TOOL AND METHOD FOR ANGLE COMPENSATION WHEN MACHINING AT LEAST ONE WORKPIECE WITH ONE TOOL

Abstract

Tool (1; 2), with a drive (13) for receiving a tool element (14) for treating at least one workpiece (6; 7), a sensor (17) attached to the tool (1; 2) for detecting a movement of the tool (1;2) is arranged in a sensor coordinate system (xS, yS, zS), a transformation unit (161) configured to determine whether the sensor coordinate system (xS, yS, zS) and the tool element axis coordinate system (XA, YA, ZA) are different from each other, and to transform the sensor coordinate system (xS, yS, zS) to a tool element axis coordinate system (XA, YA, ZA) or the tool element axis coordinate system (XA, YA, ZA) to the sensor coordinate system (xS, yS, zS) if it has been determined that the sensor coordinate system (xS, yS, zS) and the tool element axis coordinate system (XA, YA, ZA) are arranged differently from each other with respect to a fixed point (P) in space, and a compensation unit (162) to compensate for a movement detected by the sensor (17), which the tool (1; 2) during angle-controlled treatment of at least one workpiece (6;7) performs, taking into account the transformation of the transformation unit (161).;

Description

The present invention relates to a tool and a method for angle compensation when machining at least one workpiece with a tool, in particular a hand-held tool. Tools are used for many different types of workpiece machining. For example, tools are used to drive screws into or out of a workpiece. Such tools can also be used for drilling or milling. Furthermore, tools are used for riveting, welding, punching, and so on. All of these methods of machining a workpiece with a tool have in common that the tool must be positioned at a predetermined angle to the workpiece. When driving a screw with a screwdriver in industrial manufacturing, it is also essential to ensure the correct functioning of the screw connection that the screw is tightened at a predetermined angle. If screws need to be driven into locations that are difficult for the tool to access, the tool must be guided by hand.Further reasons for using hand-held tools include greater flexibility, for example in small batch production or rework assembly stations. In these situations, numerous deviations from the ideal position of the tool relative to the workpiece and / or the screw can occur. For example, it is possible to provide a tool operator with assistance before machining the workpiece to ensure the tool is correctly positioned on the workpiece and / or the fastener. Such assistance is not always quick and reliably applicable for an operator, especially if the tool needs to be held very steadily and possibly in a difficult-to-access location without adequate support. If the tool is twisted by the operator while tightening the screw, it cannot be definitively determined whether the screw was tightened to the predetermined angle. Another challenge arises from the fact that different screw heads need to be mounted on a single screwdriver for various machining tasks, such as a flat wrench, an angled head, a straight drive, an offset drive, a feed drive, etc. Positioning a sensor to measure the tool's rotation in a way that is usable for all screw drives is difficult, as the screw axis and the sensor axis typically need to coincide to measure the rotation, preferably using a rotation rate. With rotatable angled heads as tool drives, it is conceivable to mount the sensor near the tool drive so that it can also rotate. In this case, however, the sensor must be adjusted to the screw axis of the drive. The disadvantage of this approach is that the mechanical adjustment is complex and requires expert knowledge.Using an external sensor interface to solve this problem proves electrically and mechanically challenging. Furthermore, the number of output axes is limited by the restricted number of mounting positions for a sensor attached to the tool housing. Therefore, the object of the present invention is to provide a tool and a method for angle compensation when machining at least one workpiece with a tool, with which the aforementioned problems can be solved. In particular, a tool and a method for angle compensation when machining at least one workpiece with a tool, especially a hand-held tool, are to be provided, with which the predetermined machining of the workpiece with the tool can be ensured reliably and cost-effectively, both for different outputs on the tool and when the tool is moved relative to the workpiece. This problem is solved by a tool according to claim 1. The tool has a drive for receiving a tool element for processing at least one workpiece, a sensor arranged on the tool for detecting movement of the tool in a sensor coordinate system, a transformation unit configured to determine whether the sensor coordinate system and the tool element axis coordinate system are different from each other, and to transform the sensor coordinate system to a tool element axis coordinate system or the tool element axis coordinate system to the sensor coordinate system if it has been determined that the sensor coordinate system and the tool element axis coordinate system are arranged differently from each other with respect to a fixed point in space, and a compensation unit for compensating for a movement detected by the sensor.which the tool performs during angle-controlled treatment of at least one workpiece, taking into account the transformation of the transformation unit. This tool makes it very easy to compensate for the operator's movement of the tool on the screw connection when using handheld or hand-guided screwdrivers. The influence of the operator's movement can be measured and taken into account, even if the sensor coordinate system and the tool element axis coordinate system are not identical. Therefore, the output and the motion sensor do not need to be on the same axis or aligned with each other. This allows all types of outputs with different axes of rotation to be mounted on the screwdriver. All types of mechanical outputs, especially screw outputs, can be subsequently mounted on the tool, eliminating the need for subsequent mechanical adjustment of the sensors. Another advantage is that the sensors can be integrated cost-effectively into the electronics of the tool. Another advantage is that inaccuracies in the manufacturing process during the positioning of the sensors can be subsequently compensated for by a correction transformation of the sensor coordinate system. This ensures that the predetermined machining of the workpiece with the tool is reliable and cost-effective, regardless of the tool's output or whether the tool is moving relative to the workpiece. In the case of a screwdriving tool, the predetermined machining operation specifically refers to tightening a screw with a predetermined angle of rotation and / or tightening torque. Advantageous further embodiments of the tool are specified in the dependent claims. In a preferred embodiment, the sensor system of the tool described above includes a 3-spatial-axis motion sensor. The sensor may be an electronic component and mounted on the tool's electronics. Preferably, for a wide range of applications, the tool also has an interface for the detachable mounting of the output shaft, so that the output shaft can be exchanged for another output shaft. The output shaft may be an angled head, a flat wrench, a straight drive, an offset drive, or even a feed drive, all designed to accommodate a socket wrench such as a screwdriver bit or socket, etc. It is also conceivable that the interface is designed such that the output shaft can be mounted at the interface in predetermined degree increments relative to the tool's base axis. Additionally or alternatively, the interface and / or the tool can be designed such that the interface can assume any spatial axis relative to a defined base axis of the tool. Preferably, the tool is a handheld tool or mounted on a hand-held holder. According to one design variant, the tool also has a parameterization unit to guide an operator of the tool to parameterize the transformation unit in order to adapt the coordinate system transformation to the currently mounted output. The tool described above can be a screwdriver, a drill, and / or a milling tool. Alternatively, the tool can be a welding tool. Alternatively, the tool can be a riveting tool. Alternatively, the tool can be a clinching tool or a pressure joining tool. Alternatively, the tool can be a cutting tool. Alternatively, the tool can be a punching tool. The problem is further solved by a method for angle compensation when machining at least one workpiece with a tool, in particular a hand-held tool, according to claim 10. The tool has an output for receiving a tool element for processing at least one workpiece and sensors arranged on the tool to detect movement of the tool in a sensor coordinate system.The procedure comprises the following steps: Determining whether the sensor coordinate system and the tool element axis coordinate system are different from each other; Transforming, using a transformation unit of the tool, of the sensor coordinate system to a tool element axis coordinate system or of the tool element axis coordinate system to the sensor coordinate system, if it was determined in the determination step that the sensor coordinate system and the tool element axis coordinate system are arranged differently from each other with respect to a fixed point in space; and Compensating, using a compensation unit, for a movement detected by the sensor that the tool performs during angle-controlled treatment of at least one workpiece, taking into account the transformation of the transformation unit. The process achieves the same advantages as previously mentioned in relation to the tool. Other possible implementations of the invention also include combinations of features or embodiments described previously or subsequently with regard to the exemplary embodiments, even if not explicitly mentioned. In such cases, the person skilled in the art will also add individual aspects as improvements or additions to the respective basic form of the invention. The invention is described in more detail below with reference to the accompanying drawing and exemplary embodiments. Figure 1 shows a three-dimensional view of a tool according to a first embodiment; and Figure 2 shows a three-dimensional view of a tool according to a second embodiment. In the figures, identical or functionally equivalent elements are provided with the same reference symbols unless otherwise specified. Fig. 1 schematically shows a tool 1, which in the example shown is a handheld screwdriver. However, if required, the tool 1 can alternatively be used for drilling or milling. The tool 1 of Fig. 1 is held by a worker or operator 5 during the processing of at least one workpiece 6, 7 in order to screw a screw 8 into or out of the workpiece 6, 7. Alternatively, the tool 1 can also be mounted and held on a device or holder (not shown), which is moved in space, in particular by hand or manually. The tool 1, with its housing on which a handle 11 is provided, is axially symmetrical about an axis 10A, except for its tool head. The axis 10A will therefore subsequently also be referred to as the basic axis 10A of the tool 1. The handle 11 can also be used to mount the tool 1 on the device (not shown). At one end of the tool 1's housing, an interface 12 is provided for connecting an electrical cable (not shown). The tool 1 is supplied with electrical energy via this cable. At the other end of the tool 1 or its housing, an output 13 is provided, which is designed to receive a tool element 14. The output 13 can be set into a rotary motion DR about an axis 13A by a drive 15 (shown very schematically) in the direction of rotation indicated by the block arrow in Fig. 1.This also sets the tool element 14 into a rotary motion DR about an axis ZA of a tool element coordinate system XA, YA, ZA. In the coordinate system XA, YA, ZA, the axes XA, YA, ZA are each arranged perpendicular to each other. The tool element 14, when attached to the tool 1, is an interchangeable screwdriver bit for turning or tightening the screw 8 by a rotation angle DW. When correctly mounted on the tool 1, the tool element 14 is rigidly or backlash-free coupled to the output 13. Likewise, when correctly mounted on the tool 1, the output 13 is rigidly or backlash-free coupled to the drive 15. The tool 1 also has electronics 16 with a transformation unit 161 and a compensation unit 162, which are also shown very schematically. The electronics 16 can have or be a control unit with which the drive 15 is controlled. This indirectly also controls the output 13 coupled to the drive 15 and the tool element 14 coupled to the output 14. In tool 1, the electronics 16 control the rotation angle DW and, optionally, the rotational speed of the drive 15, thereby controlling the corresponding dimensions of the output 13 and the tool element 14. A sensor 17 on tool 1 detects the rotation rate or rotation angle DW of the tool element 14 about the axis 13A. The rotation angle DW is related to the angle by which the screw 8 is turned or screwed into the at least one workpiece 6, 7. However, the rotation angle DW does not exactly correspond to the angle by which the screw 8 is turned or screwed into the at least one workpiece 6, 7 by means of the drive 15 if tool 1 is rotated by the angles +ΔW or -ΔW while the screw 8 is being turned, for example, by a movement of the operator 5 of tool 1. Thus, the rotation angle DW deviates by the angle +ΔW or -ΔW during the described movements of the operator 5 of tool 1.It should also be taken into account that the operator 5 of the tool 1, while turning the screw 8, first rotates the tool 1 in the direction of an arrow in Fig. 1 by an angle +ΔW and then at least partially rotates it in the direction of an arrow in Fig. 1 by an angle -ΔW. The angle -ΔW can be larger or smaller. Furthermore, it is possible that the operator 5 performs the movement by different angles +ΔW or -ΔW several times. Therefore, the sensor 17 also detects possible rotational movement(s) of the tool 1 around the axis 13A as an angle +ΔW in the direction of rotation of the output 13 and thus of the tool element 14 and the screw 8 or an angle -ΔW against the direction of rotation of the output 13. Motion detection is performed by the sensor 17 in the sensor coordinate system xS, yS, zS, in which the axes xS, yS, zS are each perpendicular to one another. In the example shown in Fig. 1, the sensor 17 has a 3-axis motion sensor for this purpose. The sensor 17 is protected within the tool 1 as an electronic component mounted on the electronics 16. The tool element coordinate system XA, YA, ZA typically deviates from the sensor coordinate system xS, yS, zS. This deviation arises because the sensor coordinate system xS, yS, zS and the tool element axis coordinate system XA, YA, ZA are arranged differently in space relative to a fixed point 20. In the example shown, the reason could be that the output 13 of tool 1 is designed as an angled head whose axis is the same as axis 13A. As shown in Fig. 1, axes 10A and 13A are approximately perpendicular to each other. More generally, axes 10A and 13A can be aligned at a predetermined angle to each other. Furthermore, it is possible that the sensor axes 17 are not precisely aligned with the tool element coordinate system XA, YA, ZA. Therefore, transformation unit 161 is provided, which converts the sensor coordinate system xS, yS, zS to the tool element coordinate system XA, YA, ZA using a rotation matrix if transformation unit 161 determines that the tool element coordinate system XA, YA, ZA differs from the sensor coordinate system xS, yS, zS. Alternatively, transformation unit 161 can convert the tool element axis system XA, YA, ZA to the sensor coordinate system xS, yS, zS using the rotation matrix. Where The coordinate transformation is performed using the three independent Eulerian angles that describe the orientation of an object in three-dimensional space. The transformation from a so-called "space-fixed" system, which here corresponds to the sensor axes, is achieved by appropriately rotating it on a "body-fixed" system, which here corresponds to the screw output axes. Alternatively, a transformation can be performed from a so-called "body-fixed" system, which here corresponds to the screw output axes, to a so-called "space-fixed" system, which here corresponds to the sensor axes. The rotation is carried out using so-called rotation matrices (R). For coordinate transformation, the type and sequence of rotations are important. Six different rotation sequence combinations are known for three consecutive rotations around three axes. The axis of rotation can be the same for the first and third rotations. A coordinate transformation can be performed, for example, by rotating the coordinate system according to the "z, y', x''" convention, similar to the German industrial standards DIN 8855 and / or DIN 18709-4. Here, the sensor coordinate system is rotated around three different spatial axes in the sequence: rotation around the z-axis, rotation around the y-axis, and rotation around the x-axis. This allows, for example, the calculation of the rotation rate of the output caused by tool movement, which can be determined from the rotation rate measured at the sensor as shown below. Alternatively, a rotation rate of the sensor can be calculated, which can be determined from the rotation rate at the output as follows. Where the vectors and for a rotation rate can be represented with the 3 components x, y, z as Here, the rotation matrix represents a rotation from the sensor coordinate system to the screw coordinate system. The rotation matrix is ​​the vector product of the three rotation matrices about their respective spatial axes and is: where α, β, and γ describe the respective rotation angles according to Euler about the spatial axes x, y, z, and the rotation matrices are: The solution of the rotation matrix follows general mathematical principles and will not be explained further here. The aforementioned rotation angles α, β and γ around the respective spatial axes z, y, x are parameterized via a user interface provided by the operator 5. For example, a rotation about the Z-axis by the angle γ corresponds to a rotation of the angle head as shown in Fig. 2. In the embodiment according to Fig. 2, the angles a and β are each parameterized to 0°. The compensation unit 162 compensates the rotation angle DW by means of the transformation of the transformation unit 161 and the detection of the angles +ΔW, -ΔW. Thus, the compensation unit 162, taking into account all movements of the operator 5 of the tool 1 and the deviations of the coordinate systems of the sensor 17 and the tool element 14 or the screw 8, compensates the rotation angle DW of the tool element 14 or the screw 8 by the angles +ΔWK, -ΔWK. The compensation unit can therefore compensate for a movement detected by the sensor, which the tool 1 performs during angle-controlled processing of at least one workpiece 6, 7, taking into account the transformation of the transformation unit 161. The angle +ΔWK or -ΔWK determined by the compensation unit 162 is transmitted to the control unit of the electronics 16, for example via a bus system such as CAN bus, ARCNET, Ethernet, KNX, and other fieldbuses, etc. Therefore, the electronics 16, in particular the control unit for controlling the drive 15 and thus the output 13 coupled to the drive 15 and the tool element 14 coupled to the output 13, can use the angles +ΔWK or -ΔWK and compensate the rotation angle DW accordingly. Accordingly, the sensor coordinate system is converted or transformed to the screw axis coordinate system using the transformation unit 161. This allows the sensor 17 and the output 13, and therefore the tool element 14, to be positioned and oriented differently relative to each other. In the manner described above, a method for angle compensation is performed with the tool 1 when machining at least one workpiece 6, 7 with a tool 1, in particular a hand-held tool. As described, a rotational movement caused by a movement of the tool 1 by the operator 5 during the tightening of the screw 8 in the direction of rotation or against the direction of rotation is detected by the previously described design of the tool 1 and compensated for via the drive 15. With the tool 1, a transformation of a variable screw coordinate system to a sensor coordinate system within a hand-held electric screwdriver as tool 1 is possible. This allows the rotation angle DW of the screw 8 in the at least one workpiece 6, 7 to be controlled very easily, correctly and reliably. Preferably, the electronics 16, in particular the transformation unit 161 and the compensation unit 162, and the sensor system 17 are designed such that the described angle compensation is performed in real time. According to the standard DIN 44300 (Information processing), Part 9 (Processing sequences), which has since been superseded by DIN ISO / IEC 2382, real time is understood to mean the operation of a computer system in which programs for processing incoming data are constantly ready for operation, such that the processing results are available within a predetermined time period. Depending on the application, the data can be generated according to a random temporal distribution or at predetermined times.Accordingly, the electronics 16, in particular the transformation unit 161 and the compensation unit 162, and the sensor system 17 are designed such that their hardware and software do not cause or cause any delays that would prevent compliance with these conditions. Therefore, the processing of the data supplied by the electronics 16 and the sensor system 17 in the tool 1 is guaranteed to be fast enough for the machining process of the at least one workpiece 6, 7. Fig. 2 shows a tool 2 according to a second embodiment. In contrast to the first embodiment, it is possible here to detachably mount the output 13 to be installed on the tool 2 at an interface 13B at different mounting angles MW to the axis 13A. The interface 13B thus detachably receives the output 13. Otherwise, the tool 2 is constructed in the same way as described with respect to the tool 1 of the first embodiment. Therefore, the tool 2 has a parameterization unit 18 with which the operator 5 can adapt the coordinate system transformation by the transformation unit 161 to different outputs 13, such as an angle head or a flat wrench or a straight output or an offset output or a feed output, and / or different axes 13A as a screw axis. In the example shown in Fig. 2, the output is an angled head mounted at an angle of 0° to axis 13A as the screw axis. As shown in Fig. 2, however, the angled head can be rotated on the tool 2 in 15° increments relative to axis 13A as the screw axis. Of course, any other increments besides 15° are also possible. In the example shown in Fig. 2, the operator 5 would enter the degree value 0° after being prompted by the parameterization unit 18, for example, on a screen of the tool 2 or the parameterization unit 18. The entered degree value, in this case 0°, is then taken into account during the coordinate system transformation by the transformation unit 161. Otherwise, tool 2 according to the present embodiment is designed like tool 1 according to the preceding embodiment. This also allows the angle compensation method to be carried out with tool 2 when machining at least one workpiece 6, 7 with a tool 1, in particular a hand-held tool. In this process, the rotation angle DW of the screw 8 in the at least one workpiece 6, 7 can also be detected very easily, correctly, and reliably without having to rotate and laboriously adjust the sensor 17. Thus, with tool 2, a parameterizable transformation of a variable screw coordinate system to a sensor coordinate system within a handheld electric screw tool as tool 2 is possible. In a modification of the previously described tool 2, the parameterization unit 18 is at least partially a part of the electronics 16. In a modification of the previously described tool 2, the tool 2, in particular its electronics 16, communicates with an external display unit to query the data for the parameterization unit 18 from the operator 5. In a further modification of the previously described tool 2, the interface 13B and / or the tool 2 are designed such that the interface 13B can assume any spatial axis relative to a defined basic axis 10A of the tool 2. This allows the tool 2 to be used very flexibly for changing machining situations. All previously described configurations of the tools 1, 2, the electronics 16, the sensor system 17, the parameterization unit 18, and the angle compensation method can be used individually or in any possible combination. In particular, all features and / or functions of the previously described embodiments can be combined as desired. Additionally, the following modifications are particularly conceivable. The parts shown in the figures are schematic and may differ in their exact design from the forms shown in the figures, as long as their previously described functions are guaranteed. Naturally, tool 1 can also have an interface 13B for mounting various outputs 13, such as an angle head, a flat wrench, a straight output, an offset output, or a feed output. In this case, it is preferable for tool 1 to also have the parameterization unit 18 so that the operator 5 can adapt the coordinate system transformation to the different outputs 13, such as an angle head, a flat wrench, a straight output, an offset output, or a feed output, using the transformation unit 161. The sensor 17 does not have to be mounted as an electronic component on the electronics 16, but can be provided at any suitable location in the tool 1, 2. If required, the coordinate system transformation function can be configured to be deactivated. For example, deactivation can be selected when it is ensured that the sensor coordinate system xS, yS, zS and the tool element coordinate system XA, YA, ZA match. However, it is preferable that the deactivation be disabled after the output 13 has been removed. This way, after mounting a new or the same output 13, the operator 5 can be prompted again to configure the newly mounted output 13 to determine whether the coordinate system transformation function can be deactivated again. Instead of the described screwdriving, drilling, or milling tool 1, 2, the invention described above can also be used with any other tool, in particular a hand-held tool, such as a riveting tool, welding tool, cutting tool, clinching / press joining tool, or punching tool. In particular, units 16, 17, 18 can be used with any joining tool. The tools 1, 2 can also be tools 1, 2 with a suspension that can be maneuvered by the operator 5, in particular to vary the horizontal position of the tool 1, 2 in space as needed. The suspension can also make the respective tool 1, 2 adjustable vertically or in height. More generally, the position of the tool 1, 2 in space can be varied. Alternatively, the tool 1, 2 may be designed for manual operation with a battery, particularly a rechargeable battery. Alternatively or additionally, the described wired connection to a power supply network is possible. In this case, the tool 1, 2 is a corded tool.

Claims

Tool (1; 2), with a drive (13) for receiving a tool element (14) for treating at least one workpiece (6; 7), a sensor (17) attached to the tool (1; 2) for detecting a movement of the tool (1;2) is arranged in a sensor coordinate system (xS, yS, zS), a transformation unit (161) configured to determine whether the sensor coordinate system (xS, yS, zS) and the tool element axis coordinate system (XA, YA, ZA) are different from each other, and to transform the sensor coordinate system (xS, yS, zS) to a tool element axis coordinate system (XA, YA, ZA) or the tool element axis coordinate system (XA, YA, ZA) to the sensor coordinate system (xS, yS, zS) if it has been determined that the sensor coordinate system (xS, yS, zS) and the tool element axis coordinate system (XA, YA, ZA) are arranged differently from each other with respect to a fixed point (P) in space, and a compensation unit (162) to compensate for a movement detected by the sensor (17), which the tool (1; 2) during angle-controlled treatment of at least one workpiece (6;7) performs, taking into account the transformation of the transformation unit (161).; Tool (1; 2) according to claim 1, wherein the sensor (17) comprises a 3-spatial-axis motion sensor. Tool (1; 2) according to claim 1 or 2, wherein the sensor (17) is an electronic component and is mounted on an electronics (16) of the tool (1; 2). Tool (1; 2) according to one of the preceding claims, furthermore with an interface (13B) for the detachable receiving of the output (13), so that the output (13) is interchangeable with another output (13). Tool (1; 2) according to claim 4, wherein the output (13) is an angled head or a flat wrench or a straight output or an offset output or a feed output, which are designed as a tool element (14) to receive a socket wrench in the form of a screw bit or a screwdriver socket etc. Tool (2) according to claim 4 or 5, wherein the interface (13B) is configured such that the output (13) can be mounted on the interface (13B) in predetermined degree increments relative to the base axis (10A) of the tool (2), and / or wherein the interface (13B) and / or the tool (2) is configured such that the interface (13B) can assume any spatial axis relative to a defined base axis (10A) of the tool (2). Tool (1; 2) according to one of the preceding claims, wherein the tool (1; 2) is a handheld tool or is mounted on a hand-held holder. Tool (1; 2) according to one of the preceding claims, furthermore comprising a parameterization unit (18) for guiding an operator (5) of the tool (1; 2) for parameterizing the transformation unit (161) in order to adapt the coordinate system transformation to the currently mounted output (13). Tool (1; 2) according to one of the preceding claims, wherein the tool (1; 2) is a screw tool and / or a drilling tool and / or a milling tool, or wherein the tool (1; 2) is a welding tool, or wherein the tool (1; 2) is a riveting tool, or wherein the tool (1; 2) is a piercing / press joining tool, or wherein the tool (1; 2) is a cutting tool, or wherein the tool (1; 2) is a punching tool. Method for angle compensation when machining at least one workpiece (6; 7) with a tool (1; 2) having a drive (13) for receiving a tool element (14) for processing at least one workpiece (6; 7) and a sensor (17) arranged on the tool (1; 2) for detecting a movement of the tool (1; 2) in a sensor coordinate system (xS, yS, zS), wherein the method comprises the steps of determining whether the sensor coordinate system (xS, yS, zS) and the tool element axis coordinate system (XA, YA, ZA) are different from each other, transforming, with a transformation unit (161) of the tool (1;2) of the sensor coordinate system (xS, yS, zS) to a tool element axis coordinate system (XA, YA, ZA) or of the tool element axis coordinate system (XA, YA, ZA) to the sensor coordinate system (xS, yS, zS), if it was determined during the determination step that the sensor coordinate system (xS, yS, zS) and the tool element axis coordinate system (XA, YA, ZA) are arranged differently from each other with respect to a fixed point (20) in space, and compensation, with a compensation unit, of a movement detected by the sensor (17) which the tool (1; 2) performs during angle-controlled treatment of the at least one workpiece (6; 7), taking into account the transformation of the transformation unit (161).;

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