A visual guidance method for assembling H-shaped steel columns
Through the visually guided robotic arm and binocular camera system, the precise installation of H-shaped steel columns is achieved, solving the problem of insufficient alignment accuracy during the installation process, and improving assembly accuracy and efficiency.
Patent Information
- Application Number
- CN202310986260.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-08-07
- Publication Date
- 2025-08-29
- Estimated Expiration
- 2043-08-07
AI Technical Summary
It is difficult to achieve precise alignment between the pillars and the screw holes during the installation process, resulting in difficulty in installation.
The assembled robotic arm with visual guidance function is adopted, and position detection and fine-tuning is used for binocular cameras, ensuring the precise installation of the H-shaped steel columns by establishing two XY coordinate systems.
It improves the assembly accuracy of H-shaped steel columns, reduces manual cleaning frequency, reduces operating costs, and improves installation stability and efficiency.
Smart Images

Figure CN116833724B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of H-shaped steel column assembly equipment, and in particular to a visual guidance method for assembling an H-shaped steel column. Background Art
[0002] The high-speed rail contact network is erected using H-shaped steel columns. A single H-shaped steel column is heavy, and is installed using flanges welded to its bottom surface and bolts pre-buried in the ground foundation. The installation process is completed using a robotic arm clamping. However, due to the weight of the column and the robotic arm itself, there is huge inertia during the installation process, making it difficult to achieve the correct alignment accuracy between the column and the screw hole.
[0003] Therefore, it is necessary to provide a new H-shaped steel column assembly visual guidance method to solve the above technical problems. Summary of the Invention
[0004] In order to solve the above technical problems, the present invention provides a visual guidance method for assembling an H-shaped steel column.
[0005] The present invention provides a visual guidance method for assembling an H-shaped steel column, comprising the following steps:
[0006] 1) Clamp the H-shaped steel column by using an assembly robot with visual guidance function;
[0007] 2) Use an assembly robot with visual guidance function to carry the H-beam to the installation location. During the transportation process, the binocular camera at the end of the robot arm is used to detect the position. The binocular camera transmits the image model to the controller, and the controller controls the robot arm to move the H-beam accurately to the specified position;
[0008] 3) When the H-beam is moved to the designated installation location, the binocular camera system is used to guide the installation work, so that the robotic arm can make fine adjustments to ensure that the H-beam is accurately placed at the installation location. The fine-tuning process involves using the binocular camera to capture the three bolt holes arranged at right angles on the flange at the lower end of the H-beam column. The three bolt holes are used to establish the first XY coordinate system, and the three bolts pre-buried at right angles at the ground installation location establish the second XY coordinate system. The signal is fed back to the controller to guide the robotic arm to fine-tune the position of the H-beam column so that the two coordinate systems coincide. The H-beam column can then be lowered for precise installation.
[0009] Among them, the assembly robot arm with visual guidance function used in steps 1), 2) and 3) includes a robot arm body and a frame fixed on the end of the robot arm body, the outer wall of the frame away from the robot arm body is symmetrically slidably connected with a clamping assembly, the middle of the frame is installed with a driving mechanism for driving the two clamping assemblies to work and perform clamping work, a binocular camera is fixed in the middle of the bottom surface of the frame close to the clamping assembly, and a semicircular transparent glass cover is fixed to the bottom of the frame on the outside of the binocular camera.
[0010] Preferably, the bottom of the frame near the binocular camera is symmetrically and slidably connected with a protective cover, and the semicircular transparent glass cover is located inside a chamber surrounded by the two protective covers and the bottom surface of the frame, and the two protective covers are fixed with spring plates on the sides opposite to each other, and the ends of the spring plates away from the protective covers are fixed to the outer wall of the frame, and the frame is also equipped with a synchronous opening and closing mechanism for driving the two protective covers to open and close, and the synchronous opening and closing mechanism is mechanically linked with the driving mechanism so that the two protective covers can slide open away from each other in the initial stage of clamping of the clamping assembly, and the frame includes protruding edges formed at the upper and lower ends of the side near the clamping assembly, the binocular camera is fixed to a protruding edge at the bottom, the end of the spring plate is fixed to the outer wall of a protruding edge at the bottom, the semicircular transparent glass cover is fixed to the bottom of a protruding edge at the bottom, and the protective cover is slidably connected to the bottom of a protruding edge at the bottom.
[0011] Preferably, the clamping assembly consists of a vertical bar slidably connected to the frame and a clamping plate symmetrically fixed on the vertical bar.
[0012] Preferably, a slide rail is symmetrically fixed to one side of the rack close to the vertical bar, and the slide rail is arranged horizontally. A slide bar is symmetrically fixed to one side of the vertical bar close to the slide rail, and the slide bar is slidably connected to the outer wall of the slide rail.
[0013] Preferably, the driving mechanism includes:
[0014] A rotating shaft rotatably connected to the middle portion of the frame via a bearing;
[0015] a gear fixed to one end of the rotating shaft close to the clamping assembly;
[0016] A rack is fixed on the side of the vertical bar close to the gear, and the racks on the two vertical bars are arranged symmetrically with respect to the center, and both racks are meshed with the gear;
[0017] A worm gear is fixed to an end of the rotating shaft away from the gear;
[0018] A worm is rotatably connected to the inner wall of the frame via a bearing, and the worm is meshed with the worm wheel;
[0019] The motor is fixed on the inner wall of the frame, and one end of the worm gear close to the motor is fixed to the output end of the motor.
[0020] Preferably, bristles are fixed at equal intervals on the inner wall of the protective cover, and the bristles are in contact with the outer wall of the semicircular transparent glass cover.
[0021] Preferably, the synchronous opening and closing mechanism includes:
[0022] A cam is fixed to one end of the rotating shaft close to the gear, and the cam is located on the inner side of the frame;
[0023] A lifting rod is slidably connected to the inner wall of the frame, and the top of the lifting rod is rollingly connected to the outer wall of the cam;
[0024] The connecting rod is symmetrically connected to the bottom of the lifting rod through an axle pin, and the ends of the two connecting rods away from the lifting rod are respectively connected to the outer walls of the two protective covers through the axle pin.
[0025] Preferably, the top of the lifting rod is rotatably connected to a roller via an axle pin, and the roller is rollingly connected to the outer wall of the cam.
[0026] Preferably, one of the protrusions at the bottom is symmetrically fixed with sliding sleeves on both sides along the bottom surface, and two sliding rods are symmetrically fixed on opposite sides of the two protective covers, and the sliding rods are slidably connected to the sliding sleeves.
[0027] Preferably, the four clamping plates are provided with transversely arranged anti-slip grooves at equal distances on one side close to each other.
[0028] Compared with related technologies, the visual guidance method for assembling H-shaped steel columns provided by the present invention has the following beneficial effects:
[0029] By installing a binocular camera on the frame at the end of the robot arm, the binocular camera provides visual guidance when the robot arm clamps the H-beam column for assembly. The camera captures the position of the H-beam column and guides the robot arm to perform assembly work accurately, greatly improving the accuracy of H-beam column assembly.
[0030] The semicircular transparent glass cover can isolate the binocular camera and prevent dust from adhering to the binocular camera. The two protective covers installed in combination can protect the binocular camera and the semicircular transparent glass cover, so as to prevent the semicircular transparent glass cover and the binocular camera from being damaged by impact during the movement and transportation of the robot arm body. At the same time, the protective cover can cover the semicircular transparent glass cover, so as to prevent dust from adhering to the semicircular transparent glass cover and the binocular camera when the robot arm body is transported or stored, thereby ensuring that the binocular camera can capture a clear picture. The brush provided on the inner side of the protective cover can clean the semicircular transparent glass cover every time the protective cover is opened and closed, thereby further ensuring the transparency of the semicircular transparent glass cover and the cleanliness of the picture captured by the binocular camera, reducing the number of times of manual cleaning of the semicircular transparent glass cover and saving manpower.
[0031] The synchronous opening and closing mechanism cooperates with the spring clip to enable the protective cover to open and close automatically. Due to the mechanical linkage between the synchronous opening and closing mechanism and the driving mechanism, the protective cover can be opened and closed in time without the need for additional power equipment, which reduces the operating cost and improves the timeliness and stability of the opening and closing of the protective cover. BRIEF DESCRIPTION OF THE DRAWINGS
[0032] Figure 1 It is a schematic diagram of the overall structure of the present invention;
[0033] Figure 2 It is a schematic structural diagram of the clamping assembly of the present invention;
[0034] Figure 3 This is a schematic diagram of the protective cover position structure of the present invention;
[0035] Figure 4 For the present invention Figure 3 A is an enlarged view;
[0036] Figure 5 This is a schematic diagram of the bristle position structure of the present invention;
[0037] Figure 6 Schematic diagram of the binocular camera position structure of the present invention;
[0038] Figure 7 Schematic diagram of the driving mechanism structure of the present invention;
[0039] Figure 8 It is a structural schematic diagram of the synchronous opening and closing mechanism of the present invention.
[0040] Numbers in the figure: 100, assembly robot arm with visual guidance function; 1, robot arm body; 2, frame; 21, protruding edge; 3, clamping assembly; 31, vertical bar; 32, clamping plate; 4, driving mechanism; 41, rotating shaft; 42, gear; 43, rack; 44, worm gear; 45, worm; 46, motor; 5, binocular camera; 6, semicircular transparent glass cover; 7, protective cover; 71, bristles; 8, shrapnel; 9, synchronous opening and closing mechanism; 91, cam; 92, lifting rod; 921, roller; 93, connecting rod; 10, slide rail; 11, slide bar; 12, sliding sleeve; 13, slide rod; 14, anti-slip groove. DETAILED DESCRIPTION
[0041] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.
[0042] The specific implementation of the present invention is described in detail below with reference to specific embodiments.
[0043] See also Figures 1 to 8 , an embodiment of the present invention provides a visual guidance method for assembling an H-shaped steel column, comprising the following steps:
[0044] 1) Clamping the H-shaped steel column by using the assembly robot 100 with vision guidance function;
[0045] 2) Use the assembly robot 100 with visual guidance function to carry the H-beam to the installation location. During the transportation process, the binocular camera 5 at the end of the robot arm is used to detect the position. The binocular camera 5 transmits the image model to the controller, and the controller controls the robot arm to move the H-beam accurately to the specified position;
[0046] 3) When the H-shaped steel is moved to the space above the designated installation location, the binocular camera 5 system is used to guide the installation work, so that the robotic arm can make fine adjustments to ensure that the H-shaped steel is accurately placed at the installation location. The fine-tuning process involves using the binocular camera 5 to photograph the three bolt holes arranged at right angles on the flange at the lower end of the H-shaped steel column. The three bolt holes are used to establish a first XY coordinate system, and the three bolts pre-buried at right angles at the ground installation location establish a second XY coordinate system. The signal is fed back to the controller to guide the robotic arm to fine-tune the position of the H-shaped steel column so that the two coordinate systems coincide. The H-shaped steel column can then be lowered for precise installation.
[0047] Among them, the assembly robot 100 with visual guidance function used in steps 1), 2) and 3) includes a robot body 1 and a frame 2 fixed on the end of the robot body 1. The outer wall of the frame 2 away from the robot body 1 is symmetrically slidably connected with a clamping component 3. The clamping component 3 is composed of a vertical bar 31 slidably connected to the frame 2 and a clamping plate 32 symmetrically fixed on the vertical bar 31. The side of the frame 2 close to the vertical bar 31 is symmetrically fixed with a slide rail 10, and the slide rail 10 is arranged horizontally. The side of the vertical bar 31 close to the slide rail 10 is symmetrically fixed with a slide bar 11, and the slide bar 11 is slidably connected to the outer wall of the slide rail 10. When clamping, the robot body 1 is operated to make the two parts in the frame 2 move forward and backward. The two groups of clamping plates 32 on the side are respectively placed on both sides of the H-shaped steel column, and the vertical bars 31 are driven to slide close to each other along the slide rails 10, so that the two groups of clamping plates 32 on both sides can be clamped on the outer wall of the H-shaped steel column, thereby completing the clamping work, and the side where the four clamping plates 32 are close to each other are equidistantly provided with transversely arranged anti-slip grooves 14, which greatly improves the friction between the clamping plates 32 and the outer wall of the H-shaped steel column, the frame 2 includes protruding edges 21 formed on the upper and lower ends of the side close to the clamping component 3, and a driving mechanism 4 for driving the two clamping components 3 to work for clamping work is installed in the middle of the frame 2, and a protruding edge 21 at the lower end is located in the middle of the bottom surface. A binocular camera 5 is fixed, and a semicircular transparent glass cover 6 is fixed on the outside of the binocular camera 5 at the bottom of a protruding edge 21 at the lower end. A protective cover 7 is symmetrically slidably connected to the bottom of a protruding edge 21 at the lower end. The protective cover 7 also includes bristles 71 fixed on its inner wall at equal distances. The bristles 71 are in contact with the outer wall of the semicircular transparent glass cover 6. The setting of the bristles 71 can synchronously brush the outer wall of the semicircular transparent glass cover 6 when the protective cover 7 is opened and closed and slides, thereby achieving the effect of automatically cleaning the semicircular transparent glass cover 6. The semicircular transparent glass cover 6 is located inside the chamber surrounded by the two protective covers 7 and the bottom surface of the protruding edge 21, and the two protective covers 7 are fixed on the opposite sides. There is a spring piece 8, and the end of the spring piece 8 away from the protective cover 7 is fixed to the outer wall of a protruding edge 21 below, and sliding sleeves 12 are symmetrically fixed on both sides of the bottom surface of a protruding edge 21 at the bottom. Slide rods 13 are symmetrically fixed on the opposite sides of the two protective covers 7. The slide rods 13 are slidably connected to the slide sleeves 12. When the protective cover 7 slides, the slide rod 13 slides on the inside of the slide sleeve 12. The arrangement of the slide rod 13 and the slide sleeve 12 enables the protective cover 7 to slide stably. A synchronous opening and closing mechanism 9 for driving the two protective covers 7 to open and close is also installed on the frame 2, and the synchronous opening and closing mechanism 9 is mechanically linked with the driving mechanism 4, so that the two protective covers 7 can slide away from each other and open in the initial stage of clamping the clamping assembly 3.
[0048] The present application installs a binocular camera 5 at the end of the robot arm body 1, so that when the robot arm body 1 clamps the H-shaped steel column for assembly work, it can be guided by the binocular camera 5, which greatly improves the accuracy of the H-shaped steel column assembly. In addition, by providing a protective cover 7, bristles 71, a semicircular transparent glass protective cover 7 and a synchronous opening and closing mechanism 9, the binocular camera 5 can be protected during daily storage and transportation to prevent it from being impacted by the outside world, and at the same time, it can prevent dust from adhering to its surface, thereby ensuring the clarity of the picture it takes.
[0049] The driving mechanism 4 includes a rotating shaft 41, a gear 42, a rack 43, a worm wheel 44, a worm 45 and a motor 46. The rotating shaft 41 is rotatably connected to the middle part of the frame 2 through a bearing. The gear 42 is fixed to one end of the rotating shaft 41 close to the clamping assembly 3. The rack 43 is fixed to the side of the vertical bar 31 close to the gear 42, and the racks 43 on the two vertical bars 31 are arranged symmetrically. The two racks 43 are meshed with the gear 42. The worm wheel 44 is fixed to the end of the rotating shaft 41 away from the gear 42. The worm 45 is rotatably connected to the inner wall of the frame 2 through a bearing, and the worm 45 is meshed with the worm wheel 44. The motor 46 is fixed to the inner wall of the frame 2, and One end of the worm 45 close to the motor 46 is fixed to the output end of the motor 46. When it is necessary to drive the clamping components 3 to move closer to each other for clamping work, the driving motor 46 is rotated to drive the worm 45 to rotate, thereby driving the worm wheel 44 to rotate, thereby causing the rotating shaft 41 to rotate, thereby causing the gear 42 to rotate, thereby driving the two racks 43 to move closer to each other, thereby driving the two vertical bars 31 to slide closer to each other, so that the clamping plate 32 gradually approaches the H-shaped steel column until the clamping plate 32 is tightly clamped on the outer wall of the H-shaped steel column, and the clamping work is completed. Then the H-shaped steel column can be moved to the assembly position by operating the robot arm body 1.
[0050] The synchronous opening and closing mechanism 9 includes a cam 91, a lifting rod 92 and a connecting rod 93. The cam 91 is fixed on one end of the rotating shaft 41 close to the gear 42, and the cam 91 is located on the inner side of the frame 2. The lifting rod 92 is slidably connected to the inner wall of the frame 2. The top of the lifting rod 92 is rotatably connected to the roller 921 through an axle pin. The roller 921 is rollingly connected to the outer wall of the cam 91. The connecting rod 93 is symmetrically connected to the bottom of the lifting rod 92 through an axle pin, and the ends of the two connecting rods 93 away from the lifting rod 92 are respectively rotatably connected to the outer walls of the two protective covers 7 through axle pins. In the early stage of the clamping work, the rotation of the rotating shaft 41 drives the cam 91 to rotate. The rotation of the cam 91 can push open the lifting rod 92, causing the lifting rod 92 to slide downward, and then push the connecting rod 93, so that the two protective covers 7 slide in the direction away from each other, thereby exposing the binocular camera 5. The protective cover 7 is opened before the clamping plate 32 has not yet contacted the outer wall of the H-shaped steel column. , and then the clamping plate 32 clamps the H-shaped steel column, and then the process of the robot arm body 1 moving the H-shaped steel column to the assembly position and the subsequent precise positioning and assembly process are guided by the binocular camera 5. The binocular camera 5 transmits the image of the position of the flange at the bottom of the H-shaped steel column and the position image of the embedded bolts to the controller in real time. The controller controls the movement of the robot arm to ensure that the bolt holes on the flange at the bottom of the H-shaped steel column correspond to the embedded bolts at the assembly position, and then the operation is slowly lowered to complete the assembly work. After the assembly is completed, the two clamping assemblies 3 are driven away from each other, and finally the clamping assemblies 3 reach the position with the maximum spacing. During this process, after the cam 91 is reset, the action of the spring piece 8 can push the two protective covers 7 to slide close to each other until they are closed. During the closing process, the connecting rod 93 is pushed, and the two connecting rods 93 push the lifting rod 92 upward. The roller 921 at the top of the lifting rod 92 is always pressed against the outer wall of the cam 91.
[0051] The circuits and controls involved in the present invention are all prior art and will not be described in detail here.
[0052] The above descriptions are merely embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made using the contents of the present invention description and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.
Claims
1. A visual guidance method for assembling an H-shaped steel column, characterized in that: The steps include: 1) Clamping the H-shaped steel column by using an assembly robot (100) with a visual guidance function; 2) Using an assembly robot (100) with a visual guidance function to carry the H-shaped steel to the installation position, and using a binocular camera (5) at the end of the robot arm to detect the position during the transportation process. The binocular camera (5) transmits the image model to the controller, and the controller controls the robot arm to move the H-shaped steel accurately to the specified position; 3) When the H-shaped steel is moved to the space above the designated installation position, the binocular camera (5) system is continued to be used to guide the installation work, so that the robot arm is fine-tuned to ensure that the H-shaped steel is accurately placed at the installation position. The fine-tuning process is to use the binocular camera (5) to shoot the three bolt holes arranged at right angles on the flange at the lower end of the H-shaped steel column, and use the three bolt holes to establish a first XY coordinate system, and the three bolts pre-buried at right angles on the ground installation position to establish a second XY coordinate system. The signal is fed back to the controller to guide the robot arm to fine-tune the position of the H-shaped steel column so that the two coordinate systems coincide, and then the H-shaped steel column can be lowered for accurate installation; The assembly robot (100) with a visual guidance function used in steps 1), 2) and 3) comprises a robot body (1) and a frame (2) fixed to the end of the robot body (1); a clamping assembly (3) is symmetrically slidably connected to the outer wall of the frame (2) on a side away from the robot body (1); a driving mechanism (4) for driving the two clamping assemblies (3) to work and perform clamping is installed in the middle of the frame (2); a binocular camera (5) is fixed in the middle of the bottom surface of the frame (2) on the side close to the clamping assembly (3); and a semicircular transparent glass cover (6) is fixed to the bottom of the frame (2) on the outside of the binocular camera (5); The bottom of the frame (2) near the binocular camera (5) is symmetrically slidably connected with a protective cover (7), and a semicircular transparent glass cover (6) is located inside a chamber surrounded by the two protective covers (7) and the bottom surface of the frame (2). Shrapnel (8) is fixed on the opposite sides of the two protective covers (7), and the end of the shrapnel (8) away from the protective cover (7) is fixed to the outer wall of the frame (2). A synchronous opening and closing mechanism (9) for driving the two protective covers (7) to open and close is also installed on the frame (2), and the synchronous opening and closing mechanism (9) is mechanically linked with the driving mechanism (4), so that In the initial stage of the clamping assembly (3), the two protective covers (7) can slide away from each other and open, the frame (2) includes protruding edges (21) formed at the upper and lower ends of the side close to the clamping assembly (3), the binocular camera (5) is fixed to the protruding edge (21) at the bottom, the end of the spring (8) is fixed to the outer wall of the protruding edge (21) at the bottom, the semicircular transparent glass cover (6) is fixed to the bottom of the protruding edge (21) at the bottom, and the protective cover (7) is slidably connected to the bottom of the protruding edge (21) at the bottom; The synchronous opening and closing mechanism (9) comprises: cam (91); A lifting rod (92) is slidably connected to the inner wall of the frame (2), and the top of the lifting rod (92) is rollingly connected to the outer wall of the cam (91); The connecting rod (93) is symmetrically connected to the bottom of the lifting rod (92) through an axle pin, and the ends of the two connecting rods (93) away from the lifting rod (92) are respectively connected to the outer walls of the two protective covers (7) through the axle pin.
2. The visual guidance method for assembling an H-shaped steel column according to claim 1, characterized in that: The clamping assembly (3) consists of a vertical bar (31) slidably connected to the frame (2) and a clamping plate (32) symmetrically fixed on the vertical bar (31).
3. The visual guidance method for assembling an H-shaped steel column according to claim 2, characterized in that: A slide rail (10) is symmetrically fixed to one side of the frame (2) close to the vertical bar (31), and the slide rail (10) is arranged horizontally. A slide bar (11) is symmetrically fixed to one side of the vertical bar (31) close to the slide rail (10), and the slide bar (11) is slidably connected to the outer wall of the slide rail (10).
4. The visual guidance method for assembling an H-shaped steel column according to claim 3, characterized in that: The driving mechanism (4) comprises: A rotating shaft (41) is rotatably connected to the middle portion of the frame (2) via a bearing; A gear (42) is fixed to one end of the rotating shaft (41) close to the clamping assembly (3); A rack (43) is fixed on one side of the vertical bar (31) close to the gear (42), and the racks (43) on the two vertical bars (31) are arranged symmetrically with respect to the center, and both racks (43) are meshed and connected with the gear (42); a worm gear (44) fixed to an end of the rotating shaft (41) away from the gear (42); A worm (45) is rotatably connected to the inner wall of the frame (2) via a bearing, and the worm (45) is meshingly connected to the worm wheel (44); The motor (46) is fixed on the inner wall of the frame (2), and one end of the worm (45) close to the motor (46) is fixed to the output end of the motor (46).
5. The visual guidance method for assembling an H-shaped steel column according to claim 1, characterized in that: Brushes (71) are fixed at equal intervals on the inner wall of the protective cover (7), and the brushes (71) are in contact with the outer wall of the semicircular transparent glass cover (6).
6. The visual guidance method for assembling an H-shaped steel column according to claim 1, characterized in that: The top of the lifting rod (92) is rotatably connected to a roller (921) via an axle pin, and the roller (921) is rollingly connected to the outer wall of the cam (91).
7. The visual guidance method for assembling an H-shaped steel column according to claim 1, characterized in that: Slide sleeves (12) are symmetrically fixed on both sides of the bottom surface of the protruding edge (21) at the bottom, and slide rods (13) are symmetrically fixed on opposite sides of the two protective covers (7), and the slide rods (13) are slidably connected to the slide sleeves (12).
8. The visual guidance method for assembling an H-shaped steel column according to claim 2, characterized in that: The four clamping plates (32) are provided with transversely arranged anti-slip grooves (14) at equal intervals on one side thereof that is close to each other.
Citation Information
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