Rotation control device

Abstract

To provide a rotation control device that can reduce reversal when stopping rotation of an upper rotating body and can achieve accurate control of a stopping position of the upper rotating body.SOLUTION: A rotation control device 2 comprises: a hydraulic pump 4; a rotation motor 6 operated by hydraulic oil discharged by the hydraulic pump 4; a control valve 8 controlling supply of hydraulic oil from the hydraulic pump 4 to the rotation motor 6; a first pipeline 18 and a second pipeline 20 both of which connect the rotation motor 6 and the control valve 8; communication means making the first pipeline 18 communicate with the second pipeline 20; a rotation speed sensor 22 detecting a rotation speed of the rotation motor 6; an operating device 24 outputting a rotation signal for operating the control valve 8; and a controller 26 making the first pipeline 18 communicate with the second pipeline 20 by the communication means when the rotation signal is not output, the rotation speed is decreasing, and the rotation speed is within a predetermined range.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a turning control device for a turning vehicle having a lower running body and an upper turning body supported rotatably on an upper portion of the lower running body. [Background technology]

[0002] A swing vehicle such as a hydraulic excavator comprises a lower traveling body and an upper swing body supported on the upper part of the lower traveling body so as to be freely swingable. In addition, as a mechanism for swinging the upper swing body, the swing vehicle comprises a hydraulic pump, a swing motor operated by hydraulic oil discharged from the hydraulic pump, a control valve for controlling the supply of hydraulic oil from the hydraulic pump to the swing motor, and first and second pipelines connecting the swing motor and the control valve.

[0003] In such a rotating vehicle, there is a problem that the upper rotating body reverses direction when the rotation of the upper rotating body is stopped. Even if the supply of hydraulic oil from the hydraulic pump to the rotation motor is cut off, the upper rotating body continues to rotate by inertia, and the rotation motor also continues to operate. Then, the rotation motor acts as a hydraulic pump, and a pressure difference occurs between the first and second lines, and this pressure difference causes the upper rotating body to reverse direction. Furthermore, the pressure difference between the first and second lines is generated again by the reversal, so the upper rotating body reverses direction again. This reversal continues until the pressure difference between the first and second lines disappears, causing discomfort and fatigue to the operator.

[0004] Therefore, a control device for preventing reversal is sometimes installed on a turning vehicle (see, for example, Patent Document 1). The control device described in Patent Document 1 includes a solenoid valve installed in a line connecting the first and second lines, and two pressure sensors for detecting the pressure in each of the first and second lines. This control device detects a pressure increase in the lower pressure side of either the first or second line, and opens the solenoid valve for a certain period of time immediately after starting a deceleration operation and when stopping, thereby connecting the first and second lines and preventing reversal from occurring. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] CD-ROM of Japanese Utility Model Application No. 3-89853 (Japanese Utility Model Application No. 5-40601) Summary of the Invention [Problem to be solved by the invention]

[0006] However, in the control device disclosed in the above Patent Document 1, it is difficult to accurately control the stop position. The braking force acting on the swing motor during swing is caused by the pressure difference occurring between the first and second pipes. For this reason, if the solenoid valve is opened immediately after the start of the deceleration operation, a delay occurs before a pressure difference that provides an appropriate braking force occurs. In addition, if the solenoid valve is opened at the time of stopping, no braking force is exerted at the time of stopping. Therefore, between the time of performing the swing stop operation and the time of swing stop, the upper swing body swings more than the position where the operator wants to stop it. Therefore, in the above swing control device, it is difficult to accurately control the stop position.

[0007] In addition, in the above control device, the solenoid valve is opened for a fixed time, which may weaken the anti-reverse effect or increase the rotation angle. In a slewing vehicle such as a hydraulic excavator or a crane, the inertial force during rotation changes depending on the posture of the front working machine having a boom, arm, or implement. When the inertial force changes, the pressure difference between the first and second lines changes. When the pressure difference changes, the time for which the first and second lines should be connected changes. Therefore, if the connection time of the first and second lines is controlled to be constant, when a long connection time is required because the pressure difference between the first and second lines is large, the actual connection time is too short, and the anti-reverse effect is weakened. On the other hand, when a short connection time is sufficient because the pressure difference between the first and second lines is small, the actual connection time is too long, and the rotation angle until the rotation stops increases.

[0008] An object of the present invention is to provide a rotation control device that can reduce reversal when stopping the rotation of an upper rotating body and can achieve accurate control of the stopping position of the upper rotating body. [Means for solving the problem]

[0009] According to the present invention, there is provided a turning control device that solves the above problems. "A turning control device for a turning type vehicle having a lower running body and an upper turning body supported on an upper part of the lower running body so as to be able to turn freely, A hydraulic pump; A swing motor operated by the hydraulic oil discharged from the hydraulic pump; a control valve for controlling the supply of hydraulic oil from the hydraulic pump to the swing motor; a first pipeline and a second pipeline each connecting the swing motor and the control valve; a communication means for communicating the first pipeline with the second pipeline; a rotation speed sensor for detecting a rotation speed of the rotation motor; an operating device that outputs a rotation signal for operating the control valve; and a controller that connects the first pipeline and the second pipeline by the connecting means when the rotation signal is not output, the rotation speed is decreasing, and the rotation speed is within a predetermined range.

[0010] Preferably, the controller causes the first pipeline to communicate with the second pipeline by the communicating means even when the rotation signal is not being output, the rotation speed is not decreasing, and the rotation speed exceeds a threshold value. The threshold value is preferably smaller than a lower limit value of the predetermined range.

[0011] Further, a first pressure sensor for detecting a pressure in the first pipe and a second pressure sensor for detecting a pressure in the second pipe, The controller can connect the first line and the second line via the connecting means when the rotation signal is not output, the rotation speed is not decreasing, and the rotation speed exceeds the threshold value, and when the difference in pressure between the first line and the second line is less than a predetermined value.

[0012] The communication means is preferably provided in the control valve. The communication means may be a solenoid valve provided in a line connecting the first line and the second line. Effect of the Invention

[0013] According to the rotation control device of the present invention, when the rotation signal is not output and the rotation speed is decreasing, the communication means does not communicate with the first and second pipes until the rotation speed falls below the upper limit of the predetermined range, so that the pressure difference between the first and second pipes gradually increases, and a braking force caused by the pressure difference acts on the rotation motor. Then, when the rotation speed falls below the upper limit of the predetermined range, the first and second pipes communicate with each other through the communication means, so that the pressure difference between the first and second pipes does not become excessively large. As a result, the reversal is reduced. Furthermore, when the rotation speed falls below the lower limit of the predetermined range, the communication is released, and a braking force caused by the pressure difference acts on the rotation motor. Therefore, according to the present invention, it is possible to reduce the reversal when stopping the rotation of the upper rotating body, and to realize accurate control of the stop position of the upper rotating body. [Brief description of the drawings]

[0014] [Figure 1] FIG. 2 is a circuit diagram of a turning control device according to the present invention. [Diagram 2] FIG. 4 is a circuit diagram showing an example of the flow of hydraulic oil when a rotation signal is output from an operating device. [Diagram 3] 3 is a circuit diagram showing the flow of hydraulic oil when a rotation signal is no longer output from the state shown in FIG. 2. [Figure 4] FIG. 4 is a circuit diagram showing a state in which a first pipeline and a second pipeline are in communication with each other. [Diagram 5]2 is a flowchart showing an example of determination and control executed by a controller shown in FIG. 1. [Figure 6] 4 is a flowchart showing another example of the determination and control executed by the controller shown in FIG. 1 . [Figure 7] FIG. 6 is a circuit diagram of a turning control device according to another embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, preferred embodiments of a turning control device according to the present invention will be described with reference to the drawings.

[0016] (Rotation control device 2) The swing control device 2 shown in Fig. 1 can be mounted on a swing vehicle (such as a hydraulic excavator or a crane vehicle) that includes a lower traveling body and an upper swing body that is supported on the upper part of the lower traveling body so as to be freely swingable. The swing control device 2 includes a hydraulic pump 4, a swing motor 6, and a control valve 8.

[0017] (Hydraulic pump 4) The hydraulic pump 4 is driven by a drive source 10 such as an engine or an electric motor, and draws hydraulic oil from a tank 12 and discharges it to a pump line 14. As shown in Fig. 1, the pump line 14 is a line that connects the hydraulic pump 4 and the control valve 8.

[0018] (Rotation motor 6) The swing motor 6 is a hydraulic actuator that is actuated by the hydraulic oil discharged from the hydraulic pump 4 to swing the upper swing structure relative to the lower traveling structure. The swing motor 6 has a first port 6a and a second port 6b. When high-pressure hydraulic oil discharged from the hydraulic pump 4 is supplied to either the first or second port 6a, 6b, the output shaft (not shown) of the swing motor 6 rotates, thereby swinging the upper swing structure.

[0019] (Control valve 8) The control valve 8 controls the supply of hydraulic oil from the hydraulic pump 4 to the swing motor 6. The control valve 8 controls whether or not the hydraulic oil discharged from the hydraulic pump 4 is supplied to the swing motor 6, and when hydraulic oil is supplied to the swing motor 6, whether the hydraulic oil is supplied to the first or second port 6a, 6b. Furthermore, the control valve 8 also controls the amount of hydraulic oil supplied to the swing motor 6.

[0020] Four ports 8p, 8t, 8a, and 8b are formed in the control valve 8. The P port 8p of the control valve 8 is connected to the hydraulic pump 4 via a pump line 14, and the T port 8t is connected to the tank 12 via a tank line 16. The A port 8a is connected to the first port 6a of the swing motor 6 via a first line 18, and the B port 8b is connected to the second port 6b of the swing motor 6 via a second line 20.

[0021] The control valve 8 of this embodiment has four positions from a first position P1 to a fourth position P4. In the first position P1, each of the four ports 8p, 8t, 8a, and 8b is closed. In the second position P2, the P port 8p communicates with the A port 8a, and the B port 8b communicates with the T port 8t. In the third position P3, opposite to the second position P2, the P port 8p communicates with the B port 8b, and the A port 8a communicates with the T port 8t. In the fourth position P4, the A port 8a communicates with the B port 8b, and the P port 8p and the T port 8t are closed.

[0022] The control valve 8 is electromagnetic, and the control valve 8 is positioned at any one of the first position P1 to the fourth position P4 by controlling the current supplied to the control valve 8. When the control valve 8 is positioned at the first position P1 or the fourth position P4, hydraulic oil is not supplied from the hydraulic pump 4 to the swing motor 6. When the control valve 8 is positioned at the second position P2, high-pressure hydraulic oil is supplied from the hydraulic pump 4 to the first port 6a of the swing motor 6, and low-pressure hydraulic oil is returned from the second port 6b of the swing motor 6 to the tank 12. When the control valve 8 is positioned at the third position P3, high-pressure hydraulic oil is supplied from the hydraulic pump 4 to the second port 6b of the swing motor 6, and low-pressure hydraulic oil is returned from the first port 6a of the swing motor 6 to the tank 12.

[0023] The turning control device 2 also includes a communication means, a turning speed sensor 22, an operation device 24, and a controller 26. As shown in FIG.

[0024] (Communication means) The communicating means communicates the first pipe 18 and the second pipe 20. In this embodiment, the communicating means is provided in the control valve 8. That is, the fourth position P4 of the control valve 8 is the communicating means. When the control valve 8 is positioned in the fourth position P4, the A port 8a and the B port 8b communicate with each other, and therefore the first pipe 18 and the second pipe 20 communicate with each other.

[0025] (Rotation speed sensor 22) The swing speed sensor 22 detects the swing speed of the swing motor 6, and is attached to the swing motor 6. The value detected by the swing speed sensor 22 is sent to a controller .

[0026] (Operating device 24) The operating device 24 outputs a rotation signal for operating the control valve 8. The rotation signal is an electric signal, and changes according to the amount of operation of the operating device 24. For example, a joystick, a slide switch, or the like may be used as the operating device 24. Note that the operating device 24 may be configured to output other electric signals in addition to the rotation signal.

[0027] (Controller 26) The controller 26 controls the current supplied to the control valve 8 based on the swing signal output from the operation device 24. For example, when the swing signal changes in response to an increase in the amount of operation of the operation device 24, the controller 26 operates the control valve 8 so as to increase the amount of hydraulic oil supplied to the swing motor 6. The controller 26 may be composed of a computer having a processor and a memory.

[0028] (First and second pressure sensors 28, 30) The first pressure sensor 28 detects the pressure in the first pipeline 18. Meanwhile, the second pressure sensor 30 detects the pressure in the second pipeline 20. The values ​​detected by the first and second pressure sensors 28, 30 are sent to the controller 26.

[0029] (Operation of turning control device 2) Next, the operation of the turning control device 2 will be described.

[0030] When the operating device 24 is not operated and is in the neutral position, no swing signal is output from the operating device 24 to the controller 26. In this case, the controller 26 positions the control valve 8 in the first position P1 (see FIG. 1). In the first position P1, the four ports 8p, 8t, 8a, and 8b are closed, so that no hydraulic oil is supplied from the hydraulic pump 4 to the swing motor 6. Therefore, the swing motor 6 does not operate, and the upper swing body does not swing.

[0031] On the other hand, when the operating device 24 is operated, a swing signal is output from the operating device 24 to the controller 26. In this case, the controller 26 positions the control valve 8 at the second position P2 or the third position P3. Then, hydraulic oil is supplied from the hydraulic pump 4 to the swing motor 6, so that the swing motor 6 is operated and the upper swing body swings.

[0032] For example, when the operating device 24 is operated in the direction indicated by the arrow A in FIG. 2, a rotation signal for operating the swing motor 6 in the direction indicated by the arrow R in FIG. 2 is output from the operating device 24 to the controller 26. In this case, the controller 26 positions the control valve 8 at the second position P2. As a result, the P port 8p and the A port 8a communicate with each other, and the B port 8b and the T port 8t communicate with each other. Therefore, high-pressure hydraulic oil is supplied from the hydraulic pump 4 to the first port 6a of the swing motor 6. Therefore, the output shaft (not shown) of the swing motor 6 operates in the direction indicated by the arrow R, and the upper swing body swings. In addition, low-pressure hydraulic oil is returned from the second port 6b of the swing motor 6 to the tank 12. In FIG. 2, the flow of high-pressure hydraulic oil is indicated by a thick black line, and the flow of low-pressure hydraulic oil is indicated by a thick gray line.

[0033] After that, when the operating device 24 is returned to the neutral position (non-operating position), the swing signal from the operating device 24 is cut off. In this case, the controller 26 positions the control valve 8 at the first position P1 (see FIG. 3). Therefore, the supply of hydraulic oil from the hydraulic pump 4 to the swing motor 6 is cut off. However, even if the supply of hydraulic oil to the swing motor 6 is cut off, the upper swing body continues to swing due to inertia, so the swing motor 6 also continues to operate in the R direction. The operation of the swing motor 6 at this time acts as a hydraulic pump. In other words, the swing motor 6 discharges the hydraulic oil sucked in from the first pipe 18 to the second pipe 20. Therefore, the pressure in the first pipe 18 decreases and the pressure in the second pipe 20 increases, so a pressure difference occurs between the first pipe 18 and the second pipe 20.

[0034] In this way, when the rotation signal that was being output is discontinued and the control valve 8 returns from the second position P2 or the third position P3 to the first position P1, a pressure difference occurs between the first pipe 18 and the second pipe 20. This pressure difference acts as a braking force against the rotation of the upper rotating body, but it can also be a factor in causing the upper rotating body to reverse after the rotation stops.

[0035] Therefore, when a predetermined condition is satisfied, the controller 26 communicates the first pipe 18 with the second pipe 20 by the communication means. In this embodiment, as shown in Fig. 4, when a predetermined condition is satisfied, the controller 26 positions the control valve 8 at the fourth position P4 to communicate the first pipe 18 with the second pipe 20.

[0036] First, in the following cases, the controller 26 determines that a predetermined condition is satisfied and connects the first pipe 18 and the second pipe 20. That is, (a) The turn signal is not being output, (b) The turning speed is decreasing, and (c) The absolute value of the turning speed is within a predetermined range (V1 < |V| <V2) In this case, the turning speed is V, the lower limit of the predetermined range is V1, and the upper limit of the predetermined range is V2.

[0037] In the above case, by communicating the first pipe 18 with the second pipe 20, it is possible to reduce the reversal of the upper rotating body when the rotation of the upper rotating body is stopped. After the rotation signal is discontinued, the rotation speed V gradually decreases, while the pressure difference between the first and second pipes 18, 20 gradually increases. Therefore, as described above in (c), by communicating the first and second pipes 18, 20 when the rotation speed V falls below the upper limit value V2 of the predetermined range, it is possible to prevent the pressure difference between the first and second pipes 18, 20 from becoming too large. Therefore, it is possible to reduce the reversal when the rotation is stopped.

[0038] As described above in (c), unless the rotation speed V is within a predetermined range, the first pipe 18 and the second pipe 20 are not connected, so that the stop position of the upper rotating body can be accurately controlled. Immediately after the rotation signal is terminated and until the rotation speed V falls below the upper limit value V2, the first and second pipes 18 and 20 are not connected to each other, so that the pressure difference is increased, and a braking force caused by the pressure difference is applied to the rotation motor 6. When the rotation speed V falls below the lower limit value V1 of the predetermined range (i.e., immediately before the rotation stops), the communication between the first and second pipes 18 and 20 is released, so that a braking force caused by the pressure difference is applied to the rotation motor 6. In this way, the braking force caused by the pressure difference is applied to the rotation motor 6 immediately after the rotation signal is terminated and immediately before the rotation stops, so that the stop position can be accurately controlled.

[0039] In the illustrated embodiment, the communication control is performed based on the rotation speed, so that the communication time is never too short or too long. The rotation speed is related to the pressure difference between the first and second pipes 18 and 20. Therefore, even if the time to communicate changes due to a change in the pressure difference between the first and second pipes 18 and 20, in this embodiment, there is no large difference between the time to communicate and the actual communication time. In other words, compared to the conventional technology in which the communication time is controlled to be constant in all cases, this embodiment has less variation in the reversal reduction effect and the stop position control.

[0040] It is also desirable for the controller 26 to determine that the predetermined condition is satisfied and to connect the first pipe 18 and the second pipe 20 in the following cases: (a) No turning signal is output (the operation device 24 is in the neutral position), (d) The rotation speed V is not decreasing, and (e) The absolute value of the turning speed V exceeds the threshold (V3<|V|). In this case, the threshold value is V3.

[0041] In the above case, by connecting the first and second pipelines 18 and 20, further inversion after the upper slewing body has been inverted once can be reduced. In the present embodiment, while aiming to reduce the inversion of the upper slewing body, since it aims to achieve accurate control of the stop position, which is contrary to the reduction of inversion, there is a possibility that a small inversion may occur. Therefore, when an inversion occurs and the slewing speed V is on an increasing trend or constant and the slewing speed V exceeds the threshold value V3, by connecting the first and second pipelines 18 and 20, further inversion after the first inversion can be reduced.

[0042] Note that the threshold value V3 may be a value smaller than the above lower limit value V1 (V3 < V1). This is because when an inversion occurs, it is preferable to connect the first and second pipelines 18 and 20 even at a low speed.

[0043] Furthermore, in addition to (a), (d), and (e), the following (f) may be added. That is, (a) No slewing signal is output, (d) The slewing speed V is not decreasing, and (e) When the slewing speed V exceeds the threshold value V3, (f) When the difference between the pressure in the first pipeline 18 and the pressure in the second pipeline 20 is less than a predetermined value the controller 26 may determine that the predetermined conditions are satisfied and connect the first pipeline 18 and the second pipeline 20.

[0044] By determining the above (f), the stop position of the upper slewing body can be controlled more accurately. This is because when the pressure difference between the first and second pipelines 18 and 20 is greater than or equal to the predetermined value, by not connecting the first and second pipelines 18 and 20, the braking force caused by the pressure difference can act on the slewing motor 6.

[0045] Regarding the predetermined conditions as described above, the determination and control executed by the controller 26 will be described with reference to the flowcharts shown in FIGS. 5 and 6.

[0046] First, in step S1, the controller 26 determines whether a turning signal is output from the operating device 24. If no turning signal is output from the operating device 24 (i.e., if the operating device 24 is in the neutral position), the process proceeds to step S2.

[0047] Next, in step S2, the controller 26 determines whether the turning speed V is decreasing based on the detection result of the turning speed sensor 22. If the turning speed V is decreasing, the process proceeds to step S3. On the other hand, if the turning speed V is not decreasing, the process proceeds to step S5.

[0048] Next, in step S3, the controller 26 determines whether the absolute value |V| of the turning speed V is within a predetermined range (V1 < |V| < V2). If V1 < |V| < V2, the process proceeds to step S4.

[0049] In step S4, the controller 26 causes the first pipeline 18 and the second pipeline 20 to communicate with each other by means of communication. Also, the determinations in steps S1 - S3 are repeated, and while the predetermined conditions are satisfied, the communication between the first and second pipelines 18 and 20 is continued, and when the predetermined conditions are no longer satisfied, the communication between the first and second pipelines 18 and 20 is blocked.

[0050] Also, when the process proceeds to step S5 (when the determination in step S2 is No), it is determined whether the absolute value |V| of the turning speed V exceeds a threshold value V3. If V3 < |V|, the process proceeds to step S4 above, and the first pipeline 18 and the second pipeline 20 are communicated with each other until the predetermined conditions are no longer satisfied. Alternatively, as shown in FIG. 6, when V3 < |V|, the process may proceed to step S6 before proceeding to step S4.

[0051] In step S6, it is determined whether the difference between the pressure in the first pipeline 18 and the pressure in the second pipeline 20 is less than a predetermined value. Then, if the pressure difference is less than the predetermined value, the process proceeds to step S4 above, and the first pipeline 18 and the second pipeline 20 are communicated with each other until the predetermined conditions are no longer satisfied.

[0052] As described above, the rotation control device 2 of the illustrated embodiment can reduce reversal when stopping the rotation of the upper rotating body, and can realize accurate control of the stopping position of the upper rotating body.

[0053] The communication means is not limited to the above-mentioned form, and may be, for example, a form as shown in FIG. 6. In the form shown in FIG. 6, the communication means is constituted by a solenoid valve 34 provided in a connection line 32 that connects the first line 18 and the second line 20. The solenoid valve 34 as the communication means is usually positioned in a closed position. When the above-mentioned predetermined conditions are satisfied, the controller 26 positions the solenoid valve 34 in an open position to communicate the first and second lines 18, 20. However, from the viewpoint of manufacturing costs, it is preferable that the communication means is provided in the control valve 8 rather than the form shown in FIG. 6 (manufacturing costs are lower). [Explanation of symbols]

[0054] 2: Rotation control device 4: Hydraulic pump 6: Swivel motor 8: Control valve 18: 1st pipeline 20:Second conduit 22: Rotation speed sensor 24: Operating device 26: Controller 28: First pressure sensor 30: Second pressure sensor

Claims

1. A turning control device for a turning type vehicle including a lower traveling body and an upper turning body supported on an upper portion of the lower traveling body so as to be freely turned, A hydraulic pump; A swing motor operated by the hydraulic oil discharged from the hydraulic pump; a control valve for controlling the supply of hydraulic oil from the hydraulic pump to the swing motor; a first pipeline and a second pipeline each connecting the swing motor and the control valve; A communication means for communicating the first pipeline with the second pipeline; a rotation speed sensor for detecting a rotation speed of the rotation motor; an operating device that outputs a rotation signal for operating the control valve; A rotation control device comprising: a controller that connects the first pipeline and the second pipeline via the communication means when the rotation signal is not output, the rotation speed is decreasing, and the rotation speed is within a predetermined range.

2. 2. The turning control device as described in claim 1, wherein the controller connects the first pipeline and the second pipeline through the connecting means even when the turning signal is not output, the turning speed is not decreasing, and the turning speed exceeds a threshold value.

3. The turning control device according to claim 2 , wherein the threshold value is smaller than a lower limit value of the predetermined range.

4. The pressure sensor further includes a first pressure sensor that detects a pressure in the first pipeline and a second pressure sensor that detects a pressure in the second pipeline, 3. The turning control device as described in claim 2, wherein the controller connects the first line and the second line by the connecting means when the turning signal is not output, the turning speed is not decreasing, and the turning speed exceeds the threshold value, and when the difference between the pressure in the first line and the pressure in the second line is less than a predetermined value.

5. 2. The turning control device according to claim 1, wherein the communication means is provided in the control valve.

6. 2. The turning control device according to claim 1, wherein the communication means is an electromagnetic valve provided in a line connecting the first line and the second line.

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