Printing path planning method for suspended surfaces without support based on FDM printing

Abstract

The present invention relates to the technical field of 3D printing, and specifically discloses a method for planning high-quality printing paths for suspended surfaces without supports based on FDM printing, comprising the following steps: S1, surface pretreatment: geometric property classification and determination of the use of a reference reference method; S2, determination of a reference reference object: determination of a reference reference for path planning within a surface; S3, surface conversion curve: obtaining an initial path curve; S4, curve connection: converting multiple initial paths into a continuous path; S5, path optimization; S6, printing program generation: production of a self-compiled G‑Code file and parameterization of printing data. The present invention adopts the above-mentioned method for planning high-quality printing paths for suspended surfaces without supports based on FDM printing, effectively reducing material loss, the generation of defects and the probability of printing failure, and reducing production difficulty, time and economic costs in a simple printing form.

Description

Technical Field

[0001] The present invention relates to the technical field of 3D printing, and in particular to a method for planning a printing path for an unsupported suspended surface based on FDM printing. Background Art

[0002] FDM printing technology, or Fused Deposition Modeling, is one of the most commonly used and widely used technologies in 3D printing. Its principle is to melt the thermoplastic material by heating the nozzle, and then deposit the material layer by layer or along a specific path according to the path and extrusion amount set by the computer file, and finally form a three-dimensional object. By controlling the movement of the machine axis, FDM can produce complex geometric structures.

[0003] In the prior art, printing suspended structures in 3D printing slicing software usually requires adding supports or adjusting the suspended part of the model to a gradient overhanging surface. Adding supports will lead to material waste, surface defects, and extended printing time. In addition, the possibility of failure is increased due to frequent nozzle retraction and crossing the model. Adjusting the model will significantly change the original design when the suspended area or overhang angle is large, making it difficult to meet design requirements.

[0004] In addition, for the top cover geometry, the traditional layer-by-layer printing method has difficulty coping with the situation of small curvature or flat top cover, resulting in the ineffective accumulation of materials or poor interlayer bonding, which in turn affects the surface quality. Summary of the invention

[0005] The purpose of the present invention is to provide a printing path planning method for unsupported suspended surfaces based on FDM printing, which realizes efficient, high-surface-quality, unsupported manufacturing of suspended surfaces through a continuous extrusion path, effectively reduces material loss, defects and the probability of printing failure, and reduces the difficulty, time and economic cost of production in a simple printing form through parameterized automatic control of machine parameters and extrusion paths.

[0006] To achieve the above object, the present invention provides a method for planning a printing path for an unsupported suspended surface based on FDM printing, comprising the following steps:

[0007] S1. Surface pretreatment: Classification of geometric properties and determination of the use of benchmark reference methods;

[0008] S2. Determine the reference: determine the reference for path planning within the surface;

[0009] S3, surface conversion curve: get the initial path curve;

[0010] S4, curve connection: convert multiple initial paths into one continuous path;

[0011] S5, path optimization;

[0012] S6. Printing program generation: creation of self-edited G-Code files and parameterization of printing data.

[0013] Preferably, S1 comprises the following steps:

[0014] S11, the algorithm inputs the suspended surface geometry;

[0015] S12, identifying whether the geometric body attribute is Mesh or NURBS, if not, converting the attribute of the suspended surface geometric body into NURBS or Mesh according to the API of Rhino-Common;

[0016] S13, check the integrity of the surface of the suspended surface geometric body, that is, whether there is a broken surface or defect, if so, repair the surface to make it complete;

[0017] S14, selecting a subroutine method selected by a reference according to the characteristics of the suspended surface geometry and the surface geometry attributes, specifically:

[0018] Determine whether the number of exposed boundaries of the geometric surface is greater than or equal to 3. If so, determine whether the outer contour edge of the geometric surface is four boundaries and the geometric body attribute is a NURBS surface; if not, determine whether the geometric body attribute is a NURBS surface;

[0019] If the outer contour edge of the geometric surface has four boundaries and is a NURBS surface, then subroutine method S2-1 is used, otherwise subroutine method S2-2 is used;

[0020] If the number of exposed boundaries of the geometric surface is less than 3 and the geometric attribute is a NURBS surface, the subroutine method, S2-3, is used, otherwise the subroutine method, S2-4, is used.

[0021] Preferably, the subroutine method S2-1 specifically includes: using the UV interval as a four-side NURBS reference;

[0022] The subroutine method S2-2 specifically includes: using the outer contour line as a reference for various NURBS datums;

[0023] The subroutine method S2-3 specifically includes: using the IsoCurve structure line of the NURBS surface as a benchmark reference;

[0024] The subroutine method S2-4 specifically includes: using the longitude and latitude lines of the Mesh surface as a reference.

[0025] Preferably, the subroutine method S2-1 specifically includes the following steps:

[0026] S2-11, determine whether the NURBS surface is clipped, if so, restore the clipped NURBS surface topology to the unclipped surface state and copy and record the boundary UV value of the clipped NURBS surface, and then obtain the UV interval (u0, u1), (v0, v1) of the unclipped surface; if not, directly obtain the UV interval (u0, u1), (v0, v1) of the unclipped surface;

[0027] S2-12, flatten the untrimmed surface into a two-dimensional plane rectangular shape with a length of u1-u0 and a width of v1-v0 according to the UV interval value;

[0028] S2-13, using the boundary of the two-dimensional plane rectangle obtained in S2-12 as a reference;

[0029] The subroutine method S2-2 specifically includes the following steps:

[0030] S2-21, obtain all outer contour edges of non-four-sided NURBS surfaces;

[0031] S2-22, combine and connect all contour edges into a closed curve as a reference;

[0032] The subroutine method S2-3 specifically includes the following steps:

[0033] S2-31. Reset the U direction and V direction of the NURBS surface structure line IsoCurve, that is, set the closed line that does not intersect the XY plane as the U direction, and the surface structure line that intersects the XY plane after extension as the V direction;

[0034] S2-32, extract four structural curves of the NURBS surface (u0, v0), (u1, v0), (u0, v1) and (u1, v1) as benchmark references;

[0035] The subroutine method S2-4 specifically includes the following steps:

[0036] S2-41, determining whether the geometric surface of the suspended surface geometric body is a four-sided mesh. If so, extracting all line segments of the mesh surface according to Weft and combining them in the longitude and latitude directions; if not, reconstructing the geometric surface in a four-sided mesh format;

[0037] S2-42, let the closed line that does not intersect the XY plane be the U-direction latitude line, and the line that intersects the XY plane after extension be the V-direction longitude line;

[0038] S2-43. Extract four longitude and latitude polylines (u0, v0), (u1, v0), (u1, v0) and (u1, v1) on the Mesh surface as benchmark references.

[0039] Preferably, S3 is specifically to obtain multiple-circle initial four-side offset curves, which specifically includes the following steps:

[0040] S3-11, obtaining the shortest boundary segment length L1 of the rectangle according to the boundary obtained in S2-13;

[0041] S3-12, set the print line width W1 according to the printer configuration, and calculate the initial path curve according to the length L1 and W1, and print the Floor (N1=L1 / 2 / W1) circle;

[0042] S3-13, offset the rectangular boundary by N1 circles as the initial path curve;

[0043] S4 specifically processes multiple circles of four-side offset curves and connects them into a continuous curve, which specifically includes the following steps:

[0044] S4-11, obtain the multi-circle plane offset four-side closed curve of S3-13;

[0045] S4-12, select any two adjacent sides from the four sides of each curve;

[0046] S4-13, according to the print line width W1 set in S3-12, respectively extend and shorten the lengths of two adjacent sides W1 according to the G0 curvature;

[0047] S4-14, connecting all processed curves end to end to form a continuous curve, and using it as an initial continuous path for optimization;

[0048] S5 is specifically to optimize the initial continuous path composed of multiple circles of equidistant offset lines of the two-dimensional plane, which specifically includes the following steps:

[0049] S5-11, obtaining a continuous curve generated in S4-14 in a two-dimensional plane;

[0050] S5-12, after analyzing the curvature of the curve, extract the discontinuity points according to the G0 discontinuity;

[0051] S5-13, create a sphere with a radius of R1 at several discontinuous points;

[0052] S5-14, intersect the sphere with the continuous curve and find the Boolean difference of the continuous curve on several spheres;

[0053] S5-15, setting a convex value B1 of arc fitting blending and blending the beginning and the end of the curve disconnected after the Boolean operation into one curve by arc fitting;

[0054] S5-16, topologically mapping the continuous curve back to the geometric surface according to the UV value in the two-dimensional plane shape;

[0055] S5-17. Obtain an optimized continuous path curve on the four-sided geometric surface.

[0056] Preferably, S3 is specifically to obtain a multi-turn initial multilateral offset curve, which specifically includes the following steps:

[0057] S3-21, splitting the closed curve obtained in S2-22 into a plurality of contour edges according to G0 discontinuity;

[0058] S3-22, using the average method to calculate the coordinate values ​​of each mesh vertex of the geometric surface, and obtain the center point C2 of the geometric surface;

[0059] S3-23, calculate the geodesic distance D0, D1...D between the center point C2 and each contour edge i ;

[0060] S3-24. Compare the geodesic distances obtained in S3-23 and obtain the shortest geodesic distance D i ;

[0061] S3-25, set the print line width W2 according to the printer configuration, and set the shortest geodesic distance D i The initial path curve needs to be printed (N2=D i / 2 / W2) circle;

[0062] S3-26, offsetting the contour edge used as the reference on the geometric surface into an N2-circle curve as the initial path curve;

[0063] S4 specifically processes multiple loops of multi-sided offset curves and connects them into a continuous curve, which specifically includes the following steps:

[0064] S4-21, obtaining a closed curve of the multi-turn offset of S3-26;

[0065] S4-22, select any two adjacent sides of each circle curve;

[0066] S4-23, according to the print line width W2 set in S3-25, extending the tangent vectors of the endpoints of the two adjacent edges, respectively extending and shortening the geodesic distance of the lengths of the two adjacent edges W2 to the corresponding points;

[0067] S4-24, reconstruct the curve of S4-23 with adjusted length;

[0068] S4-25, connecting all processed curves end to end to form a continuous curve as an initial continuous path for optimization;

[0069] S5 is specifically to optimize an initial continuous path consisting of multiple circles of equidistant offset lines along a geometric surface, which specifically includes the following steps:

[0070] S5-21, obtaining the continuous curve generated by S4-25 in the geometric surface and analyzing the curvature change;

[0071] S5-22, select the curvature continuity standard between G0 and G3;

[0072] S5-23, extracting Gn discontinuity points on the geometric surface according to the selected curve discontinuity;

[0073] S5-24, Analyze the parameter positions of several discontinuous points on the continuous curve;

[0074] S5-25, creating a sphere of relative radius at corresponding points according to the parameter positions of several points;

[0075] S5-26, intersecting a number of spheres with a continuous curve and finding the Boolean difference of the curve on the number of spheres;

[0076] S5-27, according to the set relative fitting convex value B2, the beginning and the end of the disconnected curve are mixed by relative arc fitting according to the convex value B2;

[0077] S5-28, blending part of the curve is mapped onto the geometric surface;

[0078] S5-29. Combine the disconnected curve and the arc fitting mixed curve into a continuous path curve.

[0079] Preferably, S3 specifically obtains a plurality of NURBS surface structure curves, which specifically includes the following steps:

[0080] S3-31, extracting several V-direction structural curves in the interval from V0 to V1 according to the printing accuracy;

[0081] S3-32. Count the lengths of all structural curves in the V direction and obtain the length interval [L 3a , L 3b ];

[0082] S3-33, input the layer height range that can be extruded according to the nozzle diameter [H 3a , H 3b ], calculate Ceiling(L 3b / H 3b ) and Floor(L 3a / H 3a ) and compare the values;

[0083] S3-34, get the number interval of the U direction structure curve [N 3a , N 3b ] and select any value from the interval;

[0084] S3-35, extracting N3 closed structure curves in the U direction of the NURBS surface as initial path curves;

[0085] S4 specifically processes the U-direction structural curves of multiple NURBS surfaces and connects them into a continuous curve, which specifically includes the following steps:

[0086] S4-31, obtaining multiple U-direction structural curves extracted from the NURBS surface IsoCurve;

[0087] S4-32, setting a number of equally spaced points on multiple U-direction structural curves according to accuracy;

[0088] S4-33, transfer rank to multiple groups of equidistant points;

[0089] S4-34, setting the Nth data of each group and the N+1th data of the sub-group as the same array, and so on, reversing the rank according to the set sequence relationship of the equidistant point groups;

[0090] S4-35, flatten into a one-dimensional array according to the order within the matrix;

[0091] S4-36, sequentially connecting all points in the one-dimensional array into a continuous curve, and using it as an initial continuous path for optimization;

[0092] S5 is specifically to optimize the initial continuous path composed of multiple NURBS surface U-direction structural curves, which specifically includes the following steps:

[0093] S5-31, obtaining the continuous curve generated by S4-36 in the NURBS surface;

[0094] S5-32, pull the area where the continuous curve was originally separated from the NURBS surface due to the connection back to the surface in the form of a vertical surface projection;

[0095] S5-33, extracting each group of starting points of the plurality of groups of equidistant points in S4-32;

[0096] S5-34, collecting the nearest projection point of the starting point on the curve;

[0097] S5-35, split the curve into several segments at the nearest projection point;

[0098] S5-36, extracting the bottommost curve and projecting it vertically onto the XY plane;

[0099] S5-37. Arrange the XY plane projection line and the separated curve segments in order from low to high.

[0100] Preferably, S3 specifically obtains multiple Mesh surface structure polylines, which specifically includes the following steps:

[0101] S3-41, extracting a plurality of V-direction multi-segment meridians from V0 to V1 according to the printing accuracy;

[0102] S3-42, count the lengths of all longitudes in the V direction and obtain the length interval [L 4a , L 4b ];

[0103] S3-43, input the layer height range that can be extruded according to the nozzle diameter [H 4a , H 4b ], calculate Ceiling(L 4b / H 4b ) and Floor(L 4a / H 4a ) and compare the values;

[0104] S3-44, get the number interval of latitude lines in the U direction [N 4a , N 4b ] and select any value from the interval;

[0105] S3-45, extract N4 closed structure polylines in the U direction of the Mesh surface as the initial path curve;

[0106] S4 specifically processes multiple mesh surface latitude U-direction structure polylines and connects them into a continuous polyline, which specifically includes the following steps:

[0107] S4-41, obtain multiple latitude U-direction structure polylines extracted from the Mesh surface Weft;

[0108] S4-42, according to the accuracy, set a number of equal-distance points of the multiple latitude U-direction structure polylines;

[0109] S4-43, transfer rank to multiple groups of equidistant points;

[0110] S4-44, setting the Nth data of each group and the N+1th data of the sub-group to be the same array, and so on, reversing the rank according to the set sequence relationship of the equidistant point groups;

[0111] S4-45, flatten into a one-dimensional array according to the order within the matrix;

[0112] S4-46, sequentially connecting all points in the one-dimensional array into a continuous polyline, and using it as an initial continuous path for optimization;

[0113] S5 is specifically to optimize the initial continuous path composed of multiple Mesh surface latitude U-direction structure polylines, which specifically includes the following steps:

[0114] S5-41, obtain the continuous polyline generated by S4-36 in the Mesh surface;

[0115] S5-42, pull the area where the continuous polyline was originally separated from the Mesh surface due to connection back to the surface in the form of vertical surface projection;

[0116] S5-43, extracting each group of starting points of the plurality of groups of equidistant points in S4-42;

[0117] S5-44, collecting the nearest projection point of the starting point on the polyline;

[0118] S5-45, split the polyline into several segments at the nearest projection point;

[0119] S5-46, extract the bottom-most polyline and project it vertically onto the XY plane;

[0120] S5-47. Arrange the XY plane projection line and the separated curve segments in order from low to high.

[0121] Preferably, S6 specifically includes the following steps:

[0122] S61, converting the path curve into a number of equidistant points according to printing accuracy requirements;

[0123] S62, calculating the UV values ​​of all equidistant points on the geometric surface;

[0124] S63, print line width W according to printer configuration settings n Calculate the relative extrusion value of each point with the UV values ​​of all equidistant points;

[0125] S64, setting machine parameters, including adjusting the extrusion ratio, adjusting the printing speed, and adjusting the printing temperature;

[0126] S65, translating the machine parameters into the parameters of the geometric path to generate a G-Code file, and simulating the movement of the machine along the surface path curve and the extrusion control in a 3D visualization software;

[0127] S66, check whether there is any collision or gap between the printing path and the machine or other parts of the path. If so, readjust the parameters in the machine parameter part until there is no collision or gap, and then execute the printing file.

[0128] Therefore, the present invention adopts the above-mentioned method for planning printing paths for suspended surfaces without support based on FDM printing, and the beneficial effects are as follows:

[0129] (1) The present invention is based on Rhinoceros-Grasshopper parametric modeling software, which realizes automatic identification of geometric attributes and parameter adjustment through autonomous programming to achieve reasonable path planning, and then generates a G-code file that can be recognized by a 3D printer. Through a continuous extrusion path, efficient, high-quality, unsupported suspended surface manufacturing is achieved, effectively reducing material loss, defects and the probability of printing failure.

[0130] (2) The present invention reduces the difficulty, time and economic cost of production by parametrically automatically controlling machine parameters and extrusion paths in a simple printing form, and has significant economic and social benefits.

[0131] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0132] Figure 1 It is a general flow chart of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0133] Figure 2 It is a flow chart of surface preprocessing of an embodiment of a method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0134] Figure 3 It is a flowchart of S2-1 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0135] Figure 4 It is a flowchart of S2-2 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0136] Figure 5 It is a flowchart of S2-3 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0137] Figure 6 It is a flow chart of S2-4 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0138] Figure 7 It is a flowchart of S3-1 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0139] Figure 8 It is a flowchart of S4-1 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0140] Fig. 9It is a flowchart of S3-2 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0141] Fig.10 It is a flowchart of S4-2 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0142] Fig.11 It is a flowchart of S3-3 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0143] Fig.12 It is a flowchart of S4-3 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0144] Fig.13 It is a flow chart of S3-4 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0145] Fig.14 It is a flowchart of S4-4 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0146] Fig.15 is a flow chart of S5 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0147] Fig.16 is a flow chart of S6 of an embodiment of a method for planning a printing path for an unsupported suspended surface based on FDM printing of the present invention;

[0148] Fig.17 It is a schematic diagram of the suspended and top cover geometry types of an embodiment of the method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0149] Fig.18 It is a reference schematic diagram obtained by S2-2 of Example 1 of the method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0150] Fig.19 It is a schematic diagram of a multi-circle initial path curve obtained in S3-2 of Example 1 of the method for planning printing path for a suspended surface without support based on FDM printing of the present invention;

[0151] Fig. 20 It is a schematic diagram of an initial continuous path curve S4-2 of Example 1 of a method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0152] Fig.21It is a schematic diagram of a continuous path curve after optimization in S5-2 of Example 1 of the method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0153] Fig. 22 It is a schematic diagram of the structure of a mechanical arm for assembling an FDM printing gun tool head according to Embodiment 1 of the method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0154] Fig.23 It is a printing process and printing effect diagram of a large overhang or suspended surface according to Embodiment 4 of the method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0155] Fig.24 It is a printing process and printing effect diagram of a large overhang or suspended surface according to Embodiment 5 of the method for planning a printing path for a suspended surface without support based on FDM printing of the present invention;

[0156] Fig.25 The top cover surface printing process and printing effect diagram of the first and second embodiments of the printing path planning method for the suspended surface without support based on FDM printing of the present invention;

[0157] Fig.26 It is a schematic diagram of the continuous path curve after optimization of S5-1 in Example 3 of the method for planning printing path for a suspended surface without support based on FDM printing of the present invention. DETAILED DESCRIPTION

[0158] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0159] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0160] It should be stated in advance that the geometric attributes supported by the mainstream 3D modeling software on the market mainly include boundary representation (hereinafter referred to as B-rep), non-uniform rational B-splines (hereinafter referred to as NURBS), mesh, subdivision surface (hereinafter referred to as Sub-D), poly-surface, etc. In the Rhinoceros-Grasshopper (hereinafter referred to as RH-Gh) software environment, this method mainly identifies and analyzes the geometric bodies with the above-mentioned attributes. For the geometric attributes not listed, they must be converted into a widely compatible geometric format to ensure that they can be identified and operated in mainstream 3D modeling software.

[0161] Examples of various types of overhang and top cover geometries are: Fig.17 As shown, (a) represents the printing path of a curved top cover geometric surface with a smaller curvature, (b) represents the printing path of a large overhanging or overhanging special-shaped geometric surface, and (c) represents the printing path of a geometric surface for suspended covering on an existing grid base support.

[0162] Embodiment 1

[0163] In this embodiment, a free polygonal curved top cover without a fixed shape will be produced by path planning and unsupported suspended curved surface printing on a pre-prepared grid base. First, the source of the geometric surface can be artificial computer modeling, models downloaded from other channels, three-dimensional point cloud scanning models, etc. In this embodiment, a three-dimensional laser tracking scanning instrument is used to scan the curved top cover that needs to be printed without support into a geometric surface. The three-dimensional laser tracking scanning instrument includes a laser emission and locator MetaScan and a laser tracking and imaging instrument C-Track to achieve the above functions. Secondly, the geometric surface is picked up and input in the parametric operation platform of the three-dimensional software Rhinoceros-Grasshopper, and its geometric properties are judged to be NURBS (Non-Uniform Rational B-Splines) surfaces, and its surface is checked for damage. If there is damage, point and line inlay is performed according to the common operations of the three-dimensional software to make the geometric surface repaired. Finally, the path type sub-method is selected according to the target requirements and the manufacturing machine used. The path type sub-method of this embodiment pre-uses a robotic arm equipped with a print gun head to perform unsupported suspended printing on the curved top cover on the grid base.

[0164] like Figure 1 As shown, the printing path planning method for a suspended surface without support based on FDM printing includes the following steps:

[0165] S1. Surface pretreatment, i.e., geometric property classification and reference method use determination, the specific steps are as follows Figure 2 As shown:

[0166] S11, the algorithm inputs the suspended surface geometry, that is, the obtained geometry for path planning and printing production is input into the parametric operation platform of the 3D modeling software Rhinoceros-Grasshopper;

[0167] S12, identifying whether the geometric body attribute is NURBS or Mesh, if not, converting the suspended surface geometry of non-such attributes into NURBS or Mesh according to convenience according to the API of Rhino-Common. In this embodiment, the identified geometric body attribute is NURBS.

[0168] S13. Check the integrity of the surface of the suspended surface geometric body. If the surface is broken or incomplete, the surface is repaired or reshaped to make it a complete surface. Correspondingly, according to the identification in the previous steps, the geometry attribute of Mesh is patched by the dot mapping method, and the geometry attribute of NURBS is reshaped by the original points and boundary lines on its surface. Since the geometry attribute identified in this embodiment is NURBS and there are broken surfaces, the original points and boundary lines on its surface are identified to reshape the surface to provide a complete NURBS curved surface.

[0169] S14. Select the subroutine method selected by the corresponding type of benchmark reference according to the characteristics of the suspended surface geometry and the surface geometric attributes. That is, determine whether the number of exposed boundaries of the geometric surface is greater than or equal to 3. If greater than or equal to, determine whether the outer contour edge of the geometric surface is four boundaries and is a NURBS surface with geometric attributes. If so, use subroutine method S2-1, otherwise use subroutine method S2-2; if the exposed boundaries of the geometric surface are less than 3, determine whether the geometric surface is a NURBS surface. If so, use subroutine method S2-3, otherwise use subroutine method S2-4. In this embodiment, the number of exposed boundaries of the geometric surface with the geometry attribute of Mesh is 6, and subroutine method S2-2 is used.

[0170] S2, determine the reference, that is, determine the reference for path planning within the surface according to the selected adapted subroutine method S2-2, such as Figure 4 As shown, the specific steps are as follows:

[0171] S2-21: Get all outer contour edges of non-four-sided NURBS surfaces;

[0172] S2-22: Combine and connect all contour edges into a closed curve;

[0173] S2-23: Use this closed curve as the reference for S3-2, such as Fig.18 shown.

[0174] S3, surface conversion curve, that is, according to the reference determined by subroutine method S2-2, the geometric surface is converted into a multi-turn initial multi-edge path curve, such as Fig. 9 As shown, the specific steps are as follows:

[0175] S3-21: Split the contour edge obtained as a reference in S2-2 into several contour edge segments according to G0 discontinuity;

[0176] S3-22: Then, the coordinate values ​​of each mesh vertex of the geometric surface are calculated by using the average method, so as to obtain the center point C2 of the geometric surface;

[0177] S3-23: Calculate the geodesic distance D0, D1, ... D between the center point C2 and each contour edge i ;

[0178] S3-24: Compare these geodesic distances and get the shortest geodesic distance D i ; The shortest geodetic distance in this embodiment is 68.7mm;

[0179] S3-25: Set the appropriate print line width W2 according to the printer configuration, and the shortest geodesic distance D i It can be calculated from the print line width W2 that the initial path curve needs to print N2 circles; in this embodiment, a nozzle with a diameter of 1.0 mm is used, so a relatively suitable print line width is set to 1.2 mm.

[0180] S3-26: offset the contour edge used as the datum reference into an N2-circle curve on the geometric surface;

[0181] S3-27: The offset thick N2-circle three-dimensional space polygonal curve is used as the initial path curve of method S4-2, such as Fig.19 shown.

[0182] S4, curve connection, that is, converting the multi-loop initial multilateral path curve obtained by S3-2 into a continuous path curve, such as Fig.10 As shown, the specific steps are as follows:

[0183] S4-21: Obtaining a closed curve of a multi-turn offset calculated by S3-2 as an initial path curve;

[0184] S4-22: Take any two adjacent edges of each curve;

[0185] S4-23: according to the printing line width W2 set by method S3-2, along the tangent vectors of the endpoints of the two adjacent edges, respectively extending and shortening the geodesic distance of the lengths of the two adjacent edges W2;

[0186] S4-24: Reconstruction of these adjusted length curves;

[0187] S4-25: Connect all processed curves end to end to form a continuous curve as the initial continuous path for optimization, such as Fig. 20 shown.

[0188] S5-2, path optimization, that is, optimizing the path details of the continuous path curve obtained by S4-25 to improve the printing quality. The specific steps are as follows Fig.15 shown.

[0189] S5-21: Analysis of the curvature change of a continuous path curve on the acquired geometric surface;

[0190] S5-22: between G0 and G3 curvatures, a curvature continuity standard is selected according to the curvature properties of the curve (for example, when each part of the curve is G3 and the connection is G1, the G1 curvature is selected as the continuity standard); in this embodiment, the G1 curvature is used as the curvature continuity analysis standard;

[0191] S5-23: extracting Gn discontinuous points on the curve of the geometric surface according to the set curve discontinuity; in this embodiment, extracting G1 discontinuous points on the continuous path curve, that is, points on the curve that are not tangent;

[0192] S5-24: extracting the position parameters of these discontinuous points on the length interval of the continuous curve;

[0193] S5-25: creating a sphere with a radius of R at the parameter position of the Gn discontinuity point on the plurality of curves; the radius of the sphere involved in the Boolean operation in this embodiment is set to be 1.3 mm;

[0194] S5-26: Intersect the sphere with this continuous curve and find the Boolean difference of the curve on several spheres;

[0195] S5-27: setting a bulge value B2 of arc fitting blending (it affects the curvature of blending) and blending the beginning and the end of the curve disconnected after the Boolean operation by arc fitting; in this embodiment, the bulge value (Bulge) B2 is set to 0.5;

[0196] S5-28: Map the curve of the blended part onto the geometric surface in the vertical direction;

[0197] S5-29: The disconnected curve after the Boolean operation is combined with the mixed curve mapped onto the geometric surface to form an optimized continuous path curve, such as Fig.21 shown.

[0198] S6, print program generation, that is, the production of self-edited G-Code files and parameterization of print data for the optimized continuous path, such as Fig.16 As shown, the specific steps are as follows:

[0199] S61: converting the path curve into a number of equidistant points (e.g., one equidistant point every 0.5 mm) according to the printing accuracy requirement; in this embodiment, the accuracy of the equidistant points is 0.1 mm;

[0200] S62: Calculate the UV values ​​of all equidistant points on the geometric surface;

[0201] S63: Calculate the relative extrusion value of each point according to the print line width W2 set by the printer configuration and the statistical UV value of the equidistant points;

[0202] S64: Setting machine parameters, including adjusting extrusion ratio, printing speed and printing temperature;

[0203] S65: The machine parameters are combined with the parameters of the geometric path to generate a G-Code file, and the machine movement and extrusion control simulation along the surface path curve are visualized in the 3D visualization software Rhinoceros-Grasshopper;

[0204] S66: Check whether the printing path collides with the machine or other parts of the path itself, or whether a large gap is generated. If so, readjust the parameters in the machine parameter section until there are no obvious errors. Then, the printing file can be generated and exported.

[0205] After the path planning and optimization method program of this embodiment is executed, the printing program file is then input into the mechanical arm equipped with the printing gun head, such as Fig. 22 As shown in FIG. 1 , the machine is used to perform unsupported suspended top cover surface FDM printing on a pre-prepared grid substrate. The printing path planned on the surface is as follows: Fig.17 As shown in (c) in the figure, the printing process is as follows: Fig.25 As shown in (a) in the figure, the final printing effect is as follows Fig.25 As shown in (b) in .

[0206] Embodiment 2

[0207] The difference from the first embodiment is that the outer contour edge of the top cover geometric surface is any number of edges such as Fig.17 As shown in (a) in the figure, the outer contour of the top cover surface is 100 edges that approximate the fitting arc, and the geometric properties of the top cover surface are applicable to NURBS or Mesh. Therefore, subroutine method S2-2 is used to optimize the initial continuous path composed of multiple circles of equidistant offset lines along the geometric surface. The specific steps are as follows: Figure 4 , Figure 8 , Fig.12 and Fig.15 shown.

[0208] The printing path planning method of the first embodiment is adopted, and a mechanical arm equipped with a printing gun head is used to perform path planning on a geometric surface of a top cover without support in the suspended area, such as Fig.17 As shown in (a) of the figure, the process of printing a curved top cover with a small curvature without support using a desktop printer is as follows Fig.25 As shown in (c), the effect of the unsupported curved cap with a smaller curvature is as follows: Fig.25 As shown in (d) in .

[0209] Embodiment 3

[0210] The difference from the first embodiment is that the outer contour edge of the geometric surface is four boundaries and is a NURBS surface. The subroutine method S2-1 is used to optimize the initial continuous path composed of multiple circles of equidistant offset lines of the two-dimensional plane. The specific steps are as follows: Figure 3 , Figure 7 , Fig.11 and Fig.15 As shown, S5 specifically includes the following steps:

[0211] S5-11, obtaining a continuous curve generated in S4-14 in a two-dimensional plane;

[0212] S5-12, after analyzing the curvature of the curve, extract the discontinuity points according to the G0 discontinuity;

[0213] S5-13, create a sphere with a radius of R1 at several discontinuous points;

[0214] S5-14, intersect the sphere with the continuous curve and find the Boolean difference of the continuous curve on several spheres;

[0215] S5-15, setting a convex value B1 of arc fitting blending and blending the beginning and the end of the curve disconnected after the Boolean operation into one curve by arc fitting;

[0216] S5-16, topologically mapping the continuous curve back to the geometric surface according to the UV value in the two-dimensional plane shape;

[0217] S5-17, obtain an optimized continuous path curve on the four-sided geometric surface, such as Fig.26 shown.

[0218] Embodiment 4

[0219] The difference from the first embodiment is that in this embodiment, the number of exposed boundaries of the geometric surface with the geometry attribute of Mesh is 2, which is similar to the tubular lofted surface in geometric structure. Therefore, the subroutine method S2-4 is adopted, and the Weft longitude and latitude lines of the Mesh surface are used as the reference, such as Figure 6 As shown, the specific steps include:

[0220] It should be noted that the three-dimensional space model can be represented by a two-dimensional parameter space. Accordingly, the Mesh mesh surface can also be represented by Weft, that is, a polyline in the longitude and latitude directions. Each longitude and latitude line can be represented by a floating point precision parameter (u) between 0 and 1. i ,u i )express.

[0221] S2-41: Determine whether the geometric surface of the suspended surface geometric body is a four-sided mesh. If so, extract all line segments of the mesh surface according to Weft and combine them in the longitude and latitude directions; if not, reconstruct the geometric surface in a four-sided mesh format;

[0222] S2-42: Let the closed line that does not intersect the XY plane be the U-direction latitude line, and the line that intersects the XY plane after extension be the V-direction longitude line;

[0223] S2-43: Extract four longitude and latitude polylines (u0, v0), (u1, v0), (u1, v0) and (u1, v1) on the Mesh surface as benchmark references.

[0224] Subroutine method S2-4 is used, and the specific steps are as follows Figure 6 , Fig.13 , Fig.14 and Fig.15 As shown in the figure, the schematic diagram of the printing process of large overhang or suspended surface is as follows: Fig.23 As shown in (a) of the figure, the printing effect diagram is as follows: Fig.23 As shown in (b) in .

[0225] Embodiment 5

[0226] The difference from the first embodiment is that in this embodiment, the number of exposed boundaries of the geometric surface with the geometric attribute of NURBS is 2, and combined with the structure similar to the tubular lofted surface, the subroutine method S2-3 is adopted, and the IsoCurve structure line of the NURBS surface is used as the reference, such as Figure 5 As shown, the specific steps include:

[0227] It should be noted that the three-dimensional space model can be represented by a two-dimensional parameter space. Correspondingly, the NURBS surface can also be represented by an IsoCurve, that is, its U and V direction structural curve. Each UV line can be represented by a floating point precision parameter (u i , u i )express.

[0228] S2-31: Reset the U direction and V direction of the NURBS surface structure line IsoCurve, that is, set the closed line that does not intersect the XY plane as the U direction and the surface structure line that intersects the XY plane after extension as the V direction;

[0229] S2-32: Extract four structural curves of the NURBS surface (u0, v0), (u1, v0), (u0, v1) and (u1, v1) as benchmark references.

[0230] Step S3 is as follows Fig.11 As shown, step S4 is as follows Fig.12As shown in the figure, a schematic diagram of path planning on the surface is shown in Fig.17 As shown in (b) of the figure, the printing process diagram is as follows: Fig.24 As shown in (a) of the figure, the printing effect diagram is as follows: Fig.24 As shown in (b) in .

[0231] Therefore, the present invention adopts the above-mentioned method for planning the printing path of the suspended surface without support based on FDM printing. The development of the program method is based on the three-dimensional visual parametric modeling software Rhinoceros-Grasshopper. The program can identify various large cantilever or suspended surfaces, select relatively suitable and efficient surface path planning subroutines for them according to their geometric properties and target production methods, and perform some parametric geometric operations at the same time. Finally, by independently writing G-Code, a reasonable printing path is planned in advance on the suspended geometric surface, and a continuous extrusion printing path of "one stroke" is realized as much as possible, and the machine parameters are optimized and controlled parametrically according to the accuracy requirements and surface types. This program is an innovative method, so that the files finally generated by it can be manufactured quickly, efficiently and with high quality when dealing with various suspended surfaces or top covers, so as to improve the printing quality and reduce the probability of material loss, defects and failure. This program method provides a new way to reduce the difficulty, time and economic cost of production for the unsupported printing of suspended surfaces or top covers in a simple printing form.

[0232] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A printing path planning method for an unsupported suspended surface based on FDM printing, characterized in that: The following steps are involved: S1. Surface pretreatment: Classification of geometric properties and determination of the use of benchmark reference methods; S2. Determine the reference: determine the reference for path planning within the surface; S3, surface conversion curve: get the initial path curve; S4, curve connection: convert multiple initial paths into one continuous path; S5, path optimization; S6, Printing program generation: production of self-edited G-Code files and parameterization of printing data; S1 includes the following steps: S11, the algorithm inputs the suspended surface geometry; S12, identifying whether the geometric body attribute is Mesh or NURBS, if not, converting the attribute of the suspended surface geometric body into NURBS or Mesh according to the API of Rhino-Common; S13, check the integrity of the surface of the suspended surface geometric body, that is, whether there is a broken surface or defect, if so, repair the surface to make it complete; S14, selecting a subroutine method selected by a reference according to the characteristics of the suspended surface geometry and the surface geometry attributes, specifically: Determine whether the number of exposed boundaries of the geometric surface is greater than or equal to 3. If so, determine whether the outer contour edge of the geometric surface is four boundaries and the geometric body attribute is a NURBS surface; if not, determine whether the geometric body attribute is a NURBS surface; If the outer contour edge of the geometric surface has four boundaries and is a NURBS surface, then subroutine method S2-1 is used, otherwise subroutine method S2-2 is used; If the number of exposed boundaries of the geometric surface is less than 3 and the geometric body attribute is a NURBS surface, then subroutine method S2-3 is used, otherwise subroutine method S2-4 is used; The subroutine method S2-1 specifically includes: using the UV interval as a four-side NURBS reference; The subroutine method S2-2 specifically includes: using the outer contour line as a reference for various NURBS datums; The subroutine method S2-3 specifically includes: using the IsoCurve structure line of the NURBS surface as a benchmark reference; The subroutine method S2-4 specifically includes: using the longitude and latitude lines of the Mesh surface as a reference; The subroutine method S2-1 specifically includes the following steps: S2-11, determine whether the NURBS surface is clipped, if so, restore the clipped NURBS surface topology to the unclipped surface state and copy and record the boundary UV value of the clipped NURBS surface, and then obtain the UV interval (u0, u1), (v0, v1) of the unclipped surface; if not, directly obtain the UV interval (u0, u1), (v0, v1) of the unclipped surface; S2-12, flatten the untrimmed surface into a two-dimensional plane rectangular shape with a length of u1-u0 and a width of v1-v0 according to the UV interval value; S2-13, using the boundary of the two-dimensional plane rectangle obtained in S2-12 as a reference; The subroutine method S2-2 specifically includes the following steps: S2-21, obtain all outer contour edges of non-four-sided NURBS surfaces; S2-22, combine and connect all contour edges into a closed curve as a reference; The subroutine method S2-3 specifically includes the following steps: S2-31. Reset the U direction and V direction of the NURBS surface structure line IsoCurve, that is, set the closed line that does not intersect the XY plane as the U direction, and the surface structure line that intersects the XY plane after extension as the V direction; S2-32, extract four structural curves of the NURBS surface (u0, v0), (u1, v0), (u0, v1) and (u1, v1) as benchmark references; The subroutine method S2-4 specifically includes the following steps: S2-41, determining whether the geometric surface of the suspended surface geometric body is a four-sided mesh. If so, extracting all line segments of the mesh surface according to Weft and combining them in the longitude and latitude directions; if not, reconstructing the geometric surface in a four-sided mesh format; S2-42, let the closed line that does not intersect the XY plane be the U-direction latitude line, and the line that intersects the XY plane after extension be the V-direction longitude line; S2-43, extract four longitude and latitude polylines (u0, v0), (u1, v0), (u0, v1) and (u1, v1) from the Mesh surface as reference; S3 specifically obtains a multi-circle initial four-side offset curve, which specifically includes the following steps: S3-11, obtaining the shortest boundary segment length L1 of the rectangle according to the boundary obtained in S2-13; S3-12, set the print line width W1 according to the printer configuration, and calculate the initial path curve according to the length L1 and W1, and print the Floor (N1=L1 / 2 / W1) circle; S3-13, offset the rectangular boundary by N1 circles as the initial path curve; S4 specifically processes multiple circles of four-side offset curves and connects them into a continuous curve, which specifically includes the following steps: S4-11, obtain the multi-circle plane offset four-side closed curve of S3-13; S4-12, select any two adjacent sides from the four sides of each curve; S4-13, according to the print line width W1 set in S3-12, respectively extend and shorten the lengths of two adjacent sides W1 according to the G0 curvature; S4-14, connecting all processed curves end to end to form a continuous curve, and using it as an initial continuous path for optimization; S5 is specifically to optimize the initial continuous path composed of multiple circles of equidistant offset lines of the two-dimensional plane, which specifically includes the following steps: S5-11, obtaining a continuous curve generated in S4-14 in a two-dimensional plane; S5-12, after analyzing the curvature of the curve, extract the discontinuity points according to the G0 discontinuity; S5-13, create a sphere with a radius of R1 at several discontinuous points; S5-14, intersect the sphere with the continuous curve and find the Boolean difference of the continuous curve on several spheres; S5-15, setting a convex value B1 of arc fitting blending and blending the beginning and the end of the curve disconnected after the Boolean operation into one curve by arc fitting; S5-16, topologically mapping the continuous curve back to the geometric surface according to the UV value in the two-dimensional plane shape; S5-17, obtaining an optimized continuous path curve on a four-sided geometric surface; S3 specifically obtains a multi-turn initial multilateral offset curve, which specifically includes the following steps: S3-21, splitting the closed curve obtained in S2-22 into a plurality of contour edges according to G0 discontinuity; S3-22, using the average method to calculate the coordinate values ​​of each mesh vertex of the geometric surface, and obtain the center point C2 of the geometric surface; S3-23, calculate the geodesic distance D0, D1...D between the center point C2 and each contour edge i ; S3-24. Compare the geodesic distances obtained in S3-23 and obtain the shortest geodesic distance D i ; S3-25, set the print line width W2 according to the printer configuration, and set the shortest geodesic distance D i The initial path curve needs to be printed (N2=D i / 2 / W2) circle; S3-26, offsetting the contour edge used as the reference on the geometric surface into an N2-circle curve as the initial path curve; S4 specifically processes multiple loops of multi-sided offset curves and connects them into a continuous curve, which specifically includes the following steps: S4-21, obtaining a closed curve of the multi-turn offset of S3-26; S4-22, select any two adjacent sides of each circle curve; S4-23, according to the print line width W2 set in S3-25, along the tangent vectors of the endpoints of the two adjacent edges, respectively extending and shortening the geodesic distance of the lengths of the two adjacent edges W2 to the corresponding points; S4-24, reconstruct the curve of S4-23 with adjusted length; S4-25, connecting all processed curves end to end to form a continuous curve as an initial continuous path for optimization; S5 is specifically to optimize an initial continuous path consisting of multiple circles of equidistant offset lines along a geometric surface, which specifically includes the following steps: S5-21, obtaining the continuous curve generated by S4-25 in the geometric surface and analyzing the curvature change; S5-22, select the curvature continuity standard between G0 and G3; S5-23, extracting Gn discontinuity points on the geometric surface according to the selected curve discontinuity; S5-24, Analyze the parameter positions of several discontinuous points on the continuous curve; S5-25, creating a sphere of relative radius at corresponding points according to the parameter positions of several points; S5-26, intersecting a number of spheres with a continuous curve and finding the Boolean difference of the curve on the number of spheres; S5-27, according to the set relative fitting convex value B2, the beginning and the end of the disconnected curve are mixed by relative arc fitting according to the convex value B2; S5-28, blending part of the curve is mapped onto the geometric surface; S5-29, combining the disconnected curve and the arc fitting mixed curve into a continuous path curve; S3 specifically obtains multiple NURBS surface structure curves, which specifically includes the following steps: S3-31, extracting several V-direction structural curves in the interval from V0 to V1 according to the printing accuracy; S3-32. Count the lengths of all structural curves in the V direction and obtain the length interval [L 3a , L 3b ]; S3-33, input the layer height range that can be extruded according to the nozzle diameter [H 3a , H 3b ], calculate Ceiling(L 3b / H 3b ) and Floor(L 3a / H 3a ) and compare the values; S3-34, get the number interval of the U direction structure curve [N 3a , N 3b ] and select any value from the interval; S3-35, extracting N3 closed structure curves in the U direction of the NURBS surface as initial path curves; S4 specifically processes the U-direction structural curves of multiple NURBS surfaces and connects them into a continuous curve, which specifically includes the following steps: S4-31, obtaining multiple U-direction structural curves extracted from the NURBS surface IsoCurve; S4-32, setting a number of equally spaced points on multiple U-direction structural curves according to accuracy; S4-33, transfer rank to multiple groups of equidistant points; S4-34, setting the Nth data of each group and the N+1th data of the sub-group as the same array, and so on, reversing the rank according to the set sequence relationship of the equidistant point groups; S4-35, flatten into a one-dimensional array according to the order within the matrix; S4-36, sequentially connecting all points in the one-dimensional array into a continuous curve, and using it as an initial continuous path for optimization; S5 is specifically to optimize the initial continuous path composed of multiple NURBS surface U-direction structural curves, which specifically includes the following steps: S5-31, obtaining the continuous curve generated by S4-36 in the NURBS surface; S5-32, pull the area where the continuous curve was originally separated from the NURBS surface due to the connection back to the surface in the form of a vertical surface projection; S5-33, extracting each group of starting points of the plurality of groups of equidistant points in S4-32; S5-34, collecting the nearest projection point of the starting point on the curve; S5-35, split the curve into several segments at the nearest projection point; S5-36, extracting the bottommost curve and projecting it vertically onto the XY plane; S5-37, arrange the XY plane projection line and the separated curve segments in order from low to high positions; S3 specifically obtains multiple Mesh surface structure polylines, which specifically includes the following steps: S3-41, extracting a plurality of V-direction multi-segment meridians from V0 to V1 according to the printing accuracy; S3-42, count the lengths of all longitudes in the V direction and obtain the length interval [L 4a , L 4b ]; S3-43, input the layer height range that can be extruded according to the nozzle diameter [H 4a , H 4b ], calculate Ceiling(L 4b / H 4b ) and Floor(L 4a / H 4a ) and compare the values; S3-44, get the number interval of latitude lines in the U direction [N 4a , N 4b ] and select any value from the interval; S3-45, extract N4 closed structure polylines in the U direction of the Mesh surface as the initial path curve; S4 specifically processes multiple mesh surface latitude U-direction structure polylines and connects them into a continuous polyline, which specifically includes the following steps: S4-41, obtain multiple latitude U-direction structure polylines extracted from the Mesh surface Weft; S4-42, according to the accuracy, set a number of equal-distance points of the multiple latitude U-direction structure polylines; S4-43, transfer rank to multiple groups of equidistant points; S4-44, setting the Nth data of each group and the N+1th data of the sub-group to be the same array, and so on, reversing the rank according to the set sequence relationship of the equidistant point groups; S4-45, flatten into a one-dimensional array according to the order within the matrix; S4-46, sequentially connecting all points in the one-dimensional array into a continuous polyline, and using it as an initial continuous path for optimization; S5 is specifically to optimize the initial continuous path composed of multiple Mesh surface latitude U-direction structure polylines, which specifically includes the following steps: S5-41, obtain the continuous polyline generated by S4-36 in the Mesh surface; S5-42, pull the area where the continuous polyline was originally separated from the Mesh surface due to connection back to the surface in the form of vertical surface projection; S5-43, extracting each group of starting points of the plurality of groups of equidistant points in S4-42; S5-44, collecting the nearest projection point of the starting point on the polyline; S5-45, split the polyline into several segments at the nearest projection point; S5-46, extract the bottom-most polyline and project it vertically onto the XY plane; S5-47. Arrange the XY plane projection line and the separated curve segments in order from low to high.

2. The method for planning printing path for unsupported suspended surfaces based on FDM printing according to claim 1, characterized in that: S6 specifically includes the following steps: S61, converting the path curve into a number of equidistant points according to printing accuracy requirements; S62, calculating the UV values ​​of all equidistant points on the geometric surface; S63, print line width W according to printer configuration settings n Calculate the relative extrusion value of each point with the UV value of all equidistant points; S64, setting machine parameters, including adjusting the extrusion ratio, adjusting the printing speed, and adjusting the printing temperature; S65, translating the machine parameters into the parameters of the geometric path to generate a G-Code file, and simulating the movement of the machine along the surface path curve and the extrusion control in a 3D visualization software; S66, check whether there is any collision or gap between the printing path and the machine or other parts of the path. If so, readjust the parameters in the machine parameter part until there is no collision or gap, and then execute the printing file.

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