Cable Motion Research Articles

Research on dynamic modeling and control strategy of four anti-swing cable system for ship-mounted cranes

Ship-mounted cranes are becoming increasingly essential to modern ocean shipping. However, due to the continuous influence of waves, currents, and winds, achieving accurate and fast lifting is difficult because of the large payload swing during the lifting operation. Therefore, this study proposes a Four Anti-swing Cable System (FASCS) for ship-mounted cranes. Firstly, a dynamic model of the FASCS was established by using Robotics and Newton method, and a tension control method (TCM) is designed to reduce the swing angle of the payload. Concurrently, a sliding mode variable structure controller with improved reaching law (SMVSC-IRL) is designed to control the cooperative movement of the anti-swing cables and prevent the occurrence of snap. The dynamic characteristic analysis by MATLAB/Simulink shows that the swing angle suppression effect reaches 89.3% on average, and the projected area of the payload trajectory was reduced by 60%, which can significantly improve the efficiency of ship-mounted cranes lifting operations. In addition, the length and speed of cables in errors can approach 0 within 7 s, and the strong robustness of the designed SMVSC to control the cooperative motion of the anti-swing cables is proved. The results of this study contribute to the in-depth optimization and engineering verification of the FASCS for ship-mounted cranes.

Flexible endoscope manipulating robot using quad-roller friction mechanism

A robotic system for manipulating a flexible endoscope in surgery can provide enhanced accuracy and usability compared to manual operation. However, previous studies require large-scale, complex hardware systems to implement the rotational and translational motions of the soft endoscope cable. The conventional control of the endoscope by actuating the endoscope handle also leads to undesired slack between the endoscope tip and the handle, which becomes more problematic with long endoscopes such as a colonoscope. This study proposes a compact quad-roller friction mechanism that enables rotational and translational motions triggered not from the endoscope handle but at the endoscope tip. Controlling two pairs of tilted rollers achieves both types of motion within a small space. The proposed system also introduces an unsynchronized motion strategy between the handle and tip parts to minimize the robot’s motion near the patient by employing the slack positively as a control index. Experiments indicate that the proposed system achieves accurate rotational and translational motions, and the unsynchronized control method reduces the total translational motion by up to 88% compared to the previous method.

Vibrations of cable-suspended rehabilitation robots

AbstractRehabilitation robots help the treatment of diseases by performing cyclic exercises for a long period of time. These exercises must perform movements of the patient’s limbs; thus, the robots are required to be flexible and safe. Among rehabilitation robots, cable robots are widely used due to their unique properties, such as being lightweight and the possibility of being equipped with magnetic hooks to improve both safety and ease of use. However, the elasticity and flexibility of cables result in vibrations of the payload and hooks. In this paper, the forced vibrations due to rehabilitation exercises are studied. Since the previous studies of the authors showed a weak coupling between longitudinal and transverse vibrations, a two-cable planar model for the study of transverse vibrations is developed. The model makes it possible to study the forced transverse vibrations due to both cable motion and robot motion. Stiffness and damping of the patient’s arm are considered. Results show that the cable system exhibits a simple linear behavior when excited by robot motion and a non-linear behavior when excited by cable motion.

Hierarchical coupling control of cable-driven multi-loop crane for underactuated positioning

For the low-cost anti-swing retrofit of existing offshore heavy cranes, a (2-UPPU/UPU)UP multi-loop configuration with six cable-driven prismatic pairs and a UP underactuated pendulum is introduced. Each UPPU branch contains a fast-moving prismatic pair and a slow-moving one. A configuration tracking method utilizing three slow cable motions in 2-UPPU/UPU is proposed by motion compensation technology. A multi-loop underactuated end positioning scheme is given to achieve the cargo's horizontal positioning in inertia frame, i.e., two fast cable motions in 2-UPPU are used to drive four states comprising their tracking trajectories and two cargo swings, which frees the wave compensation and swing suppression task from crane joints and retains the original crane system. A hierarchical coupling controller with a special coupling relation matrix is designed, where the matrix-based sub-controller fusion technique provides a standardized design approach with distinct physical meaning for the application of hierarchical methodology in underactuated multi-loop systems. The stability analysis by Lyapunov method reveals multiple coupling relation matrices matching stability conditions, giving birth to five attractive coupling control modes. Simulations and experiments are conducted to compare and verify performance.

Design and implementation of fast terminal sliding mode control with synchronization error for cable-driven parallel robots

Since the cable structure generally leads to lower stiffness, cable-driven parallel robots (CDPRs) currently face some graver control challenges, where the inevitable system uncertainty will have more significant impacts on the control accuracy of CDPRs. To improve this situation, a novel sliding mode surface and the corresponding novel approaching law are defined by investigating the multi-cable synchronization, and then a new fast terminal sliding mode control strategy with synchronization error (FTSMC-SE) is proposed in this paper. Referring to the parallel structure of CDPRs, the synchronous motion of adjacent cables is ensured to obviously improve the control accuracy. Meanwhile, by deeply analyzing the finite-time convergence characteristic of the fast terminal sliding mode control, the defined synchronization error is skillfully integrated with the sliding mode surface and its novel approaching law to achieve further improvement. The Lyapunov theory is then used to analyze the finite-time stability with the error convergence guarantee of the control system. Simulation and experimental results indicate that the more synchronized cable motion and the faster error convergence can be achieved by the proposed FTSMC-SE, which together promotes the final higher precision trajectory tracking.

Internal resonance of generalized suspension bridge model considering torsional-vertical vibration

Non-linear vibration is a crucial issue for suspension bridge due to its slenderness and low damping. This study proposes a fully mathematical model of a suspension bridge considering arbitrary inclined angle of main cables by using principle of Hamilton. This is the first mathematical model that is capable of analyzing the nonlinear coupled vertical-torsional vibration of generalized bridge configurations with independently considering the motion of main cables and girder. Galerkin method is adopted for the discretization of the model, and the multi-scale method is employed to acquire modulation equations. The accuracy of the non-linear vibration obtained from proposed mathematical model are validated by a FE model. The internal resonance analysis for such a suspension bridge with spatial layout of main cables between vertical and torsional modes with frequency ratio of 2:1, and between two torsional modes respectively dominated by deck and main cables with frequency ratio of 1:1 are successively investigated in the first time within a narrow detuning frequency domain. The phenomenon of nonlinear resonance was discussed with different inclination angle of main cables and detuning parameters. Some novel and practical conclusions were obtained. Results show that 2:1 internal resonance between vertical and torsional modes may be induced only when two forces with frequencies corresponding to involved modes are applied simultaneously. In addition, significant 1:1 internal resonance is observed, with inducing Hopf bifurcation. Understanding such possible situations is favorable to the design of bridge structure.

Modal Characteristic and Nonlinear Dynamic Response of Suspension Bridge with Lateral Asymmetric Stiffness

Asymmetric stiffness in transverse direction of suspension bridge can be easily induced by many causes during its long-term service. Such phenomenon may cause the coupling effect between vertical and torsional vibrations. A cross-section model of suspension bridge with seven-degree of freedom is proposed, to investigate the asymmetry effect on the dynamic behavior of the system. Corresponding modal analysis is firstly carried out. Results show that the asymmetric stiffness will induce veering phenomenon when natural frequency loci of vertical and torsional modes approach each other. In the veering region, mode hybridization phenomenon can be observed between these two modes. In addition, asymmetry-induced nonlinear vibration of hybrid vertical and torsional modes is studied using the extended incremental harmonic balance method. The effect of asymmetry extent is also investigated in this study. Results show that both hybrid modes can be excited by either the vertical or torsional excitation. Moreover, the energy can be transferred between these two modes, because of the nonlinear stiffness introduced by the significant swaying motion of hanger and cable.

Computer-assisted assembly process planning for the installation of flexible cables modeled according to a viscoelastic Cosserat rod model

Available computer-aided assembly process planning methods fail to provide the necessary level of accuracy required by modern complex planning processes owing to the neglect of the internal friction arising in the process of cable movement and large cable deformation conditions. The present study addresses this issue by developing a computer-aided assembly process planning method that inherently considers the tensile, bending, and torsional deformations of cables based on a dynamic viscoelastic Cosserat model describing cable motion. The simulation module of the virtual cable assembly process integrates and optimizes an efficient and robust algorithm for rapidly solving the dynamic cable model based on a semi-implicit Euler method. The performance of the proposed method is verified by demonstrating the rationality and accuracy of the assembly path planning and multi-cable assembly sequence obtained by the virtual assembly simulation module for a modeled prototype of a complex electromechanical product produced in the aerospace industry.

A hamiltonian global nodal position finite element method for dynamics analysis of submarine cables

The dynamics of submarine cables can be expressed in Hamiltonian formalism, which can reduce the error accumulation over long-term numerical calculation. This paper proposes a Hamiltonian global nodal position finite element method to study the dynamic responses of submarine cables undergoing bending deformation and long-term large overall motions. The new global nodal position finite element discrete formulation is derived by Hamiltonian theory and Euler-Bernoulli beam theory, which takes the bending deformation of submarine cables into consideration. To verify the proposed method, the second-order Symplectic difference algorithm is built for numerical solution. Five-point Gauss-Legendre quadrature formulate is applied to calculate the hydrodynamic force. The calculation accuracy and efficiency of the proposed method are validated by the freefall cantilever test of submarine cable, the towing test of submarine cable with lumped mass, the motion simulation of submarine cable connected to the remotely operated vehicle (ROV) and the towing test of a submerged body. Compared with the existing Hamiltonian nodal position finite element method, all validations and results indicate that the proposed method can solve the motion of various submarine cables under different working conditions with higher accuracy and efficiency.

Dynamic geometrical configuration predictions during robotic manipulation for automated cable assembly

During robotic manipulation, flexible cables are significantly more difficult to model than rigid objects, and they cause a computationally intensive problem. This paper proposes a viscoelastic rod model to predict the dynamics of cable assembly. The spatial shape of the cable could be decomposed into the position of the centerline and the rotation of the cross section. The interaction forces and bending moments of a cable under various boundary conditions were analyzed using a discrete finite element method. Gravitational effects and friction dissipation were also considered. An improved semi-implicit Euler method was employed to solve the model, and the cable motion was simulated for different boundary conditions. A dynamic motion experimental bench was built based on the binocular vision measurement method of cable centerline projection, and the actual shape of the cable was measured. The average error between the actual and simulated coordinates for each discrete cable point along the centerline was within 5%. Experimental results verified the algorithm and the modeling method.

Real-Time Identification of Time-Varying Cable Force Using an Improved Adaptive Extended Kalman Filter.

The real-time identification of time-varying cable force is critical for accurately evaluating the fatigue damage of cables and assessing the safety condition of bridges. In the context of unknown wind excitations and only one available accelerometer, this paper proposes a novel cable force identification method based on an improved adaptive extended Kalman filter (IAEKF). Firstly, the governing equation of the stay cable motion, which includes the cable force variation coefficient, is expressed in the modal domain. It is transformed into a state equation by defining an augmented Kalman state vector with the cable force variation coefficient concerned. The cable force variation coefficient is then recursively estimated and closely tracked in real time by the proposed IAEKF. The contribution of this paper is that an updated fading-factor matrix is considered in the IAEKF, and the adaptive noise error covariance matrices are determined via an optimization procedure rather than by experience. The effectiveness of the proposed method is demonstrated by the numerical model of a real-world cable-supported bridge and an experimental scaled steel stay cable. Results indicate that the proposed method can identify the time-varying cable force in real time when the cable acceleration of only one measurement point is available.

Semi-Active Cable Damping to Compensate for Damping Losses Due to Reduced Cable Motion Close to Cable Anchor

The relative motion of transverse cable dampers is smaller than predicted by the taut string model because of the effects of bending stiffness and fixed support conditions. As a result of the reduced damper motion, the dissipated energy per cycle is reduced as well, which may explain why damping measurements on real stay cables with transverse dampers often show lower cable damping ratios than expected from the taut string theory. To compensate for the reduced damper motion and damper efficiency, respectively, a semi-active cable damper is proposed. The controllable damper is realized by a hydraulic oil damper with real-time controlled bypass valve whereby the resulting damper force is purely dissipative. The proposed control law is clipped viscous damping with negative stiffness. The viscous coefficient is adjusted in real time to the actual frequency of vibration to generate optimum modal damping while the negative stiffness component partially compensates for the reduced damper motion due to the flexural rigidity and fixed support conditions of the cable. The measurements of the prototype semi-active hydraulic damper are used to derive a precise model of the semi-active damper force including the control force constraints due to the fully open and fully closed bypass valve. This model is used to compute the cable damping ratios of the first four cable modes, for typical damper positions, for a taut string model and for a cable model with flexural rigidity and fixed supported ends. The obtained cable damping ratios are compared to those resulting from the passive linear viscous damper being optimized to the first four cable modes. The results demonstrate that the proposed semi-active cable damper with the consideration of the minimum and maximum control force constraints significantly enhances the cable damping of the first four modes compared to the linear viscous damper.

Hydrodynamic Response of Ocean-Towed Cable-Array System under Different Munk Moment Coefficients

The ocean towing system plays an important role in the ocean development process. The motion of a towed body is closely coupled with the motion of a towing cable. In this paper, the lumped mass method is used to discrete a towing cable into a lumped mass model. At the same time, on the basis of some assumptions, the relationship between the expression of Munk moments in the classical towed body kinematics and the expression of the Munk moments in the hydrodynamic analysis software OrcaFlex is established. Based on the above assumptions and the derivation, combined with the specific parameters of a certain sea state and a certain towing system, the dynamic simulation of the towing system is made by OrcaFlex. By changing the different Munk moment coefficients, the real-time response of the cable tension and the towed underwater body under different Munk moments is achieved. The effects of different Munk moment coefficients on the change of the tension are obtained; the six degrees of freedom of the towed body under the action of different Munk moment coefficients are shown. To obtain the spectral density of the six degrees of freedom of the towed body under the action of different Munk moment coefficients, Fast Fourier Transform is performed on the calculated results of the towed body in the time domain. The results provide a theoretical basis for the optimal design of a cable and towed body.

Multi-Channel Biopotential Acquisition System Using Frequency-Division Multiplexing With Cable Motion Artifact Suppression.

A multi-channel, CMOS-based biopotential acquisition system is presented that uses amplitude modulated, frequency division multiplexing (AM-FDM) to decrease wire count and provide resilience against motion artifacts and cable noise. Differential active electrode (AE) pairs capture surface biopotential signals, each modulated by a different carrier frequency and combined via current-domain summing. The presented approach requires only a single wire for signal transmission between AEs and back-end readout, along with clock and ground wires, to support multiple active electrodes using a 3-wire cable. Frequency modulation prior to transmission mitigates the effect of low-frequency cable motion artifacts and 50/60 Hz mains interference in the cable. A prototype FDM-based biopotential acquisition system was implemented in a 180 nm CMOS process, including a four-channel front-end active electrode IC for signal conditioning and modulation, and a back-end IC for demodulation and digitization. Each channel occupies 0.75 mm [Formula: see text] and consumes 43.8 μ W, inclusive of ADC power. Using both AE and BE ICs, a four-channel biopotential recording system is demonstrated using a 3-wire interface, where the system achieves attenuation of low-frequency cable motion artifacts by 15X and 60 Hz mains noise coupled into the cable by 62X.

Planar nonlinear dynamic analysis of cable-stayed bridge considering support stiffness

Support stiffness is one of important factors on structure dynamics. Considering the vertical support stiffness, a multi-cable-stayed shallow-arch model of the cable-stayed bridge is established. Its differential equation governing the planar motion of cables and the shallow arch and the boundary conditions are derived by Hamilton’s principle. Firstly, the in-plane free vibration of the system is explored in order to find the modal functions and the possible internal resonances of nonlinear dynamics. Then, the 1:2:2 internal resonance among the different modes of the shallow arch and two cables are investigated by the multiple time scale method and pseudo-arclength algorithm. Meanwhile, the frequency-/force–response curves are used to explore the nonlinear behaviors of the system, especially the influence of vertical support stiffness, excitation frequency and amplitude on the internal resonance of the system is considered. To a certain extent, the support stiffness can reduce the response amplitudes of members by absorbing some energy from excitation.

Computer vision‐based real‐time cable tension estimation in Dubrovnik cable‐stayed bridge using moving handheld video camera

Cables are essential components of the cable-stayed bridges as they serve as the main load-bearing component. Hence, continuous monitoring of such cables becomes necessary as they are vulnerable to the fatigue damage induced by dynamic loads. Sensors are attached to the cables to examine the health of the cables; however, these contact-based sensors can malfunction in harsh weather condition, which makes impossible to estimate the cable health in such unfavorable condition. Therefore, in this paper, we propose a completely noncontact video-based stay-cable tension measurement technique where the video is recorded using a moving handheld camera at a significant distance from the structure itself. Here, the cable tension is determined from vibration-based measurement, but the vibration of the cable recorded in the video includes the true vibration of the cable along with the camera motion. Hence, we amalgamated a series of image processing techniques to nullify the camera movement. First, we detect the camera movement based on the movement of the bridge deck and pylon, which are fixed objects, using Kanade–Lucas–Tomasi (KLT) feature tracking algorithm. Then we nullify the camera movement by using the affine transformation matrix obtained by random sample consensus (RANSAC) algorithm. Subsequently from the steady video, the cable motions are estimated using the phase-based motion estimation technique. From the time history of the cable vibration, real-time frequency variations are estimated using Short-Time Fourier Transform (STFT). Finally, the real-time tension is determined from this dominant frequency variation history using the taut-string theory. This paper shows the significant potential of camera-based sensing techniques in structural health monitoring as the mean estimated tension and the design cable tension are found to be comparable.

Nonlinear vibration of iced cable under wind excitation using three-degree-of-freedom model* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11290152, 11427801, and 11902220) and the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality, China (PHRIHLB).

High-voltage transmission line possesses a typical suspended cable structure that produces ice in harsh weather. Moreover, transversely galloping will be excited due to the irregular structure resulting from the alternation of lift force and drag force. In this paper, the nonlinear dynamics and internal resonance of an iced cable under wind excitation are investigated. Considering the excitation caused by pulsed wind and the movement of the support, the nonlinear governing equations of motion of the iced cable are established using a three-degree-of-freedom model based on Hamilton’s principle. By the Galerkin method, the partial differential equations are then discretized into ordinary differential equations. The method of multiple scales is then used to obtain the averaged equations of the iced cable, and the principal parametric resonance-1/2 subharmonic resonance and the 2:1 internal resonance are considered. The numerical simulations are performed to investigate the dynamic response of the iced cable. It is found that there exist periodic, multi-periodic, and chaotic motions of the iced cable subjected to wind excitation.

Post-critical behavior of galloping for main cables of suspension bridges in construction phases

The main cables of suspension bridges show various cross-sectional shapes with the evolution of construction phases, and they may suffer from severe galloping at certain conditions. The aim of this work is to provide a convenient tool for predicting the critical condition and galloping amplitude of main cables, and to explore the in-depth driving mechanism of nonlinear galloping. Firstly, a numerical scheme of fluid–structure interaction (FSI) was developed to predict the galloping performance of main cables, and the numerical results of both critical conditions and vibration amplitude of galloping were compared to those of wind tunnel tests. The validated computational scheme was then used to investigate the driving mechanism of nonlinear galloping from the perspectives of nonlinear aerodynamic damping and work of aerodynamic lift. Moreover, the amplitude dependencies of unsteady and nonlinear aerodynamic lift were studied. It is found that the hysteresis of the flow with respect to the motion of the main cable is an important reason responsible for the nonnegligible unsteadiness in aerodynamic lift. Remarkable multiple-frequency components of aerodynamic lift emerged at large vibration amplitude, which were caused by the variation of instantaneous relative wind incidence angle for main cable in oscillation. Low-order harmonic components of aerodynamic lift at small vibration amplitude were the trigger of galloping, while the high-order components which contribute negative work at large vibration amplitude were responsible for the nonlinear aerodynamic damping and limited cycle oscillation. Unsteady characteristics of aerodynamic lift were the main cause for the variation of work proportions between different order harmonic components.

Compliant Control and Compensation for A Compact Cable-Driven Robotic Manipulator

Cable-driven robotic manipulators are desirable for medical applications, for their form factor flexibility after separating actuation from the distal end. However, intended to work under high spatial constraints such as dental or other surgical applications, severe cable elongations will raise control challenges from inaccuracy to excessive compliance. It is critical to proactively regulate the system compliance, in order to achieve both compliant behavior to avoid tissue damage, and rigid behavior necessary for dental drilling. Both ends of this challenges have been extensively studied in literature, with rigidity achieved by cable elongation compensation, and virtual compliance regulation by impedance control. However, each approach worked within its own turf, with very little being studied in how to blend the two sources of compliance strategically. In this work, blending virtual compliance modulated by impedance control with transmission compliance induced by cable elasticity was investigated and demonstrated in a modified design of our proprietary dental manipulator. It was shown that direct application of impedance control in a cable-driven system would not bluntly increase compliance, and may cause instability. Instead, we proposed a compliance-blending framework with Cartesian-space super-positioning of cable motion compensation and impedance control, and validated the efficacy on the 6-DOF dental manipulator platform. Desirable results were achieved using highly common approaches in both impedance control and cable compensation, making the proposed approach applicable to a wide range of cable-driven robotic systems for impedance control.

VIV modelled using simplified cable dynamics coupled to sub-critical cylinder flow simulations in a moving reference frame

This work focuses on the study of the phenomenon of vortex-induced vibrations in overhead lines under the effect of weak winds. Full three-dimensional simulation is not feasible because of the high length to width aspect ratios of the overhead lines. Thus a quasi-3D method based on strip theory is adopted in this work. This method decouples the system of interactions between the overhead line and the wind into a series of sub-systems. The fluid flow in each sub-system is represented as a series of independent rigid oscillating cylinder flows that are only coupled through the transmission line model. To avoid the use of a moving mesh for the fluid domain, a moving reference frame approach is employed. In this approach, the coordinate axes of the flow simulation are attached to the oscillating cylinder and an acceleration term in the flow equations accounts for the cable motion. Moreover, in order to take into account the turbulent effect in the flow, turbulence models, including RANS, LES and DES, are evaluated for the present application involving flows in the sub-critical regime. Finally, numerical test cases are performed in order to validate the turbulence models and the moving reference frame approach, then cable dynamics test cases are conducted to validate the quasi-3D method.