance, heat resistance, stain resistance, and weather resistance, or may have these properties added to them using desired additives.

[0021] The 3D printer 1 includes, for example, a box-shaped main body 3 having a modeling chamber 2 inside, a modeling head 4 that can move in the X-axis direction (horizontal, i.e., left-right direction) and Z-axis direction (up-down, i.e., height direction) within the modeling chamber 2, and a modeling table 5 that can move in the Y-axis direction (horizontal, i.e., front-to-back direction) within the modeling chamber 2.

[0022] Since the modeling head 4 can move in the X-axis direction and the Z-axis direction and the modeling table 5 can move in the Y-axis direction, the modeling head 4 moves three-dimensionally relative to the modeling table 5 (as will be described later, the 3D printer 1 is not limited to the configuration shown in Figure 1, and may be configured in any way so long as the modeling head 4 moves at least three-dimensionally relative to the modeling table 5).

[0023] The 3D printer 1 also includes a first drive unit 6 that moves the modeling head 4 in the X-axis direction and Z-axis direction within the modeling chamber 2, a second drive unit 7 that moves the modeling table 5 in the Y-axis direction within the modeling chamber 2, and a control unit 8 that controls both drive units 6, 7, etc. based on 3D modeling data such as STL data.

[0024] Then, based on the control by the control unit 8, the modeling head 4 moves three-dimensionally relative to the modeling table 5, and resin (molten resin) is ejected from the nozzle 11 of the moving modeling head 4.As the ejected resin hardens and solidifies, the resin is layered on the modeling table 5, and a three-dimensional object W of the desired shape is formed.

[0025] Here, the modeling head 4 of the fused deposition modeling 3D printer 1 with a single nozzle head is, for example, a molten resin extrusion type, and has a single nozzle 11 that ejects melted resin from an outlet using heat from a heating means (not shown) within the modeling head 4.

[0026] That is, the resin that has been heated and melted by a heating means such as a heater (not shown) is extruded by an extrusion means (not shown) such as a gear inside the model-forming head 4, and is discharged (exhausted) from the outlet of one nozzle 11 for discharging the model-forming material in the direction of the central axis of the outlet, for example, downward. Note that the heating means and the extrusion means may be provided outside the model-forming head 4, rather than inside the model-forming head 4.

[0027] The shaped object W produced by the 3D printer 1 of this embodiment has a shaped portion W1 having a loop shape defined based on the torus knot, and constitutes at least a part of the porous structure.

[0028] Here, as shown in Figure 2, a torus knot K is defined as a knot that wraps around the surface of a virtual torus T. This torus knot K is defined by the following equation (hereinafter collectively referred to as equation (1)) using a parameter t.

[0029] Xt=(a·cos(d·t)+e)·cos(f·t) Yt=(b·cos(d·t)+e)·sin(f·t) Zt=c sin(d t)

[0030] The X-axis, Y-axis, and Z-axis directions correspond to the X-axis, Y-axis, and Z-axis directions of the 3D printer 1 (shown in FIG. 1). a through f are non-zero coefficients. The parameter t is between 0 and 2π [rad]. The coefficients a, b, and c set the magnification ratio of the torus T in the X-axis, Y-axis, and Z-axis directions, respectively, relative to the unit torus. The coefficient e sets the "diameter" of the torus T, and together with the coefficients a and b, sets the magnification ratio of the diameter in the X-axis and Y-axis directions relative to the unit torus. The absolute value of the coefficient d sets the number of loops in the meridian direction M of the torus knot K. The absolute value of the coefficients f sets the number of loops in the longitude direction L of the torus knot K. The coefficients d and f basically each have an absolute value of 1 or greater, and preferably at least one absolute value is 2 or greater. Any value may be used as long as a loop shape is formed. However, they are preferably selected so that the torus knot K forms a closed loop shape. For example, they are integer values. Furthermore, the coefficients d and f are preferably set so that the greatest common divisor of their absolute values ​​is 1, i.e., an integer value where one absolute value is 1 and the other absolute value is 2 or greater, or a value where the ratio of their absolute values ​​is equal to the ratio of relatively prime integers. The coefficients a, b, c, and e define the size of the loop shape and are not limited to integer values. Preferably, the coefficients a, b, c, and e are set so that the loop shape does not self-intersect, although self-intersections are acceptable. As is evident from Equation (1), a congruent torus knot K is formed even when the values ​​of Xt, Yt, and Zt are interchanged. However, to facilitate modeling using the 3D printer 1 shown in FIG. 1, it is preferable to fix the axis direction of the torus T (shown in FIG. 2) to the Z-axis direction and only allow the values ​​of Xt and Yt to be interchanged.

[0031] In this embodiment, the 3D modeling data of the modeling unit W1 is designed using a computer or the like using equation (1), and the 3D printer 1 is driven to manufacture the model W based on the designed modeling data.

[0032] Next, a method for designing the object W will be described.

[0033] When the formula (1) is used, the modeling data for manufacturing the model W can be designed by roughly dividing it into two methods.

[0034] The first design method is to create modeling data by adding thickness to a surface formed by connecting two adjacent torus knots with a line.

[0035] The second design method is to create modeling data by sweeping a predetermined cross-sectional shape along a torus knot. Sweeping refers to continuously moving a predetermined cross-sectional shape along a trajectory, in this case, a torus knot.

[0036] The first design method will be described with reference to the drawings.

[0037] FIG. 3 shows an example of a shaping portion W1 (shape W) defined based on a torus knot forming a closed loop shape with |a| = |b| = |c|, d = 1, and f = 2 in Equation (1). As shown in FIG. 4(a), two adjacent torus knots K1 and K2 of approximately similar shape, which differ only in the value (order) of the coefficient e in Equation (1), are used. A line 15, such as a straight line, is used to connect these torus knots K1 and K2 to form a surface 16. A non-self-intersecting line is preferable as the line 15. Then, as shown in FIG. 4(b), this surface 16 is made three-dimensional (solidified) by adding thickness in the normal direction, thereby forming shaping data D. The width of the formed portion W1 can be controlled by changing the difference in coefficient e in equation (1) that describes the two torus knots K1 and K2. For example, the example shown in Figure 5 is a formed portion W1 (formed object W) formed using printing data in which the difference in coefficient e in equation (1) that describes the two torus knots is smaller than in the example shown in Figure 3. Furthermore, by fixing the coefficients d and f in equation (1) and increasing the absolute values ​​of the coefficients a, b, c, and e, it is possible to expand the formed portion W1 (formed object W) in the X-axis, Y-axis, and Z-axis directions without changing the number of loops.

[0038] The shape of the shaped portion W1 (shaped object W) in the examples shown in Figures 3 and 5 varies greatly depending on the angle from which it is viewed, and can take on a circular shape with a small loop within a large loop, or, as shown in Figure 5(b) in particular, an eight shape in which the large loop and small loop extend in opposite directions.

[0039] Similarly, Figure 6 shows an example of a portion W1 (object W) defined based on a torus knot in the form of a closed loop in equation (1), where |a| ≠ |b| << |c| (|a| << |b| << |c|), d = 1, and f = 2. In this example, the absolute value of coefficient a is small compared to coefficients b and c, resulting in portion W1 being thin in the X-axis direction and having a nearly flat Möbius ring shape. The twisted structure of the surface itself is reflected in portion W1 as a twisted structure, as shown in Figure 6(f).

[0040] The thickness of the surface may be set so that there are no self-intersections, or so that some of the surfaces are self-intersecting. Note that the self-intersections can be considered as intersections in a lattice structure. For example, by adding thickness to any location of the self-intersections, impact resistance can be improved. To increase the thickness of the self-intersections, it is possible to perform operations such as increasing the amount of modeling material dispensed by the 3D printer 1.

[0041] The lines used in the first design method are not limited to straight lines and may be any curved lines. For example, Fig. 7 shows an example of a shaping portion W1 (shape of object W) defined based on a torus knot having a closed loop shape where |a| = |b| = |c|, d = 1, and f = 2 in Equation (1). As shown in Fig. 8(a), two torus knots K1 and K2 having different coefficients e in Equation (1) are connected by a sine curve as line 15 to form surface 16. Then, as shown in Fig. 8(b), thickness is added to the surface 16 to make it three-dimensional, thereby forming shaping data D.

[0042] The second design method will be described with reference to the drawings.

[0043] FIG. 9 shows an example of a shaping portion W1 (shape W) defined based on a torus knot having a closed loop shape where |a| = |b| = |c|, d = 1, and f = 2 in Equation (1). As shown in FIG. 10(a), a sweep line 20 is set using the torus knot. The center or center of gravity of a predetermined cross-sectional shape 21 shown in FIG. 10(b) is moved (circulated) along the sweep line 20 as shown in FIG. 10(c) to create a three-dimensional shape, thereby forming shaping data D. For example, the cross-sectional shape 21 is a hexagon, particularly a regular hexagon. In this example, the cross-sectional shape 21 passes through virtual lines 20a and 20b, which are torus knots obtained by increasing or decreasing a coefficient e, which is equal to the width of the cross-sectional shape 21, in Equation (1) relative to the torus knot forming the closed loop sweep line 20.

[0044] Preferably, as shown in FIG. 10(d), the cross-sectional shape 21 has a side edge 22 extending along the modeling table 5. In other words, the side edge 22 is a portion that does not substantially have a Z-axis component. The shape of the side edge 22 is preferably, for example, a straight line, but is not limited thereto. For example, the shape may be a curve approximating a straight line (with a large radius of curvature), or a shape having a straight line or a curve approximating a straight line extending along the modeling table 5 at its tip as a tangent or envelope, such as a wave shape, zigzag shape, or sawtooth shape. In this way, the cross-sectional shape 21 of the modeling part W1 has the side edge 22 extending along the modeling table 5 of the 3D printer 1. This allows the modeling part W1 to be manufactured by the 3D printer 1 using the side edge 22 as a support for the modeling table surface (or a raft surface on the modeling table surface). This allows the modeling part W1 (modeled object W) to be manufactured without supports.

[0045] FIG. 11 shows an example of a shaped portion W1 (shaped object W) defined based on a torus knot in the form of a closed loop in equation (1) where |a|=|b|<<|c|, d=1, and f=2.

[0046] The cross-sectional shape 21 is not limited to a hexagon, but may be a triangle, particularly an equilateral triangle, as shown in FIG. 12, or a polygon, such as a quadrangle, particularly a square, as shown in FIG. 13. Alternatively, the cross-sectional shape may be a circle, as shown in FIG. 14. Other shapes include hollow shapes, oval shapes such as ellipses and ovals, and any other shapes, such as a concave polygon or a convex polygon. By utilizing differences in section modulus to create any cross-sectional shape, a shaped portion W1 (shaped object W) with desired strength can be manufactured. The size of the cross-sectional shape 21 is preferably set so that no self-intersections are formed in the shaped portion W1, but may also be set so that self-intersections are formed in part of the shaped portion W1. The self-intersections are intersections in a lattice structure.

[0047] In the examples of FIGS. 11 to 14, the shaped portion W1 (shaped object W) takes on various shapes, such as a circle with overlapping large and small loops, a figure eight (Möbius ring), or a trefoil knot, depending on the viewing angle.

[0048] The forming unit W1 may form the object W by itself as shown in FIGS. 3 to 14, or may form the object W by connecting a plurality of forming units W1 together.

[0049] When connecting a plurality of shaping portions W1 to form a shaped object W, there are roughly two methods.

[0050] The first connection method is a method of connecting the shaping portions W1 so that the loop shapes intersect. The second connection method is a method of connecting the shaping portions W1 in a chain shape or a torus link shape so that the closed loop shapes do not intersect when at least a part of the shaping portions W1 has a closed loop shape.

[0051] The first connection method will be described with reference to the drawings.

[0052] FIG. 15 shows an example of a shaped object W in which two shaped portions W1a and W1b are connected, each defined based on a torus knot in the form of a closed loop in Equation (1) where |a| = |b| < |c|, d = 1, and f = 2. In this example, the shaped portions W1a and W1b are different in size and have the same number of loops, and are substantially similar in shape. This example uses, for example, the first design method described above. Two torus knots K1a and K2a with different values ​​of the coefficient e (different orders) in Equation (1) are used, and two torus knots K1b and K2b with different values ​​of the coefficient e (different orders) in Equation (1) are used, as shown in FIG. 16(a). The coefficients are selected so that the torus knots K1a and K2a and the torus knots K1b and K2b have one or more intersections with each other. In this example, the coefficients a through d and f in formula (1) are all set equal, and the coefficient e is selected so that the torus knots K1a and K1b intersect at one point, and the torus knots K2a and K2b intersect at another point. Also, by setting the difference in coefficient e in formula (1) representing the torus knots K1a and K2a equal to the difference in coefficient e in formula (1) representing the torus knots K1b and K2b, the widths of the connected shaped portions W1a and W1b can be made equal to each other.

[0053] Next, a surface 16a is formed by connecting the torus knots K1a and K2a with a line 15a, for example, a straight line, and a surface 16b is formed by connecting the torus knots K1b and K2b with a line 15b, for example, a straight line. Then, by adding thickness to each of these surfaces 16a and 16b in the normal direction as shown in FIG. 16(b), the three-dimensional (solidified) shapes are made into a Boolean sum, and the printing data D is formed. Note that the lines 15a and 15b are not limited to straight lines and may be curved. Furthermore, the lines 15a and 15b do not have to be the same type of line.

[0054] The width of the shaping portion W1 can be controlled by changing the difference in the coefficient e in equation (1) representing the torus knots K1a and K2a and the difference in the coefficient e in equation (1) representing the torus knots K1b and K2b.

[0055] When connecting a plurality of shaped portions W1 of substantially similar shapes but different sizes in this way, it is possible to easily manufacture an attractive shaped object W that has a self-similar appearance or an appearance similar thereto.

[0056] When designing the modeling data D using the first linking method, the above-described second design method may be used.

[0057] 17 and 18 show an example of a shaped object W in which two shaped portions W1a and W1b are connected, each defined based on a torus knot that forms a closed loop shape where |a| = |b| << |c|, d = 1, and f = 2 in equation (1). In this example, the shaped portions W1a and W1b have mirror-symmetric shapes, and in equation (1), the absolute values ​​of each coefficient are equal, with only the sign of Xt differing.

[0058] The printing data D for forming these printing portions W1a and W1b is formed by taking the Boolean sum of three-dimensional shapes obtained by moving (circling) the center or center of gravity of a predetermined cross-sectional shape 21 along each sweep line, with torus knots that are mirror images of each other. For example, the cross-sectional shape 21 is a hexagon, particularly a regular hexagon, as an example in Fig. 17, and a circle as an example in Fig. 18, but is not limited to these shapes and may be any shape.

[0059] In this way, in the first connecting method, by connecting the loop shapes of the multiple shaped portions W1 so that they intersect with each other, it is possible to easily manufacture an integrally connected rigid shaped object W.

[0060] For example, when viewed from the angles shown in Figures 17(f) and 18(f), the object W has an eight-shaped knot shape, and when viewed from the angles shown in Figures 17(g) and 18(g), it has an epitrochoidal knot shape.

[0061] The second connecting method, in contrast to the first connecting method, can be realized by manufacturing a shaped object W1 defined based on multiple torus knots whose coefficients in Equation (1) are selected so that no intersections occur. This second connecting method makes it easy to manufacture a chain-like shaped object W that can easily deform at the connections between the shaped objects.

[0062] The number of connected shaping portions W1 is not limited to two, but may be any number of three or more.

[0063] For example, FIG. 19 shows an example of a shaped object W in which four shaped portions W1a, W1b, W1c, and W1d are connected, each defined based on a torus knot in Equation (1) that forms a closed loop where |a| = |b| << |c|, d = 1, and f = 2. In this example, the shaped portions W1a and W1b are mirror-symmetrical to each other, and in Equation (1), the absolute values ​​of each coefficient are equal, with only the sign of Xt being different. Furthermore, the shaped portions W1a and W1c have Xt and Yt interchanged in Equation (1), and similarly, the shaped portions W1b and W1d have Xt and Yt interchanged in Equation (1). That is, the shaped portions W1c and W1d have shapes obtained by rotating the shaped portions W1a and W1b by π / 2 [rad] around the Z axis. Therefore, the shaping portions W1c and W1d have mirror-symmetric shapes, and in formula (1), the absolute values ​​of the coefficients are equal, and only the sign of Yt differs.

[0064] When designing using the first design method, the modeling data for forming these model portions W1a, W1b, W1c, and W1d is created by: setting two pairs of two torus knots of similar shapes with different coefficients e in Equation (1); connecting the two torus knots with lines to form surfaces; adding thickness to the surfaces; and then taking the Boolean sum of the resulting three-dimensional shapes. When designing using the second design method, each torus knot is used as a sweep line; the center or center of gravity of a predetermined cross-sectional shape is moved along each sweep line; and then taking the Boolean sum of the resulting three-dimensional shapes. For example, while FIG. 19 shows an example of a quadrangle, particularly a rectangle, as the cross-sectional shape 21, this is not limited to this; any shape, such as a circle as shown in FIG. 20, may be used.

[0065] Furthermore, a plurality of connected shaping portions W1 may be used as a mesh (unit shape, unit cell) and connected together to form a shaped object W. It is also possible to form a single larger shaped object W by further arranging the above-described shaped objects W as unit shapes in the left-right direction or stacking them vertically.

[0066] For example, FIG. 21 shows an example of a shaped object W in which meshes formed by combining the shaped portions W1a and W1b shown in FIG. 18 are arranged in a circular shape, while FIGS. 22 and 23 show examples of a shaped object W in which meshes formed by combining the shaped portions W1a to W1d shown in FIG. 20 are arranged in a circular shape. In these examples, the shaped object W is formed by connecting meshes arranged in a row along the Z axis at equal angles on the Z axis and / or on multiple concentric circles centered on the Z axis. The shaped object W shown in FIG. 23 differs from the shaped object W shown in FIG. 22 in that it includes an X-shaped or cross-shaped connector 25 at the center that connects the meshes. In other words, when connecting multiple shaped portions W1 to each other to form the shaped object W, separate connectors may be used in place of simply connecting some of the shaped portions W1. Furthermore, the shaped portions W1 do not have to be arranged at equal angles or at equal intervals.

[0067] FIG. 24 shows an example of a shaped object W in which meshes each consisting of a combination of the shaped portions W1a to W1d shown in FIG. 20 are connected in the X-axis direction, the Y-axis direction, and the Z-axis direction in a rectangular parallelepiped shape.

[0068] In these examples, the meshes are connected by the first connection method at positions where the loop shapes intersect to form a single shaped object W as a whole, but this is not limiting, and they may be connected by applying the second connection method at positions where the closed loop shapes do not intersect. In other words, when a shaped object W is formed by connecting multiple shaped parts W1, it is not specific parts of the shaped parts W1 that act as connecting parts, but any position of the loop shape or closed loop shape that acts as a connecting part.

[0069] In this way, by connecting multiple forming parts W1 having the same shape or mirror-symmetric shapes, it is possible to easily manufacture an attractive object W that has a symmetrical and regular appearance. An object W with symmetry and regularity can be manufactured without supports using, for example, a fused deposition modeling method or a stereolithography (DLP) method 3D printer 1 (a photograph of an example of the object W shown in FIG. 23 manufactured using a DLP method 3D printer 1 is shown in FIG. 25).

[0070] Furthermore, a structured object W formed by connecting multiple shaped portions W1 together to form a mesh is preferably used as, for example, a filter, net, cushion (cushioning material), equipment, rainwater storage tank, plant growth medium, water treatment filter material, and at least part of a filter bed for water purification. However, the structured object W (shaped portion W1) may be used as any porous article. In particular, as shown in Figures 21 to 24, by forming a structured object W by regularly arranging shaped portions W1 that have different shapes when viewed from each direction, it is possible to impart bias to the ease of passage of fluids such as air and water. Therefore, by selecting an arrangement pattern according to the shape of each shaped portion W1, the structured object W can be effectively used as a filter or filter material. Furthermore, by imparting bias to the connection structure of the shaped portions W1, the elasticity, rigidity, etc. of the structured object W can be freely manipulated. Furthermore, by connecting the forming part W1 in any arrangement pattern in accordance with biological scan data, for example, data calculated by a pressure sensor or the like along the shape of the biological body, it is also possible to form cushions, orthotics, etc. that are suitable for the shape of each individual biological body.

[0071] By changing the connection structure of the forming unit W1 (formed object W), it is possible to change the properties of the same material. For example, although not shown, cushioned chairs and other items can be formed using the same material. In this case, there is no need to separate them when disposing of them, which reduces the effort required for separation and makes them easier to recycle, which is also environmentally friendly. Furthermore, by forming cushions, plant growth mediums, and other items that often use urethane mats using the forming unit W1 (formed object W), it is possible to form items that are highly flexible and elastic, while eliminating the need for incineration and landfill disposal, as is the case with urethane. This is expected to reduce disposal costs and environmental impact.

[0072] Furthermore, since the forming part W1 (forming part W) has a loop shape, it can be used as a gripping part or a hook for a jig, and therefore can be easily replaced when formed as a mesh.

[0073] By making the connecting shaped parts W1 (shaped object W) denser, the strength is improved.

[0074] In the above embodiment, an example of the shaped portion W1 or the shaped object W is basically shown in equation (1) where |d|<|f| and is defined by a torus knot that has a trivial (unwindable) closed loop shape that is mathematically homeomorphic to a circle. However, the present invention is not limited to this, and the coefficients d and f may be selected to any values.

[0075] For example, as an example where |d| or |f| is 3 or greater, Figure 26 shows an example of a shaped portion W1 defined based on a torus knot in equation (1) that forms a closed loop shape where |a| = |b| = |c|, d = 5, and f = 6.

[0076] 27 shows an example of a shaped portion W1 defined based on a torus knot that forms a closed loop shape with |a|=|b|=|c|, d=-7, and f=4 in Equation (1), and FIG. 28 shows an example of a shaped portion W1 defined based on a torus knot that forms a closed loop shape with |a|=|b|=|c|, d=3, and f=2 in Equation (1). FIG. 29 shows an example of another torus knot K that forms a closed loop shape with d=3 and f=2 in Equation (1), similar to the torus knot that defines the loop shape of the shaped portion W1 shown in FIG. 28. However, since the absolute values ​​of the coefficients c and e are larger than those of the shaped portion W1 shown in FIG. 28, the torus knot K shown in FIG. 29 has a three-dimensional cloverleaf shape that stands up in the Z-axis direction, as shown in FIG. 29(e). In this way, even if the absolute values ​​or ratios of the coefficients d and f are equal, by selecting the other coefficients a to c and e, it is possible to easily give shape variations to the shaping portion W1.

[0077] 30 shows an example of a torus knot K that forms a closed loop shape where |a|=|b|<<|c|, d=6, and f=5. The shaping portion W1 having the closed loop shape defined by this torus knot K will have an appearance similar to a Lissajous figure. In the examples shown in FIGS. 29 and 30, the shaping portion W1 is inscribed in a cube, making it easier to handle as a unit shape when connecting the shaping portions to form the shaping object W.

[0078] Furthermore, the torus knot itself for defining the loop shape of the shaping portion W1 may self-intersect. Figure 31 shows an example of the shaping portion W1 defined based on a torus knot that forms a closed loop shape with |a| = |b| = |c|, d = 2, e = 1, and f = 5 in equation (1). In this example, the torus knot itself is close to or self-intersects near the center, i.e., the Z axis, and therefore the shaping portion W1 whose loop shape is defined by this torus knot also self-intersects. Even such an example is included in the shaping portion W1 of this embodiment.

[0079] Additionally, the torus knot may self-intersect at a position other than near the Z axis.

[0080] Thus, in the case of a formed portion W1 (formed object W) in which the absolute values ​​of the coefficients d and f in Equation (1) are set large, the loop shape of the formed portion W1 is determined by a torus knot, which forms a mathematically nontrivial (ununtilable) closed loop. In this case, the formed portion W1 (formed object W) is formed so that multiple loop shapes are intertwined, resulting in a soft feel. In particular, when the material is a soft material (elastic material), the formed object W can be configured to be elastically deformable like a spring in the Z-axis direction. In the example of the formed object W shown in Figure 26, the formed object W has particularly excellent elastic deformation performance, and can be formed into a particularly elastic cushion without connecting multiple formed portions W1 (formed object W). Furthermore, in the case of an example of a molded object W that does not have self-intersections in the molded portion W1, because it is mathematically homeomorphic to a circle, it can be deformed in various directions compared to a configuration that has self-intersections, and because it has a unicursal structure that is mathematically homeomorphic to a circle, even when pulled in the radial expansion direction, the relative positions of the loop shapes only change, and it can easily return to its original shape when the external force is released (see, for example, Figures 32(a) and 32(b)).Similarly, even when it is pushed in the radial contraction direction, it can easily return to its original shape when the external force is released.In other words, even if the molded portion W1 (molded object W) is made of a hard molding material, it is structurally capable of expansion and contraction and can have flexibility, elastic deformation performance, and impact resistance.Therefore, it can be molded using, for example, less plasticizer or no plasticizer at all, which is also environmentally friendly.

[0081] For example, when the object W is pushed into a pipeline or the like having a cross-sectional shape smaller than the outer shape of the object W, its deformation ability causes it to return to its original shape and press against the inner surface of the pipeline, making it easily attachable to the pipeline like a tension rod. Furthermore, because the outer periphery of the object W is curved (curved), it can be easily attached to a pipeline or the like even if the object W1 has a self-intersecting section. When fixing the object W to a pipeline or the like, for example, by applying an adhesive to the outer surface and then pushing the object into the pipeline, it can be easily fixed without the need for a support member or the like. Furthermore, in places with weak water flow, the object W can be attached to the pipeline simply by pushing it in, even without adhesive. In this case, the object W can be slid to any position by hand or with a jig, and the attachment position can be moved, and the lack of adhesive reduces labor and costs.

[0082] As an example, by using a stain-resistant (fouling-resistant) material, the object W can be used as a mesh or filter material placed in the piping of a plant factory where water is circulated and nutrient solution is reused to separate impurities from the cultivation tank. In particular, the object W of this embodiment can be easily shaped to have a symmetrical (non-directional) shape, making it easy to install without getting the installation direction wrong. Furthermore, if the object W is sized to fit the existing piping, it can be easily applied to plant factories where the piping cannot be easily changed (the water flow cannot be easily stopped). Furthermore, if the object W is shaped to the desired size, it can be easily installed horizontally relative to the piping. Furthermore, since the loop shape of the shaped portion W1 can be used as a hook or grip, installation and replacement are easy even when the object is installed deep inside the piping. This makes it easy to use as a filter material that requires frequent replacement and maintenance.

[0083] Furthermore, although an example of integer coefficients has been shown for equation (1), the present embodiment is not limited to this, and includes examples in which the coefficients d to f are not integers.

[0084] As described above, according to this embodiment, the shaped portion W1 (shaped object W) has a curved structure with a loop shape defined based on a torus knot, which allows the weight to be supported by compressive force, has excellent flexibility and elasticity, and allows for a flexible connection structure of the shaped portion W1, thereby further improving the degree of freedom in shaping. Furthermore, the curved structure makes it easier to grip than a linear structure, and the lack of sharp edges makes it safer.

[0085] By utilizing the continuous function of equation (1) and appropriately selecting the coefficients a to f, it becomes possible to manufacture the complex shaped portion W1, i.e., the object W, into any shape, and the shape of the portion W1, i.e., the object W, can be greatly varied depending on the viewing angle, and the shape variations of the portion W1, i.e., the object W, can be easily increased.

[0086] Furthermore, compared to a structure in which linear lattice structures are regularly connected, when multiple shaped portions W1 are connected by intersecting loop shapes, the connection positions can be set arbitrarily, and by appropriately selecting the shaping material, it is possible to provide connecting portions with various properties and set the performance of the shaped object W. For example, by adding thickness to the connecting portions at desired locations, it is possible to provide a shaped object W with excellent impact resistance.

[0087] The above-mentioned forming part W1 (formed object W) has a loop shape defined based on a torus knot K (an example of which is shown in FIG. 2), which is a smooth curve that wraps around the surface of a virtual torus T (shown in FIG. 2), and therefore does not have overhanging parts that require support materials or bridge parts that extend horizontally to the surface of the forming table, and can be produced without supports using the 3D printer 1. Furthermore, when a formed object W is constructed by connecting multiple forming parts W1, more complex shapes can be produced without supports.

[0088] For example, as a condition for supporting-less printing of the printing unit W1 (printed object W) in three-axis printing using the 3D printer 1 of this embodiment, when the angle between the central axis of the nozzle 11 and the printing table 5 is 90°, it is desirable that the rising angle of the printing unit W1 (printed object W) be 45°. However, this is not limited to this, and it has been confirmed that printing is possible if the rising angle is at least 6.5° relative to the printing table 5 (FIG. 33 shows a reference example, and FIG. 34 shows a photograph of a manufacturing example). Furthermore, in the case of a six-axis printing 3D printer 1, it has been confirmed that all of the above-mentioned printing units W1 and printed objects W can be printed without supports (FIGS. 35 and 36 show photographs of manufacturing examples).

[0089] The fused deposition model 3D printer, which is a molding manufacturing device for producing (shaping) the various molded objects (models) described above, may be a large pellet-type 3D printer with a nozzle diameter φ of 10 mm or more, and this large 3D printer can use inexpensively obtainable general pellet-shaped thermoplastic resin (recycled pellet material, etc.) as the molding material rather than a dedicated filament resin.

[0090] Furthermore, the object manufacturing device is not limited to a fused deposition model 3D printer, but may be, for example, a stereolithography (DLP or SLA) 3D printer.

[0091] Furthermore, the object manufacturing apparatus is not limited to a configuration in which a modeling head (discharge means) having a nozzle for discharging the modeling material is movable in the X-axis and Z-axis directions and a modeling table is movable in the Y-axis direction. It is sufficient that the modeling head is movable in at least three dimensions relative to the modeling table. For example, the modeling head may be movable in the X-axis and Y-axis directions and the modeling table in the Z-axis direction. Alternatively, the modeling head may be attached to the tip of a robot arm (preferably a six-axis robot arm) and movable in any direction, including the X-axis, Y-axis, and Z-axis directions. Supportless modeling is possible with three-axis and six-axis 3D printers, which eliminate the need for supports, thereby shortening the modeling time (improving the modeling speed of the object W). For example, if the object manufacturing apparatus is a six-axis modeling system, the nozzle 11 can trace a torus knot, which is a continuous function, in a single stroke when it does not interfere with the modeling unit W1 (the object W), thereby improving the modeling speed of the object W. [Explanation of symbols]

[0092] 1. Fused deposition modeling 3D printer, a modeling device 5. Build table 15 lines 16 Surfaces 21 Cross-sectional shape 22 Side edge D Modeling data K torus knot W sculpture W1 Modeling Department

Claims

1. A shaped object manufactured by the shaped object manufacturing apparatus, A shaped portion having a loop shape defined based on a torus knot, A plurality of the shaped portions are connected to form at least a part of a porous structure. A sculpted object characterized by the above.

2. The plurality of shaped portions are connected so that the loop shapes intersect with each other.

2. The shaped object according to claim 1.

3. The multiple shaped portions are connected so that the closed loop shapes do not intersect with each other.

2. The shaped object according to claim 1.

4. The plurality of shaped portions are identical to each other or have mirror-symmetric shapes.

2. The shaped object according to claim 1.

5. The multiple shaped parts have different sizes and shapes.

2. The shaped object according to claim 1.

6. 2. A method for designing a shaped object according to claim 1, comprising: The modeling data for the modeling part is formed by setting a thickness to the surface connecting two adjacent torus knots with a line. A method for designing a molded object, comprising:

7. 2. A method for designing a shaped object according to claim 1, comprising: The specified cross-sectional shape is swept along the loop-shaped torus knot to form the modeling data of the modeling part. A method for designing a molded object, comprising:

8. A shaped object is manufactured by a shaped object manufacturing device based on the shaping data formed by the shaped object design method of claim 6 or 7. A method for manufacturing a shaped object, comprising:

9. The modeling device is a 3D modeling device using the fused deposition modeling method or the optical modeling method.

9. The method for manufacturing a shaped object according to claim 8.

Images