Optimization method for smooth motion of rotating axis in five-axis in-machine measurement

Abstract

This invention proposes an optimization method for smooth rotational axis movement in five-axis in-machine measurement. By constructing two-dimensional feasibility diagrams for two rotational axes, analyzing the relative positional relationships between line segments in the diagrams, and then setting rotation angle selection criteria and priorities, the minimum sum of rotation angle distances of the rotational axis when detecting a series of measurement points is calculated to ensure smooth rotational axis movement during detection. Furthermore, by analyzing the intersection of adjacent line segments in the two-dimensional feasibility diagrams, the method ensures that the rotational axis remains stationary when there is an intersection between adjacent line segments during the detection of the corresponding measurement point. Therefore, the probe does not need to return to a safe position when detecting two adjacent measurement points, which improves the detection efficiency of five-axis in-machine measurement. This invention is computationally simple, easy to program, and can be extended to in-machine measurement on other types of five-axis machine tools.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement, and specifically relates to an optimization method for smooth motion of the rotary axis in five-axis in-machine measurement. Background Technology

[0002] In the manufacturing process of complex parts, due to their low rigidity, easily deformable structure, and poor machinability of difficult-to-machine materials, some features are difficult to complete in a single step. In such cases, the parts typically require multiple compensation machining operations on machine tools to meet specified geometric tolerances. Furthermore, for parts with small machining allowances, such as those produced through near-net-shape forming processes like precision casting, precision forging, and 3D printing, their actual geometry needs to be identified before proceeding to the next machining step. Therefore, utilizing on-machine measurement technology to obtain the actual distribution of the material to be machined on the workpiece is of great significance.

[0003] In-machine measurement enables an integrated manufacturing model of "machining-measurement-compensation" on machine tools, which is beneficial for improving productivity and reducing the scrap rate of parts, making in-machine measurement attractive to manufacturing enterprises. For complex curved surface parts, such as impellers and impeller disks, inspection is usually required on a five-axis machine tool.

[0004] To avoid interference between the probe and the workpiece, an interference-free probe axis needs to be planned for each measurement point before measurement. These probe axes are converted into the motion of the spindle and the worktable to adjust the relative posture between the probe and the workpiece. When the probe axes corresponding to a series of measurement points are different, the rotary axis needs to rotate continuously during the inspection. Before the rotary axis rotates, to ensure the safety of the probe, it needs to be retracted to a safe height, a process that greatly reduces inspection efficiency. In addition, if the rotation angle increment of the rotary axis is too large, the angular velocity of the rotary axis will surge, potentially exceeding the maximum angular velocity constraint of the machine tool's rotary axis.

[0005] In summary, to meet the five-axis inspection requirements of complex curved surface parts and multi-feature structural components, in order to ensure smooth movement of the rotary axis during five-axis in-machine measurement and improve the inspection efficiency, it is necessary to design an optimization method for the rotation angle of the rotary axis. Summary of the Invention

[0006] The technical problem solved by this invention is to address the shortcomings of existing technologies where the probe needs to be retracted to a safe height. This process significantly reduces detection efficiency and leads to excessive increases in the rotation angle of the rotary axis, causing a surge in the angular velocity of the rotary axis and potentially exceeding the maximum angular velocity constraint of the machine tool's rotary axis. To ensure the smoothness of the rotary axis's movement, this invention proposes an optimized method for smooth rotary axis movement in five-axis on-machine measurement. By optimizing the rotation angle of the rotary axis, smooth movement of the rotary axis is ensured throughout the detection process. This also helps improve the detection efficiency of five-axis on-machine measurement.

[0007] The technical solution of this invention is: an optimization method for smooth motion of the rotary axis in five-axis in-machine measurement, comprising the following steps:

[0008] Step 1: Obtain the set of feasible probe axes Ω at n measurement points through interferometry. i =(n x ,n y ,n z Let i = 1, 2, ..., n, and set the feasible probe axes Ω. i Converted into a set of machine tool rotation axis angles R i =(A i C i The calculation is as follows:

[0009]

[0010] Step 2: Based on the set of machine tool rotary axis angles R obtained in Step 1 i A three-dimensional feasibility map is constructed based on the order of measurement points. The first coordinate axis in the three-dimensional feasibility map is defined as the A-axis, the second coordinate axis as the C-axis, and the third coordinate axis as the order of measurement points, denoted as S.

[0011] Step 3: Project the 3D feasible map formed by all measurement points onto the AOS plane. The projected feasible map consists of several straight line segments, denoted as... A L i ;

[0012] Step 4: Determine the relative positional relationship between adjacent line segments on the AOS plane in turn. If there is an intersection between adjacent line segments, cut off the part of the adjacent line segments other than the intersection.

[0013] Step 5: Determine whether the extracted line segment intersects with the next line segment. If it does, repeat step 4 until all intersections between the n line segments have been determined. If there is no intersection, proceed to step 6.

[0014] Step 6: For adjacent line segments that do not intersect, if all angle values ​​on the (i+1)th line segment are greater than the angle values ​​on the ith line segment, represent the positional relationship between the ith line segment and the (i+1)th line segment as "↑", denoted as... Conversely, if all angle values ​​on the (i+1)th line segment are less than the angle values ​​on the ith line segment, the positional relationship between the ith line segment and the (i+1)th line segment is represented as "↓", denoted as...

[0015] Step 7: Select the rotation angles corresponding to n measurement points in sequence according to the set criteria.

[0016] Step 8: Obtain the minimum value A of the sum of rotation angles and distances during the movement of the A-axis when detecting n measurement points, obtained from steps 3-7. min And the set of A-axis rotation angles corresponding to each measurement point, A1, A2, ..., A n :

[0017]

[0018] Step 9: Project the 3D feasibility study onto the AOC plane, rotating it according to the selected A-axis angles A1, A2, ..., A. n By cropping the feasible graphs of each of the n measurement points, we obtain the set of C-axis angles corresponding to the n selected A-axis angle values. set Projecting onto the COS plane yields several line segments or points, denoted as . C L i ;

[0019] Step 10: Repeat steps 3-7 to obtain the minimum value C of the sum of rotation angle distances during C-axis motion when detecting n measurement points. min and the set of C-axis rotation angles corresponding to each measurement point.

[0020]

[0021] Step 11: By obtaining the minimum sum of the rotation angle distances of the A-axis and C-axis when detecting n measurement points through the above steps, the total rotation angle distance of the A-axis and C-axis in the measurement path is then calculated. The calculation is as follows:

[0022]

[0023] Based on the above steps, the feasible probe axis set can be transformed into a rotation angle feasible diagram. Then, by analyzing the relative positional relationship between adjacent straight line segments in the two-dimensional feasible diagram, the rotation angle corresponding to each measurement point is specified according to the set criteria. Finally, the measurement path with the minimum total rotation angle distance between the A-axis and C-axis is obtained, thereby ensuring the smooth movement of the rotation axis.

[0024] Furthermore, the interference checking method in step 1 is the bounding box interference checking method.

[0025] Furthermore, in step 7, three criteria are established, and the priority of the three criteria is: Criterion 1 > Criterion 2 = Criterion 3; the specific contents of the criteria are as follows:

[0026] Rule 1: For adjacent line segments that intersect, select the same rotation angle within the intersection; the specific angle value can be selected with reference to Rule 2 and Rule 3.

[0027] Rule 2: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the largest angle value on the i-th line segment and the smallest angle value on the (i+1)-th line segment;

[0028] Rule 3: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the minimum angle value on the i-th line segment and the maximum angle value on the (i+1)-th line segment.

[0029] Invention Effects

[0030] The technical advantages of this invention are as follows:

[0031] 1. This invention constructs two-dimensional feasible diagrams for two rotation axes respectively, analyzes the relative positional relationship between the straight line segments in the two-dimensional feasible diagrams, sets the selection criteria and priority for rotation angles, and finally calculates the minimum value of the sum of the rotation angle distances of the rotation axes when detecting a series of measurement points, so as to ensure the smooth movement of the rotation axes during detection.

[0032] 2. This invention analyzes the intersection of adjacent line segments in a two-dimensional feasible graph, ensuring that the rotation axis remains stationary during the detection of corresponding measurement points when such intersections exist. Therefore, the probe does not need to return to a safe position when detecting two adjacent measurement points, which improves the detection efficiency of five-axis on-machine measurement.

[0033] 3. The rotary axis motion optimization method of the present invention is simple to calculate and easy to program, and can be extended to in-machine measurement on other types of five-axis machine tools. Attached Figure Description

[0034] Figure 1 Flowchart of the implementation of the present invention

[0035] Figure 2 3D Feasibility Map of Rotation Angle

[0036] Figure 3 Two-dimensional feasible diagram of projection in the AOS plane

[0037] Figure 4 Two-dimensional feasible diagram of projection in the COS plane

[0038] Figure 5 3D Feasibility Map of 7 Measurement Points on the Blade

[0039] Figure 6 A-axis rotation angle planning diagram

[0040] Figure 7 C-axis rotation angle planning diagram Detailed Implementation

[0041] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0042] See Figures 1-7 To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0043] Step 1: Obtain the set of feasible probe axes Ω at n measurement points using the bounding box interference inspection method. i =(n x ,n y ,n z i = 1, 2, ..., n. Based on the AC axis machine tool post-processing formula, the feasible probe axis set Ω is then... i Converted into a set of machine tool rotation axis angles R i =(A i C i The calculation is as follows:

[0044]

[0045] Step 2: For a set of rotation axis angles R corresponding to a series of measurement points i A three-dimensional feasibility map can be constructed based on the sequence of measurement points. In the three-dimensional feasibility map, the first coordinate axis is the A-axis, the second axis is the C-axis, and the third axis represents the sequence of measurement points, denoted as S.

[0046] Step 3: Project the 3D feasible map formed by all measurement points onto the AOS plane. The projected feasible map consists of several straight line segments, denoted as... A L i .

[0047] Step 4: Determine the relative positional relationship between adjacent line segments on the AOS plane. If there is an intersection between adjacent line segments, cut off the parts of the adjacent line segments other than the intersection.

[0048] Step 5: Determine whether the extracted line segment intersects with the next line segment. If it does, repeat Step 4 until all intersections between the n line segments have been determined. If no intersections exist, proceed to Step 6.

[0049] Step Six: For adjacent line segments that do not intersect, if all angle values ​​on the (i+1)th line segment are greater than the angle values ​​on the ith line segment, represent the positional relationship between the ith line segment and the (i+1)th line segment as "↑", denoted as... Conversely, if all angle values ​​on the (i+1)th line segment are less than the angle values ​​on the ith line segment, the positional relationship between the ith line segment and the (i+1)th line segment is represented as "↓", denoted as...

[0050] Step 7: Select the rotation angles corresponding to the n measurement points in sequence according to the following three criteria. The priority of the three criteria is: Criterion 1 > Criterion 2 = Criterion 3.

[0051] Rule 1: For adjacent line segments that intersect, select the same rotation angle within the intersection. Specific angle values ​​can be selected with reference to Rules 2 and 3.

[0052] Rule 2: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the largest angle value on the i-th line segment and the smallest angle value on the (i+1)-th line segment.

[0053] Rule 3: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the minimum angle value on the i-th line segment and the maximum angle value on the (i+1)-th line segment.

[0054] Step 8: From Steps 3-7, we can obtain the minimum value A of the sum of rotation angles and distances during the movement of the A-axis when detecting n measurement points. min As shown in the following formula, and the set of A-axis rotation angles corresponding to each measurement point: A1, A2, ..., A n .

[0055]

[0056] Step 9: Project the 3D feasibility study onto the AOC plane, rotating it according to the selected A-axis angles A1, A2, ..., A. n By cropping the feasible graphs of each of the n measurement points, we obtain the set of C-axis angles corresponding to the n selected A-axis angle values. set Projecting onto the COS plane yields several line segments or points, denoted as . C L i .

[0057] Step 10: Repeat steps 3-7 to obtain the minimum value C of the sum of rotation angles during the C-axis motion when detecting n measurement points. min As shown in the following formula, and the set of C-axis rotation angles corresponding to each measurement point.

[0058]

[0059] Step 11: By following the above steps, we can obtain the minimum sum of the rotation angle distances of the A-axis and C-axis when detecting n measurement points. Then, the total rotation angle distance of the A-axis and C-axis along the measurement path is... The calculation is as follows:

[0060]

[0061] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0062] This embodiment takes an AC-axis dual rotary table structure machine tool as an example, and the implementation process is as follows: Figure 1 As shown:

[0063] Step 1: Obtain the set of feasible probe axes Ω at n measurement points using the bounding box interference inspection method. i =(n x ,n y ,n z i = 1, 2, ..., n. Based on the AC axis machine tool post-processing formula, the feasible probe axis set Ω is then... i Converted into a set of machine tool rotation axis angles R i =(A i C i The calculation is as follows:

[0064]

[0065] Step 2: For a set of rotation axis angles R corresponding to a series of measurement points i A 3D feasibility map can be constructed based on the sequence of measurement points. In the 3D feasibility map, the first coordinate axis is the A-axis, the second is the C-axis, and the third axis represents the sequence of measurement points, denoted as S. Figure 2 As shown.

[0066] Step 3: Project the 3D feasible map formed by all measurement points onto the AOS plane. The projected feasible map consists of several straight line segments, denoted as... A L i ,like Figure 3 As shown. Line segment A L i The minimum angle on is denoted as The maximum angle is denoted as

[0067] Step 4: Determine the relative positional relationship between adjacent line segments on the AOS plane. Starting from the i-th line segment, sequentially determine whether adjacent line segments intersect. If the i-th line segment intersects with the (i+1)-th line segment, record the intersection as... E is the intersection of the i-th line segment and the (i+1)-th line segment. i and E i+1 It is calculated by the following formula. Then, the intersection E is calculated on the i-th line segment and the (i+1)-th line segment respectively. i and E i+1 Cut off the parts that are not included.

[0068] E i =E i+1 =Q A L i (2)

[0069] In the formula, Q is the operator for trimming line segments.

[0070] Step 5: Determine the (i+1)th extracted line segment E i+1 Is it related to the (i+2)th line segment? A L i+2 If there is an intersection between the n line segments, repeat step four until all intersections between the n line segments have been determined, resulting in a set of intersections, denoted as...

[0071] Step Six: For adjacent line segments that do not intersect, if all angle values ​​on the (i+1)th line segment are greater than all angle values ​​on the ith line segment, then the positional relationship between the ith line segment and the (i+1)th line segment is represented as "↑", denoted as... This means that during the detection process from the i-th measurement point to the (i+1)-th measurement point, the rotation axis angle will increase. Conversely, if all angle values ​​on the (i+1)-th line segment are completely smaller than the angle values ​​on the i-th line segment, then the positional relationship between the i-th line segment and the (i+1)-th line segment is represented as "↓", denoted as... This means that during the detection process from the i-th measurement point to the (i+1)-th measurement point, the rotation axis angle will decrease.

[0072] Step 7: After determining the relative positional relationships between the n line segments, it is necessary to plan the rotation angles on the n line segments. When selecting the rotation angles corresponding to the n measurement points in sequence, the following three criteria must be followed, and the priority of the three criteria is: Criterion 1 > Criterion 2 = Criterion 3.

[0073] Rule 1: For adjacent line segments that intersect, in the intersection portion... Choose the same rotation angle so that the rotation axis does not rotate during the detection of the corresponding measurement point. Therefore, the selected adjacent angles must satisfy the following relationship, and the specific angle values ​​can be selected with reference to criteria 2 and 3.

[0074] A i =A i+1 (3)

[0075] Rule 2: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the largest angle value on the i-th line segment and the smallest angle value on the (i+1)-th line segment, as shown in the following formula:

[0076]

[0077] Rule 3: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the minimum angle value on the i-th line segment and the maximum angle value on the (i+1)-th line segment, as shown in the following formula:

[0078]

[0079] Step 8: From Steps 3-7, we can obtain the minimum value A of the sum of rotation angles and distances during the movement of the A-axis when detecting n measurement points. min As shown in the following formula, and the set of A-axis rotation angles corresponding to each measurement point: A1, A2, ..., A n .

[0080]

[0081] Step 9: Project the 3D feasibility study onto the AOC plane, and rotate it within this plane according to the selected A-axis angles A1, A2, ..., A. n By cropping the feasible graphs of each of the n measurement points, we obtain the set of C-axis angles corresponding to the n selected A-axis angle values. Set of n C-axis angles Projecting onto the COS plane yields several line segments or points, denoted as . C L i ,like Figure 4 As shown.

[0082] Step 10: Repeat steps 3-7 to obtain the minimum value C of the sum of rotation angles during the C-axis motion when detecting n measurement points. min and the set of C-axis rotation angles corresponding to each measurement point.

[0083]

[0084] Step 11: By following the above steps, we can obtain the minimum sum of the rotation angle distances of the A-axis and C-axis when detecting n measurement points, thus ensuring the smooth movement of the rotation axis. Therefore, the total rotation angle distance of the A-axis and C-axis in the measurement path is... The calculation is as follows:

[0085]

[0086] The following detailed description uses a five-axis in-machine measurement experiment at seven measurement points on a blade as an example:

[0087] The equipment used in this embodiment mainly includes: a JDMR600 five-axis CNC machine tool, an OMP400 trigger probe, and a centrifugal impeller.

[0088] Seven measurement points are arranged on a certain contour line of the blade. The interference-free probe axial set Ω1, Ω2, ..., Ω7 at the seven measurement points is calculated using a bounding box interference check algorithm. Then, based on a post-processing formula, the probe axial set is transformed into a rotation angle set R1, R2, ..., R7, and a three-dimensional feasibility graph is constructed, as shown below. Figure 5 As shown. The AC axis rotation angle planning process is as follows:

[0089] First, Figure 5 Projecting the 3D feasible graph onto the AOS plane yields 7 line segments. By sequentially determining the intersection between adjacent line segments, it is found that the 3rd and 4th line segments intersect. The fourth and fifth line segments intersect.

[0090] Secondly, using the rotation axis angle selection criteria in step six, plan the A-axis rotation angles for detecting the seven measurement points, namely A1, A2, A3, A4, A5, A6, and A7, as follows: Figure 6 As shown.

[0091] Subsequently, based on the selected seven rotation angles A1-A7 along the A-axis, feasible diagrams for each of the seven measurement points were extracted within the AOC plane. The extracted C-axis rotation angles were then projected onto the COS plane, yielding three straight line segments and four points, as shown below. Figure 7 As shown in the figure, the fourth point intersects with the fifth line segment. Considering the intersections of line segments within the AOS plane, it can be observed that the AC axis does not need to rotate when detecting the fourth and fifth measurement points. Therefore, the probe does not need to return to a safe position during this stage; it only needs to move from the positioning point corresponding to the fourth measurement point to the positioning point corresponding to the fifth measurement point.

[0092] Furthermore, based on the rotation axis angle selection criteria in step six, seven rotation angles of the C-axis are obtained, namely... and

[0093] Finally, based on the above planning, seven rotation angle combinations for the AC axis can be obtained. Furthermore, without considering the magnitude of the rotation angle and only ensuring that the probe and blade do not interfere, seven rotation angle combinations for the AC axis are also planned separately. Based on the two sets of planned rotation angle combinations, blade detection experiments are conducted, and the detection time for each set of experiments is recorded. The rotation angle combinations planned by the method of this invention and the conventional method are shown in Table 1.

[0094] Table 1 Comparison of planned rotation angles in the two methods

[0095]

[0096] As can be seen from the rotation axis angle planning results in the blade inspection of Example 1, the total sum of rotation axis angles obtained using the method of the present invention is 8.98°, while the total sum of rotation axis angles obtained using the traditional method is 25.10°. This indicates that the method of the present invention can reduce the rotation angle of the rotation axis and ensure smooth movement of the rotation axis. In addition, in the experiment, the safety height was 50mm and the positioning distance was 5mm. The time taken to inspect 7 measurement points on the blade using the method of the present invention was 19.70s, while the time taken by the traditional method to inspect 7 measurement points on the blade was 23.45s. The five-axis on-machine measurement efficiency was improved by about 16%, which shows that the method of the present invention is beneficial to improving the five-axis on-machine measurement and inspection efficiency.

Claims

1. An optimization method for smooth rotational axis motion in five-axis in-machine measurement, characterized in that, Includes the following steps: Step 1: Obtain the set of feasible probe axes Ω at n measurement points through interferometry. i =(n x ,n y ,n z Let i = 1, 2, ..., n, and set the feasible probe axes Ω. i Converted into a set of machine tool rotation axis angles R i =(A i C i The calculation is as follows: Step 2: Based on the set of machine tool rotary axis angles R obtained in Step 1 i A three-dimensional feasibility map is constructed based on the order of measurement points. The first coordinate axis in the three-dimensional feasibility map is defined as the A-axis, the second coordinate axis as the C-axis, and the third coordinate axis as the order of measurement points, denoted as S. Step 3: Project the 3D feasible map formed by all measurement points onto the AOS plane. The projected feasible map consists of several straight line segments, denoted as... A L i ; Step 4: Determine the relative positional relationship between adjacent line segments on the AOS plane in turn. If there is an intersection between adjacent line segments, cut off the part of the adjacent line segments other than the intersection. Step 5: Determine whether the extracted line segment intersects with the next line segment. If it does, repeat step 4 until all intersections between the n line segments have been determined. If there is no intersection, proceed to step 6. Step 6: For adjacent line segments that do not intersect, if all angle values ​​on the (i+1)th line segment are greater than the angle values ​​on the ith line segment, represent the positional relationship between the ith line segment and the (i+1)th line segment as "↑", denoted as... Conversely, if all angle values ​​on the (i+1)th line segment are less than the angle values ​​on the ith line segment, the positional relationship between the ith line segment and the (i+1)th line segment is represented as "↓", denoted as... Step 7: According to the set criteria, select the rotation angles corresponding to n measurement points in sequence; Step 8: Obtain the minimum value A of the sum of rotation angles and distances during the movement of the A-axis when detecting n measurement points, obtained from steps 3-7. min And the set of A-axis rotation angles corresponding to each measurement point, A1, A2, ..., A n : Step 9: Project the 3D feasibility study onto the AOC plane, rotating it according to the selected A-axis angles A1, A2, ..., A. n By cropping the feasible graphs of each of the n measurement points, we obtain the set of C-axis angles corresponding to the n selected A-axis angle values. set Projecting onto the COS plane yields several line segments or points, denoted as . C L i ; Step 10: Repeat steps 3-7 to obtain the minimum value C of the sum of rotation angle distances during C-axis motion when detecting n measurement points. min and the set of C-axis rotation angles corresponding to each measurement point. Step 11: By obtaining the minimum sum of the rotation angle distances of the A-axis and C-axis when detecting n measurement points through the above steps, the total rotation angle distance of the A-axis and C-axis in the measurement path is then calculated. The calculation is as follows: Based on the above steps, the feasible probe axis set can be transformed into a rotation angle feasible diagram. Then, by analyzing the relative positional relationship between adjacent straight line segments in the two-dimensional feasible diagram, the rotation angle corresponding to each measurement point is specified according to the set criteria. Finally, the measurement path with the minimum total rotation angle distance between the A-axis and C-axis is obtained, thereby ensuring the smooth movement of the rotation axis.

2. The optimization method for smooth rotational axis motion in five-axis in-machine measurement as described in claim 1, characterized in that, The interference checking method in step 1 is the bounding box interference checking method.

3. The optimization method for smooth rotational axis motion in five-axis in-machine measurement as described in claim 1, characterized in that, In step 7, three criteria are established, and the priority of the three criteria is: Criterion 1 > Criterion 2 = Criterion 3; the specific contents of the criteria are as follows: Rule 1: For adjacent line segments that intersect, select the same rotation angle within the intersection; the specific angle value can be selected with reference to Rule 2 and Rule 3. Rule 2: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the largest angle value on the i-th line segment and the smallest angle value on the (i+1)-th line segment; Rule 3: If the relative positional relationship between the i-th line segment and the (i+1)-th line segment is... Then select the minimum angle value on the i-th line segment and the maximum angle value on the (i+1)-th line segment.

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