CN117162492A - Curved surface 3D printing path planning method based on mechanical arm - Google Patents
Curved surface 3D printing path planning method based on mechanical arm Download PDFInfo
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- CN117162492A CN117162492A CN202311179372.0A CN202311179372A CN117162492A CN 117162492 A CN117162492 A CN 117162492A CN 202311179372 A CN202311179372 A CN 202311179372A CN 117162492 A CN117162492 A CN 117162492A
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Abstract
The invention discloses a curved surface 3D printing path planning method based on a mechanical arm, and belongs to the field of 3D printing; the curved surface 3D printing path planning method based on the mechanical arm comprises the following steps: inputting a single-layer geometric curved surface model, and converting the model from a curved surface to a triangular grid surface; extracting boundary conditions of the top and the bottom of the triangular mesh surface; according to the extracted boundary conditions, running Python codes, carrying out geodesic distance analysis on points on the triangular mesh surface, and obtaining a distance field; generating evenly distributed contour lines conforming to the topological structure characteristics of the curved surface according to the distance field and parameters input in the codes, and generating three-dimensional coordinates of all control points on the contour lines and vectors corresponding to the points on the curved surface; and adjusting the sequence of the points on each contour line, generating a continuous 3D printing path, processing vectors of the tool heads of the mechanical arms corresponding to the adjacent points through Euler formulas, and outputting the vectors in a source code format of the corresponding mechanical arms.
Description
Technical Field
The invention belongs to the field of 3D printing, and particularly relates to a curved surface 3D printing path planning method based on a mechanical arm.
Background
In mechanical arm plastic extrusion printing (Fused granulate fabrication, abbreviated as FGF), an explicit curved surface model or a triangular surface (mesh) model is generally established through modeling software, the surface geometry of a three-dimensional object is described in an STL data format, and a G code which can be identified by a machine is output for printing by slicing processing through general or vendor special software; in the prior art, a model is directly used for generating a printing path, a boundary condition is set only at the initial selected reference plane, a user has no adjustment space, and once the generated printing path does not meet the expected target of the user, the printing path cannot be modified.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide a curved surface 3D printing path planning method based on a mechanical arm.
The aim of the invention can be achieved by the following technical scheme:
a curved surface 3D printing path planning method based on a mechanical arm comprises the following steps:
inputting a single-layer geometric curved surface model, and converting the model from a curved surface to a triangular grid surface;
extracting boundary conditions of the top and the bottom of the triangular mesh surface;
according to the extracted boundary conditions, running Python codes, carrying out geodesic distance analysis on points on the triangular mesh surface, and obtaining a distance field;
generating evenly distributed contour lines conforming to the topological structure characteristics of the curved surface according to the distance field and parameters input in the codes, and generating three-dimensional coordinates of all control points on the contour lines and vectors corresponding to the points on the curved surface;
and adjusting the sequence of the points on each contour line, generating a continuous 3D printing path, processing vectors of the tool heads of the mechanical arms corresponding to the adjacent points through Euler formulas, and outputting the vectors in a source code format of the corresponding mechanical arms.
Further, in geodesic distance analysis, if the curved model does not diverge, when a curve is inserted over the model as part of the print path, the interpolated distance field follows the formula:
D＝(1-t)d 1 -t d 2
wherein D represents the geodesic distance obtained by interpolation after calculation, D 1 And d 2 The geodesic distance of the lowest and highest two boundaries, respectively, t is a parameter representing interpolation, ranging from (0, 1]Between them.
Further, in the geodesic distance analysis, if the curved surface model is bifurcated and has n bottom boundaries and m top boundaries, the distance fields of the n top boundaries or the m bottom boundaries need to be respectively integrated and calculated when interpolation is performed; the geodesic distance is calculated according to each curve, and two distance sets D are generated 1 ＝{d 1 ,…，d n } and D 2 {d 1 ,…,d m And calculating a plurality of geodesic distances on the same grid using a geodesic distance thermodynamic approach.
Further, the distance field integration method comprises the following steps: the minimum value is the union and the power function is the union of the second order smoothed minimum values.
Further, the minimum value union is composed of the minimum value of each set distance, and the interpolation distance function for generating K contour lines follows the following formula:
wherein U (D) 1 ) Is with distance set D 1 The union is taken, the U (D) 2 ) Is with distance set D 2 And taking a union set.
Further, the power function quadratic smoothing minima union, defined by a recursive relationship, follows the following formula for n distance fields:
h＝max(r-|d n -U n-1 ｜，0)
where r is the radius that determines the smooth range, U n Is the result of taking the union for the nth distance field, U n-1 Is toTaking the result of the union at the n-1 th distance field, d n Is the geodesic distance of the nth distance field.
Further, the parameters input in the code include: average layer height and the robotic arm lift height after partial printing is completed.
Further, the step of processing the vector of the mechanical arm tool head corresponding to the adjacent point through the Euler formula specifically comprises the following steps:
s51, generating three-dimensional coordinates of all control points on the contour line and vectors corresponding to the points on the curved surface according to the generated contour line conforming to the topological structure characteristics of the curved surface, and controlling the tool head gesture of the mechanical arm;
s52, adjusting the sequence of points on each contour line, generating a continuous 3D printing path, and firstly applying vector normalization to vectors of tool heads corresponding to adjacent points to ensure that the directions of all vectors are unchanged and the numerical value is reduced to be between 0 and 1;
s53, applying an Euler formula, reducing the included angle between the vector and the positive direction of the z axis through adjusting the coefficients, optimizing the printing path, and smoothing and excessively transferring the vector between two adjacent points through Python codes.
A robotic arm-based curved surface 3D printing path planning system, comprising:
model conversion module: inputting a single-layer geometric curved surface model, and converting the model from a curved surface to a triangular grid surface;
a convenient condition extraction module: extracting boundary conditions of the top and the bottom of the triangular mesh surface;
distance field analysis module: according to the extracted boundary conditions, running Python codes, carrying out geodesic distance analysis on points on the triangular mesh surface, and obtaining a distance field;
the contour line generation module: generating evenly distributed contour lines conforming to the topological structure characteristics of the curved surface according to the distance field and parameters input in the codes, and generating three-dimensional coordinates of all control points on the contour lines and vectors corresponding to the points on the curved surface;
and a path generation module: and adjusting the sequence of the points on each contour line, generating a continuous 3D printing path, processing vectors of the tool heads of the mechanical arms corresponding to the adjacent points through Euler formulas, and outputting the vectors in a source code format of the corresponding mechanical arms.
The invention has the beneficial effects that:
1. the invention can carry out non-planar printing with inclination angle under the condition of no support, can complete 3D printing of the model with low cost and high efficiency without a mould, and the printing path generated by the invention accords with the geometric characteristics of a curved surface and can print products with high quality.
2. When the invention is used, when a large curved building component (a multi-bifurcation structure, a tree column and a hollowed-out facade) is built, the stress between printing layers is along the stress direction, the whole model is built by partitioning the whole model and printing at one time under the condition of site permission, the printing precision and the printing speed of 3D printing can be improved, the bonding strength between layers is enhanced, and the surface texture is continuous and smooth.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, and it will be obvious to those skilled in the art that other drawings can be obtained according to these drawings without inventive effort.
FIG. 1 is a flow chart of a path planning method of the present invention;
FIG. 2 is an example of a surface model without bifurcation;
FIG. 3 is a split surface model minimum value union example;
FIG. 4 is another view from the perspective of FIG. 3;
FIG. 5 is an example of a power function quadratic smoothed minimum union;
FIG. 6 is another view from the perspective of FIG. 5;
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, a curved surface 3D printing path planning method based on a mechanical arm includes the following steps:
s1, inputting a single-layer geometric curved surface model, converting the model from a curved surface to a triangular grid surface, controlling grid precision by adjusting parameters (grid subdivision quantity), and storing by using obj format;
in the invention, a single-layer geometric curved surface is input into a Rhinoceros platform, and a model is converted into a triangular grid surface from the curved surface according to input parameters in a plugin Grasshopper.
S2, extracting boundary conditions of the top and the bottom of the triangular mesh surface, and storing the boundary conditions in a json format;
in the invention, a triangle mesh model is analyzed in an insert Grasshopper to obtain boundary conditions of the top and the bottom of a mesh surface, and the method specifically comprises the following steps:
s21, extracting grid Edges of a triangular grid model into a Curve battery by using a Mesh edge battery in a plug-in Grasshopper;
s22, processing a plurality of curves in the Curve battery in a plug-in Grasshopper, opening the highest boundary and the lowest boundary into a new Curve battery, and storing the new Curve battery through a Save to Json battery.
S3, running Python codes according to boundary conditions, and carrying out geodesic distance analysis on points on the triangular mesh surface to obtain a distance field; the uniform change of the distance field and the position of the saddle point of the bifurcation curved surface are expressed in the form of thermodynamic diagram, and the position of the saddle point can be adjusted by adjusting the geodesic distances of a plurality of top boundaries;
on a curved surface model without bifurcation, such as that shown in fig. 2, there are only the lowest and highest two boundaries, so when a curve is inserted on the model as part of the print path, the interpolated distance field follows the following formula:
D＝(1-t)d 1 -t d 2
wherein D represents the geodesic distance obtained by interpolation after calculation, D 1 And d 2 The geodesic distance of the lowest and highest two boundaries, respectively, t is a parameter representing interpolation, ranging from (0, 1]Between them.
In a bifurcated surface model, the previous formula is no longer applicable because there are more than two boundaries. For example, as shown in fig. 3, the bifurcation curved surface has three boundaries, two boundaries are located at the top, one boundary is located at the bottom, and the distance fields of the two boundaries at the top need to be integrated into one for calculation when interpolation is performed, and different distance field integration modes can generate printing paths with different characteristics.
If there are n bottom boundaries and m top boundaries, respectively, the geodesic distance is calculated from each curve, resulting in two distance sets D 1 ＝{d 1 ,…，d n } and D 2 {d 1 ,…,d m -a }; a geodesic distance thermodynamic diagram method is used, so that a plurality of geodesic distances can be calculated on the same grid;
the invention defines two distance field integration modes as follows:
1) The minimum value is taken as a union;
the combined geodesic distance approach uses a union, the simplest union of distance fields being composed of the minimum of each set distance, the interpolated distance function for generating the K contours follows:
wherein U (D) 1 ) Is with distance set D 1 The union is taken, the U (D) 2 ) Is with distance set D 2 Taking the union, shown in FIG. 3, is the result of taking the minimum value in D, which has the disadvantage of creating a sharp, non-smooth turning point near the saddle point, which can lead to abrupt changes in direction and layer height, which can cause difficulties in printing and poor product surface quality, as shown in FIG. 4.
2) The power function secondary smoothing minimum value is obtained as a union set;
the union is adjusted in such a way that these discontinuities are smoothed, with a quadratic smoothing minimum, as shown in fig. 5 and 6; for n distance fields, defined by a recursive relationship, the following formula is followed:
where r is the radius that determines the smooth range, U n Is the result of taking the union for the nth distance field, U n-1 Is the result of taking the union for the n-1 th distance field, d n Is the geodesic distance of the nth distance field.
And:
h＝max(r-|d n -U n-1 |，0)。
the initial condition U.S. 0 is a geodesic distance that is significantly higher than that which occurs in shape, and this mixing affects only the region near the transition from one distance field to another, making the direction and layer height changes in this region smoother, as opposed to smoothing the entire distance function.
S4, generating evenly distributed contour lines conforming to the topological structure characteristics of the curved surface according to the obtained distance field and the parameters input in the codes, generating three-dimensional coordinates of all control points on the contour lines and vectors corresponding to the points on the curved surface, and controlling the tool head gesture of the mechanical arm and storing the tool head gesture in an plugin Grasshopper;
wherein the parameters input in the code include; the average layer height and the lifting height of the mechanical arm after the partial printing are finished can be used for adjusting the generation result of the printing path;
s5, adjusting the sequence of points on each contour line, generating a continuous 3D printing path, processing vectors of the tool heads of the mechanical arms corresponding to adjacent points through Euler formulas, ensuring that the printing path is smooth and free of noise point interference, and outputting the printing path in a source code format corresponding to the mechanical arms, such as KRL language of a KUKA mechanical arm;
the step of processing the vector of the mechanical arm tool head corresponding to the adjacent point through the Euler formula specifically comprises the following steps:
and generating three-dimensional coordinates of all control points on the contour line and vectors corresponding to the points on the curved surface according to the generated contour line conforming to the topological structure characteristics of the curved surface, and controlling the tool head gesture of the mechanical arm. And adjusting the sequence of the points on each contour line, generating a continuous 3D printing path, and firstly applying vector normalization to the vectors of the tool heads corresponding to the adjacent points to ensure that the directions of all the vectors are unchanged and the numerical value is reduced to be between (0 and 1). And then applying an Euler formula, reducing the included angle between the vector and the positive direction of the z axis through adjusting the coefficients, optimizing the printing path, smoothing and transiting the vector between two adjacent points through a Python code, and ensuring the smoothness and noiseless interference of the printing path.
In the description of the present specification, the descriptions of the terms "one embodiment," "example," "specific example," and the like, mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims.
Claims (9)
1. The curved surface 3D printing path planning method based on the mechanical arm is characterized by comprising the following steps of:
inputting a single-layer geometric curved surface model, and converting the model from a curved surface to a triangular grid surface;
extracting boundary conditions of the top and the bottom of the triangular mesh surface;
according to the extracted boundary conditions, running Python codes, carrying out geodesic distance analysis on points on the triangular mesh surface, and obtaining a distance field;
generating evenly distributed contour lines conforming to the topological structure characteristics of the curved surface according to the distance field and parameters input in the codes, and generating three-dimensional coordinates of all control points on the contour lines and vectors corresponding to the points on the curved surface;
and adjusting the sequence of the points on each contour line, generating a continuous 3D printing path, processing vectors of the tool heads of the mechanical arms corresponding to the adjacent points through Euler formulas, and outputting the vectors in a source code format of the corresponding mechanical arms.
2. The method of claim 1, wherein in the geodesic distance analysis, if the curved surface model is not bifurcated, when a curve is inserted into the model as part of the print path, the interpolated distance field follows the formula:
D＝(1-t)d 1 -td 2
wherein D represents the geodesic distance obtained by interpolation after calculation, D 1 And d 2 The geodesic distance of the lowest and highest two boundaries, respectively, t is a parameter representing interpolation, ranging from (0, 1]Between them.
3. The method for planning a curved surface 3D printing path based on a mechanical arm according to claim 2, wherein in the geodesic distance analysis, if the curved surface model is bifurcated and has n bottom boundaries and m top boundaries, the distance fields of the n top boundaries or the m bottom boundaries need to be respectively integrated for calculation when interpolation is performed; the geodesic distance is calculated according to each curve, and two distance sets D are generated 1 ＝{d 1 ,…，d n } and D 2 {d 1 ，…，d m And calculating a plurality of geodesic distances on the same grid using a geodesic distance thermodynamic approach.
4. A curved surface 3D printing path planning method based on a mechanical arm according to claim 3, wherein the distance field integration method comprises: the minimum value is the union and the power function is the union of the second order smoothed minimum values.
5. The method for planning a 3D printing path of a curved surface based on a robotic arm according to claim 4, wherein the minimum value union set is composed of the minimum value of each set distance, and the interpolation distance function for generating K contour lines follows the following formula:
D j ＝(1-t j )∪(D 1 )-t j ∪(D 2 )，
wherein U (D) 1 ) Is with distance set D 1 Taking union, U (D 2 ) Is with distance set D 2 And taking a union set.
6. The method of claim 4, wherein the power function quadratic smoothing minima union is defined by a recursive relationship for n distance fields, and follows the following formula:
h＝max(r-|d n -∪ n-1 |，0)
where r is the radius that determines the smooth range, U n Is the result of taking the union for the nth distance field, U n-1 Is the result of taking the union for the n-1 th distance field, d n Is the geodesic distance of the nth distance field.
7. The method for planning a curved 3D printing path based on a mechanical arm according to claim 1, wherein the parameters input in the code include: average layer height and the robotic arm lift height after partial printing is completed.
8. The method for planning a curved surface 3D printing path based on a mechanical arm according to claim 1, wherein the step of processing the vector of the mechanical arm tool head corresponding to the adjacent point by using the euler formula specifically comprises the following steps:
s51, generating three-dimensional coordinates of all control points on the contour line and vectors corresponding to the points on the curved surface according to the generated contour line conforming to the topological structure characteristics of the curved surface, and controlling the tool head gesture of the mechanical arm;
s52, adjusting the sequence of points on each contour line, generating a continuous 3D printing path, and firstly applying vector normalization to vectors of tool heads corresponding to adjacent points to ensure that the directions of all vectors are unchanged and the numerical value is reduced to be between 0 and 1;
s53, applying an Euler formula, reducing the included angle between the vector and the positive direction of the z axis through adjusting the coefficients, optimizing the printing path, and smoothing and excessively transferring the vector between two adjacent points through Python codes.
9. Curved surface 3D printing path planning system based on arm, characterized by, include:
model conversion module: inputting a single-layer geometric curved surface model, and converting the model from a curved surface to a triangular grid surface;
a convenient condition extraction module: extracting boundary conditions of the top and the bottom of the triangular mesh surface;
distance field analysis module: according to the extracted boundary conditions, running Python codes, carrying out geodesic distance analysis on points on the triangular mesh surface, and obtaining a distance field;
the contour line generation module: generating evenly distributed contour lines conforming to the topological structure characteristics of the curved surface according to the distance field and parameters input in the codes, and generating three-dimensional coordinates of all control points on the contour lines and vectors corresponding to the points on the curved surface;
and a path generation module: and adjusting the sequence of the points on each contour line, generating a continuous 3D printing path, processing vectors of the tool heads of the mechanical arms corresponding to the adjacent points through Euler formulas, and outputting the vectors in a source code format of the corresponding mechanical arms.
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