Three-dimensional five-axis laser cutting path generation method
By generating cutting paths through a discrete algorithm based on a three-dimensional model, the problems of expensive equipment and insufficient precision in the existing technology are solved, and efficient and low-cost cutting path programming is achieved.
Patent Information
- Application Number
- CN202510868446.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-26
- Publication Date
- 2025-10-10
Smart Images

Figure CN120762356A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the technical field of laser cutting, in particular to a three-dimensional five-axis laser cutting path generation method and system. BACKGROUND
[0002] Three-dimensional five-axis laser cutting machines are more advanced and complex processing equipment developed on the basis of traditional two-dimensional plane laser cutting technology. The background of its emergence is the continuous improvement of the processing demand of three-dimensional complex curved surface parts in modern manufacturing industry, especially in the fields of automobile manufacturing, aerospace, mold manufacturing, etc. Many parts have complex space curves and contours, and traditional two-dimensional laser cutting cannot meet the processing requirements. Three-dimensional five-axis laser cutting machine adds two rotating axes such as A, B or C to the traditional X, Y and Z linear axes, so that the laser cutting head can deflect and position at any angle in space, thereby realizing complex contour cutting, hole opening, edge trimming and other processing of three-dimensional workpieces. Three-dimensional five-axis laser cutting machine has been widely used in high-end manufacturing field due to its high precision, high flexibility and high efficiency.
[0003] The prior art discloses a three-dimensional five-axis curved surface laser cutting trajectory generation method, comprising: scanning a three-dimensional curved surface of a thin plate workpiece and generating a dense point cloud model of the workpiece curved surface; importing the dense point cloud model into SolidWorks and establishing a curved surface model based on the dense point cloud model; drawing a cutting line on the curved surface model; sampling and processing the cutting line according to the cutting precision requirement, and extracting the cutting line trajectory points and the coordinates of the corresponding cutting line trajectory points from the sample points; transforming the coordinates of the cutting line trajectory points based on the coordinate system reference origin of the cutting line trajectory points and the compensation radius r of the laser beam, to generate a laser cutting trajectory point sequence; extracting the curved surface normal vector at the laser cutting trajectory point to generate a laser cutting attitude angle sequence; and generating NC code of the workbench and the laser cutting head based on the laser cutting trajectory point sequence and the laser cutting attitude angle sequence.
[0004] However, the existing technical solutions have the following disadvantages: 1. The model is constructed by a point cloud scanning device. The point cloud scanning device is expensive and the scanning process is slow; 2. The point cloud is constructed into a curved surface by Solidworks. Solidworks is a commercial closed-source software technology, which is uncontrollable and expensive to purchase. The point cloud fitting is a curved surface, which has a precision loss. The fitting process is time-consuming. The data processing procedure is complicated and has multiple import and export links; 3. The cutting trajectory is generated by sampling points, the cutting line is manually drawn, the automation degree is low, the programming efficiency is low, the sampling points may not be able to fully reflect the cutting line, and the cutting line itself is based on the fitted curved surface, which further reduces the precision. SUMMARY
[0005] In view of the above problems, the present invention is proposed to provide a three-dimensional five-axis laser cutting path generation method that overcomes the above problems or at least partially solves the above problems.
[0006] In order to solve the above technical problems, the embodiments of the present application disclose the following technical solutions:
[0007] In a first aspect, an embodiment of the present invention discloses a method for generating a three-dimensional five-axis laser cutting path, comprising:
[0008] S100 reads and analyzes the three-dimensional model data of the part, sets the part coordinate system according to the actual machine direction, applies the part coordinate system to the part, and completes the coordinate system setting;
[0009] S200. Extract the outer surface and contour of the part, match the contour to the outer surface on which it is located one by one, use a discretization algorithm with bow height and central angle constraints to discretize the contour, and calculate the normal at the discrete points;
[0010] S300. Generate a cutting path according to the configuration of the laser cutting machine cutting head and the normal direction at the discrete points;
[0011] S400. Adjust the cutting path according to process requirements;
[0012] S500. Output the adjusted cutting path.
[0013] Furthermore, in S200, the step of extracting the outer surface and contour of the part includes:
[0014] Connecting the various faces of the three-dimensional model of the target part surface imported into the laser cutting equipment to obtain the target face;
[0015] Determine the correspondence between curves and surfaces in the target surface and construct a line-surface dictionary;
[0016] Starting from the first surface, traverse to obtain the curve set that constitutes the first surface, and find the surface set corresponding to the curve set from the line-surface dictionary; determine whether there is a second surface tangent to the first surface in the surface set; if so, add the second surface to the surface set of the first surface and set the second surface as the first surface; otherwise, add the curve set of the first surface to the boundary set of the first surface;
[0017] When all the curved surfaces of the three-dimensional model of the target part surface are traversed, the surface of the three-dimensional model of the target part surface and the contour to be processed are obtained.
[0018] Furthermore, the correspondence between the curves and surfaces in the target surface is determined, and a line-surface dictionary is constructed. The specific steps include: using the curve as the key Key and the face set as the value Value, constructing the line-surface dictionary EFM, traversing the surface Face that constitutes the three-dimensional model, traversing the curve Edge that constitutes the surface Face, if the key Key of EFM does not contain Edge, then add it to EFM, if the key Key of EFM contains Edge, then let Edge be the Key, and add Face to the Value corresponding to the Key.
[0019] Furthermore, in S200, the contour is matched one-to-one with the outer surface on which it is located, and a discretization algorithm with bow height and central angle constraints is used to discretize the contour, and the normal at the discrete points is calculated. The specific steps include:
[0020] Determine the contour set Edges, the external surface set Faces, and the contour set to surface set mapping M;
[0021] Take an unused edge E from the contour set Edges and obtain the corresponding surface S=M(E) according to the mapping M;
[0022] Use the bow height and central angle limits to discretize E to obtain the point set Pts, take out an unused point P from the point set Pts, project P on the surface S, and obtain the parameter representation (U, V); calculate the normal N=S.normal(U, V) at P on the surface S, and add the normal N to the normal set; repeatedly take out an unused point P from the point set Pts until all points in the point set Pts are taken out.
[0023] Furthermore, in S300, the configuration of the laser cutting machine cutting head includes AC type and BC type; wherein the rotation axes of the AC type are the X axis and the Z axis; and the rotation axes of the BC type are the Y axis and the Z axis.
[0024] Furthermore, in S300, a cutting path is generated according to the configuration of the cutting head of the laser cutting machine and the normal direction at the discrete point. The specific method includes:
[0025] Take an unused edge E from the contour set Edges and determine whether the edge E type is a spline. If the edge E type is a spline, use the bisection method to fit the spline using a straight line and an arc.
[0026] Determine whether the fitted spline is an arc. If so, obtain the normals N1 and N2 closest to the midpoint and endpoint of the arc from the normal set, and convert the normals N1 and N2 into angles AC or BC according to the configuration of the laser cutting machine cutting head; generate an arc instruction CIP based on the angle AC or BC, and add the arc instruction to the path.
[0027] Furthermore, determine whether the fitted spline is an arc. If not, obtain the normal N3 closest to the endpoint of the straight line from the normal set, and convert the normal N3 into an angle AC or BC according to the configuration of the laser cutting machine cutting head; generate a straight line instruction G1 based on the angle AC or BC, and add the straight line instruction to the path.
[0028] Furthermore, the normal N3 is converted into the angle AC or BC according to the configuration of the laser cutting machine cutting head. The specific steps include:
[0029] When the configuration of the laser cutting machine cutting head is AC type, the C-axis angle C=atan2(j, i), the A-axis angle A=atan2( , k), where i, j, k are the three-dimensional vectors normal to N respectively;
[0030] When the configuration of the laser cutting machine cutting head is BC type, the C-axis angle C=atan2(i, j), the B-axis angle B=atan2( , k), where i, j, k are the three-dimensional vectors of the normal direction N respectively.
[0031] Furthermore, in S400, the cutting path is adjusted according to the process requirements, specifically including: sorting the paths according to the process requirements, adjusting the path angle according to the parts and the cutting head structure size, and performing interference checking on the adjusted path.
[0032] Furthermore, in S500, the adjusted cutting path is output. The specific steps include: determining three points on the part model and measuring the coordinates of the three points on the actual workpiece to realize the conversion from the workpiece coordinate system to the machine tool coordinate system, which means outputting the straight line or arc instructions described in the path generation.
[0033] The beneficial effects of the above technical solutions provided by the embodiments of the present invention include at least:
[0034] This invention discloses a three-dimensional, five-axis laser cutting path generation method. Based on a three-dimensional part model and incorporating surface and contour extraction algorithms, the method generates a cutting path from the model. The contours are then fitted and converted into linear and spatial arc instructions, which are then combined with normal information to ultimately generate the laser cutting path. This method relies on three-dimensional model programming rather than point cloud processing, resulting in lower costs, higher path generation efficiency, and greater accuracy than existing technologies.
[0035] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS
[0036] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:
[0037] Figure 1 This is a flow chart of a method for generating a three-dimensional five-axis laser cutting path in Example 1 of the present invention;
[0038] Figure 2 Flowchart of normal calculation at discrete points in Example 1 of the present invention;
[0039] Figure 3 Schematic diagram of the definition of the axis joint angle AC or BC in Example 1 of the present invention;
[0040] Figure 4 This is a flow chart of cutting path generation in Example 1 of the present invention. DETAILED DESCRIPTION
[0041] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.
[0042] In order to solve the problems existing in the prior art, an embodiment of the present invention provides a three-dimensional five-axis laser cutting path generation method.
[0043] Example 1: The present invention discloses a three-dimensional five-axis laser cutting path generation method, such as Figure 1 ,include:
[0044] S100 reads and analyzes the three-dimensional model data of the part, sets the part coordinate system according to the actual machine direction, applies the part coordinate system to the part, and completes the coordinate system setting;
[0045] In this embodiment, the 3D model data of the part is read and parsed by reading common CAD formats such as STEP, IGES, STL, and Parasolid. The part coordinate system is set by determining the machine tool spindle direction (usually the Z axis), the worktable movement direction (X / Y axes), and the machine tool origin position. A coordinate system alignment strategy is then applied to the part coordinate system. This completes the transition from 3D model reading to machine tool coordinate system setting, ensuring that subsequent machining programming is based on correct part positioning.
[0046] S200. Extract the outer surface and contour of the part, match the contour to the outer surface on which it is located one by one, use a discretization algorithm with bow height and central angle constraints to discretize the contour, and calculate the normal at the discrete points;
[0047] In S200 of this embodiment, the step of extracting the outer surface and contour of the part includes:
[0048] Connecting the various faces of the three-dimensional model of the target part surface imported into the laser cutting equipment to obtain the target face;
[0049] Determine the correspondence between curves and surfaces in the target surface and construct a line-surface dictionary; the specific steps include: using the curve as the key Key and the face set as the value Value, constructing the line-surface dictionary EFM, traversing the surface Face that constitutes the three-dimensional model, traversing the curve Edge that constitutes the surface Face, if the EFM key Key does not contain Edge, then add it to the EFM, if the EFM key Key contains Edge, then let Edge be the Key and add Face to the Value corresponding to the Key.
[0050] Starting from the first surface, traverse to obtain the curve set constituting the first surface, and find the surface set corresponding to the curve set from the line-surface dictionary; determine whether there is a second surface tangent to the first surface in the surface set, if so, add the second surface to the surface set of the first surface, and set the second surface as the first surface, otherwise add the curve set of the first surface to the boundary set of the first surface; wherein, determining whether there is a second surface tangent to the first surface in the surface set specifically includes: discretizing the common edge line CL of the first surface and the second surface, and taking several common points on the common edge line, taking the first tangent vector of the first surface and the second tangent vector of the second surface at the common points respectively, if the angles between the first tangent vector and the second tangent vector of all common points are less than a threshold, then it is determined that the first surface and the second surface are tangent, otherwise they are not tangent.
[0051] When all the curved surfaces of the three-dimensional model of the target part surface are traversed, the surface of the three-dimensional model of the target part surface and the contour to be processed are obtained.
[0052] In S200 of this embodiment, as Figure 2 , the contour is matched one by one with the outer surface on which it is located, and a discrete algorithm with bow height and central angle restrictions is used to discretize the contour and calculate the normal at the discrete points. The specific steps include:
[0053] Determine the contour set Edges, the external surface set Faces, and the contour set to surface set mapping M;
[0054] Take an unused edge E from the contour set Edges and obtain the corresponding surface S=M(E) according to the mapping M;
[0055] Use the bow height and central angle limits to discretize E to obtain the point set Pts, take out an unused point P from the point set Pts, project P on the surface S, and obtain the parameter representation (U, V); calculate the normal N=S.normal(U, V) at P on the surface S, and add the normal N to the normal set; repeatedly take out an unused point P from the point set Pts until all points in the point set Pts are taken out.
[0056] S300. Generate a cutting path according to the configuration of the laser cutting machine cutting head and the normal direction at the discrete points; wherein, Figure 3 The laser cutting machine cutting head has two configurations: AC and BC. The AC type has X and Z axes as its rotational axes, while the BC type has Y and Z axes as its rotational axes.
[0057] In S300 of this embodiment, a cutting path is generated according to the configuration of the cutting head of the laser cutting machine and the normal direction at the discrete points, such as Figure 4 Specific methods include:
[0058] Take an unused edge E from the contour set Edges and determine whether the edge E type is a spline. If the edge E type is a spline, use the bisection method to fit the spline using a straight line and an arc.
[0059] Determine whether the fitted spline is an arc. If so, obtain the normals N1 and N2 closest to the arc's midpoint and endpoint from the normal set. Convert these to angles AC or BC based on the laser cutting machine's cutting head configuration. Generate an arc instruction CIP based on the angles AC or BC and add the arc instruction to the path. If not, obtain the normal N3 closest to the line's endpoint from the normal set. Convert this to angles AC or BC based on the laser cutting machine's cutting head configuration. Generate a line instruction G1 based on the angles AC or BC and add the line instruction to the path.
[0060] In this embodiment, the normal N3 is converted into the angle AC or BC according to the configuration of the cutting head of the laser cutting machine. The specific steps include:
[0061] When the configuration of the laser cutting machine cutting head is AC type, the C-axis angle C=atan2(j, i), the A-axis angle A=atan2( , k), where i, j, k are the three-dimensional vectors normal to N respectively;
[0062] When the configuration of the laser cutting machine cutting head is BC type, the C-axis angle C=atan2(i, j), the B-axis angle B=atan2( , k), where i, j, k are the three-dimensional vectors of the normal direction N respectively.
[0063] S400. Adjust the cutting path. In S400, adjusting the cutting path specifically includes sorting the paths according to process requirements, adjusting the path angles based on the part and cutting head structural dimensions, and performing interference checking on the adjusted paths. Specifically, priority rules are first determined, such as roughing before finishing, inner contours before outer contours, and minimum idle travel. The paths are then sorted using a path sorting algorithm. A safety angle is then calculated based on the cutting head radius and part geometry. Finally, geometric collision checking is performed on each point along the path to ensure that the adjusted path does not collide with the part, fixture, or machine tool structure.
[0064] S500. Output the adjusted cutting path. Specifically, path output requires specifying three points on the part model and measuring the coordinates of the three corresponding points on the actual workpiece to achieve conversion from the workpiece coordinate system to the machine tool coordinate system. In S500 of this embodiment, the adjusted cutting path is output. The specific steps include: determining three points on the part model and measuring the coordinates of the three corresponding points on the actual workpiece to achieve conversion from the workpiece coordinate system to the machine tool coordinate system, which refers to outputting the straight line or arc instructions described in the path generation.
[0065] This embodiment discloses a three-dimensional five-axis laser cutting path generation method, including: reading and parsing the three-dimensional model data of the part, setting the part coordinate system according to the actual machine tool direction, applying the part to the part coordinate system to complete the coordinate system setting; extracting the outer surface and contour of the part, corresponding the contour to the outer surface on which it is located one-to-one, using a discrete algorithm with bow height and central angle restrictions to discretize the contour and calculate the normal at the discrete points; generating a cutting path based on the configuration of the laser cutting machine cutting head and the normal at the discrete points; adjusting the cutting path; and outputting the adjusted cutting path. The method disclosed in this embodiment is based on three-dimensional model programming rather than point cloud processing. Compared with existing technologies, it has lower costs, higher path generation efficiency, and higher accuracy.
[0066] It should be understood that the specific order or hierarchy of steps in the disclosed processes is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.
[0067] In the foregoing detailed description, various features are grouped together in a single embodiment to simplify the disclosure. This method of disclosure should not be interpreted as reflecting an intention that embodiments of the claimed subject matter require more features than are expressly recited in each claim. On the contrary, as reflected in the appended claims, the invention comprises less than all the features of any individual disclosed embodiment. The appended claims are therefore hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.
[0068] Those skilled in the art will also appreciate that the various illustrative logic blocks, modules, circuits, and algorithmic steps described in conjunction with the embodiments herein may be implemented as electronic hardware, computer software, or a combination thereof. In order to clearly illustrate the interchangeability between hardware and software, the various illustrative components, blocks, modules, circuits, and steps described above are generally described around their functions. Whether such functions are implemented as hardware or software depends on the specific application and the design constraints imposed on the entire system. A skilled person may implement the described functions in an adaptable manner for each specific application, but such implementation decisions should not be interpreted as departing from the scope of protection of this disclosure.
[0069] The steps of the methods or algorithms described in conjunction with the embodiments herein may be directly embodied as hardware, software modules executed by a processor, or a combination thereof. The software module may be located in a RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, register, hard disk, removable disk, CD-ROM, or any other form of storage medium well known in the art. An exemplary storage medium is connected to the processor so that the processor can read information from the storage medium and write information to the storage medium. Of course, the storage medium may also be an integral part of the processor. The processor and storage medium may be located in an ASIC. The ASIC may be located in a user terminal. Of course, the processor and storage medium may also be present in a user terminal as discrete components.
[0070] For software implementation, the techniques described in this application can be implemented using modules (e.g., procedures, functions, etc.) that perform the functions described in this application. These software codes can be stored in a memory unit and executed by a processor. The memory unit can be implemented within the processor or external to the processor. In the latter case, it is communicatively coupled to the processor via various means, which are well known in the art.
[0071] The foregoing description includes examples of one or more embodiments. Of course, it is not possible to describe all possible combinations of components or methods for the purposes of describing the above embodiments, but one of ordinary skill in the art will recognize that the various embodiments may be further combined and arranged. Therefore, the embodiments described herein are intended to encompass all such changes, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent the term "comprising" is used in the specification or claims, the term is intended to be encompassed in a manner similar to the term "including," as explained in terms of "including," used as a transitional word in the claims. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or."
Claims
1. A three-dimensional five-axis laser cutting path generation method, characterized in that: include: S100 reads and analyzes the three-dimensional model data of the part, sets the part coordinate system according to the actual machine direction, applies the part coordinate system to the part, and completes the coordinate system setting; S200. Extract the outer surface and contour of the part, match the contour to the outer surface on which it is located one by one, use a discretization algorithm with bow height and central angle constraints to discretize the contour, and calculate the normal at the discrete points; S300. Generate a cutting path according to the configuration of the laser cutting machine cutting head and the normal direction at the discrete points; S400. Adjusting the cutting path; S500. Output the adjusted cutting path.
2. The path generation method according to claim 1, wherein: In S200, the steps of extracting the outer surface and contour of the part include: Connecting the various faces of the three-dimensional model of the target part surface imported into the laser cutting equipment to obtain the target face; Determine the correspondence between curves and surfaces in the target surface and construct a line-surface dictionary; Starting from the first surface, traverse to obtain the curve set that constitutes the first surface, and find the surface set corresponding to the curve set from the line-surface dictionary; determine whether there is a second surface tangent to the first surface in the surface set; if so, add the second surface to the surface set of the first surface and set the second surface as the first surface; otherwise, add the curve set of the first surface to the boundary set of the first surface; When all the curved surfaces of the three-dimensional model of the target part surface are traversed, the surface of the three-dimensional model of the target part surface and the contour to be processed are obtained.
3. The path generation method according to claim 2, wherein: Determine the correspondence between curves and surfaces in the target surface and construct a line-surface dictionary. The specific steps include: using the curve as the key and the face set as the value, constructing the line-surface dictionary EFM, traversing the surface Face that constitutes the three-dimensional model, traversing the curve Edge that constitutes the surface Face, if the EFM key does not contain Edge, then add it to the EFM; if the EFM key contains Edge, then let Edge be the Key and add Face to the Value corresponding to the Key.
4. The path generation method according to claim 1, wherein: In S200, the contour is matched one-to-one with the outer surface on which it is located, and a discretization algorithm with bow height and central angle constraints is used to discretize the contour and calculate the normal at the discrete points. The specific steps include: Determine the contour set Edges, the external surface set Faces, and the contour set to surface set mapping M; Take an unused edge E from the contour set Edges and obtain the corresponding surface S=M(E) according to the mapping M; Use the bow height and central angle limits to discretize E to obtain the point set Pts, take out an unused point P from the point set Pts, project P on the surface S, and obtain the parameter representation (U, V); calculate the normal N=S.normal(U, V) at P on the surface S, and add the normal N to the normal set; repeatedly take out an unused point P from the point set Pts until all points in the point set Pts are taken out.
5. The path generation method according to claim 1, wherein: In S300, the configurations of the cutting head of the laser cutting machine include AC type and BC type; wherein the rotation axes of the AC type are the X axis and the Z axis; and the rotation axes of the BC type are the Y axis and the Z axis.
6. The path generation method according to claim 5, wherein: In S300, a cutting path is generated according to the configuration of the cutting head of the laser cutting machine and the normal direction at the discrete point. The specific method includes: Take an unused edge E from the contour set Edges and determine whether the edge E type is a spline. If the edge E type is a spline, use the bisection method to fit the spline using a straight line and an arc. Determine whether the fitted spline is an arc. If so, obtain the normals N1 and N2 closest to the midpoint and endpoint of the arc from the normal set, and convert the normals N1 and N2 into angles AC or BC according to the configuration of the laser cutting machine cutting head; generate an arc instruction CIP based on the angle AC or BC, and add the arc instruction to the path.
7. The path generation method according to claim 6, wherein: Determine whether the fitted spline is an arc. If not, obtain the normal N3 closest to the endpoint of the line from the normal set, and convert the normal N3 into the angle AC or BC according to the configuration of the laser cutting machine cutting head; generate the line instruction G1 according to the angle AC or BC, and add the line instruction to the path.
8. The path generation method according to claim 7, wherein: The normal N3 is converted to angle AC or BC according to the configuration of the laser cutting machine cutting head. The specific steps include: When the configuration of the laser cutting machine cutting head is AC type, the C-axis angle C=atan2(j, i), the A-axis angle A=atan2( , k), where i, j, k are the three-dimensional vectors normal to N respectively; When the configuration of the laser cutting machine cutting head is BC type, the C-axis angle C=atan2(i, j), the B-axis angle B=atan2( , k), where i, j, k are the three-dimensional vectors of the normal direction N respectively.
9. The path generation method according to claim 1, wherein: In S400, the cutting path is adjusted, specifically including: sorting the paths according to process requirements, adjusting the path angle according to the parts and the cutting head structure size, and performing interference checking on the adjusted path.
10. The path generation method according to claim 1, wherein: In S500, the adjusted cutting path is output. The specific steps include: determining three points on the part model and measuring the coordinates of the three points on the actual workpiece to realize the conversion from the workpiece coordinate system to the machine tool coordinate system, which means outputting the straight line or arc instructions described in the path generation.