Method, device, processor and storage medium thereof for realizing five-axis RTCP trajectory fairing with convexity preservation of tool shaft vector surface

Abstract

The present application relates to a kind of five-axis RTCP trajectory fairing method for realizing tool axis vector surface convexity, comprising the following steps: calculating the length of tool tip point of two sections of motion instruction before and after corner;Tool tip point trajectory fairing is carried out;The tool axis vector of trajectory endpoint and corner connecting point involved in fairing is calculated;Local rectangular coordinate system is established on the tool tip point trajectory after fairing;The rate of change about tool tip point length at the trajectory endpoint involved in fairing is calculated;Tool axis vector is calculated according to the corresponding angle of the point on tool tip point fairing trajectory;Tool tip point and tool axis vector error are calculated, and compared with parameter setting value.The present application also relates to a kind of device for realizing five-axis RTCP trajectory fairing processing for keeping tool axis vector surface convexity, processor and its readable storage medium.The five-axis RTCP trajectory fairing method for realizing tool axis vector surface convexity, device, processor and its computer readable storage medium of the present application are used, guarantee the convexity of fairing result tool axis vector surface, and get more gentle speed control result.

Description

Technical Field

[0001] The present invention relates to the field of CNC machining, in particular to the field of five-axis RTCP linkage machining, and specifically refers to a method, device, processor and computer-readable storage medium thereof for achieving five-axis RTCP trajectory smoothing while maintaining the convexity of a tool axis vector surface. Background Art

[0002] In the five-axis RTCP machining trajectory, since the speed and direction of the tool axis vector rotating as the tool tip moves are discontinuous, in order to improve the machining effect, the five-axis RTCP trajectory needs to be smoothed. Currently, there are three main types of five-axis smoothing technologies:

[0003] 1. Smooth the tool tip trajectory to obtain a tool tip trajectory spline curve; construct a reference trajectory based on the tool tip trajectory and the tool axis vector, and smooth the reference trajectory to obtain a reference trajectory spline curve; establish a mapping relationship between the two spline curves according to certain synchronization rules, and the direction of the line connecting the corresponding points of the two spline curves is the direction of the corresponding tool axis vector.

[0004] 2. Smooth the tool tip trajectory to obtain a tool tip trajectory spline curve; smooth the endpoint trajectory of the tool axis vector on the unit sphere to obtain a tool axis vector endpoint trajectory spline curve; establish a mapping relationship between the two spline curves according to certain synchronization rules to obtain a five-axis smooth trajectory.

[0005] 3. Smooth the tool tip trajectory to obtain the tool tip trajectory spline curve; smooth the rotation axis trajectory to obtain the rotation axis trajectory spline curve; establish a mapping relationship between the two spline curves according to certain synchronization rules to obtain a five-axis smooth trajectory.

[0006] The above three methods all have a common defect: they cannot guarantee that the tool axis vector surface is a convex surface, that is, there are some areas of the tool axis vector surface that change from a convex surface to a concave surface, such as Figure 1 This defect will cause the ratio of the five-axis trajectory control point length to the cutting point length to be uneven, which will lead to uneven processing speed and affect the processing effect. The reasons for this defect are:

[0007] 1. The first type of method: Since the reference trajectory is obtained by extending a small length along the tool axis vector direction based on the original tool tip trajectory, this method can only guarantee the convexity of the tool axis vector surface within the extended length, but cannot guarantee the convexity of the tool axis vector surface within a longer extended length.

[0008] 2. The second method, since the tool axis vector is obtained by smoothing the endpoint trajectory on the unit sphere, can only guarantee the convexity of the tool axis vector surface within the unit tool length range, but cannot guarantee the convexity of the tool axis vector surface within a larger range.

[0009] 3. The third method is that since the relationship between the tool axis vector and the rotation axis is related to the machine tool structure and may be a complex non-monotonic function relationship, the convexity of the tool axis vector surface cannot be guaranteed. Summary of the Invention

[0010] The purpose of the present invention is to overcome the shortcomings of the above-mentioned prior art and provide a method, device, processor and computer-readable storage medium for achieving five-axis RTCP trajectory smoothing that maintains the convexity of the tool axis vector surface, which are simple to operate, have small errors and a wide range of applications.

[0011] To achieve the above objectives, the method, device, processor, and computer-readable storage medium for achieving five-axis RTCP trajectory smoothing with convexity preservation of tool axis vector surface are as follows:

[0012] The method for achieving five-axis RTCP trajectory smoothing while maintaining the convexity of the tool axis vector surface is characterized in that the method comprises the following steps:

[0013] (1) Calculate the tool tip lengths of the two motion instructions before and after the corner, and take half of the length as the trajectory length involved in trajectory smoothing;

[0014] (2) Smoothing the tool tip trajectory for the trajectory involved in smoothing;

[0015] (3) Calculate the tool axis vector of the trajectory endpoints and corner connection points involved in smoothing;

[0016] (4) Establish a local rectangular coordinate system on the tool tip trajectory after smoothing, and calculate the angle α between the tool axis vector at the trajectory endpoints and corner connection points involved in smoothing and the corresponding local rectangular coordinate system X axis and Y axis u and β u ;

[0017] (5) Calculate the angle α at the endpoint of the trajectory participating in smoothing u and β u The rate of change of the angle of change with respect to the length of the tool tip;

[0018] (6) Construction angle α u and β u The synchronous relationship between the tool tip smooth trajectory and the point P' on the tool tip smooth trajectory corresponds to the angle α u and β u Calculate the tool axis vector;

[0019] (7) Calculate the tool tip point and tool axis vector errors, compare them with the parameter setting values, and obtain the smoothing result in which the errors meet the parameter requirements.

[0020] Preferably, the step (4) of establishing a local rectangular coordinate system on the smoothed tool tip point trajectory comprises the following steps:

[0021] Taking any point P on the original trajectory BCD u , its corresponding point on the smoothed trajectory BCD is P' u , a local rectangular coordinate system is established at P' u , specifically as follows:

[0022] The tangent direction of P' u is taken as the X-axis, the normal direction of the plane of the smoothed trajectory BCD is taken as the Z-axis, and the direction of the cross product of the Z-axis and the X-axis is taken as the Y-axis, then the angles between the tool axis vector T u at P u and the positive directions of the X-axis and the Y-axis are α u and β u respectively.

[0023] Preferably, the step (6) of calculating the tool axis vector comprises the following steps:

[0024] The tool axis vector is calculated according to the following formula:

[0025]

[0026] wherein, are the direction vectors of the positive directions of the X-axis, the Y-axis and the Z-axis of the local rectangular coordinate system at P' u .

[0027] Preferably, the step (7) comprises the following steps:

[0028] (7.1) calculating the tool tip point and tool axis vector error, and comparing it with the parameter setting value;

[0029] (7.2) if the error meets the parameter requirement, the current smoothing result is the final result; otherwise, the length of the trajectory involved in the trajectory smoothing is iterated until a smoothing result meeting the parameter requirement is obtained.

[0030] The device for implementing the five-axis RTCP trajectory smoothing process for maintaining the convexity of the tool axis vector surface, mainly characterized in that the device comprises:

[0031] a processor configured to execute computer executable instructions;

[0032] a memory storing one or more computer executable instructions, which, when executed by the processor, implement each step of the above-mentioned five-axis RTCP trajectory smoothing process for maintaining the convexity of the tool axis vector surface.

[0033] The processor for implementing the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface, wherein the processor is configured to execute computer executable instructions, and the computer executable instructions are executed by the processor to implement each step of the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface.

[0034] The computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program can be executed by a processor to implement each step of the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface.

[0035] Compared with the prior art, the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface, the device, the processor and the computer readable storage medium can guarantee the convexity of the tool axis vector curved surface, and thus a more gentle speed control result is obtained, and the method has a wide application range. BRIEF DESCRIPTION OF DRAWINGS

[0036] Figure 1 The figure is a tool axis vector curved surface after fairing of the prior art.

[0037] Figure 2 The figure is a tool axis vector curved surface after fairing of the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface.

[0038] Figure 3 The figure is a speed control result of a fairing trajectory of the prior art.

[0039] Figure 4 The figure is a speed control result of a fairing trajectory of the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface.

[0040] Figure 5 The figure is a tool path of an embodiment of the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface.

[0041] Figure 6 The figure is a flowchart of the five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface. DETAILED DESCRIPTION

[0042] In order to more clearly describe the technical content of the present application, the following further describes in combination with specific embodiments.

[0043] The five-axis RTCP trajectory fairing method for maintaining convexity of tool axis vector curved surface comprises the following steps.

[0044] (1) Calculate the length of the tool tip point of the two segments before and after the corner, and take half of the length as the trajectory length participating in the trajectory fairing;

[0045] (2) Perform tool tip point trajectory fairing on the trajectory participating in the fairing;

[0046] (3) Calculate the tool axis vector of the trajectory end point and the corner connecting point participating in the fairing;

[0047] (4) Establish a local rectangular coordinate system on the tool tip point trajectory after the fairing, and calculate the included angles α u and β u between the tool axis vector of the trajectory end point and the corner connecting point participating in the fairing and the corresponding local rectangular coordinate system X axis and Y axis;

[0048] (5) Calculate the change rate of the included angles α u and β u at the trajectory end point participating in the fairing with respect to the length of the tool tip point;

[0049] (6) Construct the synchronization relationship between the included angles α u and β u and the tool tip fairing trajectory, and calculate the tool axis vector according to the corresponding included angles α u and β u of the point P' on the tool tip fairing trajectory;

[0050] (7) Calculate the tool tip point and tool axis vector error, compare it with the parameter setting value, and obtain the fairing result meeting the parameter requirement.

[0051] As a preferred embodiment of the present application, the step (4) of establishing a local rectangular coordinate system on the tool tip point trajectory after the fairing specifically comprises the following steps:

[0052] Take any point P u on the original trajectory BCD, and its corresponding point on the fairing trajectory BCD' is P' u , and a local rectangular coordinate system is established at P' u , specifically as follows:

[0053] The tangent direction of P' u is taken as the X axis, the normal direction of the fairing trajectory BCD' is taken as the Z axis, the cross product direction of the Z axis and the X axis is taken as the Y axis, and then the positive included angles α u and β u of the tool axis vector T u at the point P u and the X axis and Y axis are calculated.

[0054] As a preferred embodiment of the present application, the step (6) of calculating the tool axis vector specifically comprises:

[0055] The tool axis vector is calculated according to the following formula:

[0056]

[0057] Wherein, P' and P are respectively the coordinates of the tool tip point in the global coordinate system and the local coordinate system. u The direction vectors of the positive directions of the XYZ axes of the local right-angle coordinate system at the point.

[0058] As a preferred embodiment of the present application, the step (7) specifically comprises the following steps:

[0059] (7.1) calculating the error of the tool tip point and the tool axis vector, and comparing with the parameter setting value;

[0060] (7.2) if the error meets the parameter requirement, the current fairing result is the final result; otherwise, the length of the trajectory participating in the trajectory fairing is iterated until the fairing result meeting the parameter requirement is obtained.

[0061] The device for implementing the five-axis RTCP trajectory fairing process for maintaining the convexity of the tool axis vector surface of the present application, wherein the device comprises:

[0062] a processor configured to execute computer executable instructions;

[0063] a memory storing one or more computer executable instructions, which, when executed by the processor, implement the steps of the above-mentioned five-axis RTCP trajectory fairing process for maintaining the convexity of the tool axis vector surface.

[0064] The processor for implementing the five-axis RTCP trajectory fairing process for maintaining the convexity of the tool axis vector surface of the present application, wherein the processor is configured to execute computer executable instructions, which, when executed by the processor, implement the steps of the above-mentioned five-axis RTCP trajectory fairing process for maintaining the convexity of the tool axis vector surface.

[0065] The computer readable storage medium of the present application, on which a computer program is stored, the computer program can be executed by the processor to implement the steps of the above-mentioned five-axis RTCP trajectory fairing process for maintaining the convexity of the tool axis vector surface.

[0066] In the specific embodiment of the present application, the trajectory formed by the tool axis vector and the included angle with the XY axis of the local coordinate system is faired by constructing a local coordinate system varying with the tool tip point spline curve. Since the local coordinate system continuously and monotonously rotates, and the relationship between the tool axis vector and the included angle is a monotonic function, the faired trajectory guarantees the convexity of the tool axis vector surface.

[0067] The method of the present application is implemented by the following steps:

[0068] (1)Calculate the length of the tool tip point of the two motion instructions before and after the corner, and take half of the length as the trajectory length participating in the trajectory fairing;

[0069] (2)Fair the tool tip point trajectory of the trajectory participating in the fairing;

[0070] (3)Calculate the tool axis vector of the end point and the corner connecting point of the trajectory participating in the fairing;

[0071] (4)Establish a local rectangular coordinate system on the fairing tool tip point trajectory, and calculate the included angle α, β between the tool axis vector of the end point and the corner connecting point participating in the fairing and the XY axis of the corresponding local rectangular coordinate system.

[0072] (5)Calculate the included angle α, β change angle about the tool tip point length change rate at the end point of the trajectory participating in the fairing;

[0073] (6)Construct the synchronization relationship between the included angle α, β and the tool tip point fairing trajectory, and calculate the tool axis vector according to the corresponding included angle α, β of the point on the tool tip point fairing trajectory;

[0074] (7)Calculate the tool tip point and the tool axis vector error, and compare it with the parameter setting value, if the error meets the parameter requirement, the current fairing result is the final result, otherwise, the trajectory length participating in the trajectory fairing is iterated until the fairing result meeting the error parameter requirement is obtained.

[0075] The tool path as shown in Figure 5 illustrates the fairing method of the application, AC and CE are two adjacent motion instructions (wherein AC and CE can be straight lines, circular arcs or curves), the connecting point is C, and the fairing implementation steps are as follows:

[0076] (1)Calculate the length of the tool tip point of the two motion instructions AC and CE as L AC and L CE , and take the end points B and D of AC and CE;

[0077] (2)Fair the tool tip point trajectory of the original tool tip point trajectory BCD to obtain the fairing trajectory BCD, wherein C' is the point corresponding to the connecting point C on the fairing trajectory;

[0078] (3)According to the RTCP tool axis vector interpolation rule, calculate the tool axis vectors T B , T C and T D of points B, C and D;

[0079] (4)For any point P u on the original trajectory BCD, if its corresponding point on the fairing trajectory BCD' is P' u , P' uThe method to establish a local rectangular coordinate system is:

[0080] P′ u Movement direction (i.e. P′ u The tangent direction is the X axis, the normal direction of the BC′D trajectory plane is the Z axis, and the cross product direction of the Z axis and the X axis is the Y axis. u Tool axis vector T at point u The angles with the positive directions of X and Y axes are α u , β u .

[0081] At points B, C′, and D, respectively, local rectangular coordinate systems are established according to the above method to calculate T B 、T C 、T D Corresponding angle α B , β B , α C , β C , α D , β D ;

[0082] (5) According to the RTCP tool axis vector interpolation rule, any point P can be calculated u The change rate of the included angle with respect to the tool tip length is:

[0083]

[0084] in AP curve u The tool tip point trajectory length is calculated according to the above method to calculate the rate of change v of the angle at points B and D with respect to the tool tip point length. B,α 、v B,β 、v D,α 、v D,β ;

[0085] (6) Construct the synchronous relationship between the angles α, β and the smooth trajectory of the tool tip, that is, given any point P′ u α u , β u The calculation method is as follows:

[0086] Constructing a Bezier spline curve

[0087]

[0088] Among them B i (t) and are the fourth-order Bezier curve basis function and control point respectively, t∈[0,1] is the curve parameter,

[0089]

[0090] Let any point on the curve represented by formula (3) be Solve the equation for P′ u The value of the corresponding parameter t

[0091]

[0092] Will Substitute the value into formula (3) to get P′ u The angle corresponding to the point P′ u The tool axis vector corresponding to the point is:

[0093]

[0094] in, P′ u The direction vector of the positive direction of the XYZ axis of the local rectangular coordinate system at the point, when T C and When the angle is greater than 90 degrees, the above formula The term is negative, otherwise it is positive.

[0095] α, β represent the angles between the tool axis vector and the X and Y axes of the local coordinate system, respectively. Figure 5 As shown, P u For any point on the original trajectory BCD, P u The tool posture at point T u , the trajectory after transition is BC′D, which is connected to P u The corresponding point is P′ u , tool posture is T′ u , T u The angles with the local coordinate system X and Y axes are denoted as α u ,β u , T′ u The angles with the local coordinate system X-axis and Y-axis are expressed as therefore, It represents the angle between the tool axis vector after transition and the XY axis of the local coordinate system, and α u ,β u It represents the angle between the tool axis vector and the local coordinate system XY axis before the transition. Before and after the transition, the tool tip point and tool axis vector will change.

[0096] (7) Calculate the tool tip error based on the smoothed trajectory BC′D, and calculate the tool tip error based on any point P′ calculated above. uThe corresponding tool axis vector calculates tool axis vector error.

[0097] The method of the application guarantees monotonicity of alpha and beta of the transition trajectory by constructing a local coordinate system and subsequent transition processing of the tool axis vector and the included angle alpha and beta between the XY axis of the local coordinate system, and formulas (3)-(9), and the local coordinate system is also monotonically changed, and formula (10) can guarantee that the tool axis vector surface obtained by the transition is a convex surface.

[0098] The innovation point of the technical scheme of the application is that a new five-axis trajectory smoothing method which can guarantee convexity of the tool axis vector surface is proposed, wherein the local coordinate system and subsequent processing are specific implementation steps of the new method, and guaranteeing convexity of the tool axis vector surface is an advantageous result of the method.

[0099] The specific implementation scheme of the embodiment can be referred to the related description in the above embodiment, which will not be repeated here.

[0100] It can be understood that the same or similar parts in the above embodiments can be mutually referred to, and the content not described in detail in some embodiments can be referred to the same or similar content in other embodiments.

[0101] It should be noted that, in the description of the application, the terms "first", "second", etc. are only used for the purpose of description, and cannot be understood as indicating or implying relative importance. In addition, in the description of the application, unless otherwise specified, the meaning of "a plurality of" is at least two.

[0102] Any process or method descriptions in flow charts or otherwise described herein represent embodiments which can be managed as one or more modules of executable code for implementation by various types of processing means. Preferred embodiments of the application therefore include additional implementations that can not be explicitly described or shown herein, but which are nevertheless within the scope of the present application. In particular, it is explicitly contemplated that one or more of the processes, functions, or procedures described herein can be performed in an order other than that explicitly described, including substantially concurrently or in reverse order unless otherwise specifically stated or inherently implied by the subject matter.

[0103] It should be understood that the various parts of the present application can be implemented in hardware, software, firmware or a combination thereof. In the above embodiments, the various steps or methods can be implemented in software or firmware stored in a memory and executed by a suitable instruction execution device. For example, if implemented in hardware, and in another embodiment, any of the following technologies, or a combination thereof, known in the art can be used: discrete logic circuitry having logic gates for implementing logic functions on data signals, application specific integrated circuits having appropriate combinational logic gates, programmable gate arrays (PGA), field programmable gate arrays (FPGA), etc.

[0104] Those skilled in the art of the present technology can understand that all or part of the steps carried out by the above-mentioned embodiment method can be completed by a program instructing the relevant hardware, and the corresponding program can be stored in a computer readable storage medium. When the program is executed, it includes one of the steps of the method embodiment or a combination thereof.

[0105] In addition, the functional units in each embodiment of the present application can be integrated in one processing module, or each unit can be physically present separately, or two or more units can be integrated in one module. The above-mentioned integrated module can be realized in the form of hardware or in the form of software function module. The integrated module, if realized in the form of software function module and sold or used as an independent product, can also be stored in a computer readable storage medium.

[0106] The storage medium mentioned above can be a read-only memory, a magnetic disk or an optical disk, etc.

[0107] In the description of the present specification, the description of the terms "one embodiment", "some embodiments", "example", "specific example" or "some examples" means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present specification, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0108] The method, device, processor and computer readable storage medium thereof for realizing five-axis RTCP trajectory smoothing of tool shaft vector surface convexity preservation of the present application, compared with the prior art, can guarantee the convexity of the smoothing result tool shaft vector surface, as shown in Figure 1 and 2 , and further obtain a more gentle speed control result, as shown in Figure 3 and 4 , which has a wide range of applications.

[0109] In this specification, the application has been described with reference to specific embodiments thereof. It is apparent, however, that various modifications and changes can be made thereto without departing from the spirit and scope of the application. Therefore, the description and drawings should be regarded in an illustrative rather than a restrictive sense.

Claims

1. A five-axis RTCP trajectory smoothing method for maintaining the convexity of the tool axis vector surface, characterized in that: The method comprises the following steps: (1) Calculate the tool tip lengths of the two motion instructions before and after the corner, and take half of the length as the trajectory length involved in trajectory smoothing; (2) Smoothing the tool tip trajectory for the trajectory involved in smoothing; (3) Calculate the tool axis vector of the trajectory endpoints and corner connection points involved in smoothing; (4) Establish a local rectangular coordinate system on the tool tip trajectory after smoothing, and calculate the angle α between the tool axis vector at the trajectory endpoints and corner connection points involved in smoothing and the corresponding local rectangular coordinate system X axis and Y axis u and β u ; (5) Calculate the angle α at the endpoint of the trajectory participating in smoothing u and β u The rate of change of the angle of change with respect to the length of the tool tip; (6) Construction angle α u and β u The synchronous relationship between the tool tip point smooth trajectory and the tool tip point smooth trajectory point P ′ Corresponding angle α u and β u Calculate the tool axis vector; (7) Calculate the tool tip point and tool axis vector errors, compare them with the parameter setting values, and obtain the smoothing result in which the errors meet the parameter requirements.

2. The five-axis RTCP trajectory smoothing method for maintaining the convexity of the tool axis vector surface according to claim 1 is characterized in that: In the step (4), a local rectangular coordinate system is established on the smoothed tool tip trajectory, specifically comprising the following steps: Take any point P on the original trajectory BCD u , its trajectory BC after smoothing ′ The corresponding point on D is P u ′ , in P u ′ A local rectangular coordinate system is established at: P u ′ The tangent direction is the X axis, and the smoothed trajectory BC ′ The normal direction of the plane of D is the Z axis, and the cross product direction of the Z axis and the X axis is set to the Y axis, then P u Tool axis vector T at point u The angles with the positive directions of the X and Y axes are α u and β u .

3. The five-axis RTCP trajectory smoothing method for maintaining the convexity of the tool axis vector surface according to claim 1 is characterized in that: The calculation of the tool axis vector in step (6) is specifically as follows: The tool axis vector is calculated according to the following formula: in, P u ′ The direction vector of the positive direction of the XYZ axis of the local rectangular coordinate system at the point, and They are tool posture T u ′ The angles with the local coordinate system's X and Y axes.

4. The five-axis RTCP trajectory smoothing method for maintaining the convexity of the tool axis vector surface according to claim 1 is characterized in that: The step (7) specifically includes the following steps: (7.1) Calculate the tool tip point and tool axis vector errors and compare them with the parameter settings; (7.2) If the error meets the parameter requirements, the current smoothing result is the final result; otherwise, the trajectory lengths involved in trajectory smoothing are iterated until a smoothing result with an error meeting the parameter requirements is obtained.

5. A device for achieving five-axis RTCP trajectory smoothing while maintaining the convexity of the tool axis vector surface, characterized in that: The device comprises: a processor configured to execute computer-executable instructions; A memory storing one or more computer executable instructions, wherein when the computer executable instructions are executed by the processor, the steps of the five-axis RTCP trajectory smoothing method for maintaining the convexity of the tool axis vector surface as described in any one of claims 1 to 4 are implemented.

6. A processor for achieving five-axis RTCP trajectory smoothing while maintaining the convexity of the tool axis vector surface, characterized in that: The processor is configured to execute computer-executable instructions. When the computer-executable instructions are executed by the processor, the various steps of the five-axis RTCP trajectory smoothing method for maintaining the convexity of the tool axis vector surface as described in any one of claims 1 to 4 are implemented.

7. A computer-readable storage medium, characterized in that A computer program is stored thereon, and the computer program can be executed by a processor to implement the various steps of the five-axis RTCP trajectory smoothing processing method for maintaining the convexity of the tool axis vector surface as described in any one of claims 1 to 4.

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