Method for manufacturing molded objects and method for designing molded objects

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 a linear shaped part W1 having a loop shape defined based on a torus knot as an outer shape.SELECTED DRAWING: Figure 21

Description

Technical Field

[0001] The present invention relates to three-dimensional shaped objects A method for manufacturing molded objects and and shaped object design methods In the law thereof.

Background Art

[0002] In recent years, as a shaped object manufacturing apparatus for manufacturing three-dimensional shaped objects, for example, a 3D printer using a fused deposition modeling method is widely known (see, for example, Patent Document 1).

[0003] [[ID=[]For shaped objects manufactured using a 3D printer, although the degree of freedom in design is higher than before and it can handle complex shapes, the more complex the shape, the more support is required to support the necessary parts of the model during shaping, and it is often difficult to remove the support that becomes unnecessary after shaping.

[0004] Also, when manufacturing shaped objects using a conventional three-dimensional printer, a lattice structure has been used (see, for example, Patent Document 2). The lattice structure is a structure in which periodically arranged lattices branched in a dendritic shape can make the interior of the shaped object hollow, so that weight reduction can be easily achieved. However, since each element (side) of this lattice structure has a linear structure, it lacks flexibility (elasticity), and when forming a curved surface (curve), it was necessary to combine a plurality of unit cells. In addition, since the lattice structure has vertices, the connection direction (angle) was limited.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0006] Therefore, one of the problems of the present invention is to create a molded object that can have a greater degree of freedom in its form. A method for manufacturing molded objects and How to design objects Law The purpose is to provide. [Means for solving the problem]

[0007] An embodiment of the present invention is a molded object manufactured by a molded object manufacturing apparatus, having a linear molded portion whose outer shape is a loop shape defined based on a torus knot.

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

[0009] In the above-mentioned molded object, multiple molded parts may be connected to each other.

[0010] In the above-described molded object, the loop shape of the molded part does not necessarily have to have a self-intersecting section.

[0011] Furthermore, the present invention's method for designing molded objects involves setting a thickness on a surface formed by connecting two adjacent torus knots with a line, thereby creating the molding data for the molded part.

[0012] The above-described method for designing a molded object may also involve forming the molding data for the molded part by sweeping a predetermined cross-sectional shape along a loop-shaped torus knot.

[0013] Furthermore, the present invention's method for manufacturing molded objects involves manufacturing a molded object using a molded object manufacturing apparatus based on the molded object design data formed by the above-described molded object design method. [Effects of the Invention]

[0014] According to embodiments of the present invention, it is possible to further improve the degree of freedom in shaping. [Brief explanation of the drawing]

[0015] [Figure 1]This is a schematic front view of a fused deposition modeling (FDM) 3D printer, which is a manufacturing apparatus for molded objects according to one embodiment of the present invention. [Figure 2] This is an explanatory diagram showing a torus knot. [Figure 3] The diagram shows an object manufactured using the same 3D printer, with (a) being a plan view from the Z-axis direction, (b) a side view from the X-axis direction, (c) a side view from the -Y-axis direction, (d) an oblique view from one direction, and (e) a perspective view from another direction. [Figure 4] Figure 3 shows a first design method for one of the fabricated objects, where (a) is a perspective view showing a surface formed by connecting two torus knots with lines, and (b) is a perspective view showing the fabrication data with thickness added to (a). [Figure 5] The following diagram shows other objects manufactured using a 3D printer based on the molding 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 6] The following diagram shows yet another object manufactured using a 3D printer based on the molding data designed by 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 an oblique view from one direction, (e) is an oblique view from another direction, and (f) is a magnified section thereof. [Figure 7] The following diagram shows yet another object manufactured using a 3D printer based on the molding data designed by the first design method described above, where (a) is a plan view shown from the Z-axis direction, (b) is a side view shown from the X-axis direction, (c) is a side view shown from the -Y-axis direction, (d) is an oblique view shown from one direction, and (e) is a perspective view shown from another direction. [Figure 8] Figure 7 shows a first design method for yet another fabricated object, where (a) is a perspective view showing a surface formed by connecting two torus knots with a line, and (b) is a perspective view showing the fabrication data with thickness added to (a). [Figure 9]A view showing still another shaped object manufactured using the same 3D printer, where (a) is a plan view shown from the Z-axis direction, (b) is a side view shown from the X-axis direction, (c) is a side view shown from the -Y-axis direction, (d) is a perspective view shown from one direction, and (e) is a perspective view shown from another direction. [Figure 10] A view showing a second design method for still another shaped object shown in FIG. 9, where (a) is a perspective view showing a torus knot serving as a sweep line, (b) is a perspective view showing an enlarged part of (a), (c) is a perspective view of shaped data obtained by sweeping a cross-sectional shape with respect to the sweep line of (a), and (d) is a perspective view showing an example where the side edge of the cross-sectional shape extends along the shaping table. [Figure 11] A view showing still another shaped object manufactured using a 3D printer based on shaped data designed by the same second design method, where (a) is a plan view shown from the Z-axis direction, (b) is a side view shown from the X-axis direction, (c) is a side view shown from the -Y-axis direction, (d) is a perspective view shown from one direction, (e) is a perspective view shown from another direction, and (f) is a cross-sectional view at a position corresponding to I-I of (b). [Figure 12] A view showing still another shaped object manufactured using a 3D printer based on shaped data designed by the same second design method, where (a) is a plan view shown from the Z-axis direction, (b) is a side view shown from the X-axis direction, (c) is a side view shown from the -Y-axis direction, (d) is a perspective view shown from one direction, (e) is a perspective view shown from another direction, and (f) is a cross-sectional view at a position corresponding to II-II of (b). [Figure 13] A view showing still another shaped object manufactured using a 3D printer based on shaped data designed by the same second design method, where (a) is a plan view shown from the Z-axis direction, (b) is a side view shown from the X-axis direction, (c) is a side view shown from the -Y-axis direction, (d) is a perspective view shown from one direction, (e) is a perspective view shown from another direction, and (f) is a cross-sectional view at a position corresponding to III-III of (b). [Figure 14]The following diagram shows yet another object manufactured using a 3D printer based on the molding 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, and (f) is a cross-sectional view at the position corresponding to IV-IV in (b). [Figure 15] The following diagram 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 16] Figure 15 shows a first design method for yet another fabricated object, where (a) is a perspective view showing a surface formed by connecting two torus knots with a line, and (b) is a perspective view showing the fabrication data with thickness added to (a). [Figure 17] The following diagrams show yet another object manufactured using a 3D printer based on the molding 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 the VV position in (b). [Figure 18] The following diagram shows yet another object manufactured using a 3D printer based on the molding data designed by the second design method described above, where (a) is a plan view shown from the Z-axis direction, (b) is a side view shown from the X-axis direction, (c) is a side view shown from the -Y-axis direction, (d) is a perspective view shown from one direction, (e) is a perspective view shown from another direction, (f) is a perspective view shown from yet another direction, (g) is a perspective view shown from yet another direction, and (h) is a cross-sectional view of (b) at the position corresponding to VI-VI. [Figure 19]The following diagram 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 the position corresponding to VII-VII in (b). [Figure 20] The following diagram 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 of (b) at the position corresponding to VIII-VIII. [Figure 21] Figure 18 shows a further manufactured object created by connecting other objects shown in Figure 18, 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. [Figure 22] Figure 20 shows a further manufactured object created by connecting other objects shown in Figure 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. [Figure 23] Figure 20 shows a further manufactured object created by connecting other objects shown in Figure 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. [Figure 24] Figure 20 shows a further manufactured object created by connecting other objects shown in Figure 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. [Figure 25] Figure 23 is a photograph showing an example of the manufacturing process of a molded object. [Figure 26] The following diagram 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 27]The following diagram 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 28] The following diagram 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 29] The diagram shows an example of a torus knot that defines the loop shape of the fabricated part of the above-mentioned 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 30] The following figure shows another example of a torus knot that defines the loop shape of the fabricated part of the above-mentioned 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 31] The following diagram 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 an oblique view from one direction, and (e) is a perspective view from another direction. [Figure 32] (a) is a photograph showing an example of the molded object shown in Figure 26 in a deformed state, and (b) is a photograph showing an example of (a) in a state after it has returned to its original deformed state. [Figure 33] This is a cross-sectional view showing a reference example of the rise angle from the build table of a supportless object that can be fabricated using the same 3D printer. [Figure 34] This is a photograph showing a manufacturing example of the reference example in Figure 33. [Figure 35] Figure 6 is a photograph showing an example of the manufacturing process of the molded object. [Figure 36] Figure 14 is a photograph showing an example of the manufacturing process of the molded object. [Modes for carrying out the invention]

[0016] One embodiment of the present invention will be described with reference to the drawings.

[0017] In Figure 1, 1 is a fused deposition modeling (FDM) 3D printer, which is a device for manufacturing molded objects. This FDM 3D printer (hereinafter sometimes simply referred to as "3D printer 1") is a molding machine that sequentially builds up layers of resin, a molding material that has been melted by heat, one layer at a time, based on 3D modeling data, to produce a three-dimensional object W.

[0018] The resin used as the molding material in 3D printer 1 is, for example, a thermoplastic resin, such as general-purpose plastics, engineering plastics, super engineering plastics, reinforced resins, recycled plastics, biomass plastics, or biodegradable plastics. More specifically, examples include PVC, POM, PBAT, AAS, PS, PLA, plant fiber-reinforced PLA, ABS, glass fiber-reinforced ABS, carbon fiber-reinforced ABS, PP, glass fiber-reinforced PP, carbon fiber-reinforced PP, PC, PC-ABS, ASA, TPE, TPU, cellulose acetate, PA, PETG, etc. The molding material can be in any shape, such as pellets or filaments. Furthermore, 3D printer 1 is, for example, a single-nozzle head specification, and only one type of resin is required for molding; a support resin (such as a water-soluble resin) is not necessary. In addition, the molding material is not limited to resin; metals, ceramics, silicones, etc., may also be used. Furthermore, these molding materials may possess one or more of the following properties: flexibility, antibacterial properties, chemical resistance, heat resistance, stain resistance, and weather resistance, or these properties may be added using desired additives.

[0019] The 3D printer 1 comprises, for example, a box-shaped main body 3 having a build chamber 2 inside, a build head 4 that can move in the X-axis direction (horizontal direction, left to right) and the Z-axis direction (vertical direction, height) within the build chamber 2, and a build table 5 that can move in the Y-axis direction (horizontal direction, front to back) within the build chamber 2.

[0020] Furthermore, since the build head 4 is movable in the X and Z axes and the build table 5 is movable in the Y axis, the build head 4 moves in three dimensions relative to the build table 5 (as will be described later, the 3D printer 1 is not limited to the configuration shown in Figure 1, and any configuration in which the build head 4 moves in at least three dimensions relative to the build table 5 is acceptable).

[0021] Furthermore, the 3D printer 1 includes a first drive unit 6 that moves the build head 4 in the X-axis and Z-axis directions within the build chamber 2, a second drive unit 7 that moves the build table 5 in the Y-axis direction within the build chamber 2, and a control unit 8 that controls both drive units 6, 7, etc., based on 3D build data such as STL data.

[0022] Then, based on the control by the control unit 8, the build head 4 moves in three dimensions relative to the build table 5, and resin (molten resin) is extruded from the nozzle 11 of the build head 4 during this movement. As this extruded resin hardens and solidifies, the resin is layered on the build table 5, creating a three-dimensional object W of the desired shape.

[0023] Here, the build head 4 of the single-nozzle head fused deposition modeling 3D printer 1 is, for example, of the fused resin extrusion type, and has a single nozzle 11 that extrudes resin melted by heat from a heating means (not shown) inside the build head 4.

[0024] In other words, the resin, 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 build head 4, and discharged (discharged) from the discharge port of one nozzle 11 for discharging the build material in the direction of the central axis of the discharge port, for example, downwards. Note that the heating means and extrusion means may be provided outside the build head 4 instead of inside it.

[0025] Furthermore, the molded object W produced by the 3D printer 1 of this embodiment has a molded portion W1 having a loop shape defined based on a torus knot, and constitutes at least a part of a porous structure.

[0026] Here, as shown in Figure 2, the torus knot K is defined as a knot that adheres to and wraps around the surface of a hypothetical torus T. This torus knot K is defined by the following equation (hereinafter collectively referred to as equation (1)) using the parameter t.

[0027] Xt=(a·cos(d·t)+e)·cos(f·t) Yt=(b·cos(d·t)+e)·sin(f·t) Zt = c·sin(d·t)

[0028] The X-axis, Y-axis, and Z-axis directions correspond to the X-axis, Y-axis, and Z-axis directions of 3D printer 1 (shown in Figure 1). a to f are non-zero coefficients. The parameter t is 0 to 2π [rad], coefficients a, b, and c are coefficients that set the scaling factor of the torus T in the X-axis, Y-axis, and Z-axis directions relative to the unit torus, respectively, coefficient e is a coefficient that sets the so-called "diameter" of the torus T, and together with coefficients a and b, sets the scaling factor of the diameter in the X-axis and Y-axis directions relative to the unit torus, coefficient d is a coefficient whose absolute value sets the number of loops in the meridian direction M of the torus knot K, and coefficient f is a coefficient whose absolute value sets the number of loops in the longitudinal direction L of the torus knot K. For coefficients d and f, basically their absolute values ​​are 1 or greater, preferably at least one of them is 2 or greater, and they can be any value as long as a loop shape is formed, but preferably they are selected so that the torus knot K forms a closed loop shape, and as an example they are integer values. Furthermore, the coefficients d and f are preferably set to values ​​such that the greatest common divisor of their absolute values ​​is 1, that is, an integer value where the absolute value of one is 1 and the absolute value of the other is 2 or greater, or a value where the ratio of their absolute values ​​is equal to the ratio of relatively prime integers. The other 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 self-intersections do not occur in the loop shape, but self-intersections may occur. As is obvious from equation (1), a congruent torus knot K is formed even when the values ​​of Xt, Yt, and Zt are swapped, but in order to facilitate fabrication by the 3D printer 1 shown in Figure 1, it is preferable to fix the axis direction of the torus T (shown in Figure 2) to the Z axis direction and only allow the swapping of the values ​​of Xt and Yt.

[0029] In this embodiment, the 3D modeling data for the modeling unit W1 is designed using formula (1) by a computer or the like, and the 3D printer 1 is driven to manufacture the modeled object W based on the designed modeling data.

[0030] Next, we will explain the design method for the shaped object W.

[0031] When using equation (1), the modeling data for manufacturing the object W can be designed in two main ways.

[0032] The first design method involves creating the modeling data by adding thickness to a surface formed by connecting two adjacent torus knots with lines.

[0033] The second design method involves creating the 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, along a torus knot.

[0034] The first design method will be explained with reference to the drawings.

[0035] Figure 3 shows an example of a molded part W1 (molded object 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 Figure 4(a), two adjacent torus knots K1 and K2, which are approximately similar in shape but differ only in the value of the coefficient e in equation (1) (different in order of magnitude), are used, and a line 15, for example a straight line, is used to connect these torus knots K1 and K2 to form a surface 16. A non-self-intersecting line is preferred for the line 15. Then, as shown in Figure 4(b), thickness is added to this surface 16 in the normal direction to create a 3D model (solid model), thereby forming the molded data D. The width of the fabricated area W1 can be controlled by changing the difference in coefficient e in equation (1) that represents the two torus knots K1 and K2. For example, the example shown in Figure 5 is a fabricated area W1 (fabricated object W) formed using fabrication data where the difference in coefficient e in equation (1) that represents the two torus knots is smaller than that 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 becomes possible to expand the fabricated area W1 (fabricated object W) in the X, Y, and Z directions without changing the number of loops.

[0036] The molded parts W1 (molded object W) in the examples shown in Figures 3 and 5 differ greatly in shape depending on the viewing angle, sometimes exhibiting a circular shape with a small loop inside a large loop, and sometimes, as shown in Figure 5(b), exhibiting a figure-eight shape where the large and small loops unfold in opposite directions.

[0037] Similarly, Figure 6 shows an example of a fabricated part W1 (formed object W) defined in equation (1) based on a torus knot forming a closed loop shape with |a|≠|b|<<|c|(|a|<<|b|<<|c|), d=1, and f=2. In this example, by taking the absolute value of coefficient a to be smaller than that of coefficients b and c, the fabricated part W1 is thin in the X-axis direction and forms a Möbius ring shape that is nearly flat. The torsional structure of the surface itself is reflected as a torsional structure in the fabricated part W1, as shown in Figure 6(f).

[0038] Regarding the thickness of the surface, it may be set so that it does not self-intersect, or it may be set so that a part of it self-intersects. The self-intersecting parts can be considered as intersections in a grid structure. Impact resistance can be improved by adding thickness to the self-intersecting parts, for example, at arbitrary locations. When increasing the thickness of the self-intersecting parts, operations such as increasing the extrusion rate of the 3D printer 1 can be performed.

[0039] The lines used in the first design method are not limited to straight lines, but can be any curve. For example, Figure 7 shows an example of a molded part W1 (molded object 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 Figure 8(a), the molded data D is formed by creating a surface 16 by connecting two torus knots K1 and K2 with different coefficients e in equation (1) using a sine curve-like line 15, and then adding thickness to this surface 16 as shown in Figure 8(b) to create a three-dimensional object.

[0040] Furthermore, the second design method will be explained with reference to the drawings.

[0041] Figure 9 shows an example of a molded part W1 (molded object W) defined in equation (1) based on a torus knot forming a closed loop shape with |a|=|b|=|c|, d=1, and f=2. As shown in Figure 10(a), a sweep line 20 is set by a torus knot, and the molded data D is formed by creating a 3D model by moving (circling) the center or centroid of a predetermined cross-sectional shape 21 shown in Figure 10(b) along the sweep line 20 as shown in Figure 10(c). For example, the cross-sectional shape 21 is shown as 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 the coefficient e, which is equal to the width of the cross-sectional shape 21 in equation (1), relative to the torus knot that forms the closed loop sweep line 20.

[0042] Preferably, as shown in Figure 10(d), the cross-sectional shape 21 has a side edge portion 22 that extends along the build table 5. That is, the side edge portion 22 is a portion that substantially does not have a Z-axis component. The shape of the side edge portion 22 is preferably a straight line, but is not limited to this, and may be a curve that approximates a straight line (large radius of curvature), or a shape that has a straight line or a curve that approximates a straight line as a tangent or envelope at the tip, such as a wave shape, zigzag shape, or saw shape, which extends along the build table 5. In this way, because the cross-sectional shape 21 of the build section W1 has a side edge portion 22 that extends along the build table 5 of the 3D printer 1, the build section W1 can be manufactured by the 3D printer 1 with the side edge portion 22 acting as a support portion for the build table surface (or the raft surface on the build table surface), so that the build section W1 (build object W) can be manufactured without supports.

[0043] Furthermore, Figure 11 shows an example of a molded part W1 (molded object W) defined in equation (1) based on a torus knot that forms a closed loop shape with |a|=|b|<<|c|, d=1, and f=2.

[0044] The cross-sectional shape 21 is not limited to a hexagon; for example, as shown in Figure 12, it may be a triangular shape, especially an equilateral triangle, or as shown in Figure 13, a quadrilateral shape, especially a square, or other polygonal shape. It is not limited to polygons; it may also be circular, as shown in Figure 14. In addition, it may be a hollow shape, an oval shape such as an ellipse or an oblong shape, or any shape, not limited to a convex polygon, such as a concave polygon. By utilizing the difference in section modulus and creating any cross-sectional shape, it is possible to manufacture a molded part W1 (molded object W) with the desired strength. Furthermore, regarding the size of the cross-sectional shape 21, it is preferable to set it so that no self-intersecting parts are formed in the molded part W1, but it may also be set so that a self-intersecting part is formed in a part of the molded part W1. The self-intersecting part becomes an intersection in the lattice structure.

[0045] In the examples shown in Figures 11 to 14, the molded part W1 (molded object W) exhibits various shapes depending on the viewing angle, such as a circular shape with overlapping large and small loops, a figure-eight (Möbius ring) shape, or a trefoil knot shape.

[0046] Furthermore, as shown in Figures 3 to 14, the molding unit W1 may form a molded object W on its own, or multiple units may be connected to form a molded object W.

[0047] When forming an object W by connecting multiple molding sections W1, there are broadly two methods.

[0048] The first connection method involves connecting the molding sections W1 such that their loop shapes intersect. The second connection method involves connecting the molding sections W1 in a way that, when at least a portion of them forms a closed loop shape, the closed loop shapes do not intersect with each other, in a manner such as a chain or torus entanglement.

[0049] The first connection method will be explained with reference to the drawings.

[0050] Figure 15 shows an example of a molded object W formed by connecting two molded parts W1a and W1b, which are defined based on a torus knot that forms a closed loop shape in equation (1) where |a|=|b|<|c|, d=1, and f=2. In this example, the molded parts W1a and W1b are of different sizes but have the same number of loops and are substantially similar in shape. In this example, for example, using the first design method described above, as shown in Figure 16(a), first, two torus knots K1a and K2a with different values ​​(different places) of the coefficient e in equation (1), and two other torus knots K1b and K2b with different values ​​(different places) of the coefficient e in equation (1), are used. At this time, the coefficients are selected so that the torus knots K1a and K2a and the torus knots K1b and K2b have one or more intersection points with each other. In this example, the coefficients a, d, and f in equation (1) are all set to be 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. Furthermore, by setting the difference between the coefficients e in equation (1) representing the torus knots K1a and K2a to be equal, the widths of the connected molded parts W1a and W1b can be made equal to each other.

[0051] 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 in the normal direction to each of these surfaces 16a and 16b as shown in Figure 16(b), the Boolean sum of the resulting three-dimensional (solid) shapes is formed to create the modeling data D. Note that the lines 15a and 15b are not limited to straight lines; they can also be curves. Furthermore, lines 15a and 15b do not need to be of the same type.

[0052] The width of the molded part W1 can be controlled by changing the difference in the coefficient e in equation (1) representing torus knots K1a and K2a, and the difference in the coefficient e in equation (1) representing torus knots K1b and K2b.

[0053] When multiple molded parts W1 of roughly similar shapes but differing in size are connected in this way, it is possible to easily manufacture an aesthetically pleasing molded object W that exhibits a self-similar appearance or a similar appearance.

[0054] When designing the molding data D in the first linking method, the second design method described above may also be used.

[0055] Figures 17 and 18 show an example of a fabricated object W in which two fabricated parts W1a and W1b are connected, defined in equation (1) based on a torus knot that forms a closed loop shape with |a|=|b|<<|c|, d=1, and f=2. In this example, the fabricated parts W1a and W1b are mirror images of each other, and in equation (1), the absolute values ​​of each coefficient are equal, with only the sign of Xt being different.

[0056] The molding data D for forming these molded parts W1a and W1b is created by taking a Boolean sum of three-dimensional shapes obtained by moving (circling) the center or centroid of a predetermined cross-sectional shape 21 along each sweep line, using torus knots that are mirror images of each other as sweep lines. For example, as the cross-sectional shape 21, Figure 17 shows an example of a hexagon, especially a regular hexagon, and Figure 18 shows an example of a circle, but it is not limited to these shapes and can be any shape.

[0057] Thus, in the first connection method, by connecting the loop shapes of multiple molded parts W1 so that they intersect with each other, a rigid molded object W that is integrally connected can be easily manufactured.

[0058] For example, when viewed from the angles shown in Figures 17(f) and 18(f), the fabricated object W exhibits a figure-eight knot shape, and when viewed from the angles shown in Figures 17(g) and 18(g), it exhibits an epitrochoidal knot shape.

[0059] The second connection method can be realized, in contrast to the first connection method, by manufacturing a molded part W1 defined based on multiple torus knots, where the coefficients in equation (1) are selected so that no intersecting positions occur. This second connection method makes it easy to manufacture chain-like molded objects W that can be easily deformed at the connection points between molded parts.

[0060] Furthermore, the number of connected molding sections W1 is not limited to two, but may be three or more.

[0061] For example, Figure 19 shows an example of a fabricated object W in which four fabrication sections W1a, W1b, W1c, and W1d are connected, defined in equation (1) based on a torus knot that forms a closed loop shape with |a|=|b|<<|c|, d=1, and f=2. In this example, fabrication sections W1a and W1b are mirror images of each other, and in equation (1), the absolute values ​​of each coefficient are equal, with only the sign of Xt being different. Also, fabrication sections W1a and W1c are the same as those in equation (1) where Xt and Yt are swapped, and similarly, fabrication sections W1b and W1d are the same as those in equation (1) where Xt and Yt are swapped. That is, fabrication sections W1c and W1d are the same as those in fabrication sections W1a and W1b, rotated by π / 2 [rad] around the Z axis. Therefore, the molded parts W1c and W1d are mirror images of each other, and in equation (1), the absolute values ​​of each coefficient are equal, with only the sign of Yt being different.

[0062] When designing using the first design method described above, the molding data for these molded parts W1a, W1b, W1c, and W1d is formed by setting two sets of two similar shapes with different coefficients e in equation (1), connecting the two torus knots in each set with lines, and then taking a Boolean sum of the three-dimensional shapes formed by adding thickness to the resulting surfaces. When designing using the second design method, each torus knot is treated as a sweep line, and the three-dimensional shapes are formed by circling the center or centroid of a predetermined cross-sectional shape along each sweep line, and then taking a Boolean sum of the resulting shapes. For example, as the cross-sectional shape 21, Figure 19 shows an example of a quadrilateral, especially a rectangle, but it is not limited to this and can be any shape, such as a circle as shown in Figure 20.

[0063] Furthermore, multiple molded parts W1 can be linked together to form a mesh (unit shape, unit cell), and a large number of these meshes can be linked together to form a single molded object W. In addition, it is possible to form a larger single molded object W by arranging the aforementioned molded objects W as unit shapes horizontally or stacking them vertically.

[0064] For example, Figure 21 shows an example of a molded object W formed by arranging meshes consisting of combinations of molding parts W1a and W1b shown in Figure 18 in a circular shape, and Figures 22 and 23 show examples of molded objects W formed by arranging meshes consisting of combinations of molding parts W1a to W1d shown in Figure 20 in a circular shape. In these examples, the molded object W is constructed 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 molded object W shown in Figure 23 has an X-shaped or cross-shaped connecting part 25 in the center that connects the meshes to the molded object W shown in Figure 22. In other words, when forming a molded object W by connecting a large number of molding parts W1 to each other, it is not necessary to simply use parts of the molding parts W1 as connecting parts, but separate connecting parts may also be used. Also, the arrangement of the molding parts W1 does not have to be at equal angles or equal intervals.

[0065] Furthermore, Figure 24 shows an example of a fabricated object W formed by connecting multiple meshes, each consisting of the combination of fabrication parts W1a to W1d shown in Figure 20, in a rectangular parallelepiped shape in the X-axis, Y-axis, and Z-axis directions.

[0066] In these examples, the meshes are connected by the first connection method at the points where the loop shapes intersect, forming a single, unified object W. However, the process is not limited to this; the second connection method may be applied at points where the closed loop shapes do not intersect. In other words, when multiple molded parts W1 are connected to form an object W, the molded parts W1 do not have specific parts acting as connecting points; rather, any position of the loop shape or closed loop shape acts as a connecting point.

[0067] In this way, by connecting multiple molded parts W1 that have the same shape or mirror-image symmetrical shape, it is possible to easily manufacture an aesthetically pleasing molded object W that exhibits a symmetrical and regular appearance. For molded objects W with symmetry and regularity, supportless fabrication is possible using, for example, fused deposition modeling (FDM) and stereolithography (DLP) 3D printers 1 (Figure 25 shows a photograph of an example of a molded object W shown in Figure 23, manufactured using a DLP 3D printer 1).

[0068] Furthermore, a fabricated object W, formed by connecting multiple fabricated sections W1 to form a mesh, is preferably used as a filter, net, cushion (cushioning material), fitting, rainwater storage tank, plant growing medium, water treatment filter material, or at least part of a water purification bed. However, the fabricated object W (fabricated section W1) may be used as any porous article, not limited to these examples. In particular, as shown in Figures 21 to 24, by regularly arranging fabricated sections W1 that exhibit different shapes when viewed from each direction to construct the fabricated object W, it is possible to create a bias in the ease with which fluids such as air and water can pass through. By selecting an arrangement pattern according to the shape of each fabricated section W1, the fabricated object W can be made to function effectively as a filter or filter material. In addition, by creating a bias in the connection structure of the fabricated sections W1, the elasticity and rigidity of the fabricated object W can also be arbitrarily manipulated. Furthermore, by connecting the molding units W1 in an arbitrary arrangement pattern according to bioscan data, such as data calculated by pressure sensors or the like along the shape of a living organism, it is possible to fabricate cushions, prosthetics, and other devices that are suitable for the shape of individual living organisms.

[0069] By changing the connecting structure of the molding unit W1 (molded object W), the properties of the same material can be altered. For example, although not shown in the diagram, a chair with a cushion can also be molded from the same material. In this case, there is no need to separate the materials when disposing of them, saving sorting effort and making recycling easier, thus contributing to environmental considerations. Furthermore, by constructing items that frequently use urethane mats, such as cushions and plant growing media, using the molding unit W1 (molded object W), it is possible to mold highly flexible and elastic items while eliminating the need for incineration and landfill disposal like with urethane. This is expected to reduce disposal costs and environmental impact.

[0070] Furthermore, since the molding section W1 (molding section W) has a loop shape, it can be used as a gripping part or a hook for a jig, making it easy to replace when molded as a mesh.

[0071] Making the connecting molded parts W1 (molded object W) denser leads to improved strength.

[0072] In the above embodiment, we basically showed an example of a molded part W1 or molded object W defined by a torus knot that is mathematically homeomorphic to a circle and has a trivial (unravelable) closed-loop shape where |d| < |f| in equation (1). However, the coefficients d and f can be any value.

[0073] For example, as an example where |d| or |f| is 3 or greater, Figure 26 shows an example of a molded part W1 defined in equation (1) based on a torus knot that forms a closed loop shape with |a|=|b|=|c|, d=5, and f=6.

[0074] Furthermore, as an example of |d|>|f|, Figure 27 shows an example of a molding section W1 defined based on a torus knot forming a closed loop shape with |a|=|b|=|c|, d=-7, and f=4 in equation (1), and Figure 28 shows an example of a molding section W1 defined based on a torus knot forming a closed loop shape with |a|=|b|=|c|, d=3, and f=2 in equation (1). Note that Figure 29 shows an example of another torus knot K forming a closed loop shape with d=3 and f=2 in equation (1), similar to the torus knot defining the loop shape of the molding section W1 shown in Figure 28. However, compared to the molding section W1 shown in Figure 28, the absolute values ​​of the coefficients c and e are larger, so the torus knot K shown in Figure 29 exhibits a three-dimensional clover shape rising in the Z-axis direction, as shown in Figure 29(e). Thus, even when the absolute values ​​or ratios of coefficients d and f are equal, variations in the molding process can be easily provided to the molding section W1 by selecting other coefficients a to c and e.

[0075] Figure 30 also shows an example of a torus knot K forming a closed loop shape with |a|=|b|<<|c|, d=6, and f=5. The molded part W1 having the closed loop shape defined by this torus knot K will exhibit a Lissajous figure-like appearance. In the examples shown in Figures 29 and 30, the molded part W1 is inscribed in a cube, making it easier to handle as a unit shape when connecting them to form a molded object W.

[0076] Furthermore, the torus knot used to define the loop shape may itself have a self-intersection in the molding section W1. Figure 31 shows an example of a molding section W1 defined based on a torus knot forming 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-intersecting in the central part, i.e., near the Z-axis, so the molding section W1 whose loop shape is defined by this torus knot also has a self-intersection. Even such an example is included in the molding section W1 of this embodiment.

[0077] Furthermore, with respect to torus knots, self-intersections may occur at locations other than near the Z-axis.

[0078] Thus, in the case of a molded part W1 (form W) where the absolute values ​​of the coefficients d and f in equation (1) are set to be large, the loop shape of the molded part W1 is defined by a torus knot that forms a mathematically non-trivial (cannot be unraveled) closed loop shape. In this case, the molded part W1 (form W) is formed in such a way that many loop shapes are intertwined, resulting in a soft tactile feel. In particular, when a soft material (elastic material) is used, a form W that can be elastically deformed in a spring-like manner in the Z-axis direction can be constructed. In the above example, the form W shown in Figure 26 has particularly excellent elastic deformation performance, and can be formed as a particularly elastic cushion even without connecting multiple molded parts W1 (form W). Furthermore, in the case of a molded object W without self-intersecting sections in the molding section W1, it is mathematically in phase with a circle, and therefore can be deformed in various directions compared to a configuration with self-intersecting sections. Moreover, because it is a single-stroke structure mathematically in phase with a circle, even when pulled in the expanding direction, only the relative positions of the loop shapes 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 contracting direction, it can easily return to its original shape when the external force is released. In other words, even if the molding material is hard, the molding section W1 (molded object W) is structurally deformable by contraction and expansion, and can possess flexibility, elastic deformation performance, and impact resistance. For example, it is possible to reduce the amount of plasticizer used or to mold without using plasticizer at all, which also contributes to environmental considerations.

[0079] For example, when the molded object W is pushed into a conduit or the like having a cross-sectional shape smaller than the outer diameter of the molded object W, its deformation properties cause it to return to its original shape and press against the inner surface of the conduit or the like, making it easily attachable to the conduit or the like in a kind of tension rod manner. Furthermore, because the outer circumference of the molded object W is formed in a curved (curved) shape, even if the molded part W1 has a self-intersecting section, it can still be easily attached to the conduit or the like. When fixing it to the conduit or the like, for example, by applying adhesive to the outer surface and then pushing it in, it can be easily fixed without the need for support members or the like. Also, in places with weak water flow, it can be attached to the conduit simply by pushing it in without adhesive. In that case, the molded object W can be slid to any position by hand or with a jig to move the attachment position, and the time and cost can be saved by not using adhesive.

[0080] For example, by creating the molded object W using a material that is resistant to dirt (has antifouling properties), it can be placed in the piping of a plant factory, such as one that circulates water and reuses the nutrient solution, and used as a mesh or filter material to separate impurities in the cultivation tank. In particular, since the molded object W of this embodiment is easy to mold into a symmetrical (non-directional) shape, it can be easily installed without making mistakes in the installation direction. Furthermore, by molding the molded object W to the dimensions of existing piping, it can be easily applied even in plant factories where the piping cannot be easily changed (water flow cannot be easily stopped), and if molded to the desired size, it can be easily installed horizontally to the piping. Moreover, since the loop shape of the molded part W1 can be used as a hook or grip, installation and replacement are easy even when installed deep inside the piping, making it easy to use as a filter material that requires frequent replacement and maintenance.

[0081] Furthermore, while equation (1) shows an example with integer coefficients, this embodiment is not limited to this example, and includes cases where, for example, coefficients d to f are not integers.

[0082] Thus, according to this embodiment, by having a curved structure W1 (formed object W) with a loop shape defined based on a torus knot, the load can be supported by compressive force, and it is possible to further improve the freedom of form by enabling a free connection structure for the formed object W1, etc. Furthermore, because it is a curved structure, it is easier to grip than a straight structure and is safer because it has no corners.

[0083] By utilizing equation (1), which is a continuous function, and appropriately selecting its coefficients a to f, it becomes possible to manufacture the molding part W1, i.e., the molded object W, which exhibits a complex shape that differs greatly depending on the viewing angle, in any arbitrary shape, and it is also possible to easily increase the variations in the molding of the molding part W1, i.e., the molded object W.

[0084] Furthermore, compared to a structure in which linear lattice structures are regularly connected, when multiple molded parts W1 are connected by intersecting loop shapes, the connection positions can be set arbitrarily. By appropriately selecting the molding material, it is possible to provide connecting parts with various properties, thereby setting the performance of the molded object W. For example, by adding thickness to the connecting parts at arbitrary locations, it is possible to provide a molded object W with excellent impact resistance.

[0085] Furthermore, the above-mentioned molding section W1 (molded object W) has a loop shape defined by a torus knot K (an example of which is shown in Figure 2), which is a smooth curve that wraps around the surface of a virtual torus T (shown in Figure 2). Therefore, it does not have overhangs that require support material or bridges that extend horizontally to the build table surface, and can be manufactured without supports using the 3D printer 1. In addition, when multiple molding sections W1 are connected to form a molded object W, more complex shapes can be manufactured without supports.

[0086] For example, in the case of the 3D printer 1 of this embodiment, the conditions for creating a build section W1 (object W) without supports in 3-axis printing are that when the angle between the central axis of the nozzle 11 and the build table 5 is 90°, it is desirable that the rising angle of the build section W1 (object W) is 45°. However, this is not the only condition, and it has been confirmed that printing is possible if the rising angle is at least 6.5° relative to the build table 5 (Figure 33 shows a reference example, and Figure 34 shows a photograph of the manufacturing example). Furthermore, in the case of the 6-axis 3D printer 1, it has been confirmed that all of the above build sections W1 and objects W can be printed without supports (Figures 35 and 36 show photographs of the manufacturing examples).

[0087] Furthermore, the fused deposition modeling (FDM) 3D printers used to manufacture the various types of molded objects (models) mentioned above can also be large pellet-type 3D printers with a nozzle diameter of 10 mm or more. These large 3D printers can use inexpensive, readily available, general-purpose pellet-shaped thermoplastic resins (such as recycled pellets) as the molding material, rather than specialized filament resins.

[0088] Furthermore, the manufacturing equipment for the fabricated object is not limited to fused deposition modeling (FDM) 3D printers; for example, stereolithography (DLP or SLA) 3D printers may also be used.

[0089] Furthermore, the object manufacturing apparatus is not limited to a configuration in which the build head (extrusion means) having a nozzle for extruding the build material is movable in the X-axis and Z-axis directions and the build table is movable in the Y-axis direction. It is sufficient if the build head is movable in at least three dimensions relative to the build table. For example, the build head may be movable in the X-axis and Y-axis directions and the build table may be movable in the Z-axis direction, or the build head may be provided at the tip of a robot arm (preferably a robot arm of a 6-axis robot) and be movable in any direction including the three directions of the X-axis, Y-axis, and Z-axis. Supportless printing is possible in 3-axis and 6-axis 3D printers, which leads to a reduction in printing time (improvement in the printing speed of the object W) because supports are not printed. For example, if the object manufacturing apparatus is 6-axis, the nozzle 11 can trace a torus knot, which is a continuous function, in a single stroke if it does not interfere with the build section W1 (object W), thus improving the printing speed of the object W. [Explanation of Symbols]

[0090] 1. 3D printer, a device for manufacturing shaped objects. 5. Build Table 15 lines 16 Surfaces 21 Cross-sectional shape D Modeling data K Torus knot W Sculpture W1 Modeling Department

Claims

1. A method for designing a linear object having a molded part that is a solid, curved linear body with an outer shape defined by a torus knot, The 3D modeling data for the 3D model is formed by setting a thickness on a surface created by connecting two adjacent torus knots with lines. A method for designing molded objects characterized by the above.

2. A method for designing a linear object having a molded part that is a solid, curved linear body with an outer shape defined by a torus knot, The molding data for the molding part is formed by sweeping a predetermined cross-sectional shape along a loop-shaped torus knot. A method for designing molded objects characterized by the above.

3. A 3D printer is used as a 3D manufacturing apparatus to manufacture a 3D object based on the 3D object design method described in Claim 1 or 2. A method for manufacturing a molded object characterized by the features described herein.

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