A full-constraint 3D printer based on flexible cable-driven parallel mechanism

Abstract

This patent discloses a fully constrained 3D printer based on a flexible cable-driven parallel mechanism, characterized by: 1. Optimized fixed platform structure, improving rigidity and reducing cost. 2. A novel linkage mechanism is designed, including a centrally hollowed-out assembly frame, sliding rods, and pulleys, achieving high-precision motion control through the scientific layout of the flexible cables. 3. Combining the novel linkage mechanism with a four-flexible cable-driven parallel mechanism, achieving two-drive, two-degree-of-freedom planar fully constrained motion through cable connections, improving printing efficiency. 4. Utilizing flexible cables to provide full constraint control in the Z-axis direction, integrating a motor and a nonlinear winch to ensure precise and smooth motion. 5. Using a reduction drive to improve transmission accuracy, introducing anti-backlash springs to compensate for motion errors, and improving overall performance. This invention aims to provide a 3D printing mechanism based on flexible cable-driven parallel mechanism technology, which has significant advantages in improving printing accuracy, printing range, and response speed, and has broad application prospects.

Description

Technical Field

[0001] This invention relates to the field of cable-driven parallel robots, and more particularly to the application of cable-driven parallel mechanisms in 3D printing technology. Background Technology

[0002] 3D additive manufacturing technology has matured, offering advantages such as faster cycle times for generating complex shapes, making it more convenient and cost-effective than traditional manufacturing methods. Due to its quick and easy forming process, the printed parts possess advantages such as high strength and long durability, and are widely used in industrial manufacturing, aerospace, and construction.

[0003] Looking at the development trend of 3D printers, they are gradually moving towards lightweight, miniaturization, large-scale production, and low cost. Traditional 3D printers use serial or parallel mechanisms. Serial 3D printers have the advantages of large working space, low cost, and simple structure, but they inevitably suffer from error accumulation and inertia problems at the end of the print head during the printing process. The flexible cable-driven parallel mechanism inherits and makes up for the shortcomings of the traditional printing mechanism. Moreover, the flexible cable-driven parallel mechanism is lightweight and easy to reconfigure, and can cope with different printing environments.

[0004] Existing cable-driven parallel mechanisms suffer from this limitation: the cables can only withstand tension, not compression. During operation, if the force in any one of the driving cables becomes negative, the cable slackens and loses its transmission function. For this reason, cable-driven parallel mechanisms are typically configured with redundant drives, meaning the number of motor drives exceeds the degrees of freedom of the end effector. This results in a lack of real-time performance in model-based dynamic control. When calculating redundant cable-driven parallel mechanisms, countless possible tension values ​​exist at any point on the trajectory of the moving platform. Therefore, a specific tension distribution optimization algorithm is needed to find an optimal tension solution that meets certain optimization criteria to achieve accurate control. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention designs a novel fully constrained 3D printer based on a flexible cable-driven parallel mechanism.

[0006] To overcome the shortcomings of the prior art, the present invention provides a fixed platform in which the 12 aluminum profiles of the main frame are connected to the adjacent aluminum profiles by profile sleeves to increase strength. This can increase the rigidity of the fixed platform while saving materials, which is beneficial to the motion accuracy of the end effector and saves costs.

[0007] To overcome the shortcomings of existing technologies, this invention proposes a flexible cable transmission mechanism. This mechanism mainly includes a rectangular assembly frame with a hollowed-out central portion, four fixed-length sliding rods, and pulleys. Fixed pulleys are mounted on the vertical rods of the assembly frame. One end of each sliding rod has a pulley, while the other end is connected via a bearing. The flexible cable first winds around the pulley on the assembly frame, then around the pulley on the sliding rod, and finally is fixed. The movement of the four-bar connection point is achieved by pressing the sliding rods with the flexible cable. This movement of the connection point is similar to that of the end effector of a parallel mechanism driven by four flexible cables. It can be considered that the flexible cables in this mechanism are replaced by rotating rods capable of performing the same movement.

[0008] As a further improvement to the above solution, this solution combines the flexible cable drive mechanism with a parallel mechanism driven by four flexible cables to form a novel flexible cable-driven parallel mechanism. The end effector of the flexible cable-driven parallel mechanism and the novel mechanism are connected by the same flexible cable, and the two are isolated by a sheet metal. By rotating the motor forward and reverse, two-drive, two-degree-of-freedom planar motion can be achieved, avoiding the consumption of motor torque during tensioning. By mounting the print head on the end effector, printing operations in the XY plane can be completed.

[0009] As a further improvement to the above solution, this invention designs a device for raising and lowering a machining bed using flexible cables, thereby enabling 3D printing in the Z-axis direction. The core of this machining bed raising device lies in using six flexible cables at specific angles to provide constraints for six degrees of freedom. Therefore, all the cables cannot be perfectly parallel to the motion, but must be at a certain angle. Its effectiveness lies in the fact that all six cables are of equal length, meaning smooth linear motion. Pairs of cables are first integrated into three independent cables, which are then connected into one and wound in a non-linear winch. The movement of the machining bed in the Z-axis direction can be achieved using a single motor.

[0010] Furthermore, the end effector 14000 includes: an end effector frame 14001, a grip 14003, a force sensor bracket 14004, a second grip bracket 14005, a first grip bracket 14006, a six-axis force sensor 14007, and a lower force sensor bracket 14008. The lower force sensor bracket 14008 is disposed on the end effector frame 14001, and the six-axis force sensor is fixedly connected to the lower force sensor bracket 14008. 14007, the upper end of the six-axis force sensor 14007 is fixedly connected to the first grip bracket 14006, the first grip bracket 14006 and the grip 14003 are fixedly connected through the second grip bracket 14005, the force sensor bracket 14004 is provided on the first grip bracket 14006, the force sensor bracket 14004 is inside the end effector frame 14001, and the grip 14003 is provided outside the end effector frame 14001.

[0011] As a further improvement to the above solution, a synchronous belt was added between the flexible cable integrating the motor and the nonlinear winch, thereby ensuring precise transmission and slip-free drive during the movement of the machining bed.

[0012] As a further improvement to the above solution, this invention designs a reduction drive, including a large pulley and two small pulleys, to drive a belt reaching the bottom of the frame. This design aims to ensure the smoothness and rigidity of the machining bed movement and improve 3D printing accuracy.

[0013] As a further improvement to the above solution, this invention adds an anti-backlash spring between the flexible cable integrated with the synchronous belt and the nonlinear winch to compensate for the linear motion error caused by the flexible cable in the nonlinear winch, thereby improving the accuracy and response speed of the equipment. This improvement also makes the system control more agile and precise.

[0014] As a further improvement to the above solution, the present invention adds a rolling ball above the end effector where the print head is installed, thereby reducing its friction with the isolation plate and improving control accuracy.

[0015] Compared with existing technologies, the advantages of this invention are: 1. By utilizing anti-tension, four flexible cables are operated through two drives to complete the movement of the end effector in two degrees of freedom, avoiding the waste of motor torque during tensioning. 2. The flexible cables are kept taut at all times, preventing slack, thus improving the stability of the end effector during operation. 3. The accuracy and response speed of 3D printing are improved, and the system control is more agile and precise.

[0016] Key points of this invention:

[0017] 1. The flexible cables are set in a specific sequence. By tightening the flexible cables to compress the sliding rod, the movement of the end effector is achieved by simulating the flexible cable drive of a parallel mechanism.

[0018] 2. Unlike traditional cable-driven parallel mechanisms, which have fewer degrees of freedom than the number of drives, this invention utilizes a cable-driven rotary mechanism whose mechanical linkages provide reverse tension without requiring additional motors. This tension is driven by the inputs of two winches, thus ensuring that the number of motors in the 3D printer matches the number of degrees of freedom.

[0019] 3. The 3D printer of this invention does not rely on linear guides, but achieves the movement of the end effector and the raising and lowering of the processing bed solely through flexible cables and belts. There is a linear relationship between the belt that actually performs the Z-axis movement and the motor rotation. The specific configuration of flexible cables and timing belts ensures the load capacity and rigidity of the 3D printer, and enables simpler design and maintenance. Furthermore, the elimination of linear guides is significant for the maintenance and durability of the 3D printer. Attached Figure Description

[0020] Figure 1 This is an overall perspective view of a specific embodiment of the present invention;

[0021] Figure 2 This is a perspective view of the fixed platform in a specific embodiment of the present invention;

[0022] Figure 3 This is a perspective view of the flexible cable rotation mechanism in a specific embodiment of the present invention;

[0023] Figure 4 This is a perspective view of the bed lifting device in a specific embodiment of the present invention;

[0024] Figure 5 This is a connection diagram of the connecting rod, assembly frame, and part of the flexible cable in a specific embodiment of the present invention;

[0025] Figure 6 This is a connection diagram of the pulley sleeve, pulley, and part of the flexible rope in a specific embodiment of the present invention;

[0026] Figure 7 This is a perspective view of the deceleration driver in a specific embodiment of the present invention;

[0027] Figure 8 This is a schematic diagram of a connection method involving aluminum profile screw connection in a specific embodiment of the present invention; Detailed Implementation

[0028] The following is in conjunction with the appendix Figure 1 -Appendix Figure 8 The present invention will be further described in detail with reference to specific embodiments. The specific embodiments described herein are only for explaining the present invention and are not intended to limit the present invention.

[0029] Unless otherwise specified, the aluminum profiles mentioned in this invention refer to SD series aluminum alloy profiles. The connection methods between parts and aluminum profiles, and between aluminum profiles, in this invention are all based on... Figure 8 There is a square nut in the slot of the aluminum profile. The axis of the through hole of the connected part is aligned with the center of the slot. It is connected to the aluminum profile by screws. After the screws are tightened with the square nut in the aluminum profile, the aluminum profile and the connected part can be fixed. There are washers on the screws and the connected part to prevent loosening and increase the strength of the connected part.

[0030] Reference Figure 1A fully constrained 3D printer based on a flexible cable-driven parallel mechanism, characterized in that it includes a fixed platform (11000), a flexible cable rotation device (12000), and a bed lifting device (13000). The flexible cable rotation device (12000) is located on the upper side of the fixed platform (11000). Utilizing a special winch support (12006) in the flexible cable rotation mechanism (12000), the upper crossbar (13000) is fixed to the fixed platform (11000) by angle iron and screws. 1001), the bed lifting device (13000) is located on the lower side of the flexible cable rotation mechanism (12000). Its flexible cable is fixed to the flexible cable fixing device (12300) which is set on the left and right rear sides of the fixed platform (11000) by screws. Its synchronous belt (13204) is fixed to the synchronous belt fixing device (13003) which is set on the lower crossbar (11004) of the fixed platform by screws. The lifting of the machining bed (13002) is realized by controlling the movement of the flexible cable and the synchronous belt by the motor.

[0031] Reference Figure 2 The supporting components of the fixed platform are all made of aluminum profiles. The 12 aluminum profiles forming the main frame (11001) are connected to adjacent aluminum profiles using profile sleeves (11002) and screws. The specific connection method is as follows: Figure 2 As shown in the enlarged view A, the upper crossbar (11003) is fixed to the top of the fixed platform by angle iron and screws, and the lower crossbar (11004) is fixed to the bottom of the fixed platform by angle iron and screws. The connection method of the angle iron is as follows. Figure 2 The enlarged view in part B is shown in the middle.

[0032] Reference Figure 3The flexible cable rotation mechanism (12000) includes an isolation plate (12003), an end effector (12007) mounted on the lower end of the isolation plate (12003) via a taut flexible cable, a nozzle support plate (12009) mounted on the end effector (12007) via screws, a nozzle (12008) mounted on the nozzle support plate (12009) via screws, an assembly frame seat (12103) mounted at the center of the isolation plate (12003) via screws, an assembly frame cover (12101) positioned and connected to the upper end of the assembly frame seat (12103) via a main shaft, a fixed pulley (12102) mounted between the assembly frame seat (12103) and the assembly frame cover (12101) and fitted onto the main shaft via an transition fit, and a flexible cable mounted on the upper end of the assembly frame cover (12101). The cable fixing device (12300), the linkage mechanism (12200) restricted inside the assembly frame by the flexible cable, the pulley (12201) set at the far end of the sliding rod (12102) by the transition fit, the winch bearing (12006) set at the four corners of the isolation plate (12003) by the clearance fit and the installation adjustment shims, the winch (12005) set inside the winch bearing (12006) by the interference fit and the rigid coupling (12004) connected to the motor (12002) shaft, the flexible cable guide device (12400) set at the edge of the isolation plate (12003) by the clearance fit and the adjustment shims, the motor seat (12001) set at the upper end of the winch bearing (12006) by the screw connection, and the servo motor (12002) set at the upper end of the motor seat (12001) by the screw connection. The assembly frame (12100) consists of an assembly frame seat (12103) on the upper side of the isolation plate, an assembly frame cover (12101) that cooperates with the assembly frame seat, and a pulley (12102) between the assembly frame seat and the assembly frame cover seat. The linkage mechanism (12200) is a device that connects the sliding rod (12202) together through the air bearing (12203). The flexible cable is set in the following order: flexible cable fixing device - sliding rod pulley - assembly frame pulley - flexible cable guiding device - winch - end effector.

[0033] Reference Figure 3The flexible cable rotating device (12000) is divided into two parts by the partition plate (12003), hereinafter referred to as the upper mechanism and the lower end effector. Ignoring the upper mechanism, the movement of the lower end effector is exactly the same as that of a conventional flexible cable driven parallel mechanism end effector; that is, the flexible cable applies force to the end effector to drive its movement. However, since the flexible cable is installed according to a specific configuration, the end effector (12007) and the flexible cable fixing device (12300) are connected by the same flexible cable. Therefore, the total length of a single flexible cable remains unchanged, and the increase in the upper flexible cable is equal to the decrease in the lower mechanism's flexible cable. The movement of the upper part of the partition plate (12003) can be described as follows: the pulley installed at the far end of the sliding rod (12202) acts as a movable pulley. Due to the decrease in the flexible cable, it pushes the sliding rod to move and rotates around the instantaneous center of motion (the assembly frame pulley). The upper sliding rod remains parallel to the lower flexible cable connected to the end effector. Due to the characteristics of the movable pulley, the displacement of the sliding rod is half the change in the flexible cable. Therefore, the size of the upper mechanism is proportional to the size of the lower flexible cable-driven parallel mechanism. The movement is achieved by adjusting the ratio of the winch radius.

[0034] Reference Figure 3 This section will demonstrate the motion of the flexible cable rotation device (12000). The design of this mechanism is based on the following conditions: (1) the flexible cable has a certain pretension during installation, that is, the flexible cable is taut in the initial state. (2) the total length of the four flexible cables connecting the upper and lower layers is consistent. The core of the motion of this device is that the upper and lower frames are set in proportion, and the lower sliding rod and the upper flexible cable are always kept parallel. For the convenience of the demonstration, we regard the end effectors of the upper and lower layers as point masses. It is known that the change in the flexible cable is related to the displacement of the lower end effector, that is

[0035] (1)

[0036] The upper mechanism can be considered as a sliding rod replacing the flexible cable, with the ratio of its displacement to the change in the flexible cable being a constant. That is, for the upper mechanism, the length of its sliding rod in the lower frame can be calculated and converted into direct kinematics.

[0037] (2)

[0038] Since the structure of the upper mechanism is already determined, and we consider the sliding rod as a point mass, for any sliding rod, it must satisfy the following:

[0039] (3)

[0040] Equation (3) expresses the distance between the end effector and the hinge point as equal to the length of the sliding rod in the lower frame. We can express equation (3) as follows, with the hinge point as... Center of the circle The circle with radius m. That is, for m circles, the point where they intersect is the mass point of the end effector. Therefore, only when the lower sliding rod and the upper flexible cable are always parallel can formula (3) be satisfied. In other words, according to the configuration mentioned above, the expected motion can be achieved. That is, when the lower end effector achieves a specific trajectory, the flexible cable hinged to it and the sliding rod of the upper mechanism are always parallel.

[0041] Reference Figure 3 This section will specifically analyze the geometric, kinematic, static, and dynamic models of the flexible cable rotation device (12000), providing a foundation for controlling 3D printing in the XY plane. The inverse kinematic model correlates the arbitrary pose / position of the end effector with the corresponding cable length. Considering pulley kinematics, its geometric model is as follows:

[0042] The total length of the rope is fixed and constant, meaning it satisfies the following formula:

[0043] (4)

[0044] in The total length of the single flexible cable connected to the lower end effector. The total length of a single flexible rope, The spiral step distance for the flexible cable winding on the winch. and These represent the number of turns wound on the upper and lower winches, respectively. It is a definite constant.

[0045] For its static model:

[0046] Considering pulley kinematics, for purely translational motion, it cannot bear or generate torque. Therefore, taking into account the force balance of the pulley mechanism, for the end effector, we can obtain the well-known formula definition:

[0047] Use a unit vector that takes into account the kinematics of pulleys. It can be obtained

[0048] (5)

[0049] For the first Local coordinate system of each pulley Corresponding global coordinate system The rotation matrix.

[0050] Given the number of flexible cables, for the upper-level mechanism, we can also obtain the classic definition equation for the structure matrix:

[0051] (6)

[0052] Therefore, for the overall mechanism, its static formula is actually a combination of formulas (5) and (6), that is...

[0053] (7)

[0054] Its dynamic model is as follows:

[0055] Using the Newton-Euler method

[0056] (8)

[0057] in For the quality matrix, Here is the damping matrix. Generalized centrifugal force and Coriolis force This represents the displacement of the end effector.

[0058] If the flexible cable is wound around a cylinder (buoy, or winch), the holding force is associated with the load force. When the cable accelerates or decelerates, some of the force is dissipated on the accelerating winch, and in order to transmit this force, some preload must be applied to the cable to prevent slippage between the cable and the pulley.

[0059] Therefore, for a pulley subjected to driving force, even ignoring friction, and with the end actuators on both sides passing through...

[0060] Even when the flexible cables are connected, different forces will still be generated on either side. Therefore, for the overall mechanism, using two drives to control the upper and lower mechanisms connected by the flexible cables will inevitably result in different forces on the same cable. This situation requires specific analysis based on the direction of the motor's rotation.

[0061] There are a total of four specific scenarios, but in actual analysis, only two scenarios need to be analyzed: the motors rotating forward simultaneously and the left motor rotating forward while the right motor rotates in reverse, because the other two scenarios are mirror images of the first two. Therefore, this article only analyzes these two scenarios.

[0062] In the first case, where the drive motors rotate forward simultaneously, the dynamic equations can be obtained as follows:

[0063] (9)

[0064] in

[0065]

[0066] For the second case, the dynamic formula remains as shown in (9), but the relationship of its structure matrix is ​​transformed into:

[0067]

[0068] Reference Figure 4 The bed lifting device (13000) includes: a machining bed (13002) connected to the upper end of a machining bed support frame (13001) by screws; a machining bed support frame (13001) connected to the upper side of a bed support body (13100) by screws; a bed support body (13100) with aluminum profiles arranged in a cross shape connected by screws using angle iron; pulley sleeves (13004) connected to the left and right rear sides of the bed support body (13100) by screws; a winch sleeve (13006) connected to the front side of the bed support body (13100) by screws; a non-linear winch (13007) threaded onto the winch sleeve (13006); a pulley (13005) fitted onto the pulley sleeve (13004) by an transition fit; and a wheel connected to the bed support body (13004) by screws. The bed support body (13100) has a flexible cable bundle device (13008) on the lower side of the center, a speed reduction drive (13200) connected to the lower side of the bed support body (13100) by screws, a servo motor (13201) connected to the side of the speed reduction drive (13200) by screws, a timing belt fixing device (13003) connected to the lower side crossbar (11004) of the fixed platform by screws, a timing belt in the speed reduction drive (13200) is fixed on the timing belt fixing device by clearance fit and the addition of adjustment shims, and a flexible cable fixing device (13003) connected to the side crossbar (11004) of the fixed platform by screws. The flexible cable is set in the following sequence: flexible cable fixing device - sliding rod pulley - assembly frame pulley - flexible cable guide device - winch - end effector.

[0069] Reference Figure 5 The diagram shows the connection of the connecting rod, the assembly frame, and a portion of the flexible cable in a specific embodiment of the present invention. The connecting rod mechanism shown consists of four sliding rods of the same length but different heights, which are hinged together using an air bearing (12203). The flexible cable configuration enables two-degree-of-freedom movement of the sliding rod hinge point within the assembly frame.

[0070] Reference Figure 6 This is a connection diagram of the pulley sleeve, pulley, and part of the flexible cable in a specific embodiment of the present invention. The fixed pulley (13005) is set on the front of the pulley sleeve (13004) through a transition fit, and the flexible cable guide pulley is set on the lower side inside the pulley sleeve (13004) through a transition fit. When the bed lifting device (13000) is in motion, the fixed pulley (13005) acts as a movable pulley to realize the lifting of the machining bed; the guide pulley realizes the winding of the flexible cable through the flexible cable bundling device (13008) and finally wound on the nonlinear winch (13007) to realize the winding of excess flexible cable.

[0071] Reference Figure 7 This is a perspective view of a speed reduction drive in a specific embodiment of the present invention. The speed reduction drive (13200) includes a gap spring (13202) connecting the flexible cable in the flexible cable bundling device (13008), a long belt (13203) connected to the gap spring, a drive pulley 1 (13205) and a driven pulley 2 (13203) disposed inside the speed reduction drive via an interlocking fit, a synchronous belt (13204) fitted between the drive pulley and the driven pulley via an interlocking fit, a long belt (13203) fitted between the driven pulley and the driven pulley via an interlocking fit, a servo motor (13201) connected to the side of the speed reduction drive (13200) via screws, and a long belt fitted to the synchronous belt fixing device (13003) via an interlocking fit.

Claims

1. A fully constrained 3D printer based on a tendon-driven parallel mechanism, characterized in that: The system includes a fixed platform, a flexible cable slewing mechanism, and a bed lifting device. The flexible cable slewing mechanism comprises a partition plate, an end effector located at the lower end of the partition plate, an assembly frame located on the upper side of the partition plate, a linkage mechanism inside the assembly frame, winch supports at the four corners of the partition plate, a winch within the winch supports, a motor mount on the upper side of the winch supports, a flexible cable fixing device on the upper side of the assembly frame, a flexible cable guide device at the edge of the partition plate, and a flexible cable. The assembly frame includes an assembly frame base on the upper side of the partition plate, an assembly frame cover that mates with the assembly frame base, and an assembly frame pulley between the assembly frame base and the assembly frame cover. The linkage mechanism consists of sliding rods connected together by bearings, with the pulley located at the distal end of the sliding rods. The flexible cable is arranged in the following sequence: flexible cable fixing device - sliding rod pulley - assembly frame pulley - flexible cable guide device - winch - end effector. The sequence is as follows: In the flexible cable rotation mechanism, the sliding rod is driven by the flexible cable to rotate by the pulley. Through the configuration of the flexible cable, the sliding rod located on the upper side of the isolation plate and the flexible cable located on the lower side of the isolation plate and connected to the end effector are always parallel. The bed lifting device includes a machining bed, a bed support body installed together by aluminum profiles, a machining bed support frame set on the upper side of the bed support body, pulley sleeves set on the left and right rear sides of the bed support body, pulleys set on the pulley sleeves, a winch sleeve set on the front side of the bed support body, a non-linear winch set on the winch sleeve, a flexible cable bundle device set on the lower side of the bed support body, a reduction drive set on the lower side of the bed support body, a synchronous belt fixing device set on the lower side of the fixed platform, a flexible cable fixing device set on the upper crossbar of the fixed platform, and a flexible cable. The flexible cables in the bed lifting device are arranged in the following order: flexible cable fixing device - pulley - flexible cable bundle device - winch - reduction drive.

2. A fully constrained 3D printer based on a flexible cable-driven parallel mechanism according to claim 1, characterized in that: The fixed platform is assembled from aluminum profiles connected together by profile clamps.

3. The fully constrained 3D printer based on cable-driven parallel mechanism according to claim 1, wherein: The winch in the flexible cable slewing mechanism is a coaxial combination of winches with different radii.

4. The fully constrained 3D printer based on the cable-driven parallel mechanism according to claim 1, wherein: The bearing connecting the sliding rod in the flexible cable rotation mechanism is an air bearing.

5. The fully constrained 3D printer based on the cable-driven parallel mechanism according to claim 1, wherein: The speed reduction drive in the bed lifting device consists of three pulleys and a synchronous belt.

6. The fully constrained 3D printer based on the cable-driven parallel mechanism according to claim 1, wherein: The winch installed in the bed lifting device is a non-linear winch.

7. The fully constrained 3D printer based on the cable-driven parallel mechanism according to claim 1, wherein: In the bed lifting device, the connecting component between the flexible cable and the synchronous belt in the reduction drive is a gap spring, which serves to eliminate gaps and compensate for assembly errors.

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