A posture trajectory calculation method for invisible braces cutting and a braces cutting tool

Abstract

The present invention discloses a method for calculating the posture trajectory of invisible braces cutting and a braces cutting tool. The method comprises: obtaining a three-dimensional cutting trajectory point sequence of invisible braces; projecting it onto an XOY plane and smoothing it; dividing the smoothed cutting trajectory point sequence into four segments; calculating the angle between the line connecting two adjacent position points in the smoothed cutting trajectory point sequence and the X-axis; setting the tool inclination angle of the invisible braces cutting tool; calculating the initial posture of each position point based on the angle corresponding to each position point in the smoothed cutting trajectory point sequence, calculating the posture Z-axis of each position point based on the tool inclination angle of each position point, and then calculating the posture X-axis of each position point based on the angle corresponding to each position point, thereby obtaining the posture trajectory of invisible braces cutting. The present invention can solve the problems of smoothing the invisible braces trajectory line and automatically generating the spatial posture of the braces trajectory line point sequence. The cutting trajectory is automatically calculated without any human intervention, and has high accuracy and smoothness.

Description

Technical Field

[0001] The present invention belongs to the technical field of invisible braces cutting, and in particular relates to a posture trajectory calculation method for invisible braces cutting and a braces cutting tool. Background Art

[0002] Compared to traditional orthodontic techniques, invisible braces, made from elastic, transparent polymer materials instead of steel wires, are more comfortable. Custom-made using digital oral scans, 3D modeling, and advanced materials, invisible braces better conform to the human oral structure, avoiding the gum-tugging sensation associated with traditional braces and thus reducing pain. Their removable design eliminates the discomfort associated with eating and post-meal cleaning during orthodontic treatment, promoting oral hygiene. Furthermore, the treatment process for invisible braces is more standardized, making maintenance more convenient.

[0003] Currently, most of the three-dimensional cutting trajectory lines obtained from 3D braces models on the market are relatively rough, which can easily lead to problems such as broken dividing lines and branch interference, and there is a lot of manual interaction. When using mechanical equipment to cut invisible braces, the posture planning of the cutting tool is also crucial to the quality of the braces. During the processing, at each processing position, the posture of the cutting tool mainly includes the direction of the tool axis and the direction of tool movement, that is, the z-axis direction and x-axis direction of the posture of each point on the cutting trajectory. However, improperly planned tool posture may cause interference between the tool and the braces, resulting in damage to the tool or the braces, and an uneven tool posture may cause burrs or cracks on the braces. Summary of the Invention

[0004] The purpose of the present invention is to provide a posture trajectory calculation method for invisible braces cutting and a braces cutting tool to solve the problem of smoothing the invisible braces trajectory line and automatically generating the spatial posture of the braces trajectory line point sequence.

[0005] The technical solutions of the present invention are as follows:

[0006] A method for calculating a posture trajectory of invisible braces cutting comprises the following steps:

[0007] Obtaining the three-dimensional cutting trajectory point sequence of invisible braces from the invisible braces model;

[0008] Projecting the three-dimensional cutting trajectory point sequence of the invisible braces onto the XOY plane of the invisible braces model, obtaining the projected cutting trajectory point sequence and performing smoothing processing;

[0009] The smoothed cutting trajectory point sequence is divided into four segments: the first segment is the left molar segment, the second segment is the right molar segment, the third segment is the inner segment, and the fourth segment is the outer segment;

[0010] Calculate the angle between the line connecting two adjacent points in the smoothed cutting trajectory point sequence and the X-axis;

[0011] Set the tool inclination angle of the invisible braces cutting tool, that is, the angle of rotation of the cutting tool around the x-axis of the initial posture of the position point; the third section sets the first tool inclination angle, and the fourth section sets the second tool inclination angle. The second tool inclination angle is greater than the first tool inclination angle. The tool inclination angles of the first and second sections adopt an average transition process to smoothly connect the third and fourth sections;

[0012] The initial posture of each position point is calculated according to the angle corresponding to each position point in the smoothed cutting trajectory point sequence, the Z-axis posture of each position point is calculated in combination with the tool inclination angle of each position point, and the X-axis posture of each position point is calculated in combination with the angle corresponding to each position point, thus obtaining the posture trajectory of invisible braces cutting.

[0013] Furthermore, the projected cutting trajectory point sequence is smoothed using median filtering.

[0014] Furthermore, the smoothed cutting trajectory point sequence is divided into four sections, specifically including:

[0015] Get the maximum value Mx, minimum value mx and intermediate value Ox of the smoothed cutting trajectory point sequence on the X-axis;

[0016] Get the Y coordinate value my corresponding to the minimum point mx, take all points whose Y coordinate values ​​are in the interval [my-t, my+t] and whose X coordinate values ​​are less than the middle value Ox, calculate the distance between the X coordinate values ​​of these points and the middle value Ox, and take the cutting trajectory point sequence between the point with the smallest distance and the minimum point mx as a segment; t is the threshold;

[0017] Get the Y coordinate value My corresponding to the maximum value Mx point, take all points whose Y coordinate values ​​are in the interval [My-t, My+t] and whose X coordinate values ​​are greater than the middle value Ox, calculate the distance between the X coordinate values ​​of these points and the middle value Ox, and take the cutting trajectory point sequence between the point with the smallest distance and the maximum value Mx point as a segment;

[0018] The remaining cutting track point sequence located on the inner side is one segment, and the remaining cutting track point sequence located on the outer side is one segment.

[0019] Furthermore, the median value is the mean of the maximum value Mx and the minimum value mx or zero.

[0020] Furthermore, the angle Q i The calculation formula is as follows:

[0021]

[0022] Where, and They are the two adjacent position points p in the smoothed cutting trajectory point sequence i and p i+1 's coordinates.

[0023] Furthermore, let the first tool inclination angle be β n , the second tool inclination angle is β w ;

[0024] The first section tool inclination angle β i =ε1 / n1, where ε1 = β n -β w , n1 is the total number of position points in the first segment of cutting trajectory sequence;

[0025] The second section tool inclination angle β i =ε2 / n2, where ε2 = β n -β w , n2 is the total number of position points in the second cutting trajectory point sequence.

[0026] Furthermore, according to the position point p i The corresponding angle Q i , calculate the position point p i Initial posture matrix T i (p i ):

[0027]

[0028] According to the initial posture and tool inclination angle β, calculate the position point p i Posture Z axis Z(p i ):

[0029]

[0030] According to the position point p i The corresponding angle Q i Calculate the position point p i X-axis of posture X(p i ):

[0031]

[0032] According to the position point p i The posture Z axis and X axis are used to obtain the posture Y axis.

[0033] Furthermore, each position point p in the first segment i Posture Z axis Z(p i )as follows:

[0034]

[0035] Each position point p in the second segment iPosture Z axis Z(p i )as follows:

[0036]

[0037] Each position point p in the third segment i Posture Z axis Z(p i )as follows:

[0038]

[0039] Each position point p in the fourth segment i Posture Z axis Z(p i )as follows:

[0040]

[0041] Then calculate the X-axis and Y-axis posture of each position point.

[0042] A braces cutting tool adopts any one of the above-mentioned invisible braces cutting posture trajectory calculation methods.

[0043] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0044] The present invention can solve the problems of smoothing the trajectory of invisible braces and automatically generating the spatial posture of the braces trajectory point sequence. The cutting trajectory is automatically calculated without any human intervention, with high precision and smoothness. It is suitable for fully automatic batch processing of braces in orthodontic treatment and has practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the posture trajectory calculation method for invisible braces cutting;

[0046] Figure 2 It is a schematic diagram of the projection of the braces trajectory line;

[0047] Figure 3 It is a schematic diagram of trajectory line projection segmentation;

[0048] Figure 4 is a schematic diagram of the tool inclination angle β;

[0049] Figure 5 This is a schematic diagram of the overall posture

[0050] Figure 6 It is a partial diagram of the posture. DETAILED DESCRIPTION

[0051] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0052] The present invention provides a method for calculating the posture trajectory of invisible braces cutting and a braces cutting tool. First, the obtained discrete closed-loop three-dimensional cutting trajectory point sequence {P} is projected. The smoothness of the trajectory {p} after projection should be considered. Secondly, the structural characteristics of the braces model are analyzed. Considering the processing requirements (tool inclination angle β) and other issues, attention should be paid to the segmentation of the trajectory after projection, as well as the calculation of the angle Q between the line connecting two adjacent position points and the X-axis of the coordinate system. i and position point p i Initial posture, finally according to the position point p i Initial posture, combined with the tool inclination angle β, the Z-axis posture of the position point is obtained, and the posture of the corresponding point {X(P i ),Y(P i ),Z(P i )}.

[0053] The method for calculating the posture trajectory of invisible braces cutting of the present invention is as follows: Figure 1 As shown, the following steps are included:

[0054] Input the obtained initial 3D cutting trajectory point sequence. Establish the coordinate system of the invisible braces model. The coordinate origin O is located at the center of gravity of the invisible braces model. The horizontal right direction is the positive direction of the coordinate system X axis, that is, the direction of the line connecting the two large teeth is the positive direction of the coordinate system X axis. The vertical direction is the positive direction of the coordinate system Y axis, and the vertical upward direction is the positive direction of the coordinate system Z axis.

[0055] The initial cutting line is projected onto the XOY plane to obtain the projected cutting trajectory point sequence {p}. The projected cutting trajectory point sequence is smoothed using a median filter.

[0056] According to the process requirements, the projected cutting trajectory point sequence is segmented. The projected cutting trajectory point sequence is divided into four sections. The first and second sections are for the left and right large teeth, where the machining tool has a large operating space. They are used as smooth transition sections, allowing the tool inclination angle to smoothly transition between the third and fourth sections. The third section is the inner side, where the machining tool has a small operating space. It is used as an adjustment section and a suitable tool inclination angle is given. The fourth section is the outer side and serves as an adjustment section, giving a suitable tool inclination angle.

[0057] Perform geometric calculations on the projected cutting trajectory point sequence and traverse each position point p i(i=1,...N), calculate the position of two adjacent points p i and p i+1 The angle Q between the line connecting the two points and the X-axis of the world coordinate system i :

[0058]

[0059] Wherein, N is the number of projection points, that is, the number of position points in the cutting trajectory point sequence after projection.

[0060] According to the rationality requirement of segmented processing, the tool inclination angle of the cutting trajectory point sequence of the adjustment segment is given a suitable inclination angle, and the tool inclination angle of the cutting trajectory point sequence of the transition segment is processed by average transition to smoothly connect the adjustment segments.

[0061] According to the position point p i The corresponding angle Q i , calculate the position point p i Initial posture matrix T i (p i ):

[0062]

[0063] Then, according to the initial posture and tool inclination angle β, the position point p is calculated i Posture Z axis Z(p i ):

[0064]

[0065] According to the position point p i The corresponding angle Q i Calculate the position point p i X-axis of posture X(p i ):

[0066]

[0067] Finally, according to the position point p i The posture Z-axis and X-axis are used to calculate the posture Y-axis. The tool axis direction and tool movement direction, that is, the Z-axis direction and X-axis direction of the posture of each point on the cutting trajectory.

[0068] The projection is as follows:

[0069] In a three-dimensional coordinate system, each spatial point can be described by (X, Y, Z). The cutting trajectory point sequence obtained from the invisible braces model is three-dimensionally discrete. Simply connecting them will cause problems such as broken dividing lines and branch interference, which will have a serious impact on data processing. The orthogonal parallel projection method is used to project the three-dimensional cutting trajectory line onto the two-dimensional xoy plane, eliminating the complexity of the three-dimensional spatial point data and making data processing more convenient. Figure 2 This is a schematic diagram of the projection of the braces trajectory line.

[0070] The projection line of the orthogonal parallel projection method forms a 90° angle with the projection plane xoy. Projecting a 3D point (X, Y, Z) onto the plane xoy using the orthogonal parallel projection method yields a 2D point (x, y). This transformation can be calculated using the orthogonal parallel transformation formula: x = X; y = Y; z = 0.

[0071] The smoothness is as follows:

[0072] The resulting projected point sequence is discrete on the XOY plane, retaining the characteristic properties of the original cutting trajectory point sequence on the X and Y axes. A median filter is then used to smooth the data and remove spikes. The filtered data retains the original image's trend while removing the impact of spikes on the analysis.

[0073] The sections are as follows:

[0074] Analyzing the structure of human teeth, the outer and inner contours of large teeth are relatively smooth, while the inner and outer contours of middle teeth are relatively compact, and the contour lines of teeth are particularly complex. At the same time, considering that during the processing of braces, the outer processing space of the middle braces is relatively large, and the inner space is relatively narrow, if the tool is not preset with a suitable inclination angle β, it will cause interference between the tool and the braces.

[0075] The projected cutting trajectory point sequence is divided into four sections. The first and second sections are the left and right large teeth. The contour lines of the large teeth are smooth and the machining tool has a large operating space. They are used as smooth transition sections. The tool inclination angles of each point are transitioned to the third and fourth sections using the average following method. The third section is the inner side. The machining tool has a smaller operating space, and to avoid collision between the tool and the workpiece, it is used as an adjustment section. It is necessary to preset a suitable tool inclination angle β. The fourth section is the outer side, which is also used as an adjustment section. However, compared with the inner side, the outer side has a larger processing space, so when the inclination angle β is preset, it can be slightly larger than the inner side. Projection segmentation is as follows Figure 3 As shown, the specific segmentation algorithm is as follows:

[0076] For the first segment of the left molar, calculate the maximum value Mx, minimum value mx, and median value Ox on the X-axis of the projected trajectory point sequence. Also, find the Y coordinate my corresponding to the point with the minimum value mx. Take the interval [my-1, my+1] and find all Y coordinates that fit within this interval. Calculate the X coordinate value of the corresponding point. Then, iterate through each point and calculate the distance l from the median value Ox. Select the point to the left of the median value Ox with the smallest distance from the median value, and determine its position as h2. Therefore, the segmented position interval for the first segment of the left molar is [h1, h2].

[0077] The calculation formula of the intermediate value Ox is as follows:

[0078]

[0079] The middle value Ox is not limited to this value, and can be roughly located in the middle of the track and can separate the left and right areas. For example, it can be directly set to zero.

[0080] The second section of the right molar: take the point on the right side of the middle value Ox with the smallest distance from the middle value, and get its position as h3, that is, the interval of the second section of the right molar is [h3, h4].

[0081] Inside the third segment; the interval is [h2, h3].

[0082] Outside the fourth segment; the interval is [h4, h1].

[0083] The angles are as follows:

[0084] The principle for solving the angle Q between the line connecting any two points in the xoy plane and the x-axis is expressed as follows:

[0085]

[0086] Perform geometric calculations on the projected cutting trajectory point sequence and traverse each position point p i (i=1,…N), especially the last position point should be connected to the first position point to form a closed loop. i and p i+1 The angle {Q} between the line connecting the two points and the X axis of the world coordinate system is calculated based on the (x, y) coordinate values ​​of the projection point sequence. i+1 The y coordinate value of the position point p is subtracted i The y coordinate value of the result Let position point p i+1 The x-coordinate value minus the position point p i The x-coordinate value of Divide a1 by b1 to get c1. The specific formula is:

[0087] When the position point p i+1 The (x,y) coordinate values ​​are all greater than p i Hour Angle:

[0088]

[0089] When the position point p i+1 The (x,y) coordinate values ​​are all less than p i Hour angle:

[0090]

[0091] When the position point p i+1 The x coordinate is less than the position point pi , the y coordinate is greater than the position point p i Hour angle:

[0092]

[0093] When the position point p i+1 The x coordinate is smaller than the position point p i , the y coordinate is less than the position point p i Hour angle:

[0094]

[0095] When the y coordinates of the two points are equal and the point p i+1 The x coordinate is greater or less than the position point p i When the angle Q i =0 and 180;

[0096] When the x coordinates of the two points are equal and the point p i+1 The y coordinate is greater than or less than the position point p i When the angle Q i =90 and 270.

[0097] The tool inclination angles are as follows:

[0098] When using mechanical equipment (multi-axis machine tools or industrial robots) to cut invisible braces, the direction of the cutting tool axis is the normal direction of the cutting position point posture, and the direction of the tool movement is the x-axis direction of the position point posture. During the processing of invisible braces, due to the compact structure of the braces, especially the relatively small space on the inner side during processing, it is easy for the tool to collide with the workpiece, affecting the quality of the workpiece. Therefore, it is necessary to preset a suitable tool inclination angle {β}, that is, the angle of rotation around the x-axis of the initial posture of the position point, such as Figure 4 As shown, the right-hand rule is followed to avoid interference between the tool and the workpiece.

[0099] For the transition section and the left and right large tooth sections, the tool inclination angle adopts average transition processing to make it smoothly connect to the adjustment section. For the adjustment section and the inner and outer sides, the inner side should be preset with a larger tool inclination angle β due to the smaller space. n , the outer space is larger, and the preset tool inclination angle β w It should be larger than the inside.

[0100] The position point posture is calculated as follows:

[0101] For the position point p obtained above i The corresponding angle Q i , use the spatial coordinate system rotation matrix algorithm to obtain the position point p i Initial posture rotation matrix, which rotates around its own Z axis Q iAngle, the specific formula is as follows:

[0102]

[0103] The first section of the left tooth and the second section of the right tooth need to connect to the inner side of the third section and the outer side of the fourth section. The tool inclination angles of the left and right tooth sections are averaged and smoothed. First, the number of segmented position points n is calculated, and then the tool inclination angle difference ε between the inner and outer sections is calculated. The specific algorithm is:

[0104] First section left big tooth

[0105] The number of position points in the first segment n1 = h2 - h1;

[0106] Tool inclination difference ε1=β n -β w ;

[0107] Tool inclination angle β at each position i =ε1 / n1;

[0108] Traverse each position point p in the first segment i , i∈[h1,h2], according to the left multiplication rule of the spatial rotation matrix, the position point p is obtained i The Z axis of the posture is expressed as:

[0109]

[0110] Second section right molar

[0111] The number of position points in the second segment n2 = h4 - h3;

[0112] Tool inclination difference ε2=β n -β w ;

[0113] Tool inclination angle β at each position i =ε2 / n2;

[0114] Traverse each position point p in the second segment i , i∈[h3,h4], according to the left multiplication rule of the spatial rotation matrix, the position point p is obtained i The Z axis of the posture is expressed as:

[0115]

[0116] Inside the third section

[0117] Tool inclination angle β at each position n ;

[0118] Traverse each position point p in the third segment i, i∈[h2,h3], according to the left multiplication rule of the spatial rotation matrix, the position point p is obtained i The Z axis of the posture is expressed as:

[0119]

[0120] Inside the fourth section

[0121] Tool inclination angle β at each position w ;

[0122] Traverse each position point p in the fourth segment i , i∈[h4,h1], according to the left multiplication rule of the spatial rotation matrix, the Z axis of the position point pi is obtained, and the formula is expressed as:

[0123]

[0124] The basic principle of solving the attitude of a point in space is to calculate the coordinate system rotation matrix, which rotates around its own Z axis. The rotation matrix formula is expressed as:

[0125]

[0126] The two adjacent position points p obtained above i and p i+1 The angle Q between the line connecting the two points and the X-axis of the world coordinate system i , traverse each position point p i (i=1,…N), according to the corresponding angle Q i , use the coordinate system rotation matrix formula to solve the X-axis position point posture:

[0127]

[0128] According to the X-axis and Z-axis of the position point posture, using the vector perpendicularity theorem, the formula for calculating the Y-axis of the position point posture is expressed as:

[0129]

[0130] Finally, we get the position point posture {X(P i ),Y(P i ),Z(P i )}. Figure 5 The final trajectory line is the posture of each position point {X(P i ),Y(P i ),Z(P i )} effect diagram, Figure 6 It is a partially enlarged schematic diagram of the overall posture diagram.

[0131] The present invention also provides a braces cutting tool, which adopts any one of the above-mentioned invisible braces cutting posture trajectory calculation methods.

[0132] In summary, the present invention can solve the problems of smoothing the trajectory of invisible braces and automatically generating the spatial posture of the braces trajectory point sequence. The cutting trajectory is automatically calculated without any manual intervention, with high precision and smoothness. It is suitable for fully automatic batch processing of braces in orthodontic treatment and has practical application value.

[0133] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0134] It will be easily understood by those skilled in the art that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for calculating the posture trajectory of invisible braces cutting, characterized in that: The following steps are involved: Obtaining the three-dimensional cutting trajectory point sequence of invisible braces from the invisible braces model; Projecting the three-dimensional cutting trajectory point sequence of the invisible braces onto the XOY plane of the invisible braces model, obtaining the projected cutting trajectory point sequence and performing smoothing processing; The smoothed cutting trajectory point sequence is divided into four segments: the first segment is the left molar segment, the second segment is the right molar segment, the third segment is the inner segment, and the fourth segment is the outer segment; Calculate the angle between the line connecting two adjacent points in the smoothed cutting trajectory point sequence and the X-axis; Set the tool inclination angle of the invisible braces cutting tool, that is, the angle of rotation of the cutting tool around the x-axis of the initial posture of the position point; the third section sets the first tool inclination angle, and the fourth section sets the second tool inclination angle. The second tool inclination angle is greater than the first tool inclination angle. The tool inclination angles of the first and second sections adopt an average transition process to smoothly connect the third and fourth sections; The initial posture of each position point is calculated according to the angle corresponding to each position point in the smoothed cutting trajectory point sequence, the Z-axis posture of each position point is calculated in combination with the tool inclination angle of each position point, and the X-axis posture of each position point is calculated in combination with the angle corresponding to each position point, thus obtaining the posture trajectory of the invisible braces cutting; Where, let the first tool inclination angle be β n , the second tool inclination angle is β w ; Then the first section tool inclination angle β i =ε1 / n1, where ε1 = β n -β w , n1 is the total number of points in the first cutting trajectory sequence; the tool inclination angle β in the second segment i =ε2 / n2, where ε2 = β n -β w , n2 is the total number of position points in the second segment cutting trajectory point sequence; According to the position point p i The corresponding angle Q i , calculate the position point p i Initial posture matrix T i (p i ): According to the initial posture and tool inclination angle β, calculate the position point p i Posture Z axis Z(p i ): According to the position point p i The corresponding angle Q i Calculate the position point p i X-axis of posture X(p i ): According to the position point p i The posture Z axis and X axis are used to obtain the posture Y axis; Specifically, each position point p in the first segment i Posture Z axis Z(p i )as follows: Each position point p in the second segment i Posture Z axis Z(p i )as follows: Each position point p in the third segment i Posture Z axis Z(p i )as follows: Each position point p in the fourth segment i Posture Z axis Z(p i )as follows: Then calculate the X-axis and Y-axis posture of each position point.

2. The method for calculating the posture trajectory of invisible braces cutting according to claim 1, characterized in that: The projected cutting trajectory point sequence is smoothed using median filtering.

3. The method for calculating the posture trajectory of invisible braces cutting according to claim 1, characterized in that: The smoothed cutting trajectory point sequence is divided into four sections, including: Get the maximum value Mx, minimum value mx and intermediate value Ox of the smoothed cutting trajectory point sequence on the X-axis; Get the Y coordinate value my corresponding to the minimum point mx, take all points whose Y coordinate values ​​are in the interval [my-t, my+t] and whose X coordinate values ​​are less than the middle value Ox, calculate the distance between the X coordinate values ​​of these points and the middle value Ox, and take the cutting trajectory point sequence between the point with the smallest distance and the minimum point mx as a segment; t is the threshold; Get the Y coordinate value My corresponding to the maximum value Mx point, take all points whose Y coordinate values ​​are in the interval [My-t, My+t] and whose X coordinate values ​​are greater than the middle value ox, calculate the distance between the X coordinate values ​​of these points and the middle value Ox, and take the cutting trajectory point sequence between the point with the smallest distance and the maximum value Mx point as a segment; The remaining cutting track point sequence located on the inner side is one segment, and the remaining cutting track point sequence located on the outer side is one segment.

4. The method for calculating the posture trajectory of invisible braces cutting according to claim 3, characterized in that: The median value is the mean of the maximum value Mx and the minimum value mx or zero.

5. The method for calculating the posture trajectory of invisible braces cutting according to claim 1, characterized in that: Angle Q i The calculation formula is as follows: Where, and They are the two adjacent position points p in the smoothed cutting trajectory point sequence i and p i+1 's coordinates.

6. A braces cutting tool, characterized in that: The braces cutting tool adopts the invisible braces cutting posture trajectory calculation method described in any one of claims 1 to 5.

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