Novel industrial robot joint speed reducer based on conjugate face gear
By adopting a nutation transmission structure with conjugate surface gears, the problems of large structure, high friction loss, and small transmission ratio of traditional reducers are solved. This achieves a compact design and high load-bearing capacity of the reducer, improves transmission accuracy, and meets the stability requirements of industrial robots under high load and high speed.
Patent Information
- Application Number
- CN202520531450.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-25
- Publication Date
- 2025-12-09
- Estimated Expiration
- 2035-03-25
AI Technical Summary
Traditional reducers have a large structure, high friction loss, small transmission ratio, poor load-bearing capacity, high precision requirements, and are difficult to manufacture, making it difficult to meet the stability requirements of industrial robots under high load, high speed and long-term operation.
The nutation transmission structure based on conjugate surface gears is adopted, including an input shaft, a fixed surface gear, an output surface gear, a nutation surface gear set, and a housing. Through the meshing transmission of conjugate surface gears, high tolerance and large transmission ratio are achieved, thereby improving load-bearing capacity and transmission accuracy.
This technology achieves a compact reducer structure, large transmission ratio, strong load-bearing capacity, and high transmission accuracy, reducing processing difficulty and meeting the stability requirements of industrial robots operating under high loads and high speeds.
Smart Images

Figure CN223648501U_ABST
Abstract
Description
Technical Field
[0001] This utility model relates to the field of speed reducer technology, and in particular to a novel industrial robot joint speed reducer based on conjugate surface gears. Background Technology
[0002] Industrial robots are widely used in manufacturing, especially in the automotive, electronics, and precision machining industries, replacing workers in certain monotonous, frequent, and repetitive long-term tasks. As one of the core components of an industrial robot, the joint reducer is mainly used to transmit power, reduce rotational speed, and minimize transmission errors. With the continuous development of industrial robot technology, especially the increasing demand for precision and reliability, the joint reducer has become increasingly important in industrial robots.
[0003] A speed reducer must not only have a high transmission ratio, but also ensure stability and durability under high load, high speed and long-term operation. Traditional speed reducers have a large structure and, while achieving the speed reduction function, they have problems such as large friction loss, small transmission ratio, poor load-bearing capacity, high precision requirements and difficult processing. Utility Model Content
[0004] In view of the above-mentioned defects or deficiencies in the existing technology, it is desirable to provide a novel industrial robot joint reducer based on conjugate surface gears. It adopts a nutation transmission structure, which is compact and has a large transmission ratio. The conjugate surface gear meshing transmission structure has a high surface meshing overlap, stronger load-bearing capacity, and the high tolerance of surface gears can reduce the processing difficulty.
[0005] This utility model provides a novel industrial robot joint reducer based on conjugate surface gears, comprising:
[0006] An input shaft includes a first shaft segment, a second shaft segment, and a third shaft segment. The axis of the first shaft segment coincides with the axis of the third shaft segment. The second shaft segment is located between the first shaft segment and the third shaft segment, and the extension line of the axis of the second shaft segment intersects the extension lines of the axes of the first shaft segment and / or the third shaft segment to form a preset angle. The input shaft is used as an input end.
[0007] A fixed-face gear is rotatably sleeved on the first shaft segment of the input shaft and serves as a fixed end.
[0008] The output gear is rotatably mounted on the third shaft segment of the input shaft and serves as the output end;
[0009] The nutating surface gear set includes a first nutating surface gear and a second nutating surface gear that are fixedly connected. Both the first nutating surface gear and the second nutating surface gear are rotatably sleeved on the second shaft segment of the input shaft. The first nutating surface gear meshes with the fixed surface gear, and the second nutating surface gear meshes with the output surface gear. When the input shaft rotates, it drives the nutating surface gear set to perform nutating motion.
[0010] Furthermore, the fixed-face gear has a tooth difference with the first nutating-face gear, the output-face gear has a tooth difference with the second nutating-face gear, and the fixed-face gear has a tooth difference with the output-face gear.
[0011] Furthermore, an output shaft is fixedly sleeved on the outer wall of the output gear.
[0012] Furthermore, the fixed-face gear, the output-face gear, the first shaft segment, and the third shaft segment are coaxially arranged; the first nutating-face gear, the second nutating-face gear, and the second shaft segment are coaxially arranged; the fixed-face gear is rotatably connected to the first shaft segment via a first inner bearing; the first nutating-face gear is rotatably connected to the second shaft segment via a second inner bearing; the second nutating-face gear is rotatably connected to the second shaft segment via a third inner bearing; and the output-face gear is rotatably connected to the third shaft segment via a fourth inner bearing.
[0013] Furthermore, an eccentric bushing is fixedly sleeved on the outer wall of the first shaft segment. The eccentric bushing is located between the first inner bearing and the second inner bearing. The inner ring of the second inner bearing is in contact with the end face of the eccentric bushing near one end face. An intermediate bushing is fixedly sleeved on the outer wall of the third shaft segment. The intermediate bushing is located between the third inner bearing and the fourth inner bearing. The inner ring of the third inner bearing is in contact with the end face of the intermediate bushing near one end face.
[0014] Furthermore, a bearing sleeve is fixedly sleeved on the inner ring of the nutating gear set, and the bearing sleeve is fixedly sleeved on the outer ring of the second inner bearing and the third inner bearing.
[0015] Furthermore, it also includes a housing, in which the input shaft, the fixed surface gear, the output surface gear, the nutating surface gear set, and the output shaft are all disposed.
[0016] Furthermore, the fixed-face gear is fixedly connected to the inner wall of the housing by screws, and the output shaft is rotatably connected to the inner wall of the housing by an outer bearing.
[0017] Furthermore, the housing is used for fixed connection with the robot support; the first shaft segment of the input shaft extends out of the housing and connects to an external input mechanism; one end of the output shaft extends out of the housing and connects to an external output mechanism.
[0018] Furthermore, the preset included angle is 2.5°.
[0019] Compared with the prior art, the beneficial effects of this utility model are:
[0020] When the input shaft of this invention rotates, it drives the nutating surface gear set to perform nutating motion. The second nutating surface gear meshes with the output surface gear. Therefore, when the second nutating surface gear performs nutating motion, it drives the output surface gear meshing with it to rotate around the axis of the input shaft. The speed reduction purpose of the reducer is achieved through surface gear transmission. This application makes the reducer structure more compact while achieving speed reduction. Moreover, this application adopts a nutating transmission structure, which has the characteristic of a large transmission ratio. The use of conjugate surface gear meshing transmission improves the gear meshing overlap ratio and increases the load-bearing capacity of the reducer. Furthermore, the high tolerance of the surface gear improves the transmission accuracy of the reducer. The surface gear structure is simple and reduces the processing difficulty.
[0021] It should be understood that the description in this utility model description section is not intended to limit the key or essential features of the embodiments of this utility model, nor is it intended to restrict the scope of this utility model. Other features of this utility model will become readily apparent from the following description. Attached Figure Description
[0022] Other features, objects, and advantages of this invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:
[0023] Figure 1 This is a cross-sectional view of the present invention;
[0024] Figure 2 This is a three-dimensional assembly drawing of the present invention (box body omitted);
[0025] Figure 3 This is an exploded view of the present invention (excluding the casing);
[0026] Figure 4 This is a schematic diagram of the input shaft structure in this utility model;
[0027] Figure 5 This is a schematic diagram of the fixed-surface gear in this utility model;
[0028] Figure 6 This is a schematic diagram of the nutating surface gear set in this utility model;
[0029] Figure 7This is a schematic diagram of the output gear and output shaft in this utility model;
[0030] The labels in the diagram are: 1. Input shaft; 200. Fixed surface gear; 300. Output surface gear; 400. Nutting surface gear set; 500. Output shaft; 600. Housing; 700. Sealing ring;
[0031] 110. First axle segment; 120. Second axle segment; 130. Third axle segment;
[0032] 410. Chapter 1 Moving Gears; 420. Chapter 2 Moving Gears;
[0033] 201. First inner bearing;
[0034] 301. Fourth inner bearing; 302. Outer bearing;
[0035] 401. Second inner bearing; 402. Third inner bearing; 403. Eccentric bushing; 404. Intermediate bushing; 405. Bearing cup. Detailed Implementation
[0036] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.
[0037] It should be noted that, where there is no conflict, the embodiments and features in the embodiments of this utility model can be combined with each other. The present utility model will now be described in detail with reference to the accompanying drawings and embodiments.
[0038] Please refer to Figures 1 to 7 The present invention provides a novel industrial robot joint reducer based on conjugate surface gears, comprising an input shaft 100, a fixed surface gear 200, an output surface gear 300, a nutating surface gear set 400, and a housing 600.
[0039] The input shaft 100 includes a first shaft segment 110, a second shaft segment 120, and a third shaft segment 130. The axis of the first shaft segment 110 coincides with the axis of the third shaft segment 130. The second shaft segment 120 is located between the first shaft segment 110 and the third shaft segment 130, and the extended line of the axis of the second shaft segment 120 intersects the extended lines of the axes of the first shaft segment 110 and / or the third shaft segment 130 to form a preset angle. The input shaft 100 is used as an input end. Specifically, the axis of the first shaft segment 110 and its center line... The axis of the third shaft segment 130 coincides with its center line O3-O3, and the center line O1-O1 of the first shaft segment 110 coincides with the center line O3-O3 of the third shaft segment 130. The axis of the second shaft segment 120 coincides with its center line O2-O2. The center line O1-O1 of the first shaft segment 110 and the center line O2-O2 of the second shaft segment 120 intersect to form a preset angle of 2.5°, making the second shaft segment 120 an eccentric shaft segment.
[0040] The fixed surface gear 200 is rotatably sleeved on the first shaft segment 110 of the input shaft 100 and is used as a fixed end; specifically, the fixed surface gear 200 is fixedly connected to the inner wall of the housing 600 and the fixed surface gear 200 remains fixed.
[0041] The output gear 300 is rotatably sleeved on the third shaft segment 130 of the input shaft 100 and is used as the output end; specifically, the output gear 300 is rotatably connected to the inner wall of the housing 600.
[0042] The nutating gear set 400 includes a first nutating gear 410 and a second nutating gear 420 fixedly connected. Both the first nutating gear 410 and the second nutating gear 420 are rotatably mounted on the second shaft segment 120 of the input shaft 100. The first nutating gear 410 meshes with the fixed gear 200, and the second nutating gear 420 meshes with the output gear 300. When the input shaft 100 rotates, it drives the nutating gear set 400 to perform nutating motion. Specifically, the first nutating gear 410 and the second nutating gear 420 are integrally set and belong to a double gear, and the two move synchronously.
[0043] In this embodiment, the first shaft segment 110 of the input shaft 100 is connected to an external input mechanism, which drives the input shaft 100 to rotate around the center line O1-O1. Since the center line O2-O2 of the second shaft segment 120 of the input shaft 100 is at an angle to the center line O1-O1 of the first shaft segment 110, when the input shaft 100 rotates around the center line O1-O1, it drives the nutating surface gear set 400 to revolve around the center line O1-O1. Since the first nutating surface gear 410 meshes with the fixed surface gear 200, the nutating surface gear set 400... While revolving around the center line O2-O2, the gear 420 rotates around itself, which is called nutation. Since the second nutation gear 420 meshes with the output gear 300, and the output gear 300 is rotatably connected to the housing 600, when the nutation gear set 400 performs nutation, it drives the output gear 300 meshing with it to rotate around the center line O3-O3 (O1-O1), thus achieving the purpose of speed reduction of the reducer. During installation, the output gear 300 is connected to an external output mechanism (such as being fixed to the robot joint) to achieve control of the robot joint.
[0044] This application achieves speed reduction while making the reducer structure more compact. It also adopts a nutation transmission structure, which has the characteristics of a large transmission ratio. It uses conjugate face gear meshing transmission to improve the gear meshing overlap and increase the load-bearing capacity of the reducer. Furthermore, the high tolerance of the face gear improves the transmission accuracy of the reducer. The face gear structure is simple and reduces the processing difficulty.
[0045] In a preferred embodiment, such as Figure 2 As shown, there is a tooth difference between the fixed-face gear 200 and the first moving-face gear 410, a tooth difference between the output-face gear 300 and the second moving-face gear 420, and a tooth difference between the fixed-face gear 200 and the output-face gear 300. Specifically, the fixed-face gear 200 has Z1 teeth, the first moving-face gear 410 has Z2 teeth, Z1 < Z2, and the difference between their tooth counts is 2-3; the second moving-face gear 420 has Z3 teeth, the output-face gear 300 has Z4 teeth, Z4 < Z3, and the difference between their tooth counts is 2-3. The transmission ratio of the reducer is changed by adjusting the tooth ratio of the fixed-face gear 200, the first moving-face gear 410, the second moving-face gear 420, and the output-face gear 300.
[0046] In a preferred embodiment, such as Figure 2 , Figure 3 and Figure 6 As shown, an output shaft 500 is fixedly sleeved on the outer wall of the output gear 300.
[0047] In this embodiment, the output shaft 500 is cylindrical and is integrally formed with the output surface gear 300. The output shaft 500 is connected to the external output mechanism. When the output surface gear 300 rotates, it drives the output shaft 500 to rotate synchronously, thereby driving the external output mechanism to rotate and achieving deceleration.
[0048] In a preferred embodiment, such as Figure 1 As shown, the fixed-face gear 200, the output-face gear 300, the first shaft segment 110, and the third shaft segment 130 are coaxially arranged. The first moving-face gear 410, the second moving-face gear 420, and the second shaft segment 120 are coaxially arranged. The fixed-face gear 200 is rotatably connected to the first shaft segment 110 through the first inner bearing 201. The first moving-face gear 410 is rotatably connected to the second shaft segment 120 through the second inner bearing 401. The second moving-face gear 420 is rotatably connected to the second shaft segment 120 through the third inner bearing 402. The output-face gear 300 is rotatably connected to the third shaft segment 130 through the fourth inner bearing 301.
[0049] In this embodiment, the input shaft 100 is supported on the fixed surface gear 200 by the first inner bearing 201, the nutating surface gear set 400 is supported on the input shaft 100 by the second inner bearing 401 and the third inner bearing 402, and the output surface gear 300 is supported on the input shaft 100 by the fourth inner bearing 301. The support function is achieved through the corresponding bearings, so that the input shaft 100, the nutating surface gear set 400 and the output surface gear 300 can rotate stably.
[0050] Preferred, such as Figure 1 As shown, the input shaft 100, fixed surface gear 200, output surface gear 300, nutating surface gear set 400, and output shaft 500 are all housed within the housing 600. Specifically, the housing 600 protects the reducer structure from impacts and external damage.
[0051] Preferred, such as Figure 1 As shown, the fixed-face gear 200 is fixedly connected to the inner wall of the housing 600 by screws, and the output shaft 500 is rotatably connected to the inner wall of the housing 600 by an outer bearing 302. Specifically, the output shaft 500 and the output face gear 300 are coaxially fixedly connected, and the output face gear 300 is supported on the inner wall of the housing 600 by the outer bearing 302, which provides stable support for the output face gear 300 and allows the output face gear 300 and the output shaft 500 to rotate as a whole relative to the housing 600.
[0052] In a preferred embodiment, such as Figure 1As shown, an eccentric bushing 403 is fixedly sleeved on the outer wall of the first shaft segment 110. The eccentric bushing 403 is located between the first inner bearing 201 and the second inner bearing 401. The end face of the inner ring of the second inner bearing 401 near the eccentric bushing 403 is in contact with the end face of the eccentric bushing 403. An intermediate bushing 404 is fixedly sleeved on the outer wall of the third shaft segment 130. The intermediate bushing 404 is located between the third inner bearing 402 and the fourth inner bearing 301. The end face of the inner ring of the third inner bearing 402 near the intermediate bushing 404 is in contact with the end face of the intermediate bushing 404.
[0053] In this embodiment, the eccentric bushing 403 is fixedly sleeved on the first shaft segment 110. One end face of the eccentric bushing 403 abuts against one end face of the inner ring of the first inner bearing 201, and the other end face abuts against one end face of the inner ring of the second inner bearing 401. The fixed position of the eccentric bushing 403 can play a positioning role for the second inner bearing 401 and prevent the second inner bearing 401 from axial displacement. Similarly, one end face of the intermediate bushing 404 abuts against one end face of the inner ring of the third inner bearing 402, and the other end face abuts against one end face of the inner ring of the fourth inner bearing 301. The fixed position of the intermediate bushing 404 can play a positioning role for the third inner bearing 402 and prevent the third inner bearing 403 from axial displacement.
[0054] In a preferred embodiment, such as Figure 1 As shown, a bearing sleeve 405 is fixedly sleeved on the inner ring of the nutating surface gear set 400, and the bearing sleeve 405 is fixedly sleeved on the outer ring of the second inner bearing 401 and the third inner bearing 402.
[0055] In this embodiment, the bearing sleeve 405 is fixedly connected to the inner ring of the nutating gear set 400 by screws. The second inner bearing 401 and the third inner bearing 402 are interference-fitted with the inner ring of the bearing sleeve 405. Before assembly, the second inner bearing 401 and the third inner bearing 402 can be pressed into the bearing sleeve 405 in advance by a press. The pressure generated by the dimensional difference makes the second inner bearing 401 and the third inner bearing 402 tightly joined with the bearing sleeve 405. During assembly, the three can be directly fitted onto the second shaft section 120 as a whole to achieve quick bearing installation. The bearing sleeve 405 provides the installation base and support for the second inner bearing 401 and the third inner bearing 402. The inner ring of the bearing sleeve 405 is provided with a positioning ring. The second inner bearing 401 and the third inner bearing 402 abut against the positioning ring during installation, which can improve the positioning accuracy of the second inner bearing 401 and the third inner bearing 402 during installation.
[0056] In a preferred embodiment, such as Figure 1 , Figure 2 and Figure 3As shown, the housing 600 is used for fixed connection with the robot support; the first shaft segment 110 of the input shaft 100 extends outside the housing 600 and is connected to an external input mechanism; one end of the output shaft 100 extends outside the housing 600 and is connected to an external output mechanism.
[0057] Preferably, in order to prevent dust and other impurities from falling into the reducer during actual use, a sealing ring 700 is installed at the left end of the reducer (between the first shaft segment 110 of the input shaft 100 and the housing 600) to provide a sealing function. A sealing structure can also be set at the right end of the reducer according to actual installation requirements.
[0058] Working principle:
[0059] The external input mechanism is fixedly connected to the first shaft segment 110 of the input shaft 100. When the external input mechanism drives the input shaft 100 to rotate around the center line O1-O1, due to the existence of a preset included angle, the nutating surface gear set 400 revolves around the center line O1-O1. Since the first nutating surface gear 410 meshes with the fixed surface gear 200, the nutating surface gear set 400 rotates around the center line O2-O2 while revolving, which is to say, it performs nutating motion. Since the second nutating surface gear 420 meshes with the output surface gear 300, and the output surface gear 300 is rotatably connected to the housing 600, when the nutating surface gear set 400 performs nutating motion, it drives the output surface gear 300 meshing with it to rotate around the center line O3-O3 (O1-O1), which in turn drives the output shaft 500, which is fixedly connected to the output surface gear 300, to rotate synchronously. The output shaft 500 is fixedly connected to the external output mechanism (such as fixed to the robot joint), thereby achieving the deceleration purpose of the reducer.
[0060] This application achieves speed reduction while making the reducer structure more compact. It also adopts a nutation transmission structure, which has the characteristics of a large transmission ratio. It uses conjugate face gear meshing transmission to improve the gear meshing overlap and increase the load-bearing capacity of the reducer. Furthermore, the high tolerance of the face gear improves the transmission accuracy of the reducer. The face gear structure is simple and reduces the processing difficulty.
[0061] In the description of this specification, the terms "connection," "installation," and "fixing," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a direct connection or an indirect connection through an intermediate medium. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.
[0062] In the description of this specification, the terms "one embodiment," "some embodiments," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.
[0063] The above are merely preferred embodiments of this application and are not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.
Claims
1. A novel industrial robot joint reducer based on conjugate surface gears, characterized in that, include: An input shaft includes a first shaft segment, a second shaft segment, and a third shaft segment. The axis of the first shaft segment coincides with the axis of the third shaft segment. The second shaft segment is located between the first shaft segment and the third shaft segment, and the extension line of the axis of the second shaft segment intersects the extension lines of the axes of the first shaft segment and / or the third shaft segment to form a preset angle. The input shaft is used as an input end. A fixed-face gear is rotatably sleeved on the first shaft segment of the input shaft and serves as a fixed end. The output gear is rotatably mounted on the third shaft segment of the input shaft and serves as the output end; The nutating surface gear set includes a first nutating surface gear and a second nutating surface gear fixedly connected. Both the first nutating surface gear and the second nutating surface gear are rotatably sleeved on the second shaft segment of the input shaft. The first nutating surface gear meshes with the fixed surface gear, and the second nutating surface gear meshes with the output surface gear. When the input shaft rotates, it drives the nutating surface gear set to perform nutating motion.
2. The novel industrial robot joint reducer based on conjugate surface gears according to claim 1, characterized in that, The fixed-face gear has a tooth difference with the first nutating-face gear, the output-face gear has a tooth difference with the second nutating-face gear, and the fixed-face gear has a tooth difference with the output-face gear.
3. A novel industrial robot joint reducer based on conjugate surface gears according to claim 1, characterized in that, An output shaft is fixedly sleeved on the outer wall of the output gear.
4. A novel industrial robot joint reducer based on conjugate surface gears according to claim 1, characterized in that, The fixed-face gear, the output-face gear, the first shaft segment, and the third shaft segment are coaxially arranged. The first nutating-face gear, the second nutating-face gear, and the second shaft segment are coaxially arranged. The fixed-face gear is rotatably connected to the first shaft segment via a first inner bearing. The first nutating-face gear is rotatably connected to the second shaft segment via a second inner bearing. The second nutating-face gear is rotatably connected to the second shaft segment via a third inner bearing. The output-face gear is rotatably connected to the third shaft segment via a fourth inner bearing.
5. A novel industrial robot joint reducer based on conjugate surface gears according to claim 4, characterized in that, An eccentric bushing is fixedly sleeved on the outer wall of the first shaft segment. The eccentric bushing is located between the first inner bearing and the second inner bearing. The end face of the inner ring of the second inner bearing near the eccentric bushing is in contact with the end face of the eccentric bushing. An intermediate bushing is fixedly sleeved on the outer wall of the third shaft segment. The intermediate bushing is located between the third inner bearing and the fourth inner bearing. The end face of the inner ring of the third inner bearing near the intermediate bushing is in contact with the end face of the intermediate bushing.
6. A novel industrial robot joint reducer based on conjugate surface gears according to claim 4, characterized in that, A bearing sleeve is fixedly fitted on the inner ring of the nutating surface gear set, and the bearing sleeve is fixedly fitted on the outer ring of the second inner bearing and the third inner bearing.
7. A novel industrial robot joint reducer based on conjugate surface gears according to claim 3, characterized in that, It also includes a housing, in which the input shaft, the fixed surface gear, the output surface gear, the nutating surface gear set, and the output shaft are all disposed.
8. A novel industrial robot joint reducer based on conjugate surface gears according to claim 7, characterized in that, The fixed-face gear is fixedly connected to the inner wall of the housing by screws, and the output shaft is rotatably connected to the inner wall of the housing by an external bearing.
9. A novel industrial robot joint reducer based on conjugate surface gears according to claim 7, characterized in that, The housing is used for fixed connection with the robot support; the first shaft segment of the input shaft extends out of the housing and connects to an external input mechanism; one end of the output shaft extends out of the housing and connects to an external output mechanism.
10. A novel industrial robot joint reducer based on conjugate surface gears according to claim 1, characterized in that, The preset included angle is 2.5°.