# Dynamic Simulation Analysis of the Antiswing Device for Ship-Mounted Batch Transfer Hanging Basket

Authors: Jianli Wang; Haolin Li; Shenghai Wang; Haiquan Chen; Yuqing Sun
Journal: Applied Bionics and Biomechanics
 (2023)

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## Abstract

When the rescue vessels use the hanging basket to transfer the wounded at sea, under the action of waves, the ship causes the hanging basket to swing significantly. To prevent the second injury to the wounded caused by the large swing of hanging basket, a rope-driven rigid-flexible hybrid hanging basket antiswing control system is designed, the control principle of the system is introduced, and an accurate dynamics model of the system is established based on the D’Alembert principle, the rigid-flexible hybrid model is used to the antiswing control and simulation of the ship-mounted batch transfer hanging basket for the first time. Analyzed its control principle and simulate the variations in length, velocity, acceleration, and force changes of the control ropes. By installing rigid bal-hinge telescopic sleeve, the simulation results indicate that the indicators of the driving ropes are smooth and continuous and the value changes are also within a suitable range. The force on the four control ropes has been reduced by ∼24.1%, 23%, 26.4%, and 25.1%, resulting in the force that is more reasonable and enhancing the safety of hanging basket system. The hanging basket antiswing device is capable of compensating for rolling and pitching motions at sea and has a strong impact on swinging.


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## Body

## 1. Introduction

The batch transfer hanging basket is primarily used to transfer the ill and injured at sea, rescue the crew in danger, and accomplish the transfer of the sick and injured at sea and on the wharf, as shown in Figures1(a) and 1(b). Under the combined action of waves, sea winds, and tides, the ship will experience complicated irregular motions with 6 degrees of freedom (DOF), such as rolling, pitching, yawing, swaying, surging and heaving [1], and the ship-mounted hanging basket will likewise experience relative motions. When the ship experiences heave movement, if the personnel in hanging baskets are not firmly secured, the personnel may be hanged or falling vertically, and the injured may collide with the hanging basket, causing secondary injuries. Due to inertia, while the ship is rolling or pitching, the injured will deviate from their original position, making it possible for them to clash with other wounded or the hanging basket, or even fall out of the hanging basket. In order to ensure the safety of the transfer of the injured at sea, the wave motion compensation technology is used to develop a ship-mounted antiswing system, which can mitigate the negative effects of the hanging basket swing on the transfer of the injured.Figure 1
(a, b) Shipboard-mounted batch transfer hanging basket.
(a)(b)The ship-mounted hanging basket is generally controlled by rope-driven system. The rope-driven parallel mechanism has the advantages of lightweight, small inertia, simple structure, and high force transfer efficiency [2], which can achieve very high response speed and acceleration and can control the ship-mounted hanging basket without manual interaction. The more famous rope-driven parallel devices include Robo crane [3], FALCON-7 [4], SEGESTA [5], IP Anema [6], and so on. In addition, the University of Waterloo in Canada has successfully developed two rigid-flexible hybrid ultra-high-speed parallel mechanisms Beta BOT [7] and Delta Bot [8]. The research work on rope-driven system first started in the United States. Since then, domestic and foreign scholars have conducted a lot of research on rope-driven system.The US Naval Research Office has developed LVI Lo/Lo crane for sea wave compensation [9], which can control the cargo to achieve 6-DOF movement through eight redundant drive ropes, at the same time, it can also use inertial measurement unit and camera array to measure the relative motion between ships it is the most advanced 6-DOF wave motion compensation technology in the world. Lv et al. [10] also proposed a 6-DOF parallel wave compensation system similar to LVI Lo/Lo and completed the relevant theoretical analysis and the construction of corresponding experimental platform, which verified the effectiveness of the technology for offshore wave compensation. Zheng [11] proposed a 6-DOF rope-driven crane robot, in which the irregular feedback linearization controller is introduced into the system to realize the asymptotically stable lifting track tracking control. Tang and Chen [12] proposed a 4-DOF rope-driven rigid-flexible hybrid wave compensation device, according to the experiments, the device can realize active wave motion compensation. Shang [13] proposed a three flexible rope-driven parallel structure with a constraint mechanism, which is supported by a rigid support rod and three flexible ropes to form a new rigid-flexible parallel device, and the effectiveness of the device is verified by MATLAB and ADAMS simulation. Kim et al. [14] developed a 6-DOF wave motion compensation device, which uses machine vision to detect the relative motion between cargo and ship and realizes wave motion compensation through intelligent platform. Hu [15] proposed a 6-DOF parallel wave compensation system controlled by rope-driven evaluated the relative motion compensation principle and swing elimination principle of the scheme, and it is theoretically proved that the scheme can completely compensate the relative motion of the 6 DOF between the two ships. Guo [16] proposed a multilink rope-driven robot, the basic unit of the structure consists of four drive cables and one passive S rigid branch chain. Kossowski and Notash [17] developed a flexible cable-driven truss, which is driven by six control cables, among them, a passive branch chain composed of 18 rotating joints is used to maintain the stability of the structure, so that the structure has three translations and one rotation 4 DOF. Mao and Agrawal [18] have developed a rehabilitation training robot that uses seven ropes to construct two-layer parallel structure, the middle branch chain is composed of some joints connected in series to form a passive branch chain, which realizes the movement of the robot in the 5° direction of freedom that imitates the human arm. Xie et al. [19] proposed a hybrid rope-driven parallel bionic eye structure, which consists of three ropes and one R–S active branch chain to realize the three-dimensional rotation of eye structure. Schmidt et al. [20] designed a hybrid-driven hyper-redundant robot that combines a rope and an intermediate rigid branch chain, but the robot’s carrying capacity is limited.In the original scheme, there are four traction ropes, which are, respectively, installed at the bottom of both sides of the hanging basket with quick hooks, which are used for the operators to control the movement posture of the hanging basket in the air by pulling the traction ropes in the lifting process of the hanging basket, so as to avoid excessive swinging of the hanging basket in the air. Under the action of wind, waves, and currents, ship rolling, pitching, heaving, and other movements, so it is difficult for operators to control the traction ropes on the deck, this scheme not only threatens the safety of operators but also has poor antiswing effect. In view of the above problems, on the basis of summarizing the dynamics and development of rope drive research at home and abroad. This paper designed a rope-driven rigid-flexible hybrid hanging basket antiswing control system, and the rigid-flexible hybrid model is used for the antiswing control and simulation of the ship-mounted batch transfer hanging basket for the first time. In order to realize the automatic control of the hanging basket antiswing system, this paper researched the design of the control system in rope-driven hanging basket antiswing device, which analyzes the swing mechanism and influencing factors of underdriven ship-mounted crane system, process control method is used to restrain the hanging basket swing, and the effectiveness of the method is proved by simulation.The research of this paper is conducive to the realization of accurate control and precise positioning of the underactuated system, improves work safety, work efficiency, and has important scientific significance and good application prospects, it brings new ideas to development of the antiswing device for ship-mounted batch transfer hanging basket.


## 2. Control Principle of Antiswing System for Hanging Basket

For the record, a lot of research has been conducted on the control methods of wire-driven parallel mechanisms at home and abroad, including servo drive control [21], feedforward control [22], passive control [23], fuzzy PID control [24], and H∞ [25]. In the calculation, such methods have their respective advantages and disadvantages in the aspects of the complexity of stability, robustness, and so on during the whole process. In this paper, on the basis of the engineering practice of the marine hanging basket system, due to the applicability and stability of the equipment and other factors, the servo control technology is adopted to control the balance of the hanging basket through the speed control mode, torque control mode, and position control mode.Proportional, integral, and differential control is abbreviated as PID control, which has the characteristics of simple principle, wide application range, strong adaptability, and good control effect [26]. The formula is as follows:(1)yt=KCe+1T1∫0tetdt+TDdetdt.Among them,KC is scaling factor, e(t) is deviation, TD is differential time coefficient, and T1 is integral time coefficient.The control principle of the hanging basket antiswing device is shown in Figure2. In the automatic control mode of the hanging basket antiswing device, the inclination signal is collected through the position controller first, and before the collected data are input to the control stage, the PID algorithm is used to output the position control signal of the proportional valve to control the retracting speed of the ropes. At the same time, it also outputs a control signal of the reversing valve to control the retracting direction of the ropes, the data processed by the PID controller controls the actuator with a pulse signal. Finally, the feedback control is completed. The specific control process is as follows: Record the length of the ropes when the moving platform is in a horizontal state, then the moving platform becomes tilted, the position controller compares the collected voltage signal with the set value, and the deviation is sent to the PID controller. The PID controller outputs pulse signal to control the servo motor and calculates the retractable rope length of each motor according to the rotation angle of the moving platform in each direction and the rope outlet angle of the motor perpendicular to that direction. Motor drives the rope to rotate according to the calculated value and the rope length needs to be changed to compensate for the inclination of the basket caused by the inclination of the moving platform, finally, the hanging basket is kept level. In practice, the speed and acceleration of the ropes can be obtained by installing a speedometer and an accelerometer. The data directly obtained by these sensors may not be ideal, so it needs to be consistent with the actual motion through subsequent processing. The acceleration data of rope length can be obtained by derivation of the motor encoder data.Figure 2
Principle block diagram of comprehensive compensation system.


## 3. Hanging Basket Antiswing System Model

In accordance with the relative relationship between the end effector DOFn and the number of ropes m, the rope-driven system can be divided into three categories: (1) m ≤ n, an underconstrained positioning system, which must be balanced on the basis of external force; (2) m = n + 1, a completely constrained positioning system, at this time, the system can achieve system balance without external force; (3) m ≥ n + 1, a redundant constraint positioning system. This paper mainly researches the antiswing problem of ship under rolling, pitching, and heave conditions, so three or more ropes can meet the stability requirements of the system, considering the structural characteristics of batch transfer basket and the space problem of lifting in use, four ropes are used for driving control.The structural diagram of batch transfer hanging basket antiswing system is shown in Figure3. The four corners of the upper platform have a group of rope controllers, respectively, which are composed of motor, gearbox, and drum. The rope is connected with the hanging basket through the upper platform, and the rope has a rope out angle ψ, ensuring that the rope has enough horizontal force to make the hanging basket difficult to swing along the horizontal direction. The upper platform is rigidly connected with the luffing mechanism of the crane through the connecting rod, the relative motion of the ship under the influence of wind, wave, and current is transmitted to the upper platform, and the coupling motion of roll, pitch, and heave is generated on the upper platform, under this condition, the servo motor drives the drum through the reducer to control the expansion amount and speed of the rope to adjust the position of the hanging basket and the attitude in the air, so as to achieve the effect of antiswing.Figure 3
Structure of batch transfer hanging basket system.


## 4. Kinematics Modeling of Swing Reducing Device of Hanging Basket

### 4.1. Rope Length Analysis of Hanging Basket Antiswing System

The attitude of ship in motion is described by the rotation of the moving coordinate system, and the angular displacement is described by three Euler angles,α, β, and γ, these three rotation angles completely determine the attitude of the ship in space, describing the rolling, pitching, and yawing of the ship, respectively, and different rotation matrices can be obtained when the ship rotates around three axes. [L] represents the transformation matrix rotating around the x-axis, while [M] represents the transformation matrix rotating around the y-axis. In this paper, the coupling of ship rolling, pitching, and heave is investigated, as shown in Figure 4, the attitude change matrix 10R of moving coordinate system relative to fixed coordinate system is obtained according to the sequence of x–y axis.(2)10R=LM=cosβ0sinβsinαsinβcosα−sinαcosβ−cosαsinβsinαcosαcosβ=C1C2C3D1D2D3E1E2E3.Figure 4
Schematic diagram of rescue vessel with antiswing device for hanging basket.The structural diagram of the hanging basket antiswing system is shown in Figure5. The moving coordinate system 0–xyz is established at the centroid O of the moving platform, the x-axis and y-axis are, respectively, between the two ropes, while the z-axis is vertically upward. The fixed coordinate system 01–x1y1z1 is established on the plane center point 01 of the hanging basket. The x1 axis and y1 axis are parallel to the x-axis and y-axis, respectively, while the z1 axis is vertically upward. The rope length from coordinate (aix,aiy,aiz) of the connecting point ai of the moving platform to coordinate (bix,biy,biz) of the connecting point bi of the hanging basket is li(i = 4). Set the coordinate of the moving platform as a1 = (a, b, 0), a2 = (a, −b, 0), a3 = (−a, −b, 0), a4 = (−a, b, 0); set the coordinates of the hanging basket plane as b1 = (a1, b1, −h), b2 = (a1, −b1, −h), b3 = (−a1, −b1, −h), b4 = (−a1, b1, −h). The displacement vector of the control rope in the system is as follows:(3)Li=10RaiT−biT,when Equation (2) is introduced into Equation (3), the displacement vector of the rope in the hull coordinate system can be expressed as follows:(4)Li=LixLiyLiz=C1aix+C2aiy−bixD1aix+D2aiy−bixE1aix+E2aiy−bix.Figure 5
Schematic diagram of hanging basket.The equation of rope length is obtained as follows:(5)li=∥Li∥=Lix2+Liy2+Liz2.


### 4.2. Analysis of Rope Expansion Speed of Hanging Basket Antiswing System

Deriving the rope lengthli can obtain the rope stretching speed l˙i of the hanging basket antiswing system, as follows:(6)l˙i=eiTvai.Among them,vai=va0+10R˙ai, ei is the unit vector along the direction of rope l˙, va0 is the variation of ship heave motion, and vai is the speed of the moving platform connection point ai. According to Formulae (5) and (6), we can get the unit vector of the rope along Li direction can be obtained.(7)ei=Lili=e1Te2Te3Te4T.From Equation (2), 10R˙ is as follows:(8)10R˙=−β˙sinβ0β˙cosβα˙cosαsinβ+β˙cosβsinα−α˙sinα−α˙cosαcosβ+β˙sinβsinαα˙sinαsinβ−β˙cosβcosαα˙cosα−α˙sinαcosβ−β˙sinβcosα.Then,(9)va0+10R˙ai=00va0+−β˙sinβ0β˙cosβα˙cosαsinβ+β˙cosβsinα−α˙sinα−α˙cosαcosβ+β˙sinβsinαα˙sinαsinβ−β˙cosβcosαα˙cosα−α˙sinαcosβ−β˙sinβcosαaixaiyaiz.It can be reduced to Equation (10):(10)va0+10R˙ai=ki1ki2ki3ki4ki5ki6ki7ki8ki9va0α˙β˙=Kva0α˙β˙.LetHi=eiTK, then,(11)l˙i=l˙1l˙2l˙3l˙4=H0H1H3H4Tva0α˙β˙,when the rolling, pitching, and heave periods of the ship are known, the control speeds of the four ropes of the hanging basket antiswing system can be obtained by Equation (11).


### 4.3. Analysis of Rope Expansion Acceleration of Hanging Basket Swing-Reducing System

Equation (11) is derived from both sides of t to obtain the acceleration of the rope.(12)l̇̈i=Hv˙a0α¨β¨+H˙va0α˙β˙.Among them,H˙=H1˙H2˙H3˙H4˙T.Therefore, when the rolling, pitching, and heave periods of the ship are known, the control accelerations of the four ropes of the hanging basket antisway system can be calculated by the Formulae (11) and (12).


## 4.1. Rope Length Analysis of Hanging Basket Antiswing System

The attitude of ship in motion is described by the rotation of the moving coordinate system, and the angular displacement is described by three Euler angles,α, β, and γ, these three rotation angles completely determine the attitude of the ship in space, describing the rolling, pitching, and yawing of the ship, respectively, and different rotation matrices can be obtained when the ship rotates around three axes. [L] represents the transformation matrix rotating around the x-axis, while [M] represents the transformation matrix rotating around the y-axis. In this paper, the coupling of ship rolling, pitching, and heave is investigated, as shown in Figure 4, the attitude change matrix 10R of moving coordinate system relative to fixed coordinate system is obtained according to the sequence of x–y axis.(2)10R=LM=cosβ0sinβsinαsinβcosα−sinαcosβ−cosαsinβsinαcosαcosβ=C1C2C3D1D2D3E1E2E3.Figure 4
Schematic diagram of rescue vessel with antiswing device for hanging basket.The structural diagram of the hanging basket antiswing system is shown in Figure5. The moving coordinate system 0–xyz is established at the centroid O of the moving platform, the x-axis and y-axis are, respectively, between the two ropes, while the z-axis is vertically upward. The fixed coordinate system 01–x1y1z1 is established on the plane center point 01 of the hanging basket. The x1 axis and y1 axis are parallel to the x-axis and y-axis, respectively, while the z1 axis is vertically upward. The rope length from coordinate (aix,aiy,aiz) of the connecting point ai of the moving platform to coordinate (bix,biy,biz) of the connecting point bi of the hanging basket is li(i = 4). Set the coordinate of the moving platform as a1 = (a, b, 0), a2 = (a, −b, 0), a3 = (−a, −b, 0), a4 = (−a, b, 0); set the coordinates of the hanging basket plane as b1 = (a1, b1, −h), b2 = (a1, −b1, −h), b3 = (−a1, −b1, −h), b4 = (−a1, b1, −h). The displacement vector of the control rope in the system is as follows:(3)Li=10RaiT−biT,when Equation (2) is introduced into Equation (3), the displacement vector of the rope in the hull coordinate system can be expressed as follows:(4)Li=LixLiyLiz=C1aix+C2aiy−bixD1aix+D2aiy−bixE1aix+E2aiy−bix.Figure 5
Schematic diagram of hanging basket.The equation of rope length is obtained as follows:(5)li=∥Li∥=Lix2+Liy2+Liz2.


## 4.2. Analysis of Rope Expansion Speed of Hanging Basket Antiswing System

Deriving the rope lengthli can obtain the rope stretching speed l˙i of the hanging basket antiswing system, as follows:(6)l˙i=eiTvai.Among them,vai=va0+10R˙ai, ei is the unit vector along the direction of rope l˙, va0 is the variation of ship heave motion, and vai is the speed of the moving platform connection point ai. According to Formulae (5) and (6), we can get the unit vector of the rope along Li direction can be obtained.(7)ei=Lili=e1Te2Te3Te4T.From Equation (2), 10R˙ is as follows:(8)10R˙=−β˙sinβ0β˙cosβα˙cosαsinβ+β˙cosβsinα−α˙sinα−α˙cosαcosβ+β˙sinβsinαα˙sinαsinβ−β˙cosβcosαα˙cosα−α˙sinαcosβ−β˙sinβcosα.Then,(9)va0+10R˙ai=00va0+−β˙sinβ0β˙cosβα˙cosαsinβ+β˙cosβsinα−α˙sinα−α˙cosαcosβ+β˙sinβsinαα˙sinαsinβ−β˙cosβcosαα˙cosα−α˙sinαcosβ−β˙sinβcosαaixaiyaiz.It can be reduced to Equation (10):(10)va0+10R˙ai=ki1ki2ki3ki4ki5ki6ki7ki8ki9va0α˙β˙=Kva0α˙β˙.LetHi=eiTK, then,(11)l˙i=l˙1l˙2l˙3l˙4=H0H1H3H4Tva0α˙β˙,when the rolling, pitching, and heave periods of the ship are known, the control speeds of the four ropes of the hanging basket antiswing system can be obtained by Equation (11).


## 4.3. Analysis of Rope Expansion Acceleration of Hanging Basket Swing-Reducing System

Equation (11) is derived from both sides of t to obtain the acceleration of the rope.(12)l̇̈i=Hv˙a0α¨β¨+H˙va0α˙β˙.Among them,H˙=H1˙H2˙H3˙H4˙T.Therefore, when the rolling, pitching, and heave periods of the ship are known, the control accelerations of the four ropes of the hanging basket antisway system can be calculated by the Formulae (11) and (12).


## 5. Dynamic Simulation of Hanging Basket Antiswing Device

Assume that the total weight of the platform moving by the hanging basket and the passengers ism, as shown in Figure 6, fi is the tension of the four ropes and va0 is the linear velocity of the ship’s heave.Figure 6
Schematic diagram of hanging basket.


### 5.1. Dynamic Model of Hanging Basket Antiswing System

The pulling force of the rope during the operation of the hanging basket antiswing system is composed of the inertial force and the pulling force during the static force is balanced. The inertial force of the rope is related to the acceleration and the mass because the hanging basket is loaded evenly and the center of hanging basket gravity coincides with the center of shape, the pulling force of the four ropes during the static balance is the same. From this, the tension of the four ropes can be calculated as follows:(13)fi=miai+mg/4.


### 5.2. Dynamic Model of Swing Reduction System of Telescopic Hanging Basket

It can be seen from Formula (13) that the rope bears not only the inertia force of the moving platform, but also the gravity force of the hanging basket and the hoisting weight, which greatly increases the stress of the ropes and adversely affects the service life of the ropes, and the power of the rope controller will be larger. In order to solve the above problems, the author designs a telescopic sleeve on the hanging basket, which is rigidly connected with the hanging basket and connected with the moving platform by a ball hinge, forming a rigid-flexible hybrid hanging basket antiswing control system, ignoring the friction of spherical hinge, as shown in Figure 7.Figure 7
Batch transfer hanging basket system with telescopic sleeve.Assumingωa0 is the angular velocity of the moving platform center, FN is the pulling force, Me is the external torque on the moving platform, and I is the inertia tensor of the moving platform center, the force model of the moving platform is shown in Figure 8.Figure 8
Schematic diagram of hanging basket.According to D’Alembert’s principle, the force balance equation of the moving platform is established as follows:(14)∑i=14fi+FN+mg−mv˙a0=01∑i=14ri×fi+Me−Iω˙a0−ωa0×Iωa0=02.Convert Equation (14) into matrix form:(15)DFi=Ws.Among them,(16)D=e0e1e2e3e4ra0×e0ra1×e1ra2×e2ra3×e3ra4×e4,Fi=f0f1f2f3f4.(17)Ws=FN+mg−mv˙a0Iω˙a0+ωa0×Iωa0−Me.From Equation (14) (1):(18)∑i=14fi+FN+mg=mv˙a0,which is as follows:(19)00mg+e0e1e2e3e4f0f1f2f3f4=m00v¨a0.From Equation (14) (2):(20)∑i=14ri×fi+Me=Iω˙a0−ωa0×Iωa0,which is as follows:(21)d0d1d2d3d4f0f1f2f3f4=Iω˙B+ωB×IωB.Among them,(22)di=rai×ei,I=IxxIxyIxzIyxIyyIyzIzxIzyIzz=∫y2+z2dm−∫xydm−∫xzdm−∫xydm∫x2+z2dm−∫yzdm−∫xzdm−∫yzdm∫x2+y2dm,(23)Ixx=ma2/12,Iyy=mb2/12,Izz=ma2+b2/12,Ixy=Iyx,Ixz=Izx,Iyz=Izy,ωB=Rx,α100α˙+Rx,αRy,β010β˙=α˙cosαβ˙sinαβ˙=100cosα0sinαα˙β˙,ω˙B=α¨−αsinαβ˙+cosαβ¨αcosαβ˙+sinαβ¨=100−αsinαβ˙+cosαβ¨0αcosαβ˙+sinαα¨β¨.Simultaneous Equations (19) and (21) can solve the tension of the four control ropes of the hanging basket antiswing device.


### 5.3. Dynamic Model of Rope Actuator for Hanging Basket Antiswing System

The stress condition of rope driver for the hanging basket antiswing system is shown in Figure9. The anticlockwise rotation direction of the driver is positive, fi is the tension of the rope, R is the equivalent radius of the driver, θi is the angle vector of the driver, Ji is the moment of inertia of therope driver, including the equivalent moment of inertia of the motor, gearbox, and drum. The torque of the rope driver is Mi. Then the dynamic equation of the cable driver is:(24)Mi=Jiθ¨i+Ciθ˙i+Rfi.Figure 9
Diagram of cable drive.Converted into matrix form:(25)Fi=Ri−1Mi−Jiθ¨i−Ciθ˙i.Among them,Fi=f1f2f3f4T, θi=θ1θ2θ3θ4T, Mi=M1M2M3M4T, Ri=diagR1R2R3R4T, Ci=diagC1C2C3C4T, Ji=diagJ1J2J3J4T.As mentioned earlier, if the system is a fully constrained positioning system, as long as the rope does not relax, the swing of the system will not occur. Because this system is an overconstrained positioning system, the swing can be eliminated by ensuring that all ropes are under tension, so the forceFi provided by the rope driving unit is slightly greater than the tensile force fi of the ropes.


### 5.4. Dynamic Equation of Hanging Basket Antiswing System (with Rope-Driven)

When the rope driver rotates, the rope length changes. According to the schematic diagram of the driver in Figure9, the relationship between the length change Δli of the rope and the radius R and rotation angle θi of the driver is as follows:(26)θi=ΔliR.Equation (26) is derived from both sides of t to get:(27)θ˙i=∂θi∂WW˙=l˙iR,θ¨i=ddt∂θi∂WW˙+∂Өi∂WW¨=l̇̈iR.Among them,W is the six-dimensional column vector of the moving platform.Taking Equation (27) into Equation (25), the dynamic equation of the rope driving unit is obtained as follows:(28)Fi=Ri−1Mi−Jil̇̈iR−Cil˙iR.Combining the force balance Equation (14) of the vertical moving platform with the dynamic Equation (28) of the rope driving unit, the dynamic equation of the ship-mounted hanging basket antiswing system designed in this paper can be obtained as follows:(29)DFi=DRi−1Mi−Jil̇̈iR−Cil˙iR=Ws.


### 5.5. Dynamic Simulation of Swing Reduction System of Hanging Basket

In this project, the overall dimensions (length × width) of the hanging basket after deployment are 2,300 mm × 1480 mm, and the total weightm is 80 kg. Assume that four wounded people can be transferred at one time and each wounded person weighs 80 kg. The external dimensions (length × width) of the moving platform are 3,400 mm × 2,480 mm, the ship roll period α = π/18sin(2πt), pitch period β = π/60sin(2πt), heave period va0 = 60sin(2πt), and the simulation time is 2 s.


#### 5.5.1. Dynamic Simulation of Uniform Loading for Swing Reduction System of Hanging Basket

As shown in Figure10, in accordance with the derived driving length, speed, acceleration, and stress equations of the hanging basket, the simulation results are obtained. The driving lengths of the four ropes are different. The initial length of all four ropes is 830 mm, rope 1 stretches first and then shortens, the reasonable range is l1 ∈ (775–880 mm), rope 2 shortens first and then stretches, the reasonable range is l2 ∈ (825–835 mm), rope 3 shortens first and then stretches, the reasonable range is l3 ∈ (825–835 mm), rope 4 stretches first and then shortens, the reasonable range is l4 ∈ (775–880 mm). The range of expansion and contraction speed of the ropes are V1 ∈ (−35 to 35 mm/s), V2 ∈ (−98 to 102 mm/s), V3 ∈ (−25 to 25 mm/s), V4 ∈ (−65 to 60 mm/s). The range of expansion and contraction acceleration of the ropes are a1 ∈ (−30 to 25 mm/s2), a2 ∈ (−200 to 140 mm/s2), a3 ∈ (−40 to 35 mm/s2), a4 ∈ (−110 to 100 mm/s2). The stress situation of each rope is also quite different, among which the extreme force of rope 2 is the largest, reaching 4,100 N, followed by rope 4, which is 2,850 N. In practical engineering, special attention should be paid to these two ropes, and regular inspection and replacement should be made to prevent fatigue fracture during work.Figure 10
Dynamic simulation analysis of antiswing device for hanging basket.
(a)(b)(c)(d)


#### 5.5.2. Dynamics Simulation of Nonuniform Loading of Suspension Basket Shimmy Reduction System

As shown in Figure11, due to the different distribution positions of the four wounded in the basket, the basket gravity center is transferred from O to D. Compared with the uniform loading diagram shown in Figure 10(d), the uneven loading diagram shown in Figure 11(a) shows that there is basically no change in the force of ropes 2, 4, but the force of rope 1 is increased. At the same time, the force range is increased from 1,000–1,200 N to 1,300–2,000 N, the force of rope 3 is reduced, and the force range is reduced from 1,000–1,300 N to 850–1,000 N. According to the rope stress characteristics obtained above, since the extreme force borne by rope 2 is larger and the extreme force borne by rope 4 is smaller, when loading, the basket gravity center is close to rope 4 and far away from rope 2, as shown in Figure 11(b), which can make the stress of the four ropes more balanced.Figure 11
Cable force of hanging basket for uneven loading.
(a)(b)


#### 5.5.3. Dynamic Simulation of Reducing Swing System of Telescopic Hanging Basket

According to the derived driving length, speed, acceleration, and force variation equations of the control rope and telescopic sleeve of the hanging basket, the simulation results are obtained, as shown in Figure12.Figure 12
Dynamic simulation analysis of hanging basket with telescopic sleeve.
(a)(b)(c)(d)The comparison of rope stress intervals under the two schemes can be obtained from Figures10(d) and 12(d), as shown in Table 1. Compared with the hanging basket scheme, in telescopic sleeve hanging basket scheme, the telescopic sleeve bears part of the pressure and tension of the hanging basket, the force of rope 1 is reduced by about 24.1%, rope 2 is reduced by about 23.0%, rope 3 is increased by 26.4%, and rope 4 is reduced by 25.1%. Since rope 3 itself is less stressed, even if the tension of rope 3 is increased after the solution is changed, the service life of the rope will not be greatly affected, it can be explained that the telescopic sleeve antisway device can effectively improve the force of the hanging basket control rope, thereby effectively reducing the motor power of the control unit.Table 1
Hanging basket rope force range.
NumberNameStress range (N)Percentage (%)Hanging basketTelescopic sleeve0Telescopic sleeve–1,750–2,000–1Rope 1980–1,010750–76024.12Rope 2980–1,170750–90023.03Rope 3980–1,125750–80026.44Rope 4980–1,090750–80025.1


## 5.1. Dynamic Model of Hanging Basket Antiswing System

The pulling force of the rope during the operation of the hanging basket antiswing system is composed of the inertial force and the pulling force during the static force is balanced. The inertial force of the rope is related to the acceleration and the mass because the hanging basket is loaded evenly and the center of hanging basket gravity coincides with the center of shape, the pulling force of the four ropes during the static balance is the same. From this, the tension of the four ropes can be calculated as follows:(13)fi=miai+mg/4.


## 5.2. Dynamic Model of Swing Reduction System of Telescopic Hanging Basket

It can be seen from Formula (13) that the rope bears not only the inertia force of the moving platform, but also the gravity force of the hanging basket and the hoisting weight, which greatly increases the stress of the ropes and adversely affects the service life of the ropes, and the power of the rope controller will be larger. In order to solve the above problems, the author designs a telescopic sleeve on the hanging basket, which is rigidly connected with the hanging basket and connected with the moving platform by a ball hinge, forming a rigid-flexible hybrid hanging basket antiswing control system, ignoring the friction of spherical hinge, as shown in Figure 7.Figure 7
Batch transfer hanging basket system with telescopic sleeve.Assumingωa0 is the angular velocity of the moving platform center, FN is the pulling force, Me is the external torque on the moving platform, and I is the inertia tensor of the moving platform center, the force model of the moving platform is shown in Figure 8.Figure 8
Schematic diagram of hanging basket.According to D’Alembert’s principle, the force balance equation of the moving platform is established as follows:(14)∑i=14fi+FN+mg−mv˙a0=01∑i=14ri×fi+Me−Iω˙a0−ωa0×Iωa0=02.Convert Equation (14) into matrix form:(15)DFi=Ws.Among them,(16)D=e0e1e2e3e4ra0×e0ra1×e1ra2×e2ra3×e3ra4×e4,Fi=f0f1f2f3f4.(17)Ws=FN+mg−mv˙a0Iω˙a0+ωa0×Iωa0−Me.From Equation (14) (1):(18)∑i=14fi+FN+mg=mv˙a0,which is as follows:(19)00mg+e0e1e2e3e4f0f1f2f3f4=m00v¨a0.From Equation (14) (2):(20)∑i=14ri×fi+Me=Iω˙a0−ωa0×Iωa0,which is as follows:(21)d0d1d2d3d4f0f1f2f3f4=Iω˙B+ωB×IωB.Among them,(22)di=rai×ei,I=IxxIxyIxzIyxIyyIyzIzxIzyIzz=∫y2+z2dm−∫xydm−∫xzdm−∫xydm∫x2+z2dm−∫yzdm−∫xzdm−∫yzdm∫x2+y2dm,(23)Ixx=ma2/12,Iyy=mb2/12,Izz=ma2+b2/12,Ixy=Iyx,Ixz=Izx,Iyz=Izy,ωB=Rx,α100α˙+Rx,αRy,β010β˙=α˙cosαβ˙sinαβ˙=100cosα0sinαα˙β˙,ω˙B=α¨−αsinαβ˙+cosαβ¨αcosαβ˙+sinαβ¨=100−αsinαβ˙+cosαβ¨0αcosαβ˙+sinαα¨β¨.Simultaneous Equations (19) and (21) can solve the tension of the four control ropes of the hanging basket antiswing device.


## 5.3. Dynamic Model of Rope Actuator for Hanging Basket Antiswing System

The stress condition of rope driver for the hanging basket antiswing system is shown in Figure9. The anticlockwise rotation direction of the driver is positive, fi is the tension of the rope, R is the equivalent radius of the driver, θi is the angle vector of the driver, Ji is the moment of inertia of therope driver, including the equivalent moment of inertia of the motor, gearbox, and drum. The torque of the rope driver is Mi. Then the dynamic equation of the cable driver is:(24)Mi=Jiθ¨i+Ciθ˙i+Rfi.Figure 9
Diagram of cable drive.Converted into matrix form:(25)Fi=Ri−1Mi−Jiθ¨i−Ciθ˙i.Among them,Fi=f1f2f3f4T, θi=θ1θ2θ3θ4T, Mi=M1M2M3M4T, Ri=diagR1R2R3R4T, Ci=diagC1C2C3C4T, Ji=diagJ1J2J3J4T.As mentioned earlier, if the system is a fully constrained positioning system, as long as the rope does not relax, the swing of the system will not occur. Because this system is an overconstrained positioning system, the swing can be eliminated by ensuring that all ropes are under tension, so the forceFi provided by the rope driving unit is slightly greater than the tensile force fi of the ropes.


## 5.4. Dynamic Equation of Hanging Basket Antiswing System (with Rope-Driven)

When the rope driver rotates, the rope length changes. According to the schematic diagram of the driver in Figure9, the relationship between the length change Δli of the rope and the radius R and rotation angle θi of the driver is as follows:(26)θi=ΔliR.Equation (26) is derived from both sides of t to get:(27)θ˙i=∂θi∂WW˙=l˙iR,θ¨i=ddt∂θi∂WW˙+∂Өi∂WW¨=l̇̈iR.Among them,W is the six-dimensional column vector of the moving platform.Taking Equation (27) into Equation (25), the dynamic equation of the rope driving unit is obtained as follows:(28)Fi=Ri−1Mi−Jil̇̈iR−Cil˙iR.Combining the force balance Equation (14) of the vertical moving platform with the dynamic Equation (28) of the rope driving unit, the dynamic equation of the ship-mounted hanging basket antiswing system designed in this paper can be obtained as follows:(29)DFi=DRi−1Mi−Jil̇̈iR−Cil˙iR=Ws.


## 5.5. Dynamic Simulation of Swing Reduction System of Hanging Basket

In this project, the overall dimensions (length × width) of the hanging basket after deployment are 2,300 mm × 1480 mm, and the total weightm is 80 kg. Assume that four wounded people can be transferred at one time and each wounded person weighs 80 kg. The external dimensions (length × width) of the moving platform are 3,400 mm × 2,480 mm, the ship roll period α = π/18sin(2πt), pitch period β = π/60sin(2πt), heave period va0 = 60sin(2πt), and the simulation time is 2 s.


### 5.5.1. Dynamic Simulation of Uniform Loading for Swing Reduction System of Hanging Basket

As shown in Figure10, in accordance with the derived driving length, speed, acceleration, and stress equations of the hanging basket, the simulation results are obtained. The driving lengths of the four ropes are different. The initial length of all four ropes is 830 mm, rope 1 stretches first and then shortens, the reasonable range is l1 ∈ (775–880 mm), rope 2 shortens first and then stretches, the reasonable range is l2 ∈ (825–835 mm), rope 3 shortens first and then stretches, the reasonable range is l3 ∈ (825–835 mm), rope 4 stretches first and then shortens, the reasonable range is l4 ∈ (775–880 mm). The range of expansion and contraction speed of the ropes are V1 ∈ (−35 to 35 mm/s), V2 ∈ (−98 to 102 mm/s), V3 ∈ (−25 to 25 mm/s), V4 ∈ (−65 to 60 mm/s). The range of expansion and contraction acceleration of the ropes are a1 ∈ (−30 to 25 mm/s2), a2 ∈ (−200 to 140 mm/s2), a3 ∈ (−40 to 35 mm/s2), a4 ∈ (−110 to 100 mm/s2). The stress situation of each rope is also quite different, among which the extreme force of rope 2 is the largest, reaching 4,100 N, followed by rope 4, which is 2,850 N. In practical engineering, special attention should be paid to these two ropes, and regular inspection and replacement should be made to prevent fatigue fracture during work.Figure 10
Dynamic simulation analysis of antiswing device for hanging basket.
(a)(b)(c)(d)


### 5.5.2. Dynamics Simulation of Nonuniform Loading of Suspension Basket Shimmy Reduction System

As shown in Figure11, due to the different distribution positions of the four wounded in the basket, the basket gravity center is transferred from O to D. Compared with the uniform loading diagram shown in Figure 10(d), the uneven loading diagram shown in Figure 11(a) shows that there is basically no change in the force of ropes 2, 4, but the force of rope 1 is increased. At the same time, the force range is increased from 1,000–1,200 N to 1,300–2,000 N, the force of rope 3 is reduced, and the force range is reduced from 1,000–1,300 N to 850–1,000 N. According to the rope stress characteristics obtained above, since the extreme force borne by rope 2 is larger and the extreme force borne by rope 4 is smaller, when loading, the basket gravity center is close to rope 4 and far away from rope 2, as shown in Figure 11(b), which can make the stress of the four ropes more balanced.Figure 11
Cable force of hanging basket for uneven loading.
(a)(b)


### 5.5.3. Dynamic Simulation of Reducing Swing System of Telescopic Hanging Basket

According to the derived driving length, speed, acceleration, and force variation equations of the control rope and telescopic sleeve of the hanging basket, the simulation results are obtained, as shown in Figure12.Figure 12
Dynamic simulation analysis of hanging basket with telescopic sleeve.
(a)(b)(c)(d)The comparison of rope stress intervals under the two schemes can be obtained from Figures10(d) and 12(d), as shown in Table 1. Compared with the hanging basket scheme, in telescopic sleeve hanging basket scheme, the telescopic sleeve bears part of the pressure and tension of the hanging basket, the force of rope 1 is reduced by about 24.1%, rope 2 is reduced by about 23.0%, rope 3 is increased by 26.4%, and rope 4 is reduced by 25.1%. Since rope 3 itself is less stressed, even if the tension of rope 3 is increased after the solution is changed, the service life of the rope will not be greatly affected, it can be explained that the telescopic sleeve antisway device can effectively improve the force of the hanging basket control rope, thereby effectively reducing the motor power of the control unit.Table 1
Hanging basket rope force range.
NumberNameStress range (N)Percentage (%)Hanging basketTelescopic sleeve0Telescopic sleeve–1,750–2,000–1Rope 1980–1,010750–76024.12Rope 2980–1,170750–90023.03Rope 3980–1,125750–80026.44Rope 4980–1,090750–80025.1


## 5.5.1. Dynamic Simulation of Uniform Loading for Swing Reduction System of Hanging Basket

As shown in Figure10, in accordance with the derived driving length, speed, acceleration, and stress equations of the hanging basket, the simulation results are obtained. The driving lengths of the four ropes are different. The initial length of all four ropes is 830 mm, rope 1 stretches first and then shortens, the reasonable range is l1 ∈ (775–880 mm), rope 2 shortens first and then stretches, the reasonable range is l2 ∈ (825–835 mm), rope 3 shortens first and then stretches, the reasonable range is l3 ∈ (825–835 mm), rope 4 stretches first and then shortens, the reasonable range is l4 ∈ (775–880 mm). The range of expansion and contraction speed of the ropes are V1 ∈ (−35 to 35 mm/s), V2 ∈ (−98 to 102 mm/s), V3 ∈ (−25 to 25 mm/s), V4 ∈ (−65 to 60 mm/s). The range of expansion and contraction acceleration of the ropes are a1 ∈ (−30 to 25 mm/s2), a2 ∈ (−200 to 140 mm/s2), a3 ∈ (−40 to 35 mm/s2), a4 ∈ (−110 to 100 mm/s2). The stress situation of each rope is also quite different, among which the extreme force of rope 2 is the largest, reaching 4,100 N, followed by rope 4, which is 2,850 N. In practical engineering, special attention should be paid to these two ropes, and regular inspection and replacement should be made to prevent fatigue fracture during work.Figure 10
Dynamic simulation analysis of antiswing device for hanging basket.
(a)(b)(c)(d)


## 5.5.2. Dynamics Simulation of Nonuniform Loading of Suspension Basket Shimmy Reduction System

As shown in Figure11, due to the different distribution positions of the four wounded in the basket, the basket gravity center is transferred from O to D. Compared with the uniform loading diagram shown in Figure 10(d), the uneven loading diagram shown in Figure 11(a) shows that there is basically no change in the force of ropes 2, 4, but the force of rope 1 is increased. At the same time, the force range is increased from 1,000–1,200 N to 1,300–2,000 N, the force of rope 3 is reduced, and the force range is reduced from 1,000–1,300 N to 850–1,000 N. According to the rope stress characteristics obtained above, since the extreme force borne by rope 2 is larger and the extreme force borne by rope 4 is smaller, when loading, the basket gravity center is close to rope 4 and far away from rope 2, as shown in Figure 11(b), which can make the stress of the four ropes more balanced.Figure 11
Cable force of hanging basket for uneven loading.
(a)(b)


## 5.5.3. Dynamic Simulation of Reducing Swing System of Telescopic Hanging Basket

According to the derived driving length, speed, acceleration, and force variation equations of the control rope and telescopic sleeve of the hanging basket, the simulation results are obtained, as shown in Figure12.Figure 12
Dynamic simulation analysis of hanging basket with telescopic sleeve.
(a)(b)(c)(d)The comparison of rope stress intervals under the two schemes can be obtained from Figures10(d) and 12(d), as shown in Table 1. Compared with the hanging basket scheme, in telescopic sleeve hanging basket scheme, the telescopic sleeve bears part of the pressure and tension of the hanging basket, the force of rope 1 is reduced by about 24.1%, rope 2 is reduced by about 23.0%, rope 3 is increased by 26.4%, and rope 4 is reduced by 25.1%. Since rope 3 itself is less stressed, even if the tension of rope 3 is increased after the solution is changed, the service life of the rope will not be greatly affected, it can be explained that the telescopic sleeve antisway device can effectively improve the force of the hanging basket control rope, thereby effectively reducing the motor power of the control unit.Table 1
Hanging basket rope force range.
NumberNameStress range (N)Percentage (%)Hanging basketTelescopic sleeve0Telescopic sleeve–1,750–2,000–1Rope 1980–1,010750–76024.12Rope 2980–1,170750–90023.03Rope 3980–1,125750–80026.44Rope 4980–1,090750–80025.1


## 6. Conclusions

In this paper, aiming at the antiswing device for ship-mounted batch transfer hanging basket, a rope-driven rigid-flexible hybrid hanging basket control system is designed. The rigid-flexible hybrid model is used to the antiswing control and simulation of the ship-mounted batch transfer hanging basket for the first time, an accurate dynamics model of the system is established, and the design of the control system in the rope-driven hanging basket device was researched, and the control system of the compensation scheme was designed to realize the function of active compensation for ship motion. Based on the research work of this article, the following conclusions are obtained:(1)
On the basis of the D’Alembert principle, the dynamic model of the hanging basket antiswing system is deduced, and the tension and force control of the rope under different carrying conditions are analyzed. When the moving platform is subjected to rolling, pitching, and heaving motion, the change curves of the length, velocity, and acceleration of each rope are obtained, each index of the rope is stable and continuous, and the change of the value is also in a reasonable range.(2)
The kinematics and dynamics equations of the telescopic sleeve type basket are simulated, The rigid spherical hinged telescopic sleeve shared a large part of the weight of the basket system. The maximum tension of rope 1 was reduced from 1,010 to 760 N, the maximum tension of rope 2 was reduced from 1,170 to 900 N, the maximum tension of rope 3 was reduced from 1,125 to 800 N, and the maximum tension of rope 4 was reduced from 1,090 to 800 N. The stress of four control cables of the hanging basket is reduced by about 24.1%, 23.0%, 26.4%, and 25.1%, respectively, the stress of control ropes is improved, and the safety of the hanging basket system is guaranteed. This paper has a certain guiding significance for the design of hanging basket antiswing system and the equipment selection of control system.



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*Source: 9950348-2023-01-29.xml*