Operating method and control device for a pneumatic unloader

The method automates the alignment of the suction nozzle's planar position using distance and angle calculations, addressing manual adjustments in conventional unloaders to ensure stable and efficient cargo suction.

JP2026052151APending Publication Date: 2026-03-24HITACHI PLANT MECHANICS
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Patent Information

Authority / Receiving Office
JP · JP
Patent Type
Applications
Current Assignee / Owner
Filing Date
2024-09-11
Publication Date
2026-03-24

AI Technical Summary

Technical Problem

Conventional pneumatic unloaders require manual adjustment of the suction nozzle's planar position when the cargo surface drops, disrupting the suction operation, which cannot be automated.

Method used

The method involves measuring and calculating the horizontal distance and angle changes of the horizontal boom to automatically correct the suction nozzle's planar position, ensuring alignment before and after elevation angle adjustments, using a control device to automate the process.

Benefits of technology

Automates cargo handling operations by ensuring the suction nozzle's planar position aligns correctly, allowing stable and efficient cargo suction without operator intervention.

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Abstract

To provide an operating method and control device for a pneumatic unloader that enables automation of cargo handling operations and reduces the burden on the operator by automatically controlling the correction of the planar position of the suction nozzle before and after changing the elevation angle of the horizontal boom. [Solution] The horizontal carriage 3 is measured to measure the distance moved from a preset reference position of the horizontal boom 2 before the elevation angle θ of the horizontal boom 2 of the pneumatic unloader 1 is changed. The horizontal distance from the base position O of the horizontal boom 2 to the suction nozzle 7 before and after the elevation angle θ of the horizontal boom 2 is changed is calculated from the reference position, the distance moved by the horizontal carriage 3 from the reference position, and the elevation angle θ of the horizontal boom 2 before and after the elevation angle θ of the horizontal boom 2 is changed. The horizontal carriage 3 is moved by a distance calculated from the difference in horizontal distance and the elevation angle θ of the horizontal boom 2 after the change, so that the plan view position of the suction nozzle 7 before and after the elevation angle θ of the horizontal boom 2 is changed.
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Description

Technical Field

[0001] The present invention relates to an operation method and an operation control device for an air unloader.

Background Art

[0002] Conventionally, as an unloader for unloading cargo consisting of various bulk goods such as grains loaded on a ship moored at a quay, a suction nozzle is inserted into the cargo, and the cargo is sucked from the suction nozzle by the suction force of a vacuum blower and unloaded into a receiver tank provided on the quay side. An air unloader is known (see, for example, Patent Documents 1 to 4).

[0003] These air unloaders include a horizontal boom that can be raised, lowered, and rotated, a horizontal carriage that moves along the horizontal boom, a horizontally extensible and retractable pipe provided along the horizontal boom and supported at its tip by the horizontal carriage, a vent pipe connected to the tip of the horizontally extensible and retractable pipe, a vertically extensible and retractable pipe connected to the vent pipe and held vertically, and a suction nozzle provided at the tip of the vertically extensible and retractable pipe for sucking the cargo.

[0004] And these air unloaders can stably suck the cargo from the suction nozzle into the cargo by automatically controlling the height position of the suction nozzle provided at the tip of the vertically extensible and retractable pipe based on the outputs of various sensors, inserting the suction nozzle by a dimension that allows the cargo to be sucked from the suction nozzle by the suction force of the vacuum blower.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

[0006] Thus, conventional pneumatic unloaders, as disclosed in Patent Documents 1 to 4, enable the automation of cargo handling operations and reduce the burden on the operator by automatically controlling the height position of the suction nozzle provided at the tip of the vertical telescopic tube. [Overview of the project] [Problems that the invention aims to solve]

[0007] Incidentally, when using a pneumatic unloader to unload cargo from a ship, if the unloading progresses and the surface position of the cargo drops, making it impossible to adjust by extending the vertical telescopic tube, the suction operation of the cargo is temporarily interrupted. The vertical telescopic tube is then retracted to raise the suction nozzle, and the elevation angle of the horizontal boom is reduced to lower the height of the suction nozzle located at the tip of the vertical telescopic tube. After that, the vertical telescopic tube is extended to insert the suction nozzle into the cargo, and the suction operation of the cargo is resumed. At this time, the plan view position of the suction nozzle before and after changing the elevation angle of the horizontal boom is made to match; that is, the plan view position of the suction nozzle when the cargo suction operation is interrupted is made to match the plan view position of the suction nozzle when the cargo suction operation is started. By inserting the suction nozzle into the depression on the surface of the cargo that is created when the cargo suction operation is interrupted and resuming the cargo suction operation, the cargo can be sucked up from the suction nozzle in a stable and efficient manner. However, this operation had to be performed manually by the operator based on visual observation.

[0008] This invention automatically corrects the planar position of the suction nozzle before and after changing the elevation angle of the horizontal boom. The objective is to provide an operating method and control device for a pneumatic unloader that enables the automation of cargo handling operations through dynamic control, thereby reducing the burden on the operator. [Means for solving the problem]

[0009] To achieve the above objective, the operating method of the pneumatic unloader of the present invention is as follows: A method for operating a pneumatic unloader comprising a horizontal boom that can be raised and lowered and rotated, a horizontal carriage that moves along the horizontal boom, a retractable horizontal telescopic tube provided along the horizontal boom and whose tip is supported by the horizontal carriage, a vented tube connected to the tip of the horizontal telescopic tube, a retractable vertical telescopic tube connected to the vented tube and held vertically, and a suction nozzle provided at the tip of the vertical telescopic tube for sucking up loads, The method involves measuring the distance the horizontal trolley has moved from a preset reference position of the horizontal boom before changing the luffing angle of the horizontal boom, calculating the horizontal distance from the base position of the horizontal boom to the suction nozzle before and after changing the luffing angle of the horizontal boom, and the difference between the horizontal distance before and after changing the luffing angle of the horizontal boom, based on the reference position, the distance the horizontal trolley has moved from the reference position, and the luffing angle of the horizontal boom before and after changing the luffing angle of the horizontal boom, and then moving the horizontal trolley by the distance calculated from the difference in horizontal distance and the luffing angle after changing the horizontal boom, thereby making the plan view position of the suction nozzle before and after changing the luffing angle of the horizontal boom the same.

[0010] In this case, the horizontal distance can be calculated based on the distance from the base end position of the horizontal boom when the horizontal trolley is positioned at a preset reference position of the horizontal boom to the intersection point of the central axis of the vertical telescopic tube and the horizontal boom.

[0011] Furthermore, the system includes a table that pre-calculates the distance from the base end position of the horizontal boom to the intersection point of the vertical telescopic tube and the horizontal boom when the horizontal trolley is positioned at a preset reference position of the horizontal boom, for each elevation angle of the horizontal boom, and the horizontal distance can be calculated using this table.

[0012] Furthermore, the pneumatic unloader operation control device of the present invention for implementing the operation method of the pneumatic unloader of the present invention is An operation control device for a pneumatic unloader comprising a horizontal boom that can be raised and lowered and rotated, a horizontal carriage that moves along the horizontal boom, a retractable horizontal telescopic tube provided along the horizontal boom and whose tip is supported by the horizontal carriage, a vented tube connected to the tip of the horizontal telescopic tube, a retractable vertical telescopic tube connected to the vented tube and held vertically, and a suction nozzle provided at the tip of the vertical telescopic tube for sucking up loads, The system includes a horizontal trolley movement distance measuring means for measuring the distance the horizontal trolley has moved from a preset reference position of the horizontal boom before the elevation angle of the horizontal boom is changed, and a horizontal distance calculation means for calculating the horizontal distance from the base position of the horizontal boom to the suction nozzle before and after the elevation angle of the horizontal boom is changed, and the difference in horizontal distance before and after the elevation angle of the horizontal boom is changed, based on the reference position, the distance the horizontal trolley has moved from the reference position, and the elevation angle of the horizontal boom before and after the elevation angle of the horizontal boom is changed. The system is characterized in that the horizontal trolley is moved by a distance calculated from the difference in horizontal distance and the elevation angle after the elevation angle of the horizontal boom is changed, thereby making the plan view position of the suction nozzle before and after the elevation angle of the horizontal boom coincide.

[0013] Furthermore, the system includes a table that pre-calculates the distance from the base end position of the horizontal boom to the intersection point of the vertical telescopic tube and the horizontal boom when the horizontal trolley is positioned at a preset reference position of the horizontal boom, for each elevation angle of the horizontal boom, and the horizontal distance can be calculated using this table. [Effects of the Invention]

[0014] According to the operating method and control device for the pneumatic unloader of the present invention, the elevation angle of the horizontal boom By automatically controlling the correction of the planar position of the suction nozzle before and after changing the angle, it is possible to automate cargo handling operations and reduce the burden on the operator. Specifically, the planar view positions of the suction nozzle before and after changing the undulation angle of the horizontal boom are made to coincide, that is, the planar view position of the suction nozzle when the loading and unloading operation of the cargo is interrupted is made to coincide with the planar view position of the suction nozzle when the loading and unloading operation of the cargo is started, and the suction nozzle is inserted into the depression on the surface of the cargo that can be formed when the loading and unloading operation of the cargo is interrupted, enabling automation of the cargo handling operation so that the suction nozzle can efficiently suck the cargo in a stable state from the suction nozzle.

Brief Description of Drawings

[0015] [Figure 1] It is an explanatory diagram showing an example of a pneumatic unloader for implementing the operation method of the pneumatic unloader of the present invention. [Figure 2] It is an explanatory diagram showing an example (change in the undulation angle of the horizontal boom (θ1 → θ2)) of the operation method of the pneumatic unloader of the present invention. [Figure 3] It is an explanatory diagram showing an example (change in the undulation angle of the horizontal boom (30° → 10°)) of the operation method of the pneumatic unloader of the present invention. [Figure 4] It is an explanatory diagram showing an example of the operation when the suction nozzle reaches the warehouse. [Figure 5] It is a flowchart showing an example of the operation when the suction nozzle reaches the warehouse.

Embodiments for Implementing the Invention

[0016] Hereinafter, embodiments of the operation method and operation control device of the pneumatic unloader of the present invention will be described based on the drawings.

[0017] FIG. 1 shows an example of a pneumatic unloader for implementing the operation method of the pneumatic unloader of the present invention. This pneumatic unloader 1, like the conventional pneumatic unloaders disclosed in Patent Documents 1 to 4, is used to unload cargo G consisting of various bulk materials such as grains loaded on a ship S that is moored at a quay W. It comprises a horizontal boom 2 that can be raised and lowered and rotated, a horizontal carriage 3 that moves along the horizontal boom 2, a retractable horizontal telescopic pipe 4 provided along the horizontal boom 2 with its tip supported by the horizontal carriage 3, a vent pipe 5 connected to the tip of the horizontal telescopic pipe 4, a retractable vertical telescopic pipe 6 connected to the vent pipe 5 and held vertically, and a suction nozzle 7 provided at the tip of the vertical telescopic pipe 6 for sucking up the cargo G. The suction nozzle 7 is inserted into the cargo G, and the cargo G is sucked up from the suction nozzle 7 by the suction force of a vacuum blower (not shown) and unloaded into a receiver tank (not shown) provided on the quay W side.

[0018] Furthermore, this pneumatic unloader, like conventional pneumatic unloaders, automatically controls the height position of the suction nozzle 7 located at the tip of the vertical telescopic tube 6 based on the output of various sensors, such as a level sensor on the suction nozzle 7 and a pressure sensor that detects the suction force of the vacuum blower. This allows the suction nozzle 7 to be inserted into the cargo G by a length that allows the cargo G to be stably sucked in from the suction nozzle 7, and the cargo is sucked in from the suction nozzle 7 by the suction force of the vacuum blower.

[0019] More specifically, this pneumatic unloader 1 can be configured as follows: a) The horizontal boom 2, horizontal trolley 3 (horizontal telescopic tube 4), and vertical telescopic tube 6 of the pneumatic unloader 1 operate independently of each other. b) The horizontal boom 2 performs luffing and slewing movements. An angle meter will be installed to detect the luffing angle θ and the slewing angle. The conditions under which cargo handling operations are possible are when the elevation angle θ is in the range of -10° to 40°. c) The horizontal telescopic tube 4 extends and retracts in accordance with the movement of the horizontal trolley 3, and the entire vertical telescopic tube 6 moves horizontally. The position of the horizontal trolley 3 is constantly calculated by the control device based on the cumulative horizontal extension and contraction time, with the extension and contraction limits of the horizontal telescopic tube 4 serving as the reference position. in particular, • Count the operating time of the horizontal telescopic motor (not shown) that moves the horizontal trolley 3. Reset the count when the horizontal extension is reduced. • The operating time is counted by the programmable controller (PLC). However, when counting is performed using a normal scan (110 msec), errors occur. Therefore, the counting process (10 msec) is performed using the PLC's periodic interrupt calculation to obtain accurate data. d) The vertical telescopic pipe 6 is extended and retracted, and the cargo G is sucked in from the suction nozzle 7 located at the tip of the vertical telescopic pipe 6. For example, a rotary blower is used as the vacuum blower to unload the collected cargo G into a receiver tank located on the quay wall W side. e) The vertical telescopic tube 6 and the suction nozzle 7 are connected by a flexible hose, and the suction nozzle 7 can be freely tilted to absorb the effects of disturbances. f) The horizontal booms 2 of the pneumatic unloader 1 are arranged in multiple systems (for example, 2 systems) side by side, and are configured to allow individual (single-handed or parallel) cargo handling operations.

[0020] Incidentally, when using this pneumatic unloader to unload cargo G loaded onto a ship S, if the unloading progresses and the surface position of cargo G lowers, making it impossible to adjust by extending the vertical telescopic tube 6, as shown in Figures 2 and 3, the suction operation of cargo G is temporarily interrupted, the vertical telescopic tube 6 is retracted to raise the suction nozzle 7, and then the elevation angle θ of the horizontal boom 2 is reduced (θ1 → θ2) to lower the height of the suction nozzle 7 located at the tip of the vertical telescopic tube 6. After that, the vertical telescopic tube 6 is extended to insert the suction nozzle 7 into cargo G, and the suction operation of cargo G is resumed. At this time, the plan view position of the suction nozzle 7 is made to coincide with the change in the elevation angle θ of the horizontal boom 2 (θ1 → θ2). In other words, the plan view position of the suction nozzle 7 when the suction operation of the cargo G is interrupted is made to coincide with the plan view position of the suction nozzle 7 when the suction operation of the cargo G is started. By inserting the suction nozzle 7 into the depression on the surface of the cargo G that is created when the suction operation of the cargo G is interrupted and resuming the suction operation of the cargo G, the cargo G can be efficiently sucked up from the suction nozzle 7 in a stable state.

[0021] The operating method of the pneumatic unloader of the present invention enables the automation of cargo handling operations and reduces the burden on the operator by automatically controlling the correction of the planar position of the suction nozzle 7 before and after changing the elevation angle θ of the horizontal boom 2 (θ1 → θ2).

[0022] The operating method of the pneumatic unloader of the present invention will be explained using a specific example. Before changing the elevation angle θ of the horizontal boom 2 of the pneumatic unloader 1 (θ1: 30°), the distance L1 (11500 mm) that the horizontal carriage 3 moved from the preset reference position of the horizontal boom 2 was measured. From the reference position, the distance L1 that the horizontal carriage 3 moved from the reference position, and the elevation angle of the horizontal boom 2 before and after the change (θ1: 30° → θ2: 10°), the distance from the base end position O of the horizontal boom 2 to the suction nozzle 7 before and after changing the elevation angle θ of the horizontal boom 2 (θ1 → θ2) was measured. The horizontal distance (N1→N2) and the difference in horizontal distance (N3=N2-N1) before and after changing the elevation angle θ of the horizontal boom 2 (θ1→θ2) are calculated from the horizontal distance (N1→N2). By moving the horizontal trolley 3 towards the base end position O of the horizontal boom 2 by a distance L2 calculated from the difference in horizontal distance N3 and the elevation angle θ2 after the change in the horizontal boom 2, the plan view position of the suction nozzle 7 before and after changing the elevation angle θ of the horizontal boom 2 (θ1→θ2) is made to coincide.

[0023] Here, horizontal distances N1 and N2 are the distances from the horizontal trolley 3 to the preset reference position of the horizontal boom 2. The horizontal distances N1 and N2 can be calculated based on the distance L0 from the base end position O of the horizontal boom 2 when it is positioned to the intersection point of the central axis of the vertical telescopic tube 6 and the horizontal boom 2. The horizontal trolley 3 is provided with a table (see Table 1 for the pneumatic unloader 1 of this embodiment) which pre-calculates the distance from the base end position O of the horizontal boom 2 to the intersection point of the central axis of the vertical telescopic tube 6 and the horizontal boom 2 for each elevation angle θ of the horizontal boom 2, and uses this table to calculate the horizontal distances N1 and N2. Note that the values ​​in Table 1 are calculated for the elevation angle θ of the horizontal boom 2 in 5° increments, but the angle increment is not limited to 5°; it can be created in 10° increments, or in 2° or 1° increments.

[0024] [Table 1]

[0025] The formulas for calculating horizontal distances N1, N2, etc., when the elevation angle θ of horizontal boom 2 is changed (θ1: 30° → θ2: 10°) are as follows. N1 = (L0 + L1) × cos30° =(19750mm+11500mm)×cos30° = 27063mm N2 = (L0 + L1) × cos 10° =(18282mm+11500mm)×cos10° = 29329mm N3 = N2 - N1 = 2266mm L2 = (N2 - N1) / cos 10° = 2300mm

[0026] Here, if the horizontal trolley 3 is moved towards the base end position O of the horizontal boom 2 by a distance L2 calculated from the difference in horizontal distance N3 and the elevation angle θ2 after the change in the horizontal boom 2, the operating time of the horizontal trolley 3 by the horizontal telescopic motor will be 27,600 msec (using a 1 msec timer in the PLC), assuming the movement speed of the horizontal trolley 3 is 5 m / min.

[0027] Incidentally, this pneumatic unloader 1, like conventional pneumatic unloaders, is designed to automatically control the height of the suction nozzle 7 located at the tip of the vertical telescopic tube 6 based on the output of various sensors. In addition, it is also designed to automatically control the operation when the suction nozzle 7 reaches the warehouse. Specifically, if the suction nozzle 7 reaches the warehouse during automatic lowering operation, cargo handling operations cannot be performed at the same position. Therefore, the system automatically detects that the nozzle has reached the warehouse, stops the automatic lowering operation, moves the suction nozzle 7 to another location, and restarts the automatic lowering operation. As shown in Figure 4(a), the vertical extension and retraction of the vertical extension tube 6 is achieved by operating the vertical extension winch motor 61 installed on the horizontal trolley 3, which winds up and down the vertical extension wire 62, thereby extending and retracting the vertical extension. The tip piping and suction nozzle 7 of the vertical telescopic tube 6, which is suspended by wire 62, are made to move up and down. The suction nozzle 7 is connected to the vertical telescopic tube 6 via a flexible hose 63, allowing the suction nozzle 7 to tilt freely and thus absorbing the effects of external disturbances. The suction nozzle 7 is equipped with a tilt switch 71 that detects the tilt of the suction nozzle 7. As shown in Figures 4(b) and 5(a), when the tilt switch 71 detects an inclination of the suction nozzle 7, that is, during vertical extension and descent while the automatic lowering operation is running, if the suction nozzle 7 reaches the warehouse and continues to descend without vertical contact between the warehouse and the suction nozzle 7, the flexible hose 63 above the suction nozzle 7 bends, causing the suction nozzle 7 to tilt, and when the tilt switch 71 detects this, the vertical extension and descent is temporarily stopped. A load limiter 64 is equipped on the lifting section of the vertical telescopic wire 62. The load limiter 64 is configured to detect slack (e.g., set value: 0.98 kN or less) and tension (e.g., set value: 9.8 kN or more) of the vertical extension wire 62, respectively. As shown in Figures 4(c) and 5(b), if the load limiter 64 detects slack in the vertical extension wire 62, that is, during automatic lowering operation, when the suction nozzle 7 reaches the warehouse and makes vertical contact with the warehouse and continues to descend, the vertical extension wire 62 will slacken, and if the load limiter 64 detects this slack, the vertical extension descent will be temporarily stopped. If the stopping process is repeated twice in one minute, it is determined that the suction nozzle 7 has reached the warehouse, and the automatic descent operation is stopped.

[0028] The operating method and operating control device for the pneumatic unloader of the present invention have been described above based on embodiments. However, the present invention is not limited to the configuration described in the above embodiments, and its configuration can be modified as appropriate without departing from the spirit of the invention. [Industrial applicability]

[0029] The operating method and control device for a pneumatic unloader of the present invention enable automation of cargo handling operations and reduce the burden on the operator by automatically controlling the correction of the planar position of the suction nozzle before and after changing the elevation angle of the horizontal boom. Therefore, it can be widely applied to pneumatic unloaders used to unload various bulk materials such as grain loaded on ships anchored at a quay. [Explanation of Symbols]

[0030] 1. Pneumatic unloader 2 Horizontal boom 3 horizontal trolley 4 Horizontal telescopic tube 5. Bent pipe 6 Vertical telescopic tube 61. Vertical Telescopic Winch Motor 62 Vertical Telescopic Wire 63 Flexible Hose 64 Load Limiter 7. Suction nozzle 71 Tilt switch G Cargo handling equipment O proximal position S ship W Wharf

Claims

1. A method for operating a pneumatic unloader comprising a horizontal boom that can be raised and lowered and rotated, a horizontal carriage that moves along the horizontal boom, a retractable horizontal telescopic tube provided along the horizontal boom and whose tip is supported by the horizontal carriage, a vented tube connected to the tip of the horizontal telescopic tube, a retractable vertical telescopic tube connected to the vented tube and held vertically, and a suction nozzle provided at the tip of the vertical telescopic tube for sucking up loads, A method for operating a pneumatic unloader, characterized by measuring the distance the horizontal trolley has moved from a preset reference position of the horizontal boom before changing the luffing angle of the horizontal boom, calculating the horizontal distance from the base position of the horizontal boom to the suction nozzle before and after changing the luffing angle of the horizontal boom, and the difference between the horizontal distance before and after changing the luffing angle of the horizontal boom, based on the reference position, the distance the horizontal trolley has moved from the reference position, and the luffing angle of the horizontal boom before and after changing the luffing angle of the horizontal boom, and moving the horizontal trolley by a distance calculated from the difference in horizontal distance and the luffing angle after changing the horizontal boom, so as to make the plan view position of the suction nozzle before and after changing the luffing angle of the horizontal boom the same.

2. The method for operating a pneumatic unloader according to claim 1, characterized in that the horizontal distance is calculated based on the distance from the base end position of the horizontal boom when the horizontal trolley is positioned at a preset reference position of the horizontal boom to the intersection point of the central axis of the vertical telescopic tube and the horizontal boom.

3. The method for operating a pneumatic unloader according to claim 2, characterized in that it includes a table that pre-calculates the distance from the base end position of the horizontal boom to the intersection point of the vertical telescopic tube and the horizontal boom for each elevation angle of the horizontal boom, when the horizontal trolley is positioned at a preset reference position of the horizontal boom, and calculates the horizontal distance using the table.

4. An operation control device for a pneumatic unloader comprising a horizontal boom that can be raised and lowered and rotated, a horizontal carriage that moves along the horizontal boom, a retractable horizontal telescopic tube provided along the horizontal boom and whose tip is supported by the horizontal carriage, a vented tube connected to the tip of the horizontal telescopic tube, a retractable vertical telescopic tube connected to the vented tube and held vertically, and a suction nozzle provided at the tip of the vertical telescopic tube for sucking up loads, An operation control device for a pneumatic unloader, comprising: a horizontal carriage movement distance measuring means for measuring the distance the horizontal carriage has moved from a preset reference position of the horizontal boom before the elevation angle of the horizontal boom is changed; and a horizontal distance calculating means for calculating the horizontal distance from the base position of the horizontal boom to the suction nozzle before and after the elevation angle of the horizontal boom is changed, and the difference in the horizontal distance before and after the elevation angle of the horizontal boom is changed, based on the reference position, the distance the horizontal carriage has moved from the reference position, and the elevation angle of the horizontal boom before and after the elevation angle of the horizontal boom is changed; wherein the horizontal carriage is moved by a distance calculated from the difference in horizontal distance and the elevation angle after the elevation angle of the horizontal boom is changed, thereby making the plan view position of the suction nozzle before and after the elevation angle of the horizontal boom coincide.

5. The pneumatic unloader operation control device according to claim 4, comprising a table that pre-calculates the distance from the base end position of the horizontal boom to the intersection point of the vertical telescopic tube and the horizontal boom for each elevation angle of the horizontal boom, when the horizontal trolley is positioned at a preset reference position of the horizontal boom, and the horizontal distance is calculated using the table.

Citation Information

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