JP6923688B2 - Robots and robot systems - Google Patents

Description

The present invention relates to robots and robot systems.

Conventionally, in a system in which a robot supplies and discharges a work to a machine tool, even if the relative positional relationship between the machine machine and the robot changes due to the relocation of the robot, a camera provided at the tip of the robot arm is used. A robot system is known that measures a relative positional relationship by photographing a visual target provided on the outer surface of a machine tool and corrects the operating position of the robot based on the measured relative positional relationship (for example, a patent). See Document 1 and Patent Document 2.).

Japanese Unexamined Patent Publication No. 11-58273 Japanese Unexamined Patent Publication No. 62-54115

However, in the systems of Patent Document 1 and Patent Document 2, the camera is attached to the wrist tip of the robot. For this reason, the hand and other tools attached to the tip of the wrist become larger by the amount including the camera, and there is an inconvenience that it becomes difficult to insert the tip of the wrist into the narrow machine tool. In addition, since a part of the payload is the weight of the camera, there is an inconvenience that the weight of tools such as hands must be reduced.

Further, when the camera is attached to the hand, it is necessary to calibrate the camera every time the hand is replaced, which is complicated. Further, since the camera attached to the tip of the wrist is inserted close to the spindle of the machine tool, it is easily exposed to cutting fluid and may deteriorate.

The present invention has been made in view of the above circumstances, and provides a robot and a robot system capable of correcting an operating position with respect to a work target device without attaching a visual device such as a camera to the tip of the wrist. I am aiming.

In order to achieve the above object, the present invention provides the following means.
One aspect of the present invention includes a wrist unit to which a tool for performing work on a work target device can be attached, and a movable portion for changing the position of the wrist unit, and the movable portion has a longitudinal axis. The robot is provided with an arm having the wrist unit attached to the tip of the robot, and the visual sensor is fixed to the arm in a posture in which the central axis of the visual field of the visual sensor intersects the longitudinal axis.

According to this aspect, by installing the robot on the work target device fixed to the installation surface and operating the movable part, the three-dimensional position of the wrist unit attached to the tip of the arm of the movable part is changed. By operating the wrist unit, the posture of the tool attached to the tip surface can be changed, and the work can be performed by the tool on the work target device. Then, since the visual sensor's field of view moves depending on the movement of the movable part and / or the wrist unit, if the visual target is provided at a position where the relative positional relationship with the work target device is determined, the target is photographed by the visual sensor. Then, the relative positional relationship between the robot and the work target device can be measured, and the operating position of the robot with respect to the work target device can be corrected.

In the above aspect, the visual sensor may be located closer to the proximal end than the distal end of the wrist unit. In this case, since the visual sensor is not attached to the tip surface of the wrist unit, the degree of freedom of the posture of the visual sensor is reduced by at least the degree of freedom of the selection surface, but the visual field in the direction intersecting the longitudinal axis of the arm is defined. By attaching it so as to have it, the position of the visual sensor can be moved over a wide range according to the movement of the arm even with a degree of freedom lower than the degree of freedom of the robot. As a result, when there are multiple visual targets provided, it is possible to shoot visual targets arranged at different positions, and when there is a single visual target provided, the visual sensors are moved to multiple visual targets. You can shoot from the viewpoint. That is, by not attaching the visual sensor to the tip surface, it is possible to reduce the influence on the payload as compared with the case where the visual sensor is attached to the tip surface or the tool. In addition, the space around the tool can be reduced, and the wrist unit can be easily inserted into a narrow space. Further, when the work target device is a machine tool for cutting, it is possible to prevent the cutting fluid from being applied to the camera even if the wrist unit is inserted close to the spindle.

Moreover, even when the tool attached to the tip surface is replaced, it is not necessary to remove the visual sensor each time. Once the visual sensor is installed on the arm and calibrated for positioning the visual sensor, recalibration of the visual sensor becomes unnecessary regardless of the status of the tool, and complicated start-up work is required at the work site. Can be eliminated.

In the above aspect, the rotating body the movable portion, and the base over scan, a rotating body rotatably supported on the vertical axis direction with respect to the base, about the axis of the direction intersecting the vertical axis It may be provided with the arm rotatably supported with respect to the arm.

By doing so, the swivel body and two or more arms can be operated to move the three-dimensional position of the wrist unit. Even if the position with respect to the work target device is roughly set, the three-dimensional position of the visual sensor attached to the base end side of the wrist unit is moved by the movement of the movable part, and the relative positional relationship with the work target device. The operating position of the robot can be corrected by photographing a visual target provided at a fixed position and measuring the relative positional relationship between the robot and the work target device.

In the above embodiment, the arm includes a first arm which is rotatably supported with respect to the rotating body about the axis of the intersecting direction, is supported on the distal end of the first arm rotation can be A second arm may be provided, and the wrist unit may be attached to the tip of the second arm.
By doing so, the swivel body is rotated around the axis perpendicular to the base, the first arm is rotated around the axis horizontal to the swivel body, and the axis is horizontal to the first arm. By rotating the second arm, the wrist unit attached to the tip of the second arm can be moved to an arbitrary three-dimensional position. Further, by arranging the visual sensor near the tip of the second arm, the visual sensor can also be moved to an arbitrary three-dimensional position.

In the above embodiments, the movable portion, and the base over the scan, the rotation can be supported rotating body vertically about an axis relative to the base, one or more parallel to the axis of said pivot cylinder The arm may be provided so as to be rotatably supported around the axis.
By doing so, the moving range of the arm can be widened with respect to the floor surface. When the visual target is installed on a surface substantially parallel to the floor surface, a wide detection range can be secured, which is effective.

Further, in the above aspect, the base may be fixed, and a trolley for moving the movable portion, the wrist unit, and the visual sensor with respect to the work target device may be provided.
By doing so, the robot can be mounted on the trolley to be movable, and the trolley can be operated to move the robot to a different position with respect to the work target device.

Further, by making the dolly movable, the robot can be easily relocated according to the operating status of the work target device. Further, when a human performs work such as adjustment of a work target device, the robot can be easily moved to secure a work space.
Further, in the above aspect, the trolley may be a self-supporting mobile trolley.
Further, in the above aspect, the trolley may be a hand-push type trolley.

Further, in the above aspect, the visual sensor may have a field of view in a direction along a plane substantially orthogonal to the longitudinal axis of the arm.
By doing so, by arranging the robot so that the arm extends substantially parallel to the surface of the work target device facing the robot, the direction in which the visual field of the visual sensor faces can be substantially orthogonal to the work target device. , The visual field can be easily moved to a plurality of positions by the operation of the movable portion.

Further, in the above aspect, the central axis of the visual field of the visual sensor may be installed substantially horizontally with respect to the installation surface.
By doing so, the relative positional relationship with the work target device is determined, and the visual sensor is always held substantially perpendicular to the visual target provided on the surface perpendicular to the non-installation surface. The detection accuracy of the visual target can be improved.

Further, in the above aspect, the central axis of the visual field of the visual sensor may be installed substantially vertically with respect to the installation surface.
By doing so, when the visual target is installed on a surface substantially parallel to the floor surface, the visual sensor is always held substantially vertically to the surface substantially parallel to the floor surface. The detection accuracy of the visual target can be improved.
Further, in the above aspect, it may be a horizontal articulated robot.

Another aspect of the present invention, prior SL work object device and, the upper SL one robot, the robot as measured by photographing the visual target provided in a predetermined position by the visual sensor on the basis of the relative positional relationship between the operation target device and a robot system and a correcting unit for correcting the operating position of the robot.

According to this aspect, the robot is installed on the work target device fixed to the installation surface, the visual sensor's field of view is moved by the movement of the movable part and / or the wrist unit, and the relative positional relationship with the work target device. By photographing the visual target provided at the determined position, the relative positional relationship between the robot and the work target device can be measured, and the correction unit can correct the operating position of the robot with respect to the work target device.

In the above aspect, the visual target may be provided on the outer surface of the work target device.
By doing so, it is possible to utilize the characteristic shape of the outer surface of the work target device, the originally installed mark, etc. as a visual target, and it is more troublesome to install than when the visual target is installed separately from the work target device. And costs can be reduced. Further, a new visual target can be provided on the outer surface of the work target device, and the space can be used more effectively and the system can be made more compact than when the visual target is provided on a peripheral device other than the work target device.

According to the present invention, there is an effect that the operating position with respect to the work target device can be corrected without attaching a visual device such as a camera to the tip of the wrist.

It is an overall block diagram which shows the robot system which concerns on one Embodiment of this invention. It is a side view which shows an example of the robot which concerns on one Embodiment of this invention provided in the robot system of FIG. It is a top view of the robot of FIG. It is a top view which shows the state which the robot of FIG. 2 is positioned with respect to a machine tool. FIG. 5 is a plan view showing a state in which the robot of FIG. 2 is moved and then repositioned with respect to the machine tool. It is a top view which shows the state which the 1st arm and the 2nd arm of the robot of FIG. 2 are arranged substantially parallel to the front surface of a machine tool. It is a flowchart explaining the operation of the robot system of FIG.

The robot 3 and the robot system 1 according to the embodiment of the present invention will be described below with reference to the drawings.
As shown in FIG. 1, the robot system 1 according to the present embodiment includes a machine tool (work target device) 2 for cutting a work, a robot 3 for supplying and discharging a work to the machine tool 2. It includes a control device 4 that controls the robot 3. A correction unit (not shown) described later is provided in the control device 4.

The machine tool 2 is fixed to a floor surface (installed surface), and is a device that performs cutting and the like with a tool attached to a work (not shown) supplied by the robot 3 to a spindle.
Of the outer surface of the machine tool 2, the outer surface (front surface) facing the robot 3 is provided with visual targets 5 at three places, for example. As the visual target 5, for example, a mark such as a circle having a shape capable of accurately detecting the center position or the position of the center of gravity can be used by taking a picture with the visual sensor 16 described later. Each visual target 5 is fixed to the outer surface of the machine tool 2 so that its center position accurately matches a known coordinate position.

The robot 3 has a traveling carriage (trolley) 6 capable of traveling on the floor surface in an arbitrary direction, a movable portion 7 mounted on the traveling carriage 6, and a wrist unit 8 attached to the tip of the movable portion 7. I have.
As shown in FIGS. 2 and 3, the movable portion 7 includes a base 9 fixed to the traveling carriage 6 and a swivel cylinder 10 rotatably supported around the first axis A perpendicular to the base 9. The first arm (arm) 11 rotatably supported around the second axis B horizontal to the swivel body 10 and the third axis C horizontal to the tip of the first arm 11 can be rotated. It is provided with a supported second arm (arm) 12.

The wrist unit 8 has a first wrist axis 13 attached to the tip of the second arm 12 and rotatably supported around the fourth axis D arranged along a plane orthogonal to the third axis C, and a fourth. The second wrist axis 14 rotatably supported around the fifth axis E orthogonal to the axis D and the third wrist axis 15 rotatably supported around the sixth axis F orthogonal to the fifth axis E. I have. A tip surface 15a that is rotated around the sixth axis F is provided at the tip of the third wrist shaft 15, and a hand (not shown) for gripping the work is attached to the tip surface 15a.

The robot 3 according to the present embodiment includes a camera (visual sensor) 16 attached to a second arm 12 located on the proximal end side of the distal end surface 15a. The camera 16 is arranged so that the field of view is directed along a plane substantially orthogonal to the fourth axis D, which is the longitudinal axis of the second arm 12.

The correction unit processes the image of the visual target 5 acquired by the camera 16, detects the center position of the visual target 5, and based on the detected center position, the relative positional relationship between the robot 3 and the machine tool 2. Is to be measured.
Then, the correction unit corrects the position of the work supply / discharge operation by the robot 3 which is taught or programmed in advance based on the measured relative positional relationship. In the figure, reference numeral 17 is a teaching operation panel.

The operations of the robot 3 and the robot system 1 according to the present embodiment configured in this way will be described below.
According to the robot system 1 according to the present embodiment, as shown in FIG. 4, the teaching operation for the robot 3 is performed with the robot 3 positioned at a predetermined installation position with respect to the machine tool 2. A teaching program is generated in which the work is supplied to the machine tool 2 by the robot 3 and the work after cutting is discharged.

By executing the generated teaching program by the control device 4, a series of operations of supplying the work by the robot 3, cutting by the machine tool 2, and discharging the work by the robot 3 are automatically performed.
After this, by moving the traveling carriage 6, the robot 3 is moved to a different position, for example, a position for supplying and discharging the work to another machine tool 2, and then again to the original machine tool 2. On the other hand, a case where the work is moved to a position where it can be supplied and discharged will be described.

In such a case, as shown in FIG. 5, when the traveling carriage 6 shown by the solid line is not strictly installed at the predetermined installation position of the robot 3 in which the first teaching operation is performed shown by the chain line. Even if the teaching program is executed as it is, the work cannot be correctly supplied and discharged to the machine tool 2.
In the present embodiment, even if the traveling carriage 6 is installed rotating with respect to the machine tool 2, the position and rotation deviation of the traveling carriage 6 are automatically detected by photographing the visual target 5 with the camera 16. , The operating position of the teaching program can be corrected. Further, when the position and rotation deviation of the traveling carriage 6 are large and the visual target 5 is out of the field of view of the camera 16 in a predetermined robot operation for photographing the visual target 5, the visual target 5 is placed in the field of view of the camera 16. Automatically change the robot movement.

That is, as shown in FIG. 7, when the robot 3 is relocated (step S1), it is determined whether or not the visual target 5 in front of the machine tool 2 is within the field of view of the camera 16 (step S2). When the visual target 5 is not within the field of view of the camera 16, the first arm 11 is moved to the second axis B in a state where the robot 3 is not strictly installed at a predetermined installation position and the traveling trolley 6 remains displaced. The second arm 12 is rotated around the third axis C (step S3), and the robot 3 is automatically operated so that the visual target 5 on the front surface of the machine tool 2 is within the field of view of the camera 16.

If the visual target 5 does not enter the field of view of the camera 16 even when the first arm 11 and the second arm 12 are operated, the fourth axis of the second arm 12 is automatically set as shown in FIG. The swivel cylinder 10 is rotated around the first axis A so that D is substantially parallel to the front surface of the machine tool 2, and the visual target 5 is placed in the field of view of the camera 16. As a result, the camera 16 attached to the tip of the second arm 12 directs its field of view toward the front surface of the machine tool 2.
Then, with the visual target 5 within the field of view of the camera 16, the camera 16 is operated to photograph the visual target 5 and acquire an image (step S4).

The visual target 5 is photographed from two directions at different angles with respect to the perpendicular line on the front surface of the machine tool 2. As a result, the coordinates of the visual target 5 in the direction along the front surface of the machine tool 2 can be detected from the position of the visual target 5 in the image, and the machine tool is obtained from two images obtained from two different angles. The coordinates of the visual target 5 in the direction orthogonal to the front surface of 2 can be detected.

The acquired image is sent to the correction unit, and the correction unit performs image processing to detect the center position thereof (step S5). The process from step S2 is repeated until the center positions of the three visual targets 5 are acquired (step S6).

In the correction unit, the relative positional relationship between the robot 3 and the machine tool 2 is obtained from the three acquired center positions (step S7). Then, in the correction unit, the operation position in the teaching program previously taught is corrected based on the obtained relative positional relationship (step S8).
As a result, according to the robot system 1 according to the present embodiment, when the traveling carriage 6 is operated to move the robot 3 between different machine tools 2 and used in common, for each machine tool 2. Even if the traveling carriage 6 is not positioned at exactly the same position, there is an advantage that the teaching program once generated can be corrected and reused without performing the teaching operation again.

Therefore, the work can be supplied and discharged to each machine tool 2 with high accuracy, and the robot 3 can be fixed not by anchor bolts but by a simple fixture.

According to the robot 3 and the robot system 1 according to the present embodiment, since the camera 16 is not attached to the tip surface 15a of the wrist unit 8, the camera 16 cannot be operated with 6 degrees of freedom, but the second arm 12 By attaching it to the tip of the robot, it can be operated in a wide operating range with three degrees of freedom. Further, since the field of view is oriented in the direction along the plane orthogonal to the fourth axis D, even if the traveling carriage 6 is arranged at an angle with respect to the machine tool 2, the fourth axis D is placed on the machine tool 2. It can be arranged in parallel with each other, and the visual targets 5 arranged at a plurality of locations on the front surface of the machine tool 2 can be easily photographed. Further, if the traveling carriage 6 is arranged at an angle with respect to the machine tool 2 and the visual target 5 cannot be photographed in this state, the swivel body 10 is manually or automatically rotated around the first axis A for visual observation. Take a picture of target 5.

As a result, since the camera 16 is not attached to the tip surface 15a of the wrist unit 8, the dimensions of the tool including the hand attached to the tip surface 15a can be kept small, and the insertion into the machine tool 2 can be facilitated. There is an advantage that it can be done.
Further, by not attaching the camera 16 to the tip surface 15a, it is possible to prevent the camera 16 from consuming the payload. That is, there is an advantage that the weight of the camera 16 does not reduce the weight of tools such as other hands.

Further, since there is a high possibility that the wrist unit 8 inserted inside the machine tool 2 is exposed to the cutting fluid, by attaching the camera 16 to the second arm 12 away from the wrist unit 8, the cutting fluid is applied to the camera 16. There is an advantage that the camera 16 can be maintained in a healthy state by reducing such possibility.

Further, even when the tool attached to the tip surface 15a is replaced, it is not necessary to remove the camera 16 each time, the camera 16 is installed on the second arm 12, and the positioning of the camera 16 is calibrated once. This has the advantage that recalibration of the camera 16 is not required regardless of the status of the tool, and complicated start-up work can be eliminated at the work site.

Further, by making the traveling carriage 6 movable, there is an advantage that the robot 3 can be easily relocated according to the operating status of the machine tool 2. Further, when a human performs work such as adjustment of the machine tool 2, there is an advantage that the robot 3 can be easily moved to secure a work space.

Further, the characteristic shape of the outer surface of the machine tool 2 and the originally installed mark can be utilized as the visual target 5, which requires more labor and cost than the case where the visual target 5 is installed separately from the machine tool 2. Can be reduced. Further, a new visual target can be provided on the outer surface of the machine tool 2, and the space can be effectively utilized as compared with the case where the visual target 5 is provided on a peripheral device or the like different from the machine tool 2. There is an advantage that the robot system 1 can be made compact.

In the robot system 1 according to the present embodiment, a circular mark is illustrated as the visual target 5, but as described above, any feature point such as a center point or a center of gravity point can be detected. , A mark having another shape may be used, or a part of the characteristic shape of the machine tool 2 may be used as the visual target 5.
Further, although the case where a plurality of visual targets 5 are provided on the machine tool 2 is illustrated, instead of this, a single visual target 5 may be provided on the machine tool 2.

Further, the position of the visual target 5 is preferably the front surface of the machine tool 2 extending in the vertical direction, but instead, it may be on a plane extending in the horizontal direction or on an inclined surface. good.
Further, it may be arranged inside the machine tool 2.

Further, in the present embodiment, the visual target 5 provided on the outer surface of the machine tool 2 is illustrated, but the visual target 5 does not necessarily have to be provided on the outer surface of the machine tool 2, and the machine tool 2 and the like. It suffices if it is installed at a position where the relative positional relationship of is fixed. For example, the visual target 5 may be provided on the floor on which the machine tool 2 is installed, or on a peripheral device having a relative positional relationship with the machine tool 2.

Further, in the present embodiment, the camera 16 is attached to the tip of the second arm 12, but the present invention is not limited to this. In order to accurately measure the relative positional relationship between the robot 3 and the machine tool 2, it is preferable that the visual targets 5 are arranged over a wide range. Therefore, in order to photograph such a visual target 5, a wide operating range is used. An achievable tip of the second arm 12 is preferred.

Instead of this, even if it is attached to the intermediate position, the proximal end portion, the tip end, the intermediate position, the proximal end portion, or the swivel cylinder 10 of the second arm 12, it can be moved over a predetermined operating range. Therefore, the camera 16 may be attached to these positions.
Further, the camera 16 may be attached to the first wrist shaft 13 or the second wrist shaft 14 excluding the tip surface 15a of the wrist unit 8. In this case, the degree of freedom for moving the camera 16 is increased, and the camera 16 can be moved while maintaining a constant posture. As a result, the change in the relative posture of the camera 16 with respect to the visual target 5 is small, so that the detection accuracy can be improved.

Further, when the camera 16 is mounted at a position substantially horizontal to the floor surface, the camera 16 is always held substantially perpendicular to the visual target 5 provided on the outer surface of the machine tool 2. Therefore, the detection accuracy of the visual target 5 can be improved.

Further, in the present embodiment, the automatic correction of the robot motion has been described as an example, but instead of this, a plurality of robots 3 are operated by the user to be provided on the front surface of the machine tool 2 by the camera 16. The operating position of the teaching program may be corrected by photographing the visual target 5.

Further, in the present embodiment, a robot 3 having a 6-axis vertical articulated movable portion 7 is illustrated, but the robot 3 is not limited to this, and is not limited to this, and is a vertical articulated robot having an arbitrary number of axes and is horizontal. An articulated robot or a linear robot may be adopted.
When the robot 3 is a horizontal articulated robot, the camera 16 may be mounted at a position substantially vertical to the floor surface. As a result, when the visual target 5 is installed on a surface substantially parallel to the floor surface, the camera 16 is always held substantially vertically to the surface substantially parallel to the floor surface, so that the visual target 5 is held. Detection accuracy can be improved. Further, even when the robot 3 is a vertical articulated robot, the camera 16 may be mounted at a position substantially vertical to the floor surface.

Further, although the machine tool 2 has been illustrated as the work target device, the present invention is not limited to this, and any other work target device on which the robot 3 performs the work may be adopted.
Further, although the robot 3 provided with the traveling carriage 6 which is a self-sustaining moving carriage is illustrated, the method is not limited to this, and the base 9 of the first axis A is directly fixed to the installed surface such as the floor surface after transportation. It may be a robot 3 or a robot 3 mounted on a manually moving hand-held trolley.

1 Robot system 2 Machine tool (work target device)
3 Robot 5 Visual target 6 Traveling trolley (trolley)
7 Movable part 8 Wrist unit 9 Base 10 Swing torso 11 1st arm (arm)
12 Second arm (arm)
15a Tip surface 16 Camera (visual sensor)
A, B, C axes

Claims (16)

It is provided with a wrist unit to which a tool for performing work on the work target device can be attached, and a movable part for changing the position of the wrist unit.
The movable portion includes an arm having a longitudinal axis and having the wrist unit attached to the tip thereof.
A robot in which a visual sensor is fixed to the arm in a posture in which the central axis of the visual field of the visual sensor intersects the longitudinal axis. The robot according to claim 1, wherein the visual sensor is located closer to the base end side of the tip end of the wrist unit. The movable portion is rotatably supported with respect to the base, a swivel body rotatably supported around the axis perpendicular to the base, and an axis in a direction intersecting the vertical axis. The robot according to claim 1 or 2, further comprising the arm. The arm includes a first arm rotatably supported with respect to the swivel body around an axis in the intersecting direction, and a second arm rotatably supported at the tip of the first arm.
The robot according to claim 3, wherein the wrist unit is attached to the tip of the second arm. The movable portion is rotatably supported around a base, a swivel body rotatably supported around an axis perpendicular to the base, and one or more axes parallel to the axis of the swivel body. The robot according to claim 1, further comprising the arm. The robot according to any one of claims 3 to 5, wherein the base is fixed, and the robot includes the movable portion, the wrist unit, and a trolley for moving the visual sensor with respect to the work target device. The robot according to claim 6, wherein the trolley is a self-sustaining mobile trolley. The robot according to claim 6, wherein the trolley is a hand-push type trolley. The robot according to claim 3 or 4, wherein the central axis of the visual field of the visual sensor is installed so as to be substantially horizontal to the surface to be installed. The robot according to claim 5, wherein the central axis of the visual field of the visual sensor is installed substantially vertically with respect to the surface to be installed. The robot according to claim 10, which is a horizontal articulated robot. The work target device and
The robot according to any one of claims 1 to 11.
A correction unit that corrects the operating position of the robot based on the relative positional relationship between the robot and the work target device measured by photographing a visual target provided at a predetermined position with the visual sensor. Robot system equipped with. The robot system according to claim 12, wherein the visual target is provided on a plane extending in a substantially vertical direction with respect to the installation surface. The robot system according to claim 12 or 13, wherein the visual target is provided on the outer surface of the work target device. A control device for controlling the robot is provided.
When the visual target is photographed by the visual sensor, the control device controls the robot so that the arm is arranged substantially parallel to the outer surface and the central axis of the field of view of the visual sensor is outside the outer surface. The robot system according to claim 14, which is directed to a surface. A wrist unit and an arm having a longitudinal axis and having the wrist unit attached to the tip thereof are provided.
A robot in which a visual sensor is fixed to the arm in a posture in which the central axis of the visual field of the visual sensor intersects the longitudinal axis.

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