Construction method, device and equipment for transition track of numerical control machine tool and storage medium

Abstract

The invention provides a construction method and device for a transition track of a numerical control machine tool, electronic equipment and a storage medium, and the method comprises the steps: obtaining geometric parameters of adjacent program segments, including a starting point, an end point, a tangential direction and a curvature; based on the starting point, the ending point, the tangential direction and the curvature, constructing a transition curve meeting position continuity, tangential direction continuity and curvature continuity; wherein the curvature change rate of the transition curve is minimum; the deviation between the transition curve and the original program segment is restrained not to exceed a preset tolerance; the transition curve is inserted between numerical control instruction points, a continuous and smooth transition track is generated, the curvature change rate is controlled while it is guaranteed that the position, speed or acceleration is continuous, higher-order smoothness is guaranteed, and it is guaranteed that the deviation of the transition track is controllable through constraint tolerance.

Description

Technical Field

[0001] This invention relates to the field of CNC machining technology, and in particular to a method, apparatus, electronic device, and storage medium for constructing transition trajectories for CNC machine tools. Background Technology

[0002] In CNC machining, the smoothness of the transition trajectory between program segments directly affects machining accuracy and surface quality. Traditional methods typically use high-order polynomial curves (such as fifth-order polynomials) or piecewise cubic curves to construct the transition trajectory. While this ensures continuity of position, velocity, or acceleration, high-order curves can lead to drastic curvature changes, causing trajectory distortion or looping, affecting motion stability. Furthermore, traditional methods do not constrain the deviation between the transition trajectory and the original program segment, making it difficult to guarantee machining accuracy. Summary of the Invention

[0003] This invention provides a method, apparatus, electronic device, and storage medium for constructing transition trajectories for CNC machine tools, in order to solve the defects of traditional CNC machine tool transition trajectories, such as drastic curvature changes and large deviations between the transition trajectory and the original program segment.

[0004] This invention provides a method for constructing the transition trajectory of a CNC machine tool, comprising: Obtain the geometric parameters of adjacent program segments, including start point, end point, tangent direction, and curvature; Based on the starting point, ending point, tangent direction, and curvature, a transition curve is constructed that satisfies positional continuity, tangent direction continuity, and curvature continuity; wherein the rate of curvature change of the transition curve is minimized. The deviation between the transition curve and the original program segment is constrained to not exceed a preset tolerance; The transition curve is inserted between CNC command points to generate a continuous and smooth transition trajectory.

[0005] According to the method for constructing the transition trajectory of a CNC machine tool provided by the present invention, the method for minimizing the rate of change of curvature of the transition curve includes: The jerk at each point on the transition curve is obtained, and the rate of change of curvature of the transition curve is minimized by minimizing the L2 norm of the jerk.

[0006] According to the method for constructing the transition trajectory of a CNC machine tool provided by the present invention, the step of minimizing the rate of change of curvature of the transition curve by minimizing the L2 norm of the jerk includes: Calculate the first derivative of the tangential angle to obtain the rate of change of the tangential angle of the curve with respect to the arc length; When calculating the L2 norm of the jerk, the rate of change of the tangential angle of the curve with respect to the arc length is replaced with the first derivative of the tangential angle in the second-order equation of the L2 norm, thus reducing the second-order equation to a first-order equation.

[0007] According to the method for constructing the transition trajectory of a CNC machine tool provided by the present invention, the solution of the rate of change of the tangential angle of the curve with the arc length includes the Lemniscate sine function.

[0008] According to the method for constructing the transition trajectory of a CNC machine tool provided by the present invention, constraining the deviation between the transition curve and the original program segment to not exceed a preset tolerance includes: Align the original trajectory in the original program segment to the standard plane using a rotation matrix; Calculate the vertical or radial distance from the transition curve to the standard plane; The amplitude of the transition curve is adjusted by a scaling factor so that the vertical distance does not exceed the preset tolerance, and the radius of curvature of the transition curve is adjusted so that the radial distance does not exceed the preset tolerance.

[0009] The present invention also provides a device for constructing a transition trajectory for a CNC machine tool, comprising: The acquisition module is used to acquire the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature. A construction module is used to construct a transition curve that satisfies positional continuity, tangential direction continuity, and curvature continuity based on the starting point, ending point, tangential direction, and curvature; wherein the rate of curvature change of the transition curve is minimized. The constraint module is used to constrain the deviation between the transition curve and the original program segment to not exceed a preset tolerance; The generation module is used to insert the transition curve between CNC command points to generate a continuous and smooth transition trajectory.

[0010] According to the CNC machine tool transition trajectory construction apparatus provided by the present invention, the construction module is further configured to: The jerk at each point on the transition curve is obtained, and the rate of change of curvature of the transition curve is minimized by minimizing the L2 norm of the jerk.

[0011] According to the CNC machine tool transition trajectory construction device provided by the present invention, the constraint module is specifically used for: Align the original trajectory in the original program segment to the standard plane using a rotation matrix; Calculate the vertical or radial distance from the transition curve to the standard plane; The amplitude of the transition curve is adjusted by a scaling factor so that the vertical distance does not exceed the preset tolerance, and the radius of curvature of the transition curve is adjusted so that the radial distance does not exceed the preset tolerance.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for constructing the transition trajectory of a CNC machine tool as described in any of the preceding claims.

[0013] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for constructing the transition trajectory of a CNC machine tool as described in any of the preceding claims.

[0014] The present invention provides a method, apparatus, electronic device, and storage medium for constructing transition trajectories for CNC machine tools. This involves acquiring the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature; constructing a transition curve based on the start point, end point, tangent direction, and curvature that satisfies position continuity, tangent direction continuity, and curvature continuity; wherein the rate of curvature change of the transition curve is minimized; constraining the deviation of the transition curve from the original program segment to not exceed a preset tolerance; inserting the transition curve between CNC command points to generate a continuous and smooth transition trajectory; controlling the rate of curvature change while ensuring continuity of position, velocity, or acceleration to ensure higher-order smoothness; and ensuring controllable deviation of the transition trajectory through tolerance constraints. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0016] Figure 1 This is a flowchart illustrating the method for constructing the transition trajectory of a CNC machine tool provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of the trajectory to be processed provided in the embodiments of the invention; Figure 3 This is a comparison diagram of the original trajectory and the transition trajectory provided in the embodiments of the present invention; Figure 4 This is a schematic diagram of the first-order tangent vector of a single axis and the first-order tangent vector of a composite axis provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the second-order tangent vector of a single axis and the modulus of the second-order tangent vector of the synthesized axis provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the modulus of the third-order tangent vector of a single axis and the third-order tangent vector of the synthesized axis provided in an embodiment of the present invention; Figure 7 This is a functional structure diagram of the CNC machine tool transition trajectory construction device provided in an embodiment of the present invention; Figure 8 This is a functional structure diagram of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0018] Figure 1 A flowchart of the method for constructing the transition trajectory of a CNC machine tool provided in an embodiment of the present invention is shown below. Figure 1 As shown, the method for constructing the transition trajectory of a CNC machine tool provided in this embodiment of the invention includes: Step 101: Obtain the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature; Step 102: Construct a transition curve that satisfies positional continuity, tangential direction continuity, and curvature continuity based on the starting point, ending point, tangential direction, and curvature; wherein the rate of curvature change of the transition curve is minimized. Step 103: Constrain the deviation between the transition curve and the original program segment to not exceed the preset tolerance; Step 104: Insert the transition curve between CNC command points to generate a continuous and smooth transition trajectory.

[0019] Traditional methods for constructing transition trajectories for CNC machine tools typically employ high-order polynomial curves (such as fifth-order polynomials) or piecewise cubic curves. While these methods can ensure continuity in position, velocity, or acceleration, high-order curves can lead to drastic curvature changes, causing trajectory distortion or looping, thus affecting motion smoothness. Furthermore, traditional methods do not constrain the deviation between the transition trajectory and the original program segment, making it difficult to guarantee machining accuracy.

[0020] The method for constructing a transition trajectory for a CNC machine tool provided in this invention involves acquiring the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature; constructing a transition curve that satisfies position continuity, tangent direction continuity, and curvature continuity based on the start point, end point, tangent direction, and curvature; wherein the curvature change rate of the transition curve is minimized; constraining the deviation of the transition curve from the original program segment to not exceed a preset tolerance; inserting the transition curve between CNC command points to generate a continuous and smooth transition trajectory, controlling the curvature change rate while ensuring position, velocity, or acceleration continuity to ensure higher-order smoothness, and ensuring controllable transition trajectory deviation through tolerance constraints.

[0021] Based on any of the above embodiments, the method for minimizing the rate of change of curvature of the transition curve includes: The jerk at each point on the transition curve is obtained, and the rate of change of curvature of the transition curve is minimized by minimizing the L2 norm of the jerk.

[0022] In this embodiment of the invention, minimizing the rate of change of curvature of the transition curve by minimizing the L2 norm of the jerk includes: Calculate the first derivative of the tangential angle to obtain the rate of change of the tangential angle of the curve with respect to the arc length; When calculating the L2 norm of the jerk, the rate of change of the tangential angle of the curve with respect to the arc length is replaced with the first derivative of the tangential angle in the second-order equation of the L2 norm, thus reducing the second-order equation to a first-order equation.

[0023] In this embodiment of the invention, the solution for the rate of change of the curve tangential angle with arc length includes the Lemniscate sine function.

[0024] In this embodiment of the invention, a transition segment is constructed for the following standard smoothing problem. Since two straight lines determine a plane, any local smoothing problem can be transformed into a solution within the plane.

[0025] The specific steps include: given point coordinates: P0(0, 0), P1(a, b), P2(2a, 0), a, c>0.

[0026] Using the tangential angle θ(s) as a parameter, the curvilinear velocity vector is: v(s)=[cos(θ(s)),sin(θ(s))]T The derivation process of kinematic quantities is as follows: Position x(s) is obtained by velocity integration; acceleration a(s) is related to the tangential angular derivative θ'(s); jerk j(s) involves the second derivative. The embodiments of the present invention directly optimize the third derivative (jerk) based on the arc length parameter, rather than the parameterized third derivative, which is more in line with the actual motion control requirements.

[0027] By minimizing the maximum (L2 norm) value of the jerk at each point, i.e. The solution to this problem must satisfy (assuming θ is twice continuously differentiable). For ease of study, this problem is normalized (i.e., the arc length is scaled so that C = 1). Additionally, θ(s) should satisfy the initial conditions θ(0) = θ0 > 0, θ'(0) = 0. Let p(s) = θ'(s), then... It can be seen that the change of θ(s) has nothing to do with θ0, and the results obtained by solving for any θ0 can all be obtained through rotation transformation. Therefore, θ = π / 4 is taken below. The solution of the above equation about p(s) is where sl is the lemniscate sine function, and s0 = ∫0¹ (1 / √(1 - t²)) dt ≈ 1.311028777146060. Then Assume x(0)=0, s < s0, where s0 is the initial length of the interpolation trajectory and s is the length of the trajectory after interpolation. When s > s0, the solution to this problem is the unit circle.

[0028] The above gives the standardized solution. The following problems need to be considered in actual applications: Transform the original problem into a standard problem (calculate the rotation matrix) and determine θ0 = arctan(b / a).

[0029] Determine the standard curve according to θ0 (rotated from the above π / 4 standard curve), and note to select until θ(s)=0, and symmetrically supplement the remaining part.

[0030] Regarding the calculation of the sl function, the sl function can be directly calculated using the Jacobi elliptic function, as follows: where the sn function (the inverse of the first kind of elliptic integral) can be calculated by calling the standard function library, such as ellipj (MATLAB, scipy).

[0031] Based on any of the above embodiments, the deviation of the constraint on the transition curve from the original program segment not exceeding the preset tolerance includes: Align the original trajectory in the original program segment to the standard plane through the rotation matrix; Calculate the perpendicular distance or radial distance from the transition curve to the standard plane; Adjust the amplitude of the transition curve through the scaling factor so that the perpendicular distance does not exceed the preset tolerance, and adjust the radius of curvature of the transition curve so that the radial distance does not exceed the preset tolerance.

[0032] In the embodiments of the present invention, if the original program segment is a straight line, the tolerance is the shortest distance from the points on the transition curve to the straight line.

[0033] If the original program segment is an arc, the tolerance is the radial distance from the transition curve to the arc.

[0034] Trajectory to be processed, such as Figure 2 As shown, the original trajectory and the transition trajectory are compared, for example... Figure 3 As shown, the original trajectory is a broken line or a path with abrupt curvature changes. The transition trajectory constructed in this embodiment of the invention is a smooth path without abrupt changes. By comparing the difference between the original trajectory (without transition) and the trajectory after inserting the transition curve, the improvement in smoothness is highlighted.

[0035] like Figure 4 As shown, the first-order tangent vector of a single axis and the first-order tangent vector of the composite axis are the velocity components and composite velocity of each servo axis (X / Y / Z axis), obtained through... Figure 4 As can be seen, the embodiments of the present invention can ensure the continuity of the transition curve with respect to speed.

[0036] like Figure 5 As shown, the second-order tangent vector of a single axis and the magnitude of the second-order tangent vector of the composite axis are the acceleration components and composite acceleration of each servo axis, respectively. Figure 5 It can be seen that the embodiments of the present invention can ensure the continuity of acceleration for the transition curve.

[0037] like Figure 6 As shown, the modulus of the third-order tangent vector of a single axis and the third-order tangent vector of the composite axis are the jerk components and composite jerk of each servo axis. Figure 6 This demonstrates the optimization effect of the transition curve on the rate of curvature change (higher-order smoothness). Embodiments of this invention suppress machine tool vibration and extend mechanical life by increasing jerk continuity.

[0038] The method for constructing CNC machine tool transition trajectories provided in this invention significantly improves the smoothness and accuracy of CNC machining trajectories by constructing high-order smooth transition curves that satisfy position, tangential direction, and curvature continuity, and by constraining the maximum deviation from the original program segment to not exceed a preset chord height error. Specifically, this method minimizes the rate of curvature change by minimizing the L2 norm of the jerk, effectively reducing machine tool vibration and impact, thereby improving the surface machining quality of the workpiece. Simultaneously, based on the analytical solution design of the Lemniscate sine function or a high-order polynomial, it balances real-time computational efficiency with motion control stability, making it suitable for complex surface machining scenarios requiring high precision and high dynamic response.

[0039] The following describes the apparatus for constructing the transition trajectory of a CNC machine tool provided by the present invention. The apparatus for constructing the transition trajectory of a CNC machine tool described below can be referred to in correspondence with the method for constructing the transition trajectory of a CNC machine tool described above.

[0040] Figure 7 This is a schematic diagram of the structure of the CNC machine tool transition trajectory construction device provided in an embodiment of the present invention, as shown below. Figure 7 As shown, the CNC machine tool transition trajectory construction device provided in this embodiment of the invention includes: The acquisition module 701 is used to acquire the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature. The construction module 702 is used to construct a transition curve that satisfies positional continuity, tangential direction continuity, and curvature continuity based on the starting point, ending point, tangential direction, and curvature; wherein the curvature change rate of the transition curve is minimized. The constraint module 703 is used to constrain the deviation between the transition curve and the original program segment to not exceed a preset tolerance; The generation module 704 is used to insert the transition curve between CNC command points to generate a continuous and smooth transition trajectory.

[0041] In this embodiment of the invention, the building module is further configured to: The jerk at each point on the transition curve is obtained, and the rate of change of curvature of the transition curve is minimized by minimizing the L2 norm of the jerk.

[0042] In this embodiment of the invention, the constraint module is specifically used for: Align the original trajectory in the original program segment to the standard plane using a rotation matrix; Calculate the vertical or radial distance from the transition curve to the standard plane; The amplitude of the transition curve is adjusted by a scaling factor to ensure that the vertical distance does not exceed the preset tolerance, and the radius of curvature of the transition curve is adjusted to ensure that the radial distance does not exceed the preset tolerance.

[0043] The CNC machine tool transition trajectory construction device provided in this embodiment of the invention acquires the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature; constructs a transition curve that satisfies position continuity, tangent direction continuity, and curvature continuity based on the start point, end point, tangent direction, and curvature; wherein the curvature change rate of the transition curve is minimized; constrains the deviation of the transition curve from the original program segment to not exceed a preset tolerance; inserts the transition curve between CNC command points to generate a continuous and smooth transition trajectory, controlling the curvature change rate while ensuring position, speed, or acceleration continuity to ensure higher-order smoothness, and ensuring controllable transition trajectory deviation through tolerance constraints.

[0044] Figure 8 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 8As shown, the electronic device may include a processor 810, a communication interface 820, a memory 830, and a communication bus 840. The processor 810, communication interface 820, and memory 830 communicate with each other via the communication bus 840. The memory 830 includes computer programs, an operating system, and acquired data. The processor 810 can call logical instructions in the memory 830 to execute a method for constructing a CNC machine tool transition trajectory. This method includes: acquiring the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature; constructing a transition curve based on the start point, end point, tangent direction, and curvature that satisfies positional continuity, tangent direction continuity, and curvature continuity; wherein the curvature change rate of the transition curve is minimized; constraining the deviation between the transition curve and the original program segment to not exceed a preset tolerance; and inserting the transition curve between CNC command points to generate a continuous and smooth transition trajectory.

[0045] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to related technologies, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0046] On the other hand, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a method for constructing a CNC machine tool transition trajectory provided by the methods described above. This method includes: acquiring geometric parameters of adjacent program segments, including a start point, an end point, a tangent direction, and curvature; constructing a transition curve based on the start point, end point, tangent direction, and curvature that satisfies positional continuity, tangent direction continuity, and curvature continuity; wherein the rate of curvature change of the transition curve is minimized; constraining the deviation between the transition curve and the original program segment to not exceed a preset tolerance; and inserting the transition curve between CNC command points to generate a continuous and smooth transition trajectory.

[0047] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0048] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the parts that contribute to the related technology, can be embodied in the form of software products. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing the transition trajectory of a CNC machine tool, characterized in that, include: Obtain the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature; Based on the starting point, ending point, tangent direction, and curvature, a transition curve is constructed that satisfies positional continuity, tangent direction continuity, and curvature continuity; wherein the rate of curvature change of the transition curve is minimized. The deviation between the transition curve and the original program segment is constrained to not exceed a preset tolerance; The transition curve is inserted between CNC command points to generate a continuous and smooth transition trajectory.

2. The method for constructing the transition trajectory of a CNC machine tool according to claim 1, characterized in that, The method for minimizing the rate of change of curvature of the transition curve includes: The jerk at each point on the transition curve is obtained, and the rate of change of curvature of the transition curve is minimized by minimizing the L2 norm of the jerk.

3. The method for constructing the transition trajectory of a CNC machine tool according to claim 2, characterized in that, The method of minimizing the rate of change of curvature of the transition curve by minimizing the L2 norm of the jerk includes: Calculate the first derivative of the tangential angle to obtain the rate of change of the tangential angle of the curve with respect to the arc length; When calculating the L2 norm of the jerk, the rate of change of the tangential angle of the curve with respect to the arc length is replaced with the first derivative of the tangential angle in the second-order equation of the L2 norm, thus reducing the second-order equation to a first-order equation.

4. The method for constructing the transition trajectory of a CNC machine tool according to claim 3, characterized in that, The solution to the rate of change of the tangential angle of the curve with respect to the arc length includes the Lemniscate sine function.

5. The method for constructing the transition trajectory of a CNC machine tool according to claim 1, characterized in that, The constraint that the deviation between the transition curve and the original program segment does not exceed a preset tolerance includes: Align the original trajectory in the original program segment to the standard plane using a rotation matrix; Calculate the vertical or radial distance from the transition curve to the standard plane; The amplitude of the transition curve is adjusted by a scaling factor so that the vertical distance does not exceed the preset tolerance, and the radius of curvature of the transition curve is adjusted so that the radial distance does not exceed the preset tolerance.

6. A device for constructing the transition trajectory of a CNC machine tool, characterized in that, include: The acquisition module is used to acquire the geometric parameters of adjacent program segments, including the start point, end point, tangent direction, and curvature. A construction module is used to construct a transition curve that satisfies positional continuity, tangential direction continuity, and curvature continuity based on the starting point, ending point, tangential direction, and curvature; wherein the rate of curvature change of the transition curve is minimized. The constraint module is used to constrain the deviation between the transition curve and the original program segment to not exceed a preset tolerance; The generation module is used to insert the transition curve between CNC command points to generate a continuous and smooth transition trajectory.

7. The apparatus for constructing the transition trajectory of a CNC machine tool according to claim 6, characterized in that, The building module is also used for: The jerk at each point on the transition curve is obtained, and the rate of change of curvature of the transition curve is minimized by minimizing the L2 norm of the jerk.

8. The apparatus for constructing the transition trajectory of a CNC machine tool according to claim 6, characterized in that, The constraint module is specifically used for: Align the original trajectory in the original program segment to the standard plane using a rotation matrix; Calculate the vertical or radial distance from the transition curve to the standard plane; The amplitude of the transition curve is adjusted by a scaling factor so that the vertical distance does not exceed the preset tolerance, and the radius of curvature of the transition curve is adjusted so that the radial distance does not exceed the preset tolerance.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method for constructing the transition trajectory of a CNC machine tool as described in any one of claims 1 to 5.

10. A non-transitory readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the method for constructing the transition trajectory of a CNC machine tool as described in any one of claims 1 to 5.

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