Robot spiral path online measurement compensation method, working method of robot and robot

Abstract

The invention belongs to the technical field of robot track control and machining process measurement and control, and particularly relates to a robot spiral path on-line measurement compensation method, a robot working method and a robot. The robot spiral path on-line measurement compensation method comprises the steps that the radius, the lead, the number of turns, the number of sampling points and the feeding speed of spiral motion are set, and a nominal cutter location point sequence is generated; when the robot executes a spiral track, radius error and attitude angle data are synchronously collected, and time-angle alignment is completed; measuring shaft rotation calculation is completed by combining attitude information, a displacement error is projected to an actual measuring shaft direction, a compensation vector is calculated in a target plane, and smooth transition of feeding and retracting is achieved; the nominal cutter location point sequence is corrected through a compensation vector, and equal-arc-length resampling is carried out based on the accumulated arc length; and finally, outputting the compensated control program, and issuing the compensated control program to a robot controller to realize online compensation. According to the invention, the roundness and lead error of the spiral path can be effectively reduced, and the geometric accuracy and machining consistency of the workpiece are improved.

Description

Technical Field

[0001] This invention belongs to the field of robot trajectory control and machining process measurement and control technology, and particularly relates to an online measurement and compensation method for robot spiral path, a robot working method, and a robot. Background Technology

[0002] Helical trajectory machining is an important process in the industrial manufacturing field, including milling, laser additive manufacturing, and cladding. Helical milling is widely used in scenarios such as hole drilling, hole enlargement, cylindrical surface machining, and processing of difficult-to-machine materials due to its advantages such as low cutting force, good heat dissipation and chip removal, and friendly requirements for equipment rigidity. Laser additive manufacturing and cladding achieve workpiece shaping and surface modification through helical scanning, and their applications are becoming increasingly widespread in high-end manufacturing.

[0003] Robots, as flexible machining execution platforms, have become an important carrier for realizing helical trajectory machining. However, in practical applications, robots still face many technical challenges when performing helical path machining. The high flexibility of robots, servo lag, and acceleration / deceleration effects can easily cause trajectory deviations, which are reflected in the roundness, coaxiality, and lead errors of the helical cross-section. At the same time, slow-varying disturbances such as spindle error motion and thermal drift can further affect machining accuracy. Changes in the posture of the tool or nozzle will change the direction of the displacement projection measured by the sensor. If compensation is performed according to a fixed coordinate axis or a preset normal, the observed and compensated directions are prone to inconsistencies, leading to under-compensation or over-compensation posture displacement coupling problems. In laser additive manufacturing and cladding processes, the nozzle-workpiece gap has a significant impact on machining quality. Existing technologies mostly use single-variable closed-loop control to monitor and maintain this gap, but this is disconnected from the multi-axis pose compensation of the helical trajectory and is difficult to integrate into the same control link, making it impossible to achieve collaborative optimization.

[0004] In existing technologies, some solutions focus on the programmed process and parameterized control of helical milling, without realizing the fusion compensation of online attitude information and displacement observation. Other solutions perform closed-loop control of process parameters for laser cladding, but do not couple it with the pose compensation of the helical trajectory. A general method that can take into account multiple processes, integrate displacement and attitude measurement, and achieve unified compensation has not yet been formed. Summary of the Invention

[0005] The purpose of this invention is to provide an online measurement and compensation method for a robot's spiral path, a robot's working method, and a robot in order to solve the above-mentioned problems.

[0006] To achieve the above objectives, the present invention provides the following solution: A method for online measurement and compensation of a robot's helical path, comprising the following steps: S1. The robot executes the preset spiral motion parameters according to the nominal blade position sequence, and acquires the radius error data and attitude angle information in real time during the working process. The sampling amount and sampling frequency of the radius error data and attitude angle information are matched with the nominal blade position of the preset spiral motion parameters. S2. Based on the acquired attitude angle information, perform measurement axis rotation calculation, project the displacement error onto the actual measurement axis direction, and extract the visible error components in the projection plane; S3. Calculate the compensation vector in the projection plane based on the radius error data and visible error components; S4. Based on the compensation vector, the nominal knife site sequence is corrected to generate the corrected knife site sequence; S5. Based on the cumulative arc length, the corrected tool position sequence is resampled with equal arc length to generate and output the compensated spiral path control program, which is then sent to the robot controller for execution.

[0007] Preferably, step S1 further includes preprocessing the radius error data and the attitude angle information. The preprocessing steps include filtering, interpolation, outlier removal, and boundary correction.

[0008] Preferably, step S3 further includes achieving a smooth transition between the tool advance stage and the tool retraction stage through a cosine window weighting function.

[0009] Preferably, in step S3, amplitude and rate of change constraints need to be applied to the compensation vector.

[0010] A method for operating a robot involves processing a workpiece using a compensated helical path control program obtained from the aforementioned online measurement and compensation method for the robot's helical path.

[0011] A robot, used to perform robot working methods.

[0012] Preferably, it includes a robot body, an end effector, a workpiece fixing mechanism, and an online measurement component.

[0013] Preferably, the online measurement component includes a displacement measurement sensor and a tilt measurement sensor. The tilt measurement sensor is mounted on the end effector. One end of the displacement measurement sensor is connected to the end effector, and the other end is connected to a positioning ball rod. The positioning ball rod is connected to a positioning ball on a positioning ball base, and the positioning ball base is fixedly mounted on a workpiece fixing mechanism.

[0014] Preferably, the robot body includes a cutting robot, the workpiece fixing mechanism includes a fixed workbench, the end effector includes a spindle motor fixed to the end of the cutting robot, the output end of the spindle motor is equipped with a cutting tool, and the workpiece is fixed on the working surface of the fixed workbench.

[0015] Preferably, the robot body includes a laser processing robot, with a laser head mounted at the end of the laser processing robot, and the workpiece fixing mechanism includes a rotary table, with the workpiece fixed on the working surface of the rotary table.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: This invention achieves the fusion processing of displacement and attitude information. By calculating the rotation of the measurement axis, the displacement error is projected onto the actual measurement axis direction, effectively solving the undercompensation or overcompensation problem caused by attitude displacement coupling, and improving the accuracy of compensation. The method of this invention can effectively suppress trajectory deviations caused by factors such as robot compliance, servo dynamics, and thermal drift, improve the roundness, coaxiality, and lead accuracy of the helical cross section, and enhance the stability of the nozzle-workpiece gap in laser additive manufacturing and cladding processes. This ensures the consistency of workpiece geometric accuracy and processing quality, and provides technical support for the high-precision realization of robot helical trajectory processing.

[0017] The integrated compensation framework of this invention can be applied to various processing scenarios such as milling, laser additive manufacturing, cladding, and coating, without requiring significant adjustments for different processes, thus improving the versatility of the technical solution.

[0018] The cosine window smoothing and amplitude and rate of change constraints set in the compensation process of this invention can avoid abrupt trajectory changes and dynamic instability. Combined with equal arc length resampling, it can ensure uniform robot movement and reduce the impact of speed fluctuations on machining accuracy. At the same time, the engineering measures such as plane compensation and per-axis amplitude limiting provided can be stably deployed on robot platforms of different brands.

[0019] This invention supports online updates and offline program export of the real-time trajectory interface, adapts to different robot controller access requirements, and can also form linkage control with process parameters such as feed, power, and powder feeding. It can also superimpose advanced strategies such as frequency domain selective compensation and iterative learning control to achieve continuous optimization of processing accuracy. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort: Figure 1 This is a schematic diagram of the spiral path trajectory error measurement in this invention; Figure 2 This is a flowchart of the spiral trajectory error measurement and compensation process in this invention; Figure 3This is a schematic diagram of the error measurement of the helical trajectory of a cylindrical workpiece based on an industrial robot in this invention; Figure 4 This is a schematic diagram of helical milling of cylindrical workpieces based on a cutting robot in this invention; Figure 5 This is a schematic diagram of the application of laser additive / coating spiral trajectory processing based on a laser processing robot in this invention; Among them, 1. Displacement measurement sensor; 2. Positioning ball rod; 3. Positioning ball base; 4. Inclination measurement sensor; 5. Cutting robot; 6. Spindle motor; 7. Cutting tool; 8. Workpiece; 9. Fixed worktable; 10. Laser head; 11. Laser processing robot; 12. Rotary worktable. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0023] Reference Figures 1 to 2 This invention discloses an online measurement and compensation method for a robot's helical path, the steps of which are as follows: S1. The robot executes the preset spiral motion parameters according to the nominal blade position sequence, and acquires the radius error data and attitude angle information in real time during the working process. The sampling amount and sampling frequency of the radius error data and attitude angle information are matched with the nominal blade position of the preset spiral motion parameters. S2. Based on the acquired attitude angle information, perform measurement axis rotation calculation, project the displacement error onto the actual measurement axis direction, and extract the visible error components in the projection plane; S3. Calculate the compensation vector in the projection plane based on the radius error data and visible error components; S4. Based on the compensation vector, the nominal knife site sequence is corrected to generate the corrected knife site sequence; S5. Based on the cumulative arc length, the corrected tool position sequence is resampled with equal arc length to generate and output the compensated spiral path control program, which is then sent to the robot controller for execution.

[0024] In this invention, the robot first executes a preset program, generates a standard program after online measurement and compensation, and then sends the standard program to the robot controller for execution.

[0025] The step size range for equal arc length resampling is 0.25–1 mm.

[0026] Further optimization of the scheme includes preprocessing the radius error data and the attitude angle information in step S1. The preprocessing steps include filtering, interpolation, outlier removal, and boundary correction.

[0027] Data preprocessing includes zero-phase filtering, Savitzky-Golay bidirectional filtering, or median absolute deviation filtering.

[0028] Further optimization of the scheme includes, in step S3, using a cosine window weighting function to achieve a smooth transition between the tool approach and retraction phases. Cosine window fade-in and fade-out processing is employed to avoid abrupt changes in the tool trajectory during tool approach and retraction.

[0029] To further optimize the scheme, in step S3, it is also necessary to apply amplitude and rate of change constraints to the compensation vector.

[0030] The amplitude limit is set based on the equipment travel and the allowable fluctuations in the process, while the rate of change limit is used to suppress abrupt changes between adjacent sampling points.

[0031] A method for operating a robot involves using a compensated helical path control program obtained through an online measurement and compensation method for the robot's helical path to process a workpiece.

[0032] Reference Figures 3 to 5 A robot, used to perform the working methods of a robot.

[0033] Further optimization of the solution includes the robot body, end effector, workpiece fixing mechanism, and online measurement components.

[0034] The scheme is further optimized. The online measurement component includes a displacement measurement sensor 1 and an inclination measurement sensor 4. The inclination measurement sensor 4 is installed on the end effector. One end of the displacement measurement sensor 1 is connected to the end effector, and the other end is connected to the positioning ball rod 2. The positioning ball rod 2 is connected to the positioning ball on the positioning ball base 3. The positioning ball base 3 is fixedly installed on the workpiece fixing mechanism.

[0035] The design is further optimized so that the robot body includes a cutting robot 5, the workpiece fixing mechanism includes a fixed workbench 9, the end effector includes a spindle motor 6 fixed to the end of the cutting robot 5, the output end of the spindle motor 6 is equipped with a cutting tool 7, and the workpiece 8 is fixed on the working surface of the fixed workbench 9.

[0036] Further optimization of the scheme: the robot body includes a laser processing robot 11, a laser head 10 is installed at the end of the laser processing robot 11, and the workpiece fixing mechanism includes a rotary table 12, with the workpiece 8 fixed on the working surface of the rotary table 12.

[0037] The tilt sensor 4 has a measurement range of ±5–30°, an accuracy of 0.001–0.01°, and a sampling rate of 100–1000Hz.

[0038] Detailed method: The first step is to define the plane to be executed by the helical path, such as the XY plane, the direction of the tool's linear axis movement such as the Z-axis, the radius R of the helical motion execution, the helical lead h, the number of helical turns N, the number of sampling points K, and the feed rate, and complete the helical motion program based on the predetermined robot platform.

[0039] The second step is to set the required spiral motion, construct an equally spaced angular sequence, and calculate the nominal knife position and nominal radial vector; select a sufficient sampling rate to ensure that the spiral motion information can be fully collected; and then compare the nominal / observed / compensated values ​​at the same angular position and avoid phase mismatch caused by velocity fluctuations.

[0040] Specifically: Generate equally spaced angle sequences And calculate the coordinates of the nominal knife position. With the nominal radial vector . in, The initial height in the Z-axis direction of the helical motion; Let be the geometric angle of the k-th position in the spiral motion space, and let its range be [0, 2πN].

[0041] The third step involves installing a radius measurement sensor and a dual-axis angle sensor. While the robot performs a preset helical motion, the sensor collects helical motion data and synchronizes the data, ensuring alignment in time and angle. The radius error value during the helical motion is also collected. The bidirectional angle values, along the X and Y axes, are respectively The corresponding polar angle Then, first correct the fixed delay / estimate the slowly varying delay, and then interpolate each observation; process missing measurements (interpolation), duplicate angles (reduplication / averaging), and out-of-bounds (truncation) to obtain an equal-length, co-located angle domain sequence.

[0042] Specifically: in, It is a timestamp sequence representing the i-th moment of the measurement process, where x is the set of signals measured (x∈ ).

[0043] The fourth step is to process the collected data after it has been collected. Preprocessing is performed to complete zero-phase smoothing and outlier suppression. This prevents high-frequency noise from being "materialized" into jitter, thus achieving outlier suppression and avoiding "bad pixels ruining the entire spectrum." The collected data is smoothed using a centered moving average / zero-phase filter or bidirectional SG filter; signal spikes are filtered out using the median absolute deviation, and neighborhood interpolation is performed.

[0044] The specific data processing procedure is as follows: in, The value represents the smoothed window length, with a recommended value of 1121. MAD represents the median absolute deviation.

[0045] The fifth step involves performing attitude rotation calculations on the preprocessed results to determine the measurement axis position, ensuring that the error value is compensated in the correct compensation direction. The measurement data is rotated to the current measurement axis direction in a fixed sequence (determined by the measurement plane).

[0046] The specific operation process is as follows: in, and These represent rotation matrices around the X and Y axes respectively; the rotation order is "Rx first, then Ry"; This represents the intermediate measurement axis vector before rotation; This represents the unit vector of the measurement axis; This is a protection threshold to prevent division by zero and determine if the projection is too small. It ensures numerical stability and triggers backoff when the measurement axis is almost parallel to Z, avoiding the amplification of minor noise into significant XY compensation jitter.

[0047] Step 6: Perform compensation motion within the preset XY plane, focusing on compensating for visible errors within the plane. This improves the planar profile / roundness without changing the Z-lead. Specifically, this involves... Projected onto the XY plane and normalized to .

[0048] in, This represents the projection of the measurement axis onto the XY plane and the normalization process. It represents Projection in the X and Y directions.

[0049] Step 7: Compensation vector calculation. The compensation value is calculated point-by-point in reverse along the available direction based on the observation. For tool entry and exit, a co-rotation window is used to achieve gradual entry and exit, thereby avoiding traces caused by the tool contacting and exiting the workpiece.

[0050] in, For the compensation vector, This represents the weight during tool advance and retraction, with a value ranging from 0 to 1; This represents the choice between starting the cut and retracting the cut. When, it represents a tool retraction operation; when When, it represents the cutting operation.

[0051] The eighth step involves limiting the maximum amplitude or the rate of change of adjacent samples for the compensation vector along each axis to suppress abnormally large movements and high-frequency jagged edges, preventing abnormal spikes from being amplified into a single large compensation, which could trigger sudden stops or even physical collisions. In laser scenarios, this can also lead to instantaneous abrupt changes in layer thickness / energy density, leaving step patterns. Specifically, geometrical limiting ± is applied to ΔX and ΔY. It can also limit the rate of change of adjacent samples.

[0052] Specifically, the clamp function aims to restrict the value x to the interval [a, b]. It is determined by a combination of factors including equipment travel, safety clearance, and allowable process fluctuations. This represents the rate of change limit at the k-th position.

[0053] Step 9: Calculate the coordinates of the tool position after compensation. (The mathematical compensation value is...) ) converted into an executable trajectory ( ), and exclude protruding angles and abnormalities.

[0054] Step 10: Equidistant resampling of arc length enables the controller to maintain uniform speed operation, reducing dynamic shape errors and process fluctuations caused by speed. An equidistant grid is constructed based on the accumulated arc length, and a uniform point array is obtained by interpolating the X / Y / Z coordinates according to the arc length.

[0055] in, For the cumulative arc length The target arc length step size (within the range of 0.251); This represents an equidistant arc-length grid; This is the generated sequence of points with equal arc lengths; It is a one-dimensional interpolation function; Finally, by combining the robot platform, a helical machining control program with path trajectory error compensation is generated.

[0056] Example 1: Milling platform based on cutting robot 5.

[0057] Reference Figure 4 Taking a typical robotic milling platform as an example, the implemented system includes: a cutting robot 5 and a controller; an end-effector motor 6 and a cutting tool 7; a displacement measurement sensor 1 such as a ballbar or a linear variable differential transformer (LVDT); an inclination measurement sensor 4 preferably using a tilt meter or an IMU sensor outputting TCP attitude (Euler angles around X / Y); and control / compensation and interface: a real-time interface between an edge industrial computer and the robot.

[0058] Taking a common 6065T6 aluminum alloy cylindrical workpiece as an example, the workpiece needs to be machined with a diameter of 50 mm, a cutting depth of 12 mm, a spindle speed of 5000 RPM, a feed rate of 1200 mm / min, and a radial depth of cut of 2 mm. The cutting tool 7 used is a 10 mm diameter three-flute end mill with a 45-degree helix angle. The settings for helix measurement and compensation are as follows: R=50 mm, h=3 mm / turn, N=4, the sampling rate of the displacement sensor and tilting instrument is 100 Hz (corresponding to Ts=100 ms), the smoothing window w=11; the amplitude limit is [0.2,0.2,0.1] mm; the constant arc length step ds=0.5 mm. Comparing the roundness of the workpiece before and after processing revealed that the contour error curve showed that the peak-to-peak value was 0.2 mm before compensation and 0.08 mm after compensation, which was significantly reduced. The measured roundness value decreased from 90 µm before compensation to 55 µm.

[0059] Example 2: Laser Additive / Cladding / Coating Processing Platform Based on Laser Processing Robot 11 Reference Figure 5 The implemented system includes: a laser processing robot 11 and a controller; a laser head 10 suitable for directional energy deposition, cladding, or coating, whose nozzle and optical axis are defined as the z-axis direction of the tool position point; a displacement measurement sensor 1 using a linear variable differential transformer (LVDT) for real-time measurement of the distance from the nozzle end to the workpiece surface; an inclinometer 4 using an inclinometer for acquiring the nozzle tool position point posture (Euler angles around X / Y); control / compensation and interface are implemented by an edge industrial computer, and compensation signals are sent through the robot's real-time interface.

[0060] Taking a common cylindrical workpiece as an example, the workpiece has an outer radius of 50 mm and is coated using a spiral path method; the spiral pitch is 1.8 mm / turn, the weld width is approximately 3 mm, and the corresponding overlap rate is approximately 40%. The process reference parameters are: feed rate F0 = 600 mm / min, laser power... =800 W, powder delivery volume =8 g / min. To achieve stable molten pool and layer thickness, the sensor compensation settings are as follows: sampling rate 100–200Hz (corresponding sampling period Ts=5–10ms), smoothing window w=11; compensation limit [0.3,0.3,0.3]mm; constant arc length step ds=0.5mm. The height deviation ΔL output by the LVDT is used for real-time displacement compensation, and the attitude angle output by the inclinometer ( and It is used to correct the additional height error caused by nozzle tilt.

[0061] Comparing the processing effects before and after compensation, it can be seen that: the high fluctuation peak-to-peak value has been reduced from a large range of 0.5 mm before compensation to a significantly smaller range of 0.2 mm after compensation; the thickness of the cladding layer is more uniform, reduced from 0.25 mm before compensation to 0.12 mm, and the interlayer overlap texture is significantly improved.

[0062] In summary, under typical milling scenarios, the compensation method described in this invention reduces the peak-to-peak value of the contour error by 60.0%, and the roundness error by 38.9%, resulting in an overall improvement of approximately 49.5%. Under laser cladding scenarios, it reduces the peak-to-peak value of high-frequency fluctuations by 60.0%, improves coating thickness uniformity by 52.0%, and results in an overall improvement of approximately 56.0%. The results demonstrate that this invention can significantly suppress trajectory errors and process disturbances, improving workpiece geometric accuracy and process stability.

[0063] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0064] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for online measurement and compensation of a robot's helical path, characterized in that, The steps are as follows: S1. The robot executes the preset spiral motion parameters according to the nominal blade position sequence, and acquires the radius error data and attitude angle information in real time during the working process. The sampling amount and sampling frequency of the radius error data and attitude angle information are matched with the nominal blade position of the preset spiral motion parameters. S2. Based on the acquired attitude angle information, perform measurement axis rotation calculation, project the displacement error onto the actual measurement axis direction, and extract the visible error components in the projection plane; S3. Calculate the compensation vector in the projection plane based on the radius error data and visible error components; S4. Based on the compensation vector, the nominal knife site sequence is corrected to generate the corrected knife site sequence; S5. Based on the cumulative arc length, the corrected tool position sequence is resampled with equal arc length to generate and output the compensated spiral path control program, which is then sent to the robot controller for execution.

2. The method for online measurement and compensation of a robot helical path according to claim 1, characterized in that: Step S1 further includes preprocessing the radius error data and the attitude angle information. The preprocessing steps include filtering, interpolation, outlier removal, and out-of-bounds correction.

3. The method for online measurement and compensation of a robot helical path according to claim 1, characterized in that: Step S3 also includes achieving a smooth transition between the tool advance and retraction stages using a cosine window weighting function.

4. The method for online measurement and compensation of a robot helical path according to claim 1, characterized in that: In step S3, amplitude and rate of change constraints also need to be applied to the compensation vector.

5. A method for operating a robot, characterized in that, The compensated helical path control program obtained by the robot helical path online measurement and compensation method according to any one of claims 1-5 is used to process the workpiece.

6. A robot for performing the working method of the robot provided in claim 5.

7. A robot according to claim 6, characterized in that, It includes the robot body, end effector, workpiece fixing mechanism, and online measurement components.

8. A robot according to claim 7, characterized in that, The online measurement component includes a displacement measurement sensor (1) and an inclination measurement sensor (4). The inclination measurement sensor (4) is installed on the end effector. One end of the displacement measurement sensor (1) is connected to the end effector, and the other end is connected to the positioning ball rod (2). The positioning ball rod (2) is connected to the positioning ball of the positioning ball base (3). The positioning ball base (3) is fixedly installed on the workpiece fixing mechanism.

9. A robot according to claim 6, characterized in that, The robot body includes a cutting robot (5), the workpiece fixing mechanism includes a fixed workbench (9), the end effector includes a spindle motor (6) fixed at the end of the cutting robot (5), the output end of the spindle motor (6) is equipped with a cutting tool (7), and the workpiece (8) is fixed on the working surface of the fixed workbench (9).

10. A robot according to claim 6, characterized in that, The robot body includes a laser processing robot (11), with a laser head (10) installed at the end of the laser processing robot (11). The workpiece fixing mechanism includes a rotary table (12), with the workpiece (8) fixed on the working surface of the rotary table (12).

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