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. A shaped article (W) produced by a 3D printer has a linear shaped part (W1) having a loop shape defined based on a torus knot as an outer shape.

Description

FORMED OBJECT, FORMED OBJECT DESIGN METHOD, AND FORMED OBJECT MANUFACTURING METHOD

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

[0002] 2. Description of the Related Art In recent years, fused deposition modeling 3D printers have become widely known as object manufacturing devices for manufacturing three-dimensional objects (see, for example, Patent Document 1).

[0003] When creating objects using a 3D printer, there is more freedom in design than before and they can handle complex shapes, but the more complex the shape, the more support is required to support the parts of the model that need support during creation, and it is often difficult to remove supports that are no longer needed after creation.

[0004] Furthermore, lattice structures have traditionally been used to manufacture 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 its 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). In addition, because lattice structures have vertices, the connection direction (angle) is limited.

[0005] JP-T-2000-500709 A JP-A-2015-93461 A

[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.

[0007] A shaped object according to an embodiment of the present invention is a shaped object manufactured by a shaped object manufacturing apparatus, and has a linear shaped portion whose outer shape is a loop shape defined based on a torus knot.

[0008] In the above-described shaped object, the loop shape of the shaped portion may be a closed loop shape.

[0009] The above-described shaped object may be configured by connecting a plurality of shaped portions.

[0010] In the above-described shaped object, the loop shape of the shaped portion may not have a self-intersecting portion.

[0011] Furthermore, the object design method of the present invention forms the modeling data of a modeling part by setting a thickness on a surface formed by connecting two adjacent torus knots with a line, or by sweeping a predetermined cross-sectional shape along a loop-shaped torus knot.

[0012] 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.

[0013] According to the embodiment of the present invention, it is possible to further improve the degree of freedom in shaping.

[0014] 1 is a schematic front view of a fused deposition modeling 3D printer, which is an apparatus for manufacturing a model according to an embodiment of the present invention; 2 is an explanatory diagram showing a torus knot; 3 is a diagram showing a model 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, and (e) is a perspective view from another direction; 4 is a diagram showing a first design method for the model shown in FIG. 3, where (a) is a perspective view showing a surface connecting two torus knots with a line, and (b) is a perspective view showing modeling data with thickness added to (a); 5 is a diagram showing another model manufactured using a 3D printer based on modeling data designed using the same 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; 7A and 7B are diagrams showing 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 a perspective view from one direction, (e) is a perspective view from another direction, and (f) is a partially enlarged view thereof.

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[0079] 10A and 10B are diagrams showing yet another object manufactured using the same 3D printer, in which (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.9 shows a second design method for the still 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 modeling data in which one cross-sectional shape is swept with respect to 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.

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[0089] 1A and 1B are diagrams showing yet another object manufactured using a 3D printer based on modeling data designed by the second 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, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position corresponding to II-II in (b). 1A and 1B are diagrams showing yet another object manufactured using a 3D printer based on modeling data designed by the second 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, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position corresponding to III-III in (b). 15 shows yet another object manufactured using a 3D printer based on modeling data designed by the second 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, (e) is a perspective view from another direction, and (f) is a cross-sectional view at a position corresponding to IV-IV in (b). Also shown are yet another object manufactured using the 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. The first design method for the yet another object shown in FIG. 15 is shown, where (a) is a perspective view showing a surface connecting two torus knots with a line, and (b) is a perspective view showing modeling data with thickness added to (a).10A and 10B are diagrams showing yet 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 V-V in (b). 1A and 1B are diagrams showing yet another object manufactured using a 3D printer based on modeling data designed by the second design method, (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 corresponding to VI-VI in (b). 1A and 1B are diagrams showing yet another object manufactured using the 3D printer, (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 corresponding to VII-VII in (b). 18A and 18B are diagrams showing 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 corresponding to VIII-VIII in (b). 18A and 18B are diagrams showing yet another object manufactured by further connecting the yet another object shown in FIG. 18A and 18B, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, and (c) is a perspective view. 18B and 18C are diagrams showing yet another object manufactured by further connecting the yet another object shown in FIG. 20A and 20B, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, and (c) is a perspective view. 20A to 20C are diagrams illustrating yet another object manufactured by further connecting the yet another object shown in Fig. 20, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, and (c) is a perspective view. 20A to 20C are diagrams illustrating yet another object manufactured by further connecting the yet another object shown in Fig. 20, where (a) is a plan view from the Z-axis direction, (b) is a side view from the X-axis direction, and (c) is a perspective view.24 is a photograph showing a manufacturing example of the object shown in FIG. 23. It is a diagram showing 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, and (e) is a perspective view from another direction. It is a diagram showing 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, and (e) is a perspective view from another direction. It is a diagram showing 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, and (e) is a perspective view from another direction. 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. 1B 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. 1C are diagrams showing 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, and (e) is a perspective view from another direction. 3A is a photograph showing an example of a deformed state of the object shown in FIG. 26 , and FIG. 3B is a photograph showing an example of a restored deformed state of the object shown in FIG. 26 . FIG. 3B is a cross-sectional view showing a reference example of a rise angle from a modeling table of an object that can be support-less modeled by the same 3D printer. FIG. 3C is a photograph showing a manufacturing example of the reference example of FIG. 33 . FIG. 3D is a photograph showing a manufacturing example of the object shown in FIG. 6 . FIG. 3E is a photograph showing a manufacturing example of the object shown in FIG. 14 .

[0015] An embodiment of the present invention will be described with reference to the drawings.

[0016] In Figure 1, reference numeral 1 denotes a fused deposition model 3D printer, which is a model manufacturing device. This fused deposition model 3D printer (hereinafter sometimes simply referred to as "3D printer 1") is a modeling machine that produces a three-dimensional model W by sequentially layering resin, which is a modeling material that has been melted (fused) by heat, one layer at a time based on 3D modeling data.

[0017] 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. Furthermore, the modeling material is not limited to resin; metal, ceramic, silicone, and the like 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.

[0018] 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.

[0019] 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).

[0020] The 3D printer 1 also includes a first drive unit 6 that moves the modeling head 4 in the X-axis direction and the 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 the two drive units 6, 7, etc. based on 3D modeling data such as STL data.

[0021] 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 modeling head 4 while it is moving.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.

[0022] Here, the modeling head 4 of the single-nozzle-head fused deposition modeling 3D printer 1 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.

[0023] 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 modeling head 4, and is discharged (ejected) from the outlet of one of the nozzles 11 for discharging the modeling 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 modeling head 4, rather than inside the modeling head 4.

[0024] The object W manufactured by the 3D printer 1 of this embodiment has a formed portion W1 having a loop shape defined based on a torus knot, and constitutes at least a part of the porous structure.

[0025] 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.

[0026] Xt=(a・cos(d・t)+e)・cos(f・t) Yt=(b・cos(d・t)+e)・sin(f・t) Zt=c・sin(d・t)

[0027] The X-axis, Y-axis, and Z-axis directions correspond to the X-axis, Y-axis, and Z-axis directions in the 3D printer 1 (shown in FIG. 1). a to f are non-zero coefficients. The parameter t is set to 0 to 2π [rad]. The coefficients a, b, and c are coefficients that 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 is a coefficient that sets the so-called "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 is a coefficient that sets the number of loops in the meridian direction M of the torus knot K. The absolute value of the coefficients f is a coefficient that sets the number of loops in the longitude direction L of the torus knot K. The absolute values ​​of the coefficients d and f are basically 1 or greater, and preferably at least one of them has an absolute value of 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 clear 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.

[0028] 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.

[0029] Next, a method for designing the object W will be described.

[0030] When the formula (1) is used, the modeling data for manufacturing the model W can be designed by roughly dividing it into two methods.

[0031] The first design method is a method in which modeling data is formed by adding thickness to a surface formed by connecting two adjacent torus knots with a line.

[0032] The second design method is a method of forming modeling data by sweeping a predetermined cross-sectional shape along a torus knot. Note that sweeping refers to continuously moving the predetermined cross-sectional shape along a trajectory, in this case, the torus knot.

[0033] The first design method will be described with reference to the drawings.

[0034] FIG. 3 shows an example of a shaping portion W1 (shape W) defined based on a torus knot forming a closed loop shape where |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, e.g., a straight line, is used to connect these torus knots K1 and K2 to form a surface 16. A non-self-intersecting line is preferably used 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 Fig. 5 is a formed portion W1 (object W) formed using forming 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 Fig. 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 (object W) in the X-axis, Y-axis, and Z-axis directions without changing the number of loops.

[0035] 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, a figure-eight shape in which the large loop and small loop extend in opposite directions.

[0036] Similarly, Figure 6 shows an example of a shaping 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| (|a| << |b| << |c|), d = 1, and f = 2. In this example, the absolute value of coefficient a is set small compared to coefficients b and c, resulting in a Möbius ring-like shaping portion W1 that is thin in the X-axis direction and nearly flat. The twisted structure of the surface itself is also reflected as a twisted structure in the shaping portion W1, as shown in Figure 6(f).

[0037] The thickness of the surface may be set so that there are no self-intersections, or so that there are partial self-intersections. Note that the self-intersections can be considered as intersections in a lattice structure. For example, by providing thickness at 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.

[0038] 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.

[0039] The second design method will be described with reference to the drawings.

[0040] 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), thereby creating 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.

[0041] Preferably, as shown in FIG. 10(d), the cross-sectional shape 21 has side edges 22 extending along the modeling table 5. In other words, the side edges 22 are portions that have substantially no Z-axis component. The shape of the side edges 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 unit W1 has side edges 22 extending along the modeling table 5 of the 3D printer 1. This allows the modeling unit W1 to be manufactured using the 3D printer 1, with the side edges 22 serving as supports for the modeling table surface (or a raft surface on the modeling table surface). This allows the modeling unit W1 (model W) to be manufactured without supports.

[0042] FIG. 11 shows an example of a shaping portion W1 (shaping 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.

[0043] 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 quadrilateral, particularly a square, as shown in FIG. 13 . Alternatively, it may be a circle, as shown in FIG. 14 . It may also be a hollow shape, an oval shape such as an ellipse or an oval, or any other shape, such as a concave polygon or a convex polygon. By utilizing differences in the 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 become intersections in a lattice structure.

[0044] In the examples of Figures 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) shape, or a trefoil knot, depending on the viewing angle.

[0045] 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.

[0046] When connecting a plurality of forming portions W1 to form a shaped object W, there are roughly two methods.

[0047] 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 portion of the shaping portions W1 has a closed loop shape.

[0048] The first connection method will be described with reference to the drawings.

[0049] 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 that forms a closed loop shape with |a| = |b| < |c|, d = 1, and f = 2 in Equation (1). In this example, the shaped portions W1a and W1b are different in size, have the same number of loops, and have substantially similar shapes. This example uses, for example, the first design method described above. As shown in FIG. 16( a), first, 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). In this case, 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 to 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.

[0050] Next, a surface 16a is formed by connecting the torus knots K1a and K2a with a line 15a, e.g., a straight line, and a surface 16b is formed by connecting the torus knots K1b and K2b with a line 15b, e.g., 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 modeling 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.

[0051] The width of the shaped portion W1 can be controlled by changing the difference in coefficient e in equation (1) representing the torus knots K1a and K2a and the difference in coefficient e in equation (1) representing the torus knots K1b and K2b.

[0052] When connecting a plurality of shaped portions W1 of roughly 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.

[0053] When designing the modeling data D using the first linking method, the second design method described above may be used.

[0054] 17 and 18 show an example of a shaped object W in which two shaped portions W1a and W1b are connected, and the shaped portions W1a and W1b are 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 the coefficients are equal, with only the sign of Xt differing.

[0055] The shaping data D for forming these shaping 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.

[0056] 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.

[0057] For example, when viewed from the angles shown in Figures 17(f) and 18(f), the object W has a figure-eight knot shape, and when viewed from the angles shown in Figures 17(g) and 18(g), it has an epitrochoid knot shape.

[0058] The second connecting method, in contrast to the first connecting method, can be realized by manufacturing a shaped object W1 defined based on a plurality of torus knots in which the 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 be easily deformed at the connection points between the shaped objects.

[0059] The number of connected shaping portions W1 is not limited to two, but may be any number of three or more.

[0060] For example, Figure 19 shows an example of a shaped object W in which four shaped portions W1a, W1b, W1c, and W1d are connected and defined based on a torus knot in Equation (1) that forms a closed loop shape 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 shaped portions W1c and W1d have mirror-symmetric shapes, and in formula (1), the absolute values ​​of the coefficients are equal, with only the sign of Yt being different.

[0061] When designing using the first design method described above, the shaping data for forming these shaped portions W1a, W1b, W1c, and W1d is formed 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, the shaping data is formed by taking the Boolean sum of the three-dimensional shapes formed by orbiting the center or center of gravity of a predetermined cross-sectional shape 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, and any shape, such as a circle as shown in FIG. 20, may be used.

[0062] 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 up and down.

[0063] 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 arranging and connecting a row of meshes at equal angles in the Z axis direction on the Z axis and / or on multiple concentric circles centered on the Z axis. Furthermore, 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 connecting portion 25 that connects the meshes in the center. In other words, when forming the shaped object W by connecting multiple shaped portions W1 to each other, separate connecting portions may be used in addition to simply connecting portions between portions of the shaped portions W1. Furthermore, the shaped portions W1 do not have to be arranged at equal angles or at equal intervals.

[0064] FIG. 24 shows an example of a shaped object W in which meshes each consisting of a combination of shaped portions W1a to W1d shown in FIG. 20 are connected in a rectangular parallelepiped shape in the X-axis direction, the Y-axis direction, and the Z-axis direction.

[0065] 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 the meshes 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 portions W1, it is not specific portions of the shaped portions W1 that act as connecting portions, but any positions of the loop shapes or closed loop shapes that act as connecting portions.

[0066] In this way, by connecting multiple forming units W1 having the same shape or mirror-symmetric shapes, it is possible to easily produce an attractive object W that has a symmetrical or regular appearance. The object W having symmetry or regularity can be produced without support using, for example, a fused deposition modeling method or a stereolithography (DLP) 3D printer 1 (a photograph of an example of the object W shown in FIG. 23 produced by a DLP 3D printer 1 is shown in FIG. 25).

[0067] Furthermore, a structured object W formed by connecting multiple shaped portions W1 together to form a mesh is preferably used as at least part of, for example, a filter, net, cushion (cushioning material), equipment, rainwater storage tank, plant growth medium, or water treatment filter, particularly 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 regularly arranging shaped portions W1 that have different shapes when viewed from different directions, the ease of passage of fluids such as air and water can be varied. 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. Furthermore, by varying the connection structure of the shaped portions W1, the elasticity, rigidity, etc. of the structured object W can be manipulated as desired. 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.

[0068] 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 environmentally friendly. Furthermore, by forming items that often use urethane mats, such as cushions and plant growth media, 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.

[0069] 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.

[0070] By densely connecting the shaped portions W1 (shaped objects W), the strength is improved.

[0071] In the above embodiment, an example of a shaped portion W1 or a shaped object W is shown in which, in equation (1), |d| < |f| is basically satisfied and the shaped portion W1 or the shaped object W 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 have any values.

[0072] For example, as an example where |d| or |f| is 3 or more, 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 with |a| = |b| = |c|, d = 5, and f = 6.

[0073] As an example of |d|>|f|, Fig. 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 Formula (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 Formula (1). Fig. 29 shows an example of another torus knot K that forms a closed loop shape with d = 3 and f = 2 in Formula (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 impart shape variations to the shaping unit W1.

[0074] 30 shows an example of a torus knot K that has a closed loop shape where |a| = |b| << |c|, d = 6, and f = 5. The shaping portion W1 having a 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, which makes it easier to handle as a unit shape when connecting the shaping portions W to form the shaping object W.

[0075] 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 in equation (1) where |a| = |b| = |c|, d = 2, e = 1, and f = 5. In this example, the torus knot itself is close to or self-intersects near the center, i.e., the Z-axis, and therefore self-intersects in the shaping portion W1 whose loop shape is defined by this torus knot. Even such an example is considered to be included in the shaping portion W1 of this embodiment.

[0076] Additionally, the torus knot may self-intersect at a position other than near the Z axis.

[0077] Thus, in the case of a shaped portion W1 (shaped object W) in which the absolute values ​​of the coefficients d and f in Equation (1) are set large, the loop shape of the shaped portion W1 is determined by a torus knot, which is a mathematically nontrivial (ununtilable) closed loop. In this case, the shaped portion W1 (shaped object W) is formed so that multiple loops are intertwined, providing a soft feel. In particular, when the shaped portion W1 (shaped object W) is made of a soft material (elastic material), the shaped object W can be elastically deformed in the Z-axis direction like a spring. In the example shown in FIG. 26 , the shaped object W has particularly excellent elastic deformation performance, and can be formed into a particularly elastic cushion without connecting multiple shaped portions W1 (shaped object W). Furthermore, in the case of an example of a molded object W that does not have self-intersecting portions 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-intersecting portions, 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 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.

[0078] 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 property causes it to return to its original shape and press against the inner surface of the pipeline, making it easily attachable to the pipeline or the like 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 portion. 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 locations 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 installation position can be changed, and the lack of adhesive reduces labor and costs.

[0079] 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, the loop shape of the shaped portion W1 can be used as a hook or grip, making it easy to install and replace, even when installed deep inside the piping. This makes it easy to use as a filter material that requires frequent replacement and maintenance.

[0080] 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.

[0081] 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 object to support weight with a 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 straight structure, and the lack of sharp edges makes it safer.

[0082] 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.

[0083] 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 thereby 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.

[0084] The above-mentioned forming unit W1 (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 portions that require support materials or bridge portions that extend horizontally to the surface of the forming table, and can be produced without supports using the 3D printer 1. Furthermore, when a plurality of forming units W1 are connected to form an object W, more complex shapes can be produced without supports.

[0085] For example, in three-axis modeling using the 3D printer 1 of the present embodiment, the conditions for supporting the modeling unit W1 (model W) are that when the angle between the central axis of the nozzle 11 and the modeling table 5 is 90°, the rise angle of the modeling unit W1 (model W) is preferably 45°. However, this is not limited to this, and it has been confirmed that modeling is possible if the rise angle is at least 6.5° relative to the modeling table 5 (see FIG. 33 for a reference example and FIG. 34 for a photograph of a manufacturing example). Furthermore, in the case of a six-axis modeling 3D printer 1, it has been confirmed that all of the above-mentioned modeling units W1 and models W can be supported (see FIGS. 35 and 36 for photographs of manufacturing examples).

[0086] The fused deposition model 3D printer, which is a modeling device for producing (shaping) the various models described above, may be a large-scale pellet-type 3D printer with a nozzle diameter φ of 10 mm or more, and this large-scale 3D printer can use inexpensively obtainable general pellet-shaped thermoplastic resin (which may be recycled pellet material, etc.) as the modeling material, rather than a dedicated filament resin.

[0087] Furthermore, the object manufacturing device is not limited to a fused deposition model 3D printer, but may also be, for example, a stereolithography (DLP or SLA) 3D printer.

[0088] 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 eliminates 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.

[0089] REFERENCE SIGNS LIST 1 3D printer as a model manufacturing device 5 Modeling table 15 Line 16 Surface 21 Cross-sectional shape 22 Side edge D Modeling data K Torus knot W Model W1 Modeling unit

Claims

1. A shaped object manufactured by a shaped object manufacturing device, characterized in that the shaped object has a linear shaped portion whose outer shape is a loop shape defined based on a torus knot.

2. The object according to claim 1, wherein the loop shape of the forming part is a closed loop shape.

3. The object according to claim 1 or 2, characterized in that it is composed of a plurality of connected shaped parts.

4. A shaped object according to any one of claims 1 to 3, characterized in that the loop shape of the shaped portion does not have any self-intersecting portions.

5. A method for designing a model according to any one of claims 1 to 4, characterized in that the modeling data for the modeling part is formed by setting a thickness to a surface formed by connecting two adjacent torus knots with a line, or by sweeping a predetermined cross-sectional shape along a loop-shaped torus knot.

6. A method for manufacturing a shaped object, comprising the steps of: manufacturing a shaped object by a shaped object manufacturing device based on the shaping data formed by the shaped object design method according to claim 5.

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