A method for three-dimensional cycloid trajectory planning and material removal uniformity control in robotic belt grinding and polishing

Abstract

The present invention relates to a method for planning a three-dimensional cycloid trajectory and regulating material removal uniformity of a robot abrasive belt grinding and polishing, comprising the following steps: obtaining a three-dimensional model of a workpiece to be polished, selecting a polishing area, and setting relevant polishing process parameters; calculating the polishing area, converting the polishing surface from a three-dimensional mapping to a two-dimensional parameter domain, and generating a two-dimensional parameter grid model; extracting the central axis of the polishing surface from the two-dimensional parameter grid model, and generating a planar variable-radius cycloid trajectory along the central axis; inversely mapping the planar variable-radius cycloid trajectory back to the three-dimensional model of the workpiece to be polished, and obtaining a three-dimensional variable-radius adaptive cycloid trajectory with an initial step; establishing a contact model, simulating the grinding and polishing process on the contact model, and calculating the amount of grinding and polishing material removed; quantitatively evaluating the uniformity of the distribution of grinding and polishing material removed on the entire surface, and iteratively optimizing the step value of the three-dimensional variable-radius adaptive cycloid trajectory; and post-processing to obtain a three-dimensional cycloid polishing trajectory with uniform material removal.

Description

Technical Field

[0001] The present invention relates to the field of mechanical processing technology, and in particular to a method for planning three-dimensional cycloid trajectory and regulating material removal uniformity in robot abrasive belt grinding and polishing. Background Art

[0002] In modern manufacturing, precision machining technology is crucial to improving product quality and production efficiency. As an efficient and automated surface treatment method, robotic belt grinding and polishing is widely used in surface finishing of various materials such as metal, wood, and stone. However, achieving high-precision and high-efficiency grinding and polishing operations faces two core challenges: one is how to accurately plan the grinding and polishing trajectory on complex curved workpieces to ensure that the trajectory closely fits the workpiece contour and improves machining accuracy; the other is how to effectively control the amount of material removed during the grinding and polishing process to achieve consistency and uniformity in surface treatment, avoiding dimensional deviations caused by over-polishing and surface roughness problems caused by under-polishing.

[0003] Existing technologies for 3D trajectory planning often rely on simple linear or circular interpolation strategies. These methods struggle to accurately follow the workpiece contour when processing irregular or highly variable surfaces, resulting in limited machining accuracy. Furthermore, traditional methods rely heavily on manual experience to control material removal uniformity, lacking scientific and systematic analysis and optimization methods. This not only increases the difficulty of process development but also impacts machining efficiency and the stability of finished product quality.

[0004] Especially during the grinding and polishing of complex three-dimensional surfaces, adaptively adjusting the grinding trajectory and cycloidal parameters based on the workpiece's actual geometric characteristics to achieve efficient and uniform material removal has become a pressing technical challenge. Existing trajectory planning algorithms often ignore the interaction between the local geometric characteristics of the workpiece surface and the grinding and polishing dynamics, making it difficult to accurately predict and control the contact state and material removal rate during the grinding and polishing process. Summary of the Invention

[0005] The purpose of the present invention is to overcome the defects and shortcomings of the prior art and provide a method for three-dimensional cycloid trajectory planning and material removal uniformity control of robotic belt grinding, which can adaptively adjust the grinding trajectory and cycloid parameters according to the actual geometric characteristics of the workpiece to achieve efficient and uniform material removal.

[0006] The purpose of the present invention can be achieved through the following technical solutions:

[0007] A method for three-dimensional cycloid trajectory planning and material removal uniformity control for a robot belt grinding and polishing process includes the following steps:

[0008] Step 1: Import the model data of the workpiece to be polished into the CAM software, obtain the 3D model of the workpiece to be polished, select the polishing area, and set the relevant polishing process parameters;

[0009] Step 2: Calculate the polishing area selected in step 1 according to conformal geometry theory, transform the polishing surface from a 3D mapping into a 2D parametric domain, and generate a 2D parametric mesh model;

[0010] Step 3: Extract the central axis of the polished surface in the two-dimensional parameter domain from the two-dimensional parametric mesh model generated in step 2, and generate a planar variable radius cycloid trajectory along the central axis;

[0011] Step 4: The planar variable radius cycloid trajectory generated in step 3 is inversely mapped back to the polishing area selected by the three-dimensional model of the workpiece to be polished to obtain a three-dimensional variable radius adaptive cycloid trajectory of the initial step length;

[0012] Step 5: Establish a contact model, simulate the grinding and polishing process of the contact model based on the three-dimensional variable radius adaptive cycloid trajectory of the initial step obtained in step 4, and calculate the grinding and polishing material removal;

[0013] Step 6: Quantitatively evaluate the uniformity of the distribution of polishing material removal across the entire surface. Based on the polishing material removal calculated in step 5, iteratively optimize the step size of the three-dimensional variable radius adaptive cycloid trajectory to achieve a uniform trajectory distribution.

[0014] Step 7: Post-processing to obtain a three-dimensional cycloid trajectory with uniform material removal.

[0015] As a preferred embodiment, in step 2, a conformal mapping algorithm is used to transform the polished surface from a three-dimensional mapping into a two-dimensional parameter domain.

[0016] As a preferred embodiment, in step 3, extracting the central axis of the polished surface in the two-dimensional parameter domain and generating a planar variable radius cycloid trajectory along the central axis includes the following steps:

[0017] Step 31: Perform Delaunay triangulation on the two-dimensional parametric grid model generated in step 2 and generate a Voronoi diagram;

[0018] Step 32: Construct the central axis using the Voronoi diagram algorithm;

[0019] Step 33: Using the central axis constructed in step 32 as a guide line, generate a periodic two-dimensional cycloid trajectory, and adaptively adjust the step value of the two-dimensional cycloid trajectory fed along the central axis;

[0020] Step 34: Based on the adaptive two-dimensional cycloid trajectory step calculated in step 33, two-dimensional adaptive cycloid trajectories are generated in sequence to fill the entire plane parameter area to obtain a plane variable radius cycloid trajectory with variable radius and step.

[0021] As a preferred embodiment, in step 33, the central axis constructed in step 32 is used as a guide line to generate a two-dimensional cycloid trajectory of one cycle, and the step value of the two-dimensional cycloid trajectory fed along the central axis is adaptively adjusted. The first point on the guide line is selected as the starting point of a cycloid cycle. According to the set number of cycloids m and the cycloid step value S, the two-dimensional cycloid trajectory of the next cycle is generated by continuous iterative calculation until all points on the guide line are traversed. The specific method includes the following steps:

[0022] Step 331: Preset the number of cycloid subdivisions m and the initial step length S of the cycloid. Subdivide the central axis constructed in step 32 according to S. A central axis of a distance S represents one cycle of the two-dimensional cycloid. The central axis of each cycle is further subdivided according to m to generate a plane central axis point set.

[0023] Step 332: Select the first point in the plane mid-axis point set generated in step 331 as the starting point for calculating the two-dimensional cycloid trajectory, and generate the two-dimensional cycloid trajectory according to the mathematical model of the two-dimensional cycloid trajectory.

[0024] As a preference, in step 332, the mathematical model of the two-dimensional cycloid trajectory is:

[0025]

[0026]

[0027]

[0028] is the first point on the central axis, and the corresponding point on the cycloid is , The coordinates of are known to be , Coordinate values ​​of Depend on The coordinate values ​​of are calculated. is a vector and coordinate system The angle of the axis, for point The position in the current cycle, is the current cycloid arc radius, is the tool radius.

[0029] As a preferred embodiment, in step 5, the contact model is established based on Hertz contact theory and Preston equation, including the following steps:

[0030] Step 51: Determine contact geometry and elastic parameters based on the geometric dimensions of the grinding wheel and the workpiece;

[0031] Step 52: Based on the contact geometry and elastic parameters determined in step 51, the contact pressure distribution at the contact point is calculated using Hertz contact theory;

[0032] Step 53: Calculate the material removal rate using the Preston equation combined with the contact pressure distribution obtained in step 52;

[0033] Step 54: Using numerical simulation technology, the data obtained in steps 51 to 53 are converted into a mathematical model of the contact model.

[0034] As a preference, in step 54, the mathematical model of the contact model is:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040] in The material removal depth of the polishing track point, is the contact pressure between the workpiece and the contact wheel, is the complete elliptic integral of the second kind, is the complete elliptic integral of the first kind, is the equivalent elastic modulus, is the ellipticity, is the contact pressure in the elliptical contact area, is the central pressure of the ellipse point, is the y coordinate of the current point, is the x coordinate of the current point, is the wear coefficient, is the contact pressure, is the relative speed between the grinding wheel and the workpiece, is the dwell time of the point, a is the major axis of the ellipse, b is the semi-axis of the ellipse, A is the maximum principal curvature, and B is the minimum principal curvature.

[0041] As a preferred embodiment, in step 6, the material removal variance is used as an iterative indicator to iteratively optimize the step value of the three-dimensional variable radius adaptive cycloid trajectory.

[0042] As a preference, in step 6, the iteration logic is: set a suitable mean square error of the material removal depth, gradually increase the step size at a smaller step size, stop the iteration when the mean square error of the material removal depth reaches the set value, otherwise continue to increase the step size.

[0043] As a preferred embodiment, in step 6, the formula for calculating the mean square error of the material removal depth is:

[0044]

[0045] in Remove the mean square error for the material, is the average material removal depth, The depth of material removal at each vertex of a triangulated mesh.

[0046] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0047] 1. The present invention extracts the three-dimensional geometric information of the workpiece to be polished and uses conformal geometry theory and angle-preserving mapping algorithms to generate a fine two-dimensional parametric grid model on the complex surface, thereby generating a planar variable-radius cycloid trajectory that adapts to changes in the workpiece surface, improving the fit between the trajectory and the workpiece surface, and thus improving the accuracy of trajectory planning.

[0048] 2. The present invention establishes a grinding and polishing contact model based on a planar variable radius cycloid trajectory, fully considers the influence of mechanical factors in the grinding and polishing process, calculates the material removal depth of the grinding and polishing contact point, and obtains a three-dimensional cycloid polishing path with uniform material removal through iterative optimization of the step size, which is beneficial to improving the grinding and polishing accuracy and efficiency.

[0049] 3. The present invention not only focuses on trajectory planning, but also regulates the uniformity of material removal. By establishing a simulation model and calculating the material removal rate based on Hertz contact theory and Preston equation, it can accurately predict and regulate the grinding and polishing process, ensure that the material removal is more evenly distributed on the workpiece surface, optimize the uniformity of material removal, avoid over- or under-polishing, and improve the polishing quality.

[0050] 4. The present invention iteratively optimizes the step value of the three-dimensional variable radius adaptive cycloid trajectory, and based on the mean square error of the material removal depth as a feedback indicator, realizes dynamic adjustment of the polishing process, can automatically find the optimal step setting, reduce human trial and error, and achieve the best polishing effect efficiency.

[0051] 5. The present invention utilizes simulation, including calculation of polishing material removal and distribution uniformity evaluation, to provide reliable predictions before actual operation, reducing the cost and time of physical experiments; at the same time, the iterative logic based on the simulation results ensures the scientific nature and efficiency of the optimization process.

[0052] 6. The present invention takes into account a variety of polishing process parameters, such as contact pressure, contact radius, elastic modulus, etc. The flexible setting of these parameters enables the method to be widely applicable to workpieces of different materials and shapes, enhancing the versatility and practicality of the method. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a flow chart of the method for three-dimensional cycloid trajectory planning and material removal uniformity control of the robot belt grinding and polishing of the present invention;

[0054] Figure 2 It is a schematic diagram of the three-dimensional mesh model;

[0055] Figure 3 It is a schematic diagram of a two-dimensional parametric mesh model obtained by using the conformal mapping algorithm;

[0056] Figure 4 It is a schematic diagram of the central axis of the two-dimensional parametric grid model;

[0057] Figure 5 It is a schematic diagram of the two-dimensional cycloid trajectory;

[0058] Figure 6 It is a schematic diagram of the plane variable radius cycloid trajectory on the two-dimensional parametric grid model;

[0059] Figure 7 It is a schematic diagram of the three-dimensional variable radius adaptive cycloid trajectory with the initial step length;

[0060] Figure 8 is a schematic diagram of the contact model;

[0061] Figure 9 It is a schematic diagram of the three-dimensional trochoidal polishing trajectory with uniform material removal. DETAILED DESCRIPTION

[0062] The present invention will be described in further detail below with reference to the embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0063] like Figure 1 As shown, a method for three-dimensional cycloid trajectory planning and material removal uniformity control of a robot belt grinding and polishing process includes the following steps:

[0064] Step 1: Import the workpiece model data into the CAM software to obtain a 3D model of the workpiece. Select the polishing area and set the relevant polishing process parameters. These parameters include the contact pressure between the workpiece and the abrasive wheel, the abrasive wheel's speed, the workpiece geometry, the mean square error (MSD) iteration target for the material removal depth, and the tool radius and shape. The 3D model of the workpiece to be polished is created using a triangular mesh.

[0065] Step 2: Calculate the polishing area selected in step 1 according to conformal geometry theory, and use the conformal mapping algorithm (ABF++ parameter mapping technology) to transform the polishing surface from 3D mapping to 2D parameter domain to generate a 2D parameter mesh model. Figure 2 and Figure 3 As shown in the figure, there are three-dimensional mesh model and two-dimensional parametric mesh model obtained by using conformal mapping algorithm.

[0066] Step 3: From the two-dimensional parameter mesh model generated in step 2, extract the center axis of the polished surface in the two-dimensional parameter domain, and generate a planar variable radius cycloid trajectory along the center axis. Figure 4 Shown is the extracted central axis in the 2D parametric mesh model.

[0067] The method of extracting the central axis of the polished surface in the two-dimensional parameter domain and generating a planar variable radius cycloid trajectory along the central axis includes the following steps:

[0068] Step 31: Perform Delaunay triangulation on the two-dimensional parametric grid model generated in step 2 and generate a Voronoi diagram;

[0069] Step 32: Construct the central axis using the Voronoi diagram algorithm;

[0070] Step 33: Using the central axis constructed in step 32 as a guide line, generate a periodic two-dimensional cycloid trajectory, and adaptively adjust the step value of the two-dimensional cycloid trajectory fed along the central axis;

[0071] In step 33, the central axis constructed in step 32 is used as the guide line to generate a two-dimensional cycloid trajectory of one cycle, and the step value of the two-dimensional cycloid trajectory fed along the central axis is adaptively adjusted. The first point on the guide line is selected as the starting point of a cycloid cycle. According to the set number of cycloids m and the cycloid step value S, the two-dimensional cycloid trajectory of the next cycle is generated by continuous iterative calculation until all points on the guide line are traversed. The specific method includes the following steps:

[0072] Step 331: Preset the number of cycloid subdivisions m and the initial step size S of the cycloid. Subdivide the central axis constructed in step 32 according to S. The central axis of a distance S represents one cycle of the two-dimensional cycloid. The central axis of each cycle is further subdivided according to m to generate a plane central axis point set. When a step size value is small, the distribution of the two-dimensional cycloid should be relatively redundant.

[0073] Step 332: Select the first point in the plane mid-axis point set generated in step 331 as the starting point for calculating the two-dimensional cycloid trajectory, and generate the two-dimensional cycloid trajectory according to the mathematical model of the two-dimensional cycloid trajectory.

[0074] The schematic diagram of the two-dimensional cycloid trajectory is as follows Figure 5 shown.

[0075] In step 332, the mathematical model of the two-dimensional cycloid trajectory is:

[0076]

[0077]

[0078]

[0079] is the first point on the central axis, and the corresponding point on the cycloid is , The coordinates of are known to be , Coordinate values ​​of Depend on The coordinate values ​​of are calculated. is a vector and coordinate system The angle of the axis, for point The position in the current cycle, is the current cycloid arc radius, is the tool radius.

[0080] Step 34: Based on the adaptive two-dimensional cycloid trajectory step calculated in step 33, two-dimensional adaptive cycloid trajectories are generated in sequence to fill the entire plane parameter area to obtain a plane variable radius cycloid trajectory with variable radius and step.

[0081] In step 34, for each plane mid-axis point set, the corresponding cycloid knife contact point is calculated using the mathematical model of the two-dimensional adaptive cycloid trajectory in step 33, generating a period of two-dimensional adaptive cycloid trajectory. Step 33 is repeated until all plane mid-axis point sets on the mid-axis are traversed, generating a complete plane variable radius cycloid trajectory in the two-dimensional parameter domain. Figure 6 As shown, the planar variable radius cycloid trajectory generated on the two-dimensional parametric grid model.

[0082] Step 4: The plane variable radius cycloid trajectory generated in step 3 is inversely mapped back to the polishing area selected by the three-dimensional model of the workpiece to be polished to obtain the three-dimensional variable radius adaptive cycloid trajectory of the initial step; Figure 7 As shown, a schematic diagram of a three-dimensional variable radius adaptive cycloid trajectory with an initial step distance generated on a three-dimensional model of a workpiece to be polished.

[0083] Step 5: Establish a contact model, simulate the grinding and polishing process of the contact model based on the three-dimensional variable radius adaptive cycloid trajectory of the initial step obtained in step 4, and calculate the grinding and polishing material removal;

[0084] The schematic diagram of the contact model is as follows Figure 8As shown, the workpiece contacts the grinding wheel at point 𝑜, 𝑦𝑒 is the direction of the maximum relative principal curvature, 𝑥𝑒 is the direction of the minimum relative principal curvature, 𝑦l is the direction of the tool contact speed, 𝑥l is perpendicular to 𝑦l, 𝑘𝑤1 is the direction of the minimum principal curvature of the workpiece, 𝑘𝑡1 is the direction of the minimum principal curvature of the grinding wheel (the axial direction of the grinding wheel), and 𝑘𝑡2 is the direction of the maximum principal curvature of the grinding wheel, where 𝑘𝑡1=0, 𝑅𝑐 is the radius of the grinding wheel. 𝜓 is the angle between the direction of the tool contact velocity 𝑦l and the direction of the minimum principal curvature of the workpiece 𝑘𝑤1; 𝛾 is the angle between the direction of the minimum principal curvature of the workpiece 𝑘𝑤1 and the direction of the minimum principal curvature of the grinding wheel 𝑘𝑡1; 𝛼 is the angle between the direction of the minimum principal curvature of the grinding wheel 𝑘𝑡1 and the vertical direction of the tool contact velocity 𝑥l.

[0085] In step 5, the contact model is established based on Hertz contact theory and Preston equation, including the following steps:

[0086] Step 51: Determine contact geometry and elastic parameters based on the geometric dimensions of the grinding wheel and the workpiece;

[0087] Step 52: Based on the contact geometry and elastic parameters determined in step 51, the contact pressure distribution at the contact point is calculated using Hertz contact theory;

[0088] Step 53: Calculate the material removal rate using the Preston equation combined with the contact pressure distribution obtained in step 52;

[0089] Step 54: Using numerical simulation technology, the data obtained in steps 51 to 53 are converted into a mathematical model of the contact model.

[0090] In step 54, the mathematical model of the contact model is:

[0091]

[0092]

[0093]

[0094]

[0095]

[0096] in The material removal depth of the polishing track point, is the contact pressure between the workpiece and the contact wheel, is the complete elliptic integral of the second kind, is the complete elliptic integral of the first kind, is the equivalent elastic modulus, is the ellipticity, is the contact pressure in the elliptical contact area, is the central pressure of the ellipse point, is the y coordinate of the current point, is the x coordinate of the current point, is the wear coefficient, is the contact pressure, is the relative speed between the grinding wheel and the workpiece, is the dwell time of the point, a is the major axis of the ellipse, b is the semi-axis of the ellipse, A is the maximum principal curvature, and B is the minimum principal curvature.

[0097] In the present invention, the workpiece is stationary relative to the grinding wheel, so 𝑣 is represented by the rotational speed of the grinding wheel.

[0098] Step 6: Quantitatively evaluate the uniformity of the distribution of polishing material removal across the entire surface. Based on the polishing material removal calculated in step 5, iteratively optimize the step size of the three-dimensional variable radius adaptive cycloid trajectory to achieve a uniform trajectory distribution.

[0099] In step 6, the material removal variance is used as an iterative indicator to iteratively optimize the step value of the three-dimensional variable radius adaptive cycloid trajectory.

[0100] The iterative logic is: set a suitable mean square deviation of the material removal depth, gradually increase the step size at a smaller step size, and stop the iteration when the mean square deviation of the material removal depth reaches the set value, otherwise continue to increase the step size.

[0101] The formula for calculating the mean square deviation of material removal depth is:

[0102]

[0103] in Remove the mean square error for the material, is the average material removal depth, The depth of material removal at each vertex of a triangulated mesh.

[0104] Step 7: Post-processing to obtain a three-dimensional cycloid trajectory with uniform material removal.

[0105] The three-dimensional cycloidal polishing trajectory with uniform material removal is finally obtained through iterative calculation, such as Figure 9 shown.

[0106] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be determined by the appended claims.

Claims

1. A method for three-dimensional cycloid trajectory planning and material removal uniformity control for abrasive belt grinding and polishing robot, characterized in that: The following steps are involved: Step 1: Import the model data of the workpiece to be polished into the CAM software, obtain the 3D model of the workpiece to be polished, select the polishing area, and set the relevant polishing process parameters; Step 2: Calculate the polishing area selected in step 1 according to conformal geometry theory, transform the polishing surface from a 3D mapping into a 2D parametric domain, and generate a 2D parametric mesh model; Step 3: Extract the central axis of the polished surface in the two-dimensional parameter domain from the two-dimensional parametric mesh model generated in step 2, and generate a planar variable radius cycloid trajectory along the central axis; Step 4: The planar variable radius cycloid trajectory generated in step 3 is inversely mapped back to the polishing area selected by the three-dimensional model of the workpiece to be polished to obtain a three-dimensional variable radius adaptive cycloid trajectory of the initial step length; Step 5: Establish a contact model, simulate the grinding and polishing process of the contact model based on the three-dimensional variable radius adaptive cycloid trajectory of the initial step obtained in step 4, and calculate the grinding and polishing material removal; Step 6: Quantitatively evaluate the uniformity of the distribution of polishing material removal across the entire surface. Based on the polishing material removal calculated in step 5, iteratively optimize the step size of the three-dimensional variable radius adaptive cycloid trajectory to achieve a uniform trajectory distribution. Step 7: Post-processing to obtain a three-dimensional cycloid trajectory with uniform material removal; In step 5, the contact model is established based on Hertz contact theory and Preston equation, including the following steps: Step 51: Determine contact geometry and elastic parameters based on the geometric dimensions of the grinding wheel and the workpiece; Step 52: Based on the contact geometry and elastic parameters determined in step 51, the contact pressure distribution at the contact point is calculated using Hertz contact theory; Step 53: Calculate the material removal rate using the Preston equation combined with the contact pressure distribution obtained in step 52; Step 54: using numerical simulation technology, converting the data obtained in steps 51 to 53 into a mathematical model of the contact model; In step 54, the mathematical model of the contact model is: Where 𝑀𝑅𝑅 is the material removal depth of the grinding and polishing trajectory point, 𝛿 is the contact pressure between the workpiece and the contact wheel, ℱ(𝜅) is the complete elliptic integral of the second kind, 𝜀(𝜅) is the complete elliptic integral of the first kind, 𝐸𝑐 is the equivalent elastic modulus, 𝑘 is the ellipticity, 𝑝(𝑥𝑒,𝑦𝑒) is the contact pressure of the elliptical contact area, 𝑝𝑜 is the central pressure of the elliptical point, 𝑦𝑒 is the y-coordinate of the current point, 𝑥𝑒 is the x-coordinate of the current point, 𝐾𝑝 is the wear coefficient, 𝑝 is the contact pressure, 𝑣 is the relative speed between the grinding wheel and the workpiece, ∇𝑡 is the dwell time at the point, a is the major axis of the ellipse, b is the semi-axis of the ellipse, A is the maximum principal curvature, and B is the minimum principal curvature; In step 6, the material removal variance is used as an iterative indicator to iteratively optimize the step value of the three-dimensional variable radius adaptive cycloid trajectory; In step 6, the iteration logic is: set a suitable mean square error of the material removal depth, gradually increase the step size at a smaller step size, and stop the iteration when the mean square error of the material removal depth reaches the set value, otherwise continue to increase the step size.

2. A method for three-dimensional cycloid trajectory planning and material removal uniformity control for abrasive belt grinding and polishing robot according to claim 1, characterized in that: In step 2, a conformal mapping algorithm is used to transform the polished surface from a three-dimensional mapping to a two-dimensional parameter domain.

3. The method for three-dimensional cycloid trajectory planning and material removal uniformity control of a robot belt grinding and polishing process according to claim 1, characterized in that: In step 3, extracting the central axis of the polished surface in the two-dimensional parameter domain and generating a planar variable radius cycloid trajectory along the central axis includes the following steps: Step 31: Perform Delaunay triangulation on the two-dimensional parametric grid model generated in step 2 and generate a Voronoi diagram; Step 32: Construct the central axis using the Voronoi diagram algorithm; Step 33: Using the central axis constructed in step 32 as a guide line, generate a periodic two-dimensional cycloid trajectory, and adaptively adjust the step value of the two-dimensional cycloid trajectory fed along the central axis; Step 34: Based on the adaptive two-dimensional cycloid trajectory step calculated in step 33, two-dimensional adaptive cycloid trajectories are generated in sequence to fill the entire plane parameter area to obtain a plane variable radius cycloid trajectory with variable radius and step.

4. The method for three-dimensional cycloid trajectory planning and material removal uniformity control for abrasive belt grinding and polishing by a robot according to claim 3, characterized in that: In step 33, the specific method includes the following steps: Step 331: Preset the number of cycloid subdivisions m and the initial step length S of the cycloid. Subdivide the central axis constructed in step 32 according to S. A central axis of a distance S represents one cycle of the two-dimensional cycloid. The central axis of each cycle is further subdivided according to m to generate a plane central axis point set. Step 332: Select the first point in the plane mid-axis point set generated in step 331 as the starting point for calculating the two-dimensional cycloid trajectory, and generate the two-dimensional cycloid trajectory according to the mathematical model of the two-dimensional cycloid trajectory.

5. The method for three-dimensional cycloid trajectory planning and material removal uniformity control of a robot belt grinding and polishing process according to claim 4, characterized in that: In step 34, for each plane mid-axis point set, the corresponding cycloid knife contact point is calculated through the mathematical model of the two-dimensional adaptive cycloid trajectory in step 33, and a periodic two-dimensional adaptive cycloid trajectory is generated. Step 33 is repeated until all plane mid-axis point sets on the central axis are traversed, and a complete plane variable radius cycloid trajectory in the two-dimensional parameter domain is generated.

6. The method for three-dimensional cycloid trajectory planning and material removal uniformity control for abrasive belt grinding and polishing by a robot according to claim 5, characterized in that: In step 332, the mathematical model of the two-dimensional cycloid trajectory is: is the first point on the central axis, and the corresponding point on the cycloid is , The coordinates of are known to be , Coordinate values ​​of Depend on The coordinate values ​​of are calculated. is a vector and coordinate system The angle of the axis, for point The position in the current cycle, is the current cycloid arc radius, is the tool radius.

7. The method for three-dimensional cycloid trajectory planning and material removal uniformity control for robotic belt grinding and polishing according to claim 1, characterized in that: In step 6, the formula for calculating the mean square deviation of material removal depth is: Where 𝑀 is the mean square error of material removal, 𝑄̅ is the average material removal depth, and 𝑄𝑖 is the material removal depth at each vertex of the triangular mesh model.

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